Mathematics High School

25 Select the correct answer. What is the average rate of change of f(x), represented by the graph, over the interval [-1, 2]? A. -2.5 B. -2 C. 2.5 D. 3 E. 6

Answers

Answer 1

The average rate of change of the function over the interval [-1, 2] is: C. 2.5.

How to Find the Average Rate of Change?

The average rate of change over an interval of a function is: f(b) - f(a) / b - a.

Given the interval [-1, 2]:

a = -1; f(a) = -5

b = 2; f(b) = 2.5

Average rate of change = (2.5 - (-5)) / (2 - (-1)) = 7.5/3

Average rate of change = 2.5 (option C).

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25 Select The Correct Answer. What Is The Average Rate Of Change Of F(x), Represented By The Graph, Over

Related Questions

find the volume of the rectangle prism

Answers

Answer:176

Step-by-step explanation:

8 x 2 x 11

In a lab, a substance was cooled by 6 degrees celsius each hour for 12 hours.
The total change in temperature was what?

Answers

Answer:

72 degrees 72° Celsius. It changed by 72 degrees.

Step-by-step explanation:

6 * 12 because it changed 6 degrees each hour for 12 hours

6 *

—-

Answer:

72 degree Celsius

Step-by-step explanation:

Since every hour the temperature is cooled by 6⁰C and the total time spent was 12 hour we can do a simple multiplication shown:

6 * 12 = 72

Find the volume (to the nearest cubic foot) of a cone with base radius 4 ft. and height 8 ft. a. 43 cu. ft. c. 134 cu. ft. b. 128 cu. ft. d. 402 cu. ft.

Answers

Volume is a three-dimensional scalar quantity. The volume of a cone with a base radius of 4 ft. and height of 8 ft. is 134 ft³.

What is volume?

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of a cone with a base radius of 4 ft. and height of 8 ft. can be written as,

Volume = (π/3)×(Radius)²×Height

= (π/3)×(4)²×8

= 134.0412 ft³ ≈ 134 ft³

Hence, the volume of a cone with a base radius of 4 ft. and height of 8 ft. is 134 ft³.

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use decomposition to find the area of the figure

Answers

the area of the diamond equals to the small diameter times the big diameter divided by 2 so we have:
6.12/2 => 36cm

Hello i need help ASAP i cant figure this out its just like part A
and i i have 1 hour

Answers

Number of unmarked wolves: 928 - 232 = 696

probability of next wolf being unmarked = 696 / 928 = 0.75

0.75 x 100 = 75%

Answer: 75%

Question 21 of 25
f(x) = 3x + 2
What is f(5)?
OA. 17
OB. 15
OC. 10
01

Answers

Answer:

A. 17

Step-by-step explanation:

f(x) = 3x + 2

f(5) = 3(5) + 2

= 15 +2

= 17

The answer should be A.17
;)

△ABC ~ △AMN and AM = 6, MB = 4, AN = 8, then what is the value of AC?

Answers

Answer:

AC = 13.3

Make proportional relationship:

[tex]\sf \dfrac{AB}{AC} = \dfrac{AM}{AN}[/tex]

Insert values

[tex]\rightarrow \sf \dfrac{10}{AC} = \dfrac{6}{8}[/tex]

Cross multiply

[tex]\rightarrow \sf AC = \dfrac{10(8)}{6}[/tex]

Simplify

[tex]\rightarrow \sf AC =13.3[/tex]

Frank has $500 in a savings account that earns 2% interest per year. The interest is not compounded. How much interest will Frank earn in 5 years?

Answers

Answer:

$50 interest

Step-by-step explanation:

Simple interest formula

I = Prt

where:

I = interested earnedP = principal amountr = interest rate (in decimal form)t = time (in years)

Given:

P = $500r = 2% = 0.02t = 5 years

Substitute the given values into the formula and solve for I:

⇒ I = 500 · 0.02 · 5

⇒ I = 50

Therefore, Frank will earn $50 interest in 5 years.

