What is the center of the circle?
A.(-1,-6)
B.(3,−1)
C.(−1,3)
D.(−6,1)

Answer:

10/4=20

Step-by-step explanation:

x=50

Step-by-step explanation:

10/4=x/20

this will give you x=50

9514 1404 393

Answer:

  (x, y) = (31/37, 2 36/37) ≈ (0.8378, 2.9730)

Step-by-step explanation:

There are several ways we can go at this.

Method 1

Find the point of intersection with the perpendicular line through (-5, 2).

The perpendicular line will have the x- and y-coefficients swapped, one of them negated, and a new constant consistent with the given point.

  x -6y = (-5) -6(2) = -17

So, we're looking for the solution of the system of equations ...

Using Cramer's Rule, we can find the solution to be ...

  x = ((1)(-17) -(-6)(8))/((1)(1) -(-6)(6)) = 31/37 ≈ 0.837_837*

  y = ((8)(1)-(-17)(6))/37 = 110/37 ≈ 2.972_972

The closest point is (x, y) = (31/37, 2 36/37).

__

Method 2

We can write the given line in parametric form, then find the point on it such that the direction along the line is perpendicular to the direction to the given point.

Solving the given equation for y, we have ...

  y = 8 -6x

So, the parametric form of the given line can be written as ...

  (x, y) = (0, 8) +t(1, -6) . . . . for some parameter t

The direction to the given point from (x, y) is then ...

  (-5, 2) -(x, y) = (-5, 2) -((0, 8) +t(1, -6)) = (-5-0-t, 2-8+6t) = (-t-5, 6t-6)

The dot-product of this direction vector with the direction vector of the original line will be zero for the value of the parameter at the closest point.

  (1, -6) · (-t-5, 6t-6) = 0 = (1)(-t -5) +(-6)(6t -6)

  0 = -t -5 -36t +36 = -37t +31

  31/37 = t

So, filling this value into the parametric equation gives the closest point as ...

  (0, 8) +(31/37)(1, -6) = (31/37, 2 36/37) = (x, y)

__

Method 3

Find the point of tangency of the given line with a circle centered at (-5, 2).

The equation of a circle centered at (-5, 2) is ...

  (x +5)^2 +(y -2)^2 = r^2

The given line will meet the circle at a point that satisfies this equation and the equation of the circle. Writing an expression for y using the given line, we can substitute into the circle equation to get ...

  (x +5)^ +((8 -6x) -2)^2 = r^2

  x^2 +10x +25 +36 -72x +36x^2 = r^2

  37x^2 -62x + (some constant) = 0

This will have one solution when the constant is chosen to make the left-side expression a perfect square. That perfect square will be ...

  37(x -31/37)^2 = 0

which is to say the tangent point of the line and the circle will have x-coordinate x = 31/37. The y-coordinate is 8 -6(31/37) = 2 36/37.

The closest point is (x, y) = (31/37, 2 36/37).

_____

* repeated decimal fractions are signified in typeset text with an overbar over the repeating digits. In plain text, we sometimes use a preceding underscore to identify the repeating digits.

Answer:

336 in²

Step-by-step explanation:

Surface area of triangular prism = bh + (s1 + s2 + s3)H

Where,

b = 6 in

h = 8 in

s1 = 10 in

s2 = 6 in

s3 = 8 in

H = 12 in

Surface area of triangular prism = 6*8 + (10 + 6 + 8)12

= 48 + (24)12

= 336 in²

Answer:

You can easily rule out A and D, and the mean is 39 which essentially makes B irrelevant. The answer is C.

Answer:

[tex]List = \{GBB; BGB; BBG; GGB; BGG; GBG; GGG\}[/tex]

Step-by-step explanation:

Given

[tex]Children = 3[/tex]

Required

List all cases of having at least 1 girl

We have:

[tex]B = Boy[/tex]

[tex]G = Girl[/tex]

For 1 girl, we have:

GBB; BGB; BBG

For 2 girls, we have:

GGB; BGG; GBG

For 3 girls, we have:

GGG

Hence, the list is:

[tex]List = \{GBB; BGB; BBG; GGB; BGG; GBG; GGG\}[/tex]

Answer:

Step-by-step explanation:

(x + 2)^2 + (y -1 )^2 = 3^2

(x + 2)^2 + (y -1)^2 = 9

I have used Desmos to draw this for you. Notice that the center is not (2, -1) but is at -2,1 just as the question requested. The signs are always reversed when the center of a circle must be obtained by squaring the numbers in parenthesis.

Further two points are shown. The one you should pay attention to is (-2,4) which is 3 units away from the center. The other point is also 3 units away, but you have to use the distance formula which you may not be familiar with. If you measure it with a ruler, you will find it is the same distance away from the center as (-2,4) is Since they are equal, they both must represent the length of the radius.

Answer:

It would be B. 815.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

On edge

Answer:

I've never had to deal with this before but I would say C

Answer:

The best option is C ( y=(1/4) x +3)

Answer:it’s C

Step-by-step explanation:

That’s the answer on edge

Answer:

4/8

Step-by-step explanation:

7/8 - 3/8 = 4/8

Answer:

the structure or conditions of economic life in a country, area, or period also : an economic system.

Step-by-step explanation:

I'm just gonna so you how I got it

Step-by-step explanation:

6x - 3y - 5 = 0 has slope 6/3 = 2. A perpendicular line will have slope -1/2 (since slopes of two perpendicular lines must have a product of -1), so its general form will be 3x + 6y - a = 0.

Now to find a. We know a point on the line, (4,10), and so we plug those coordinates in:

3*4 + 6*10 - a = 0

12 + 60 - a = 0

72 = a

3x + 6y - 72 = 0.

