Answer:
Step-by-step explanation:
Re-write the equation, for convinience, as
y = 1/4(x) + 4
set x = 0 to get y = 1 and set y = 0 to get x = -4.
You have the coordinates of 2 points, (0 , 1) and ( -4 , 0).
Join the two points which obviously cuts the y-axis at y = 1,
3. Which equation has a solution of 2/3 for n?
a. n - 1 = %
b. 16n = 24
c. 15n = 10
d. 1% + n = 3
What’s the answer
Answer:
C) 15n=10
Step-by-step explanation:
Because 15(2/3)=5*2=10.
2) Your class is raising money for a class trip. You make $10 on each pizza and $4 on each box of cookies that you sell.
How many items of each type must you sell to raise more than $100? Write and graph an inequality to model the
situation. Define the variables and state the constraints. Give three possible combinations that you could sell.
Answer:
The variables are 'p' and 'c'.
The inequality is: [tex]10p+4c\geq100[/tex]
The graph is plotted below.
Three possible solutions are: (0, 25), (10, 0) and (5, 20)
Step-by-step explanation:
Let the number of pizzas sold be 'p' and number of cookies sold be 'c'.
Given:
Price per pizza = $10
Price per cookie = $4
Minimum amount to be earned = $100
Price for 'p' pizzas sold = [tex]10p[/tex]
Price for 'c' cookies sold = [tex]4c[/tex]
As per question:
[tex]10p+4c\geq100[/tex]
Also, number of pizzas and cookies can't be negative. So,
[tex]p\geq0,c\geq0[/tex]
Plotting the above inequalities on a graph using DESMOS.
The region that is common to all the above inequalities is the solution region and is shown in the graph below.
The solution region also includes all the points on the line.
So, the three possible combinations of solutions can be any 3 points in the solution region. One such combination is:
(0, 25), (10, 0) and (5, 20)
Mr. Johnson's lunch bill is 29.90, which includes a 15% tip
What is the price before the tip?
**URGENT 100 POINTS**
Answer:
26.
Step-by-step explanation:
15% of 29.90 is 3.90
26+3.90= 29.90
The price of Mr Johnson's lunch bill before the 15% tip paid is $26.
What is the price before tip?Percentage can be described as a fraction of an amount expressed as a number out of hundred.
In order to determine the price before the tip, divide the lunch bill by the percentage tip.
Price before the tip = lunch bill / ( 1 + percentage tip)
29.90 / 1/15 = $26
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please help :) this study island was due last week, and I cannot get past this question
Answer: For number one it's decreasing
Step-by-step explanation:
Find three ratios equivalent to the ratio described in each situation . The ratio of cats to dogs in park is 3/4
Answer:
6/8, 9/12, and 12/15
Step-by-step explanation:
3/4 + 3/4 = 6/8
6/8 + 3/4 = 9/12
9/12 + 3/4 = 12/15
Which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"?
The algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three" is [tex]\frac{-8}{n+3}[/tex] or [tex]-8 \div n+3[/tex]
Solution:Given statement is "the quotient of negative eight and the sum of a number and three"
To write the algebraic expression, follow these steps:
Let "n" be the number
The expression "negative eight" is equivalent to -8
Now look at the statement "the sum of a number and three"
"The sum of a number and three" is equivalent to n + 3
Now put all the statements together:
Quotient means you are dividing. So use division
"The quotient of negative eight and the sum of a number and three" = [tex]\frac{-8}{n+3}[/tex] or [tex]-8 \div n+3[/tex]
The region bounded by y=(3x)^(1/2), y=3x-6, y=0
Answer:
4.5 sq. units.
Step-by-step explanation:
The given curve is [tex]y = (3x)^{\frac{1}{2} }[/tex]
⇒ [tex]y^{2} = 3x[/tex] ...... (1)
This curve passes through (0,0) point.
Now, the straight line is y = 3x - 6 ....... (2)
Now, solving (1) and (2) we get,
[tex]y^{2} - y - 6 = 0[/tex]
⇒ (y - 3)(y + 2) = 0
⇒ y = 3 or y = -2
We will consider y = 3.
Now, y = 3x - 6 has zero at x = 2.
