Jill made a New Year's resolution to learn how to play the cello. She bought an Introduction to
Cello class pack from the Purple Harp music shop, which covers the cost of 15 cello lessons.
She also paid $35 to rent a cello. In all, Jill paid $425.
Which equation can you use to find the cost, c, of each cello lesson?
A. 35(c +15) = 425
B. 15c + 35 = 425
C. 15(c + 35) = 425
D. 35c+15= 425

Answer:

A

Step-by-step explanation:

Answer:

r = 8 cm

Step-by-step explanation:

V = π·r²·h

1004.8 = 3.14(5)·r²

r² = 1004.8/15.7

r² = 64

r = √64 = 8

Answer:

(8, 0)

(-2, 0)

(-3, 0)

Step-by-step explanation:

x - 8 = 0

x = 8

x + 2 = 0

x = -2

x + 3 = 0

x = -3

\((x-8)(x+2)(x+3) =0\\\\\implies x -8 =0~~~ \text{or}~~~x+2 =0 ~~~ \text{or}~~~x+3 = 0\\\\\implies x = 8 ~~~~~~~~ \text{or}~~~~~~x = -2 ~~~ \text{or}~~~ x = -3\\\\\\\text{Hence the roots are}~ 8, -2 ~\text{and} ~-3\)

The required quadratic equation of h(x) is given as h(x) = (x + 1)² + 2. Option C is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The required function that shows the relationship shown in the table can be evaluated just by putting values in the function,
So by putting value in each function this values only satisfied in function,
h(x) = {x + 1}² + 2
As,
h(0) = 3
h(-1) = 2

Thus, the required quadratic equation of h(x) is given as h(x) = (x + 1)² + 2. Option C is correct.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ1

Answer:

48 degrees

Step-by-step explanation:

1) Solve for x

Complementary angles add up to 90 degrees. Therefore, m<A + m<B is equal to 90:

\(A+B=90\\(2x+20)+(3x)=90\)

Open up the parentheses

\(2x+20+3x=90\\5x+20=90\)

Subtract 20 from both sides

\(5x+20-20=90-20\\5x=70\)

Divide both sides by 5

\(\frac{5x}{5} =\frac{70}{5} \\x=14\)

Therefore, x is equal to 14.

2) Determine angle A

\(A=2x+20\)

Substitute x with 14

\(A=2(14)+20\\A=28+20\\A=48\)

Therefore, the measure of angle A in degrees is 48 degrees.

I hope this helps!

The solution to the system of equations is (3, 6) and (-3, 18) after equating both the equations.

Any equation of the form \(\rm ax^2+bx+c=0\)  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

\(\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}\)

We have a system of equation:

f(x) = x² - 2x + 3

f(x) = -2x + 12

Find a solution for the system of equations equates to the equations:

x² - 2x + 3 = -2x + 12

x² = 9

x = ±3

Plug the above values in the linear equation:

f(3) = 6

f(-3) = 18

(3, 6) and (-3, 18)

Thus, the solution to the system of equations is (3, 6) and (-3, 18) after equating both the equations.

Learn more about quadratic equations here:

brainly.com/question/2263981

#SPJ1

Answer: Im going to say C

Step-by-step explanation: Because the lines both look the same they could be even.

It looks like you want to evaluate the iterated integral of the function 2x(x + 2y) over a given region S. To evaluate the iterated integral, we first integrate with respect to y (dy) and then with respect to x (dx).

Let's first integrate with respect to y:

∫(2x(x + 2y)) dy = 2x(xy + y^2) + C₁

Now, we need to evaluate this expression for the limits of integration for y, which are not given in your question. I'll assume they are y = a and y = b, so we have:

[2x(xb + b^2) - 2x(xa + a^2)]

Next, we'll integrate this expression with respect to x:

∫(2x(xb + b^2) - 2x(xa + a^2)) dx = x^2(xb + b^2) - x^2(xa + a^2) + C₂

Finally, we need to evaluate this expression for the limits of integration for x, which are also not given in your question. Assuming they are x = c and x = d, we have:

[(d^2(dc + b^2) - d^2(da + a^2)) - (c^2(cc + b^2) - c^2(ca + a^2))]

This expression represents the value of the iterated integral for the function 2x(x + 2y) over the region S, given the limits of integration for x and y. Please provide the limits of integration for a more specific answer.

To learn more about integration visit;

brainly.com/question/30900582

#SPJ11

Answer:

  20 units

Step-by-step explanation:

You want the diameter of a right circular cone with a height of 21 units and a volume of 700π cubic units.

The formula for the volume of a cone is ...

  V =1/3πr²h

The radius (r) is half the diameter (d), so the formula can be written as ...

  V = 1/3π(d/2)²h = (π/12)d²h

Substituting the given values, we can solve for d:

  700π = (π/12)d²(21)

  400 = d² . . . . . . . . . . . multiply by 12/(21π)

  20 = d . . . . . . . . . take the square root

The diameter of the cone is 20 units.