We can simplify this by dividing all numbers by 3, getting:

x + 2y - 24 = 0

Answer:

1) c = 25 cm

2) a = 11.532562594 cm

I hope it's helps you

Step-by-step explanation:

Using Pythagoras Theorem:

[tex]c = \sqrt{{a}^{2} + {b}^{2} }[/tex]

7.

[tex]c = \sqrt{ {a}^{2} + {b}^{2} } \\ c = \sqrt{ {24}^{2} + {7}^{2} } \\ c = \sqrt{625} \\ c = 25[/tex]

8.

[tex]a = \sqrt{ {c}^{2} - {b}^{2} } \\ a = \sqrt{ {13}^{2} - {6}^{2} } \\ a = \sqrt{133} \\ a = 11.5[/tex]

(cor. to the nearest tenth)

Answer:

105

Step-by-step explanation:

< 7 is also 105- they are alternate exterior angles

Answer:

There are 7 total family members.

Step-by-step explanation:

The mother and father make 2, the 4 daughters make 6, and they have one brother among them, making 7.

Answer:

hi

Step-by-step explanation:

hiiii

Answer:

12-c

Step-by-step explanation:

This is quite simple

We know grandma has made 96 cookies and IF all children 8 receive equal cookies

They would have 12 cookies each

Cindy got c less cookies

so we can say

12-c is what Cindy got

I guess grandma got hungry

Answer:

Step-by-step explanation:

98 = 8 = 12

cindy cookies = 12-c

Answer:

Step-by-step explanation:

The Letter pi (π) = 3.14

The radius (r) = the diameter / 2

The diameter = 8

the radius (r)= d/2 = 8/2 = 4

The Area = 3.14 * 4*4

But they tell you to use 3 and not 3.14.

So the area = 3 * 4 * 4

The area = 48

By the way, if you are interested, the Bible uses 3 for π and not 3.14

Step-by-step explanation:

a. The random variable is a binomial distribution.

b. the sample space, X = {0, 1, 2, 3, 4, 5}

the pmf

we solve for this using

nCx * P^x * (1-p)^n-x

n = 5

p = 0.3

for x = 0

5C0 * 0.3⁰(1-0.3)^5-0

= 1 * 1* 0.7⁵

= 0.16807

for x = 1

5C1*0.3¹(1-0.3)^5-1

= 5*0.3(0.7)⁴

= 5x0.3x0.2401

= 0.36015

for x = 2

5C2 * 0.3² * (1-0.3) ^5-2

= 0.30870

for x = 3

5C3 * 0.3³ * (1-0.3) ^ 5-3

= 10 * 0.027 * 0.7²

= 0.1323

for x = 4

5C4 * 0.3⁴ (1-0.3) ^ 5-4

= 5 * 0.0081 * 0.7

= 0.02835

for x = 5

5C5 *0.3⁵ (1- 0.3) ^5-5

= 1*0.00243*0,7⁰

= 0.00243

c. E[X] = N*p = 5*0.3 = 1.5

var[X] = np(1-p) = 5*0.3*0.7 = 1.05

d. 20/9 = 2.222

so we have that if x is greater than or equal to 3, cost will exceed 20

p(x=3) + p(x=4) + p(x=5)

= 0.1323 + 0.02835 + 0.00243

probability = 0.16308

E[C] = 1.5 * 9 = 13.5

VAR[C] = 1.05 * 9 = 9.45

Step-by-step explanation:

F) Nine hundred thirty two and 76 hundredth

hope it is helpful to you

Answer:

can we go with D. 54 ?

the height and length is 9 and 6

9x6= 54

Answer:

B . 27 square units

Step-by-step explanation:

Area of triangle is 1/2 ×b×h

base is MN = 6 units

hight is 9 unis

so 1/2 ×6×9 = 3×9 =27 square Units

Answer:

The chocolate covered pretzels in Sophie's bag weighed [tex]\frac{2}{3} = 0.6667[/tex] kilograms.

Step-by-step explanation:

Sophie filled a bag with 2 2/3 kilograms of candy.

This means that the total weight is of:

[tex]2\frac{2}{3} = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3}[/tex]

The total weight is of 8/3 kilograms.

1/4 of the weight of the candy was from chocolate covered pretzels. How much did the chocolate covered pretzels in Sophie's bag weigh?

1/4 of 8/3. So

[tex]\frac{1}{4} \times \frac{8}{3} = \frac{1*8}{4*3} = \frac{2}{3} = 0.6667[/tex]

The chocolate covered pretzels in Sophie's bag weighed [tex]\frac{2}{3} = 0.6667[/tex] kilograms.

Assuming that the ".." at the end of the number represents it being continuous, then it would be irrational.

0.121121112.. is an irrational number but not rational.

A number system is defined as a system of writing to express numbers.

0.121121112... is rational or irrational is to consider its decimal representation and whether it is a repeating or terminating decimal.

We can see that 0.121121112... is not a terminating decimal because it goes on forever.

Additionally, it is not a repeating decimal because there is no fixed pattern of digits that repeats continuously.

Therefore, we can conclude that 0.121121112... is an irrational number.

To learn more on Number system click:

https://brainly.com/question/22046046

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Answer:

48 and prob in 1984

Step-by-step explanation:

Answer:

-1/3

Step-by-step explanation:

Use this equation : slope= y2-y1/x2-x1

Answer:

A and D are the true number sentences

Answer:

2/3 serving

Step-by-step explanation:

(1/2)/(3/4) = 1/2 x 4/3 = 4/6 = 2/3 serving