Therefor, the required are = [tex]\int\limits^3_0 {(3x)^{\frac{1}{2} } } \, dx - \int\limits^3_2 {(3x - 6)} \, dx[/tex]
= [tex]\sqrt{3} [{\frac{x^{\frac{3}{2} } }{\frac{3}{2} } }]^{3} _{0} - [\frac{3x^{2} }{2} - 6x ]^{3} _{2}[/tex]
= [tex][\frac{\sqrt{3}\times 2 \times 3^{\frac{3}{2} } }{3}] - [13.5 - 18 - 6 + 12][/tex]
= 6 - 1.5
= 4.5 sq. units. (Answer)
is (1, 3), (2, 5), (2, 7), (4, 9) a function
Answer:
no becase the x value 2 has two y values 5 and 7. for it to be a function each x value can only have 1 y value
Step-by-step explanation:
Answer:
no it is not
Step-by-step explanation:
A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40t+4 . Suppose the juggler missed and ball hit the ground . Find the maximum height of the ball and time it took to reach the ground.
Answer:
29 feet
2.6 seconds
Step-by-step explanation:
h(t) is a downwards parabola, so the maximum is at the vertex.
t = -b / (2a)
t = -40 / (2×-16)
t = 1.25
h(1.25) = -16(1.25)² + 40(1.25) + 4
h(1.25) = 29
When the ball lands, h(t) = 0.
0 = -16t² + 40t + 4
0 = 4t² − 10t − 1
t = [ -(-10) ± √((-10)² − 4(4)(-1)) ] / 2(4)
t = (10 ± √116) / 8
t = (5 ± √29) / 4
t is positive, so:
t = (5 + √29) / 4
t ≈ 2.6
For which discriminant is the graph possible
b2-4ac=0
b2-4ac=-1
b2-4ac=4
Answer:
The graph is possible for [tex]b^2-4ac=4[/tex]
Step-by-step explanation:
we know that
The discriminant of a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]D=b^2-4ac[/tex]
If D=0 the quadratic equation has only one real solution
If D>0 the quadratic equation has two real solutions
If D<0 the quadratic equation has no real solution (complex solutions)
In this problem , looking at the graph, the quadratic equation has two real solutions (the solutions are the x-intercepts)
so
[tex]b^2-4ac > 0[/tex]
therefore
The graph is possible for [tex]b^2-4ac=4[/tex]
Answer:
b^2 – 4ac = 4
what’s the slope intercept form of -5y=2x+11?
Answer:
y = (2/5) x + (11/5)
Step-by-step explanation:
recall that the slope-intercept form of a linear equation takes the general form:
y = mx + b
In this case, we simply have to use algebra rules to rearrange the given equation such that it looks like the one above:
-5y = 2x + 11 (divide both sides by -5)
y = -(2/5) x - (11/5) (answer)
Rewrite 27+36 using the GCF and distributive property
Answer:
27 + 36 = 9(3 + 4)Step-by-step explanation:
[tex]\text{Distributive property:}\ a(b+c)=ab+ac\\\\27=\boxed{9}\cdot3\\\\36=\boxed{9}\cdot4\\\\GCF(27,\ 36)=\boxed{9}\\\\\\27+36=\boxed{9}\cdot3+\boxed{9}\cdot4=\boxed{9}(3+4)[/tex]
The ratio of chicken to vegetables in a soup is 2:3. If there are 9 cups of chicken, how many cups of vegetables are in the soup?
Answer:
13.5
Step-by-step explanation:
2/3=9/x
2x=9*3
2x=27
x=27÷2
x=13.5
Final answer:
There are 13.5 cups of vegetables in the soup.
Explanation:
If the ratio of chicken to vegetables in a soup is 2:3, and there are 9 cups of chicken, we can find the number of cups of vegetables by setting up a proportion. According to the ratio, for every 2 cups of chicken, there are 3 cups of vegetables. Since we have 9 cups of chicken, we want to know how many cups of vegetables correspond to this amount.
Write the ratio of chicken to vegetables as a fraction: 2/3.
Set up a proportion where 2 cups of chicken is to 3 cups of vegetables as 9 cups of chicken is to x cups of vegetables.
2/3 = 9/x
Cross multiply to solve for x: 2x = 9 × 3
2x = 27
Divide both sides by 2 to solve for x: x = 27/2
x = 13.5
Therefore, there are 13.5 cups of vegetables in the soup.
HELP ASAP PLS
The starting salary for a delivery driver is $35,000 per year with a yearly increase of 3%. Which type of function best models this situation?
A) exponential
B) linear
C) quadratic
D) radical
A) exponential is the right answer.
