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4 years ago

14

A rock is dropped from a height of 25 feet. The function h=-16t^2 +25 gives the height h of the rock after t seconds. When does

it hit the ground?

1 answer:

scZoUnD [109]4 years ago

3 0

Answer:

5 seconds

Step-by-step explanation:

The ground is 25 eet, so 25=-16t^2+400

-16t^2=-400, 16t^2=400

t^2=25, dividing both sides by 16

t=5 seconds.

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Write a formula for the function g(x) obtained when the graph of f(x) = 1/x is shifted down 4 units and to the right 6 units .

charle [14.2K]

Answer: $g(x) = \frac{1}{x-6} - 4$

This can be written out as g(x) = 1/(x-6) - 4

The "x-6" is in the denominator, while the "-4" is not.

=============================================================

Explanation:

We'll start with the parent function $f(x) = \frac{1}{x}$

When we shift 4 units down, we're subtracting 4 from the y coordinate of each point on the curve. Which is the same as subtracting 4 from f(x) because y = f(x).

So we have $h(x) = f(x) - 4 = \frac{1}{x} - 4$ as an intermediate step.

Then to shift 6 units to the right, we'll replace every x with "x-6". Imagine we kept the h(x) curve completely still, and instead we moved the xy axis 6 units to the left. This would give the illusion of h(x) moving 6 units to the right if we made the xy axis stay still. So that's why we go for "x-6" instead of "x+6".

Therefore, we end up with $g(x) = \frac{1}{x-6} - 4$

Side note: plugging in x = 6 leads to a division by zero error. This would mean x = 6 is not in the domain.

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3 years ago

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kirill115 [55]

Hi there!

c=74

<u><em>Equation:</em></u>

26+c=100

c+26=100

100-c=26

100=c+26

100=26+c

<u><em>1.Find the meaning:</em></u>

so 26 contacts and then the total would be 100 which would be 26+c=100...

<em><u>2.Subtract the two terms:</u></em>

<em><u /></em> $100-26=74$ <em><u /></em>

Therefore, c=74

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3 years ago

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Expand and simplify x(x + 2)(x + 4)

babymother [125]

Answer:

Step-by-step explanation:

Comment

Expand the second and 3rd factors first. Then worry about the x.

Solution

x(x + 2)(x + 4)

<em>first</em>: x * x = x^2

<em>Outside</em>: 4*x = 4x

<em>Inside</em>: 2*x = 2x

<em>Last:</em> 2*4 = 8

Combine

x^2 + 4x + 2x + 8

x^2 + 6x + 8

Now is the time to worry about the extra x

x(x^2 + 6x + 8)

remove the brackets.

x*x^2 + x*6x + 8*x

Combine

Answer: x^3 + 6x^2 + 8x

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2 years ago

-4(v + 1) = 2(1 - 20) - 6

Flura [38]

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3 years ago

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In ∆ABC the angle bisectors drawn from vertexes A and B intersect at point D. Find ∠ADB if:

icang [17]

Answer:

155°

Step-by-step explanation:

In Δ ABC, let A = x°

By Angle-sum property,

A + B + C = 180°

But, it is given that C = 130°

So, x + B + 130 = 180

B = 180 - 130 - x

B = 50 - x

Since AD and BD are internal bisectors of A and B,

∠ DAB = x/2 and

∠ DBA =

In Δ ADB, by angle-sum property,

∠ DBA + ∠ DAB +∠ ADB = 180°

+ ∠ ADB = 180°

25 + ∠ ADB = 180°

∠ ADB = 180 - 25 = 155°

Hence, ∠ ADB = 155°

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3 years ago