1. Kathy is building a bed for her dollhouse. She used her real bed as a guide for how to

A circle is centered at the point (-7, -1) and passes through the point (8, 7).

Lisa [10]

Answer:

Part 1) The radius of the circle is 17 units

Part 2) The point (-15,14) and (-15,-16) lies on this circle

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance from a circle's center to any point on the circle is called the radius of the circle

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the distance (radius) between the points (-7,-1) and (8,7)

substitute in the formula

$r=\sqrt{(7+1)^{2}+(8+7)^{2}}$

$r=\sqrt{(8)^{2}+(15)^{2}}$

$r=\sqrt{(289}\ units$

$r=17\ units$

step 2

Find the equation of the circle in center radius form

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

where

(h,k) is the center of the circle

r is the radius of the circle

we have

$(h,k)=(-7,-1)\\r=17\ units$

substitute

$(x+7)^2+(y+1)^2=17^2$

$(x+7)^2+(y+1)^2=289$

Remember that

If the point (-15,y) lie on the circle, then the ordered pair must satisfy the equation of the circle

substitute the value of x=-15 in the equation

$(-15+7)^2+(y+1)^2=289$

solve for y

$(-8)^2+(y+1)^2=289$

$64+(y+1)^2=289$

$(y+1)^2=225$

take square root both sides

$y+1=(+/-)15\\y=-1(+/-)15$

$y=-1+15=14\\y=-1-15=-16$

therefore

The point (-15,14) and (-15,-16) lies on this circle

see the attached figure to better understand the problem

8 0

4 years ago

GEOMETRY!!! Will give brainliest

Vika [28.1K]

Answer:

TIME REMAINING

54:28

The battle that resulted in both a Confederate victory and the death of General “Stonewall” Jackson was

Step-by-step explanation:

TIME REMAINING

54:28

The battle that resulted in both a Confederate victory and the death of General “Stonewall” Jackson was

8 0

3 years ago

A basketball player made 17 out of 20 free throws at a practice. What percent of the free throws did the player miss?

s2008m [1.1K]

Answer:

he missed 97%

Step-by-step explanation:

subtract 17-20 to get 3 and subtract 3 from 100% to get 97%, then multiply 97 by 3

3 0

3 years ago

How many distinct permutations can be formed using the letters of the word prepared

Troyanec [42]

Answer:

5,040

Step-by-step explanation:

Hmmm...this one is a bit tricky. First, prepared contains 8 letters. To find the number of ways this can be rearranged use the fundamental counting principle.

First letter - 8 choices

Second letter - 7 choices

Third letter - 6 choices

So the number of outcomes would be $8! = (8)(7)(6)(5)(4)(3)(2)(1)=40,320$

But wait, there's more. Prepared has some duplicate letters, the P, R, and E. That means if the letters were written ppeerrad it would be indistinguishable if it was the first or second P written first. So that means the letter P generates 2 outcomes that appear the same

$\frac{40,320}{2}=20,160$

Same for the letter R

$\frac{20,160}{2}=10,080$

And same for the letter E

$\frac{10,080}{2}=5,040$

5 0

3 years ago

Ralphie has a large tropical fish collection. He gives 2/3 of his fish to a local high school. Then he gives 2/5 of the remainin

Lubov Fominskaja [6]

Let initially number of fishes =x

He gives 2/3 of his fish to a local high school, that is he gives 2x/3 fish .

So number of fishes left = x -(2x/3) = x/3 . And he gives 2/5 of x/3 to an elementary school , that is , he gives 2x/15 fishes to the elementary school. And finally the number of fishes left =30 , that is

$x-(\frac{2x}{3}+\frac{2x}{15})=30$

$x-\frac{12x}{15}=30$

$\frac{3x}{15}=30$

$x = 150$

So initially he have 150 fishes .

7 0

3 years ago