A dune buggy rental company charges $35.50 plus 9¢ per mile
for each mile you drive. You are charged $60.25 for the rental.
You want to know the number of miles you drove.

Represent the situation with an equation and solve the
equation using any of the methods you learned in the last
topic.

Answers

The number of miles he drove for a cost of $30.50 is 275 miles.

How to find the number of miles using linear equation?

Using linear equation,

y = mx + b

where

m = slopeb = y-intercept

Therefore,

9 cents = $0.09

y = 35.50 + 0.09x

where

x = number of miles drove

y = total cost

Therefore,

60.25 = 35.50 + 0.09x

60.25 - 35.50 = 0.09x

24.75 = 0.09x

x = 24.75 / 0.09

x = 275 miles

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One of the legs of a right triangle measures 6 cm and its hypotenuse measures 8 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

Answers

Well, this is a Pythagorean theorem problem. A^2 + B^2 = C^2, where C^2 is equal to the hypotenuse. 8 squared equals 64, so c^2 = 64 cm. The other leg can be represented by A^2, which is 36 cm. 36 + ? = 64. 64 - 36 = 28, so B^2 equals 28. Now, to find the measurement of the other leg, we need the square root of 28. The square root of 28 is 5.3 cm.

Your final answer is 5.3 cm.

How would you write the equation with a slope of 2/3 and a y-intercept of -3
y = (3/2)x + 3
y = (2/3)x - 3
y = 2/3 + 3
y = 3/2 - 3

Answers

the answer is B. Y= (2/3)X - 3

Answer:

y = (2/3)x - 3

Step-by-step explanation:

The general structure of an equation in slope-intercept form is:

y = mx + b

In this equation, "m" represents the slope and "b" represents the y-intercept. You were given the slope and y-intercept, so finding the final equation is just a matter of substituting the variables.

slope = m = (2/3)

y-intercept = b = -3

y = mx + b

y = (2/3)x + (-3)

y = (2/3)x - 3

you deposit a check for $254.67 into your savings account. Your account has a balance of $419.33 after the deposit. Find the balance of your savings account before the deposit.

Answers

Answer:

$164.66

Step-by-step explanation:

Just subtract them from each other

4.
In the diagram of AABC below, DE || BC,
AD= 3, DB=2, and DE = 6.m
6
E
2
B
What is the length of BC?
1) 12
2) 10
3) 8
4) 4
C

Answers

Length of bc is 8
hope this helps :))

In her monthly tests, Mary got 20 more marks in Mathematics than in English. The total of her
marks for both tests were 130. Find her marks in each test

Answers

Answer:

75 on mathematics and 55 on English!

Step-by-step explanation:

Answer:

English test score: 55

Mathematics test score: 75

Step-by-step explanation:

Let [tex]e[/tex] be Mary's score on the English test.

We can say that [tex]e + 20[/tex] is her score on the Mathematics test, as the score for the Mathematics test is just the English test score but 20 higher.

Since both scores add up to 130, we can set up an equation to solve for the English test score. Since we said [tex]e + 20[/tex] is Mary's score on the Mathematics test, [tex]e + e + 20[/tex] is the total of her 2 test scores.

[tex]e + e + 20 = 130\\2e + 20 = 130\\2e = 110\\\boxed{e = 55}[/tex]

This means that Mary got a 55 on her English test score.

To solve for the Mathematics test score we can substitute 55 for [tex]e[/tex] in [tex]e + 20[/tex].

[tex]e + 20 = 55 + 20 \rightarrow \boxed{75}[/tex]

This means Mary got a 75 on her Mathematics test.

Those are the answers

- Kan Academy Advance

If a line has a slope of 2 and contains the point (-2, 1), what is its equation in
point-slope form?

A. y +2=-2(x-1)
B. y-2 =-2(x-1)
C. y-1=2(x-2)
D. y- 1 = 2(x+ 2)

Answers

Answer:

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = 2 and (a, b ) = (- 2, 1 ) , then

y - 1 = 2(x - (- 2)) , that is

y - 1 = 2(x + 2)

A line segment has more then one midpoint true or false

Answers

Answer:

false

Step-by-step explanation:

any line segment or distance has only one midpoint.

there is only one middle to everything.

how would that look like, if something had 2 middles ?

then they would not be a middle, and the middle between these 2 middles would then be the real middle ...

