Mathematics High School

Given f(x)=17-x^2, what is the average rate of change in f(x) over the interval [1, 5]?

Answers

Answer 1

Answer:A

Step-by-step explanation:

(f(5) - f(1))/(5 - 1) =

(17 - 5^2 - (17 - 1^2))/4 =

(17 - 25 - 17 + 1)/4 = 6

Related Questions

Find the discriminant of the following equation.
4x2 + 16x + 16 = 0 ...?

Answers

Discriminant = b^2 - 4ac

a = 4

b = 16

c = 16

16^2 - 4(4 x 16)

256 - (4x64)

256 - 256 = 0

Therefore it only has one root

Write the equation of a line in slope-intercept form from the graph below.
Write the equation of a line in slope-intercept form from the graph below.

Answers

y=x

Slope of 1, y-intercept of (0,0)

y=1x+0...same as the initial answer

Answer: Y=x or y=1x

Step-by-step explanation:

Slope of 1 y-intercept of (0,0)

What Is The Slope Of The Line In The Graph Shown Below?

-2
-1
1
2

Answers

1-3/1-0 = -2/1 SO, the answer is -2 :) by using y2-y1/X2-X1

a rectangeler field is twice as long as it is wide a golf cart travrling at 12 miles per hour takes 7.5 minutes to travel the perimeter of the field what is the length (in miles) of the field

Answers

25 meters of 34 feet in the air of the miles so its 27 miles

Help please =]

Solve system of equations using any method 2x-6y=8 and 2x-6y=3

Answers

Let z be any number (like x would be)

if we set z equal to 2x-6y, then we get z = 2x-6y

The system

2x-6y = 8
2x-6 = 3

turns into this new system

z = 8
z = 3

but z is a single number. It can't be both 8 and 3 at the same time. So there are no solutions

The answer is no solution. If you use elimination, by subtracting the second equation from the first, you come out with 0=5, which is a false statement. Therefore, there is no solution.

How are rigid transformations used to justify the SAS congruence theorem?

Answers

(Refer to the diagram in the attached photo.)

In this diagram there is defined two Sides and an Angle in between (SAS).

Notice how there are two loose endpoints in the diagram. A single line segment can be drawn connecting the endpoints, forming a unique triangle.

If the original diagram is transformed, the dimensions and angles formed by the third line segment remains the same relative to the first two.

Therefore, if two triangles have the same SAS configuration, then they are congruent.

The method in which rigid transformations used to justify the SAS congruence theorem is given.

What is rigid transformation?

A rigid transformation (also called an isometry) is a transformation of the plane that preserves length. In a rigid transformation the pre-image and image are congruent (have the same shape and sizes).

We are given that;

Theorem is SAS

Now,

The SAS congruence theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. To prove this theorem using rigid transformations, we can start with two distinct triangles that have a pair of corresponding congruent sides and a corresponding congruent included angle23. Then we can use a translation to move one triangle so that its congruent side matches the other triangle’s congruent side. Next, we can use a rotation to align the congruent angles of both triangles. Finally, we can use another translation to move the second congruent side of one triangle to match the second congruent side of the other triangle. By doing these rigid transformations, we have shown that one triangle can be mapped onto the other triangle exactly, which means they are congruent

Therefore, by the transformations the answer will be given above.

Learn more about rigid transformations;

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Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?

a. v +4 = 8 – v
b. v +4 = 8
c. 4 + v = 8 – v
d. 2v + 4 = 8

Answers

The first step is to group like terms on each side of the equation. This would give you (v + v) + 4 = 8. There is no point in writing v + v as such, so 2v + 4 = 8 would be better. This is equation d.

d. 2v + 4 = 8.

Answer:

The resulting equation after the first step is 2v+4=8

d is the correct option

Step-by-step explanation:

We have been given the equation v + 4 + v = 8. In order to solve it for v, we'' perform the below mentioned steps.

Add the like terms in the left hand sideSubtract 4 to both sides of the equationFinally divide both sides by 2

Hence, in the first step, we can group the like terms and combine. In the left hand side v and v are like terms and hence, we can add them

On adding v and v we get 2v

Thus, we have

[tex]v+v+4=8\\2v+4=8[/tex]

Thus, the resulting equation after the first step is 2v+4=8

f(x)=2x*e^2x. find lim of f(x) as x--> - infinity and +infinity ...?

