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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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3 years ago
Choices:<br><br> One-sixth cups<br> Five-sixths cups<br> 1 and two-thirds cups<br> 1 and 5 / 6 cups
navik [9.2K]

Answer:

Patel will require more orange juice = \frac{371}{660} cups

Step-by-step explanation:

Patel needs the orange juice for his family = 3 cups

He needs more orange juice = 3 cups - Sum of juice squeezed from different oranges

=3-(\frac{13}{15}+\frac{1}{5}+\frac{9}{20}+\frac{5}{11}+\frac{7}{15})

L.C.M. of the denominators = 660

=3-\frac{572+132+297+300+308}{660}

=3-\frac{1609}{660}

= \frac{1980-1609}{660}

= \frac{371}{660}

Therefore, amount of orange juice required more = \frac{371}{660} cups

3 0
3 years ago
What is the slant height of a square pyramid that has a surface area of 319 square feet and a side length of 11 feet?
Dafna1 [17]

Step-by-step explanation:

Surface area of a square pyramid is the area of the square base plus the area of the four triangles made from the base and the slant height.

SA = s² + 4(sh/2)

which reduces to:

SA = s² + 2sh

You are told that s = 11 and SA = 319. You can now solve for h:

319 = 11² + 2(11)h

319 = 121 + 22h

198 = 22h

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I hope it's helpful!!

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The volume v of a gas kept at constant temperature varies inversely with the pressure p. If the pressure is 24 pounds per square
daser333 [38]

Answer:

V=12\ ft^{3}

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form y*x=k or y=k/x

In this problem

P*V=k

step 1

Find the value of K

For P=24\ psi ,V=15\ ft^{3}

substitute

24*15=k

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the equation is P*V=360

step 2

For P=30\ psi ,V=\ ft^{3}

substitute in the equation

(30)*V=360

V=360/30=12\ ft^{3}

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3 years ago
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