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4 years ago

How does understanding place value help you to subtract across zeroes?

2 answers:

7 0

When you are subtracting over zeroes, you may need to carry over. This being said, you may need to take some from a previous number and put it into a zero, and continue carrying over until you can do what you needed to do. If you don't know the place value of the zero in mind, you will not end up completing this correctly.

just olya [345]4 years ago

7 0

When you subtract with bigger numbers, then you sometimes you have to carry over. But when you carry over, your work gets messy. It is also helpful when you know place value because it you do this:
25
- 10
You would get it wrong. This is the correct way:
25
- 10

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A toy cannon ball is launched from a cannon on top of a platform. The equation h(t) =- 5<img src="https://tex.z-dn.net/?f=t%5E%7

DanielleElmas [232]

Answer:

Part A)

Part B)

About 2.9362 seconds.

Step-by-step explanation:

The equation $\displaystyle h(t)=-5t^2+14t+2$ models the height h in meters of the ball t seconds after its launch.

Part A)

To determine whether or not the ball reaches a height of 14 meters, we can find the vertex of our function.

Remember that the vertex marks the maximum value of the quadratic (since our quadratic curves down).

If our vertex is greater than 14, then, at some time t, the ball will definitely reach a height of 14 meters.

However, if our vertex is less than 14, then the ball doesn’t reach a height of 14 meters since it can’t go higher than the vertex.

So, let’s find our vertex. The formula for vertex is given by:

$\displaystyle (-\frac{b}{2a},h(-\frac{b}{2a}))$

Our quadratic is:

$\displaystyle h(t)=-5t^2+14t+2$

Hence: a=-5, b=14, and c=2.

Therefore, the x-coordinate of our vertex is:

$\displaystyle x=-\frac{14}{2(-5)}=\frac{14}{10}=\frac{7}{5}$

To find the y-coordinate and the maximum height, we will substitute this value back in for x and evaluate. Hence:

$\displaystyle h(\frac{7}{5})=-5(\frac{7}{5})^2+14(\frac{7}{5})+2$

Evaluate:

$\displaystyle \begin{aligned} h(\frac{7}{2})&=-5(\frac{49}{25})+\frac{98}{5}+2 \\ &=\frac{-245}{25}+\frac{98}{5}+2\\ &=\frac{-245}{25}+\frac{490}{25}+\frac{50}{25}\\&=\frac{-245+490+50}{25}\\&=\frac{295}{25}=\frac{59}{5}=11.8\end{aligned}$

So, our maximum value is 11.8 meters.

Therefore, the ball doesn’t reach a height of 14 meters.

Part B)

To find out how long the ball is in the air, we can simply solve for our t when h=0.

When the ball stops being in the air, this will be the point at which it is at the ground. So, h=0. Therefore:

$0=-5t^2+14t+2$

A quick check of factors will reveal that is it not factorable. Hence, we can use the quadratic formula:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Again, a=-5, b=14, and c=2. Substitute appropriately:

$\displaystyle x=\frac{-(14)\pm\sqrt{(14)^2-4(-5)(2)}}{2(-5)}$

Evaluate:

$\displaystyle x=\frac{-14\pm\sqrt{236}}{-10}$

We can factor the square root:

$\sqrt{236}=\sqrt{4}\cdot\sqrt{59}=2\sqrt{59}$

Hence:

$\displaystyle x=\frac{-14\pm2\sqrt{59}}{-10}$

Divide everything by -2:

$\displaystyle x=\frac{7\pm\sqrt{59}}{5}$

Hence, our two solutions are:

$\displaystyle x=\frac{7+\sqrt{59}}{5}\approx2.9362\text{ or } x=\frac{7-\sqrt{59}}{5}\approx-0.1362$

Since our variable indicates time, we can reject the negative solution since time cannot be negative.

Hence, our zero is approximately 2.9362.

Therefore, the ball is in the air for approximately 2.9362 seconds.

5 0

3 years ago

Read 2 more answers

S=2(lw+lh+wh) solve for w

wolverine [178]

we have

$s=2(lw+lh+wh)$

Solve for w means that clear variable w

$s=2(lw+lh+wh)\\s=2lw+2lh+2wh$

Group terms that contain the variable w, and move the other terms to the opposite side of the equation

$(s-2lh)=(2lw+2wh)$

Factor the variable w

$(s-2lh)=w(2l+2h)$

Divide both sides by $(2l+2h)$

$(s-2lh)/(2l+2h)=w(2l+2h)/(2l+2h)$

$w=(s-2lh)/(2l+2h)$

therefore

<u>the answer is</u>

$w=(s-2lh)/(2l+2h)$

7 0

4 years ago

Read 2 more answers

Given: AG and IC are common internal tangents of H and B. HI = 8, ED = 2, and EF = ED. What is the measure of AE?

ki77a [65]

AE = 6

This is because ABE is a right triangle with the right angle being angle BAE. We know that AB = 8 and EB = 10, so we can use the Pythagorean Thoerem to find AE.

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3 years ago

Rick and two friends share a large bag of popcorn which cost $6.25 and a large soda which cost $3.25. They divide the cost evenl

romanna [79]

Add the prices together
Then divide by 3.

*6.25 + 3.25 = 9.50/3 = 2 of them pay 3.16 while the other pays 3.17.

7 0

3 years ago

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Danny used the following table to write his equation :

Anna71 [15]

The answer to the problem is 36

6 0

3 years ago