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The average rate of change of the function f(x)  = 8x² - 6 is given as  8h + 16x

It quantifies how much the function changed per unit on average throughout that time span. The slope of the straight line connecting the interval's ends on the function's graph is used to calculate it.

f(x) = 8x^2 - 6

Avge rate : [ f(x+h) - f(x)]/(x +h - x)

f(x+h) = 8(x+h)^2 - 6

f(x) = 8x^2 - 6

f(x+h) - f(x) = 8x^2 + 8h^2 + 16xh + 6 - 8x^2 -6 = 8h^2 + 16xh

Avg rate = ( 8h^2 + 16xh)/h

= 8h + 16x

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The average rate of change of the function over the interval is 8(b + 1)

The given parameters are

Function: f(x) = 8x^2 - 6

Interval: [1, b]

Calculate f(1) and f(b) using the function definition

So, we have

f(1) = 8(1)^2 - 6 = 2

f(b) = 8(b)^2 - 6 = 8b^2 - 6

The average rate of change of the function over the interval is then calculated as

Rate = [f(b) - f(1)]/[b - 1]

This gives

Rate = [8b^2 - 6 - 2]/[b - 1]

Evaluate

Rate = [8b^2 - 8]/[b - 1]

Factorize the numerator

Rate = [8(b + 1)(b - 1)]/[b - 1]

Divide through by b - 1

Rate = 8(b + 1)

Hence, the average rate of change of the function over the interval is 8(b + 1)

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The concentration of a contaminant that enters a lake is a function of time and initially rises rather quickly. However, it is due to the lake's inherent mixing and self-cleansing activity.

Concentration in chemistry is calculated by dividing a constituent's abundance by the total volume of a mixture. The terms "concentration" can refer to any type of chemical mixture, but are most frequently used to describe the solutes and solvents in solutions. There are four different types of concentrations that can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration. There are different types of molar (quantity) concentrations, including normal concentration and osmotic concentration.

Concentration is frequently expressed qualitatively in everyday, non-technical language using words like "dilute" for solutions with a low concentration and "concentrated" for solutions with a high concentration.

If y increases quickly with x, the slope of the graph will be greater (i.e. will be steeper). The slope of the graph will be lower if y increases slowly with x. (i.e. will be less steeper). Straight lines result from constant slope in graphs. 1. Less investment results in a significant boost in production at first. Consequently, graph

1) Begins with a steeper slope. The rate of expansion slows down at the end, therefore the graph

2) will be more gradual. So, D is the proper graph. 2. The slope of the graph increases while train speed stays constant. As a result, graph will be

3) Straight line So, C is the proper graph.  The focus rises quickly at first. Small time therefore yields large

4) an improvement in concentration Therefore, graph will be steeper in beginning. At end, the concentration becomes constant, so graph will be almost horizontal at end.

5)Thus correct graph is B. In beginning, the population increases slowly. Thus large time gives less increase in population. Therefore, graph will be less steep in beginning. At end, the population increases rapidly, so graph will be more and more steeper at end. Thus correct graph is A.

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Answer:

Step-by-step explanation:

If you're asking to determine if the slope is positive or negative by plotting these points and drawing a line to connect them and deriving the slope from that,

No, the slope is positive.

Her door should be 3 cm on scale .

It is given that dimension of the kitchen table is 60m by 2 m .

Let the width of the door be " x".

We given Mal's Kitchen door is 1.2 m wide .

The ratio is given by

   [tex]x:1.2[/tex]     ......(1)

She decides on a scale of 1 to 40 which means 1 : 40    .....(2)

Equating equation (1) and (2) , we get

     [tex]x:1.2=1:40[/tex]

Representing in fraction , we get

        [tex]\frac{x}{1.2} =\frac{1}{40} \\\\x=\frac{1.2}{40} \\\\x=0.03m\\x=3cm[/tex]

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The complete question is mention below :

Mai wants to make a scale drawing of her kitchen. her kitchen is a rectangle with length 6m and width 2m. She decides on a scale of 1 to 40. Mal's Kitchen door is 1.2 m wide. How wide should the door be on the scale drawing?How wide should the door be on the scale drawing?

