To solve the equation t² - t = 12 by factoring, you would use t(t - 1) = 12 t(t - 1) - 12 = 0 (t - 4)(t + 3) = 0

x - number of miles

[tex]0.19x+75\geq100\qquad|\text{subtract 75 from both sides}\\\\0.19x\geq25\qquad|\text{divide both sides by 0.19}\\\\x\geq132[/tex]

speed=d/t=200X2/5=80km/hr

d=sXt=13X80/4=260km

865/110=173/22hr=173X60/22=173X30/11=467min

Multiplication and division have the same precedence, binding tighter than addition and subtraction.  Among operators with the same precedence we go left to right.

So the first operation to do is division.   ÷

PEDMAS notwithstanding if your expression depends on the details of the left to right rules, you're better off adding parenthesis to make things clearer.

Final answer:

Carl's daily allowance is the square of the date, resulting in amounts that are perfect square numbers like 1, 4, 9, or 100 cents, depending on the day of the month.

Explanation:

Carl earns an allowance in cents equal to the square of the date of the month. Therefore, the number of cents Carl could earn on any given day is the date squared. For example, on the 2nd day of the month, he would earn 22 or 4 cents, and on the 10th day, he would earn 102 or 100 cents. So, any perfect square (1, 4, 9, 16, 25, 36, ... up to the largest square number within a given month) can be an amount Carl earns in a single day.

The corresponding point on the graph of the function -3/4 f(x) when given that (2,8) is on the graph of f(x) is (2, -6), achieved by scaling the y-value by a factor of -3/4.

The question involves finding the corresponding point on the graph of the function -3/4 f(x) given that (2,8) is on the graph of f(x). Since f(x) at x=2 is 8, for the new function -3/4 f(x) at the same x value, the y value will be scaled by a factor of -3/4.

Therefore, we calculate the new y value by multiplying 8 by -3/4, which results in -6. The corresponding point on the graph of the function -3/4 f(x) when x=2 is therefore (2, -6).

First of all, you can sum the two terms involving g on the left hand side:

[tex] -6g + 3g + 12 > -18 \iff -3g + 12 > -18 [/tex]

Subtract 12 from both sides:

[tex] -3g > -30 [/tex]

Divide both sides by -3: note that since we're dividing by a negative number, we must invert the inequality sign:

[tex] g< 10 [/tex]

Final answer:

When solving the inequality, we combine like terms, subtract 12 from both sides, and divide by -3, reversing the inequality sign to find that g < 10, hence the correct answer is (c).

Explanation:

To solve the inequality -6g + 3g + 12 > -18, we first combine like terms to simplify the left side of the inequality:

Next, we subtract 12 from both sides of the inequality:

Now we divide by -3, remembering to reverse the inequality sign because we are dividing by a negative number:

Therefore, the correct answer is (c) g < 10.

1. d. d = 66t

The maximum speed of the wildebeest is v=66 ft/s. Speed is defined as the ratio between the distance covered (d) and the time taken (t):

[tex]v=\frac{d}{t}[/tex]

Re-arranging the formula, we get

[tex]d=vt[/tex]

And substituting v=66 ft/s, we find

[tex]d=66t[/tex]

2. c. y = 5 - n

In fact, we can check that this rule satisfies all the numbers of the sequence:

n=3 --> y = 5 - 3 = 2

n=4 --> y = 5 - 4 = 1

n=5 --> y = 5 - 5 = 0

n=6 --> y = 5 - 6 = -1

3. d. $5.50, $11.00, $16.50; E = 5.50h

In fact, if we use the rule E=5.50 h, we see that the table is completed as follows:

h=1 --> E=(5.50)(1 h)=5.50$

h=2 --> E=(5.50)(2 h)=11.00 $

h=3 --> E=(5.50)(3 h)=16.50$

h=4 --> E=(5.50)(4 h)=22.00$

h=5 --> E=(5.50)(5 h)=27.50$

4. c. if d ≥ 5 then C = 4.70d, if d < 5 then C = 4.70d - 1; $17.80, $32.90

If the number of days is more than 5, the cost is 4.70$ per day, therefore c=4.70d (where d is the number of days); if the number of days is less than 5, one dollar is returned, so the cost will be C=4.70d-1. By applying this rule, we can calculate the rental cost after d=4 days and d=7 days:

- d=4 --> c=4.70*4-1=17.80$

- d=7 --> c=4.70*7=32.90$

5. b. y = 3x + 3

In fact, we can check this is the correct rule by substituting the numbers:

x=0 --> y=3*0+3=3

x=1 --> y=3*1+3=6

x=2 --> y=3*2+3=9

x=3 --> y=3*3+3=12

x=4 --> y=3*4+3=15

7. x -2 -1 0 1 2

y (-16 ) (-6 ) (4 ) (14 ) (24 )

The rule we have to apply is:

-10x + y = 4

Re-arranging it, we can solve for y:

y = 10x + 4

So, let's substitute the different values of x:

x=-2 --> 10*(-2)+4=-20+4= -16

x=-1 --> 10*(-1)+4=-10+4= -6

x=0 --> 10*0+4= 4

x=1 --> 10*1+4=10+4= 14

x=2 --> 10*2 +4 =20+4 = 24

8. y = -5x - 1

In fact, if substitute the different values of x given by the problem, we find:

x = -2 --> y = -5*(-2) -1= 10 -1 = 9

x = -1 --> y = -5*(-1) -1 = 5 -1 = 4

x = 0 --> y = -5*0 -1 = -1

x = 1 --> y = -5*1 - 1 = -6

x = 2 --> y = -5*2 -1 = -11

Answer:

1)  D

2) C

3) D

4) C

5) B

6) B

Step-by-step explanation:

A number is prime if its only divisors are 1 and the number itself.

Out of your numbers, 36 and 38 are even, and thus divisible by 2, so they aren't prime.

Similarly, 35 ends with 5, so it's divisible by 5, and is not prime.

37 is divisible only by 1 and 37, and thus it's prime.

Out of the numbers listed (36, 37, 35, 38), the number 37 is the only prime number, as it is the only number that has no positive divisors other than 1 and itself.

The question asks which of the listed numbers is a prime number. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. Therefore, we need to determine if any of the numbers given (36, 37, 35, 38) have divisors other than 1 and themselves.

36 is divisible by 1, 2, 3, 4, 6, 9, 12, 18, and 36, so it is not a prime number.

37 has no divisors other than 1 and itself, making it the prime number in the list.

35 is divisible by 1, 5, 7, and 35, so it is not a prime number.

38 is divisible by 1, 2, 19, and 38, so it is not a prime number.

Therefore, the number 37 is the only prime number from the list provided.

Answer:

greater than or >

Let [tex] b [/tex] be the number of three points baskets, and [tex] t [/tex] be the number of three points tries. We are given

[tex] \dfrac{b}{t} = \dfrac{2}{7} \iff 2t=7b [/tex]

Also, we know that the team scored 30 points from three points baskest. Since these baskest are worth 3 points, we have

[tex] 3b=30 \iff b = 10 [/tex]

Now, we also know that [tex] 2t=7b [/tex]. If we plug the known value for b, we can solve for t:

[tex] 2t = 7\cdot 10 \iff 2t = 70 \iff t = 35 [/tex]

17.

x = -2 is not a solution of -1 < x < 5 because -2 < -1 (-1 < -2 < 5 FALSE).

18.

m = 5 is a solution of 5 ≤ m because 5 ≤ 5 ( 5 ≤ m → m ≥ 5 greater than 5 or equal 5, 5 is equal 5)

19.

k = 10 is not solution of 2k - 3 < 1 because:

put the value of k to the inequality:

2(10) - 3 < 1

20 - 3 < 1

17 < 1 FALSE

James hand is bigger because when you compare decimals you make sure that there's an equal amount of numbers so 0.17 becomes 0.170 and 0.165 stays the same so James's hand is bigger

Final answer:

Using a system of linear equations, it was determined that 57 child tickets were sold at the movie theatre when 155 tickets were sold for a total of $1312.20.

Explanation:

To determine how many child tickets were sold at the movie theatre when 155 tickets were sold for a total of $1312.20, we can set up a system of linear equations. Let's define C as the number of child tickets and A as the number of adult tickets. We know that child admission is $6.00 and adult admission is $9.90.

The first equation represents the total number of tickets sold:
C + A = 155

The second equation represents the total sales:
6C + 9.9A = 1312.20

To solve this system, we can use either substitution or elimination. Here, we'll go with substitution:

So, 57 child tickets were sold that day.

40%

to calculate rate of discount,

[tex]\frac{discount}{original cost}[/tex] × 100%

discount = $60 - $36 = $24

[tex]\frac{24}{60}[/tex] × 100% = 40%

Answer:

it is 40%

Step-by-step explanation:

Range represents all of the y-values possible for the function.  

What is the highest point on the graph? The coordinate is (2, 50) so the y-value of the highest point is 50.

What is the lowest point on the graph? there isn't one because it continues downward to infinity.

Range: (-∞, 50]

I hope this helped!