Answer:false

Step-by-step explanation: If a line segments has endpoints A and B, then the midpoint of that line segment is a point, M Such that M. Becuase A line segment can only IM SAYING ONLY 1 MIDPOINT!

Construction This section of a concrete skateboard ramp has the shape of a triangular prism. Find the volume
of the triangular prism. Find the value of the concrete used in the ramp if the cost of concrete is $4.00 per cubic
foot.

Answers

Answer:

volume = 73.3ft³

value = $194.4

Step-by-step explanation:

volume of prism = (½bh)l

=(½×4×4)×9.2

=73.6ft³

value of concrete

1ft³ : $4.00

73 .6ft³ : X

X : (73.6ft³ × $4.00) ÷ 1ft³

X : $294.4

Concentrate is diluted with water in the ratio 3 : 2. How much concentrate is there in 125 mL of total solution?

Answers

125ml (concentrate+water) -> ratio 3:2

125ml/5 = 25ml

25ml *3 = 75ml concentrate

25ml*2 = 50 ml water

Answer: there is 75 ml concentrate in the total solution

Answer:

75 mL.

Step-by-step explanation:

3/(3+2) = 3/5 of the solution is concentrate.

So the answer is 125 * 3/5

= 3*25

= 75 mL.

For what values of t can 10x2+tx+8 be written as the product of two binomials?

Answers

Answer:

Step-by-step explanation:

I need help please answer fast!!!

Answers

Answer:

2 and -4 :) because -2×4=-8, and 4+(-2)=2. Solve x-2=0 and x+4=0, you get the answer I previously mentioned!

A gift shop owner bought fifty vases for $210. she sells seven vases for what she paid for ten originally. what profit does she make on the fifty vases, which were all sold?

Answers

The profit earned by the gift shop owner on fifty vases will be $ 91.07.

What is profit?

The amount of money earned by any seller on the cost price is called the profit. It is given that A gift shop owner bought fifty vases for $210. she sells seven vases for what she paid for ten originally.

The profit will be calculated as we will create the expressions for all the selling and purchasing given in the question.

The total cost price of vases:-

50 vases = $210

1 Vase = 210 / 50 = 4.25

So 10 vases will be purchased at the price of:-

10 Vase = 4.25 x 10 = 42.5

Now from the question of the amount he paid for 10 vases, he gained it by selling 7 vases.

7 Vase = 42.5

1 Vase = 42.5 / 7 = 6.07

So he sold one vase for $6.07 and purchased it at $4.25.

The profit will be = 6.07 - 4.25 = 1.821

So profit for selling 50 vases will be:-

Profit = 50 x 1.821 = $91.07

Therefore profit earned by the gift shop owner on fifty vases will be $ 91.07.

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The Question is in the picture because I could not type it out correctly for some reason.

Answers

Step-by-step explanation:

the circumference of a complete circle (360°) is

2×pi×r

in our case

2×pi×3 = 6pi (= 18.84955592... ft)

5 ft is now what fraction of the whole circumference ?

because the corresponding arc angle is the same fraction of 360°.

5 ft are 5/(6pi) of the whole circumference.

so, the arc angle AB is

5/(6pi) × 360 = 5×60/pi = 300/pi = 95.49296586...°

but maybe you need the angle in radians instead of degrees ?

then remember, 360° = 2pi radians.

and then the arc angle AB is

5/(6pi) × 2pi = 10/6 = 5/3 = 1.666666... radians.

Graph the function f(x) = 2^x - 7 on the set of axes, if g(x) = 1.5x - 3 determine if f(x) > g(x) when x - 4

Answers

The inequality expression f(4) > g(4) is true when x = 4

How to determine if f(x) > g(x)?

