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adell [148]
3 years ago
6

hala can ride her bike 7 1/2 miles in an hour, How far will she ride in 3 hours? how fat will she ride in 1/3 of an hour?

Mathematics
1 answer:
harkovskaia [24]3 years ago
5 0
In 3 hours she will ride 22 1/2 miles. And in 1/3 of an hour she will ride 2 1/2 miles. 

Explanation: Since you already know how much she can ride in one hour, but you need to know three hours, you multiply how many miles she can bike in one hour by three. 
7 1/2 x 3 = 15/2 x 1/3 = 45/2 = 22 1/2

Then to find how much she can bike in 1/3 of an hour, you multiply 7 1/2, the amount of one hour, by 1/3, the amount of time. 
7 1/2 x 1/3 = 15/2 x 1/3 = 15/6= 2 3/6 = 2 1/2 

(And in case you don't know how to multiply fractions, whole, and mixed numbers then here: make all numbers into fractions [both proper and improper], and then just multiply across or cross cancel if possible. Simplify if necessary.)


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How can Kendra determine if the function is actually linear?
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Answer:

D. She can check to see if the rate of change between the first two ordered pairs is the same as the rate of change between the first and last ordered pairs.

Step-by-step explanation:

Find the rate of change between first two ordered pairs and the second two ordered pairs:

1. Points (2,4) and (3,9). Rate of change:

\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{9-4}{3-2}=\dfrac{5}{1}=5

2. Points (3,9) and (4,16). Rate of change:

\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{16-9}{4-3}=\dfrac{7}{1}=7

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13
zepelin [54]

Answer:

The required equation is: \mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}

Step-by-step explanation:

We need to find equation from the table given

x     f(x)

3     -5

7     -2

11     1

15    4

We can write equation in the form of y=mx+b

where m is slope and b is y-intercept.

Finding Slope

We can used the slope formula to find slope: Slope=\frac{y_2-y_1}{x_2-x_1}

From the table we have: x_1=3, y_1=-5, x_2=7, y_2=-2

Putting values and finding slope

Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-2-(-5)}{7-3} \\Slope=\frac{-2+5}{7-3}\\Slope=\frac{3}{4}

So, we get slope m=\frac{3}{4}

Now, finding y-intercept

Using the slope m=\frac{3}{4} and point (3,-5) we can find y-intercept

y=mx+b\\-5=\frac{3}{4}(3)+b\\-5=\frac{9}{4}+b\\b=-5-\frac{9}{4}\\b=\frac{-5*4-9}{4}\\b=\frac{-20-9}{4}\\b=\frac{-29}{4}

The y-intercept is b=\frac{-29}{4}

So, the equation having slope m=\frac{3}{4} and y-intercept b=\frac{-29}{4} will be:

y=mx+b\\y=\frac{3}{4}x-\frac{29}{4}

The required equation is: \mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}

6 0
2 years ago
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