All categories

3 years ago

It’s a review please HELP ASAP I’ve been stuck on it for awhile now

Mathematics

1 answer:

AlladinOne [14]3 years ago

6 0

<h3>Answer: 7 goes in the blank space</h3>

The range of values for x is 2 < x < 7

========================================

Explanation:

The hinge theorem says that the larger the opposite side is, the larger the angle will be.

AD = 11, DC = 8

Since AD > DC, this means angle ABD > angle DBC.

--------

angle ABD > angle DBC

20 > 4x-8

20+8 > 4x-8+8 ... add 8 to both sides

28 > 4x

4x < 28 ... flip both sides and the inequality sign

4x/4 < 28/4 ... divide both sides by 4

x < 7

--------

At the same time, the angle 4x-8 cannot be 0 or negative.

So we say 4x-8 > 0. Let's solve this for x.

4x-8 > 0

4x-8+8 > 0+8 ... add 8 to both sides

4x > 8

4x/4 > 8/4 ... divide both sides by 4

x > 2

2 < x ... flip both sides and the inequality sign

--------

We have 2 < x and x < 7. Both of these combine to the compound inequality 2 < x < 7

We can pick any value between 2 and 7 as long as we dont pick x = 2 or we dont pick x = 7.

You might be interested in

If A = (0, 0) and B = (8, 2), what is the length of AB?

dezoksy [38]

8, 2 because A doesn't add anything.

5 0

3 years ago

Two years ago, Sally had 5,000 dogs in her dog shelter. Now she has 24,575 dogs. What is the

vodomira [7]

Two years ago, Sally had 5,000 dogs in her dog shelter. Now she has 24,575 dogs. The rate of change is 391.5 % increase

<em><u>Solution:</u></em>

Given that Two years ago, Sally had 5,000 dogs in her dog shelter

Now she has 24,575 dogs

To find: rate of change

A rate of change is a rate that describes how one quantity changes in relation to another quantity

<h3><u>Steps to follow:</u></h3>

First: work out the difference (increase) between the two numbers you are comparing.

Increase = New Number - Original Number.

Then: divide the increase by the original number and multiply the answer by 100.

% change = Increase ÷ Original Number x 100

$\text {rate of change }=\frac{\text { new value }-\text {original value}}{\text {original value}} \times 100$

$\begin{array}{l}{\text { rate of change }=\frac{24,575-5000}{5000} \times 100} \\\\ {\text { rate of change }=\frac{19575}{5000} \times 100=391.5}\end{array}$

Thus the rate of change is 391.5 % increase

5 0

3 years ago

A survey in 2012 of U.S. households showed that 60% had a traditional landline

Vikentia [17]

Answer:

0.51

Step-by-step explanation:

4 0

3 years ago

Please help!! A scale on a hiking map shows at 3 inches represents 1.25 miles. What number of inches on the map represents 10 ac

Semenov [28]

Answer:

24 miles

Step-by-step explanation:

Set up a proportion:

3 inches/1.25 miles = x inches/10 miles

Then cross multiply

30=1.25x

Divide 1.25 on both sides

x=24

5 0

3 years ago

Twice the sum of three and a number is 30. Find the number

DedPeter [7]

9514 1404 393

Answer:

2(x +3) = 30
12

Step-by-step explanation:

When x represents the number, "the sum of 3 and a number" is (x+3). Twice that sum is 2(x+3). "Is 30" means this expression is equal to 30:

2(x +3) = 30 . . . . an equation for the given conditions

We can solve this equation by dividing by 2:

x + 3 = 15

x = 12 . . . . . . subtract 3

The number is 12.

5 0

3 years ago