All categories

3 years ago

What is the solution to the compound inequality 5x + 7 > −8 and 3x + 7 ≤ 19?

1 answer:

3 0

Solve each

5x+7>-8
minus 7 both sides
5x>-15
divide by 5
x>-3

3x+7≤19
minus 7 both sides
3x≤12
divide by 3
x≤4

so we got
x>-3 AND x≤4
and means that the solution set must satisfy both at once
so x is bigger than -3 and less than or equal to 4
so between -3 and 4 including 4
-3<x≤4

last one

You might be interested in

What is the range of g(x) = 3 |x - 1| - 1?

Anastaziya [24]

C.( 1, infinity) of the range

5 0

3 years ago

HELP!!!!!!! Choose the graph that matches the following system of equations:

pshichka [43]

Answer:

The answer in the attached figure

Step-by-step explanation:

we have

$4x + 2y = -2$ -----> equation A

$x-3y=24$ -----> equation B

Isolate the variable x in the equation B

$x=3y+24$ ----> substitute in the equation A and solve for y

$4(3y+24) + 2y = -2$

$12y+96+ 2y = -2$

$14y = -2-96$

$14y = -98$

$y = -7$

Find the value of x

$x=3(-7)+24=3$

The solution of the system of equations is the point (3,-7)

8 0

3 years ago

Seven days ago, the gas tank on Roses car was filled with 20 gallons of gasoline. Today there are 6 gallons of gasoline. What in

katovenus [111]

Answer:

-14

Step-by-step explanation:

The amount of change is found by subtracting the original amount from the new amount:

6 gal - 20 gal = -14 gal

The appropriate integer is -14.

7 0

4 years ago

Read 2 more answers

Find the sum of this infinite geometric series: 4 - 2.88 + 2.0736- 1.492992+...

kirza4 [7]

Let $r$ be the common ratio between terms. Then

$-2.88=4r\implies r=-0.72$

Now denote the $n$ th partial sum of the series by

$S_n=4-2.88+2.0736-1.492992+\cdots+4(-0.72)^{n-1}+4(-0.72)^n$

Multiply both sides by $-0.72$ , then subtract from the above to get

$S_n-(-0.72S_n)=4-4(-0.72)^{n+1}$
$1.72S_n=4(1-(-0.72)^{n+1})$
$S_n=2.32558(1-(-0.72)^{n+1})$

As $n\to\infty$ , you're left with

$S_\infty=2.32558$

3 0

4 years ago

there are 13 animals in the barn. some are chickens and some are goats. there are 48 legs in all. how many of each animal are th

romanna [79]

Answer:

Step-by-step explanation:

chickens + goats = 13

so...

c + g = 13, so...

g = (13 - c)

2 legs times the number of chickens (2c) + 4 legs times the number of goats (4g) = 48 total legs. So...

2c + 4(13-c) = 48, so

2c + 52 - 4c = 48, so

-2c = -4, so

2c = 4, so

c = 2.

There are 2 chickens, and therefore 11 goats.

5 0

3 years ago