Answers

I am assuming it is f(x)=2x e^2x
2x times e raised to the 2x power, and not 2 times e raised to the 2x**

as it approaches infinity, your f(x) --> infinity
we can see by inspection, as 2x will approach inf, and e^(2x) will approach infinity even faster.
inf x inf = inf

as it approaches neg infinity, your f(x) --> 0
we can see by inspection, as 2x will approach neg inf, and e^(2x) will approach zero.
- inf x 0 = - 0

The minimum(or maximum) is given when the derivative = 0
Using the product rule,
f ' (x) = 2e^(2x) + 4x e(2x)
f ' (x) = 2e^(2x) ( 1 + 2x )
We find the roots
2e^(2x) will never equal 0
1 + 2x = 0, x = -1/2

The minimum value will be when x = -0.5

in the decimal number .98703, the 0 holds what place value

Answers

Answer:

it is in the 10 thousansth place.

Step-by-step explanation:

.98703

9=10nth place

8=100th place

7=thousandth place

0=ten thousandth place

3=hundred thousandth place

I hope this helps.

What is the common ratio for the geometric sequence?

54, 36, 24, 16...

Answers

Geometric ration, r = 36/54 or 24/36 which is equal to 2/3

So, your final answer is 2/3

Hope this helps!

Answer:

Here is the answer and proof :)

Step-by-step explanation:

Determine the indicated side length of the golden rectangle. round your answer to the nearest hundreth....
(Picture below)....
....a. 4.85 ... b. 4.94 ... c. 5.26 ... d. 3.09

Answers

I think its d. Because it is to the nearest thousands. And you cannot find the long sides of the rectangle,because you need another one info. about the number of the long sides or the perimeter or the area. Im happy if i helped you

Answer:

a. 4.85

Step-by-step explanation:

im right

? = a+b

a = 3

(3+b)/3=3/b

b= -4.85 or 1.85

it cant be negive.

so ? = 3+1.85 = 4.85

125, 0.12, 0.1 listed to least to greatest

Answers

0.1 , 0.12 , 125

hope this helps you

My math homwork is asking me for the word form and the expanded form for 3.4 and 2.51,and i don't understand this. we just started it today and she my teacher gave us 3 pages of the math.

Answers

3.4:
the word form would be three and four tenths
the expanded form would be :
3.0 = 3
0.4 = .4
2.51:
the word form would be two and fifty one hundredths
the expanded form would be 2.00 + 0.50 + 0.01

hope this helps you

The complement of an acute angle is always

Answers

it is always an acute angle, even if the angle was the minimum 1 degree the complement is still 89 degrees which is still acute

1000 millimeters equals what =

Answers

I don't know what you want 1000 milliliters to be equivalent to so ill give u a small list. Hope this helps.

1000 millimeters equals:
0.001 kilometers
1 meter
100 centimeters
1e+6 Micrometers
1e+9 Nanometers
0.000621371 Miles
1.09361 Yard
3.28084 Feet
39.3701 Inches
0.0005399570950324 Nautical Miles

sin^2(75)-cos^2(75)=?

Answers

There are 2 ways of solving this:
1: puting numbers in calculator and get answer
2: try to simplify this and than calculate.

We will do second way.

there is trigonometric formula: cos2α = cos^2(α) - sin^2(α)

if we take "-" in front of our expression:
-(cos^2(75) - sin^2(75)) = -cos(2*75) = -cos(150) = -√3/2

answer is -√3/2

how do i solve z+18=y

Answers

Simplifying z + 18 = y Reorder the terms: 18 + z = y Solving 18 + z = y Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + z = -18 + y Combine like terms: 18 + -18 = 0 0 + z = -18 + y z = -18 + y Simplifying z = -18 + y

in DEF DE=17 m angle =32 Find DF nearest tenth

Answers

Since we are asked to find DF, and we are given an angle and the side opposite to it, we can use the sine function to find DF.
let x be the length of side DF.

sin(32)= 17/x
x= 17 / sin(32)
x= 32.08

approximately 32.1

Answer:

(A) 32.1

Step-by-step explanation:

It is given that in ΔDEF, DE=17 and m∠F=32, thus

Using the trigonometry, we have

[tex]sinx=\frac{Perpendicular}{Hypotenuse}=\frac{DE}{DF}[/tex]

⇒[tex]sin32^{\circ}=\frac{17}{DF}[/tex]

⇒[tex]DF=\frac{17}{sin32^{\circ}}[/tex]

⇒[tex]DF=\frac{17}{0.529}[/tex]

⇒[tex]DF=32.1[/tex]

Therefore, the value of DF is 32.1.

Hence option A is correct.

How is the graph of Y=√X) -5 translated from the graph of √X ?

shifted 5 units right

shifted 5 units down

shifted 5 units left

shifted 5 units up

Answers

Shifted 5 units to the left.