Step-by-step explanation:

We know that,

[tex] ➟\sf \: fv \: of \: annuity \: = p( \frac{(1 + r) {}^{n} - 1}{r} )[/tex]

where,

FV of annuity = $35,450

P = monthly payment,

r = rate of interest = 5.5% annually = [tex] \frac{5.5}{12}%[/tex]

n = number period = 20 years = 240 months

Putting all the values,

[tex] \sf35450 = p( \frac{(1 + \frac{0.055}{12} ) {}^{240} - 1}{ \frac{0.055}{12} } )[/tex]

[tex] \sf \: p = \frac{35450}{( \frac{(1 + \frac{0.055}{12} ) {}^{240} - 1}{ \frac{0.055}{12} } )}[/tex]

[tex] \sf \: p \: = \: \$81.36[/tex]

Therefore, they should deposit $81.38 monthly.

the original price of the workout tops is $18.95

Let's say that the original price is x, we know that the tops are on sale for $6.00 off the original price, so if Yazmin buys 4 of these, the cost will be:

C(x) = (x - $6.00)*4

And we know that the cost is $51.80, replacing that we get:

$51.80 = (x - $6.00)*4

Now we need to solve this linear equation for x.

$51.80/4 = x - $6.00

$51.80/4 + $6.00 = x = $18.95

We conclude that the original price of the workout tops is $18.95

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Answer:

4 7/8

Step-by-step explanation:

First lets make 6 1/2 an improper fraction
Multiply the denominator by the whole number and add the result to the numerator to get the improper fraction

6 1/2

13/2

Multiply the numerators by eachother, same with the denominators

3* 13
---------
4*2

39/8

Finally, simplify by dividing 39 by 8

4 7/8

Number of groups of 3/4 are in 6 1/2 is, 26/3

We have to given that,

To find number of groups of 3/4 are in 6 1/2.

Let us assume that,

Number of groups of 3/4 are in 6 1/2 = x

Hence, We get;

x = (6 1/2) ÷ (3/4)

x = (13/2) × (4/3)

x = (13 × 4) / (2 × 3)

x = (13 × 2) / 3

x = 26/3

Therefore, There are 26/3 groups of 3/4 are in 6 1/2.

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Based on the depth of the local river in January and the depth of the river in July, the difference between depths in January and July is 22 feet.

The difference in the depth between July and January can be found as:

= Absolute value of depth in July - Absolute value of depth in January

Solving for the difference in depth gives:

= 27 - 5

= 22 feet

In conclusion, the difference in depths between January and July is 22 feet.

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so this is complicated

1)

y = 180°-(21°+34°)

y = 180°-55°

y = 125°

x = 180°-125°

x = 55°

Answer:

54º, 108º and 18º respectively

Step-by-step explanation:

Answer: $455

Step-by-step explanation:

I would think you would divide 260 by 4 and that would get you 65 and then multiply 65*7 and that would be $455

Answer:

Question 7: 20° and 160°, Question 8: 10° and 80°

Step-by-step explanation:

Complementary angles add to 90° and supplementary angles add to 180°.

Answer: 5,2 2,3 2,2

Step-by-step explanation:

The inequality that represents the heights of every other person who ever lived is, 9 ≥ x

We have to find the inequality that represents the heights of every other person who ever lived, where the tallest person who ever lived was approximately 9 feet tall, according to the question.

Here x denotes the height of every person who ever lived,

So, the inequality is, 9 ≥ x

Every person ever lived, must be equal to or lesser than 9 feet.

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Tom drives 243 miles in 3 hours.

What is speed?

So, to find how many miles Tom can drive in 3 hours:

Tom drives 81/2 miles every 1/30 hour.

81/2 miles = 40.5 miles

1/30 hours = 30 minutes

So, in 30 minutes Tom drives 40.5 miles.

Then, in 1 hour Tom will drive 40.5 + 40.5 = 81 miles.

Miles Tom will drive in 3 hours = 81 × 3 = 243 miles.

Therefore, Tom drives 243 miles in 3 hours.

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Answer:

Step-by-step explanation:

32 meals;

to solve, divide 24 by 0.75 (3/4) or you can do 24/1 times 4/3

The value of x will be 8 for the number 67081 which is a perfect square.

In the given situation, it is stated that a number 670X1 is equal to 67100, correct to three significant digits. This tells us that the second digit should be greater than 5.

So, we get x ≥ 5.

By keeping all values of x ≥ 5 in 670X1, we get these numbers.

67051 , 67061, 67071, 67081, 67091

We need to find out which of the following numbers is a perfect square.

Taking √67081, we get a perfect square.

√67081 = 259.

So, 67081 is a perfect square of 259.

Hence, the value of X will be 8 for the number 670X1.

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Answer:

[tex](x+3)^2=-4(y-3)[/tex]

Step-by-step explanation:

Standard form of a parabola with a vertical axis of symmetry

[tex]\large\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}[/tex]

[tex]\textsf{Vertex}=(h, k)[/tex]

[tex]\textsf{Focus}=(h,k+p)[/tex]

[tex]\textsf{Directrix}:y=(k-p)[/tex]

[tex]\textsf{Axis of symmetry}:x=h[/tex]

If p > 0, the parabola opens upwards.

