2
Using
f'(x) = instantaneous = lim f(x+h)-f(x).
rate of change
h→0
h
find f'(x) when f(x) = -4x² - 6x + 7

The statement that correctly compares the number of songs on Georgia and Scarlet's playlists are is  17 < 36.

Georgia has 17 songs on her playlist while Scarlet has 36 songs on her playlist.

In the number line, the number 36 comes after the number 17. This means that 36 is greater than 17.

The statement that therefore correctly compares the number of songs in the playlist is:

17 < 36

In conclusion, the statement that correctly compares the songs in the two playlists is 17 < 36.

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Work Shown:

x = some unknown number

2x = twice the number

2x+x = add on the number

2x+x = 87

3x = 87

x = 87/3

x = 29

Answer:

56.25

Step-by-step explanation:

9/4×25

=225/4

=56.25

Answer:

6 is my final answer

Step-by-step explanation:

set as brainliest

Answer:

y = 3

Step-by-step explanation:

Points: (1, y), (-5, -1)

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (-1 - y)/(-5 - 1) = (-1 - y)/(-6)

slope = 2/3

(-1 - y)/(-6) = 2/3

Multiply both sides by -6.

-1 - y = -6 × 2/3

-1 - y = -12/3

-1 - y = -4

-y = -3

y = 3

The required measure of the angle m∠B is 121°.

Given that,
Angle A and B are two vertical equal angles.
m∠B = 3x - 17
m∠A = 2x + 29

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
m∠A = m∠B
2x + 29 = 3x - 17
-x = - 46
x = 46

Now,
m∠B = 3  *46 - 17
m∠B =  138 - 17
m∠B = 121°

Thus, the required measure of the angle m∠B is 121°.

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Answer:

1. A U C = {a, b, c, d, e}

2. B intersect A = {a, b, d}

3. B' = {c, f, g, h}

4. A - (B intersect C') = {a,c}

Step-by-step explanation:

U is a big set with all the letters a through f in it. Set A, B, and C are subsets of U. They have some of the letters in them. You could pick out the contents of set A, for example, from set U. Same with B and C. There's a little bit of overlap between A and B and C.

So for #1, the U shaped symbol means "Union" and you can remember that because of the U shape symbol. "Union" means throw everything in all together. A U C means all of A and all of C all together. But you don't have to write repeats, just list the letters once.

A is {a,b, c, d} and C is {a, e} so A U C is all of both of them:

{a, b, c, d, e}

The upsidedown Usymbol is "intersect" and that is only what the two sets have in common (whats the same) between the two sets.

BintersectA is what is the same in B{b,e,a,d} and A{a,b,c,d}. They both have a, b and d so that is the answer to BintersectA = {a,b,d}

The "apostrophe" looking mark means "Not this set". So B' means NotB. You list everything that is NOT in B. B is {b,e,a,d} so B' is NotB = {c,f,g,h}

The last one has what looks like a minus sign. Thats like normal "takeaway" along with parenthesis, use that normally like grouping/"do this first" and also intersect and Not. So basically all the work, all in one problem.

C = {a,e} so C' is NotC is {b,c,d,f,g,h}

The BintersectC' is what are the same beween B and NotC:

BintersectC' = {b,d}

A take away {b,d}

would be

{a,b,c,d} - {b,d}

= {a,c}

By adding the number of cups needed for each cake, we conclude that you will need 25 cups of ingredients to make the 4 cakes.

We know that the recipe calls for:

That is for a single cake, so in a single cake you need a total of cups given by the sum of the above quantities, this gives:

(1 + 3/4) + (4 + 1/5) + 3/10 = (1 + 4) + (3/4 + 1/5 + 3/10)

= 5 + (3/4 + 2/10 + 3/10) = 5 + (3/4 + 5/10) = 5 + (3/4 + 1/2) = 5 + 5/4

= 5 + 4/4 + 1/4 = 6 + 1/4

Each cake needs (6 + 1/4) cups of ingredients, so 4 cakes will need:

4* (6 + 1/4) = 24 + 4/4 = 25

You will need 25 cups of ingredients to make the 4 cakes.