For spring break this year your family decided to visit Michigan, but it snows the first weekend you are there. You decide to make a snowman. If the bottom ball is 3 feet across, the middle ball is 2 feet across, and the top is 1 foot across, how much snow is needed to build the whole snowman? Round your answer to the nearest cubic foot.
A)
19 cubic feet of snow
B)
31 cubic feet of snow
C)
511 cubic feet of snow
D)
1022 cubic feet of snow ...?

Answers

Answer:

Step-by-step explanation:

Final answer:

To find the amount of snow needed to build the snowman, we need to calculate the volume of each ball and then add them together. The total volume is 18.84 cubic feet, rounded to 19 cubic feet.So,Option A.19 cubic feet of snow is correct.

Explanation:

To find how much snow is needed to build the whole snowman, we need to calculate the volume of each ball and then add them together. The volume of a sphere can be found using the formula V = (4/3) * pi * r³, where r is the radius of the sphere.

The bottom ball has a diameter of 3 feet, so the radius is 3/2 = 1.5 feet. The volume of the bottom ball is (4/3) * 3.14 * (1.5³) = 14.13 cubic feet.

The middle ball has a diameter of 2 feet, so the radius is 2/2 = 1 foot. The volume of the middle ball is (4/3) * 3.14 * (1³) = 4.19 cubic feet.

The top ball has a diameter of 1 foot, so the radius is 1/2 = 0.5 feet. The volume of the top ball is (4/3) * 3.14 * (0.5³) = 0.52 cubic feet.

The total volume of the snowman is 14.13 + 4.19 + 0.52 = 18.84 cubic feet. Therefore, the answer is 19 cubic feet of snow.

2 1/7 into a improper fraction

Answers

it would be (2 x 7) + 1

as an improper fraction it would be 15/7

hope this helps you

It's is 15/7.
2x7=14
14+1=15
The. Put that over the original denominator

In the triangle below, determine the value of a.

Answers

51sin(47) because 51 is the hypotenuse and a is the opposite so we use sine because sine=opp/hypotenuse therefore sin(47)=a/51 then rearrange the formula to make a the subject the final answer is 37.3 to the nearest 3 significant figures

What is the product? enter your answer as a fraction, in simplified form, in the box. −1/4⋅(−6/11)?

Answers

(−1/4)⋅(−6/11)=(3/22)

yeah it would be 3/11 i just did the test

39x10^3 in standard form

Answers

it would be 3.9 x 10^4

hope this helps you

What unit of measurement would Guatemalans typically use to measure the weight of flour?

Answers

In general, Guatemalans also use the metric system, but also some traditional units of measurement (that come from Spain) and influence from US English units. Among the Guatemalan units of measurement some are based on old Spanish units. The libra, arroba, quintal and garrafón units of weight and volume. Guatemalans use also measures like spoons and cups. Therefore, when they weigh the measure of flour, they are using either the ibra, arroba, quintal and garrafón units. Hope this helps.

Guatemalans use grams to measure the weight of flour.

The tax rate on Harriet walker $80,000 vacation home is 2 mills. The property is assessed at full value. How much will Harriet Walker pay in taxes this year?

Answers

1 thousand 6 hundred

Answer:

Step-by-step explanation:

1600

If i drove 34 times over a 7 mile bridge. how many miles in all did i drive?

Answers

7 * 34 =
Miles times amount =
238 miles in total.

Hope this helped!

To figure out this answer, you need to multiply 34 by seven. This results in 238 miles in all. I hope this helps! :)

heeeelp!

Line segments with the same length are said to be __________.

Answers

parallels!!!!!!!!!!!!!!

A heart beats 8 times in 3 seconds.About how many times will a cats heart beat in 2 minutes

Answers

first figure out how many 3 seconds are in 1 minute = 20 then double = 40
then mulitpity 40x8= 240
the answer is 240 beats in 2 minutes

Rewrite 30/6 as a whole number

Answers

your answer would be 5. This is because you just divide 30 by 6, which equals 5, because 6*5=30.

Final answer:

The fraction 30/6 can be rewritten as the whole number 5 after performing the division operation 30 ÷ 6.

Explanation:

The problem asks to rewrite 30/6 as a whole number. In mathematics, this implies using the operation of division. Division is one of the four basic operations in math, along with addition, subtraction, and multiplication.

To solve this problem, you need to divide 30 by 6. Perform the division operation as follows: 30 ÷ 6. The result of this operation is 5.

Therefore, the fraction 30/6 can be rewritten as the whole number 5.

Learn more about Division here:

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