Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur. f (x )equals8 x minus 5 (A) [0,4] (B) [negative 4 comma 3 ]

Answers

Answer 1

Answer:

Answer:

a. Maximum= 27, minimum= -5

b. Maximum= 19, minimum=-37

Step-by-step explanation:

We have the function $f(x)=8x-5$ . Since the function correspond to a line, then the maximum and minimum values of the function over an interval are in the endpoints of the interval.

Observe that if the line has negative slope then the minimum value is in the right endpoint. If the line has positive slope the minimum value is in the left endpoint of the interval.

The function f(x) has slope m=8. Then

a. the minimum value of f(x) in the interval [0,4] is reach when x=0, and the minimum is $f(0)=8*0-5=-5$ and the maximum is $f(4)=8(4)-5=32-5=27$

b. the minimum value of f(x) in the interval [-4,,3] is reach when x=-4, and the minimum is $f(-4)=8(-4)-5=-32-5=-37$ and the maximum is $f(3)=8(3)-5=24-5=19$

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What will the time be after 1 hour 5 minutes from 8:15 am

Answers

Answer:

9:20 am

Step-by-step explanation:

Add 1 hour

8:15 to 9:15

Add 5 minutes

9:15 to 9:20

Answer:

9:20 am

Step-by-step explanation:

So, lets go over two things.

Minutes and hours.

Minutes changes the second number.

You know how when a number goes from 9 to 10 how the ones place is set to 0, and the tens place goes up? Its the same with time, only when the number goes from 59 to 60, the hour goes up.

Hours changes the hours place, and when it hits 12, it resets to 1, and the words am go to pm, or pm goes to am.

In this case. we are moving the minutes place up by 5:

15+5=20

So the minutes place is 20, and does not change the hours place since it is below 60.

Next we have a increase in hours by 2:

8+1=9

So the hours place is 9, and does not reset or change the pm/am since its below 12.

Answer:

9:20am

Hope thias helps!

Ruben bought 666 comic books for \$21$21dollar sign, 21. Each comic book was the same price. What was the cost for 111 comic books?

Answers

Answer:

Each comic book is $3.30

Step-by-step explanation:

$21 divided by 6= $3.50

Answer:

Each comic book is $3.30

Step-by-step explanation:

$21 divided by 6= $3.50

Verify the identity Cotx/tanx+cotx = 1-sin^2x

Answers

$\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \n\n\n tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)} \qquad \qquad cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}\n\n -------------------------------\n\n \cfrac{cot(x)}{tan(x)+cot(x)}=1-sin^2(x) \n\n\n \textit{doing the left-side}\implies \cfrac{(cos(x))/(sin(x))}{(sin(x))/(cos(x))+(cos(x))/(sin(x))}\implies \cfrac{(cos(x))/(sin(x))}{(sin^2(x)+cos^2(x))/(cos(x)sin(x))}$

$\bf \cfrac{(cos(x))/(sin(x))}{(1)/(cos(x)sin(x))}\implies \cfrac{cos(x)}{\underline{sin(x)}}\cdot \cfrac{cos(x)\underline{sin(x)}}{1}\implies cos^2(x)\implies 1-sin^2(x)$

Let f be the linear function (in blue) and let g be the parabolic function (in red) below. I have already tried 0,2,-1 and none of them work for the g o g(2) one and I'm soo confused. Please help!

Answers

Based on the graph of the linear function (in blue) and parabolic function (in red), the corresponding output values include the following;

(f∘g)(2) = -1.

(g∘f)(2) = 1.

(f∘f)(2) = 0.

(g∘g)(2)= 4.

(f + g)(4) = 7.

(f/g)(2) = DNE.

What is a function?

In Mathematics and Geometry, a function composition is an operation (∘) that combines two functions f(x) and g(x), in order to produce a composite function h(x) = (g∘f)(x), such that h(x) = g.

In this exercise, we would determine the corresponding output values for each of the composite functions by using the substitution method as follows;

(f∘g)(2) = f(g(2))

f(g(2)) = f(0)

f(0) = -1.

Part 2.

(g∘f)(2) = g(f(2))

g(f(2)) = g(1)

g(1) = 1.

Part 3.

(f∘f)(2) = f(f(2))

f(f(2)) = f(1)

f(1) = 0.

Part 4.

(g∘g)(2) = g(g(2))

g(g(2)) = g(0)

g(0) = 4.

Part 5.

(f + g)(4) = f(4) + g(4)

f(4) + g(4) = 3 + 4

f(4) + g(4) = 7.

Part 6.

(f/g)(2) = f(2)/g(2)

f(2)/g(2) = 1/0

f(2)/g(2) = DNE.

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Step-by-step explanation:

g(g(2))

= g(0)

= 4

4. Find the slope and y-intercept.
y= 1/5 x + 4

Answers

Answer:

The slope is $\bold{(1)/(5)}$ and the y-intercept is $\bold{4}$ .

Step-by-step explanation:

We are given an equation in slope-intercept form (y = mx + b).

In this equation, we can define the following variables:

m = slope
b = y-intercept

The slope in an equation and of a line is the rise over run of a line. The numerator of the fraction will be how many y-coordinates the line will ascend or descend (depending on the sign). The denominator will signify how many x-coordinates the line will move to the left or the right.

The y-intercept is the coordinate at which the line crosses the y-axis. The value of x is 0 and the coordinate can be positive or negative.

Therefore, by looking at our equation, we can see that $(1)/(5)$ is the slope, and 4 is the y-intercept.

According to the graph, what is the value of the constant in the equationbelow?
25+
(3.25)
Height
Constant
Width
20 +
15
(5, 15)
Height
10
(15,5)
(25,3)
10
15
20
25
Width
O A. 5
B. 100
O c. 10
O D. 75

Answers

The value of the constant in the equation below is 100. So, the correct option is (C).

What is Height?

Height also known as elevation is defined as the vertical distance either between the top and bottom of something or between a base and something above it. It refers to something measured vertically high or low.

Height is body measurement usually measured in feet (feet) + inch (in) and centimeter (cm) where these are length measurements, so the SI unit will be meter.

Height equation: H= C/W

where, H is the height, C is the constant and W is the width.

We choose a point given in the graphic, I will choose (4,25), which means that when W=4 and H=25 . We use this to find the constant. So

25=C/3

C= 100

Thus, the value of the constant in the equation below is 100. So, the correct option is (C).

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Answer:The Answer is C

Step-by-step explanation:

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