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3 years ago

Hich is an equation of a circle with center (-5, -7) that passes through the point (0, 0)?

1 answer:

3 0

$(a;\ b)-the\ coordinates\ of\ center\\r-the\ radius\\\\The\ equation\ of\ the\ circle:(x-a)^2+(y-b)^2=r^2\\\\The\ radius\ is\ equal\ the\ distance\ between\ points\ (-5;-7)\ and\ (0;\ 0)\\\\The\ distance\ between\ A(x_A;\ y_A)\ and\ B(x_B;\ y_B):\\d=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\\\subtitute:\\r=\sqrt{(0-(-5))^2+(0-(-7))^2}=\sqrt{5^2+7^2}=\sqrt{25+49}=\sqrt{74}\\\\\boxed{(x-(-5))^2+(y-(-7))^2=(\sqrt{74})^2\to(x+5)^2+(y+7)^2=74}$

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Let f(x) = 3x + 2 and g(x) = 4–5x. Find f(x) + g(x)

Vadim26 [7]

Answer:

-2x + 6

Step-by-step explanation:

Step 1: Define

f(x) = 3x + 2

g(x) = 4 - 5x

Step 2: Find f(x) + g(x)

3x + 2 + 4 - 5x

-2x + 6

3 0

3 years ago

Read 2 more answers

Need more help please!!

IrinaK [193]

46: 24a+40

First we are going to take a look at a) 8(3a+5)

a) We then simplify it by multiplying the numbers inside the parenthesis by 8.

a) 24a+40

Now we ask ourselves, is this equivalent to 24a+40? YES!

So your answer for #46 is a) 8(3a+5)

7 0

3 years ago

Can you help meee get this ?

nikdorinn [45]

Answer: y=4/5x-2 or y=4/5x+(-2)

Step-by-step explanation:

The formula for slope-intercept form is y=mx+b.

To find the slope, we can use the formula $m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$ and plugging in the points given.

$m=\frac{6-2}{10-5} =\frac{4}{5}$

We know our slope is 4/5. We can plug this into our slope-intercept form and then plug in a point to find b, y-intercept.

$y=\frac{4}{5} x+b$

$2=\frac{4}{5}(5)+b$

$2=4+b$

$b=-2$

We know the y-intercept is -2.

THe final equation is y=4/5x-2 or y=4/5x+(-2).

4 0

3 years ago

The marketing club at school is opening a student store. They randomly survey 50 students about how much money they spend on lun

Luden [163]

Answer:

The expected value for a student to spend on lunch each day = $5.18

Step-by-step explanation:

Given the data:

Number of students______$ spent

2 students______________$10

1 student________________$8

12 students______________$6

23 students______________$5

8 students_______________$4

4 students_______________$3

Sample size, n = 50.

Let's first find the value on each amount spent with the formula:

$\frac{num. of students}{sample size} * dollar spent$

Therefore,

For $10:

$\frac{2}{50} * 10 = 0.4$

For $8:

$\frac{1}{50} * 8 = 0.16$ l

For $6:

$\frac{12}{50} * 6 = 1.44$

For $5:

$\frac{23}{50} * 5 = 2.3$

For $4:

$\frac{8}{50} * 4 = 0.64$

For $3:

$\frac{4}{50} * 3 = 0.24$

To find the expected value a student spends on lunch each day, let's add all the values together.

Expected value =

$0.4 + $0.16 + 1.44 +$2.3 + $0.64 + $0.24

= $5.18

Therefore, the expected value for a student to spend on lunch each day is $5.18

7 0

2 years ago

In the diagram below,AB is the diameter of the circle with centre P.Point C lies on the y-axis.Given the coordinates of A and B

Step2247 [10]

Answer:

The coordinates of P are (-2,0)

The radius of the circle is 5.

Step-by-step explanation:

Analytic geometry

The diagram shows a circle with center P, and two points A(-6,3) and B(2,-3) that form the diameter of the circle.

The center of the circle lies at the midpoint of A and B. The midpoint (xm,ym) can be calculated by:

$\displaystyle x_m=\frac{x_1+x_2}{2}$

$\displaystyle y_m=\frac{y_1+y_2}{2}$

Substituting x1=-6, x2=2, y1=3, y2=-3:

$\displaystyle x_m=\frac{-6+2}{2}=\frac{-4}{2}=-2$

$\displaystyle y_m=\frac{3-3}{2}=0$

Thus, the coordinates of P are (-2,0)

b) The radius of the circle is the distance from the center to any point in its circumference. We can use the distance from P to A or B indistinctly.

Given two points A(x1,y1) and P(x2,y2), the distance between them is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substituting x1=-6, x2=-2, y1=3, y2=0:

$r=\sqrt{(-2+6)^2+(0-3)^2}$

$r=\sqrt{4^2+(-3)^2}$

$r=\sqrt{16+9}=\sqrt{25}=5$

The radius of the circle is 5.

4 0

3 years ago