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Viktor [21]
4 years ago
12

If x represents time, the average rate of change of the function f(x) in the first three seconds is ___.

Mathematics
2 answers:
DaniilM [7]4 years ago
7 0
<h2>Answer</h2>

If x represents time, the average rate of change of the function f(x) in the first three seconds is -50.

<h2>Explanation</h2>

The average rate of change of a linear function is the slope of the liner function. To find the slope of our linear function, we are using the slope formula:

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

where

m is the slope of the line

(x_{1},y_{1}) are the coordinates of the first point on the line

(x_{2},y_{2}) are the coordinates of the second point

From our graph we can get the points (0, 150) and (3, 0), so x_{1}=0, y_{1}=150, x_{2}=3, and y_{2}=0. Let's replace the values in our formula to find the slope of our linear function:

m=\frac{0-150}{3-0}

m=\frac{-150}{3}

m=-50

Since the average of change a linear function is equal to its slope, the average rate of change of the function in the first three seconds is -50

Tresset [83]4 years ago
3 0
The average rate of change is -5/4
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(b) Factorise fully 2 a²b + 6ab2
den301095 [7]

Answer:

<h2>2ab(a+3b)</h2>

Step-by-step explanation:

2 {a}^{2} b + 6a {b}^{2}

Factor out common term : 2ab

2 {a}^{2}b \div 2a = a \\ 6a {b}^{2}  \div 2ab = 3b  \\ 2ab(a + 3b)

6 0
2 years ago
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Kelly has a rock garden with a length of 6 feet. She constructs a scale model of the rock garden using the
Annette [7]

Answer:

  • (a) 3 inches

  • (b)  Her scale model drawing will not fit on a piece of paper that is 8.5 inches by 7 inches because the dimensions are not proportional to the scale.

Explanation:

(a) What is the length of the garden in her model? Show your work, including your proportion

<u>1. Scale</u>:

  • model length / real length = 1 inch / 2 feet

<u>2. Proportion</u>:

Naming x the model length:

  • 1 inch / 2 feet = x / 6 feet

Cross multiply:

  • 1 inch × 6 feet = 2 feet × x

Divide both sides by x:

  • x = 1 inch × 6 feet / 2 feet = 3 inch.

Answer: 3 inches

(b) If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?​

Both the width and the length must use the same scale, thus the corresponding sides of the scale model and the drawing must be proportional.

In the model the ratio of the length to the width is 3 inch / 5 inch

In the paper the ratio of the length to the width is 8.5 inch / 7 inch

Hence, you can see that in the model the length (mumerator of the fraction) is less than the width (denominator) while in the paper it is the opposite. Bieng the two ratios different, they are not proportional, and you conclude that her scale model drawing will not fit on a piece of paper that is 8.5 inches by 7 inches.

8 0
3 years ago
PLEASE HELP I WILL MARK YOU AS BRAINLEST
denpristay [2]

Answer:

(i) Five number summary: Minimum value = 1, Q_1=18,Median=18.5, Q_3=20.5, Maximum value = 26.

(ii) IQR = 2.5, upper fence = 24.25 and lower fence = 14.25.

(iii) 26 is an outlier of the data.

Step-by-step explanation:

The given data set is

19, 18, 23, 18, 18, 26, 19, 16, 20, 18, 17, 21

Arrange the data set in ascending order.

16, 17, 18, 18, 18, 18, 19, 19, 20, 21, 23, 26

Divide the data set in 4 equal parts.

(16, 17, 18), (18, 18, 18), (19, 19, 20), (21, 23, 26)

Minimum value = 16

Q_1=\frac{18+18}{2}=18

Median=Q_2=\frac{18+19}{2}=18.5

Q_3=\frac{20+21}{2}=20.5

Maximum value = 26

The inter quartile range (IQR) of the data is

IQR=Q_3-Q_1=20.5-18=2.5

Upper fence :

Q_3+1.5(IQR)=20.5+1.5(2.5)=24.25

Lower fence :

Q_1-1.5(IQR)=18-1.5(2.5)=14.25

If the any element of the data set lies out side the upper fence and lower fence, then it is called an outlier.

26 ∉ [14.25, 24.25]

Therefore, 26 is an outlier of the data.

4 0
3 years ago
Read 2 more answers
Can you make a triangle with angles 45 degrees, 90 degrees, and 35 degrees?
nata0808 [166]

Answer:

No

Step-by-step explanation:

To make a triangle the angles have to add up to 180 degrees so 90+45+35=170 degrees not 180.

7 0
2 years ago
3x2 - 2x = 0<br> Factorise and solve
malfutka [58]

 Solve  :    3x-2 = 0  

Add  2  to both sides of the equation :  

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Divide both sides of the equation by 3:

                    x = 2/3 = 0.667

Two solutions were found :

x = 2/3 = 0.667

x = 0

hope this helped

6 0
3 years ago
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