Factor the trinomial and enter the factorization below. Write each factor as a

The difference between two numbers is 9, and the sum of the squares of each number is 153. What is the value of the product of t

Mandarinka [93]

Numbers are 3 and 12
The product is 36

3 0

3 years ago

Distribute and combine like terms. Please show all of your work. -5(3x + 7) - 4(x - 4) + 11

Varvara68 [4.7K]

For this case we have the following expression:

$-5 (3x + 7) -4 (x-4) +11$

For simplicity we follow the steps:

We apply distributive property to the terms within the parenthesis, bearing in mind that:

$- * + = -\\- * - = +\\-15x-35-4x + 16 + 11 =$

We add similar terms taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed.

$-15x-4x-35 + 16 + 11 =\\-19x-8$

ANswer:

$-19x-8$

5 0

3 years ago

Read 2 more answers

(Hehe...Please ignore the markings)

inysia [295]

Answer:

See below:

Step-by-step explanation:

Problem 1:

Multiply Equation 1 by 4, keep Equation 2 the same.

x+y=8, multiply each term by 4:

4*x=4x, 4*y=4y, 8*4=32

so, the equivalent system is: 4x+4y=32 and x-y=2

Solve the system of equations:

x-y=2 becomes x=y+2

plug into 4x+4y=32 to solve for y

4(y+2)+4y=32---> 4y+8+4y=32--->8y=24---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 1 Answer:

Equivalent system: 4x+4y=32, x-y=2; solution: x=5, y=3

Problem 2:

Keep Equation 1 the same. Add 1 and 2.

To add an equation, add the left sides together, and then the rights.

so: x+y=8 + x-y=2 gives us: 2x=10

solve for x ---> 2x/2=10/2--->x=5

plug x into x+y=8--->5+y=8--->y=3

Problem 2 answer:

Equivalent system: x+y=8, 2x=10; solution:x=5, y=3

Problem 3:

Subtract Equation 2 from 1, and keep 2 the same.

To subtract an equation, subtract the left sides, then the rights. We are subtracting 1 from 2, so its 2-1.

x-y=2 - x+y=8 gives us: -2y=-6

Solve for y by dividing by -2-->-2y/-2=-6/-2---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 3 answer:

Equivalent system: -2y=-6, x-y=2; solution: x=5, y=3

Problem 4:

Multiply the sum of Equation 1 and 2 by a factor of 3. Keep equation 2 the same.

First we add 1 and 2: (we did this earlier) ---> 2x=10 ---> now we multiply it all by 3---> 2x*(3)=10*(3)---> this gives us: 6x=30---> now divide by 6 to solve for x: 6x/6=30/6 gives us: x=5

Now, solve for y by plugging x into equation 2: x-y=2---> 5-y=2--->y=3

Problem 4 answer:

Equivalent system: 6x=30, x-y=2; solution: x=5, y=3

______

Quick Tip: One thing inherent of Equivalent systems is that they have the same set of solutions. Thus, we know the systems are equivalent when they have the same set of solutions for x and y. Moreover, you don't need to solve every time after you attempt to find an equivalent system, instead, just plug in the values found in problem 1 to each new set of equations to test if they are equivalent.

If we find x=5 and y=3 for x+y=8 and x-y=2, then all we have to do is plug them in to 6x=30 and -2y=-6 to see if they are equivalent.

6(5)=30 ---> true

-2(3)=-6 ---> true

3 0

3 years ago

Consider the statistical study below and then

bagirrra123 [75]

Answer:

a) The population is all people who exercise regularly; population parameters are test scores for all, categorized by whether or not each individual was given a suggestion.

b) The sample is the 98 studied; the sample statistic is the test scores for the 98 studied, categorized by whether or not each individual was given a suggestion.

c) Experiment

Step-by-step explanation:

Rewriting for the sake of clarity

98 people who exercise regularly were given cognitive tests. It was discovered that those participants who were given a suggestion, their exercise habits might affect their performance on the test actually did worse on the test.

a. identify the population and the population parameter of interest,

In Statistics, Population is a Set under scrutiny.

The Parameter of a Population is any descriptive measure that helps to draw the Distribution curve. So in this case, it is fair to say that:

The population is all people who exercise regularly; population parameters are test scores for all, categorized by whether or not each individual was given a suggestion.

b. describe the sample and sample statistic for the study,

The sample is any subset within the Population.

The sample statistic might be any to measure in this case, the suggestion and see if there is any correlation between them and the results in what extent, etc. to deeper analyze it.

Then:

The sample is the 98 studied; the sample statistic is the test scores for the 98 studied, categorized by whether or not each individual was given a suggestion.

c. identify the type of study.

The statistical study here is an experiment since the 98 people were undergone to cognitive tests then their results were scrutinized.

6 0

3 years ago

A restaurant critic for a newspaper examines the prices restaurants charge for their meals and discovers that the restaurants th

maksim [4K]

Answer:

When customers wait longer for tables, they are more likely to pay higher prices.

Step-by-step explanation:

Supply/Demand relationships predict that changing one side will influence the other. If demand exceeds capacity, suppliers can raise prices without risk of losing products sold. In fact, total income will rise. The restaurant may raise it's price to the point that supply meets demand. In this case, the goal of the higher priced meals is to reduce wait times, not meals sold. If the meals sold are all at a higher price/meal, then income rises and wait times are reduced. What's not to like, if you own the restaurant?

7 0

2 years ago