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soldier1979 [14.2K]
1 year ago
5

Solve the inequality. Graph the solution set, and write it using interval notation. |5x+4|less than or equal to 10

Mathematics
1 answer:
aniked [119]1 year ago
8 0

we have the inequality

\lvert5x+4\rvert\leq10

step 1

Find out the first solution (positive case)

\begin{gathered} +(5x+4)\leq10 \\ 5x\leq10-4 \\ 5x\leq6 \\ x\leq\frac{6}{5} \\ x\leq1.20 \end{gathered}

The first solution is all real numbers less than or equal to 1.20

Interval (-infinite,1.20]

step 2

Find out the second solution (negative case)

-(5x+4)\leq10

Multiply by -1 both sides

\begin{gathered} (5x+4)\ge-10 \\ 5x\ge-10-4 \\ 5x\ge-14 \\ x\ge-\frac{14}{5} \\ x\ge-2.8 \end{gathered}

The second solution is all real numbers greater than or equal to -2.8

the interval [-2.8, infinite)

step 3

Find out the solution to the given inequality

The solution is

[-2.8, infinite) ∩ (-infinite,1.20]=[-2.8,1.20]

the solution is the interval [-2.8,1.20]

see the attached figure to better understand the problem

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2) Suppose 120 people are surveyed and asked about their eating habits. 50 people
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Answer:

1/6

Step-by-step explanation:

Given that :

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What is the probability that someone surveyed likes both Raising Cane's and Layne's chicken fingers?

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3 years ago
Divide £52 in the ratio 11:2
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Divide 52 by 13 to find one 'part' of the ratio. (52 ÷ 13 = 4)

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The ratio will be £44:8.

We can check if this is correct by adding 44 and 8 to see if it adds up to 52. (44 + 8 = 52). It does, so it's correct.
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How many European Union cities have a population of more than 800 000 people?
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Find the area of the trapezoid!!!! PLEASE HELP!!!!
san4es73 [151]

ANSWER

32 \sqrt{3}  {ft}^{2}

EXPLANATION

The area of a tra-pezoid is half times sum of the bases times the vertical height.

From the diagram ( see attachment) we use the Pythagoras Theorem to obtain,

{x}^{2}  +  {(4 \sqrt{3}) }^{2}  =  {8}^{2}

{x}^{2}  +  48  =  64

{x}^{2}  =  64 - 48

{x}^{2}=16

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=  \frac{1}{2} (10 + 6) \times 4 \sqrt{3}

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=  8\times 4 \sqrt{3}

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6 0
4 years ago
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