a = -4 and b= 3 2a + 3b

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:

https://brainly.com/question/1559324

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:

y-2=3(x+7) point-slope form

Step-by-step explanation:

y-2=3(x-(-7))

y-2=3(x+7)

Answer:

the answer is B

Step-by-step explanation:

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:

st 1 _ r 3

st 2 _ r 1

st 3 _ r 2

st 4 _ r 4

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:

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:

Step-by-step explanation:

f(x) = |x - 3| + 2

g(x) = |x + 1| - 5

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:

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

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:

yes, they will be equal

Step-by-step explanation:

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

Answer:

Step-by-step explanation:

D

Answer:

The true properties of segment MN are;

1) MN is parallel to CB

2) MN = 2

Step-by-step explanation:

From the figure, we have;

The length of segment AN = 1

The length of segment NC = 2 = 2 × The length of segment AN

The length of segment AM = 1.8

The length of segment MB = 3.6 = 2 × The length of segment AM

The length of segment AC = 1 + 2 = 3

The length of segment AB = 1.8 + 3.6 = 5.4

Therefore, the length of transversal segments AC and AB are proportionally cut by the two lines, MN and CB

By the triangle proportionality theorem, two transversals are proportionally divided when they are crossed by two or more parallel lines

1) Therefore, lines MN and CB are parallel lines

Whereby we have that MN CB, we get;

ΔAMN ~ ΔABC

Therefore;

AN/AC = MN/CB

Plugging in the values, we get;

1/3 = MN/6

NM = 6 × 1/3 = 2

2) MN = 2

The length of segment CB = 6

Therefore, what must about segment MN are;

MN is parallel to CB and MN = 2.

By applying properties of similar triangles we got that MN is equal to 2 units.

Triangles whose shape are same are known as similar triangle .

In the given figure we can see that

in triangle  ABC and AMN

AN=1  

NC=2

So AC= AN+NC=1+2=3

AM=1.8

MB=3.6

So AB=AM+MB=5.4

[tex]\frac{AN}{NC}=\frac{1}{3} \\\\[/tex]

and

[tex]\frac{AM}{AB} =\frac{1.8}{5.4}=\frac{1}{3}[/tex]

And angle A is common in both triangles

Hence by SAS property  triangle  ABC and AMN are similar .

So

[tex]\frac{MN}{CB}=\frac{1}{3} \\\\\\\\\frac{MN}{6}=\frac{1}{3} \\\\\\\\MN=2[/tex]

By applying properties of similar triangles we got that MN is equal to 2 units.

To learn more about similar triangles visit:https://brainly.com/question/2644832

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: 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:

Sandra went to bed at 10:30 p.m.

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:

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: 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:

D - 2in

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

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