Use the given set to determine the solution for each equation.

13y + 8 = 125 {1, 6, 9, 15}

y = _________

Answer:

Step by step

Step-by-step explanation:

Since we have the endpoints of the diameter, the midpoint coordinates of the line segment joining them gives the centre of the circle.

That is, centre (a,b) = ( [1+(-3)]/2, [4+2]/2) = (-1,3)

Distance between the given points give the diameter and half of that is the radius length.

So, radius r = (1/2)* sqrt ( [1-(-3)]^2 + [4–2]^2) = sqrt(5)

Thus equation required is: (x-a)^2 + (y-b)^2 = r^2

So, (x+1)^2 + (y-3)^2 = 5

The equation of the circle is (x + 1)² + (y - 3)² = 5

The endpoints of the diameter are given as:

(1, 4) and (−3, 2)

Start by calculating the midpoint using:

Midpoint = 0.5 * (x₁ + x₂, y₁ + y₂)

So, we have:

Midpoint = 0.5 * (1 - 3, 4 + 2)

Evaluate

Midpoint = (-1, 3)

So, the center (a,b) of the circle is:

(a,b) = (-1,3)

Calculate the length of the diameter using:

D² =(x₁ - x₂)² + (y₁ - y₂)²

This gives

D² = (1 + 3)² + (4 - 2)²

D² = 20

Take the square roots

D = 2√5

Divide by 2 to calculate the radius

r = √5

Square both sides

r² = 5

The equation of the circle is then represented as:

(x - a)² + (y - b)² = r²

This gives

(x + 1)² + (y - 3)² = 5

Hence, the equation of the circle is (x + 1)² + (y - 3)² = 5

Read more about circle equations at:

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Answer:

Triangular prism

Step-by-step explanation:

A triangular prism has 9 edges, 6 vertices and 5 faces. I don't think there is any other shape which fits 9 edges and 6 faces.

Answer:

=(a-b)(a^2+ab+b^2)

= a^3+a^2b+ab+ab^2-ba^2-ab^2-b^3

SIMPLIFY

=a^3+ab-b^3

Answer:JKL

Step-by-step explanation:A 270 degree rotation represents three 90 degree rotations

Rotating ABC by 90 degrees three times places it in the position of JKL

So, the answer is B. JKL

Answer:

x(x+3)(x-3)

Step-by-step explanation:

Factor out common term x

=x(x^2-9)

Factor x^2-9;

(x+3)(x-3)

=x(x+3)(x-3)

Answer:

x(x + 3)(x - 3)

Step-by-step explanation:

What we're given is a difference of squares multiplied by x.  If we start by factoring x out, we can simply expand the binomial:

x³ - 9x

= x(x² - 9)

= x(x + 3)(x - 3)

Any time you see an expression in the format a² - b², that is called a difference of squares, and can always be expanded out to (a + b)(a - b).  In this case, a is x, and b is 3.

Answer:

C

Step-by-step explanation:

Volume of a cylinder is πr²h

V = π * 5² * 8

V = π * 25 * 8

V = π * 200

V = 200π

Answer:

D - 2in

Step-by-step explanation:

Answer:

yes, they will be equal

Step-by-step explanation:

I think they will be equal, because 10 dimes=$1

Answer: the answer is 11 :)

Step-by-step explanation: I hope this helped!

Answer:

11

Step-by-step explanation:

19 - 7 = 12 - 15 = -3 + 14 = 11

or, if your brain likes it better, add the positives, then add the negatives, then subtract:

19 + 14 = 33

-7 -15 = -22

33 - 22 = 11

Answer:

just use the app Math-way it had a feature where you can take a picture of it and it will answer and give an explanation for your problem

Answer:

about 14 or 14.3 to be more specific

Step-by-step explanation:

Step-by-step explanation:

here is the my estimation for this is is 14.43

Answer:

140 ft

Step-by-step explanation:

Given data

Area= 14 square feet

Height a = 1/5 ft

Base b=????

