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zaharov [31]
2 years ago
15

12x+7<-11 AND 5x-8=>40

Mathematics
2 answers:
Sladkaya [172]2 years ago
6 0

12x + 7 < -11

12x < -18

x <  -1.5

5x - 8 => 40

5x => 48

x =>  9.6


Andreyy892 years ago
5 0

Answer:

The values of x = [-1.5, -∞) and [9.6, ∞)

Step-by-step explanation:

Here we have to solve the given system of inequalities.

12x +  7 ≤  -11 and 5x - 8  ≥ 40

Here we have to solve for x. Let's take the first inequality and solve for x.

12x + 7 ≤ -11

Subtracting 7 from both sides,

12x + 7 - 7 ≤ -11 - 7

12x ≤ -18

Dividing both sides by 12, we get

x ≤ \frac{-18}{12}

We can simplify this fraction.

x \leq \frac{-3}{2}

x \leq -1.5

Now let's solve the second inequality.

5x - 8 ≥ 40

Add 8 on both sides,

5x - 8 + 8 ≥ 40 + 8

5x ≥ 48

Dividing both sides by 5, we get

x ≥ \frac{48}{5}

x ≥ 9.6

So, solving those inequalities, we get

x ≤ -1.5 and x ≥ 9.6

This means, the values of x = [-1.5, -∞) and [9.6, ∞)

Let's draw the solution in a number line.

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2 years ago
A radio station plays a total of 272 pop, rock, and hip-hop songs during a day. The number of pop songs is 3 times the number of
Norma-Jean [14]
Let the daily played number of pop songs be P, the number of rock songs be R and the number of hip-hop songs be H.

i) 
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means that : P+R+H=272

ii) 
"The number of pop songs is 3 times the number of rock songs. "

so, P=3R

iii)
"The number of hip-hop songs is 32 more than the number of rock songs."

means: H=32+R

iv)

since both P and H can be written in terms of R, we have:

P+R+H=272

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3R+R+32+R=272

5R+32=272

5R=272-32=240

R=240/5=48


vi) 

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5 0
2 years ago
Please help it’s geometry and it’s hard
zzz [600]

Measure of the angle m ∠ RQS = 58 ° for the given circle with arc RS subtending m ∠RPS=14 x + 46 ° at the center P and m ∠ RQS = 3 x + 43 ° at Q, on the circumference.

As given in the question,

Measure of the angle is given by :

m ∠ RPS=14 x + 46 °                                  

m ∠ RQS=3 x + 43 °                                      

m ∠ RPS = twice m ∠RQS (angle subtended at center of the circle)

14 x +46 =2(3 x + 43)

⇒ 14x + 46 = 6x +86

⇒ 14x-6x=86-46

⇒8x=40

⇒ x=5°

m ∠ RQS = (3 x + 43) °  

                 =[3(5) + 43 ]°

                 = 58°

Therefore, measure of the angle in the given circle m ∠RQS is equal to the  58 °

Learn more about angle here

brainly.com/question/28451077

#SPJ1

6 0
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