The point enter your response here is also on the graph of the equation.

Step 1

Write out the question.

We need to find f(5) and g(-3)

First, we will solve f(5), for this, we have the following function:

Second, we will solve g(-3), for this, we have the following function:

In conclusion, f(5) = -16 and g(-3) = 39

The other number that is a part of the fact family of 3,4 is 7.

According to the question,

We have the following information:

Two numbers of the fact family is 3 and 4.

Now, we know that in a fact family, if two numbers are given then the third number can be found by adding the two given numbers.

(More to know: fact family is often used to prove commutative property of addition. It can be used to find any number of other numbers of fact family are given.)

4+3 = 3+4 = 7

Hence, the other number that is a part of the fact family of 3,4 is 7.

To know more about fact family here

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Answer

Surface area = 2260.8 cm²

Explanation

The surface area of a normal sphere is given as

Surface area = 4πr²

where,

π = pi = 3.14

r = radius of the sphere = 12 cm

But this sphere has the middle of the sphere as part of the surface too

Surface area = 4πr² + πr² = 5πr²

Surface area = 5 (3.14) (12²)

Surface area = 2260.8 cm²

Hope this Helps!!!

The percentage can be changed to decimal as,

Thus, the required decimal is 11.75.

Answer:

Books in Bookcase = 5/6

Science Books = 1/6

Explanation:

Given:

Total number of books Alissa put in a bookcase;

2/5 history books

1/3 math books

1/10 art books

We can go ahead and determine the fraction of the total number of books that are history, math, or art books in the bookcase by adding the given fractions together as seen below;

So the fraction of the total number of books that are history, math, or art books in the bookcase is 5/6

Let x represent the fraction of the total number of books that will be science.

We can go ahead and determine the value of x by subtracting the fraction of the total number of books that are history, math, or art books in the bookcase from 1;

So the fraction of the total number of books that will be science is 1/6

We want to know the center and the radius of the circle:

We remember that the equation of a circle is given by:

In this case, we complete the square by adding 1 and substracting 1:

This means that the center is the point (1,0), and:

Hello there. To solve this question, we need to pay attention to the data given by the question and set up an equation for the amount of rabbits in that colony.

In the year 2000 there were 1200 rabits in a colony, and it was observed that their population was increasing at a rate of 21% each year

For this type of question, we call f(x) the function that shows the population in a certain time x.

This function varies directly to the initial population and grows exponentially according to the rate .

Thus, we have that f(x) = P0 * (1+r)^x

In this case, P0 = 1200 and r = 0.21 (21% converted into decimals)

f(x) = 1200 * (1 + 0.21)^x

f(x) = 1200 * 1.21^x

This is the function that models the population of this colony for a year x.

To find how many rabbits you'll have in the year 2007, plug in x = 7

f(7) = 1200 * 1.21^7

Calculate the value

f(7) = 1200 * 3.797 = 4556

In which year will the population be equal to 5000

Making f(x) = 5000, we solve for x

5000 = 1200 * 1.21^x

Divide both sides of the equation by 1200

25/6 = 1.21^x

Take the natural log on both sides of the equation

ln(25/6) = ln(1.21^x)

Apply the logarithm power rule: log(a^b) = b * log(a)

ln(25/6) = x * ln(1.21)

Rewriting 1.21 as 121/100 = (11/10)², we get:

ln(25/6) = 2x * ln(11/10)

Divide both sides of the equation by a factor of 2ln(11/10)

x = ln(25/6)/(2ln(11/10)) approx. 7.4867 years

Rounding up to the next year, x = 8 years.

In a normal distribution, 68% of data will fall within two standard deviations of the mean

ANSWER :

(f - g)(x) = x^2 + 8

EXPLANATION :

From the problem, we have :

(f - g)(x) is the difference between the two functions

That will be :

4x = 2 + 14

4x = 16

4 is multiplying on the left, then it will divide on the right

x = 16/4

x = 4

The scenario formed a right triangle with an adjacent side of 24.2 ft. and included an angle of 37°.

First, let's recall the three main trigonometric functions.

In the scenario, the height of the flagpole appears to be the Opposite Side of the right triangle formed.

Since the function that we will be equating involves the Opposite Side and Adjacent Side of a right triangle, we will be applying the Tangent Function to find the height of the flagpole.

We get,

Therefore, the height of the flagpole is 18.2 ft.

Since we want the total amount, we first can add the red and green ribbon:

Martha has 15 feet of ribbon.

To converto to yards, we can just divide the amount in feet by 3. So, in yards:

So

Martha has 5 yards of ribbon.