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all that sides which can be applicable in the given side of triangle are:

F.5

A.7

C.9

Third Side of a Right Angle Triangle Pythagorean Theorem. The length of the hypotenuse in a right triangle can be determined using the Pythagorean Theorem. You can determine the length of the missing side using algebra and square roots as long as you are only given two lengths.

a,b and c are the sides of a triangle if it satisfies:

a<b+c  , b<a+c and c<b+a

Here, a=4 and b=7

We have to find c

i.e. all those c which satisfies:

4<7+c , 7<4+c and c<4+7=11

D.3   it is not true since it doesn't satisfies second inequality

F.5   it is true

A.7   it is true

C.9   it is true

E.11   This is clearly false, since it doesn't satisfies inequality third

F.5 This is clearly false, since it doesn't satisfies inequality third

Hence, correct options are:

F.5

A.7

C.9

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Answer:

4 lines

Step-by-step explanation:

We know that a parallelogram is constructed using two parallel lines intersecting other pairs of parallel lines so basically we require 4 lines to construct a parallelogram.

Answer:4

Step-by-step explanation:

Answer:

−19 5/7

None of the options match the answer

Step-by-step explanation:

−9 2/7 −10 3/7

=−65/7 −10 3/7

= −65/7 −10 3/7

= −65/7 − 73/7

= −138/7

= −19 5/7

12 is the population mean or sample mean of given data.

Given that

The collected data

17, 10, 3, 5, 25

To find

The population mean or sample mean

So, according to the question

we have,

The collected data

 17, 10, 3, 5, 25

For calculate the the population mean or sample mean, We have to find out the total of data, and total number of data.

Total of data = 17+ 10 +3 + 5+ 25

Total of data = 60

Total number of data (n) = 5,

So, we know that

Sample mean = [tex]\frac{total\;of\;data}{n\;number\;of\;data}[/tex]

Now, putting the all values,

We will get,

Sample mean =  60/5  

 = 12          

The Sample mean of given data is 12.

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Answer:

72

Step-by-step explanation:

(6)^2+7(6)-6

36+42-6

72

The years where the spending will be more than $89 billion are: after 2009, i.e., 5 years after 2004, as found by basic algebra.

Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.

Given: y = 14.4x + 17,

where: x = number of years after 2004

y = amount spent by businesses

To find: number of years where spending

$89 billion.

Finding:

We are given: y = 89, for which, we have to find the x, i.e., the number of years.

By basic algebra, substituting the value of y and solving for x:

89 = 14.4x + 17

72 = 14.4x

x = 5

Hence, The years where the spending will be more than $89 billion are: after 2009, i.e., 5 years after 2004, as found by basic algebra.

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By using the given graph, we can see that f(-5) = 3.

Here we have an image with the graph of the function y = f(x).

Remember that each point on that grid has the coordinates (x, y), where the values of x are on the horizontal axis, and the values of y are in the vertical axis.

So, if we want to find f(-5), then we want to see what value of y takes f(x) when x = -5.

So, first we need to go to the horizontal axis and find x = -5.

Once we find that value, now we need to move up or down along a vertical line (depending on where is the graph of the function). In this case we would move upwards. Now, count how many units we move up until we hit the graph of the function, that number of units will be the value of y.

In this case, we need to move 3 units upwards to hit the graph, then we have y = 3.

This means that the value of the function when x = -5 is y = 3, so we can write:

f(-5) = 3

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Answer:

true

Step-by-step explanation:

its true frfr

Answer:

0.234

Step-by-step explanation:

The total number of people in the age range from 30-49 is 7282 (3752 + 3530 the totals at the bottom of the column.  The total number of people out of that group that have completed high school is 1704 (787 + 917 the number of people in that column that have finished high school).

[tex]\frac{1704}{7282}[/tex] = .23400164789  Rounded to the nearest thousandths place is .234

The equation of the two-step problem is 2x = x + 19

The conditions are given as

Let the variable in the equation be x

So, a possible equation is as follows

2x = x + 19

The solution to the equation is as follows

2x = x + 19

Subtract x from both sides

x = 19

Hence, the equation of the two-step problem is 2x = x + 19

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Answer:

2r+24

Step-by-step explanation:

The number is R · R is added to 12 : R + 12. Double the result: 2 (R + 12). = 2 R + 24. So the answer is ultimatley 2r+24.

Answer: 2R+24

Step-by-step explanation:

(R+12)*2= ==> multiplication comes before addition, so in order to indicate that addition occurs before multiplication, there should be parentheses around

2(R+12)=

2R+2*12=2R+24

No, the picture frame will not fit into a box that measures 7.5 inches on each side because the side of the frame will be greater than it that is 7.54 inches.

Length of picture frame is given as:

= 7 (6 / 11)

= 7.54 inches

The length of Box is given as = 7.5 inches

From the above, we can see that the length of the box is smaller than the length of the picture frame.

So, the picture frame will not be able to fit in the box.

