Mathematics High School

Drake wants to save $750 so that he can take a class on computer analysis for cars. The class is being held on various dates over the next several months. Drake is planning to take the class 6 weeks from now, so he plans to save $125 each week. Unfortunately, Drake had to take out a little money from his savings in the 3rd week. After 4 weeks, Drake has $470. He knows that he must adjust his plan in order to meet his goal. Drake came up with the following options: Option A: Stay with saving the original amount each week but take the class a week later than originally planned. Option B: Increase the amount of money he saves each week by $15 from his original plan. Which of the following is a true statement? a. Only option A will allow him to meet his goal. b. Only option B will allow him to meet his goal. c. Both options A and B will allow him to meet his goal. d. Neither option A nor option B will allow him to meet his goal.

Answers

Answer 1

The answer here is C. both options will allow him to meet his goal. hope this helped

Answer 2

answer- C

total money required = 750

total money saved = 470

weeks left = 2

money earned in each week = 125

money earned in 2 weeks = 250

470 + 250 = 720( so, drake is short of 30 )

option A- by postponing the classes for 1 week, he will earn 125 more, so it is an option to meet his goal as 125>30

option B- by increasing the savings by 15 for two weeks, he will save 30 more which is the amount drake needs. so , it is also a good option

Related Questions

A principal of $400 is invested in an account at 6% per year compounded annually. What is the total amount of money in the account after 5 years? A. $526.00 B. $531.37 C. $535.29 D. $520.00

Answers

To find the outcome of compounded money, we use the following formula:
[tex]e = b \times (1 + \frac{i}{100} ) {}^{n} [/tex]

In this formula:
e represents the outcome
b represents the money at the beginning
i represents the interest rate
n represents the number of years.

Filling in this formula, we get:
[tex]e = 400 \times (1 + \frac{6}{100}) {}^{5} [/tex]
[tex]e = 400 \times 1.06 {}^{5} [/tex]
[tex]e = 535.29[/tex]
Therefore the answer is C. $535.29

The total amount of money in the account after 5 years is $535.29.

To calculate the total amount of money in the account after 5 years, we can use the compound interest formula: [tex]A = P{(1 + r/n)}^{(nt)[/tex], where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times compounded per year, and t is the number of years.

Given that the principal is $400, the annual interest rate is 6%, and the compounding is done annually, we have:

A = 400(1 + 0.06/1)^(1*5) = 400(1.06)^5 = 400 * 1.338225 = $535.29

Therefore, the total amount of money in the account after 5 years is $535.29.

Learn more about Compound interest here:

https://brainly.com/question/24924853

#SPJ2

If p is a true statement and q is false then p V q is true

Answers

This is correct. p V q is basically an "or" statement. So the question is asking if p or q is true. So, as long as one of them is true, the overall question is true.

Answer:

Step-by-step explanation:

True

What is the solution of the equation (x – 5)2 + 3(x – 5) + 9 = 0? Use u substitution and the quadratic formula to solve.

Answers

(x – 5)² + 3(x – 5) + 9 = 0

x² - 10x + 25 + 3x - 15 + 9 = 0

x² - 7x - 16 = 0

[tex]x = \frac{7 + \sqrt{(-7)^2-4(1)(-16)} }{2} [/tex] or [tex]x = \frac{7 - \sqrt{(-7)^2-4(1)(-16)} }{2} [/tex]

[tex] x = \frac{7 + 3i \sqrt{3} }{2} [/tex] or [tex] x = \frac{7 - 3i \sqrt{3} }{2} [/tex]

(Answer B)

Answer: [tex]x=\frac{7\pm 3i\sqrt{3}}{2}[/tex]

Explanation:

Since, given quadratic function, [tex](x-5)^2 + 3(x-5) + 9 = 0[/tex] -----(1)

let us consider,[tex]x-5=p[/tex] -----(2)

Put this value in equation (1),

We get, [tex]p^2+3 p+9=0[/tex], which is also a quadratic equation.

