Solve each equation by square roots

Find three consecutive even integers such that the sum of twice the smallest number and three times the largest is 42.

Otrada [13]

The difference between two consecutive integers is 2.
Let n be the smallest of the three even integers.
Then the next larger even integer is n + 2.
The largest even integer is n + 4.
Now we follow what the problem tells us.

Twice the smallest is 2n
3 times the larges is 3(n + 4)

2n + 3(n + 4) = 42

2n + 3n + 12 = 42

5n + 12 = 42

5n = 30

n = 6

n + 2 = 8

n + 4 = 10

The integers are 6, 8, 10

7 0

3 years ago

1. Charlene wants to center a rectangular pool in her backyard so that the edges of the pool are an equal distance from the edge

Inga [223]

First, we have to calculate the length of the sides of the pool, we are told that the scale factor of the backyard to the pool size equals 1/2, then we can find the length of the sides of the pool by multiplying the lengths of the sides of the backyard by 1/2, like this:

length of the pool = length of the yard * 1/2

width of the pool = width of the yard * 1/2

By replacing the 60 m for the length of the yard and 50 m for the width, we get:

length of the pool = 60 * 1/2 = 30

width of the pool = 50 * 1/2 = 25

Let's call x1 to the distance from the base of the pool to the bottom side of the yard and x2 to the distance from the top side of the pool to the top side of the yard, then we can formulate the following equation:

width of the yard = width of the pool + x1 + x2

Since we want the edges to be at an equal distance, x1 and x2 are the same, then we can rewrite them as x:

width of the yard = width of the pool + x + x

width of the yard = width of the pool + 2x

Replacing the known values:

60 = 30 + 2x

From this equation, we can solve for x to get:

60 - 30 = 30 - 30 + 2x

30 = 2x

30/2 = 2x/2

15 = x

x = 15

Now, let's call y1 to the distance from the right side of the corresponding side of the yard and y2 to the distance from the left side of the pool to the left side of the yard, with this, we can formulate the following equation:

length of the yard = length of the pool + y1 + y2

Since we want the edges to be at an equal distance, y1 and y2 are the same, then we can rewrite them as y:

length of the yard = length of the pool + y + y

length of the yard = length of the pool + 2y

Replacing the known values:

50 = 25 + 2y

50 - 25 = 25 - 25 + 2y

25 = 2y

25/2 = 2y/2

12.5 = y

y = 12.5

Now, we know that the pool must be at a distance of 15 m from the horizontal sides of the pool to the horizontal sides of the yard and that it must be at a distance of 12.5 m from the vertical sides of the pool to the vertical sides of the yards.

Here is a figure that depicts the results:

5 0

1 year ago

the circumference, or perimeter, of a circle can be found by multiplying its diameter by 3.14. what is the circumference of a ci

Dahasolnce [82]

Answer:

4.71238898

Step-by-step explanation:

The formula used to calculate circle circumference is:

C = π · ø

Enter the diameter of a circle. The diameter of a circle is the length of a straight line drawn between two points on a circle where the line also passes through the centre of a circle, or any two points on the circle as long as they are exactly 180 degrees apart

This is the total length of the edge around the circle with the specified diameter, if it was straightened out.

8 0

3 years ago

natka813 [3]

The value of x from the given circle is 12

<h3>Circle theorem</h3>

Angle at the vertex of the circle is half the angle at its intercepted arc.

From the given circle;

The measure of <DEF = 80/2 = 4x -8

Equate both angles

4x - 8 = 80/2

Add 8 to both sides

4x - 8 + 8 = 40 + 8

4x = 48

x =12

Hence the value of x from the given circle is 12

Learn more on circle theorem here: brainly.com/question/26594685

#SPJ1

7 0

2 years ago

What are the zeros of 3x²(x+π)³(x-4)²

Aneli [31]

Hi again!

The zeros are the values of x. This is where the graph intersects the x - axis. In order to find the zeros, replace y with 0 and solve for x.

The answer is x = 0, -π, 4

I am not sure what grade are you or the level, but for me, they sometimes asked me to find their multiplicities as well

The multiplicity of a root is the number of times the root appears.

So, the answer are
x = 0 and the multiplicity of 2
x = -π and the multiplicity of 3
x = 4 and the multiplicity of 2

Good luck with your studies!

5 0

3 years ago