Consider the function and the value of a.
f(x) = 5 - x - x^2, a = 0
(a) Use Mtan = lim h->0 [f(a + h) – f(a)] / h
to find the slope of the tangent line mtan = f'(a).​

Answers

Answer 1

Answer:

Mtan=1-2a

Step-by-step explanation:

Mtan=lim h->0[5-(a+h)-(a+h)^2-(5-a-a^2)/h

=lim h->0[5-a-h-a^2-2ah-h^2-5+a+a^2]/h

=lim h->0[h-2ah-h^2+5-5-a+a-a^2+a^2]/h

=lim h->[h-2ah-h^2 +0+0+0]/h

=lim h->o[h(1-2a-h)/h

=lim h->0 (1-2a-h)

=1-2a-0

=1-2a

Mtan=1-2a.


Related Questions

Mr. Alvarez makes a walkway out of 3 cement slabs. He uses 14 cubic feet of cement to make the walkway. Each square slab has a volume of 4 cubic feet. How many cubic feet of cement is the middle slab?


Need help Pls!!​

Answers

Answer: [tex]6\ ft^3[/tex]

Step-by-step explanation:

Given

[tex]14\ ft^3[/tex] cement is used

The volume of each square cement slab is [tex]4\ ft^3[/tex]

So, Volume of two square slab=[tex]2\times 4=8\ ft^3[/tex]

The volume of middle slab= Total Volume -Volume of square slabs

                                           =[tex]14-8=6\ ft^3[/tex]

Answer:

6

Step-by-step explanation:

Find the area of the shaded regions. GIve your answer as a completely simplified exact value in terms of pi. (No approximations)

Answers

Answer:

A = 27π cm²

Step-by-step explanation:

Area of the shaded region = area of full circle of O - Area of the unshaded sector

= (πr²) - (θ/360*πr²)

Where,

r = 6 cm

θ = 360

Area of shaded region = (π*6²) - (90/360*π*6²)

= (36π) - (¼*π*36)

= 36π - 9π

Area of shaded region = 27π cm²

HELP PLS ASAP!!!!!! WILL GIVE FIRST ANSWER BRAINLIEST!!!!

Answers

Answer:

step by step below

Step-by-step explanation:

14. y = x²+4x+1

    y=x+1

x+1 = x²+4x+1

x²+3x=0        x(X+3)=0

x=0 or x=-3

18. y=x²-3x-20

y=-x-5

-x-5 = x²-3x-20         x²-2x-15 = 0      (x-5)(x+3) = 0

x=5 or x=-3

20. y=x²+5x+1

y=x²+2x+1

x²+2x+1 = x²+5x+1            3x = 0

x = 0

22. y=-x²-3x-2

y=x²+3x+2

x²+3x+2 = -x²-3x-2        2x²+6x+4 = 0    2(x²+3x+2) = 2 (x+1)(x+2) = 0

x = -1 or x = -2

(2k^3 - 7k^2 + 3k) - (-4k^2 + 5k) in polynomial standard form PLEASE HELP

Answers

Answer:

2 k 3 − 3 k 2 − 2 k

Step-by-step explanation:

Answer: ...

2k^3−3k^2−2k

Find the mean and median of the data set.
39, 21, 15, 13, 12

The mean is-
The median is-

Answers

Step-by-step explanation:

The mean is- 100 ÷ 5= 20

The median is- 15

hope it helps!

Answer:

Mean Is 20

12, 13, 15, 21, 39

median is 15

Step-by-step explanation:

5. Jada is making circular birthday invitations for her friends.
The diameter of the circle is 12 cm. She bought 180
cm of ribbon to glue around the edge of each invitation.
How
many invitations can she make?

Answers

Answer:

Step-by-step explanation:

Jada is making circular invitations

we have d=12 cm, the radius r=6

she needs to find out the circumference

C=2x3.14x r

C=2x 3.14x6=37.68

180/37.68=4.77

she can make just 4 invitations

Which set of points on the graph represents equivalent ratios?


points C, D, and F
points B, C, and D
points B, C, and F
points A, C, and D

Answers

Answer:

points B, C, and D

Step-by-step explanation: 2021 edge

Answer:

give the other person brainliest please

Step-by-step explanation:

pleasee help me i hate graphs xD

Answers

Answer:

8.54 units (3s.f.)

Step-by-step explanation:

Distance between 2 points

[tex] = \sqrt{(y1 - y2)^{2} + {(x1 - x2)}^{2} } [/tex]

Identify the coordinates of the 2 endpoints of the line:

(-5, 5) and (-2, -3)

Using the distance formula above,

length of line segment

[tex] = \sqrt{[5 - ( - 3)]^{2} + [ - 5 - ( - 2)]^{2} } \\ = \sqrt{ {(5 + 3)}^{2} + ( -5 + 2)^{2} } \\ = \sqrt{ {8}^{2} + {( - 3)}^{2} } \\ = \sqrt{73} \\ = 8.54 \: units \: (3 \: s.f.)[/tex]

have been trying and think I love the way

What is the minimum value of the function g(x) = x^2 - 6x - 12?