Since, quadratic formula for finding the root of quadratic equation of type [tex]ax^2+bx+c=0[/tex] is, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}} {2a}[/tex]

Here, a=1, b=3 and c=9, so, [tex]p=\frac{-3\pm\sqrt{3^2-4\times1 \times9}} {2\times1}[/tex]

Thus, [tex]p=\frac{-3\pm3\sqrt{-3}} {2}[/tex] ⇒ [tex]p=\frac{-3\pm3i\sqrt{3}} {2}[/tex] (because √-1=i)

Now, from equation(2) [tex]x-5=\frac{-3\pm3i\sqrt{3}} {2}[/tex]

⇒[tex]x=\frac{-3\pm3i\sqrt{3}} {2}+5=\frac{7\pm 3i\sqrt{3}}{2}[/tex]

⇒[tex]x=\frac{7\pm 3i\sqrt{3}}{2}[/tex]

Find the missing measure for a right circular cone given the following information. Find L.A. if r = 6 and h = 8 48 60 96

Answers

[tex]\bf \textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=6\\ h=8 \end{cases}\implies LA=\pi(6)\sqrt{6^2+8^2} \\\\\\ LA=6\pi \sqrt{100}\implies LA=6\pi (10)\implies LA=60\pi [/tex]

Final answer:

The Lateral Area (L.A.) of a right circular cone with a base radius of 6 and a height of 8 is 60π square units, calculated by finding the slant height using the Pythagorean theorem and then applying the formula for L.A.

Explanation:

The student is asked to find the Lateral Area (L.A.) of a right circular cone given the base radius (r) is 6 and the height (h) is 8. First, we need to find the slant height of the cone, which can be done using the Pythagorean theorem in a right triangle where one leg is the height of the cone, the other leg is the radius of the base, and the hypotenuse is the slant height (l). The formula is l = [tex]\sqrt{(r^2 + h^2)[/tex]. After calculating l, we use the formula for the Lateral Area: L.A. = π r l.

Calculating the slant height: l = [tex]\sqrt{(6^2 + 8^2)}[/tex] = [tex]\sqrt{(36 + 64)[/tex]= [tex]\sqrt{100[/tex]= 10.

Now, we calculate the Lateral Area: L.A. = π * 6 * 10 = 60π. Hence, the Lateral Area of the cone is 60π square units.

What is the measure of AC ? (First Picture)
Enter your answer in the box.
What is the measure of BC ? (Second Picture)
Enter your answer in the box.

Answers

Answer:

Part 1) [tex]arc\ AC=33\°[/tex]

Part 2) [tex]arc\ BC=130\°[/tex]

Step-by-step explanation:

Part 1) What is the measure of AC ?

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m<ABC=\frac{1}{2}(arc\ AC)[/tex]

substitute the values and solve for x

[tex]2.5x+4=\frac{1}{2}(7x-2)[/tex]

[tex]5x+8=(7x-2)[/tex]

[tex]7x-5x=8+2[/tex]

[tex]2x=10[/tex]

[tex]x=5\°[/tex]

Find the measure of arc AC

[tex]arc\ AC=7x-2=7(5)-2=33\°[/tex]

Part 2) What is the measure of BC ?

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m<BDC=\frac{1}{2}(arc\ BC)[/tex]

substitute the values

[tex]65\°=\frac{1}{2}(arc\ BC)[/tex]

[tex]2*65\°=(arc\ BC)[/tex]

[tex]arc\ BC=130\°[/tex]

What is the sum of 2 numbers is 100 and their difference is 6?

Answers

x +y = 100
x -y = 6
Adding these equations gives
2x = 106
x = 53

y = 53 -6 = 47

The numbers are 47 and 53.

Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1). Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.) Xi 2 –1 P(xi) What is Miguel’s expected value from playing the game? answer= $2 Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays? answer= $2 What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation. A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue. Landing on the blue sector will give 3 points, landing on a yellow sector will give 1 point, landing on a purple sector will give 0 points, and landing on a red sector will give –1 point. Let X = the points you have after one spin. Fill out the missing values in the table. Xi P(xi) If you take one spin, what is your expected value? What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values. The point guard of a basketball team has to make a decision about whether or not to shoot a three-point attempt or pass the ball to another player who will shoot a two-point shot. The point guard makes three-point shots 30 percent of the time, while his teammate makes the two-point shot 48 percent of the time. Xi 3 0 P(xi) 0.30 0.70 Xi 2 0 P(xi) 0.48 0.52 What is the expected value for each choice? Should he pass the ball or take the shot himself? Explain. Claire is considering investing in a new business. In the first year, there is a probability of 0.2 that the new business will lose $10,000, a probability of 0.4 that the new business will break even ($0 loss or gain), a probability of 0.3 that the new business will make $5,000 in profits, and a probability of 0.1 that the new business will make $8,000 in profits. Claire should invest in the company if she makes a profit. Should she invest? Explain using expected values. If Claire’s initial investment is $1,200 and the expected value for the new business stays constant, how many years will it take for her to earn back her initial investment?