We are given the following system of equations:

We will substitute the value of "y" from the first equation into the second equation:

Now we subtract "3x" from both sides:

Adding like terms:

Now we subtract 10 from both sides:

Adding like terms:

Now we multiply by -1 on both sides of the equation:

Now we factor in the left side. We need two numbers that when multiplied the product is 800 and their algebraic sum is -60. Those numbers are -40 and -20. Therefore, we get:

Now we set each factor to zero:

For the next factor:

These are the two values of "x" for the solution. To get the corresponding value of "y" we substitute in the second equation. Substituting the first value we get:

Now we substitute the second value:

Therefore, the solutions of the system are:

grow at 200% each year

so, population becomes twice in each year, then after 20 years:

answer: population is 5,242,880 after 20 years

Given:

To graph the given equation, we can plug in any values for x to get values for y as shown below:

Example 1:

Let x= 0

We plug in x= 0 into y=2x:

Based on the above values of x and y, our point is (0,0).

Example 2:

We let x =2:

It means that the point is (2,4).

Hence, the graph of y=2x is:

To answer this question, we can use the standard normal distribution, and use the z-scores for finding the minimum and maximum values in the distribution.

The z-score is given by:

We have that the maximum and minimum are within three standard deviations. The z-scores are a measure of the standard deviations from the population mean. Then, the values are for minimum, z = -3, and for maximum, z = 3.

The population's mean is equal to 58 (mu), and the standard deviation is equal to 17.

We are going to find the raw score, x, for the minimum and maximum values 3 standard deviations below and above the mean. Then, we have:

Minimum

Maximum

Let x, y and z denote the weighs of car X, car Y and car Z, respectively.

We know that car X weighs 136 more than car Z, this can be express by the equation:

We also know that Y weighs 117 pounds more than car Z, this can be express as:

Finally, we know that the total weight of all the cars is 9439, then we have:

Hence, we have the system of the equations:

To solve the system we can plug the values of x and y, given in the first two equations, in the last equation; then we have:

Now that we have the value of z we plug it in the first two equations to find x and y:

Therefore, car X weighs 3198 pound, car Y weighs 3179 pounds and car Z weighs 3062 pounds.

24 + 36

First, we have to solve the parentheses, by applying distributive property:

Add and subtract alike terms:

Given

Hours (h) = 1, 2, 3, 4, 5, 6, 7

Pages (p) = 40, 80, 120, 160, 200, 240, 280

Procedure

The answer would be p = 40h

1) Simplifying 7 -5m -10m we'll need to combine like terms. So

7 -5m -10m Combine Like terms

7 -15m

2) Given the options, the answer is 7 -15m

Explanation

Answer

A. 2

Express f (x) = x^2 -2x in the form f(x) = (x - h ) ^2 - k

x^2 - 2x = +2

h = -b/2a and k = h^2

a = 1 , b= -2

h= -(-2)/ 2(1) = 2/2 = 1

k = h^2 = 1^2 = 1

So, x^2 - 2x = (x-1) ^2 - 1

To rewrite the complete equation

f(x) = (x - 1)^2 - 1 - 2

f(x) = (x - 1)^2 - 3,

The minimum value is is -3

Option D is the answer

We are asked to convert 11.77 hours into hours and minutes. The first step is to divide the whole number from its decimal part, that is:

Now we convert the decimal hours into minutes. To do that we use the conversion factor 1h = 60 minutes. We get:

Therefore, 11.77 hours is approximately 11 hours and 46 minutes.

Let's define the next variables:

x: the first odd integer

y: the next odd integer

Since they are consecutive:

x + 2 = y

The product of them is 195, then:

x*y = 195

Replacing the y from the first equation into the second one:

x*(x + 2) = 195

x*x + x*2 - 195 = 0

x² + 2x - 195 = 0

Solving with help of the quadratic formula:

Given that we are only interested in positive integers, the solution x = -15 is discarded.

Therefore, the integers are 13 and 15

The sum of them is 13 + 15 = 28

Option (a)

Given:

The value of slope is, m = -2/3.

Pass throught he point, (x1, y1) = (2,-3)

The objective is to find the equation of the line.

The general equation of straight line is,

Now, substitute the given values in the above equation.

Hence, option (a) is the correct answer.

Since putting 8 sticks in each lunch box doesn't give any leftover, that means that number of carrot sticks she had is a multiple of 8.

Pretty simply!

Let's see the multiples of 8.

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, ....

Out of the choices, only 48 is a multiple of '8'.

Therefore,

D is correct

There are 10 males and 14 females.

So the order doesn't matter and we cant repeat a person.

Given the before information, we are going to use combinations

Where n is the total of people and r the election, so:

For males:

n=10

r=1

For females:

n=14

r=1

Finally, multiply both results:

10* 14 = 140

Therefore, there are 140 ways that the casting can be done.

Solution

for this case we can do the following: