Show that the ratios 14/18 and 28.36 form a proportion

#2. Use substitution to solve the system of equations<br> x=3y<br> 34-5y =12<br> Solution: (

zalisa [80]

Answer:

I hope this helps:)))))

7 0

3 years ago

NO LINKS!!! Please help me with these problems

nadezda [96]

<h3>Answers:</h3>

7) Center= (-1,2) Radius= $\boldsymbol{\sqrt{8}}$ Equation: $(x+1)^2+(y-2)^2 = 8$

8) Center= (3,13) Radius= 13 Equation: $(x-3)^2+(y-13)^2 = 169$

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Explanation:

Problem 7

Let's find the distance from (-1,2) to (-3,4)

$(x_1,y_1) = (-1,2) \text{ and } (x_2, y_2) = (-3,4)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-1-(-3))^2 + (2-4)^2}\\\\d = \sqrt{(-1+3)^2 + (2-4)^2}\\\\d = \sqrt{(2)^2 + (-2)^2}\\\\d = \sqrt{4 + 4}\\\\d = \sqrt{8}\\\\$

This is the radius because it stretches from the center to a point on the circle, so $r = \sqrt{8}$

Squaring both sides will get us $r^2 = 8$

One useful template for a circle is the equation $(x-h)^2+(y-k)^2 = r^2\\\\$

(h,k) is the center

r is the radius

Let's plug in the given center (h,k) = (-1,2) and the r^2 value we found earlier.

$(x-h)^2+(y-k)^2 = r^2\\\\(x-(-1))^2+(y-2)^2 = 8\\\\(x+1)^2+(y-2)^2 = 8\\\\$

You can confirm this by using a tool like Desmos. See below.

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Problem 8

The endpoints of the diameter are (-2,1) and (8,25)

The center is the midpoint of these endpoints.

The midpoint of the x coordinates is (-2+8)/2 = 3

The midpoint of the y coordinates is (1+25)/2 = 13

The center is (h,k) = (3,13)

Now find the distance from the center to one of the points on the circle, let's say to (8,25)

$(x_1,y_1) = (3,13) \text{ and } (x_2, y_2) = (8,25)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-8)^2 + (13-25)^2}\\\\d = \sqrt{(-5)^2 + (-12)^2}\\\\d = \sqrt{25 + 144}\\\\d = \sqrt{169}\\\\d = 13\\\\$

The radius is exactly 13 units.

So,

$(x-h)^2+(y-k)^2 = r^2\\\\(x-3)^2+(y-13)^2 = 13^2\\\\(x-3)^2+(y-13)^2 = 169\\\\$

is the equation of this particular circle.

Visual confirmation is shown below.

8 0

3 years ago

Read 2 more answers

How do you do this equation: 9|5x+8|=54

Sergio [31]

Answer (2 answers):

x = -2/5, x = -14/5

Step-by-step explanation:

First step is to try and get the absolute value by itself on one side and everything else that's not inside the absolute value on the other side.

9|5x+8|=54

|5x+8| = 54/9

|5x+8| = 6

Remember how absolute values turn everything positive? For example

|-4|=4, but |4|=4 as well. So we must do the same to our problem by splitting up the absolute equation into two parts.

|5x+8| = 6 and |-(5x+8)| = 6

now solve the first equation.

(Just remove the absolute value sign and solve it normally)

5x+8 = 6

5x = -2

x = -2/5

Now solve the other equation

-(5x+8) = 6

-5x - 8 = 6

-5x = 14

x = -14/5

3 0

3 years ago

Could someone help with 14 I know it’s not a Consecutive interior but it could be A) alternate interior B) alternate exterior C)

GenaCL600 [577]

1, 4, 6, and 7 are all alternate exterior angles because they are crossed by the transversal line through the middle and they are all on the outside, or exterior, and they are alternate, or opposite. they would be congruent only if they are parallel.

-hope this helps

8 0

4 years ago

Please help me on this

Citrus2011 [14]

B is the answer i say .

5 0

3 years ago