Answers

1) We have that there are in total 6 outcomes If we name the chips by 1a, 1b, 3 ,5 the combinations are: 1a,3 \ 1b, 3 \1a, 5\ 1b, 5\ 3,5\1a,1b. Of those outcomes, only one give Miguel a profit, 1-1. THen he gets 2 dollars and in the other cases he lose 1 dollar. Thus, there is a 1/6 probability that he gets 2$ and a 5/6 probability that he loses 1$.
2) We can calculate the expected value of the game with the following: E=[tex] \frac{1}{6}*2- \frac{5}{6} *1[/tex]. In general, the formula is [tex]E= \sum{p*V}[/tex] where E is the expected value, p the probability of each event and V the value of each event. This gives a result of E=2/6-5/6=3/6=0.5$ Hence, Miguel loses half a dollar ever y time he plays.
3) We can adjust the value v of the winning event and since we want to have a fair game, the expecation at the end must be 0 (he must neither win or lose on average). Thus, we need to solve the equation for v:
0=[tex] \frac{1}{6}v -\frac{5}{6} =0 [/tex]. Multiplying by 6 both parts, we get v-5=0 or that v=5$. Hence, we must give 5$ if 1-1 happens, not 2.
4) So, we have that the probability that you get a red or purple or yellow sector is 2/7. We have that the probability for the blue sector is only 1/7 since there are 7 vectors and only one is blue. Similarly, the 2nd row of the table needs to be filled with the product of probability and expectations. Hence, for the red sector we have 2/7*(-1)=-2/7, for the yellow sector we have 2/7*1=2/7, for the purple sector it is 2/7*0=0, for the blue sector 1/7*3=3/7. The average payoff is given by adding all these, hence it is 3/7.
5) We can approach the problem just like above and set up an equation the value of one sector as an unknown. But here, we can be smarter and notice that the average outcome is equal to the average outcome of the blue sector. Hence, we can get a fair game if we make the value of the blue sector 0. If this is the case, the sum of the other sectors is 0 too (-2/7+0+2/7) and the expected value is also zero.
6) We want to maximize the points that he is getting. If he shoots three points, he will get 3 points with a probability of 0.30. Hence the average payoff is 0.30*3=0.90. If he passes to his teammate, he will shoot for 2 points, with a success rate of 0.48. Hence, the average payoff is 0.48*2=0.96. We see that he should pass to his player since 0.06 more points are scored on average.
7) Let us use the expections formula we mentioned in 1. Substituting the possibilities and the values for all 4 events (each event is the different profit of the business at the end of the year).
E=0.2*(-10000)+0.4*0+0.3*5000+0.1*8000=-2000+0+1500+800=300$
This is the average payoff of the firm per year.
8) The firm goes even when the total profits equal the investment. Suppose we have that the firm has x years in business. Then x*300=1200 must be satisfied, since the investment is 1200$ and the payoff per year is 300$. We get that x=4. Hence, Claire will get her investment back in 4 years.

Answer:

To check all the events (6), we label the chips. Suppose one chip with 1 is labeled R1 and the other B1 (as if they were red and blue). Now, lets take all combinations; for the first chip, we have 4 choices and for the 2nd chip we have 3 remaining choices. Thus there are 12 combinations. Since we dont care about the order, there are only 6 combinations since for example R1, 3 is the same as 3, R1 for us.

The combinations are: (R1, B1), (R1, 3), (R1, 5), (B1, 3), (B1, 5), (3,5)

We have that in 1 out of the 6 events, Miguel wins 2$ and in five out of the 6 events, he loses one. The expected value of this bet is: 1/6*2+5/6*(-1)=-3/6=-0.5$. In general, the expected value of the bet is the sum of taking the probabilities of the outcome multiplied by the outcome; here, there is a 1/6 probability of getting the same 2 chips and so on. On average, Miguel loses half a dollar every time he plays.

