It is about solving equations by substitution. if you can help plzzz

Mumz [18]

Break down every term into prime factors. ...Look for factors that appear in every single term to determine the GCF. ...Factor the GCF out from every term in front of parentheses, and leave the remnants inside the parentheses. ...Multiply out to simplify each term.

5 0

3 years ago

A ball is thrown downward from a cliff. Its position at time t seconds is given by the formula s(t) = 16t2 + 32t, where s is in

Rom4ik [11]

Answer:

It takes 2.8 seconds for the ball to fall 215 ft.

Step-by-step explanation:

We are given a position function s(t) where s stands for the number of feet the ball has fallen, so we have to replace s with the given value of 215 ft and solve for the time t.

Setting up the equation.

The motion equation is given by

$s(t) =16t^2+32t$

We can replace there s = 215 ft to get

$215=16t^2+32t$

Solving for the time t.

From the previous equation we can move all terms in one side to get

$16t^2+32t-215=0$

At this point we can solve for t using quadratic formula.

$t = \cfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

where a, b and c are the coefficients of the quadratic equation

$at^2+bt+c=0$

So we get

$a=16\\b=32\\c=-215$

Replacing on the quadratic formula we get

$t = \cfrac{-32\pm \sqrt{32^2-4(16)(-215)}}{2(16)}$

Using a calculator we get

$t=-4.8 , t = 2.8$

Physically speaking the only result that makes sense is to move forward in time that give us t = 2.8 seconds.

We can conclude that it takes 2.8 seconds for the ball to fall 215 ft.

3 0

3 years ago

A parallelogram with a base of y units and a height of x units is changed to have a new base of 3y units and a height of 2x unit

nataly862011 [7]

The formula for the area of a parallelogram is

A=b*h where b=base and h=height

if the base were to increase by 3times and the height were to increase by 2 times then
6A=b*h
The area of the parallelogram would be 6 times larger

So if the original area was 47units², then the new area would be

47*6=282units²

Answer=282units²

5 0

3 years ago

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When 7 is subtracted from three times a certain number, the result is 28. what is the number

OverLord2011 [107]

Answer: 35/3 or 11.6

Step-by-step explanation:

3x-7=28

Add 7 to each side

3x=35

Divide by 3

6 0

3 years ago

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Find the distance between the two points in simplest radical form. (1, -7) and (7,0)

denis23 [38]

Answer:

The distance between the two given points is equal to √85.

Step-by-step explanation:

Let's recall what the distance formula is:

$\displaystyle \huge\math\boxed{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} }$

We are defined our two points as:

(x₁, y₁) → (1, -7)
(x₂, y₂) → (7, 0)

We can rewrite this into our different "variables":

x₁ = 1
y₁ = -7
x₂ = 7
y₂ = 0

Now given our distance formula and our variables, we can find the distance between the two points:

$\displaystyle\huge\begin{aligned}d & = \sqrt{(1 - 7)^2 + (7 - 0)^2} \\& = \sqrt{(-6)^2 + (7)^2} \\& = \sqrt{36 + 49} \\& = \math\boxed{\sqrt{85}} \\\end{aligned}$

∴ since the radical is already in its simplest form, our distance between the two points is equal to √85.

Hope this helps!

5 0

2 years ago

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