Answer 10x8=80+3

Step-by-step explanation:

i.d.k 83?????

Answer: f(7) = -128

g(7) =  26

Equation of f(x):  f(x)= -11x-51

Equation of g(x): g(x)=3x+5

Step-by-step explanation:

Rate of change of a function: \(\dfrac{f(x_2)-f(x_1)}{x_2-x_1}\)

From the table. Rate of change in f(x)= \(\dfrac{f(1)-f(0)}{1-0}=\dfrac{-62+51}{1}=-11\)

Rate of change in g(x)= \(\dfrac{g(1)-g(0)}{1-0}=\dfrac{8-5}{1}=3\)

Also, the rate of change throughout the function is the same, hence both are linear functions.

Equation of linear function:  \(f(x)=mx+c\), where m= rate of change of function, c = f(x) at x=0.

From table, f(0)= -51 , g(0)=5

Equation of f(x): f(x)= -11x-51

Equation of g(x): g(x)=3x+5

f(7) = -11(7)-51 = -77-51 = -128

g(7) = 3(7)+5 = 21+5 = 26

f(7) = -128

g(7) =  26

The slope of the line of image 1 is 2

The slope of the line of image 2 is 5/2

The slope of the line of image 3 is 2/5.

The same number is given for every two different points on the same line when the ratio is stated as a quotient ("rise over run"). On a falling line, there is a negative "rise." In a diagram that depicts a roof or a road as a description or a design, the line may be practical as established by a road surveyor.

The slope of the line of image 1 is:

The line is passing through the points (6, 10 and (2, 2)

So,

Slope=(y₂-y₁)/(x₂-x₁)

m=(2-10)/(2-6)

m=8/4

m=2

Therefore, the slope of the line for image 1 is 2.

Hence, option A is correct.

The slope of the line for image 2 is:

The line is passing through the points (3, 4) and (7, 14)

Slope=(y₂-y₁)/(x₂-x₁)

m=(14-4)/(7-3)

m=10/4

Therefore, the slope of the line for the image 2 is 5/2.

Hence, option F is correct.

The slope of the line for image 3 is:

The line is passing through the points (2, 1) and (7, 3)

Slope=(y₂-y₁)/(x₂-x₁)

m=(3-1)/(7-2)

m=2/5

Therefore, the slope of the line for the image 3 is 2/5

Therefore, option D is correct.

To know more about slope, visit:

https://brainly.com/question/3605446

#SPJ1

\(\\ \sf\longmapsto \dfrac{67}{100}\times 85\)

\(\\ \sf\longmapsto 85(0.67)\)

\(\\ \sf\longmapsto 56.95\)

\(\\ \sf\longmapsto \dfrac{33}{100}\times 76\)

\(\\ \sf\longmapsto 76(0.33)\)

\(\\ \sf\longmapsto 25.08\)

Add both

\(\\ \sf\longmapsto 56.95+25.08\)

\(\\ \sf\longmapsto 82.03\)

Using weighed averages, it is found that the final grade is was of 82.03.

-------------------

-------------------

Using the data given in the exercise, for the grades, and the weighed average concept, the final grade is:

\(G = 85(0.67) + 76(0.33) = 82.03\)

The final grade was of 82.03.

A similar problem is given at https://brainly.com/question/24447096

The percentage of published studies that supported the tested hypothesis has changed from 70 to 85% over the past 25 years.

Hypothesis testing:

A hypothesis testing means investigates a proposed mathematical model to determine whether there is sufficient evidence from a sample of data to reject the defined null hypothesis.

Given,

The percentage of published studies that supported the tested hypothesis has changed from _____ to _____ over the past 25 years.

Here we need to find the change in the percentage for the past 25 years.

Based on the details, the percentage of published studies that supported the tested hypothesis has changed from 70 to 85% over the past 25 years.

To know more about Tested Hypothesis here.

https://brainly.com/question/17099835

#SPJ4

Answer:

Sales = 20

Step-by-step explanation:

Simply make the equation "1300 = 65s" to solve the problem

1300 = 65s

Divide both sides by 65.

1300/65 = 65s/65

Divide 1300 by 65 to get 20.

20=s

Swap sides so that all variable terms are on the left-hand side.

s=20

The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

More on volume of stacked books can be found here: https://brainly.com/question/1058070

#SPJ1

The probability that both Bonnie and Kelly will sit court-side is 1/55, or approximately 0.018. To express this as a percentage, we multiply by 100: the answer is 1.8%

The probability of Bonnie and Kelly both choosing court-side seats can be calculated as the number of favorable outcomes divided by the total number of possible outcomes. There are two court-side seats and two people choosing, so there is only one favorable outcome: both Bonnie and Kelly choose court-side seats. The total number of possible outcomes is the number of ways to choose two seats from the available two court-side seats, five upper-level seats, and four general admission seats. This can be calculated as the number of combinations of two seats from the total of eleven available seats, which is 11 choose 2 or 11C2 = 55.