Tamara says that raising the number i to any integer power results in either -1 or 1 as the result, since i^2 = -1. Do you agreed or disagree with Tamera? Explain

Answers

Final answer:

Tamara's claim that raising the complex number i to any integer power results in either -1 or 1 is incorrect. The powers of i follow a cyclic pattern which includes i, -1, -i, and 1.

Explanation:

I must disagree with Tamara's statement that raising the complex number i to any integer power results in either -1 or 1. The powers of i actually follow a recurring pattern: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1, and then the pattern repeats.

For i to the power of 1, the result is just i itself.For i to the power of 2 (i^2), the result is indeed -1.For i to the power of 3 (i^3), the result is -i.For i to the power of 4 (i^4), the result is back to positive 1.

So, while -1 and 1 are indeed in the sequence of results, they're not the only possibilities. Specifically, -i and i are also possible results of raising i to an integer power.

Learn more about Complex Numbers here:

https://brainly.com/question/20566728

#SPJ12

Two cities are 124 miles apart from each other. The cities are 4cm on a map, what is the Scale factor?

Answers

Actual distance = 124 miles
Distance on map = 4 cm

Scale factor = 4 cm : 124 miles
Divide through by 4

Scale factor = 4 cm/4 : 124 miles /4
= 1 cm : 31 miles

The scale factor is 1 cm : 31 miles

Use the quadratic formula to solve 9x2 + 6x – 17 = 0.

Answers

the answer is c after solving the whole problem

Answer:

The person that answered “C” is completely wrong. The answer is D. Mark me brainliest after you get the answer right :)

Step-by-step explanation:

Jennifer recorded the temperature of water samples and the time it took 50g of salt to dissolve in the samples. Jennifer's data models a direct variation. Which table contains Jennifer's data?

Answers

the answer is c. it look like this
80°32
83°33.2
84°33.6
90°36

Answer:

The answer is C.

Step-by-step explanation:

I know that its c because i literatly just tried it and it said corect it was on USA. test prep

A rectangular note card has a perimeter of 18 inches and an area of 20 square inches. What are the dimensions of the note card?

Answers

5 by 4

4 x 5 = 20

5 + 5 + 4 + 4 = 18

The dimensions are 5 by 4,
hope I helped (:

7 cakes cost £5.60 , what would be the cost of:
10 cakes
5 cakes
12 cakes

Answers

1 cake cost 5.60÷7=£0.8
so 10 cake costs 10×0.8=£8
5cake costs 5×0.8=£4
12 cake costs 12×0.8=£9.6

cost of 1 cake:£5.60÷7=£0.8

10 cakes: £0.8×10=£8
5 cakes: £0.8×5=£4
12 cakes: £0.8 ×12=£9.6

The probability that a bakery has demand for 2 3 4 or 5 birthday cakes on any given day are 0.32, 0.24, 0.25 and 0.19 respectively. construct a probability distribution for this data

Answers

This would just look like a bar graph.

On the horizontal axis, put your 4 different categories of 2, 3, 4, or 5.

On the vertical axis, label it by the percents: 0.10, 0.20, 0.30, 0.40

Then, make a bar at the correct height for each category.

Brian deposited $4000 into an account with 5.4% interest, compounded monthly. Assuming that no withdrawals are made, how much will he have in the account after 6 years?

Answers

The future value of the amount deposited will be given by:
FV=p(1+r/100n)^nt

where:
FV=future value
p=principle
r=rate
n=terms
t=time
thus substituting our values in the formula we get:
FV=4000(1+5.4/1200)^(6×12)
FV=$5,526.57

Answer: $5,526.57

A recipe calls for 1/4 cup of flour.Carter only a measurement cup that holds 1/8 cup. How can carter measure the flour he needs for his recipe

Answers

Carter needs an additional ⅛ cup.
⅛ + ⅛ = ¼

Answer:

Carter can measure the flour he needs for his recipe by filling his measurement cup twice.

Step-by-step explanation:

Since Carter has a smaller cup, he would have to fill his cup a number of times until the sum of the number of cups he has fill repeatedly adds up to the recipe requirement.

The number of times Carter would have to measure his cup with flour to get the recipe call may be computed by dividing the recipe call amount with the size of Carter's measurement cup

= 1/4 ÷ 1/8

= 1/4 × 8/1

= 2

what should you do first to simplify the expression (43 + 9) ÷ 76 + 5

Answers

Hi there!

