5m + 9n if m = -7 and n = 4

Answer:

center = [tex](-4,8)[/tex]

Radius = 7 units

Step-by-step explanation:

Given: Equation of circle is [tex]x^2+y^2+8x-16y+31=0[/tex]

To find: Radius and center of the circle

Solution:

Equation of circle is [tex](x-a)^2+(y-b)^2=r^2[/tex]

Here, [tex](a,b)[/tex] is the center and r is the radius.

[tex]x^2+y^2+8x-16y+31=0\\\left [ x^2+2(4)x+4^2 \right ]+\left [ y^2-2(8)y+8^2 \right ]+31=4^2+8^2[/tex]

Use formula [tex](u+v)^2=u^2+v^2+2uv[/tex]

[tex](x+4)^2+(y-8)^2=16+64-31\\(x+4)^2+(y-8)^2=49=7^2[/tex]

On comparing this equation with equation of circle,

center = [tex](-4,8)[/tex]

Radius = 7 units

Answer:

center: (4,-4)

Radius: 9

Step-by-step explanation:

KHAN ACADEMY

Answer:

Students to attend camp = 56 x 44/100 = 24.64

Students to attend camp = 25

Step-by-step explanation:

Answer:

≈25 students

Step-by-step explanation:

Find out 44% of 56:

(44*56)÷100=

2464÷100=

24.64

So about 25 students out of 56 said yes, they were going to attend summer camp.

Answer:

8

Step-by-step explanation:

f(x)=5x^2−3x+8

Let x=0

f(0) = 5(0) -3(0) +8

     = 8

Answer:

Step-by-step explanation:

the distributive properrty of 6 + 30

6(1 + 5)

Answer:

[tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

Let A be the event of getting an odd number.

P(A) be the probability of getting an odd number.

Total odd numbers here are 6 i.e. [tex]\{1,3,5,7,9,11\}[/tex]

Here, total numbers in the game are 12 i.e [tex]\{1,2,3,....,12\}[/tex].

Formula for probability of an event E can be observed as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

[tex]P(A) = \dfrac{6}{12}\\\Rightarrow \dfrac{1}{2}[/tex]

Let B be the event of getting 11.

P(B) be the probability of getting 11.

Total number of possible cases is 1.

[tex]P(B) = \dfrac{1}{12}[/tex]

[tex]P(A \cap B)[/tex] is the probability that we get 11 and an odd number.

Possible number of cases = 1

[tex]P(A\cap B) = \dfrac{1}{12}[/tex]

P(B/A) is the probability that we get an 11 given that it is an odd number.

[tex]P(B/A) = \dfrac{P(A \cap B)}{P(A)}\\\Rightarrow \dfrac{\dfrac{1}{12}}{\dfrac{1}{2}}\\\Rightarrow \dfrac{1}{6}[/tex]

Hence, P(B/A) = [tex]\dfrac{1}{6}[/tex]

Answer:

The probability in fraction is [tex]\frac{1}{12}[/tex].

Step-by-step explanation:

Total number of outcomes is = 12

Now we have to find the probability that spun number is 11.

That means favorable outcome is 1.

In this case, the probability can be determined by dividing the number of favorable outcomes by the total outcome. Accordingly, the total outcomes are 12 and favorable outcome is 1.  

[tex]\text{P(The spun number is 11)}= \frac{\text{Favorable outcomes}}{\text{total outcomes}} \\\text{P(The spun number is 11)}= \frac{1}{12} \ (in \ fraction)\\\text{P(The spun number is 11)} = 0.083 \ (in \ decimal)[/tex]

Answer:

I think the answer is 3 for 1 length side. And in you need 12 for both length sides. So the total is 36 and one side is 12. Since it's a rectangle,you now know two side lengths since they are the same,just opposite from each other. So 12 + 12 = 24. You do 36 – 24 because you need to get the total number for length which is 12. 12 divided by 2 is 6 which is one length side. You can check by doing 6 + 6 + 12 + 12 and you get 36.

Hope this helped!

Can I get brainliest?

Answer:

2450

Step-by-step explanation:

First you will divide;

200÷4=50

Then you multiply;

50×9=450

Last you add;

2000+450=2450

Hope this helps :D

Answer:

4949 is your answer

Step-by-step explanation:

Answer:

1/10

Step-by-step explanation:

10 balls in the bag, there is one yellow

Answer:

answer 1/10

Step-by-step explanation:

Answer:

[tex] x^2 + \frac{1}{49} =1 [/tex]

And solving for x we got:

[tex] x^2 = 1- \frac{1}{49}[/tex]

[tex] x^2 = \frac{48}{49}[/tex]

And taking square root we got:

[tex] x = \sqrt{\frac{48}{49}}= \frac{\sqrt{48}}{7} = \frac{4\sqrt{3}}{7}[/tex]

Step-by-step explanation:

For this case we have the following point given [tex] P(x , -1/7)[/tex]

