Answer:
y=45x+115
Step-by-step explanation:
We can find the slope of a line tangent to a curve at a point by evaluating the derivative of the function at that point.
We are given the function
f ( x ) = 4 x 3 + 12 x 2 + 9 x + 7
= f ( x ) = 4 x 3 + 12 x 2 + 9 x 1 + 7 x 0
Using the power rule, let's now compute the derivative of f( x )
f ' ( x ) = ( 3 ⋅ 4 x 2 ) + ( 2 ⋅ 12 x ) + ( 1 ⋅ 9 x 0 ) + 0 ⋅ 7 x − 1
f ' ( x ) = 12 x 2 + 24 x + 9
We can now find the slope of f ( x ) at x = − 3 by substituting this value into f ' ( x )
f ' ( − 3 ) = 12 ( − 3 ) 2 + 24 ( − 3 ) + 9
f'(-3)=12(9)+24(-3)+9
f'(-3)=108-72+9
f'(-3)=45(slope of the tangent line at x = − 3
Now that we have a slope for the tangent line, we need to identify a point on the line.
We know the tangent line touches the function f ( x ) at the point x = − 3 , so let's find the value of f ( x ) at this point:
f(-3)=4(-3)3+12(-3)2+9(-3)+7
f(-3)=4(-27)+12(9)+9(-3)+7
f(-3)=108+108-27+7
f'(-3)=-20
So we know the tangent line goes through the point
(-3,-20)
Finally, we can use the point-slope formula for a line to find the equation of the tangent line.
y=mx+b
To find the value of b , substitute the values we have calculated for the point and slope of the tangent line:
(-20)=(45)(-3)+b
-20=-135+b
b=115
So our final answer for the equation of the tangent line is:
y=45x+115
Can you guys please help me zoom in if you can’t see I’ll mark you brainliest be genuine !
Answer:
Volume: 528 ft^3
Surface Area: 444.72
Step-by-step explanation:
For the surface area, I'm not quite sure, but the volume is correct.
Hope this helped! :)
( ﾟдﾟ)つ Bye
Using the vertical line test. Is this a function?
Answer:
Can't get one(Read explanation)
Step-by-step explanation:
What you do to find out if its a function is see if any of the dots are in the same x value. If they are, its not a function. If they aren't it is a function.
For large parties, a restaurant charges a reservation fee of $30, plus $20 per person. The total charge for a party of x people is f(x) = 20x + 30. How will the graph of this function change if the reservation fee is raised to $65 and the per-person charge is lowered to $12?
MAFS.912. G-GMD. 1.3
A regular pyramid has a square base. The perimeter of the base is 36
inches and the height of the pyramid is 15 inches. What is the volume of
the pyramid in cubic inches?
A. 180
B. 405
C. 540
D. 1215
Answer:
b
Step-by-step explanation:
The volume of the square pyramid is 405 cubic inches.
The correct answer is option (B).
What is the volume of the square pyramid?V = 1/3 × base area × h,
where h is the height of the pyramid.
What is the perimeter of square?P = 4 × a
where, 'a' represents the side of the square
For given example,
Let 'a' be the side length of the square base.
We have been given the perimeter of the square base is 36.
⇒ P = 36
⇒ 4 × a = 36
⇒ a = 9
So, the length of the side of the square base is 9 in.
Using the formula of the volume of the pyramid,
⇒ V = (1/3) × base area × h
⇒ V = (1/3) × a² × h
⇒ V = (1/3) × (9)² × 15
⇒ V = 27 × 15
⇒ V = 405 cubic inches
Therefore, the volume of the square pyramid is 405 cubic inches.
The correct answer is option (B).
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pls answer fast will give branliest
if u send links will report so mf fast
Answer:
m∠1= 17°
m∠2=73°
m∠3=90°
m∠4=51°
m∠5=17°
m∠6=129°
Step-by-step explanation:
Hope it helps...
Have a great day!!
The time needed to complete a final examination in a particular college course is normally distributed with a mean of 79 minutes and a standard deviation of 8 minutes. Answer the following questions.