Step-by-step explanation:
The formula used for increase after same number of time is:
[tex]A_t = A_0(1+r)^t\\Here\\A_0\ is\ the\ initial amount\\r\ is\ the\ rate\\and\\t\ is\ time[/tex]
We are given
A_0 = 35000
r = 3%
[tex]A_t = 35000(1+0.03)^t\\A_t = 35000(1.03)^t[/tex]
The function is an exponential function is the value of t can be put equal to 1,2,3,4..... which will increase the final output exponentially
Hence,
A) exponential is the right answer.
Keywords: Functions, Exponential function
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The band at Brown High School sells tickets for catered dinners to raise money for field trips. Spaghetti dinner
tickets cost $7.25, and barbecue dinner tickets cost $8.75. The band sold twice as many spaghetti dinners as
barbecue dinners and raised $2,790. Which of the following sets of equations can be used to determine the number
of spaghetti dinner tickets, x, and the number of barbecue dinner tickets, y, sold?
x = 2y
7.25x + 8.75y = 2,790
2x = y
7.25x + 8.75y = 2,790
© x = 2y
8.75x + 7.25y = 2,790
© 2x = y
8.75x + 7.25y = 2,790
Answer: First option.
Step-by-step explanation:
Let be "x" the number of spaghetti dinner tickets sold and "y" the number of barbecue dinner tickets sold.
You know that 1 spaghetti dinner ticket costs $7.25; so the total amount of money earned selling these tickects can be represented with this expression:
[tex]7.25x[/tex]
Since 1 barbecue dinner ticket costs $8.75; the total amount of money earned selling them can be represented with this expression:
[tex]8.75y[/tex]
Knowing that the total amount of money the band raised was $2,790, we can write the following equation to represent this situation:
[tex]7.25x+8.75y=2,790[/tex]
The band sold twice as many spaghetti dinners as barbecue dinners, which means that the amount of spaghetti dinners sold was two times the amount of barbecue dinners sold.
This can be represented with this equation:
[tex]x=2y[/tex]
Therefore, the set of equations that can be used to find "x" and "y", is:
[tex]\left \{ {{x=2y} \atop {7.25x+8.75y=2,790}} \right.[/tex]
Thomas buys 6 souvenirs for his friends and family. each gift takes up 1/15 of his suitcase. If he has two suitcases, how much room is left for his own belongings in his suitcases?
Answer:
Thomas still has 1 3/5 suitcases available for his own belongings.
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Number of souvenirs bought by Thomas = 6
Space that each souvenir takes of Thomas suitcase = 1/15
Number of Thomas suitcases = 2
2. How much room is left for his own belongings in his suitcases?
Let's find out how much space the souvenirs take:
Number of souvenirs * Space that each souvenir takes
6 * 1/15 = 6/15 = 2/5 (Dividing by 3 the numerator and the denominator)
The souvenirs take 2/5 of one suitcase.
Now, we can calculate the room that is left for Thomas' belongings.
2 Suitcases - 2/5 for the souvenirs
2 - 2/5 = 10/5 - 2/5 = 8/5 = 1 3/5
Thomas still has 1 3/5 suitcases available for his own belongings.
Note: Same answer to question 14040097, answered by me.
A machine bolts that are 12 mm long. The bolts are considered acceptable if they are within 0.2 mm of 12 mm. a. What is the longest the bolt can be and still be acceptable? SHOW WORK PLEASE!!!!!
Answer:
The longest bolt that can be acceptable is [tex](12+0.2)=12.2\ mm[/tex]
Step-by-step explanation:
To find the acceptable measure of the bolt we have to add and subtract the clearance limit.
a.For longest measure of the bolt we will perform addition.
And for shortest measure of the bolt we will go with subtraction.
So the longest acceptable measure of the bolt [tex]=12\ mm +0.2\ mm = 12.2\ mm[/tex]
Hope there question b is missing.
b.
The shortest measure of the bolt [tex]=12\ mm -0.2\ mm = 11.8\ mm[/tex]
The acceptable measure of the bolt are:
For longest it is [tex]12.2\ mm[/tex] and for shortest it is [tex]11.8\ mm[/tex]
Pick the expression that matches this description:
A 3^rd degree binomial with a constant term of 8
Choose 1 answer:
(Choice A)
8x^3+2x+3
(Choice B)
x^3-x^2+8
(Choice C)
2x^8+3
(Choice D)
-5x^3+8
Answer: Choice D, -5x^3 + 8
A binomial consists of two terms being added or subtracted. The two terms are -5x^3 and 8. The term -5x^3 has a leading coefficient -5 and exponent 3. The largest exponent determines the degree of the polynomial. The 8 is constant as there are no variables attached or multiplying with it.
