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Temka [501]
3 years ago
15

The table below represents a linear function f(x) and the equation represents a function g(x):

Mathematics
1 answer:
Elza [17]3 years ago
6 0

Answer:

(a) The slope of f(x) is greater than the slope of g(x)

(b) f(x) has a greater y intercept

Step-by-step explanation:

Given

\begin{array}{cc}x & {f(x)} & -1&-9&0&-1&1&7 \ \end{array}

g(x) = 3x - 2

Solving (a): Compare the slopes

The slope (m) of f(x) is calculated as;

m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}

This gives:

m = \frac{f(0) - f(1)}{0 - 1}

m = \frac{f(0) - f(1)}{- 1}

Substitute values for f(0) and f(1)

m = \frac{-1 - 7}{- 1}

m = \frac{-8}{- 1}

m = 8

The slope of g(x) can be gotten using the following comparison

g(x) = mx + b

m \to slope

So:

g(x) = 3x -2

m = 3

m_{f(x)} > m_{g(x)}

Solving (b): Compare the y intercept

y intercept is when x = 0

From the table of f(x)

f(0) = -1

From the equation of g(x)

g(x) = 3x -2

g(0) = 3*0-2

g(0) =-2

<em></em>f(0) > g(0)<em></em>

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Answer: The cost of 1 bottle of juice is $0.33 or 33 cents.

Step-by-step explanation: Divide the total cost by the amount of bottles of juice to find how much each bottle costs.

\frac{3.96}{12} = 0.33

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If f(x)=4x^2+1 and g(x)=x^2-5 find(f+g)(x)
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Answer:

\large\boxed{(f+g)(x)=5x^2+6}

Step-by-step explanation:

(f+g)(x)=f(x)+g(x)\\\\f(x)=4x^2+1,\ g(x)=x^2-5\\\\\text{Substitute:}\\\\(f+g)(x)=(4x^2+1)+(x^2-5)\\\\=4x^2+1+x^2-5\qquad\text{combine like terms}\\\\=(4x^2+x^2)+(1+5)\\\\=5x^2+6

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3 years ago
The graph shows the distance a car traveled, y, in x hours:
meriva

Answer:

The correct answer is 30

Step-by-step explanation:

Given: The x-axis represents the time in hours and the y-axis represents the distance in miles.

The line passes through the points (2,60) and (4,120)

To find: The rise-over-run value for the relationship in the graph.

\begin{aligned}m &=\frac{R i s e}{R u n} \\&=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\&=\frac{120-60}{4-2} \\&=\frac{60}{2} \\&=30\end{aligned}

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A small radio transmitter broadcasts in a 53 mile radius. If you drive along a straight line from a city 70 miles north of the t
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Answer:

29% of the drive

Step-by-step explanation:

The plot of the problem is:

Transmitter at origin (0,0)  

City to the north at (0,70)

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The path from city to city is a line with slope:

m = (-70)/74 = -35/37

and y-intercept at y = 70, so the equation is y = (-35/37)*x + 70.

The transmitter reach the area enclosed by the next circle:

x^2 + y^2 = 53^2

See the picture attached

The intersection is gotten from the picture or solving:

x^2 + [(-35/37)*x + 70]^2 = 53^2

the points approximately are: (24.1, 47.2) and (45.8, 26.7)

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4 0
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First, she needs to find her resting heart rate by counting her pulse for one minute immediately after she wakes up for 5 days i
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Answer:

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She finds her average resting heart rate to be 62 after  5 days.

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If the last day was 58 and all the other days were the same.

Let x be her pulse on the other days,

Then,

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Her pulse on all the other days is 63.

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