Answers

9514 1404 393

Answer:

  -21

Step-by-step explanation:

I find it convenient to read the value from the graph created by a graphing calculator. The minimum is -21.

__

The function can be rearranged to vertex form, which also shows the minimum value.

  g(x) = (x^2 -6x +9) -12 -9*

  g(x) = (x -3)^2 -21 . . . . . . . . vertex form

The vertex is (3, -21), so the minimum is -21.

_____

* we added the square of half the x-coefficient inside parentheses, and its opposite outside parentheses. This makes the expression inside parentheses a perfect square trinomial.

Answer:

 -21

Step-by-step explanation:

i did it

Your running speed is 8.5 miles per hour. A greyhound dog's speed is about 4.5 times faster than yours. What is the dog's speed?

Answers

Answer:

Step-by-step explanation:

8.5*4.5=38.25 MPH

Answer:

38.25

Step-by-step explanation:

8.5 times 4.5 =38.25

Simon has a farm and has to buy a certain amount of feed for each animal. He buys feed once a month and counts all of his animals to see how much feed he needs to buy. Chicken feed is about $0.5 per chicken, each horse eats about $5 worth of feed, and goats eat about $4 worth of feed. What equation should he use to find how much he should spend on feed?

A. 0.50 +5h + 4g = total spent on feed
B. 9.5a = total spent on feed
C. 0.50 +5h + 40 = 100
D. 0.59 +49 +5g = total spent on feed​

Answers

Answer:

A

Step-by-step explanation:

youre looking for the total spent, and then each variable from the word equation

Answer:It is B because you add 5+4 and you get 9 and than you have 9 you have 5 cences

so it is $9.05

Given the equation: y= 2x +
graph the y-intercept. Use full sentences.

Answers

Answer:

In this equation, y = 2x - 5, it is already in that form and so the cumber in front of the x is the slope (2) and the constant number is the y-intercept (-5) - it's negative because of the minus sign in front of the number. So, the slope is 2 and the y-intercept is -5.

Step-by-step explanation:

A man who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

Answers

He had no hair at all

In the following circle paragraph what percent of the students have a C in Miss Rogers science class 81% 16% 19% or 21%

Answers

Given:

In Miss Rogers science class, 32%, 33%, 11%, 5% of students have A, B, D, F respectively.

To find:

The percent of the students have a C in Miss Rogers science class.

Solution:

We know that, sum of the percentages of all parts of pie chart is 100%. So,

[tex]A+B+C+D+F=100\%[/tex]

Substituting the given values, we get

[tex]32\%+33\%+C+11\%+5\%=100\%[/tex]

[tex]C+81\%=100\%[/tex]

[tex]C=100\%-81\%[/tex]

[tex]C=19\%[/tex]

So, 19% of the students have a C in Miss Rogers science class.

Therefore, the correct option is C.

Answer:

I think it's 81%

Step-by-step explanation:

Trust me

If wrong tell me i'll fix it

What is the slope of the line 4х – 1 = 3y + 5

Answers

Answer:

4/3 or

Step-by-step explanation:

Let's get this equation into y=mx+b form.

m=slope b=y-int

Subtract 5 from both sides to isolate y on a side.

4x-6=3y

Divide both sides by 3 to isolate y on one side.

(4/3)x-2=y

y=(4/3)x-2

m=4/3

b=-2

So our slope is 4/3

Which of the following fraction is the smallest?

12/14
13/19
17/21
7/8

Answers

Answer:

13/19

Step-by-step explanation:

12/14 = 0.86

13/19 = 0.68

17/21 = 0.81

7/8 = 0.88

13/19 is smallest

Answer:

A.  (8, 7), B (19, −12), C (−21, 14)

Step-by-step explanation:

You swap the X and Y coordinate for reflections over y=x

I need help with this question. if your not good with math, this questions not for you lol. and can you give me a explanation please.

Answers

Answer:

im not good at math

Step-by-step explanation:

How many 2/7 s are in 3?

Answers

Answer: 11 is the answer.

there are 11 2/7's in 3 with a remainder of 1/7, 11 1/7.

Step-by-step explanation:

Answer:

10.5 or 21/2

Step-by-step explanation:

The question is asking how many 2/7 are in 3. So let make 3 a equivalent fraction that has 7 as it denomanater. 7/7 is 1, 14/7 is 2, so 21/7 is 3. Now let divide 21/7 by 2/7.  flip 2/7 around to 7/2 then multiply by 21/7 which equals

[tex]\frac{147}{14}[/tex] which equals 10.5 or 21/2.

Determine if the triangles are congruent. If yes, by which theorem?
O no
O yes, SSS
O yes, SAS
Ο Ο.
O yes, ASA
O yes, AAS
O yes, HL

Answers

Answer:

Yes ASA.

Step-by-step explanation:

ASA

22 – 25x + 5 = -63 + 5x​

Answers

Answer: x = 3

Step-by-step explanation:

first, we calculate.

27 - 25x = -63 + 5x

then, we move the terms around.

-25x - 5x = -63 - 27

next, we collect the like terms.

-30x = -90

finally, we divide both sides.

x = 3

Hannah has a chicken coop with 6 hens. Let X be the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table.

A 2-column table with 7 rows. Column 1 is labeled number of eggs with entries 0, 1, 2, 3, 4, 5, 6. Column 2 is labeled probability with entries 0.02, 0.03, 0.07, 0.12, 0.30, 0.28, 0.18.

What is the standard deviation of the distribution?

1.39
1.95
2.16
4.67

Answers

Answer:

1.39

Step-by-step explanation:

Creating a table:

X :___0 __ 1 __ 2 ___ 3 ____ 4 ___ 5 ___ 6

P(x):0.02_0.03_0.07, 0.12, 0.30_ 0.28_0.18.

The standard deviation = sqrt(Var(x))

Var(x) = Σx²*p(x) - E(x)²

E(x) = ΣX*p(x)

E(x) = (0*0.02) + (1*0.03) + (2*0.07) + (3*0.12) + (4*0.30) + (5*0.28) + (6*0.18) = 4.21

Var(X) :

((0^2*0.02) + (1^2*0.03) + (2^2*0.07) + (3^2*0.12) + (4^2*0.30) + (5^2*0.28) + (6^2*0.18)) - 4.21^2

19.67 - 17.7241

= 1.9459

Standard deviation = sqrt(Var(X))

Standard deviation = sqrt(1.9459)

Standard deviation = 1.3949551

= 1.39

Re-do
-3 > 2/3p
Find inequality! :D

Answers

Answer:

p < -9/2 or p < -4.5

Step-by-step explanation:

-3 > 2/3p

-3 * 3> 2p

-9/2 > p

-9/2 > p or -4.5 > p

Solve for f: ax+3b=2f ​

Answers

Final Answer: [tex]f = \frac{ax}{2} + \frac{3b}{2}[/tex]

Steps/Reasons/Explanation:

We will be trying to rewrite the equation. To do this we will move [tex]2f[/tex] to the left. Then, we will move [tex]ax + 3b[/tex] to the right.

Question: Solve for [tex]f[/tex]: [tex]ax + 3b = 2f[/tex].

Step 1: Rewrite the equation.

[tex]2f = ax + 3b[/tex]

Step 2: Divide each term by [tex]2[/tex] and simplify.

[tex]\frac{2f}{2} = \frac{ax}{2} + \frac{3b}{2}[/tex]

Step 3: Cancel out the common factor of [tex]2[/tex].

[tex]\frac{Cancel 2 f}{Cancel 2} = \frac{ax}{2} + \frac{3b}{2}[/tex]

Step 4: Divide [tex]f[/tex] by [tex]1[/tex].

[tex]f = \frac{ax}{2} + \frac{3b}{2}[/tex]

~I hope I helped you :)~

10 times as much as 6,000 is 1/10 of?

Answers

Answer:

10 x 6,000 is 60,000. now divide it by ten. its 6,000 because its 1/10 of it so yes, 6,000

rocky,tony,junior received all there weekly salaries,tony received $3000 while junior received:$9000 if the ratio of tony salary to rocky salary is 3:6 what is the ratio of rocky salary to junior salary? ​

Answers

Answer:

6:9 or 2:3

Rocky's salary is $6000

{(0, 8), (1,2), (3,7), (5,9), (3,6)}
Function or not

Answers

Answer:

No

Step-by-step explanation:

The is only one output for each value

In Δ,∠=70°,∠=50° ∠ .
ℎ ∠.

Answers

Answer:

100°

Step-by-step explanation:

A triangle is a polygon shape with three sides. Triangles are of different types such as obtuse, scalene, equilateral, isosceles etc.

In triangle ABC:

70° + 50° + ∠C = 180° (sum of angles in a triangle)

120 + ∠C = 180

∠C = 180 - 120

∠C = 60°

Since ∠C is bisected into ∠ACD and ∠BCD, hence:

∠ACD = ∠BCD = ∠C / 2

∠ACD = ∠BCD = 60 / 2

∠ACD = ∠BCD = 30°

In triangle ACD:

∠A + ∠ACD + ∠ADC = 180° (sum of angles in a triangle)

50 + 30 + ∠ADC = 180

∠ADC + 80 = 180

∠ADC = 100°

what is the area of a 10 inch circle

Answers

Answer:

79 square inches

Step-by-step explanation:

Perform the operation. Enter your answer in scientific notation.


7 × 106 − 5.4 × 106 =

Answers

Answer:

849

Step-by-step explanation:

1556

Answer:

1.696  × [tex]10^{2}[/tex]

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  10

.

If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

A pair of jeans costs $32 at Old Navy. If there is an 11% sales tax, how much will the total price of the jeans be

Answers

Answer:

35.52

$ total for the jeans

Answer:

The price of the jeans will be $28.48

Step-by-step explanation:

11% of $32 is $3.52

Do $32 - $3.52 and you get your answer of $28.48

I hope this answered your question

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