The sum of three consecutive odd integers is 76 less then seven times the middle number.Find three integers
The sum of three consecutive odd integers is 76 less then seven times the middle number. The three integers are 17, 19 and 21 respeectively
Solution:Since each consecutive odd integer is separated by a difference of 2
Let "n" be the first integer
n + 2 be the second integer
n + 4 be the third integer
Given that the sum of three consecutive odd integers is 76 less then seven times the middle number
Which means,
The sum of ( n, n + 2, n + 4) is equal to 76 less than seven times the middle number ( 7(n + 2))
That is,
n + n + 2 + n + 4 = 7(n + 2) - 76
3n + 6 = 7n + 14 - 76
4n = 68
n = 17
So we get:
First integer = n = 17
Second integer = n + 2 = 17 + 2 = 19
Third integer = n + 4 = 17 + 4 = 21
Thus the three consecutive odd integers are 17, 19 and 21 respeectively
find the equation of a parabola that opens up and has the following x intercepts (-3,0) and (4,0)
The equation of a parabola that opens up and has the following x intercepts (-3,0) and (4,0) is [tex]y=x^{2}-x-12[/tex]
Solution:We have to find the equation of a parabola that opens up and has the following x intercepts (-3, 0) and (4, 0)
x-intercepts of the parabola are (−3, 0) and (4, 0)
So, we can form an equation:
Also x = 4
x – 4 = 0
x – 4 = 0 is another factor of quadratic equation.
The quadratic function is:
[tex]\begin{array}{l}{y=(x+3)(x-4)} \\\\ {y=x^{2}-4 x+3 x-12} \\\\ {y=x^{2}-x-12}\end{array}[/tex]
Hence, the equation of the parabola is [tex]y=x^{2}-x-12[/tex]
To find the equation of a parabola with x-intercepts at (-3,0) and (4,0), we can use the factored form of a quadratic equation. By plugging in the values of the roots and simplifying, we can determine that the equation of the parabola is y = x^2 - x - 12.
Explanation:To find the equation of a parabola that opens up and has x-intercepts at (-3,0) and (4,0), we can start by recognizing that the x-intercepts are the points where the parabola intersects the x-axis. This means that the parabola has roots of -3 and 4. To find the equation, we can use the factored form of a quadratic equation: (x - root1)(x - root2) = 0. Plugging in the values of the roots, we get (x - (-3))(x - 4) = 0. Simplifying this, we have (x + 3)(x - 4) = 0. Expanding this, we have x^2 - x - 12 = 0. Therefore, the equation of the parabola is y = x^2 - x - 12.
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Special Right Triangles: Decimal Answer ! What’s H and C ?! Help me please?! Round to the nearest tenth.
Answer:
h = 1.41
c = 3.46
Step-by-step explanation:
See the triangles diagram attached.
For the first triangle, Base = h, Hypotenuse = 2 and the angle between base and hypotenuse is 45°.
Therefore, [tex]\cos 45 = \frac{\textrm {Base}}{\textrm {Hypotenuse}} = \frac{h}{2}[/tex]
⇒ [tex]h = 2 \cos 45 = \frac{2}{\sqrt{2} } = \sqrt{2} = 1.414 = 1.41[/tex] (Answer)
{Rounded to the nearest tenth}
Again in the second triangle, Perpendicular = c, Hypotenuse = 4 and the angle between base and hypotenuse is 60°.
Therefore, [tex]\sin 60 = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} = \frac{c}{4}[/tex]
⇒ [tex]c = 4 \sin 60 = \frac{4 \times \sqrt{3} }{2} = 2\sqrt{3} = 3.46[/tex] (Answer)
{Rounded to the nearest tenth}
At one really small university, there are 1,200 people. Of these students, 53% are undergraduates. 37% are graduates, and the rest are going for their doctorate. How many professors are at the university?
