Which is the correct center and radius for a circle given by the equation (x + 2)2 + (y + 3)2 = 4?

a.Center (-2,-3), radius 4

b.Center (2,3), radius 2

c.Center (2,3), radius 4

d.Center (-2,-3), radius 2

Answer:

Step-by-step explanation:

[tex]\frac{150km}{2hr}[/tex] divided by two is [tex]\frac{75km}{1hr}[/tex].

Answer:

r  =  22 ft  the sprinkler sends water until 22 feet away

Step-by-step explanation:

A circular pattern has an area of  1,519,76 ft²

And  the areaof a circle is:

A(c) = π*r²

A(c) = 3,14 * r²     ⇒   1,519,76  =  3,14 * r²

r²  =  1,519,76/3,14      ⇒   r²  = 484

r  = √484

r  =  22 ft

Answer:

22 ft

Step-by-step explanation:

The sprinkler is located in the middle of the circular pattern created by the sprinkler therefore the distance from the center to the end of the circular pattern is called the RADIUS

note:

area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]

      1519.76 = 3.14 * [tex]r^{2}[/tex]

therefore [tex]r^{2}[/tex] = 1519.76 / 3.14 = 484

therefore radius ( r ) = [tex]\sqrt{484}[/tex]  =  22 ft

The sprinkler is 22 feet away from the spread water

Answer:

q < 5

Step-by-step explanation:

Answer:

Width = 160

Length = 110

Step-by-step explanation:

Perimeter is the sum of all the sides

They tell you that the length is 50 m shorter than the width

so L = W - 50

W = W

540 = W + W + W-50 + W-50

540 = 2W + 2(W-50)

540 = 2W + 2W - 100

540 = 4W - 100

640 = 4W

W = 160

L = 160 - 50

L = 110

Answer:

Length: 110 m

Width: 160 m

Step-by-step explanation:

The formula for perimeter of a rectangle is P = 2L + 2W.

We can write the length in terms of width if width is w:

Length: w - 50

Width: w

Plug the values into the formula.

540 = 2(w - 50) + 2w

540 = 2w - 100 + 2w

540 = 4w - 100

640 = 4w

w = 160

find length by subtracting 50 from the width

160-50=110

Therefore, the length is 110 and the width is 160.

Answer:

The population density is 150 persons per square mile

Step-by-step explanation:

Firstly, we need to calculate the area of the trapezoid.

Mathematically, the area of a trapezoid is

(a+b)/2 * h

from the grid, we can obtain the lengths

on the x-axis , each line is 40(200/5 thin lines)

on the y-axis, each thin line also is 40(200/5 thin lines)

thus a = (8 * 40) = 320

b = (10* 40) = 400

h = (3 * 40) = 120

Inserting this into the area equation, we have the area of the trapezoid as (320 + 400)/2 * 120 = 43,200 units

since each unit = 1 mile, the area of Tennessee = 43,200 units

The population density is thus ; 6,495,978/43,200= which is approximately 150 persons per square mile

The population density is a number that gives the number of people located within the state.

[tex]\mathrm{The \ population \ density \ is \ approximately}\ \underline{150}\ \frac{persons}{mi.^2}[/tex]

Reasons:

The population of Tennessee = 6,495,978

The dimensions of the trapezoid model of the territory are;

Base length, a = 320

Base length, b = 400

Height of the trapezoid, h = 120

[tex]Area \ of \ the \ trapezoid = \mathbf{\dfrac{a + b}{2} \cdot h}[/tex]

Which gives;

[tex]Area \ of \ the \ trapezoidal \ territory = \mathbf{\dfrac{320 + 400}{2} \times 120 }= 43,200[/tex]

Area of the trapezoidal territory of the state = 43,200 mi²

[tex]The \ ratio \ of \ the \ population \ to \ the \ territory = \dfrac{6,495,978}{43,200} = 150.36986\overline 1[/tex]

Therefore;

[tex]The \ population \ density \approx \underline{150}\ \frac{persons}{mi.^2}[/tex]

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Answer: A,C,E

Step-by-step explanation:

I took the test and got it right

Answer:

the is a, c, and e

Step-by-step explanation:

hope this helps

Answer: m<B = 66.42

Step-by-step explanation:

Use cosine to find the missing angle.

Cosine = adjacent/hypotenuse

cos x = 2/5

since you know the side lengths and you’re finding the angle, use inverse cosine

cos -1 (2/5) = 66.4218215...

m<B = 66.42

Hey there!

We are looking for an angle. Whenever we want to look for an angle in a right triangle given two sides, we use inverse trigonometric functions. This is basically the inverse operation of the sine, cosine, and tangent. You could use it to undo any of these in an equation. If you said that the sine of x was equal to 1/2, you would do the inverse sine of 1/2 and get that x=30.

In our case, we see that the cosine of our angle is 2/5. How do we know that?

Well, we can remember the trigonometric functions using the mnemonic "soh cah toa"

SOH

Sine= Opposite/Hypotenuse

CAH

Cosine= Adjacent/Hypotenuse

TOA

Tangent= Opposite/Adjacent

If we look at the number values we have, we have 2 (the adjacent side to the angle) and 5 (the hypotenuse). This is adjacent over hypotenuse, which is the cosine. So, the cosine of our angle is 2/5.

Now, we can put this into an equation. I will call the measure of our mystery angle Θ (theta).

cosΘ= 2/5

We want to get the theta by itself to solve the equation. To do this, we have to use the inverse cosine on both sides of the equation to cancel out our cosine and figure out the value of theta. The inverse trig functions can be found on a calculator :)

cos[tex]^-1[/tex]cosΘ=cos[tex]^-1[/tex] 2/5

Θ ≈ 66.42

I hope that this helps! Now you will be able to find any angle given two sides of a right triangle! Have a wonderful day!

First you graph "y = 2x +2." You shade in the region below it, because it's y "LESS THAN" and you keep the line solid (not dotted) because it's "equal to" 2x+2 too.

Answer:

$10

Step-by-step explanation:

The hardcover books are $12 each which would be $60 out of the $100. There are four more paperbacks meaning they would be $10 each and cost $40 total.

I hope this helped!!! :)

The price of hardcover book is $12.Identity equations and conditional equations are the two types of equations. All possible values of the variables result in an identity.

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. An equation is created by joining two expressions with the equals sign ("=").

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this article, let's learn more about math equations.

Given ,

We suggest a set of equations for this situation:

Let a be the variable for the price of hardback books.

B: Make the variable for the price of paperback books.

The statement information we have indicates:

[tex]5a+4b=100[/tex]

[tex]b=a-b[/tex]

Adding the second equation to the first one results in:

[tex]5a+4(a-2)= 100\\5a+4 a- 8= 100\\9a =100+8\\9 a=108\\a=108/9\\a=12[/tex]

Consequently, hardcover books are $12.

To learn more about mathematical equation refer to:

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#SPJ2

Answer:

1 hour and 5 minutes

Step-by-step explanation:

Because Sam started cycling at 2:40 and he stopped cycling at 3:45 so cycled for 1 hour and 5 minutes its asking for total time cycling so its 1 hour and 5 minutes

Answer:

The height of the tree is Greater than 50 feet, so Iva’s house is not safe

Step-by-step explanation:

Find the height of the tree

Let

h ----> the height of the tree

we know that

The tangent of angle of 50 degrees is equal to divide the opposite side to the angle of 50 degrees (height of the tree) by the adjacent side to the angle of 50 degrees (tree’s distance from the house)

so

tan(50°)=h/50

h=(50)tan(50°)=59.6 ft

therefore

The height of the tree is Greater than 50 feet, so Iva’s house is not safe

Answer:

Step-by-step explanation:

a) Complete the table

                          Monday             Tuesday            Wednesday             Total

Female       21-14=7                 38-13-7= 18                 13                          38

Male              14                       33-18= 15                 26-13 =13            80-38=42

Total        80-33-26= 21                 33                          26                      80

b) P(the student is a female) = 38/80= 0.475

c) P(the student visited the library on Tuesday) = 33/80= 0.4125

Answer:

a) Monday Total: 21.

Monday Female: 7.

Tuesday Female: 18.

Tuesday Male: 15

Wednesday Male: 13

Male Total: 42.

b) 47.5% probability that the student is a female.

Step-by-step explanation:

a) How to find Monday Total: We have the totals for Tuesday and Wednesday, and we know the total of all three days is 80. So, we need to find the difference between Tuesday + Wednesday & all 3 days, to find the total of Monday. What we do is add 33 + 26 which equals to 59. Then, we remove 59 from 80 (80-59). The answer we get is 21, which is the difference between the two. That's Monday's total.

How to find Male Wednesday: We already have Wednesday Female, and the total for Wednesday. But now we're finding the Wednesday Male. Find the difference between Wednesday Total and Female (26-13). The answer is 13! The Wednesday Male is therefore 13.

How to find Male Total: We have to find the difference between the complete total (80) and the Female total (38). Subtract: (80-38). The answer you get is 42!

How to find Tuesday Male: Now that we have the Wednesday Male, and the Male Total, we can easily find the Tuesday Male! The Male Total is 42, and we know the Male Monday is 14, along with the Male Wednesday being  13. Add Male Monday and Male Wednesday together. (13+14=27). Now take that and remove it from 42. (42-27). The answer we get is 15. 15 is our Tuesday Male.

How to find Monday Female: We already know what the Monday Total is from previous calculations(21), so all we have to do now is find the difference from the Monday Total and the Male Monday to find the Female Monday. Subtract: (21-14) The answer we will get is 7. The Monday female is 7.

How to find Tuesday Female: We already have Tuesday Male, and the Tuesday Total, so we subtract the Tuesday Male from the Tuesday Total. (33-15). The answer we get is 18.

b) The answer would be 47.5% because 38 is 47.5% of 80. How? Divide 38 by 80. The answer would be 0.475. Now, multiply that answer by 100. You get 47.5! That's the percentage.

This is my first question that I've answered, I'm sorry if there are any mistakes!

Answer:

A. 4.1

Step-by-step explanation:

3+4+ 5+ 3+ 4+ 5+ 6+ 7+ 1+ 2+ 3+ 4+ 5+ 6+ 4+ 8+ 4+ 3+ 2= 79

79/ 19 = 4.1

Answer:

integer and rational hth

Step-by-step explanation:

Answer: Answer is B

Step-by-step explanation:

Remeber that the shorter a container is doesn't mean it has less mass or volume. the width can mean it holds more. If the radius is twice as big that can mean the contents is more and your getting a better deal.   hOpe this will help.

Answer:

(x-2)^2-11

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let number of songs are played in a commercial be a

     number of songs are played in a movie be b

Adrian earned a total of $1010 -> a*40 + b*130 = 1010  (1)

14 commercials and movies -> a+b = 14                          (2)

(1) - (2)*40 =  a*40 + b*130 - a*40 -b*40 = 1010 -14*40

-> b*90 = 450

-> b = 5

-> a = 14-5 = 9

The system of equation should be used is 40a + 130b = 1010

And, a + b = 14

And, the number of commercials and the number of movies on which Adrian's songs were played is 9 and 5

The following information should be considered:

So, the equations are

40a + 130b = 1010

a + b = 14

b = 14 - a

Now

40a + 130(14 - a) = 1010

40a + 1,820 - 130a = 1010

-90a = -810

a = 9

And, y = 14 -9

= 5

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Answer:

2. The correct option is;

D. 112

3. The predicted number of cellular subscription per 100 people in Australia in 2030 is 217 subscriptions

4. The equation of the quadratic regression curve is y = x² - 6×x + 4.1

5. The closest option is;

C. 4191

Step-by-step explanation:

2. The equation for the number of customers in a store is presented as follows;

y = -8.74·x² + 50.57·x + 39.02

Where:

x = Number of hours after opening

∴ When x = 3 hours

y = -8.74×3² + 50.57×3 + 39.02 = 112.07 ≈ 112 people

The correct option is D. 112

3. The expression of the regression equation is presented as follows

y = -0.107·x² + 9.008·x +28.851

Where:

x = Number of years since 1990, hence

When x = 2030 - 1990 = 40 Years

Hence, the predicted number of cellular subscriptions per  people in 2030 is presented as follows;

y = -0.107×40² + 9.008×40 +28.851 = 217.971 Subscribers

To round down to the nearest whole number as y = 217 subscribers

4. The general form of a quadratic equation is presented as follows;

y = a·x² + b·x + c

When x = 0, y = 4.1, therefore;

4.1 =  a×0² + b×0 + c = c

∴ c = 4.1

When x = 1, y = -0.9, therefore;

-0.9 =  a×(1)² + b×1 + c = c

-0.9 =  a + b + 4.1

∴ a + b = -0.9 - 4.1 = -5.0

When x = 2, y = -3.9, therefore;

-3.9 =  a×(2)² + b×2 + c = c

-3.9 =  4·a + 2·b + 4.1

∴ 4·a + 2·b = -3.9 - 4.1 = -8.0

Thus we have two equations;

a + b = -5.0..................(1) and

4·a + 2·b = -8.0 ..........(2)