The probability that both Bonnie and Kelly will sit court-side is 1/55, or approximately 0.018. To express this as a percentage, we multiply by 100:

0.018 * 100 = 1.8%

For more such questions on Probability

https://brainly.com/question/25870256

#SPJ4

Answer:

6.68

Hope this helps!!!!

Have a great day!!!! :)

Each person buys a number of cakes

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Andy buys x cakes, Betty buys 4 times as many cakes as andy, and colin buys 3 more cakes than andy

So,

Andy has = x Cakes

Betty have = 4x Cakes

Clin has = x +3 Cakes

Since each cake costs 65p and the total cost of the cakes is £52.65

thus,

0.65( x + 4x + x +3) = 52.62

x + 4x + x +3 = 81

6x = 78

x = 13

Therefore,

Andy has = 13 cakes

Betty has = 4x = 4*13 = 52 cakes

Colin has = x + 3 = 16 cakes

Learn more about Mathematical operations here:

https://brainly.com/question/20628271

#SPJ1

The table in this problem that shows a proportional relationship is given as follows:

Table b.

The rule is given as follows:

y = x/3.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

In table b, we have that each value of y is one third of the equivalent value of x, hence the constant is given as follows:

k = 1/3.

Thus the equation is:

y = x/3.

More can be learned about proportional relationships at https://brainly.com/question/7723640

#SPJ1

same question how many times...?

3( 7 + x ) = 21 + 3x

..................................

A quadratic equation with the given solutions of 2√11 and -√/11 can be expressed as x^2 - 4√11x + 1 = 0, but there are multiple correct equations.

To find an equation with the given solutions, we start by using the fact that for a quadratic equation in the form ax^2 + bx + c = 0, the solutions can be determined using the quadratic formula: x = (-b ± √(b^2 - 4ac))/(2a).

Given the solutions 2√11 and -√/11, we can see that the square root of 11 is common in both solutions. We can therefore rewrite the solutions as 2√11 and -√11/11.

By comparing this with the quadratic formula, we can see that b = -4√11 and ac = 1. Plugging these values into the quadratic formula, we get x = (-(-4√11) ± √((-4√11)^2 - 411))/(21), which simplifies to x = (4√11 ± √(176 - 4))/(2).

To make the equation easier to work with, we can further simplify the expression as x = (4√11 ± √172)/(2). Finally, by rationalizing the denominator, we get x = (2√11 ± √43)/(1), which can be expressed as x^2 - 4√11x + 1 = 0.

For more information on equation visit: brainly.com/question/25812462

#SPJ11

No, rectangle DABC is not the result of a dilation of rectangle HEFG with a center of dilation at the origin.

Dilation is a geometrical transformation that changes the size of a shape or figure. It is one of the four basic transformations of geometry alongside translation, rotation, and reflection. Dilation involves resizing a shape by a scale factor and keeping its overall shape intact. The scale factor is the ratio of the size of the image to the size of the original figure.

Dilation involves a scaling of a shape, where each point on the shape is moved away from or closer to the center of dilation, proportional to its distance from the center. In this case, the angles of rectangle DABC are different from the angles of rectangle HEFG, so it is not the result of a dilation. The angles of rectangle HEFG are ∠2, ∠33, ∠EDC, whereas the angles of rectangle DABC are ∠ADB, ∠BDC, and ∠CDB.

To learn more about dilation
https://brainly.com/question/26855848
#SPJ1

Answer:

Min: 143

Q1: 150

Med: 161

Q3: 168

Max: 180

Step-by-step explanation:

The line in the box means median, The line furthest to the right is the highest number, the line furthest to the left is the lowest number. The lines that create the box are (from left to right) the first quartile and the third quartile.

The answer from left to right:

143

152

161

168

180

Answer:

Since she started with $80 and ended with with $35,24, we can find the total amount she spent by subtracting these amounts:

$80 - $35.24 = $44.76

This means that she spent $44.76 on coffee. If each pound cost $7.46, we can divide $44.76 by $7.46 to see how many pounds she bought (ignoring tax):

44.76 / 7.46 = 6 pounds of coffee purchased

I hope it help you

Follow me please

Mark brainliest

Answer:

$19.00

Step-by-step explanation:

She made 52.50.

she had -14.

52.50-14= 38.50

tickets are 9.50

9.50×2= 19.00

hope this helps let me kno if i did somthing wrong!

Answer:

The input variable is 5 i.e 15/3

Step-by-step explanation:

Volume of a sphere is given by

\(V = \frac{4}{3} \pi {r}^{3} \)

Where r is the radius of the sphere

From the question

radius = 41 in

Substitute the value into the above formula

We have

\(V = \frac{4}{3} \times {41}^{3} \pi\)

\( = \frac{275684}{3} \pi\)

= 288695.6097

We have the final answer as

Hope this helps you

The answer on deltamath is

288695.6 in³