14 Find the percent increase or decrease for each of the following values (indicate whether each is an increase or a decrease). a. 4x to x/ b. 0.25m to 0.5m 5 c. + 2p to d.y to 0.687 8 р 15 Consider the following relationships. TI. 1

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 :

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

Add and subtract alike terms:

Solution

for this case we can do the following:

SOLUTION

So the first option is the correct answer

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

Let x the total of Hungry-Man Meals bought.

let y the total of burritos bought.

He decides to buy 50 total frozen entrees.

x + y = 50

If we solve the equation for x

x = 50 - y

We also know that he spends $150 on all the frozen food.

Therefore:

x Hungry-Man Meals for $3.25

y burritos for $2.00

x(3.25) + y(2.00) = 150

3.25x + 2.00y = 150

Now substituting 50-y from the first equation into the second equation and solve for y:

3.25x + 2.00y = 150

3.25(50-y) + 2.00y = 150

3.25*50 - 3.25*y + 2.00y = 150

162.5 - 3.25y + 2.00y = 150

162.5 - 1.25y = 150

Subtract both sides by 150

162.5 - 150 - 1.25y = 150-150

12.5 -1.25y = 0

Add both sides 1.25y

12.5 -1.25y+1.25y= 0+1.25y

12.5 +0 = 1.25y

Divide both sides by 1.25

12.5/1.25 = 1.25y/1.25

10 = y

Substitute 10 for y in the result of the x equation:

x = 50 - y

x = 50- 10

x = 40

So 40 Hungry-Man meals and 10 burritos Jack bought.

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

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

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:

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

4x = 2 + 14

4x = 16

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

x = 16/4

x = 4

Step 1

The meaning of QUADRATIC EQUATION is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Step 2

We are required to Identify the two tables which represent quadratic relationships.

In a quadratic equation, we have a polynomial in x with degree 2. Hence the result in y or P(x) do get repeated as a polynomial contains x² in it.

Looking at the tables we will observe that;

The answers will be;

The first clue only tells us that there is one digit that is in the right place, so it could be any one of the following.

The second one tells us that one of the digits is right but in the wrong place, we still cannot confirm if 5 is the number we are talking about.

The fourth clue says that all the numbers are incorrect, so the digits are 2, 5, 0 or 1, now we must find out the correct order.

From clues 3 and 5 we can assume that 0 is one of the digits and that it comes first.

We will discard the number 5 because in clue 3 they talk about 2 correct digits, we already know that 0 is one and we choose 2 instead of the number five because of clues 1 and 2, which talk about only one digit in the correct place but in both of them the 5 remains in the same place.

The 3 digists are: 1, 0 and 2

The correct order is 012

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.

24 + 36

The aritmetic sequence has the characteristic that each term is the term before plus a constant number. Then we can create the following system of equations:

where p is the constant value which is added in each term, and x the number between 34 and 345. If we replace the value of "x" from the second equation into the first one:

Finally, the term betwen 34 and 345 is 34+p, 189.5

Hence the answer is 189.5

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

The percentage can be changed to decimal as,

Thus, the required decimal is 11.75.

Explanation

Answer

A. 2

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!!!

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.

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:

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.

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

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 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:

Step 1

Write out the question.

the x-intercepts are all the x coodinates in which the function will be equal to 0

to find the x intercepts equal the equation to 0

equal all factors involving the x to 0 because if there is any factor equal to 0 then the product between of al products will be 0 as well

solve both of the equations

the x-intercepts will be

(-4,0) & (6,0)

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.