Multiply equation (1) by 2 and subtract it from equation (2), we have

4·a + 2·b - 2×(a + b) = *8.0 - (2 ×-5.0)

∴ 2·a = 2

a = 1

From equation (1,)  we have;

a + b = -5.0..................(1)

Therefore, where a = 1 we have, 1 + b = -5.0

Hence, b = -5.0  - 1 = -6.0

Therefore, the equation of the quadratic regression curve is presented as follows;

y = x² - 6×x + 4.1

5. The quadratic regression equation is found as follows;

The general form of a quadratic equation is presented as follows;

y = a·x² + b·x + c

When x = 55, y = 3650, therefore;

3650=  a×55² + b×55+ c................(1)

When x = 65, y = 4569, therefore;

4569=  a×65² + b×65+ c ...........(2)

When x = 75, y = 6147, therefore;

6147=  a×75² + b×75+ c............(3)

Solving the system of equation;

3650=  a×55² + b×55+ c................(1)

4569=  a×65² + b×65+ c ...........(2)

6147=  a×75² + b×75+ c............(3)

Subtracting equation (1) from (2), we obtain;

4569 - 3650 =  a×65² + b×65 + c - (a×55² + b×55 + c)

919 = 1200·a + 10·b...........(4)

Subtracting equation (2) from (3), we obtain;

6147 - 4569 =  a×75² + b×75 + c - (a×65² + b×65+ c)

Which gives;

1578 = 1400·a + 10·b...........(5)

Subtracting equation (4) from equation (3), we obtain;

1578 - 919 = 1400·a + 10·b - (1200·a + 10·b)

659 = 200·a

a = 659/200= 3.295

Substituting the value of a in equation (4), we have;

919 = 1200×3.295 + 10·b = 3954 + 10·b

∴ 10·b = 919 -3954 = -3035

b = -3035/10 = -303.5

Substituting the value of a and b in equation (1), we have;

3650 =  (3.295)×55² + (-303.5)×55+ c

3650 = -6725.125 + c

∴ c = 3650 - (- 6725.125)= 10375.125

Therefore, the quadratic regression equation is presented as follows;

y = 3.295·x - 303.5·b +10375.125

Hence, in 1961, x = 1961 - 1900 = 61, we have

y = 3.295×61² - 303.5×61 10375.125= 4122.32

Therefore, the closest option is C. 4191.

Answer:

Step-by-step explanation: I took the test and here are the answers

Answer:

2 1/2

Step-by-step explanation:

take 25 and divide it by 10 giving you 5/2 but that equals 2.5 and 2.5 equals 2 1/2

Answer:

x=2

Step-by-step explanation:

36=18x

x=36/18

x=2

Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

[tex]36 = 18x \\ divide \: both \: sides \: by \: 18\\ \\ 2 = x[/tex]

Answer:

5

Step-by-step explanation:

We know that a^b^c = a^ (b*c)

1/25 ^(-2/3* 3/4)

1/25^ (-2/4)

1/25 ^ -1/2

Rewriting 1/25 as 5^-2

5^-2 ^-1/2

Again a^b^c = a^ (b*c)

5^(-2*-1/2)

5 ^ 1

5

Answer: The data values have a range of 70 centimeters. Intervals with a range of 10-20 centimeters should be reasonable.

Answer:

it might be

69

10-20

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

In the parenthesis with x it up or down on the y axis, and then after the function is what where after or before the origin the line starts on the x-axis.

Answer:

I think it would be 20%.

Step-by-step explanation:

$5 was taken off the original price, which is about 1/5 of $24.99. So, since 1/5 as a percent is 20%, I think the answer would be 20%.

Answer:

the answer is 7

Answer:

7

Step-by-step explanation:

Answer:

6.285

Step-by-step explanation:

π·22≈12.56637 divided by 2 (half) is 6.285

Answer:

12.56 units squared

Step-by-step explanation:

find the area of the whole circle:

formula for this is: pi multiplied by the radius which is squared.

The math for this is Below

3.14 x 2 squared

2 squared is 4

so 4 times 3.14 which is 12.56

Answer:

r + 7

Step-by-step explanation:

Sum means addition, so in this particular expression something is being added, and the two numbers given are r and 7. Therefore, the expression is r + 7.

Answer:

It's B.

Step-by-step explanation:

Z=-3, z=6