expand and simplify (x-7)^2

Using compound interest, it is found that he must deposit $56,389.

Compound interest:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

In this problem:

Then:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]80000 = P(1 + \frac{0.0175}{12})^{12(20)}[/tex]

[tex]P = \frac{80000}{(1 + \frac{0.0175}{12})^{12(20)}}[/tex]

[tex]P = 56389[/tex]

He must deposit $56,389.

A similar problem is given at https://brainly.com/question/25263233

Answer:

$50,000 at 8%; $150,000 at 6%

Step-by-step explanation:

$50,000 x .08 = $4000

$150,000 x .06 = $9000

$4000 + $9000 = $13,000

Answer:

12

(If needed explanation ask in the comments! ty)

Hope This Helps! •v•

Answer:

its 35

Step-by-step explanation:

Answer:

a = 18

Step-by-step explanation:

Slope = (7-6)/(4-8) = -1/4

y-intercept = 7 - (-1/4)(4) = 8

Equation of the line: y = - 1/4x + 8

(Substitute y for 3.5. When y is 3.5, what is x)

3.5 = - 1/4x + 8

3.5 - 8 = - 1/4x

(-4.5) / (- 1/4) = x

x = 18

Answer:

Knowns:

initial velocity (v₀) = 0

final velocity (v₁) = 100 km/h

acceleration (a) = 9.00 m/s²

Unknowns: how long the acceleration took (Δt) = ?

Step-by-step explanation:

Use one of the kinematics equations to find what you're looking for.

This equation with a little algebra should help

v₁ = v₀ + aΔt

Answer:

4th option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

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

with (x₁, y₁ ) = (- 6, 0 ) and (x₂, y₂ ) = (0, - 9) ← 2 points on the line

m = [tex]\frac{-9-0}{0-(-6)}[/tex] = [tex]\frac{-9}{0+6}[/tex] = [tex]\frac{-9}{6}[/tex] = - [tex]\frac{3}{2}[/tex]

The line crosses the y- axis at (0, - 9 ) ⇒ c = - 9

y = - [tex]\frac{3}{2}[/tex] x - 9 ← in slope- intercept form

Multiply through by 2 to clear the fraction

2y = - 3x - 18 ( add 3x to both sides )

3x + 2y = - 18 ← in standard form

Answer:

Nonlinear association, B

Step-by-step explanation:

Answer:

strong  

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

C  - 6  <    4

    +6     +6  

C       < 10    

Open circle at 10 and shade to the left.

Now, the R² value comes out as 0.996 and it is an exponential model and it is close to 1. Hence, option A is correct.

What is an exponential model?

Quantity rises over time through a process called exponential growth. It happens when the derivative, or instantaneous rate of change, of a quantity with respect to time is proportionate to the original quantity. A quantity that is growing exponentially is referred to as an exponential function of time, meaning that the exponent is the variable that represents time (in contrast to other types of growth, such as quadratic growth).

The amount declines over time and is said to be experiencing exponential decay if the constant of proportionality is negative. It is also known as geometric growth or geometric decay when the discrete domain of definition has equal intervals since the function values form a geometric progression.

Given that a fitness trainer is tracking the combined weight loss of several new customers.

She is recording for 6 months.

Now, we have to find the best mathematical model with the corresponding R² value

Given, the combined weight loss are - 175, 120, 95, 63, 44 and 30.

The formula for coefficient of determination R² = (x-x')(y-y')/√∑(x-x')²(y-y')²

≈ 0.996

Now, the R² value comes out as 0.996 and it is an exponential model and it is close to 1. Hence, option A is correct.

To know more about exponential model:

brainly.com/question/28596571

#SPJ1

Answer:

C

Step-by-step explanation:

The vertical line test determines that more than 1 point falls on the vertical line making the graph NOT a function

Answer:

c

Step-by-step explanation:

Step-by-step explanation:

=>-10x²+3x+4

=>-10x²-5x+8x+4

=>-5x(2x+1)+4(2x+1)

=>(2x+1)(4-5x)

hope this helps you.

