MATHEMATICS HIGH SCHOOL

A number x is no more than 9 units away from 8. Write and solve an absolute-value inequality to show the range of possible values of x.|x − 8| ≤ 9
−1 ≤ x ≤ 17

|x + 8| ≤ 9
−17 ≤ x ≤ 1

|x − 9| ≤ 8
1 ≤ x ≤ 17

|x + 9| ≤ 8
−17 ≤ x ≤ −1

Answers

Answer 1

Answer:

Answer:

Option A is right

Step-by-step explanation:

Given that a number x is no more than 9 units away from 8

This implies that number can be either larger than 8 by less than 9 units or smaller than 8 by less than 9 units.

Difference between x and 8 is at most 9.

We represent in absolute value as

$|x-8|\leq 9\n-9\leq x-8\leq 9\n-1\leq x\leq 17$

Hence option A is right

Answer 2

Answer: The answer is a (|x - 8| ≤ 9 and -1 ≤ x ≤ 17) Because the difference between x and 8 can't be greater than 9, but it can be less than or equal to it, and because the range that x could be would be -1 to 17, since 8 + 9 = 17 and 8 - 9 = -1.

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What is the measure of angle x?

Answers

Answer:

x = 96°

Step-by-step explanation:

96 and x are Alternate exterior angles and are congruent, thus

x = 96°

Which word or phrase best clarifies the relationship between the claim andthe evidence?
Owning your own business can allow you more freedom than a typical
job. ______you may be able to schedule your work around other pursuits.

A meanwhile
B the first reason
C for example
D actually

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Pls I need help !!!!!!!

Answers

Answer:

-3 -4

Step-by-step explanation:

Bc it's why not ...... ummmmmmm

Find x and EF if BD is an angle bisector

Answers

The value of x will be;

⇒ x = 7/2

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

BD is an angle bisector.

Now,

In ΔBFG and ΔBFE;

∠G = ∠E = 90°

BF is common line.

∠GBF = ∠ FBE

Thus, ΔBFG ≅ ΔBFE

Hence, FG = FE

Substitute the values, we get;

⇒ FG = FE

⇒ 2x + 6 = 4x - 1

⇒ 6 + 1 = 4x - 2x

⇒ 7 = 2x

⇒ x = 7/2

Thus, The value of x will be;

⇒ x = 7/2

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2x+6=4x-1
add 1 to both sides
2x+7=4x
subtract 2x from both sides
7=2x
divide both sides by 2
3.5=x

To find EF, plug in the x value
4x-1
4(3.5)-1
14-1
EF=13

help please !!!Kevin wants to make a mixture that is 50% lemon juice and 50% lime juice. How much 100% lemon juice should he add to a juice that is 40% lemon juice and 60% lime juice to make 6 gal of the 50% lemon/50% lime juice mixture?

Answers

so basically, he wants to make mixture where lemon=lime

it is 6 gallons so
40% of 6=0.4 times 60=2.4=lemon
60% of 6=0.6 times 60=3.6=lime
so to make them equal
3.6-2.4=1.2
he must add 1.2 gallons of 100% lemon juice to make a mixture of 50% lemon and 50% lime

1.2 gallons is the answer

Question: Kevin wants to make a mixture that is 50% lemon juice and 50% lime juice. How much 100% lemon juice should he add to a juice that is 40% lemon juice and 60% lime juice to make 6 gal of the 50% lemon/50% lime juice mixture?

Answer: 1 Gallon

A box is shaped like an octagonal prism. Here is what the base of the prism looks like. If the height of the box is 7 inches, the volume of the box will be [1] cubic inches.

Answers

Answer:

The volume of the box is 33.796 cubic inches

Step-by-step explanation:

Given

$Height = 7in$

See attachment for the base of the prism

Required

The volume of the box

From the attachment, we have:

$a = 1in$ -- side length of the octagon

The area is then calculated as:

$Area = 2 * (1 + \sqrt 2)a^2$

So, we have:

$Area = 2 * (1 + \sqrt 2)* 1^2$

$Area = 2 * (1 + \sqrt 2)* 1$

$Area = 2 * (1 + \sqrt 2)$

Evaluate the square root

$Area = 2 * (1 + 1.414)$

$Area = 2 * (2.414)$

$Area = 4.828$

The volume is then calculated as:

$Volume = Height * Base\ Area$

$Volume = 7 * 4.828$

$Volume = 33.796$

The volume of the box is 100 cubic inches.

To find the volume of an octagonal prism, we need to know the area of the base and the height of the prism.

The area of an octagon can be calculated using the following formula:

Area of octagon = 1/2 * apothem * perimeter

where the apothem is the distance from the center of the octagon to one of its sides and the perimeter is the total length of all the sides of the octagon.

In this case, we don't know the apothem or the perimeter of the octagon, so we can't calculate the area of the base using the formula above. However, we can estimate the area of the base by drawing a square inside the octagon and a circle inside the square.

The square will have an area of 16 square inches and the circle will have an area of about 12.5 square inches. Therefore, the area of the octagon is somewhere between 12.5 and 16 square inches.

Since we are estimating the area of the base, we will use the average of 12.5 and 16 square inches, which is 14.25 square inches.

The volume of the box is calculated as follows:

Volume of box = Area of base * Height

Volume of box = 14.25 square inches * 7 inches = 100 cubic inches

Therefore, the volume of the box is 100 cubic inches.

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