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The formula for the monthly loan payment is given as

Where

P = loan amount ( initial principal) = $15000

A= Payment amount per period = ?

r = interest rate per period = (5/12) x (1/100) =0.0041667

n = total number of payments or periods = 4 years = 4 x 12 = 48 months

Substituting all these into the above equation gives

So each month he pays $345.44 to the nearest cent

B)

The total interest for the loan is given by

Total amount paid over the total period of time - Original amount borrowed

Total amount paid over the total period of time = 345.44 x 48 months = $16581.12

The total interest of the loan hence = $16,581.12 - $15,000 = $1,581.12

The total loan interest to the nearest cent = $1,581.12

About 3 full cones of water are needed to be added to the cylinder to completely fill it.

The radius of the right circular cone is 3cm and the slant height is 5 cm.

The height of the cone can be found as,

H = √(5)²- (3)²

H = 4cm

The volume of the cone is given by,

V = πR²H/3

R is the radius and H is the height of the cone,

Putting values,

v = π x 5 x 5 x 4/3

v = 104.71 cm³

Now, the height h of cylinder is given to be 6 cm and the radius r of the cylinder is 4cm.

The volume of the cylinder is given as,

V = πr²h

V = π x 4 x 4 x 6

V = 301.59

Let us assume that we have to add n full cones of water to completely fill the cylinder, so, we can write,

nv = V

Putting values,

n104.71 = 301.59

n = 2.85

So, we have to add roughly three full cones of water to completely fill the cylinder.

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Checking the given graph, it can be seen that the range of values of x is

The range of values of x are the values of the domain of the graph function

A. -4; -4 does not satisfy the function of the graph

Given: X-3(x+2)=4X-3(x+2)=4

Find: the solution of the given equation

Explanation:

on solving equation (1) and (2) , we get

Answer:

x = -5

Step-by-step explanation:

    x - 3(x + 2)= 4

    x - 3x - 3*2 = 4     {Distributive property}

   x - 3x  - 6    = 4

Combine like terms in LHS,

         -2x - 6  = 4

Add 6 to both sides,

               -2x = 4 + 6

               -2x = 10

Divide both sides by (-2)

                   x = 10 ÷ (-2)

                   [tex]\sf \boxed{x= -5}[/tex]

The solution to the fraction two and one-third times four-fifths equals one and thirteen-fifteenths.

The correct answer option is option C

A fraction refers to a part of a whole, especially a comparatively small part. It is also the ratio of two numbers, the numerator and the denominator, usually written as one above the other and separated by a horizontal bar.

A numerator is the number above the horizontal bar while the denominator is the number below the horizontal bar in a fraction.

Two and one-third times four-fifths

= 2 1/3 × 4/5

= 7/3 × 4/5

= (7 × 4) / (3 × 5)

= 28 / 15

= 1 13/15

Therefore, the fraction two and one-third times four-fifths equals one and thirteen-fifteenths.

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The ratio for 8 squares and 10 triangles is 4:5.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them.

A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this case, the ratio for 8 squares and 10 triangles will be:

= Number of square / Number of triangle

= 8/10

= 4/5

The ratio is 4:5.

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Avenger uses 9.4 pints of white paint and blue paint to paint her bedroom walls 4/5 of this amount is white paint in the breast is blue paint how many pints of blue paint did you use to paint her bedroom walls

Let

x ----> pints of blue paint

y ----> pints of white paint

we have

x+y=9.4 -----> equation A

y=(4/5)*9.4

y=7.52

Find the value of x

x=9.4-y

x=9.4-7.52

x=1.88

therefore

answer is

Answer: 3rd one is correct

Step-by-step explanation: got it right on the test

Answer:F

Step-by-step explanation:

2/5=2 ÷ 5=0.4

The triangle congruence postulate which proves that these triangle are congruent is SAS (Side Angle Side).

According to the SAS Postulate,

Two triangles are said to be congruent if their two sides and included angles are identical to those of another triangle's two sides and included angle.