And we want to find the value of x, since P lies on the unitray circle if we find the distance from P to the center of the unitary circle (0,0) we need to get 1. Using the definition of Euclidean distance that means:

[tex] d = \sqrt{(x -0)^2 +(-1/7 -0)^2}=1[/tex]

And if we square both sides of the last equation we got:

[tex] x^2 + \frac{1}{49} =1 [/tex]

And solving for x we got:

[tex] x^2 = 1- \frac{1}{49}[/tex]

[tex] x^2 = \frac{48}{49}[/tex]

And taking square root we got:

[tex] x = \sqrt{\frac{48}{49}}= \frac{\sqrt{48}}{7} = \frac{4\sqrt{3}}{7}[/tex]

There are 118 adult tickets sold

This is because 354/3 =118

and 118+118=236

236 are the child tickets

therefore 118 are the adult tickets.

Hope this helped!

The total number of adult ticket sold is 118 tickets.

Let's write "x" to represent how many adult tickets were sold.

The information provided indicates that there were twice as many student tickets sold as adult tickets. The quantity of student tickets sold can therefore be stated as 2x.

There were 354 total tickets sold, which includes both student and adult tickets.

We may construct an equation based on the total number of tickets to resolve this issue:

x + 2x = 354

Combining comparable variables

3x = 354

x = 354 / 3

x = 118

118 adult tickets were consequently sold.

Learn more on linear equation here: https://brainly.com/question/12788590

#SPJ2

Answer:

[tex]-\frac{15}{4}[/tex]

Step-by-step explanation:

To find the slope or the gradient of a line you have to utilise the formula

[tex]\frac{y2-y1}{x2-x1}[/tex]

Y₂ = -7

Y₁ = 8

X₂ = 7

X₁ = 3

So,

[tex]\frac{-7-8}{7-3}[/tex]

→ Simplify

[tex]-\frac{15}{4}[/tex]

By using the given points, we will see that the slope is -15/4.

If we know that a given line passes through two known points (x₁, y₁) and (x₂, y₂), then the slope can be written as:

[tex]s = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here the line passes through the points (3, 8) and (7, -7).

Using the above formula, we can see that the slope is:

[tex]s = \frac{-7 - 8}{7 - 3} = \frac{-15}{4}[/tex]

If you want to learn more about linear equations, you can read:

https://brainly.com/question/4074386

Answer:

r = 26

Step-by-step explanation:

C = 2 π r

163.28 = 2 (3.14) (r)

163.28 / 2 / 3.14

26 = r

Answer:

26 yards

Step-by-step explanation:

2πr=163.28

2×3.14×r=163.28

r=163.28÷6.28=26 yards

Answer:

y/x = 1 got it right on edg

Step-by-step explanation:

Answer:

y/x = 1  on E2020

Step-by-step explanation:

Have a Great Day :)

Answer:

y=x-4

Step-by-step explanation:

The general scaffold for the slope intercept form is y=mx+b, where m is the slope and b is the y intercept. You can rearrange the equation that you are given like this:

2x-2y=8

-2y=-2x+8

y=x-4

Hope this helps!

Answer:

Rearrange the equation so that it is written in slope intercept form:

y=mx+b.

2x+2y=8.

2y=−2x+8.

y=−x+4.

Answer:

The width of the patio is 11.29 feet while the length of the patio is 13.29 feet

Step-by-step explanation:

Mathematically, the area of the patio can be calculated by multiplying the length by the breadth of the patio

Thus we have ;

(x + 7)(x + 9) = 150

x^2 + 7x + 9x + 63 = 150

x^2 + 16x + 63 = 150

x^2 + 16x + 63 -150 = 0

x^2 + 16x -87 = 0

we can use the quadratic formula to solve this completely

x = {-b ± √(b^2 - 4ac)}/2a

where a = 1, b = 16 and c = -87

Plugging the values we have

x = {-16 ± √(16^2 - 4(1)(-87)}/2

x = {-16 ± √(256+ 348)}/2

x = {-16 ± √(604}/2

x = (-16 + 24.58)/2 or (-16-24.58)/2

x = 4.29 or -20.29

Choosing x = -20.29 will make our dimensions negative, so we ignore it and make do with the positive value only

Thus our dimensions are 4.29 + 7 and 4.29 + 9

This is equal to 11.29 feet and 13.29 feet respectively

Answer:

5 minutes

Step-by-step explanation:

Do a proportion

440/75= 1760/x

cross multiply

440x=1760(75)

simplify

132000/440

Answer:39?

