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dsp73
3 years ago
7

What is a number line for 5a + 18 < -27?

Mathematics
2 answers:
devlian [24]3 years ago
4 0

Answer:

Letter C.

Step-by-step explanation:

Let’s start by subtracting \blue{18}18start color #6495ed, 18, end color #6495ed from both sides of the inequality:

\qquad \begin{aligned} 5a + 18 &< -27\\ 5a + 18 \blue{-18} &< -27\blue{-18}\\ 5a &< -45\\ \end{aligned}

5a+18

5a+18−18

5a​  

<−27

<−27−18

<−45

Hint #22 / 4

To isolate aaa, we need to divide both sides by \green{5}5start color #28ae7b, 5, end color #28ae7b:

\qquad\begin{aligned} 5a &< -45\\ \\ \dfrac{5a}{\green{5}} &< \dfrac{-45}{\green{5}}\\ \\ a &< \purple{-9}\\ \end{aligned}

5a

5

5a

a

<−45

<

5

−45

<−9

​Hint #33 / 4

To graph the inequality a < \purple{-9}a<−9a, is less than, start color #9d38bd, minus, 9, end color #9d38bd, we first draw a circle at \purple{-9}−9start color #9d38bd, minus, 9, end color #9d38bd. This circle divides the number line into two sections: one that contains solutions to the inequality and one that does not.

Since the solution uses a less than sign, the solution does not include the point where a= \purple{-9}a=−9a, equals, start color #9d38bd, minus, 9, end color #9d38bd. So the circle at \purple{-9}−9start color #9d38bd, minus, 9, end color #9d38bd is not filled in.

Because the solution to the inequality says that a < \purple{-9}a<−9a, is less than, start color #9d38bd, minus, 9, end color #9d38bd, this means that solutions are numbers to the left of \purple{-9}−9start color #9d38bd, minus, 9, end color #9d38bd.

Hint #44 / 4

The graph that represents the solution of the inequality a < \purple{-9}a<−9a, is less than, start color #9d38bd, minus, 9, end color #9d38bd is shown in

Alexandra [31]3 years ago
3 0

a < -9

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                    5*a+18-(-27)<0  

Step by step solution :

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  5a + 45  =   5 • (a + 9)  

Equation at the end of step  1  :

Step  2  :

2.1    Divide both sides by  5  

Solve Basic Inequality :

2.2      Subtract  9  from both sides

           a < -9

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RUDIKE [14]

Answer:

47 degrees

Explanation:

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4 0
2 years ago
Solve the inequality<br> 4b−4≤−20
devlian [24]

Answer:

b ≤ -4

Step-by-step explanation:

4b−4≤−20

4b - 4 + 4 ≤ - 20 + 4

4b ≤ -16

Divide both sides by 4

b ≤ -4

8 0
2 years ago
The inside of a beaker is shaped like a circular cylinder with a base diameter of 121212 centimeters (\text{cm})(cm)(, start tex
Radda [10]

Answer:

9 cm

Step-by-step explanation:

Since the container is a cylinder of base diameter d₁ = 12 cm and thus radius r = 12/2 = 6 cm. The water height is 8 cm. The initial volume of water is thus V₁ = πr²h = π × 6² × 8 = 288π cm³.

The sphere of diameter d = 6 cm has radius r₁ = 6/2 = 3 cm. Its volume V₂ = 4πr³/3 = 4π × 3³/3 = 36π cm³

Since the sphere displaces it own volume of liquid, the new volume V = V₁ + V₂ = 288π cm³ + 36π cm³ = 324π cm³

This is the new volume of water in the cylinder. Since the water level rises by h' cm and V = πr²h'

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5 0
3 years ago
4÷2/3=<br><br>1/10÷3=<br><br>1/4÷7=<br><br>9÷1/3=<br><br>4/5÷4=​
Artyom0805 [142]

━━━━━━━☆☆━━━━━━━

▹ Answer

<em>4 ÷ 2/3 = 6</em>

<em>1 ÷ 10/3 = 3/10</em>

<em>1 ÷ 4/7 = 1 3/4</em>

<em>9 ÷ 1/3 = 27</em>

<em>4 ÷ 5/4 = 3 1/5</em>

▹ Step-by-Step Explanation

4 ÷ 2/3 = 4 × 3/2 = 12/2 = 6

1 ÷ 10/3 = 1 × 3/10 = 3/10

1 ÷ 4/7 = 1 × 7/4 = 7/4 = 1 3/4

9 ÷ 1/3 = 9 × 3/1 = 27/1 = 27

4 ÷ 5/4 = 4 × 4/5 = 16/5 = 3 1/5

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

8 0
2 years ago
Simplify this expression<br>n-10+9n-3
ivolga24 [154]
1. <span>n-10+9n-3
2. (n+9n)+ (-10-3)
3. 10n -13</span>
4 0
2 years ago
Read 2 more answers
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