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3 years ago

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Skylar and Rodrigo each recorded how far they traveled while skateboarding. Skylar traveled 65 feet in 5 seconds and Rodrigo tra

veled 108 feet in 8 seconds. How much farther did Rodrigo travel per second than Skylar?

1 answer:

ICE Princess25 [194]3 years ago

6 0

The answer to your question is 13.5

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PLEASE HELP ASAP

Crank

Option D: $f(x)=-2(x+2)(x-4)$ is the function

Explanation:

Let the general form of quadratic equation be $y=a x^{2}+b x+c$

The function passes through the intercepts $(-2,0)$ and $(4,0)$ and also passes though the point $(-1,10)$

Substituting the points $(-2,0)$ , $(4,0)$ and $(-1,10)$ in the equation $y=a x^{2}+b x+c$ , we get,

$4a -2b+c=0$ -----------(1)

$16a +4b+c=0$ ----------(2)

$a-b+c=10$ -----------(3)

Subtracting (1) and (2), we get,

$\ \ 4a -2b+c=0\\ 16a +4b+c=0\\\---------\\ \ \ -12a-6b=0$ -----------(4)

Subtracting (2) and (3), we get,

$16a +4b+c=0\\\ \ a \ \ - \ \ b \ +c=10\\---------\\15a+5b=-10$ ------------(5)

Multiplying equation (4) by 5 and equation (5) by 4, to cancel the term b when adding, we get,

$-60a-30b=0\\\ 90a+30b=-60\\--------\\30a=-60\\\ \ a=-2$

Thus, the value of a is $a=-2$

Substituting $a=-2$ in equation (4), we get,

$\begin{aligned}-12 a+6 b &=0 \\-12(-2)-6 b &=0 \\ 24-6 b &=0 \\ 24 &=6 b \\ 4 &=b \end{aligned}$

Thus, the value of b is $b=4$

Now, substituting the value of a and b in equation (1), we have,

$\begin{aligned} 4 a-2 b+c &=0 \\ 4(-2)-2(4)+c &=0 \\-8-8+c &=0 \\ c &=16 \end{aligned}$

Thus, the value of c is $c=16$

Now, substituting the value of a,b and c in the general formula $y=a x^{2}+b x+c$ , we get,

$y=-2x^{2} +4x+16$

Taking out the common term as -2 we get,

$y=-2(x^{2} -2x-8)$

Factoring , we get,

$y=-2(x+2)(x-4)$

Thus, the function is $f(x)=-2(x+2)(x-4)$

7 0

3 years ago

Jameson is seeking a loan with a simple interest rate of 3% per year. If he wants to borrow $8000, then how much will he be char

Thepotemich [5.8K]

Answer:

$960

Step-by-step explanation:

You are going to want to use the simple interest formula for this. The one below is modified for solving the interest earned.

$I=Prt$

<em>I = interest amount </em>

<em>P = principal amount </em>

<em>r = interest rate (decimal form) </em>

<em>t = time </em>

The first step is to change 3% into a decimal:

3% -> $\frac{3}{100}$ -> 0.03

Now, lets plug in the values into the equation:

$I=8,000(0.03)(4)$

$I=960$

Jameson will be charged $960 of interest after 4 years.

8 0

3 years ago

A local fast food restaurant takes in $9000 in a 4 hour period, where the amount taken in varies directly with the number of hou

Zepler [3.9K]

As per the direct variation formula, it take 11 hours : 6 minutes : 36 seconds to earn $25,000 for the restaurant.

Direct variation:

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other.

Direct variation equation: y = kx

Given,

A local fast food restaurant takes in $9000 in a 4 hours period. Write a direct variation equation for the relationship income and number of hours.

Here we need to estimate how many hours it would take the restaurant to earn $25,000.

a) Let us consider income (I) directly varies to number of hours (h) where k is the constant of variation.

I = kh ⇒ Direct variation equation

Solve for k:

9,000 = (k)(4)

k = 9,000/4

k = 2,250

b) When income (I) = 25,000, find the number of hours:

I = kh

25,000 = (2,250) (h)

h = 25,000/2,250

h = 11.11

It will take approximately 11 hours : 6 minutes : 36 seconds for the restaurant to earn $25,000.

To know more about Direct variation here.

brainly.com/question/14254277

#SPJ1

4 0

1 year ago

Magan decides to research the relationship between the length in inches and the

GrogVix [38]

Based on the line of best fit, the length of this catfish can be predicted to be 38 inches.

<u>Given the following data:</u>

Weight of catfish, x = 40 pounds.

<h3>What is a line of best fit?</h3>

A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.

From the graph of the data, we have the following linear equation:

$y=\frac{1}{2} x+18$

Substituting the value of x, we have:

$y=(\frac{1}{2} \times 40 )+18\\\\y=20+18$

y = 38 inches.

Read more on scatterplot here: brainly.com/question/6592115

3 0

2 years ago

Help me with 20 please

Murrr4er [49]

24%------360(24% is 360m)

100%-------x (100% is x)

to find x we have too cross multiply

x=100*360/ 24= 1500

hope this helps

8 0

3 years ago