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3 years ago

Solve the inequality: −1<|2 x − 3|<7

Mathematics

1 answer:

andriy [413]3 years ago

5 0

Answer:

Step-by-step explanation:

1. subtract over the x on the right side of the inequality so you get 4x<16 divide 4 over to get x alone the inequality turns into x<4.

2. subtract over the x on the right side so you get 11x<22 divide over 11 to get x<2

3. Add over 10 to get -8x>7x+30 subtract over 7x to get -15x>30 divide by -15 to get x<-2 make sure to flip over the sign since you're dividing by a negative

4. Add over the 4 to get 13x<12x+3 subtract over 12 and get x<3

5. I can't solve five since their is no inequality sign, the answers show it both ways so i need a starting one to go off on but it is either A or B just flip over the original sign and that will be the answer .

6. Distribute the 7 to get 7x-14<-5 add over the 14 and get 7x<9 divide over the 7 and get x<9/7

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Which equation is equivalent to log3(x+5)=2

Lisa [10]

In exponential form: 10^2=3(x+5)
If we were to solve, x=85/3

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2 years ago

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The height of the tunnel at the center is 54 ft, and the vertical clearance must be 18 ft at a point 8 ft from the center. Find

IrinaVladis [17]

the standard form for a horizontal ellipse is

X^2/a^2 + y^2/b^2 = 1

Substitute 54 for b and and use (8,18) as the

point to find a

x=8

y=18

8^2/a^2 + 18^2/54^2 =1

64/a^2 + 324/2916 = 1

324/2916 reduces to 1/9

64/a^2 + 1/9 = 1

64/a^2= 1-1/9

64/a^2 = 8/9

64*9/8 = a^2

576/8 = 72

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So formula

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3 years ago

A=1/4 and b=6.<br><br> −8ab=

podryga [215]

Answer:

When $a=\frac{1}{4}$ and $b=6$ :

$-8ab=-12$

Step-by-step explanation:

-8ab can be seen as -8×a×b. Insert the given values:

$-8*\frac{1}{4} *6$

Simplify multiplication from left to right:

$-8*\frac{1}{4} \\\\\frac{-8}{1} *\frac{1}{4} =\frac{-8}{4} =-2$

Insert and solve:

$-2*6=-12$

:Done

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3 years ago

To the nearest tenth, which is the BEST estimate for the volume of the given pyramid?

mixer [17]

Answer:

4.2 cubic inches

Step-by-step explanation:

Find the diagram attached

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B is the base area

H is the height of the pyramid

Given

Base area = 3.2in * 1.4in

Base area = 4.48sq. in

Height = 2.8in

Volume of the rectangular pyramid = 4.48*2.8/3

Volume of the rectangular pyramid = 12.544/3

Volume of the rectangular pyramid = 4.2 cubic inches

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2 years ago

Tommy purchased a riding lawnmower with an original value of $2,500. If the value of the riding lawnmower decreases by $300 per

Eva8 [605]

Answer:

$1000.

Step-by-step explanation:

Let x represent number of years.

We have been given that Tommy purchased a riding lawnmower with an original value of $2,500. The value of the riding lawnmower decreases by $300 per year. We are asked to find the value of lawnmower after 5 years.

Since the value of the riding lawnmower decreases by $300 per year, so value of lawnmower decrease in 5 years would be 5 times $300.

The final value of lawnmower would be initial value minus value decreased in 5 years.

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2 years ago

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