Therefore, we get that, the picture frame will not be able to fit into a box that measures 7.5 inches on each side because the side of the frame will be greater than it that is 7.54 inches.

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Your question was incomplete. Please refer the content below:

Rochelle needs to pack a picture frame that measures 7 6/11 (fraction 6 over 11) inches

on each side. Will it fit into a box that measures 7.5 inches on each

side?

They sold 10 bags of butter popcorn, 20 bags of kettle corn and 26 bags of cheddar cheese.

Here, we are given that two boy scouts were selling popcorn for a fundraiser.

Their total revenue = $640

Let the bags of butter popcorn be x

then, the bags of kettle corn sold = 2x

and the bags of cheddar popcorn sold = 2x + 6

Cost of kettle corn = $15/ bag

Cost of butter popcorn = $8/ bag

Cost of cheddar popcorn = $10/ bag

Thus, the total revenue from from kettle corn = $30x

total revenue from from butter popcorn = $8x

total revenue from from cheddar popcorn = $10(2x + 6)x

Thus, we will get the following equation-

30x + 8x + 10(2x + 6) = 640

38x + 20x + 60 = 640

58x + 60 = 640

58x = 580

x = 580/ 58

x = 10

Thus, 2x = 20 and 2x + 6 = 26

Hence, they sold 10 bags of butter popcorn, 20 bags of kettle corn and 26 bags of cheddar cheese.

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Answer:

She have to study 4 hours and 42 minutes to get 93 marks.

Step-by-step explanation:

when she studied 4 hours she got 79

when she studied 1 hour she got 4/79

[tex]4 \div 79\times 93[/tex]

is the time when she got 93

= 4.70

It means the time will be 4 hours 42 minutes

Answer:

y=1/5x

y=0

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

So: 2x-8=4+x

x-8=4

x=12

Answer: 48 represents total amount and s represents scarves

Step-by-step explanation:

It tells you when you read the sentence carefully.

The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).

In this problem we find a system of three linear equations with three variables, which can be resolved by several methods. In this case, we shall use the method of substitution. First, clear the variable x in the third equation:

x = 4 - 3 · y

Second, substitute x in the first two equations:

3 · (4 - 3 · y) + 2 · y - z = 8

12 - 9 · y + 2 · y - z = 8

- 7 · y - z = - 4

2 · (4 - 3 · y) + 2 · z = - 4

8 - 6 · y + 2 · z = - 4

- 6 · y + 2 · z = - 12

Third, clear z in the first equation derived in the previous step:

z = 4 - 7 · y

Fourth, substitute z in the second equation derived in the second step:

- 6 · y + 2 · (4 - 7 · y) = - 12

- 6 · y + 8 - 14 · y = - 12

- 20 · y = - 20

y = 1

Fifth, calculate y and x:

z = 4 - 7 · 1

z = - 3

x = 4 - 3 · 1

x = 1

The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).

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A) The reason why Chris had higher savings by retirement age, is because he saved $5000 annually from ages 25 to 65 while susan did so only from ages 25 to 35 .

B) The reason why Susan had a higher retirement savings than bill is because Susan started investing 10 years earlier than bill and so her investment had a longer period to compound.

A) From the given exponential graph, we see that Chris curve was simialr to that of susan between ages 25 to 35 and suddenly Chris curve began to rise at a faster rate than that of Susan after that until when retired at 65 years of age.

Since we are told that chris continued that amount till retirement at 65, we are told that susan contributed the same amount for only that period between ages 25 and 35. Thus, it means that the reason why Chris had higher savings by retirement age, is because he saved $5000 annually from ages 25 to 65 while susan did so only from ages 25 to 35 .

B) The reason why susan had a higher retirement savings than bill is because susan started investing 10 years earlier than bill and so her investment had a longer period to compound.

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Answer:

  [tex]\textsf{C}\quad f^{-1}(x)=24-6x[/tex]

Step-by-step explanation:

You want the inverse function of f(x) = 24 -x/6.

The function relates x to y by y = f(x). The inverse function gives the reverse relation: x = f(y). Solving this for y gives the inverse function in the form you want.

  x = f(y)

  x = 4 -y/6 . . . . . use definition of f(x)

  6x = 24 -y . . . . multiply by 6

  y = 24 -6x . . . . add y-6x

  f⁻¹(x) = 24 -6x . . . . write using function notation

Answer:

B. 6

Step-by-step explanation:

$10.35 × 24 = 248.4 per week

248.4 × 30% = 74.52 {30% of her earnings}

$74.52 × 6 weeks = $447.12

∴ She needs to work for 6 weeks in order to save up to $399