We know that the area of a triangle is given as

Area= (1/2)B*H

substitute

14= 1/2* B* 1/5

14= B/10

cross multiply

B= 140

Hence the base is 140 ft

Answer:

the answer is B

Step-by-step explanation:

Answer:

157.08

Step-by-step explanation:

Hello There!

The first step in solving this problem is to find the formula for volume of a cylinder

To find the volume of a cylinder we use this formula

[tex]V=\pi r^2h[/tex]

Where r = radius and h = hypotenuse

we are given the height and the diameter

To convert the diameter to radius we divide the diameter by 2

5/2=2.5

so the radius is 2.5

now we plug in the values

[tex]V=\pi 2.5^28\\2.5^2=6.25\\6.25\pi =19.63495408\\19.63495408*8=157.0796327[/tex]

So the volume of the cylinder is 157.0796327

now we just round to the nearest hundredth and get that the volume of the cylinder is 157.08

Answer:

Step-by-step explanation:

2x=x(1.07)^t

2=(1.07)^t

t=log2/(log 1.07) ≈10.2 4 years

so it doubles in approximately in  10.2 years

To solve the problem we must know about Compounding.

Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time.

It is given by the formula,

[tex]A = P(1+r)^t[/tex]

where A is the value after t period of time,

P is the value of the asset at the beginning, and,

r is the rate of interest.

The value of the home doubles once each decade.

Given to us

As it is given that the value of a home increases by 7% each year, therefore, the value of the home is compounding every year.

We know the formula of compounding,

[tex]A = P(1+r)^t[/tex]

Now, let's assume a house whose value is 'P' today, therefore, substitute the value of the house in the formula of compounding,

[tex]A = P(1+r)^t[/tex]

Substitute the rate at which the value is increasing,

[tex]A = P(1+0.07)^t[/tex]

We know that in a decade there are 10 years,

[tex]A = P(1.07)^{10}[/tex]

[tex]A = 1.967P\approx 2P[/tex]

As we can see that the value of the home is almost 2 times the 'P' therefore, twice the value of the home at the beginning.

Hence, the value of the home doubles once each decade.

Learn more about Compounding:

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Answer:

1296 sq inches

Step-by-step explanation:

To start, you need to get the total area of each individual roll of wrapping paper. To do this, you need to multiply the length x width, which would be 18 x 24 = 432. Then, you have three rolls so you mutiply that by three, which is 432 x 3 = 1296. You add the unit, and that leaves you with 1296 sq inches.

Answer:

f(y) = 12 + 4x

Step-by-step explanation:

Output is 12 more than 4 timea the input

The dependent variable = y

The dependent variable = x

The input is the independent variable, x

Output is the dependent variable, y

Output = 12 + (4 * input)

Hence, the function rule can be written has :

f(y) = 12 + 4x

Answer:

st 1 _ r 3

st 2 _ r 1

st 3 _ r 2

st 4 _ r 4

Answer: 20

Step-by-step explanation:

Total worth of test = 50

Percentage of test score to be gotten = 40%

Then , the total point the student need to get to get 40% will be:

= x/50 = 40%

x/50 = 40/100

x/50 = 0.4

Cross multiply

x = 50 × 0.4

x = 20

The student needs to score 20 points

Answer:

I don't know if ur asking for the answer to the equation but its called an algebraic expression, I think.

Answer:

Note that the three identities above all involve squaring and the number 1.You can see the Pythagorean-Theorom relationship clearly if you consider the unit circle, where the angle is t, the "opposite" side is sin(t) = y, the "adjacent" side is cos(t) = x, and the hypotenuse is 1.. We have additional identities related to the functional status of the trig ratios:

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

x=3 and y= -1

Step-by-step explanation:

2x-7y=13

3x+y=8

Isolate y to get your third equation

y=8-3x

Sub third equation into first

2x-7(8-3x)=13

2x-56+21x= 13

23x= 13+56

x= 69/23

x=3

Sub x into third equation to get y value

y=8-3(3)

y= -1