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3 years ago

Write an absolute value inequality for the graph below. Use x for your variable.

Mathematics

1 answer:

Gnoma [55]3 years ago

7 0

Answer:

|x| ≥ 7

Step-by-step explanation:

Taking the absolute value means that any value of x will always be positive, meaning that the absolute value of -7 or less would be 7 or greater, which satisfies the inequality above and line graph.

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An explosion causes debris to rise vertically with an initial speed of 120 feet per second. The formula h equals negative 16 t s

Novay_Z [31]

Answer:

The debris will be at a height of 56 ft when time is <u>0.5 s and 7 s.</u>

Step-by-step explanation:

Given:

Initial speed of debris is, $s=120\ ft/s$

The height 'h' of the debris above the ground is given as:

$h(t)=-16t^2+120t$

As per question, $h(t)=56\ ft$ . Therefore,

$56=-16t^2+120t$

Rewriting the above equation into a standard quadratic equation and solving for 't', we get:

$-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0$

Using quadratic formula to solve for 't', we get:

$t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s$

Therefore, the debris will reach a height of 56 ft twice.

When time $t=0.5\ s$ during the upward journey, the debris is at height of 56 ft.

Again after reaching maximum height, the debris falls back and at $t=7\ s$ , the height is 56 ft.

5 0

3 years ago

Solve it plz 29x < 38x + 18

storchak [24]

Answer:

x= -2

Step-by-step explanation:

The first thing I did was isolate the x's on one side. I subtracted 38x from both sides. This gives me:

-9x=18.

Now i divide both sides by -9. Giving me x=-2

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3 years ago

Bert already has $50 but needs a total of at least $250 for his vacation. He gets paid $20 per day for delivering papers. What i

kati45 [8]

Answer:

I got 10

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

How many shapes are in the world

Montano1993 [528]

There are an infinite number of shapes, because a shape can have any number of sides. This is where we get into our laws of fractals. A fractal is a shape with an infinite perimeter and area, meaning that every level of infinity is another shape, but can be beat by another shape. However, this is all philosophical math and goes way beyond the context of your question.

To keep it short and simple, there are an infinite number of shapes in the world.

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3 years ago

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The rectangle below has a total perimeter of 125 cm:

Jlenok [28]

A rectangle has four sides, two equal to the width and two equal to the length. So, the perimeter is

$p = 2w+2l$