A sports club charges an initiation fee and a monthly fee. At the end of the 5 months, a member had paid a total of $450. At the end of the 10 months, she had paid a total of $500.

a) Write a linear system to model the situation
b) Solve the linear system by substitution to solve the related problem: What are the initiation fee and the monthly fee?

Answer:

Skyla looks for the x-value at which the graph of the function [tex]2^x[/tex] intersects the horizontal line defined by the constant function: [tex]f(x)=128[/tex]

Step-by-step explanation:

Look for an answer that involves something like:

By looking for the point where both functions intersect, Skyla can find for which x value the following equation is verified: [tex]2^x=128[/tex]

She must read at which x-value the intersection occurs, and that is the answer.

Answer: Intersect at (7,128) and x=7

Step-by-step explanation:

Answer:

slope = 0

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 8, - 3) and (x₂, y₂ ) = (- 12, - 3)

m = [tex]\frac{-3+3}{-12+8}[/tex] = [tex]\frac{0}{-4}[/tex] = 0

Slope is rise per run. Rise is difference of y ordinates and run is difference of corresponding x abscissa.

The slope of the line that passes through the given points is 0

Slope of the line that passes through given points.

In graphing, we use Cartesian plane and assume y axis to be perpendicular and mostly we take height or depth related stuffs on y axis, that's why y ordinates will be considered to calculate the rise and x axis is like flat ground, thus x abscissa will be used to calculate the run.

Let the points' coordinates are denoted by symbols as:

[tex](x_1, y_1) = (-8,-3)\\ (x_2, y_2) = (-12, -3)\\ [/tex]

[tex]slope = \dfrac{rise}{run} = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{(-3) - (-3)}{(-12)-(-8)} = \dfrac{0}{-4} = 0[/tex]

Slope is zero means you run whatever, the rise is 0, which means the line is not going to rise and stay flat (horizontal).

Learn more about slope of straight lines here:

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Answer:

et's solve your equation step-by-step.

(x+3)2−1=35

Step 1: Simplify both sides of the equation.

x2+6x+8=35

Step 2: Subtract 35 from both sides.

x2+6x+8−35=35−35

x2+6x−27=0

Step 3: Factor left side of equation.

(x−3)(x+9)=0

Step 4: Set factors equal to 0.

x−3=0 or x+9=0

x=3 or x=−9

Answer:

x=3 or x=−9

Answer:

Add 1 to each side

Take the square root of each side

Subtract 3 from each side

Step-by-step explanation:

(x+3)^2  -1 = 35

Add 1 to each side

(x+3)^2  -1+1 = 35+1

(x+3)^2   = 36

Take the square root of each side

sqrt ((x+3)^2)   =±sqrt (36)

x+3 = ±6

Subtract 3 from each side

x+3-3 = -3±6

x = -3±6

x = -3+6          x = -3-6

x = 3                x = -9

Answer: 2

Step-by-step explanation:

Answer:

5^10 / 5^8 = 5^2 = 25 so the equation becomes 25 = (1/5) ^ n. This means that n = -2.

Answer:

[tex]n=-2[/tex]

Step-by-step explanation:

[tex]\frac{5^{10}}{5^8}=(\frac{1}{5})^n[/tex]

Use the law of exponents.

[tex]5^{10-8}=\left(\frac{1}{5}\right)^n[/tex]

1/5 can be written with a base of 5.

[tex]5^{10-8}=\left(5^{-1}\right)^n[/tex]

Cancel the base 5 on both sides.

[tex]10-8=-1\times \:n[/tex]

[tex]2=-n[/tex]

Multiply both sides with -1.

[tex]n=-2[/tex]

Answer:

A. a numerical equation

Step-by-step explanation:

Answer:

x^2+6x+9

Step-by-step explanation:

x^2 +6x

Take the coefficient of x

6

Divide by 2

6/2 = 3

Square it

3^2 = 9

Add 9 to each side

x^2+6x+9

Answer:

Quadratic Equations ⇒ D, E, F

Step-by-step explanation:

Let us say that each of these equations can only be defined as a quadratic equation if it can be factored / solved through completing the square / application of quadratic formula as solve for the value of x;

[tex]A. 2x - 1 = 0, Add + 1 to either side,\\2x = 1, Divide sides by 2,\\x = 1 / 2 ; Not Quadratic Equation[/tex]

[tex]B. 2x^2 - 1 = 0, Add + 1 to either side,\\2x^2 = 1, Divide sides by 2,\\x^2 = 2, Take | | of x, \sqrt{x} - either side \\\| x | = \sqrt{1 / 2},\\x = \sqrt{1 / 2} = - \sqrt{1 / 2} ; NotQuadraticEquation[/tex]

[tex]C. 2x^2 - 1, NotInForm - ax^2 + bx + x = 0 ; NotQuadraticEquation[/tex]

[tex]D. 3x^2 + 5x - 1 = 0, Add 1 to either side,\\3x^2 + 5x = 1, Divide sides by 3,\\x^2 + 5x / 3 = 1 / 3, Solve for a,\\2ax = 5 / 3x, Divide sides by 2x,\\a = 5 / 6, Add a^2 - ( 5 / 6 )^2 to either side,\\x^2 + ( 5x / 3 )^2 + ( 5 / 6 )^2 = 1 / 3 + ( 5 / 6 )^2, simplify,\\( x + 5 / 6 )^2 = 37 / 36, solve for x,\\x = ( \sqrt{37} - 5 ) / 6 = ( - \sqrt{37} - 5 ) / 6 ; QuadraticEquation[/tex]

[tex]E. x - x^2 + 5 = 0, Similar Form ; QuadraticEquation\\[/tex]

[tex]F. - 4x^2 + x = 0, Factor the Expression,\\- x * ( 4x - 1 ) = 0, Apply Zero Product Property,\\x = 0, and, 4x - 1 = 0,\\x = 0 = 1 / 4 ; QuadraticEquation[/tex]

The quadratic equations are:

2x² - 1 = 0

2x² - 1

3x² + 5x - 1 = 0

x - x² +5 = 0

-4x² + x = 0

Options B, C, D, E and F are the correct answer.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

A polynomial with degree 2 is called a quadratic equation.

