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3 years ago

Compare and contrast the solution of |2x + 8| > 6 and the solution of |2x + 8| < 6.

Mathematics

1 answer:

svet-max [94.6K]3 years ago

3 0

Answer:

The solution of |2x + 8| > 6 includes all values that are less than –7 or greater than –1.

The solution of |2x + 8| < 6 includes all values that are greater than –7 and less than –1.

Step-by-step explanation:

You can find the solution by "unfolding" the absolute value, then dividing by 2 and subtracting 4:

-6 > 2x +8 > 6 . . . . . read this as -6 is less than 2x+8 or 2x+8 is greater than 6

-3 > x +4 > 3 . . . . . . .divide by 2

-7 > x > -1 . . . . . . . . . solution to the first inequality: x is less than -7 or greater than -1.

___

The solution to the other inequality is identical, except the direction of the comparison is reversed. It is read differently, because the segments overlap, rather than being disjoint.

-7 < x < -1 . . . . . . . . solution to the second inequality: x is greater than -7 and less than -1.

These descriptions match choice B.

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A chef uses 8 1/2 cups flour for his gig nine 3/4 cup flour for his pies and 25 2/3 cups flour for his bread will he have any fl

katen-ka-za [31]

Answer:

50-25 2/3 - 9 3/4 - 8 1/2 = 6 1/12

Step-by-step explanation:

To do this without a calculator you need to get common denominator

a good choice would be 12 for the common denominator

50 x 12 = 600

25 x 12 = 300

convert to 2/3 to x/12, multiply top and bottom by 4

2/3 x 4 = 8/12

add this to the 300 to get 308/12

same with the other terms

9 x 12 = 108

convert 3/4 to x/12, multiply top and bottom by 3

3/4 x 3 = 9/12

add this to the 108 to get 117/12

and do the same for the 8 1/2

8x 12 = 96

convert 1/2 to x/12, multiply top and bottom by 6

1/2 = 6/12, add this to the 96

do the subtraction and simplify

8 0

3 years ago

The volume of this regular pentagonal pyramid is 82.5 cubic meters. What is the height of the pyramid?

a_sh-v [17]

the height of the pentagonal pyramid is 5. 70 meters

<h3>Volume of a regular pentagonal pyramid</h3>

The formula for determining the volume of a regular pentagonal pyramid is given as;

V=5/12tan(54°)ha^2

Where

a is the base edge
h is the height

We have the volume to be;

volume = 82. 5 cubic centers

height = h

a = 5m

Substitute the values

$82. 5 = \frac{5}{12}$ × $tan 54$ × $h$ × $5^2$

$82. 5 = 0. 42$ × $1. 3764$ × $25$ × $h$

Make 'h' subject of formula

$h = \frac{82. 5}{14. 45}$

h = 5. 70 meters

The height of the pentagonal pyramid is 5. 70 meters

Thus, the height of the pentagonal pyramid is 5. 70 meters

Learn more about a pentagonal pyramid here:

brainly.com/question/16315924

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11 months ago

Please help me please!

Mumz [18]

Step-by-step explanation:

a,b) you can place all 17 in the middle and both circle will have 17 each. then remove 2 and place one each on separate sides. you can do this 8 times so that at the you'll end up with 1 in the middle and 8 each on separate sides.

the ways to do is then 9.

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2 years ago

What is the answer to 17=5k-2

nadezda [96]

17=5k-2

[add 2 on both sides]

19=5k

[divide 5 on both sides]

k=19/5(3.8)

HOPE THIS HELPS!!!!!!

6 0