Answer:
A) 0.0088
B) 0.2997
C) 5
Step-by-step explanation:
Given: Mean: Ч = 79 minutes
Standard deviation : б = 8 minutes
The formula for z score:
z= x-ц/σ
a) For x=60 minutes
z= 60-79/8 = -2.375
The p-value = P(z< -2.375) = 0.0087745 ≈ 0.0088
b) For x= 75 minutes
z= 75-79/8 = -0.5
The p-value = P(60 < x < 75) = P (-2.375 < z < -0.5)
= P(-0.5)-P(-2.375)= 0.3085 -0.0088 =0.2997
c) For x=90 minutes
z= 90-79/8 = 1.375
The p-value = P (z > 1.375)= 1-P(z < 1.375)
= 1-0.9154342 = 0.0845658
If the number of students in the class=60.
Then, the number of students will be unable to complete the exam in the alotted time = 0.0845658 x 60 = 5.073948 ≈ 5
Wells Fargo has realized that they lose home mortgage business to other banks that can process the loan applications with less variability in the time it takes to process each application. The bank recently studied this problem, and found that the processing time T is normally distributed with a mean of 13 days. They didnt measure the standard deviation, but they know that 50% of all applications were processed in between 10.5 and 15.5 days. After learning all this, they then fired half of their mortgage loan officers and replaced them with new recruits. They then sampled 25 applications, and found a sample mean of 13 days (same as the old) and a sample standard deviation of 2.5 days.
(a) Test whether their actions have significantly changed their processing time T.
(b) Based on the sample of 25 applications, give a 90% confidence interval for the parameter that
has changed.
Answer: B
Step-by-step explanation:
HELP ME OUTT PLSS BXJXID
Answer:
d
Step-by-step explanation:
Answer: D
Step-by-step explanation:
The probability of picking a brown pencil greater than the probability as NOT picking a brown pencil because there more brown pencils than purple so there is a higher chance you will get a brown than NOT get a brown.
An equation is shown.
3.8+y=14.2
What is the value for x that makes the equation true?
Answer:
y=10.4
Step-by-step explanation:
If you mean Y instead of x then the answer is 10.4
3.8+y=14.2
-3.8 -3.8
y=10.4
Answer:
y/x=10.4
Step-by-step explanation:
3.8+y=14.2 Subtract 3.8 from both sides
y=10.4
Solve the equation (216/739)^1/3
The plane was flying long so it's true!
Suppose that you're paid $63.24 for 7 hours of work. What is your hourly pay rate?
Answer:
$9.03
Step-by-step explanation:
Using x for pay rate
63.24=7x Divide both sides by 7
x=9.03
There were 16 skittles in a bag there were 3 yellow, 4 red, 2 purple, 6 orange, and 1 green. What is the probability of pulling a red skittle (simplify your answer). The probability of a red is /
Answer:
1 out of 8, or 12.5 percent.
Step-by-step explanation:
There were 2 red skittles out of 16 total skittles, and then we divide the numbers by 2, then we get 1 out of 8. Converting it into a percentage, there is a 12.5% chance of pulling out a red skittle.
A square originally starts with an area of 64 cm. If each side of the square is increased by 2 cm, what is the area of the new square? A. 68 cm2 B. 72 cm2 C. 81 cm? D. 100 cm2
Answer:
D
Step-by-step explanation:
A grocery store bought milk for $2.60 per half gallon and stored it in two refrigerators. During the night, one refrigerator malfunctioned and ruined 15 half gallons. If the remaining milk is sold for $4.08 per half gallon, how many half gallons did the store buy if they made a profit of $69.04?
Answer:
88 half gallons
Step-by-step explanation:
We can solve this problem by creating an equation. First we will need a variable. Since we are trying to find how many half gallons the store bought, that will be what our variable represents.
Let g = the number of half gallons
Since the store bought milk for $2.60 per half gallon, the amount of money they spent will be 2.6g.
The remaining milk is sold for $4.08 per half gallon. Remember, the store lost 15 half gallons so the number of gallons is currently g-15. This means that to find the amount of profit they made, we use 4.08(g-15).
We already know that the profit is $69.04, so we can make this into an equation.
This profit is the amount of money made minus the cost.
