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poizon [28]
3 years ago
13

The diameter of Circle Q terminates on the circumference of the circle at (3,0) and (-4,0). Write the equation of the circle in

standard form. Show all of your work for full credit.
Mathematics
1 answer:
sladkih [1.3K]3 years ago
7 0

Answer: (x+0.5)^2+y^2=49

Step-by-step explanation:

Given

The diameter of circle terminates on the circumference with coordinates

(3,0) and (-4,0)

Distance between the two points is the diameter of the circle. The distance is given by distance formula i.e. d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}

Insert the values

\Rightarrow d=\sqrt{\left(-4-3\right)^2+\left(0-0\right)^2}\\\\\Rightarrow d=\sqrt{(-7)^2+0}\\\Rightarrow d=7\\\text{So, the radius is r=}3.5\ \text{units}

The center of the circle is the mid-point of the two points i.e.

\Rightarrow x=\dfrac{3-4}{2}\\\\\Rightarrow x=-\dfrac{1}{2}\\\\\Rightarrow y=\dfrac{0+0}{2}\\\\\Rightarrow y=0\\\Rightarrow (x,y)\rightarrow (-\dfrac{1}{2},0)

The equation of the circle is given by

\Rightarrow (x-(0.5))^2+(y-0)^2=7^2\\\\\Rightarrow (x+0.5)^2+y^2=49

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Please help me thank you.
Alona [7]

Answer:

\large\boxed{1.\ (4)^{-3x^2}=\left(\dfrac{1}{4}\right)^{3x^2}}

\large\boxed{2.\ ab^{-3x}=a\left(\dfrac{1}{b}\right)^{3x}=a\left[\left(\dfrac{1}{b}\right)^3\right]^x}

Step-by-step explanation:

Use:\ a^{-n}=\left(\dfrac{1}{a}\right)^n\\------------\\\\(4)^{-3x^2}=\left[(4)^{-1}\right]^{3x^2}=\left(\dfrac{1}{4}\right)^{3x^2}

Use:\ a^{-n}=\left(\dfrac{1}{a}\right)^n\ and\ (a^n)^m=a^{nm}\\--------------------\\\\ab^{-3x}=a\cdot b^{-3x}=a\left[(b)^{-1}\right]^{3x}=a\left(\dfrac{1}{b}\right)^{3x}\\\\ab^{-3x}=a\left(\dfrac{1}{b}\right)^{3x}=a\left[\left(\dfrac{1}{b}\right)^3\right]^x

8 0
3 years ago
A car that is traveling from one city to another has a velocity that is increasing at a constant slope of 3. If the car started
Masteriza [31]

Answer:

c is the answer

Step-by-step explanation:

It is the only graph  that starts at (1,0)

and if you look closely the slope is 3

3 0
3 years ago
Read 2 more answers
Alexis, Becca, and Cindy do volunteer work at Adopt-a-Pet Animal Shelter. They worked a total of 285 hours at the shelter last s
swat32

Alexis worked for 59 hours, Becca worked for 74 hours and Cindy worked for 152 hours.

Step-by-step explanation:

Given,

Total hours worked by three of them = 285 hours

Let,

x represent the hours of Alexis.

y represent the hours of Becca.

z represent the hours of Cindy.

According to given statement;

x+y+z=285    Eqn 1

Alexis worked 15 hours less than Becca.

x = y-15         Eqn 2

z = 2y+4        Eqn 3

Putting value of x and z from Eqn 2 and 3 in Eqn 1

(y-15)+y+(2y+4)=285\\y-15+y+2y+4=285\\4y-11=285\\4y=285+11\\4y=296

Dividing both sides by 4

\frac{4y}{4}=\frac{296}{4}\\y=74

Putting y=74 in Eqn 2

x=74-15\\x=59

Putting y=74 in Eqn 3

z=2(74)+4\\z=148+4\\z=152

Alexis worked for 59 hours, Becca worked for 74 hours and Cindy worked for 152 hours.

Keywords: linear equation, division

Learn more about division at:

  • brainly.com/question/9510228
  • brainly.com/question/9443926

#LearnwithBrainly

3 0
3 years ago
HELP PICTURE IS SHOWN
docker41 [41]
I think the answer is c
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3 years ago
James Works in a flower shop he will put 27 tulips in vases for a wedding he must use the same number of tulips in each vase the
Svetllana [295]
Umm..can you help  i dont get it.
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