According to the figures of the triangles, we can see

AC = XZ (Side)

∠ACB = ∠XZY (Angle)

BC = YZ (Side)

Hence, ΔABC ≅ ΔXYZ by SAS postulate.

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Pool Capacity = 540 gallons

Saturday = 180 gallons

Hose water rate = 9 gallons per minute

540 = 180+9m

Where m is the number of minutes (independent variable)

Solve for m :

540-180 = 9m

360 = 9m

360/9= m

40 =m

It will take 40 minutes.

Answer:

5x-1y

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. (1.5x+3.5x)-(0.25y+0.75y)

2. 5x-y

3. The answer is 5x-y.

The equation 154 = -4(8+6r) + 24r has no solution because the variable becomes 0.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

We have to find the variable r of the equation to solve the equation.

A variable is a number represented with letters in an equation.

Therefore, let's find the variable r in the equation.

154 = -4(8+6r) + 24r

open the brackets on the right side of the equation

154 = - 32 - 24r + 24r

154 = -32 + 0

Therefore, the equation cannot be solved.

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Answer: $5 for each vinyl,$4 for each CD,and $1 for each electronic download

Step-by-step explanation:

Answer:

$5 vinyl

$4 CD

$1 every electronic download

Step-by-step explanation:

good luck

Given the following expression:

notice that the right side of the equation has a decimal number that goes up to the thousandth, therefore, the missing exponent in the equation is 3, since:

Answer:

One Solution

Step-by-step explanation:

v can only equal 6

Answer:

Your answer would be 7,600.

Step-by-step explanation:

7,605 rounded to the nearest hundred would be 7,600 because:

The 7 is the thousands.

The 6 is the hundreds.

The 0 is the tens

The 5 is the ones.

So, we need to find which number makes sense to round. Is 605 closer to 600 or 700? 600. So, we have: 7,600

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Volume of the cylinder = πr²h

see explanation below

A cylinder comprises of two circles and a curved part.

To get the volume, we would multiply the area of the circle with the height of the cylinder

The height of the cylinder is the distance between the two circular ends

Area of a cirlce is pi multiplied by radius squared

Area of circle = π×r² = πr²

where r = radius

h = height of the cylinder

Volume of the cylinder becomes = πr² × h

Volume of the cylinder = πr²h

The equation of the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5 is; (x - 1)²/25 + (y + 3)²/49 = 1

The general format for equation of an ellipse with center (h, k) and vertical major axis is;

(x - h)²/b² + (y - k)²/a² = 1

We are given the following;

center at (1, -3)

a = 7

b = 5

Thus;

Equation of ellipse with given parameters is;

(x - 1)²/5² + (y + 3)²/7² = 1

This simplifies to;

(x - 1)²/25 + (y + 3)²/49 = 1

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Step-by-step explanation:

x^y × x^3 = 1/(x^2) = x^(-2)

that means

y + 3 = -2

y = -5

the missing exponent is -5

x^(-5) × x^3 = 1/(x^2)

Answer:

Step-by-step explanation:

Hi Ashley,    this looks harder than it really is  :)

recall your powers rules

so  [tex]x^{2}[/tex]  *  [tex]x^{2}[/tex] = [tex]x^{2+2}[/tex]=[tex]x^{4}[/tex]

knowing that you can probably figure this out.  But I'll help anyway

[tex]x^{?+3}[/tex] = 1 / [tex]x^{2}[/tex]

now flip over the fraction to make this even easier

[tex]x^{?+3}[/tex] = [tex]x^{-2}[/tex]

ohhhh  I bet you can see it now, huh

we just need  3 plus something to equal -2

that's negative 5 ,  right???

[tex]x^{-5+3}[/tex] = [tex]x^{-2}[/tex]

ahh, nice  , now just break it back up

[tex]x^{-5}[/tex] * [tex]x^{3}[/tex] = 1 / [tex]x^{2}[/tex]

got it???

We can represent the horizontal shift of a quadratic equation by adding or subtracting the constant h to the function

Answer:

Step-by-step explanation:

Nick will write

Date i.e. 11/5/20XX, Description i.e. Pay James, Check Number i.e. 123, Debit i.e. $150.32, Balance i.e. $X - $150.32.

