MATHEMATICS HIGH SCHOOL

Which inequality represents the values of X that insure triangle ABC exists

Answers

Answer 1

Answer:

Answer:

7/4 < x < 11/2

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.

Please have a look at the attached photo.

My answer

Given the information:

AB: 2x + 4
BC: 6x
AC: 16

All of these three triangle inequalities must be satisfied:

AB +BC > AC

<=> 2x + 4 + 6x > 18

<=> 8x > 14

<=> x > 7/4

BC +CA > BA

6x + 18 > 2x + 4

<=> 4x > -14

<=> x > -14/4

CA +AB > CB

18 + 2x + 4 > 6x

<=> 22 > 4x

<=> x < 11/2

So the inequality represents the values of X that insure triangle ABC exists is: 7/4 < x < 11/2

Hope it will find you well.

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An animal shelter has a ratio of dogs to cats that's 3:2. If there are 30 cats at the shelter, how manydogs are there?
A. 15
B. 90
C. 20
D. 45

Answers

In the question "An animal shelter has a ratio of dogs to cats that's 3:2. If there are 30 cats at the shelter, how many dogs are there" the correct answer is 45 (option D). To solve the problem, let the number of dogs be x, then dogs / cats = 3 / 2 = x / 30. i.e. 2x = 3(30) = 90. x = 90 / 2 = 45. Therefore, there are 45 dogs in the animal shelter.

An animal shelter has a ratio of dogs to cats that's 3:2. If there are 30 cats at the shelter, 45 dogs are there . 3/2 = x/30 , x= 30*3/2 =45

The sum of two times a number and 5 more than the number is the same as the difference between -15 and twice the number. What is the number?

Answers

(2x)(x+5) = 2x-15

4x^2 + 5x = 2x-15

4x^2 = 7x -15

16x = 7x - 15

16x + 15 = 7x

2 2/7 + 2 1/7 = x

x = 4 3/7

What is the next number?
2, 7, 26, 101, 400, ?

Answers

It is 1595. Put it on excel so you can better have an overview how it is done. You need 5 columns, column A-E. On column A, put 1 to 5 in rows 1 to 5. On column C, put the answers: 2, 7, 26, 101 and 400. On column D, put number 3 in all 5 rows. Back on column B, insert =sum(C1-A1) on row 1 and copy till row 5. On column E, insert =sum(B1+C1*D1) on row 1 and copy till row 5 and you will get 1595 at the end.

7/2=3.5
26/7=3.7
101/26=3.9
400/101=4
400 x 4 or 4.1 = 1600 or 1640

Please help me ASAP ...