4.08(g-15) - 2.6g = 69.04
We can begin to solve this by simplifying the left side.
4.08(g-15) - 2.6g
4.08g - 61.2 - 2.6g
1.48g - 61.2
This makes our new equation:
1.48g - 61.2 = 69.04
We can begin to isolate our variable, g, by adding 61.2 to both sides.
1.48g = 130.24
Then we divide both sides by 1.48.
g = 88
You have been commissioned to design a monument to Mr. Mullen. The monument consists of a pool 100 ft long where observers stand on one side of the pool and a giant statue of Mr. Mullen holding a cat stands on the other. If you want the angle of elevation from the ground to be 42 degrees, how tall must you make the statue?
a. 100 ft
b. 90 ft.
c. 111 ft
d. 67 ft
e. 74 ft
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Answer:
b. 90 ft
Step-by-step explanation:
The opposite and adjacent sides of the relevant triangle are given.
Tan = Opposite/Adjacent
tan(42°) = h/(100 ft)
h = (100 ft)tan(42°) ≈ 90.04 ft
The statue must be about 90 ft tall.
Answer:
a. 100 ft
b. 90 ft.
c. 111 ft
d. 67 ft
e. 74 ft
its b.90 ft.
What is 2×2×2×5÷5÷100×100-100+1000
Answer:
908
Step-by-step explanation:
Answer:
908
Step-by-step explanation:
from 2005 to 2015, a population of lions decreased by 2% annualy. there were 1500 of this population of likns in 2005. how many lions wew left by 2015
Answer:
30
Step-by-step explanation:
I think that's the answer but if I'm wrong tell me right away I'll try another method.
-
A rectangular prism has how many flat surfaces?
Answer:
it has 6 faces
Step-by-step explanation:
A rectangular prism has 6 flat surfaces.
How to find a rectangular prism?A rectangular prism is a polyhedron with two congruent and parallel bases.
Another name for a rectangular prism is cuboid.
A rectangular prism has 6 faces, 8 vertices and 12 edges.
Flat surface are called plane.
We see that a rectangular prism has six sides and all of its sides are rectangles.
Therefore, all the sides of a rectangular prism are flat surfaces. Since a rectangular prism has six sides; it has six flat surfaces.
The diagram is a rectangular prism.
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In the formula, l = a + (n - 1)d make d as the subject. Find d when l = 10, a = 2, n = 5.
I = a + (n - 1)d [Given formula]
To Find:-Find d when I = 10, a = 2, n = 5
Solution:-I = a + (n - 1)d [Given]
Putting the value of I = 10, a = 2, n = 5 we get,
10 = 2 + (5 - 1)d
10 = 2 + 4d
10 - 2 = 4d
8 = 4d
d = [tex] \frac{8}{4} [/tex]
d = 2
Value of d is 2. [Answer]Can somebody please help? It would be very appreciated. C:
Answer:
31/100
Step-by-step explanation:
Answer:
5/58 = 0.0862...
So, multiply that by 100.
8.62%.
Target sells 12 bottles of water for 2$ and sells 24 bottles for 3$, what is the better price?
Answer:
The 24 bottles for 3$
Step-by-step explanation:
12 bottles for 2$ x 2
= 24 bottles for 4$
This means the 24 bottles for 3$ is the better price per bottle.
Complete the point-slope equation of the line through (-9,6) and (−7,−8)
y−6=
Answer:
its 9 :)
Step-by-step explanation:
hkjgh
Rachael has 20 thin rods whose lengths, in centimetres, are 1, 2, 3, ... 20. Any two rods can be connected at their ends. Rachael selects three rods to make a triangle, then three other rods to make a second triangle, and so on. a Only one of Rachael's rods cannot be the side of a triangle. Determine which one. b Rachael uses six of her rods that are no more than 7 cm to make two triangles. In how many ways can she do this? c Show how Rachael could use 15 of her rods to make five triangles, each with an even perimeter. d Rachael wants to use 18 rods to form a set of six triangles with equal perimeters. Either find such a set or explain why no such set exists.