The functions are given as:

[tex]f(x) = 2^x - 7[/tex]

g(x) = 1.5x - 3

See attachment for the graph of both functions.

From the graph, we have:

f(4) = 9

g(4) = 3

This means that:

f(4) > g(4) when x = 4

Hence, the inequality f(4) > g(4) is true when x = 4

Answers

The measure of x, p, q and r are 65, 20 , 40 and 40 degrees respectively.

Sum of interior angle of a triangle

The sum of interior angle of a triangle is 180 degrees. Applying the theorem to each question.

3) 40 + x + 75 = 180

115 + x = 180

x = 180 - 115

x = 65 degrees

4) p + 40 + 120 = 180

p + 160 = 180

p = 20degrees

5). The triangle is isosceles showing that the base angles are equal.

100 + q + r = 180

100 + 2q = 180

2q = 80

q =r = 40 degrees

Hence the measure of x, p, q and r are 65, 20 , 40 and 40 degrees respectively.

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Which equations represent inverse variation? Check all that apply.
y=2x
pv = 13
z = ²/x
4=v/x
h=9g/5

Answers

The equations representing inverse variation are: pv = 13 and z = (2 / x) , option B and C are the answer.

What is an Inverse Variation ?

When on increasing one quantity the other quantity decreases , such variation between the two entities is called Inverse Variation

For this case, what you should know is that the equations that represent an inverse variation are those that could not form a straight line, for example.

The equations are given in the question and it has to be checked if they represent inverse variation

y = 2x

y and x are in a direct variation

pv = 13

p = 13 / v

P and v are represent an inverse variation.

z = (2 / x)

z and x are represent an inverse variation.

4 = v/x

v =4x

v and x are in direct variation

h=9g/5

h and g are in direct variation

therefore , the equations representing inverse variation are:

pv = 13 and z = (2 / x)

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The nth term of a different sequence is 2^n+5 show that 36 is not part of the sequence

Answers

Answer:

It is not a term of the sequence

Step-by-step explanation:

See attached image

Which of the following is true about a function that is constant?

It is a horizontal line.

It moves in an upward direction.

It moves in a downward direction.

It is a curve.

Answers

A function assigns the values. The correct option that describes a constant function is that It is a horizontal line.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The correct option that describes a constant function is that It is a horizontal line.

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Answer: the answer is A the others are linear or higher

It moves in a horizontal line. Its 'y value' does not change.

Step-by-step explanation:

(100 POINTS) Use the Internet or another resource to find the definition of the Fundamental Counting Principle. What does this principle state? How can the principle be used to help you identify a sample space for a compound event? What are the limitations of using the Fundamental Counting Principle when determining the probability of an outcome? Support your answers with an example.

Answers

Answer:

The fundamental counting principle is a rule used to count the total number of possible outcomes in a situation

Ginger has 52 stamps and 68 regular
stickers. What is the ratio of stamps to
regular stickers? What is the simplified
ratio?

Answers

Answer:

13 stamps : 17 stickers

Step-by-step explanation:

52 stamps : 68 stickers can be simplified down to 13 stamps : 17 stickers because their greatest common factor is 4

As air is moved through a duct by a fan, friction between the air molecules and the sides of the duct creates a resistance to movement. Friction loss charts are available to determine the friction loss for a given quantity of air passing through a given size of duct, per 100 feet of duct. You know that a section of exhaust duct is 64 meters long, but you cannot determine the friction loss unless the duct length is in feet. You know that one meter is equal to 3.28 feet. How long is the 64-meter section of duct in feet? Round your answer to a whole number.

Answers

The length of the 64 meters section in feet is 210 feet

How to determine the length of the section of duct in feet?

The given parameters are:

Length = 64 meters1 meter = 3.28 feet

Multiply both sides of 1 meter = 3.28 feet by 64

64 * 1 meter = 3.28 feet * 64

Evaluate

64 meters = 209.92 feet

Approximate

64 meters = 210 feet

Substitute 64 meters = 210 feet in Length = 64 meters

Length = 210 feet

Hence, the length of the section in feet is 210 feet