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2 years ago

Calista runs one mile in 12 minutes, while Bethany runs one

Mathematics

1 answer:

romanna [79]2 years ago

6 0

Answer:

So, although Calista starts behind Bethany, she hopes to pass her sister

Step-by-step explanation:

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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:

Factored form of a parabola

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

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

The perimeter of the square park is 240m, then the side of the square park is _______.

Colt1911 [192]

Step-by-step explanation:

A square's perimeter consists of 4 equal sides.

Therefore side of square park = 240m/4 = 60m.

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3 years ago

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Brainliest is given to the correct answer.

Svet_ta [14]

Answer:

Step-by-step explanation:

4 0

3 years ago

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A sedan will drive ten miles north, 15 miles east, 13 miles south, 15 miles west, and 22 miles north. The sedan gets 20 miles pe

larisa [96]

You would have enough gas to go another 25 miles

3 0

3 years ago

A motor club has estimated that a 325 mile car trip will take 6 1/2 hours. What is the club assuming to be the average speed mil

In-s [12.5K]

Answer:

The average speed that the club is assuming is 50 miles per hour

Solution:

We know that Distance = Speed × Time.

Here it is given that distance is 325 miles and the time to cover 325 miles is $6_{2}^{1}$ hours which is equal to $\frac{13}{2}$ hours.

Now to find the average speed mile per hour we use the formula

$\begin{aligned} \text { Speed } &=\frac{\text { Distance }}{\text { time }} \\ &=\frac{325}{\frac{13}{2}} \\ &=\frac{325 \times 2}{13} \end{aligned}$

By cancelling 325 by 13 we get 25

= 25 × 2

= 50 miles per hour

Thus the average speed that the club is assuming is 50 miles per hour.

3 0

3 years ago