What is the center and the radius of the circle: ( x + 6 ) 2 + ( y - 9 ) 2 = 121 ?

2(x+3)= 12

2x+6 = 12

2x = 12-6

2x = 6

x = 6/2

x = 3.

So the answer is 3.

The answer is:

Work/explanation:

Use the distributive property:

[tex]\sf{2(x+3)=12}[/tex]

[tex]\sf{2x+6=12}[/tex]

Subtract 6 on each side

[tex]\sf{2x=6}[/tex]

Finally, divide each side by 2

[tex]\sf{x=3}[/tex]

ANSWERS

a) Domain: x ∈ (-∞, -1) ∪ (-1, ∞)

b) Domain: x ∈ (-∞, 0) ∪ (0, ∞)

EXPLANATION

These compositions are:

a)

And

b)

To find the domain in each function we have to find the values that x cannot take. If there aren't any, then the domain is all real values.

For composition a) note that x is in the denominator as (x+1). As we know, for real numbers the denominator can't be 0, so that's our restriction:

Solving for x:

The domain for f º g is all real values except x = -1

For composition b) we have x in the denominator too, but it is alone. Therefore, as said before, x cannot be 0.

Given:

There are given the two systems of the equation:

Explanation:

According to the question:

We need to solve the equation by using the elimination method.

So,

To solve the above equation, we need to perform the elimination method.

So,

Then,

We need to subtract equation (3) from equation(4):

Then,

Final answer:

Hence, the solution is 0.

Given:

Distance, d = 508 km

Time, t = 2 hours

Let x be the speed of one train.

Let x-16 be the speed of another train.

To find: Speed of the two trains

Explanation:

We know that,

Let us frame the equation as follows,

Final answer:

The speed of the faster train is 135 km/h.

The speed of slower train is 119 km/h

(17) The First part of the question asked us to find the formula used in determining measure of the amount of space in a rectangular prism which is invariably the volume.

The three dimensions needed to determine the Volume of a rectangular prism are:

Length

width

Height.

To get the volume, we mutiply the three together.

So:

Volume = Length * Width * Height.

V = L * W * H

Therefore, the correct option is C, which is V = L x W x H.

(18) Givne the following dimensios of a rectangular prism as:

Length = 4 cm

Width = 3 cm

Height = 5 cm

We are to find the volume

Recall, the formula for finding volume of the rectangular prism is:

V = L x W x H

V = 4 x 3 x 5

V = 60 cm³

Therefore, the volume of the rectangular prism = 60 cm³

So, the correct option is C, which is 60 cm³.

To answer this question, we need to remember that we are using here the function notation. We are requested to tell what the value of the function is when x = -2.

If we see the table, we can check that the value of the function when x = -2 is equal to 1:

Therefore, the answer is f(-2) = 1 (third option).

The equation of a circle with Center (a, b) and Radius 'r' is given by,

Given,

Center (-7, -4)

Diameter = 8

We know the radius is half of diameter.

So,

Radius = 8/2 = 4

Now we can write the equation of the cirle,

Start by calculating the area of a single brownie using

To find the amount of brownies Joe can make in his pan, divide the area of the pan into the single brownie area

Joe had 16 brownies.

For the given probabilities:

Answer:

$8,400

Explanation:

The interest can be calculated using the following equation:

Where P is the original amount of the loan, r is the interest rate, and t is the time that the person tool to pay it back.

So, we can replace I by $1,050, r by 2.5% or 0.025, and t by 5 years. Then:

Finally, we can solve for P as:

Therefore, the original amount of the loan was $8,400

Given:

Number of shirts Jose has to fold = 12

Where N is the number of shirts he would have left after folding F of them.

Let's write an equation rlating N to F.

We have the equation:

N = 12 - F

Let's graph the equation.

Let's create points from the equation.

• At F = 1:

Substitute 1 for F and solve for N

N = 12 - 1

N = 11

We have the point:

(F, N) ==> (1, 11)

• At F = 2:

N = 12- 2

N = 10

We have the point:

(F, N) ==> (2, 10)

• At F = 0:

N = 12 - 0

N = 12

We have the point:

(F, N) ==> (0, 12)

• At F = 5:

N = 12 - 5

N = 7

We have the point:

(F, N) ==> (5, 7)

Therefore, we have the points:

(F, N) ==> (1, 11), (2, 10), (0, 12), (5, 7)

Let's plot the points and connect them using a straight edge.

Here, F is represented on the x-axis while N is represented on the y-axis.

We have the graph below:

ANSWER:

N = 12 - F

The word expression can be express mathematically as follows

Since the division sign is involve, using law of indicies we subtract the powers as follows

To get the radian measure of an angle we have to do this conversion:

The radian measure of an angle of 54° is 0.9425 radians.

