MATHEMATICS HIGH SCHOOL

The length of a rectangle is 3 inches more than its width. The area of . the rectangle is 40 square inches. What is the length, in inches, of the . rectangle?. (1) 5 (2) 8 (3) 8.5 (4) 11.6

Answers

Answer 1
Answer:   Let's say W=the width of the rectangle 

if width times length equals the area, then... 

W x (3+W)=40 
  Length = 8 
Width = 5 
I started by factorising 40: 
2, 2, 2, 5. 
Then you just find a way to arrange those numbers that works
Answer 2
Answer: Area of a rectangle=lenght x width.
width=x
length=x+3
we can suggest this equation:
x(x+3)=40
x²+3x=40
x²+3x-40=0
we solve this square equation:
x=[-3⁺₋√(9+160)] / 2
x=(-3⁺₋13)/2
we have two solutions:
x₁=(-3-13)/2=-8  this solution isn´t valid.
x₂=(-3+13)/2=5

lenght=x+3=5+3=8

Answer: the lenght, in inches, of the rectangle  is 8 .
(2) 8

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F(x) = 2/x + 7

Write steps and inverse

Answers

Answer:

y=2/(x−7)

Step-by-step explanation:

To find the inverse function, swap x and y, and solve the resulting equation for x. If the initial function is not one-to-one, then there will be more than one inverse. So, swap the variables: x=7+(2/y) for y. y=2/(x-7).

What rational number could be graphed between 0 and 1?

Answers

Answer:

1\4

Step-by-step explanation:
Answer: is 1
Assuming 0 and 1 are arithmetic (elementary branch of mathematics)

Simplify the following expression:7x − 4y + 5z − 2x − 10y + z

5x − 14y + 6z
9x − 14y + 6z
5x − 6y + 6z
9x − 6y + 6z

Answers

If you would like to simplify 7x − 4y + 5z − 2x − 10y + z, you can do this using the following steps:

7x − 4y + 5z − 2x − 10y + z = 7x - 2x - 4y - 10y + 5z + z = 5x - 14y + 6z

The correct result would be 5x - 14y + 6z.

You earn $420 per week. You pay social security taxes of 7.65%, federal taxes of 22%, and state taxes of 5.95%. What is your take home pay?

Answers

If you would like to know what is your take home pay, you can calculate this using the following steps:

social security taxes: $420 - 7.65% * $420 = 420 - 7.65/100 * 420 = $387.87
federal taxes: $387.87 - 22% * $387.87 = 387.87 - 22/100 * 387.87 = $302.54
state taxes: $302.54 - 5.95% * $302.54 = 302.54 - 5.95/100 * 302.54 = $284.54

Your take home pay would be $284.54.

A cell phone manufacturer chose 200 people at random and asked them whether they would purchase the newest model for $300. The manufacturer repeated this survey using the same method three more times.Do any of the surveys appear to be biased?

Would purchase new model for $300? Survey
1 2 3 4
Yes 127 131 128 133
No 73 69 72 66


A.
Yes, because the results from Survey 1 differ the most from the other surveys’ results.

B.
Yes, because the results from Survey 4 differ the most from the other surveys’ results.

C.
No, because the sampling methods are all different but have about the same results.

D.
No, because all four surveys have about the same number of people saying “yes” and about the same number of people saying “no.”

Answers

Yes, because the results from Survey 4 differ the most from the other surveys’ results.

A coin is tossed and a six​-sided die numbered 1 through
6 is rolled. Find the probability of tossing a
head and then rolling a number greater than 4.

Answers

The probability of tossing a head and then rolling a number greater than 4 is 1/6. The probability says the number of possible outcomes from the total outcomes of an event.

What is probability?

The probability is defined as the ratio of the count of the favorable outcomes to the total count of the outcomes of the sample.

P(A) = n(A)/n(S)  where A is n event, n(S) is the total count of the sample, and n(A) is the count of favorable outcomes.

Calculating the probability:

The given events are tossing a coin and rolling a dice.

The favorable outcomes for these events are given as tossing a head and rolling a number greater than 4.

Calculating the probability of tossing a coin:

The total outcomes of the event are 2 (head and tail)

The favorable outcome = 1 (only head)

So, the probability of tossing a head = 1/2

Calculating the probability of rolling a dice:

The total outcomes of the event are 6 ( a dice has 6 faces with a number on each face (1 to 6))

So, there are only two numbers that are greater than 4 (5, 6)

The favorable outcomes = 2

So, the probability of rolling a numbergreater than 4 = 2/6 =1/3

Calculating the probability of two events at the same time:

To get this probability- multiply both the probabilities.

⇒ 1/2 × 1/3 =1/6

Therefore, the required probability is 1/6.

Learn more about probabilities here:

brainly.com/question/10837034

#SPJ2
tossing a head = 1/2
rolling a number greater then 4 = 2/6 = 1/3

1/2 * 1/3 = 1/6 <==
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