There are 120 professors at the university
Step-by-step explanation:
At one really small university:
There are 1,200 people53% are undergraduates37% are graduatesThe rest are going for their doctorateWe need to find how many professors are at the university
Assume that the number of people the university is 100%
∵ 53% of the people in the university are undergraduates
∵ 37% of the people in the university are graduates
∵ There are 100% people in the university
- To find the rest subtract the sum of the undergraduates and
graduates from 100%
∵ The rest = 100% - (53% + 37%)
∴ The rest = 100% - 90%
∴ The rest = 10%
∴ The rest is 10% from 1200 people in the university
∵ The rest are going for their doctorate
∴ The rest is the number of the professors in the university
∵ The rest is 10% from 1200 people in the university
∴ The number of professors = 10% × 1200
∵ 10% = 10 ÷ 100 = 0.1
∴ The number of professors = 0.1 × 1200
∴ The number of professors = 120
There are 120 professors at the university
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4. Write a number story to show 917 + 67 = . Solve the problem.
Answer:
Sally had 917 bottles of water \she plans on buying 67 more bottles of water so in all she will have 984 bottles of water.
Step-by-step explanation:
estimate 394/24 by first rounding each number so that it has only 1 nonzero digit.
Answer:
48 million
Step-by-step explanation:
Since 48,000,000 has TWO non-zero numbers, not one, it can't be the
answer.
The largest digit in the given number is the ten-millions digit, so
you want to round to the nearest ten million, rather than the nearest
million.
47,859,600 rounds to 50,000,000, to one significant digit.
Normally, we would say "round to one significant digit," but you
probably have not seen that term. Your question means the same th
To estimate 394/24, round 394 to 400 and 24 to 20, to get an estimated quotient of 20 after dividing the rounded figures.
Explanation:To estimate 394/24 by rounding each number to have only one nonzero digit, we round 394 to 400 and 24 to 20. Now, let's divide the rounded figures:
400 ÷ 20 = 20This gives us an estimated result. To round to the nearest whole number, we start with our original rounded figures since both have 0 decimal places. Therefore, our final estimate after rounding is 20.
When performing mathematical operations like this, it's important to use the rounding rules properly. For division and multiplication, we round the final answer to the number of significant figures that matches the number with the least significant figures used in the calculation.
Ratio equivalent to 3 : 4
Answer:
8:6
Hope it helped. :)
Answer: 6:8
to Find any equivalent ratio, you multiply both numbers (in this example, 6 and 8) by the same number (in this example, 2).
which value is equivalent to the expression 2^3 + 3^4
Answer:
89
Step-by-step explanation:
2^3=2*2*2=8
3^4=3*3*3*3=9*9=81
8+81=89
Please help!!!! Questions are in the picture above!! Question is worth 20 points please answer it correctly!!!!
Answer:
Step-by-step explanation:
points that lie on an axis do not lie in any quadrant.
So point A lies in the positive x-axis
The origin (0,0) does't lie on any quadrant.
Origin is the point that lies on both x-axis and y-axis
+
A student earned 30 out of 35
points on an exam. C What percent
of the total points did the student
earn? Round to the nearest
percent
w
mother age is three times biger than from the daughter.In 10 years mother's age will be 2 times bigger than the daughter.How many years the daughter and mmother are
Answer:
20 years apart.
Step-by-step explanation:
Daughter is 10 years old, and mother is 3 times older. This makes mother 30 years old. There is a 20 year difference between them.
Ten years later, the daughter is 20 years old. Since the mother is 20 years older, she is now 40, which is 2 times older than the daughter.
find a polynomial of degree 3 with real cofficients and zeros of -3,-1,4 for which f(-2)=24
[tex]\bf \textit{zeros at } \begin{cases} x = -3\implies &x+3=0\\ x = -1\implies &x+1=0\\ x = 4\implies &x-4=0 \end{cases}\qquad \implies (x+3)(x+1)(x-4)=\stackrel{y}{0} \\\\\\ (x^2+4x+3)(x-4)=0\implies x^3~~\begin{matrix}+ 4x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+3x~~\begin{matrix} -4x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-16x-12=0 \\\\\\ x^3-13x-12=0[/tex]
we know that f(-2) = 24, namely when x = -2, y = 24, let's see if that's true
[tex]\bf x^3-13x-12=y\implies \stackrel{x = -2}{(-2)^3-13(-2)-12}=y \\\\\\ -8+26-22=y \implies 6=y[/tex]
darn!! no dice.... hmmmm wait a second.... 4 * 6 = 24, if we could just use a common factor of 4 on the function, that common factor times 6 will give us 24, let's check.
[tex]\bf 4(x^3-13x-12)=y\implies \stackrel{x = -2}{4[~~(-2)^3-13(-2)-12~~]}=y \\\\\\ 4[~~-8+26-22~~]=y\implies 4[6]=y\implies 24=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 4x^3-52x-48=y~\hfill[/tex]