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3241004551 [841]

2 years ago

10

Which of the following statements is true?

1 answer:

Schach [20]2 years ago

8 0

Answer:

Over the interval [0, 2], the average rate of change of f is greater than that of g. The y-intercept of f is the same as the y-intercept of g.

Step-by-step explanation:

The function i.e mentioned in the question is

$f(x)=5^x-4$

Now Placing x = 0, to compute the y-intercept

$f(0)=5^(0)-4=1-4=-3$

f(x) y-intercept is -3

As we can see in the given graph the graph of g(x) intersects the y-axis at -3

Therefore the y-intercept of g(x) is -3.

Hence, both functions with respect to the y-intercepts i.e f(x) and g(x) would remain the same

Now At x=2,

So, the value of the function is

$f(2)=5^2-4=25-4=21$

The average rate of change of f over the interval [0,2] is

$m=\frac{f(2)-f(0)}{2-0}$

$m=\frac{21-(-3)}{2}=12$

From the mentioned graph as we can see that the graph of g(x) is crossing through the points (0,-3) and (2,12).

The average rate of change of g over the interval [0,2] is

$m=\frac{g(2)-g(0)}{2-0}$

$m=\frac{12-(-3)}{2}=7.5$

Therefore this is the correct answer but the same is not provided in the given options

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the length of a rectangle is five feet less than its width. If the area of the rectangle is 84 square feet, find its dimensions

KIM [24]

Let
x---------> the length of the rectangle
y--------> the width of the rectangle

we know that
A=84 ft²
[area of rectangle]=x*y-----> 84=x*y-----> equation 1
x=y-5------> equation 2
substitute 2 in 1
84=[y-5]*y-----> 84=y²-5y---------> y²-5y-84=0

using a graph tool-----> to resolve the second order equation
see the attached figure

the solution is
y=12
x=y-5-----> x=12-5-----> x=7

the answer is
the length of the rectangle is 7 ft
the width of the rectangle is 12 ft

6 0

3 years ago

For each pair of points below, think about the line that joins them. For which pairs is the line parallel to the y-axis? Circle

zaharov [31]

Answer:

a) Not parallel to y-axis

b) Not parallel to y-axis

c) Parallel to y-axis

Step-by-step explanation:

The best way to check whether a line passing through two points is parlle to y-axis is by plotting them on graph.

The equation of line: $(y-y_1) = \frac{y_2 - y_1}{x_2 - x_1}(x-x_1)$

a) The line joining the points (4,12) and ( 6,12) is not parallel to y-axis.

It is parallel to x-axis. Another two points that can lie on this line are : (5,12) and ( $\frac{9}{2}$ ,12).

b) The line joining the points $(\frac{3}{5}, \frac{13}{5}), (\frac{1}{5} ,\frac{8}{5})$ is not parallel to y-axis.

Equation of line: $5y - 7.5x = 5.5$

Another points that could be lie on this line are (0.6,2) and (0.25,1.475)

c) The line joining the points $(0.8, 1.9), (0.8,2.3)$ is parallel to y-axis because points have the same x-coordinate.

Another points that could be lie on this line are (0.8,2) and (0.8,2.1)

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3 years ago

The quantity a varies directly with b and c and inversely with dThe quantity d is tripledWhich of the following must be true for

EastWind [94]

Answer:

We have the next relation:

A = (b*d)/c

because we have direct variation with b and d, but inversely variation with c.

Now, if we have 3d instead of d, we have:

A' = (b*(3d))/c

now, we want A' = A. If b,c, and d are the same in both equations, we have that:

3bd/c = b*d/c

this will only be true if b or/and d are equal to 0.

If d remains unchanged, and we can play with the other two variables we have:

3b'd/c' = bd/c

3b'/c' = b/c

from this we can took that: if c' = c, then b' = b/3, and if b = b', then c' = 3c.

Of course, there are other infinitely large possible combinations that are also a solution for this problem where neither b' = b or c' = c

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2 years ago

Find the X-Intercepts of <br> y=-x^2-2x+1

bekas [8.4K]

Answer:

(1,0)

Step-by-step explanation:

we can't factor this so we'll use the quadratic formula

$\frac{-b+\sqrt{b^2-4ac} }{2a}\\\frac{-b-\sqrt{b^2-4ac} }{2a}$

(use both of them because usually there are two zeroes)

We have

$\frac{2+\sqrt{4-4}}{2}=\frac{2}{2}=1$

Therefore the x intercept is just (1,0)

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2 years ago

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faltersainse [42]

Answer:580cm

Step-by-step explanation:

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