Step-by-step explanation:

Answer:

43

Step-by-step explanation:

+ Total age of 5 people: 37 x5 = 185

+ Total age of 6 people (when 1 person enters the room): 38 x 6 = 228

+ The age of the person who enter the room is: 228 - 185 = 43 age

Answer:

1. Put the numbers in order.

2. Cross off high/low pairs.

3. Add the leftover numbers.

4. Divide the sum by 2.

Step-by-step explanation:

Given:

24, 16, 23, 30, 18, 29

The ordered steps involved in Calculating the median of the data set given :

1.) put the numbers in order: This involves arranging the numbers in the dataset usually in ascending order :

16, 18,23,24,29,30

2.) Cross off high/low pairs: take out equal amount of input from both the left and right hand side. Here we have (23, 34) left

3) Add the leftover numbers: Since the values left is more than one, both values are summed, we have (23+24) = 47

4.) Divide the sum by 2 : Get the average of the two numbers to obtain the median value. Here the average is (23+24)/2 = 47/2 = 23.5

Answer:

A: 1. Put the numbers in order.

2. Cross off high/low pairs.

3. Add the leftover numbers.

4. Divide the sum by 2.

Step-by-step explanation:

edg2020

Hope this helps

Answer: [tex]y=3x[/tex]

Step-by-step explanation:

parallel lines have the same slope so you can have any line that is y=3x plus a number thats not 4

EXAMPLES:

[tex]y=3x-3[/tex]

[tex]y=3x+5[/tex]

[tex]y=3x-2[/tex]

Answer:

Step-by-step explanation:

43feet

Answer:

5/7

Step-by-step explanation:

Billy experienced a rate of catfish to toral fish of 10/14. This is 5/7. So if this rate continues, he could expect the probability of catching a catfish to be : 5/7

Answer:

a^2 +a -6

Step-by-step explanation:

(a + 3)(a - 2)

FOIL

first: a*a = a^2

outer: -2*a = -2a

inner: 3*a =3a

Last : -2*3 = -6

Add them together

a^2 -2a+3a -6

Combine like terms

a^2 +a -6

Answer:

a² + a - 6

Step-by-step explanation:

(a + 3)(a - 2) = a² - 2a + 3a - 6 = a² + a - 6

Answer:

The range is 12

Step-by-step explanation:

the range is the biggest number minus the smallest

the biggest number is 33

the smallest number is 21

so 33-21=12 so

The range is 12

Answer: 12

Step-by-step explanation: The range is the difference between the greatest number in the data set and the least number in the data set which in this case is 33 - 21 or 12.

So the range of this data set is 12.

Answer:

1. B

2. A

3. B

4. ???

5. A

6 ???

7. I can't see it

Step-by-step explanation:

Complete question:

Noah drew a triangle so that all the sides are 5 inches long. He wants to draw a new triangle, but increase the length of each side by x inches. The perimeter of the new triangle is 24 inches. Find the value of x and length of the new side.

Answer:

x = 3 inches

The length of the new sides of the triangle is 8 inches

Step-by-step explanation:

If each of the sides of the original triangle is 5 inches, then it is an equilateral triangle.

Let the length of each of the side of the new triangle be, A, B and C.

A = 5 + x

B = 5 + x

C = 5 + x

A + B + C = 24

(5 + x) + (5 + x)  + (5 + x) = 24

15 + 3x = 24

3x = 24 -15

3x = 9

x = 9/3

x = 3

A = B = C = 5 + x = 5 + 3 = 8 inches

The length of the new sides of the triangle is 8 inches

Answer:

57 miles

Step-by-step explanation:

Answer:

57 miles

Step-by-step explanation:

divide 199.5/3.5 and you will get 57 miles

Answer:

71.57% of student heights are lower than Darnell's height

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 150, \sigma = 20[/tex]

Darnell has a height of 161.4 centimeters. What proportion of student heights are lower than Darnell's height?

This is the pvalue of Z when X = 161.4.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{161.4 - 150}{20}[/tex]

[tex]Z = 0.57[/tex]

[tex]Z = 0.57[/tex] has a pvalue of 0.7157

71.57% of student heights are lower than Darnell's height

Answer:

0.7157

Step-by-step explanation:

Darnell's height is 161.4 - 150 = \goldD{11.4}161.4−150=11.4161, point, 4, minus, 150, equals, start color #e07d10, 11, point, 4, end color #e07d10 relative to the mean.

This is \dfrac{\goldD{11.4}}{20} = \blueD{0.57}  

20

11.4

​  

=0.57start fraction, start color #e07d10, 11, point, 4, end color #e07d10, divided by, 20, end fraction, equals, start color #11accd, 0, point, 57, end color #11accd standard deviations relative to the mean. This is Darnell's z-score.

Hint #22 / 4

We want to find the proportion of student heights below a z-score of \blueD{0.57}0.57start color #11accd, 0, point, 57, end color #11accd:

Answer:

see below

Step-by-step explanation:

Experimental means what actually happened

P(odd) = (number of 1 + number of 3 + number of 5) / total

           = (10+8+8) / 50

           = 26/50

           = 13/25 = 52%

Theoretical means  what we expect to happen

P (odd) = (number of 1 + number of 3 + number of 5) / total

             =(1+1+1)/6

             =1/2 = 50%

We rolled an odd just a little more than the expected amount of times

Answer:

yes

Step-by-step explanation: