Bonus Question:
a. Consider the function f(x) = ax^2 + c
Find f'(x)

b. Point A (-2, 5) lies on the graph of y = f(x).
The gradient of the tangent to this graph at A is -6. Find the value of a.

c. Find the value of c.

Please answer this question and please show your work too. Anyone who is able to do this correctly will receive 50 points from me. (This assignment is about Derivatives)

Answer:

(B) Parallel to x-axis

Step-by-step explanation:

y = 7

This is a constant line, in which the value of y is always of 7, no matter the value of x.

In a line in which the value of y is constant, this line is parallel to the x-axis, so the correct answer to this question is given by option b.

Answer:

4th graph

Step-by-step explanation:

x + 3y > -3

3y > -x - 3

y > -(1/3)x - 1

Blue Line

y < 1/2x + 1

Orange Line

y- intercepts = -1 and 1

Answer:

Step-by-step explanation:

f(x) = (x + 3)(x - 2​) has two zeros:  One stems from (x + 3) = 0 and is (-3, 0); the other stems from (x - 2) = 0 and is (2, 0).  

The axis of symmetry is a vertical line located halfway between -3 and 2:  

x =  -1/2.

The graph opens up because the given (x + 3)(x - 2) has a positive leading coefficient (+1).

With this information we can eliminate the last two possible answers.  Note that the x-intercepts of the first graph are -3 and 2,  Thus, the first graph is the correct one.

Answer:

1190 m^3

Step-by-step explanation:

l = 1700 cm = 17 m

b = 14 m

h = 1000 cm = 10 m

Total volume = l × b × h

= 17 × 14× 10

= 2380 m^3

since it is half filled ,

Volume is half , so,

volume of water in pond = 2380 ÷ 2

= 1190 m^3

Answer:

C

Step-by-step explanation:

Given that the equation of the revenue is R=2x2+55x+10 and the equation of the cost is C=2x2 – 15x – 40, you will get the profit by subtracting the revenue from the cost: R-C=P. Therefore, P=(2x2+55x+10)-(2x2 – 15x – 40). You will get P=70x+50 where x is is the number of cellphones sold. If 240 cellphones are sold, then the profit is 16850 dollars.

The profit, if 240 cell phones are sold, is $16,850.

Profit = 70x + 50

Option C is the correct answer.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The profit, in dollars, can be found by subtracting the cost from the revenue:

Profit = Revenue - Cost

= (2x² + 55x + 10) - (2x² - 15x - 40)

= 70x + 50

The expression for profit is 70x + 50.

To find the profit if 240 cell phones are sold, we substitute x = 240 into the expression for profit:

Profit = 70x + 50

= 70(240) + 50

= 16,850

Therefore,

The profit, if 240 cell phones are sold, is $16,850.

Learn more about expressions here:

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Answer:

Step-by-step explanation:

Answer:

31 batches

Step-by-step explanation:

Find how many batches of orange punch smoothies he can make by dividing 560 by 18:

560/18

= 31.11

Since we can only have a whole number answer, round down.

So, he can make 31 batches of orange punch smoothies.

Answers:

=================================================

Explanation:

To get the mean, you add up the numbers and then divide by n = 8, since there are 8 scores

Adding the scores gets us: 87+60+76+92+63+91+88+75 = 632

Divide that over n = 8 to get 632/n = 632/8 = 79

The mean is 79

You have the correct answer. Nice work.

---------------

The mode is the most frequent value.

In this data set, we don't have any repeated values. Each unique number is listed one time only. So that tells us we don't have a mode here.

---------------

To get the median, we need to sort the items from smallest to largest

{87,60,76,92,63,91,88,75} sorts to {60,63,75,76,87,88,91,92}

Because we have n = 8 values, which is an even number, this tells us that the median is between slot n/2 = 8/2 = 4 and slot 5

The values 76,87 are in slots four and five in that order. Add them up and divide by 2:  (76+87)/2 = 163/2 = 81.5 is the median

Answer:

-17 =s

Step-by-step explanation:

-8s +4 = -7s +21

Add 8s to each side

-8s+8s +4 = -7s+8s +21

4 = s+21

Subtract 21 from each side

4-21 = s+21-21

-17 =s

Answer:

s = -17

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

-8s + 4 = -7s + 21

Step 2: Solve for s

Answer:

3 * 45 = 135 which is NOT 180

45, 45, 90 would work

Step-by-step explanation:

hope it helps!

Answer:

15

Step-by-step explanation:

50 * .30=15

Answer:

= 24 3/4x

Step-by-step explanation:

3* 8 1/4x

Here 8 1/4 is a mixed fraction.

Convert it to improper fraction

8 1/4 = 33/4

So, 3*33/4 x

99/4 x

= 24 3/4x

That is

Hope this will helpful.

gimmie brainlist :)

Answer:

The percentages are as follows: 1) 16.6%, 2) 12.5%, 3) 200%, 4) 225%, and 5) 1.5%.

Step-by-step explanation:

To find the rate, or percent, for each of the following items, the following calculations must be performed:

1) Base 72; percentage 12 = 12/72 = 0.1666 x 100 = 16.6

2) Percentage 28; base 224 = 28/224 = 0.125 x 100 = 12.5

3) Base 20; percentage 40 = 40/20 = 2 x 100 = 200

4) Base 44; percentage 99 = 99/44 = 2.25 x 100 = 225

5) Percentage 126; base 8400 = 126/8400 = 0.015 x 100 = 1.5

Therefore, the percentages are as follows: 1) 16.6%, 2) 12.5%, 3) 200%, 4) 225%, and 5) 1.5%.

Answer:

Step-by-step explanation:

Answer:

small = 35 pounds

large = 45 pounds

Step-by-step explanation:

Let x = large boxes

y = small boxes

two equations can be derived from the question

x + y = 80  equation 1

60x + 65y = 4975 equation 2

multiply equation 1 by 60

60x +60y = 4800 equation 3

subtract equation 2 from 3

5y = 175

y = 35

substitute for y in equation 1

x + 35 = 80

x = 80 - 35

x = 45

1) angle LJK

2) angle KJL

The marked angle can be named as angle LJK and angle KJL.

An angle is a corner whether constituting a projecting part or a partially enclosed space. It is a combination of two rays with a common endpoint.

The angle can be named in two ways depending on the rays that are making angle.In our question the marked angle can be named as LJK and opposite if this KJL because it does not change the value of angles. Whether we start writing from one point to second point and from second point to first point. Main point is that the point at which the angle is formed comes in between both the points of rays.

Hence the marked angle can be named as angle LJK and angle KJL.

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Answer:

Associative property

Step-by-step explanation:

The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.

Hope this helps

Answer: 1/4

Step-by-step explanation:

Reword the problem. It says what is the probability of landing on 2 or 1. That is 2 possibilities out of 8 so 2/8 = 1/4

Answer:

A = 4a² - 4ab + b²

Step-by-step explanation:

The area (A) of a square is calculated as

A = s² ( s is the side length ) , so

A = (2a - b)² ← expand using FOIL

   = (2a)² - 2ab - 2ab + (- b)²

   = 4a² - 4ab + b²

Step-by-step explanation:

side length

a = 10 m

side length

b = 18 m

diagonal

p = q = 20.591260281974 m

perimeter

P = 56 m

area

A = 180 m2

Answer:

reading books (458), science books (957), mathematics books (1054)

Step-by-step explanation:

458 is less than 957 and 1054, while 957 is less than 1054 but more than 458, and 1054 is more than 957 and 458.

458<957<1054

Answer:

The height reached by the ladder is 8 m.

Step-by-step explanation:

A 10 meter long ladder is leaning against the wall. The foot of the ladder is 6 meters from the wall. What height reaches the ladder on the wall?

Length of ladder, L = 10 m

foot of ladder, D = 6 m

Let the height reached is H.

[tex]L^2 = D^2 + H^2\\\\10^2 = 6^2 + H^2\\\\100 - 36 = H^2\\\\H = 8 m[/tex]

Answer:

<d = 25 degrees and <e = 130 degrees

Step-by-step explanation:

We have a vertical angle, so the opposite sides of this angle are the same. This means that the angle opposite to 25 degrees also measures 25 degrees. We have one angle of the triangle. Since the triangle is isosceles, the angle d is the same as 25 degrees.

<d = 25 degrees

The interior angles of a triangle add up to 180 degrees, and we now have 2 angles, so:

<e = 180 - 25 - d

<e = 155-25

<e = 130 degrees

Answer:

<d = 25 degree and <e = 130 degree

Step-by-step explanation:

Let <d, <e and <f be the respective angles

<f = 25 degree (Vertically opposite angles are equal)

side fe = side ed (given)

Therefore, <f = <d (angles opposite to equal sides are equal)

Therefore, <d = 25 degree

<d + <e + <f = 180 degrees (Angle sum property)

25 + 25 + <e = 180

50 + <e = 180

<e = 180 - 50

<e = 130 degree

Therefore, <d = 25 degree and <e = 130 degree

Hope u understood

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Thank You

Answer:

The answer is D

Step-by-step explanation:

-x is n

Y=0

Answer:

D

Step-by-step explanation:

Basically....... graph shown in picture

Answer:

The answer is (x+4)

Step-by-step explanation:

Just write the expression as a product with the factor x and 4

x²+2×x×4+4+16

then write the number in the exponential form with an exponent of 2

x²+2×x×4+4²

then use a² +2ab +b² = (a+b)² yo factor the expression which you get (x+4)

Answer:

D

Step-by-step explanation:

The starting term is a1.

That's the very first term.

a1 = - 10

The second term = -17 which means that you added - 7 to - 10.

So d must be - 7

The formula must be

an = a1 + (n - 1)*d

an = -10 + (n - 1)(-7)

You might wonder why it is n - 1. The reason is because the first term is already added on the right side. The -1 means that we have already included the first term.

We should try the formula out to see what it does. Let's find a4

a4 = -10 + (4 -1)*-7

a4 = -10 + 3(-7)

a4 = -10 - 21

a4 = - 31 which is what the question suggests.

Answer:

Step-by-step explanation:

Given,

Length of the room = 12m

Width of the room = 5m

Therefore,

Area of the room = l × w

= 12m × 5m

= 60 sq.m (Ans)

Answer:

11

Step-by-step explanation:

2(x + 1) - 3

Let x= 6

2(6+1) -3

Parentheses first

2(7) -3

Then multiply

14-3

Then subtract

11