You should always find the value inside the parenthesis first when simplifying an equation.
Tell me if you need help solving the equation!

Hope this helps!

always find the value inside the parenthesis first when simplifying an equation.

expression (43 + 9) ÷ 76 + 5

43+9 =52 52 ÷ 76 + 5

Bc¯¯¯¯¯ is parallel to de¯¯¯¯¯. what is ab? enter your answer in the box.

Answers

this can help you to understand it

The firing of a Revolutionary War cannon is used to open the local Fourth of July festivities. The muzzle of the cannon barrel is 6 feet above ground level. The height of the cannon ball being fired from the Revolutionary War cannon as a function of elapsed time is modeled by the function h(t) = –16t2 + 75t + 6, where h(t) is the height of the cannon ball in feet, and t is the elapsed time since firing in seconds. Determine at approximately what elapsed time(s) the cannon ball will be at a height of 55 feet.

Answers

In order to find the elapsed time(s) the cannon ball will be at a height of 55, we need to solve the equation:
[tex]-16t^2 + 75t + 6=55\\-16t^2+75t-49=0. \text{ Computing the discriminant:}\\75^2-4(-16)(-49)=2489.\text{ So by quadratic formula we get the sol:}\\\dfrac{-75-\sqrt{2489}}{-32}=3.9\text{ seconds.}[/tex]

7. Given the vertices of ∆ABC are A (2,-5), B (-4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices: a. Rx = 3 b. T<3,-6> c. r(90◦, o)

Answers

Q1)
Rx = 3
in this reflection, the image has been reflected along the x = 3 line. then all the points on the image are reflected along this vertical line. the distance between each point and the vertical line is noted and by that same distance its moved to the opposite side of the vertical line, while the y coordinates stay the same.
A(2,-5)- x coordinate is 2, its 1 unit away from x=3, it should move by 1 unit to the other side of x = 3, then x = 4. y stays as it is.
A' - (4,-5)

B(-4,6) - distance from x = 3, is (-4-+3) is seven units, moves by 7 units to the other side
B' (10,6)

C(3,1) = distance from 3 = 0, therefore the point stays at is,
C' (3,1)

Q2)
next is a translation, in translation the size nor shape changes, each point in the original image moves the same distance in the same direction.
T (3,-6) (x,y) = this means that the x coordinates move by +3 points to the right and y coordinates move downwards by 6 units
A (2,-5) ---> (2+3,-5-6)
A' (5,-11)
B (-4,6) ---> (-4+3,6-6)
B' (-1,0)
C (3,1) ---> (3 + 3, 1-6)
C' (6,-5)

Q3)
r(90°,0)
this is a rotation done in the clockwise direction. then the image takes a rotation to the right direction around the origin.
then the x, y coordinates of the preimage become ;
(x,y) = (y,-x)
A(2,-5) --> A' = (-5,-2)
B(-4,6) ---> B' = (6,4)
C(3,1) ---> C' = (1,-3)

The price of a 250 dollar coat increased 7% last year. The coat is now on sale for one half off. What is the sale price?

Answers

start: 250increase: 250(1 + 0.07), 250(1.07)sale: 0.5(250(1.07)

What is the sum of the first eight terms of the series?

(−600)+(−300)+(−150)+(−75)+(−37.5)+...

Round the answer to two decimal places.

−1200.50

−1195.31

−1190.63

−1181.25

Answers

the answer is -1195.31

Which ordered pair (a, b) is a solution to the given system?

Answers

Since you are given a list of choices, you can go through each choice to plug them into the equations. It turns out that choice B is the answer

(3,1) means that a = 3 and b = 1
Plug in a = 3 and b = 1 into the first equation
2a - 5b = 1
2*3 - 5*1 = 1.... replace 'a' with 3, replace b with 1
6 - 5 = 1
1 = 1
we get a true equation, so we have confirmed the first equation

Do the same for the second equation
3a+5b = 14
3*3+5*1 = 14 .... replace 'a' with 3, replace b with 1
9+5 = 14
14 = 14
we get a true equation, so the second equation has been confirmed

Both equations are true when (a,b) = (3,1). So the answer (3,1) has been confirmed fully

Quick question!