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we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

In the triangle ADB we have that

mwe have that

m because AD bisects angle CAB

so

msubstitute

34+95+m

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Answer:

Explanation:

The below formula can be used to find the surface area of a square pyramid;

where A = area of the base

p = perimeter of the base

s = slant height = 6 in

Since the base of the pyramid is a square, let's go ahead and find the area of the square;

Let's go and find the perimeter of the square;

Let's substitute the values into our above formula and solve for SA;

The general form of the equation of an ellipse is given as:

37.5%

1) Examining the Spinner we can see that the total possibilities are:

90+45+90+135 = 360

2) Since the question is P(green or red) we can write out:

Note that the event of picking red or picking green can't exist simultaneously so they are mutually exclusive.

The result in percentage will be obtained by multiplying it by 100

3) Hence, the answer is 37.5%

Solution:

Let us denote by x the number of child tickets sold and by y the number of adult tickets sold. According to the problem, we have that 137 tickets were sold, then we get the following equation:

Equation 1:

On the other hand, according to the problem, child admission is $5.80 and adult admission is $9.70 and the total sales were S1094.90.

Thus, we get the following equation:

Equation 2:

Thus, we get the following system of linear equations:

Equation 1:

Equation 2:

Now, solving for x, the equation 1, we get:

Equation 3:

replacing this into equation 2, we obtain:

now, applying the distributive property, we get:

this is equivalent to:

this is equivalent to:

solving for y, we get:

Now, replacing this data into equation 3, we obtain:

So that, we can conclude that the correct answer is:

the number of child tickets sold = x = 60

the number of adult tickets sold = y = 77

We have the functions,

We move over to g(x), g(x) is an exponential function;

We move over to h(x),

If we rank the rates of change of the function , we see that,

So, the rates of change from least to greatest is;

g,h,f.

Option B

SOLUTION

We want to solve for x in

This becomes

Hence the answer is

GIVEN

The number of novels read is N and the number of months is M.

Dan is to read 4 novels per month.

SOLUTION

In one month, Dan reads 4 novels.

In two months, Dan is to read:

In three months, Dan is to read:

Therefore, in M months, Dan is to read:

Hence, the equation will be:

The graph of the equation can be drawn using the table of values given below:

where

Given:

a.) You deposit $4000 in an account earning 8% interest compounded monthly.

Question: How much will you have in the account in 15 years?

We will be using the following formula:

Where,

A=final amount

P=initial principal balance = $ 4,000

r=interest rate = 8% = 8/100 = 0.08

n=number of times interest applied per time period = monthly = 12

t=number of time periods elapsed = 15 years

We get,

Therefore, in 15 years, you will have $13,235.57 in your account.

Solution:

Given:

Hence, this is an exponential function.

Hence, the function can be represented by;

The time that had passed when the bacteria was 32,400 will be;

Therefore, 4 hours have passed when the bacteria became 32,400

Answer:

A. cos a

Explanation:

The relevant trigonometric formula we have is

Now comparing the above formula with the one given in the question tells us that the missing term in the equation is cos a.

Therefore, choice A is the right answer!

To look for f(-3) we are going to use the first portion of the formula

f(x) = 5 - 4x, because here we will find all the x - values from -∞ to 1

So

f(-3) = 5 - 4 (-3) = 5 + 12 = 17

Data:

l = 3w

d = 98

To find the area, lets start drawing the field:

The area of rectangle is

In this case

b = w

h= l = 3w

To determine the value of w, we can use the right triangle and the value of the diagonal that is the hypotenuse of the triangle. Then using Pythagoras theorem:

We can clear the w from this equation:

Now we know the value of w = 40

Given ramp constitutes a right angles triangle, therefore the Pythagoras Theorem is applicable.

Let H be the horizontal distance of the ramp.

The hypotenuse is 37 inches, and the height is 12 inches.

Then, according to the Pythagoras Theorem,

Thus, the horizontal distance of the ramp is 35 inches.

Answer:

$7/hour

Explanation

From the question we are told that a computer programmer worked for 10 hours and earned $70, this can be expressed as;

10 hours = $70

We are to find amount he is earning per hour. This can be written as;

1 hour = $x

Divide both expression

10/1 = 70/x

Cross multiply

10 * x = 70 * 1

10x = 70

x = 70/10

x = 7

Hence the rate per hour is $7/hour

Valor final = 5000

Valor inicial = ?

VF = VI • ( + r/100) ^T

5000 = VI• ( 1+ 7.5/100) ^10

VI = 5000/ [(1+7.5/100)^10 ]

VI= 5000/ (2.06)= $2426