9514 1404 393
Answer:
a) 1
b) 3
c) {{3, 6, 7}, {8, 12, 14}, {9, 10, 17}, {11, 13, 16}, {15, 18, 19}
d) cannot do. The numbers cannot add up.
Step-by-step explanation:
a) The minimum difference between rod lengths is 1. A unit-length rod cannot be used, because the sum of that and another length cannot exceed a third length. 1 + 2 = 3; is not greater than 3.
__
b) The 3 possible pairs of triangles are
{2, 3, 4}, {5, 6, 7}
{2, 4, 5}, {3, 6, 7}
{2, 6, 7}, {3, 4, 5}
__
c) There are numerous ways to make 5 triangles having an even perimeter. One is shown above. Several more are ...
{5, 12, 15}, {7, 17, 18}, {8, 10, 16}, {9, 13, 20}, {11, 14, 19}
{5, 15, 16}, {6, 9, 13}, {7, 14, 19}, {8, 11, 17}, {10, 12, 18}
{3, 9, 10}, {5, 15, 16}, {7, 13, 18}, {8, 11, 17}, {12, 14, 20}
{4, 9, 11}, {5, 12, 13}, {7, 18, 19}, {8, 15, 17}, {10, 16, 20}
{5, 12, 13}, {7, 18, 19}, {8, 11, 15}, {9, 17, 20}, {10, 14, 16}
__
d) No such set exists.
The sum of the 19 rod lengths is 209. Even if we throw out the rod of length 20 (to make a set of 18 rods), the perimeter must be at least 2(19)+1 = 39. Six triangles with that perimeter would require a total rod length of 6(3) = 234. The total length of rods is insufficient to make the required triangles.
The mean annual salary of classroom teachers is approximately the normal with a mean of $ 45,969. Assume a standard deviation of $7600. Do the following for the variable "annual salary" of classroom teachers.
Determine the sampling distribution of the sample mean for samples of size 64.
The sample mean is μₓ
Answer:
$7,600
Step-by-step explanation:
You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53. 2 3 5 5 7 8 8 9 9 10 11 11 12 12 12 12 13 13 13 14 15 15 15 16 16 17 17 18 18 19 At the 5% level of significance, the conclusion of the test is that the
Answer:
At 5% level of significance the conclusion of the test is that the number of intervals used to test the hypothesis is : 5
Step-by-step explanation:
At 5% level of significance the conclusion of the test is that the number of intervals used to test the hypothesis is : 5
since each interval contains equal number of values lets divide the data into 6 groups i.e. frequency in the third group = 30 /6 = 5
hence we can say that the number of intervals used to test the hypothesis is 5
What is the answer for this using substitution?
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Answer:
(x, y) = (2, -2)
Step-by-step explanation:
We would normally choose to use substitution when x or y could be easily solved-for without having fractions involved. That is not the case here. However, we observe that the term 3y appears in both equations, so we can substitute for "3y" instead of "y".
From the second equation, ...
3y = 5x -16
Substituting into the first equation, ...
2x +(5x -16) = -2
7x = 14 . . . . . . . . . add 16
x = 2 . . . . . . . . . . divide by 7
Using our equation for y, we get ...
3y = 5(2) -16 = -6
y = -2 . . . . . . . . . divide by 3
The solution is (x, y) = (2, -2).
Is it possible for a cross section of a cylinder to have a triangular shape?
It is not possible for a cross section of a cylinder to have a triangular shape
What is cross section?Cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces
What is Cylinder?A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes
What is triangular shape?A triangle is a shape formed when three straight lines meet
Cross section of the cylinder is depends on how we cut .The cross-section of a cylinder may be either circle, rectangle, or oval
Hence, the cross section of of a cylinder can not be a triangular shape
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Solve the equation for x, where x is restricted to the given interval.
y=8cot4x, for x in (0, pi/4)
Harper can do 5 math problems in 1 2/3 minutes.How many problems can she complete in 1 minute?.
Answer:
bjrkhfjehrukfe
Step-by-step explanation:
rnfewklnfeklr
Answer:
Step-by-step explanatioN
30
5. Select all of the ordered pairs that are a solution of y= 8x-1*
Please do asap
I need point really sorry :/ksjsjs
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