Which investment vehicles historically provide the lowest annual rates of return?

A)Government bonds and U.S. Treasury bills
B)Large company stocks and government bonds
C)Small company stocks and large company stocks
D) U.S. Treasury bills and small company stocks

Answers

Stocks have a higher rate of return than either U.S. treasury bills or bonds.
C) Small company stocks and large company stocks
Note: Small company stocks generally have a higher rate of return than large company stocks. Small company stocks are a riskier investment because they are more volatile. Stock investments in general are riskier investments than treasury bills or bonds. In general, the possible rate of return increases as the risk of the investment increases.

a(1)= -2
a(n)=a(n-1)-5
whats the 4th term in the sequence?

Answers

Hello,
[tex]A_1=-2\\ A_2=A_1-5=-2-5=-7\\ A_3=A_1-2*5=-2-2*5=-12\\ A_4=A_1-3*5=-2-3*5=-17\\ [/tex]

Answer:

The fourth term in the sequence is -17

Step-by-step explanation:

To find the 4th term of the sequence, we will simply follow the steps below;

a(1) = -2

a(n) = a(n-1)-5

We will find the value of the sequence when n = 1, n= 2 n =3 n=4

The first one has been done for us, so we have the first term to be a(1) = -2

The next thing to do, is to find the second term, ie. when n=2

a(n) =a(n-1)-5

a(2) =a(2-1)-5

=a(1) - 5

but a(1) = -2

a(2) =a(1) - 5

=-2-5

=-7

a(2) = -7

next is to find the third term, ie. when n=3

a(n) =a(n-1)-5

a(3) =a(3-1)-5

=a(2) - 5

but a(2) = -7

a(3) =a(2) - 5

=-7-5

=-12

a(3) = -12

next is to find the fourth term, ie. when n=4

a(n) =a(n-1)-5

a(4) =a(4-1)-5

=a(3) - 5

but a(3) = -12

a(4) =a(3) - 5

=-12-5

=-17

a(4) = -17

Therefore, the fourth term in the sequence is -17

There are many penguins on a hill. 53 penguins waddled off the hill. Now 21 penguins remain on the hill. How many penguins were on the hill to start?

74 penguins

72 penguins

32 penguins

34 penguins

Answers

Answer:

74 Penguins

Step-by-step explanation:

1. 53+21

2. =74

Penguins are my favorite animal. What's yours?

Answer:

There were originally 74 penguins on the hill.

Step 1: Determine the Values we Need

For starters, we need to define the variable that we will use to solve this equation. I will use x.

We know that our original amount is x, and we need to find it to solve the problem.

The Factsx stands for the original amount of penguins on the hill.53 penguins waddle off of the hill.21 penguins remain after the 53 penguins waddle off of the hill.

To find x, we will set up an algebraic equation that allows us to find the value easily.

Step 2: Set up the Algebraic Equation

Now, we will need to set up the equation with the facts we have determined.

We know that we need to set our equation equal to x to find our total. To do this, we know that our initial amount is x, and we remove 53 penguins from this total since they waddle off of the hill.

Since we "remove" from the total, this means that we will subtract 53 penguins from x, our initial amount. We are left with the 21 penguins that do not leave the hill, or otherwise, remain on the hill.

[tex]x - 53 = 21[/tex]

Step 3: Rearrange and Solve the Equation

Finally, we are ready to solve the equation to find our initial amount of penguins.

To solve this equation, we must combine our like terms.

Because our numbers (constants) do not have any letters (variables) attached to them, we will combine them.

The main goal of an algebraic equation is to get the variable (in this case, x) by itself. To do this, we can perform reverse operations to get the constants together.

You'll notice that 21 does not have a sign associated with it, but 53 does, and it is a subtraction symbol.

The reverse operation of subtraction is addition. Therefore, to combine the two values, we can add both 53 and 21 to each other to find x.

[tex]x = 53 + 21[/tex]

Using any method of choice, add the two values together.

[tex]x = 53 + 21 = 74[/tex]

Then, to simplify, remove the operation and only leave the sum of the operation.

[tex]\boxed{x = 74}[/tex]

Therefore, the initial number of penguins—the number of penguins on the hill to start—is equivalent to 74 penguins.