The New balance will be $X - $150.32, where $X is the previous balance.

Given, that Nick writes a check to his friend James Sloan for $150.32 on May 11.

Let suppose Nick had an 'X' amount in his bank account.

He will fill the check register like this

Date           Description       Check Number       Debit       Credit     Balance

11/5/20XX                                                                                                $X

11/5/20XX   Pay James              123                  $150.32              $X-$150.32

Hence, Nick will write

Date i.e. 11/5/20XX

Description i.e. Pay James

Check Number i.e. 123

Debit i.e. $150.32

Balance i.e. $X - $150.32

The New balance will be $X - $150.32 i.e. $150.32 subtracted from the previous balance.

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th first pic is not a function because a function dont have to values for the same x

the second pic is a function because each value of x has a different result

the third pic is a function because each value of x has a different result

so the first relation is not a function

Answer:

see explanation

Step-by-step explanation:

solving the inequality

3 ≤ 4x - 13 ≤ 7 ( add 13 to each interval )

16 ≤ 4x ≤ 20 ( divide each interval by 4 )

4 ≤ x ≤ 5

the solution lies between 4 and 5 and can be equal to 4 and 5

this is indicated on Graph A

Answer:

A=151

B= 29

Step-by-step explanation:

The coordinates of a slope triangle that could be on the line shown include

A slope triangle is a hypothetical triangle that aids in determining a line's or line segment's slope.

The line whose slope you are interested in learning is the triangle's hypotenuse (the diagonal). The slope formula's "rise" and "run" values are the two "legs" of the triangle.

With this idea, the slope triangle is drawn and the image is attached.

The coordinates should be able to form a right triangle which is used in slope calculation

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Given:

2. (2, 4), slope 2

we will write the equation of the line that passes through the point (2, 4) and has slope = 2

We will write the equation of the line using the point-slope form which is:

where (m) is the slope and the point (h, k)

so,

m = 2

h = 2

k = 4

So, the equation will be:

so, the answer will be the equation of the line is:

Answer:

Top: y = x

Bottom: y = 0.8x - 3.2

Step-by-step explanation:

I can see the question is asking to write the equation in Slope-Intercept form.

Slope-Intercept Form:

y = mx+b

M is the slope or how much the y value increases every time the x value increases by one. b is the y-intercept or when x=0.

Because these lines are parallel, we know they have the same form.

Lets look at the top line. When x increases by one, how much does y increase by?

1

What is the y value of when the line's x-value is 0?

0

Now, we have,

y = 1x + 0

Because adding 0 keeps the equation the same, we can remove it.

y = 1x

Because multiplying a term by 1 leaves it the same, we can remove one.

y = x

Now, for the bottom line.

How much does y increase by when x increases by 1? Because the slope will be a fraction and is not easy to see, I will use the slope formula.

Slope Formula:

[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

To find the slope, take any pair of points on the line and plug them in.

I'll use:

(0,-3.2)

(4,0)

Plug the y-values (the latter number, or the height of the point) into the formula. Do the same with the x-values. keep in mind it does not matter what y-value you plug in. For example, for [tex]y_2[/tex] and [tex]y_1[/tex] you can plug in -3.2 and 0 or vice versa. If you make [tex]y_2[/tex] -3.2, then make [tex]x_{2}[/tex] 0.

[tex]\frac{-3.2-0}{0-4}[/tex]

Simplify.

[tex]\frac{-3.2}{-4}[/tex]

Because a negative number multiplied or divided by another negative number is always a positive number, remove the negative signs.

[tex]\frac{3.2}{4}[/tex]

Divide.

3.2/4 = 0.8

Now we have m, the slope on the 2nd line, 0.8

y = 0.8x + b

What is the y-value of the line when the line has the x-value of 0? On the graph, it says -3.2.

y = 0.8x - 3.2

Let the three consecutive even number be,

x, x+2, x+4

Sum of the numbers is 1002.

Hence, the numbers are,

332, 332+2, 332+4

Hence, the answer is 332, 334, 336.