A.

2x – 1 = 0

This is not a degree 2 equation.

B.

2x² - 1 = 0

This has degree 2.

C.

2x² - 1

This has degree 2.

D.

3x² + 5x - 1 = 0

This has degree 2.

E.

x - x² +5 = 0

-x² + x + 5 = 0

This has degree 2.

F.

- 4x² + x = 0

This has degree 2.

Thus,

B, C, D, E,  and F are quadratic equations.

Learn more about polynomials here:

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Answer:

See below

Step-by-step explanation:

1) x=2-1

x=1

2) (x+1)(x+1)=2(x+1)

3) 10x-20 -11 = 4+3x

10x-3x=20+11+4

7x=35

x=5

Answer:it is 9 because you subtract 6 from the 8 and then you add 2 and 7 to get 9

Step-by-step explanation:

Answer:

≈82698.73 kg m²/s

Step-by-step explanation:

K.E.=1/2mv²=1/2×745×14.9²=82698.725 kg m²/s

Answer:

Reflect over the x-axis and shift up 3.

Answer:

Reflect over the x-axis and shift up 3

Step-by-step explanation:

Answer:

A=314 feet

Step-by-step explanation:

[tex]A=\pi r^{2}[/tex]

[tex]A=3.14*10^{2}[/tex]

[tex]A=3.14*100[/tex]

[tex]A=314 feet[/tex]

Answer:

p(1)=100

Step-by-step explanation:

p(1) just means "substitute the value (1) in for (x) in the equation"

So,

[tex]1^{99}[/tex]+99= 100

(1 to any power is always equal to 1, including 0)

Answer: Verticals angles are when 2 line intersect at a point forms 2 pairs of angles. The pairs will be opposite of each other.

The picture I have attached should give a good representation of what I mean.

The A angles are the same and the B angles are the same in the picture.

Answer:

C

Step-by-step explanation:

Blue is postive and Red is Negative so you would just write them down as seen and because x^2 is negative in the second equation there will be a subtraction sign to represent it.

4^2 = 4 * 4.

4 * 4 = 16.

Therefore, p ^2 = 16.

Answer:

16

Step-by-step explanation:

i showed the work in the picture above

Answer:

[tex]-7[/tex]

Step-by-step explanation:

[tex]f(-3)=-7[/tex]

Answer:

2635*'fhhdgjvsvaksgwksygwi at gwjsksgeieh egg ejei

Steps:

Shape: Cone

Solved for radius

Height: 36 cm

Volume: 588 cm3

Formula= r=√3v/πh

R= Radius

H= Height

Description:

Using the formula  r=√3v/πh, we have to calculate the radius.  We know that the height is 36 and the volume of 588. We use the formula and get the answer. The answer we get is r≈3.95cm.

Answer: r≈3.95cm

Please mark brainliest

Hope this helps.

Answer:

r = 7cm

Step-by-step explanation:

[tex]h = 36 \\Volume = 588pi\\r = \\588pi = \frac{1}{3}pir^{2} 36\\Cross-multiply\\1764pi=36pir^{2} \\Divide-both-sides-of-the-equation-by-36pi\\r^{2} =\frac{1764pi}{36pi} \\r^{2} = 49\\Square -root-both-sides-of-the-equation.\\\sqrt{r^{2} } =\sqrt{49} \\r = 7[/tex]

Answer:

The discriminant is 0

That means there is one real zero

Step-by-step explanation:

3x^2 + 24x + 48

This in the form

ax^2 +bx+c

a=3 b=24 c = 48

The discriminant is

b^2 - 4ac

24^2 - 4(3)(48)

576-576

0

The discriminant is zero

That means there is one real zero

Answer:

6/8 which simplifies to 3/4

Step-by-step explanation:

2/8 + 4/8

Since the denominator is the same, we can just add the numerators

2+4 =6

6/8

Simplifying the fraction by dividing the top and bottom by 2

3/4

Answer:

x = -2

-2(-2^2) + 4(-2)

-2(4) + -8

Answer:

Using the information given, we can use the point-slope form:

y - y1 = m(x - x1)

y - 7 = -1(x + 3)

y - 7 = -x - 3

  +7        +7

y = -x + 4, this is slope-intercept form

x + y = 4, this is standard form

Answer:

Step-by-step explanation:

4x + 8 = 8

4x = 0

x = 0

onw

Answer:

One solution x=0

Step-by-step explanation:

2x+8=-2x+8

Add 2x to each side

2x+2x+8=-2x+2x+8

4x+8=8

Subtract 8 from each side

4x+8-8=8-8

4x = 0

x=0

There is one solution

x=0

Answer:

[tex]0.38 \times 22[/tex]

Step-by-step explanation:

The correct expression used to find 38 percent of 22 is

[tex]0.38 \times 22[/tex]

Answer:

x=2.5

Step-by-step explanation:

Put the like terms together, like so:

10x-2x=34-14

The result is this:

8x=20

Simplify to get:

x=2.5

Answer:

x= 2 1/2 or x=2.5

Answer:

98=49bb+49tt

Explain:

so u have the same amount of both

Answer:

$21.23 - $5.25 = d

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I am not good at math, but I know because it's basically out and not with the other dots lol.