Answer:

3.5 hours

Step-by-step explanation:

You are trying to isolate X (get X by it self) to do that you need to divided both sides of the equation by 60 resulting in X=3.5

Divide both sides by 60 to isolate x

x=3.5 hours

Hope this helps you! :)

[tex]GraceRosalia[/tex]

Answer:

A = 1.5, B = 10, C = 0, D = 20

Step-by-step explanation:

A = 10 * 15% = 1.5

b = 10

c = 0

(10 + x) * 5% = 1.5

0.5 + 0.05x = 1.5

0.05x = 1

x = 20

(assume 'x' is added solution)

d = 20

Answer: A. 1.5 B. 10 C. 0 D. X

Angle ADB is a right angle --- Given

Angle ADB is 90 degrees --- Definition of a Right Angle

Angle CDB is 90 degrees --- Definition of Supplementary Angles

Angle ADB = Angle CDB --- Definition of Congruent Angles

Proofs can be tricky! What helps me is thinking through them step by step and how I would prove I did something. While I'm not entirely sure what options you have for this proof, I've given my best guess.

Hope this helps!! :)

Answer:

3/7 times 2/3 is 2/7

Step-by-step explanation:

I used a calculator ! Please let me know if i am incorrect.

Answer:

0.28571428571

basically 0.28

Step-by-step explanation:

gooogle calculator

Answer:

4/5

Step-by-step explanation:

Take two points on the lines. From here, we can get (5, 2) and (10, 6). Slope formula involves taking RISE/RUN, which is where you take y-y/x-x. Stay consistent on how you order the numbers. I like positive numbers, so we'll do (6-2)/(10-5). That gives us 4/5, which is your slope.

The GCF of numbers is the greatest common factor of the numbers.

The numbers are given as: 4 and 9.

Factorize both:

[tex]\mathbf{4 = 1 \times 2 \times 2}[/tex]

[tex]\mathbf{9 = 1 \times 3 \times 3}[/tex]

The common factor between  both is 1.

So, we have:

[tex]\mathbf{GCF = 1 }[/tex]

Hence, the GCF of 4 and 9 is 1

Read more about GCFs at:

https://brainly.com/question/20061154

Answer:

7) 3x=45( corresponding angles formed on parallel lines)

x=45/3

x=15

8)120=2x+10(corresponding angles formed on parallel lines)

or,120-10=2x

or,110/2=x

or,x=55

Answer:

74/5

Step-by-step explanation:

15x5 =75 5ths. 1/5 + 74/5 = 75/5

Answer: The slope of the line is 6.

You can use the distance formula to find the slope (Y2-Y1/X2-X1). You can plug in any two points seen on the graph into the formula. I will use (0,-1) and (1,5). When I plug in the values, 5-(-1)/1-0=6/1=6. So the slope of the line is 6.

:)

Answer:

x = 42 degrees

y = 37 degrees

Step-by-step explanation:

Those are right angle triangles. So you know the right angles are 90 degrees, and each triangle gives you the measurement of another angle.

So, take the triangle in the top left (x):

180 - 90 - 48 = x

Same with the other triangle (y)

180 - 90 - 53 = y

Answer:

The answer is 6

Step-by-step explanation:

Why is it 6? because surface means like the total faces it has.

A rectangle has 4 coordinates.

The coordinate of the last vertex is (-2,-8)

The points are given as:

[tex]\mathbf{A = (-7,-4)}[/tex]

[tex]\mathbf{B = (1,6)}[/tex]

[tex]\mathbf{C = (6,2)}[/tex]

Calculate distance AB

[tex]\mathbf{AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]

So, we have:

[tex]\mathbf{AB = \sqrt{(-7 - 1)^2 + (-4 - 6)^2}}[/tex]

Calculate distance CD

[tex]\mathbf{CD = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]

So, we have:

[tex]\mathbf{CD = \sqrt{(x - 6)^2 + (y - 2 )^2}}[/tex]

Equate AB and CD

[tex]\mathbf{ \sqrt{(x - 6)^2 + (y - 2)^2} = \sqrt{(-7 - 1)^2 + (-4 - 6)^2}}\\[/tex]

Cancel out the squares

[tex]\mathbf{ (x - 6)^2 + (y - 2)^2 = (-7 - 1)^2 + (-4 - 6)^2}[/tex]

By comparison

[tex]\mathbf{x -6 = -7-1}[/tex]

[tex]\mathbf{y-2 = -4-6}[/tex]

So, we have:

[tex]\mathbf{ x = 6-7-1 }[/tex]

[tex]\mathbf{ x = -2}[/tex]

[tex]\mathbf{y = 2-4-6 }[/tex]

[tex]\mathbf{y = -8}[/tex]

Hence, the coordinate of the last vertex is (-2,-8)

Read more about coordinates at:

https://brainly.com/question/2254540