MATHEMATICS HIGH SCHOOL

Which of the solution sets is all real numbers?
|x| < -1
|x| = -1
|x| > -1

Answers

Answer 1

Answer:

The solution sets is all real numbers in case of:

|x| > -1

Step-by-step explanation:

We know that modulus is a function with the property such that:

if a<0 then |a|= -a

that is the modulus of a negative number is positive and if a≥0

then |a| =a

and modulus of a positive value is also positive.

i.e. modulus function always gives positive value.

Hence,

|x|<-1

This is not possible as modulus function always gives a value ≥0 for all real numbers.

|x|= -1

This is also not possible as modulus of any number can't be negative.

|x| > -1

The modulus of any number will definitely be greater than or equal to zero.

Hence, the solution set contain all the real numbers.

Answer 2

Answer: The last one is all real number

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Which quantity is best expressed as +5?A. a purchase of $5 B. a profit of $5 C. a loss of $5 D. an overdraft of $5

William wants to hang a mirror in his room. The mirror and frame must have an area of 50 square feet. The mirror is 5 feet wide and 8 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?3x2 + 13x − 20 = 0
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4x2 + 26x − 10 = 0
2x2 + 2x − 10 = 0

Answers

The last one. 2x2+2x-10=0

A+5 a+5 a

please help me write it in simplest form

Answers

Answer:

Therefore, the simplest form of the expression "A + 5a + 5a" is "A + 10a"

Step-by-step explanation:

To simplify the expression "A + 5a + 5a" in its simplest form, we can combine like terms. "A" and "5a" are like terms because they both have the variable "a" raised to the power of 1. So, combining "A" and "5a" gives us: A + 5a + 5a = A + 10a

A group of biologists found a total of 28 loggerhead turtle nests along a beach during a certain season. This was 40% of the total number of turtle nests the group found during that season. What was the total number of turtle nests the group found during that season?70
85
110
143

Answers

First divide 28 by 40 to get the unit rate which is 0.7. Then, since that is 1% mulitiply 0.7 times 100 to get 70 turtles as your answer. hope that helped!

28=.4x
70=x
They found 70

Pablo wrote four division equations with 6 as the quotient. what could have been the four division equations he wrote?

Answers

$(18)/(3)=6 \n \n (12)/(2)=6 \n \n(6)/(1)=6$

Which product is equivalent to 25x2 – 16?(5x − 4)(5x + 4)
(5x + 8)(5x − 8)
(5x − 4)(5x − 4)
(5x − 8)(5x − 8)

Answers

The product that is equivalent to the given expression is: A. (5x-4)(5x+4)..

What are Equivalent Expressions?

Equivalent expressions are expressions that have equal value when simplified.

(5x-4)(5x+4) is equivalent to 25x² – 16 because if we expand we would have:

5x(5x+4) -4(5x+4)

5x² + 20x - 20x - 16

Add like terms

25x² – 16

Therefore, the product that is equivalent to 25x² – 16 is: A. (5x-4)(5x+4).

Learn more about equivalent expressions on:

brainly.com/question/22365614

#SPJ9

the answer is (5x-4)(5x+4)

A college student realized that he was spending too much money on fast food. For the remaining 5 months of the year his goal is to spend a mean of $50 a month towards fast food. How much can he spend in December, taking into consideration that in the other 4 months he spent $100, $25, $80, and $30, respectively? Round your answer to two decimal places, if necessary.

Answers

Answer:

The college student can spend $15.00 in December.

Step-by-step explanation:

This can be calculated as follows:

Let y represents the amount to spend in December.

The can now us the formula for calculating a mean is as follows:

Mean = Sum of montlhy spending / Number of months ...... (1)

From the question, we have:

Mean = $50

Sum of monthly spending = $100 + $25 + $80 + $30 + y = $235 + y

Number of months = 5

Substituting the values into equation (1) and solve for y, we have:

$50 = ($235 + y) / 5

$50 * 5 = $235 + y

$250 = $235 + y

$250 - $235 = y

$15.00 = y

Therefore, the college student can spend $15.00 in December.

Final answer:

To achieve a mean expenditure of $50 per month on fast food across 5 months, the student can only spend $15 in December, considering that he has already spent a total of $235 in the other 4 months. This keeps his total spending at $250, giving an average of $50 per month.

Explanation:

The student wants to spend a mean of $50 per month on fast food for 5 months. In 4 of those months, he has already spent $100, $25, $80, and $30, respectively. That totals to $235 in spent funds already. Since the goal is a $50 monthly average, we multiply $50 by 5 months to get a total desired spending of $250. To find out how much he can spend in December, we subtract the total already spent from the total desired spending. As such, he can spend $250 - $235, which equals to $15 in December.