To learn more about algebraic equations, please visit the following link: https://brainly.com/question/14791317

helpppppppppppppppppppppppppp

Answers

Answer:
perimeter = 6 + 3√2 ft

Explanation:
The triangle given is an isosceles right-angled triangle.
This means that two of its legs are equal = 3 ft
Now, we will get the length of the third leg which is the hypotenuse using the Pythagorean theorem as follows:
(third leg)^2 = (3)^2 + (3)^2
(third leg)^2 = 18
third leg = sqrt(18) = 3√2 ft

Finally, we will get the perimeter as follows:
perimeter = 3 + 3 + 3√2
perimeter = 6 + 3√2 ft

Hope this helps :)

Can someone check my answers?

1. Simplify the sum or difference.
sqrt 5 + 6 sqrt 5
A) 6 sqrt 5
B) 30
C) 6 sqrt 10
D) 7 sqrt 5

2. Simplify the sum or difference.
4 sqrt 2 - 7 sqrt 2
A) negative sqrt 6
B) -3 sqrt 2
C) -11 sqrt 2
D) 11 sqrt 2

3. Simplify the sum or difference.
3 sqrt 7 - sqrt 63
A) -2 sqrt 7
B) -6 sqrt 7
C) -4 sqrt 3
D) 0

4. Simplify the sum or difference.
-6 sqrt 10 + 5 sqrt 90
A) 9 sqrt 10
B) -9 sqrt 10
C) -39 sqrt 10
D) -10

5. Simplify the product.
sqrt 6 (sqrt 2 + sqrt 3)
A) sqrt 8 + 3
B) sqrt 30
C) 2 sqrt 3 + 3 sqrt 2
D) 4 sqrt 2 + 3

Answers

1. sqrt5 + 6sqrt5 = (1+6)sqrt5 = 7sqrt5 (answer is D)
2. 4sqrt2 - 7sqrt2 = (4-7)sqrt5 = -3sqrt2 (answer is B)
3. 3sqrt7 - sqrt63 = 3sqrt7 - sqrt7 * sqrt9 = 3sqrt7 - 3sqrt7 = 0 (answer is D)
4. -6sqrt10 + 5sqrt90 = -6sqrt10 + 5*(sqrt10 * sqrt9) = -6sqrt10 + 5*(3sqrt10)
= -6sqrt10 + 15sqrt10 = 9sqrt10 (answer is A)
5. sqrt6*(sqrt 2 + sqrt 3) = sqrt12 + sqrt18 = 2sqrt3 + 3sqrt2 (answer is D)

1 - D

2 - B

3 - D

4 - A

5 - C

6 - A

7 - D

8 - B

9 - B

10 - C

i just took the "Operations with Radical Expressions practice" for WA connexus, these answers are 100 percent correct

find all the zeros for each function.
p(x)=2x^3-3x^2+3x-2

*show work*

Answers

I like to let a graphing calculator help with polynomials of higher degree.

A graph of p(x) shows it has one real zero, at x=1. Dividing that out (and dividing out the scale factor of 2) reveals the remaining factor to be
.. (x -1/4)^2 +15/16
When we set this to zero, we have
.. (x -1/4)^2 +15/16 = 0
.. (x -1/4)^2 = -15/16
.. x -1/4 = i√(15/16)
and the remaining roots are
.. x = 1/4 ±i√(15/16)
.. x = (1 ±i√15)/4

The zeros are x = 1, x = (1 ±i√15)/4.

_____
You could use synthetic or long division to find
.. p(x)/(x -1) = 2x^2 -x +2
and then use any of several methods to determine the zeros of this are
.. x = (1 ±i√15)/4

Is 11p-7q polynomial

Answers

Answer: Yes; this is polynomial.

Specifically, it is a "polynomial EXPRESSION" ; but not a "polynomial equation" ; because it is not an "equation.

There are more than one variables/variable expressions, so it is a polynomial.