If p < 0, the parabola opens downwards.

From inspection of the given graph:

Therefore:

Substitute the found values of h, k and p into the formula:

[tex]\implies (x-(-3))^2=4(-1)(y-3)[/tex]

[tex]\implies (x+3)^2=-4(y-3)[/tex]

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Supplementary angles have a sum of 180°

Therefore, we can add the expressions for Angles A and B and set their sum equal to 180.

( 7x - 15 ) + ( 2x - 3 ) = 180

Now we can combine like terms and use inverse operations to find the value of x:

( 7x - 15 ) + ( 2x - 3 ) = 180

9x - 18 = 180

9x - 18 + 18 = 180 + 18

9x  = 198

9x/9 = 198/9

x = 22

Then Angle A will have a measure of 7x - 15 or 7• 22 -15 = 154 - 15 = 139°

m∠A = 139°

The measure of Angle b will be 2x - 3 = 2 • 22 - 3 = 44 - 3 = 41°

m∠ B = 41°

NOTE:  139 + 41 = 180

Answer: 3 = b (maybe, usually unsure)

Step-by-step explanation: bing

y = mx + b, this is the formula.

b = y-intercept
m = slope

1. We know that (-1,6) is our pair.

2. The formula when written with the info is y = -3x + b

3. We know that -1 is the x and the y is 6, so subbing the x and y in the formula, it is 6 = -3(-1) + b.

4. When multiplied, it becomes 6 = 3 + b

5. Then we combine like terms, by subtracting 3 into 6, making 3 = b

6. So, it is 3 = b

Answer: False

Step-by-step explanation:

4 x 10^6 = 4000,000

400,000 is 4 x 10^5

Answer:

False

Step-by-step explanation:

10^6=1,000,000   ==> 10^6 has 6 zeros after the '1', making 10^6=1 million.

4*10^6=4,000,000, not 400,000

Answer:2 and 5

Step-by-step explanation:

i don't know a lot but hope it helped

The linear equation that shows how many packages of breadsticks Dirk bought as (1/4)b.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have Dirk who brought [b] breadsticks to a potluck. The breadsticks are packaged in bags of 4.

Assume that he bought [x] bags of breadsticks. Then, we can write the linear equation that shows how many packages of breadsticks Dirk bought as -

x = (1/4)b

Therefore, the linear equation that shows how many packages of breadsticks Dirk bought as (1/4)b.

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Answer:

18

Step-by-step explanation:

24 x 20 = 480 (amount of seats on main floor)

786 - 480 = 306 (amount of seats needed on balcony)

306 ÷ 17 = 18 (amount of seats on each row of balcony)

Step-by-step explanation:

The main floor has 24*20 = 480 seats.

So you need 786- 480 = 306 more seats

There are 17 rows in the balcony and let's say there are x seats in each row. Since you need 323 seats, this means

19x = 323

x = 306/17

x = 18

So there must be 18 seats in each row up in the balcony.

Answer:

119

Step-by-step explanation:

41+78+119

Easy just remember this formula

Answer: x=1/2, x=-4/3 ==> A and F

Step-by-step explanation:

6x² +5x-4 = 0

6x²-3x+8x-4 = 0

3x(2x-1)+4(2x-1) = 0

(3x+4)(2x-1)=0

3x+4=0

3x=-4

x=-4/3

2x-1=0

2x=1

x=1/2

x=1/2, x=-4/3 ==> A and F

Answer:

-21 If that is a option

Step-by-step explanation:

Answer: I hope this helps.

Step-by-step explanation:

Based on the explanation below, the solution for c from the equation in the question is 2 - d.

Before answering the question, the correct complete question is provided as follows:

Solve for c from the equation 7(c+d)=14.

We can now solve for c from the equation in the question as follows:

7(c+d)=14

c + d = 14 / 7

c + d = 2

c = 2 - d

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The input value is x = 1.5

In the graph the intersection both functions is the point when f(x)=g(x)

the point of intersection both graphs is (1,5,2)

that means

for the input value of x = 1.5

f(1.5) = g(1.5) = 2

The input value is x = 1.5

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The question is incomplete, the complete question is

Use the graph to determine the input value for which f(x) = g(x) is true.

A. x = 0.5

B. x = 1

C. x = 1.5

D. x = 2

Answer:

x=1.5

Step-by-step explanation:

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