Answer:

The given function is

  y≥2-2x

Writing this inequality in equation form and then in slope intercept form

  [tex]y=2-2x\\\\2x+y=2\\\\\frac{2x}{2}+\frac{y}{2}=1\\\\ \frac{x}{1}+\frac{y}{2}=1[/tex]

Option D

Graph of a solid line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A solid line passes through begin ordered pair 1 comma 0 end ordered pair and begin ordered pair 0 comma 2 end ordered pair. The region above the solid line is shaded.

The correct representation of the inequality y≥2−2x is: Graph of a solid line on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. A solid line passes through the ordered pair (0, -2) and (1, 0). The region above the solid line is shaded.

In mathematics and data visualization, a graph is a visual representation of data or mathematical relationships. It typically consists of points (nodes or vertices) connected by lines or curves (edges) that show relationships or connections between the points. Graphs are used to represent various data structures and relationships, such as in graph theory, network analysis, and data plotting.

This representation correctly shows a solid line (not dashed) and shades the region above the line, which indicates the solution to the inequality y ≥ 2 − 2x.

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Answer: Isaiah earned $400.16

Step-by-step explanation:

1. You have that Isaiah earns a weekly salary of $320 and a comission of 3% on all of his sales and the last week this sales were $2,672.

2. Therefore, to solve this problem you must caculate the 3% of $2,672 and add this result to his weekly salary, as following:

[tex](2,672)(0.03)=80.16[/tex] dollars

[tex]320+80.16=400.16[/tex] dollars

The land area of Pennsylvania is 44,816 square miles. Rounding it to the nearest hundred gives us 44,800 square miles.

The land area of Pennsylvania is 44,816 square miles. To round this number to the nearest hundred, we look at the digit in the hundreds place. The digit in the hundreds place is 4, so we keep the 4 and change all the digits to the right of it to zeros. Therefore, the land area of Pennsylvania rounded to the nearest hundred is 44,800 square miles.

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Answer:

$38.40

Step-by-step explanation:

It is right on Plato

4 refrigerators = 1000

2 dishwashers = 300

add em up to 1300

We are given statements :  Premise: If the sides of a triangle are all 4 cm, then the triangle is equilateral.

Premise: The triangle is equilateral.

According to law of Detachment : Statement 1: If q, then q.

and Statement 2: p

   Conclusion: q.

According to given reasoning :

p : If the sides of a triangle are all 4 cm.

q :  Then the triangle is equilateral.

Therefore, Statement 1 : If( the sides of a triangle are all 4 cm), then (the triangle is equilateral).

Statement 2:  (the triangle is equilateral).

Conclusion : The sides of the triangle are 4 cm.

Therefore, option B is correct "Law of Detachment".

Answer is B ! Good luck bro

The domain of a graph is the set of input values the graph can take.

The graph that represents y = [x] over the domain -4≤x≤-1 is the 1st graph.

The domain is given as:

[tex]\mathbf{-4 \le x \le -1}[/tex]

The inequalities at -4 and -1 are both "less than or equal to"

In inequalities, "less than or equal to" is represented by a closed circle

This means that, the circles at x = -4 and x =-1 on the graph must be a closed circle.

From the given options, we have the following observations

Hence, the graph that represents y = [x] over the domain -4≤x≤-1 is the 1st graph.

Read more about domains at:

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Answer: The combined mass of the quarters is  11.863 g.

Step-by-step explanation:

1. You have the following information given in the problem above:

- The mass of the modern quarter is 5.623 g.

- The mass of the older silver quarter is 6.24 g.

2. Therefore, to calculate the combined mass of the quarters, you only need to add the mass of the modern quarter (5.623 g) and the mass of the older silver quarter is (6.24 g), as you can see below:

Let's  call the combined mass of the quarters [tex]x[/tex]. Then:

[tex]x=5.623g+6.24g\\x=11.863g[/tex]

Answer:

11.863 g

Step-by-step explanation:

because if you add those 2 numbers then it will give you 11.863 g

Here is the equation:

[tex]4x+y=z[/tex]

You need to find x. To do that, the variable must be alone on one side. On the right side, you have:

[tex]4x+y[/tex]

To leave 4x by itself, you need to remove y by doing the opposite sign of it. Since it's +y, you need to -y(subtract y) from both sides.

[tex]4x+y-y = z-y \\ 4x=z-y[/tex]

Now the variable is alone. You have 4x and you need to find x alone. To do that, you need to divide both sides by 4.

[tex]\frac{4x}{4} = \frac{z-y}{4}[/tex]

Your answer is:

[tex]x = \frac{z-y}{4}\ \checkmark[/tex]

If you have any questions, feel free to ask! :)

( - ∞, ∞ )

f(x) is defined for all real values of x

I believe the answer for this question would $be:

$15+$1.50 = $16.50

$25 / $16.50 = 15.45

I believe that he ran 15 - 15.5 laps.