Other Questions

how does Shakespeare present romeo as romantic in act 2 scene 2 or romeo and juliet? are these correct?? Read the passage and answer the question that follows."Thus absolutely lost in thought, and dying with the very thoughts of drowning, I come up with the post, who I did not see 'til very deliberately a few paces, when we entered a thicket of trees and shrubs, and I perceived by the horse's going, we were on the decent of a hill, which, as we come nearer the bottom, 'twas totally dark with the trees that surrounded it. But I knew by the going of the horse we had entered the water, which my guide told me was the hazardous river he had told me of; and he, riding up close to my side, bid me not fear-we should be over immediately. I now rallied all my courage, knowing that I must either venture my fate of drowning, or be left like the children in the wood. So, as the post bid me, I gave reins to my nag; and sitting as steady as just before in the canoe, in a few minutes got safe to the other side, which he told me was the Narragansett country." (Sarah Kemble Knight, The Private Journal)Who is the intended audience of this passage?(Points : 3) the author herself specific to the children - specific to the horse general2.How can a reader find the main idea of a passage?Please select all answers that apply.(Points : 3)analyze the connotations of the words-summarize the passage -identify the audience-enter details into a graphic organizerparaphrase difficult language3. The best graphic organizer to use to better understand a narrative is:(Points : 3) a Venn diagram an idea web - a timeline an illustration hierarchy4. The best graphic organizer to use to better understand a descriptive passage is:(Points : 3) a Venn diagram an idea web a timeline - an illustration hierarchy5. A timeline would be most likely to help in understanding which of these types of passages?(Points : 3) - a non-fiction passage a persuasive passage a narrative passage any type of passage ^^I have no idea what this is, means or is asking so help please, thanks! 18 out of 24 of Emils CDs are country music 5 out of 8 of Imanis CDs are country music. Which is a true statement A Half of each CD coleection consists of country music B less than half od ech CD collection consists of country music E Emil has a greater fraction of country music than ImaniD imani has greater fractionof country music than Emil which one is true A B C or D Which mathematical property is demonstrated? 40 (25 74) = (40 25) 74 A. commutative property of addition B. associative property of multiplication C. associative property of addition D. commutative property of multiplication Refer to Explorations in Literature for a complete version of this passage.Read this excerpt from "Here Is New York."each embraces New York with the intense excitement of first love, each absorbs New York with the fresh eyes of an adventurer, each generates heat and light to dwarf the Consolidated Edison Company.How does the author use imagery in Here Is New York to advance his viewpoint?A: The imagery emphasizes that individual people can find opportunities in New York that they cannot find elsewhere.B: The imagery expresses the majesty of New York City and illustrates how the writer sees New York. C: The imagery illustrates his view of what a true New Yorker is and the relationship that a New Yorker should have with the city.D: Specific references to personal experiences illustrate how the writer felt when he first came to New York. A Type I statistical error occurs when a researcher claims that there is not enough support to establish significance for the research hypothesis, but in fact there is enough.True or false? How many triangles can be constructed with angles measuring 120, 40, and 10?A. One B. None C. More than one Which one of the following sentences contains an incorrect usage of the singular possessive? A. The alpha male is often the pack's leader. B. Icarus's fate was sealed when he approached the sun. C. The north forty has always been my family's land. D. Mary was dominant among Jesus' disciples. Write at least one sentence for each. What is a winter storm Advisory? The length of a rectangle is 3 times its width. if the width is diminished by 1 inch and the length is increased by 3 inches. the area of the the new rectangle is 72 square inches. find the dimensions of the original rectangle. Whats the first 200 digits of pie????????? What is the sum of the polynomials If guy walks from his house to school which is 5/10 away and back, how far does he walk? In the cannon-bard theory of emotion, the thalamus sends simultaneous messages to the _____.a. cortex and autonomic nervous systemb. central nervous system and peripheral nervous systemc. endocrine system and muscular systemd. parasympathetic nervous system and sympathetic nervous system When copper (ii) carbonate is heated if forms copper (ii) oxide and carbon dioxide? Read the excerpt from Chapter 13 in Frankenstein. ???Felix seemed ravished with delight when he saw her, every trait of sorrow vanished from his face, and it instantly expressed a degree of ecstatic joy, of which I could hardly have believed it capable; his eyes sparkled, as his cheek flushed with pleasure; and at that moment I thought him as beautiful as the stranger.??? Choose two words from the description. Explain the impact that one of the chosen words has on the tone, and the impact that the other word has on the meaning of the excerpt. Use examples and evidence from the text to support the ideas in your response. Women did not create visual arts until the mid-19th century. True False What plays a major role in Indias agricultural production In the diagram, the radius of the outer circle is 2x cm and the radius of the inside circle is 6 cm. The area of the shaded region is 288 cm.What is the value of x?