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3 years ago

10

Every jump a game piece makes measures 8/9 . The piece starts at point A = 7 and jumps to the right. As soon as the piece jumps

over B = 24, it switches direction and jumps to the left. The piece then stops at point A. How many jumps did the game piece take?

1 answer:

frutty [35]3 years ago

4 0

Answer:

There will be a total 40 jumps.

Step-by-step explanation:

Every jump a game piece makes measures $\frac{8}{9} = 0.889$ .

Now, the piece starts at point A = 7 and jumps to the right.

So, the piece will jump over B = 24 after $\frac{24 - 7}{0.889} = 19.122$ ≈ 20 complete jumps.

Then it switches direction to the left and the piece then stops at point A.

So, there will be a total (20 + 20) = 40 jumps. (Answer)

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Write the equation of the parabola that has its x-intercepts at (1+<img src="https://tex.z-dn.net/?f=%5Csqrt%7B5%7D" id="TexForm

VladimirAG [237]

Answer:

$y=2x^2-4x-8$

Step-by-step explanation:

<u>Factored form of a parabola</u>

$y=a(x-p)(x-q)$

where:

p and q are the x-intercepts.
a is some constant.

Given x-intercepts:

(1+√5, 0)
(1-√5, 0)

Therefore:

$\implies y=a(x-(1+\sqrt{5}))(x-(1-\sqrt{5}))$

$\implies y=a(x-1-\sqrt{5})(x-1+\sqrt{5})$

To find a, substitute the given point (4, 8) into the equation and solve for a:

$\implies a(4-1-\sqrt{5})(4-1+\sqrt{5})=8$

$\implies a(3-\sqrt{5})(3+\sqrt{5})=8$

$\implies4a=8$

$\implies a=2$

Therefore, the equation of the parabola in factored form is:

$\implies y=2(x-1-\sqrt{5})(x-1+\sqrt{5})$

Expand so that the equation is in standard form:

$\implies y=2(x^2-x+\sqrt{5}x-x+1-\sqrt{5}-\sqrt{5}x+\sqrt{5}-5)$

$\implies y=2(x^2-x-x+\sqrt{5}x-\sqrt{5}x+\sqrt{5}-\sqrt{5}+1-5)$

$\implies y=2(x^2-2x-4)$

$\implies y=2x^2-4x-8$

6 0

1 year ago

Connie has saved up $15 to purchase a new CD from the local store. The sales tax in her county is 5% of the sticker price. Write

Sholpan [36]

Answer:

$x + 0.05x = 15$ , solution is $14.29

Step-by-step explanation:

We can create an equation for this scenario to try and solve it.

Assuming the cost of the CD is x, it’s sale tax will be 0.05x (as that is 5% of x, 0.05.)

We can write the equation in two ways:

$x + 0.05x = 15$ or $1.05x = 15$ .

Assuming we take the second one (easier to work with), we can divide both sides by 1.05. The equation simplifies to x = 14.289... which rounds to x = 14.29.

Therefore, the equation is $x + 0.05x = 15$ and the solution is $14.29.

Hope this helped!

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4 years ago

Read 2 more answers

2. Three points of a parallelogram are (4, 3), (-4, 3), and (2, 3). Find the coordinates of the 4th point to complete the parall

antiseptic1488 [7]

Parallelograms have equal and parallel opposite sides

<em>The coordinates of the 4th point is (-2,3)</em>

Let the parallelogram be ABCD, such that:

$A = (4,3)$

$B =(-4,3)$

$C = (2,3)$

A and B have the same y-coordinates, while their x-coordinates are additive inverse

This means that:

The y-coordinates of point C and point D will be the same, while their x-coordinates will be additive inverse.

<u>For point C</u>

We have:

$x = 2$

$y = 3$

<u>For point D</u>

The coordinates would be:

$x =- 2$

$y = 3$

Hence, the coordinates of D is (-2,3)

Read more about parallelograms at:

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2 years ago

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anyanavicka [17]

Measurement of one angle and length of one side I think

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4 years ago

Use the quadratic formula to solve the equation x2+7x

monitta

The solution of the equation x2+7x is 0, -7 using the quadratic formula.

Step-by-step explanation:

x2 + 7x = 0

-b ± √ b2 - 4(ac)/ 2a

substitution,

a = 1, b = 7, c = 0

= -7 ± √(7)2 - 4(1 x 0) / 2 x 1

= - 7 ± 7 / 2

x = 0 , -7

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4 years ago