Solve the inequality. |4x + 2| < 26 A. –32 < x < 20

B. –7 > x > 6

C. –6 < x < 6

D. –7 < x < 6

Answers

Answer 1

Answer: Hello,
Answer D

1) if 4x+2>0 then |4x+2|=4x+2
==> 4x+2<26
==>4x<24
==>x<6

2) if 4x+2<0 then |4x+2|=-(4x+2)=-4x-2

==>-4x-2<26
==>-4x<28
==>x>-7

thus -7<x<6

Answer 2

Answer:

Answer:

D. –7 < x < 6

Step-by-step explanation:

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Round 0.977 to the nearest hundredth

Answers

.98 since the hundredth place is higher than a five it is rounded up

A number is selected at random from the set {2, 3, 4, … 10}. Which event, by definition, covers the entire sample space of this experiment?a. The number is greater than 2.
b. The number is not divisible by 5.
c. The number is even or less than 12.
d. The number is neither prime nor composite.
e. The square root of the number is less than 3.

Answers

let's do process of elimination

a) 2 is part of the set and 2 is not greater than 2. NO

b) 5 and 10 in the set are divisible by 5. NO

c) 2,4,6,8,10 are even but the rest are odd ( BUT note the word "or"). the rest are less than 12. YES

d) 0 and 1 are the only numbers that are neither prime nor composite (they're not even part of the set). NO

e) the square root of 9 is 3 so the maximum number is 9 (but what happened to 10?) NO

For our given sample, the only true statement is:

c. The number is even or less than 12.

Which event, covers the entire sample space of this experiment?

The sample for the experiment is the set:

{2, 3, 4, 5, 6, 7, 8, 9, 10}

So, we need to see which ones of the statements are true for every digit in that set.

For example:

a "The number is greater than 2."

Is false, because the outcome can be 2, as 2 belongs to the set.

The true statement is:

c. The number is even or less than 12. (all the numbers are less than 12).

If you want to learn more about sets:

brainly.com/question/251701

#SPJ5

Distance between (-1,2) (7,8)

Answers

The distance between any two points is

   square root of ( [difference in the 'y's]² + [difference in the 'x's]² )

Difference in the 'y's = 8 - 2 = 6
Difference in the 'x's = 7 - (-1) = 8

Distance between them =

   square root of ( 6² + 8² ) =

   square root of ( 36 + 64 ) =

   square root of ( 100 ) = 10 .

Answer: 10

Step-by-step explanation: In this problem, we're asked to find the distance between the points (-1,2) and (7,8) so we use the distance formula which states that the distance between two points is equal to

$d =\sqrt{(x^(2) - x^(1))^(2) + (y^(2) - y^(1))^(2) }$ .

Our first point, (-1,2) represents ( $^(x) 1$ , $^(y)1$ ) and our second point,

(7,8) represents ( $^(x)2$ , $^(y)2$ ).

So, plugging the given information into the formula, we have $\sqrt{7 - (-1))^(2) + (8 - 2)^(2)}$ .

Next, we simplify inside the parentheses to get $\sqrt{(8)^(2) + (6)^(2)}$ .

Next, 8² is 64 and 6² is 36 so we have $√(64 + 36)$ or $√(100)$ which is 10.

So the distance between the points (-1,2) and (7,8) is 10.

Find the perimeter of a square with each side measuring 2 inches.

Answers

A square as four sides.
All the sides of a square are the same length
so this square has 4 sides that are each 2 inches long.
The formula for perimeter is all the sides added up.
Lets do the math:)

2 + 2 + 2 + 2 = 8

So this means that...
the perimeter of the square is 8 inches.

=)

Answer:

B. 8 inches

The explination is that I am just that cool lol

Transform the equation x-3y=15 to express it in slope-intercept form