Answer:
[tex]f"'(x) = 2(x-4)^2 - 1[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^2[/tex] --- the quadratic function
Vertically stretched by 2
Translation: [tex]4\ units[/tex] left and [tex]1\ unit[/tex] down
Required
Determine the new function
[tex]f(x) = x^2[/tex]
The rule for vertical stretch is:
[tex](x,y) \to (x,ay)[/tex]
In this case:
[tex]a = 2[/tex]
So, we have:
[tex]f(x) = x^2[/tex]
[tex]f'(x) = a * f(x)[/tex]
[tex]f'(x) = a * x^2[/tex]
Substitute: [tex]a = 2[/tex]
[tex]f'(x) = 2 * x^2[/tex]
[tex]f'(x) =2x^2[/tex]
Translation: 4 units left
The rule is:
[tex](x,y) \to (x - c,y)[/tex]
In this case: [tex]c =4[/tex]
So, we have:
[tex]f"(x) = 2(x - 4)^2[/tex]
Translation: 1 unit down
The rule is:
[tex](x,y) \to (x,y-d)[/tex]
In this case, [tex]d=1[/tex]
So, we have:
[tex]f"'(x) = f"(x) - 1[/tex]
[tex]f"'(x) = 2(x-4)^2 - 1[/tex]
This graph shows the relationship between the number of cubic yards and total cost of topsoil at a garden shop.
Mulch
The equation, y=25x, represents
the cost, y, in dollars, of x cubic
yards of mulch at the garden shop.
Type an equation to represent the cost of the topsoil. Show your work.
and
How does the cost of the topsoil compare to the cost of the mulch?
Answer: y=30x
top soil is 5 more dollars than mulch
Step-by-step explanation:
to find y=30x
see what y equals when x equals 1
The cost of the topsoil is $5 more than the cost of the mulch.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, the equation, y=25x, represents the cost, y, in dollars, of x cubic yards of mulch at the garden shop.
From the, graph we have coordinates (1, 30) and (2, 60)
We know that, slope of points is (y2-y1)/(x2-x1)
Now, (60-30)/(2-1)
= 30
Substitute, m=30 and (x,y)=(1, 30) in y=mx+c, we get
30=30(1)+c
c=0
Substitute, m=30 and c=0 in y=mx+c, we get
y=30x
Per 1 cubic yard
Topsoil is y=30x=$30 and cost of the mulch is y=25x=$25
So, difference in cost is 30-25=5
Comparing cost in both the situation, the cost of the mulch is less than topsoil
Therefore, the cost of the topsoil is $5 more than the cost of the mulch.
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b. 21.8°
5. Find the measure of the angle to the nearest tenth of a degree.
cos Y=0.5135
30.9
c.
The dimensions of a rectangle are shown. What is the area of the rectangle?
Your answer:
128xunits
8x + 10 units
16x + 20 units
15x2 + 46x + 16 units
Answer:
=(3x+8) (5x+2)
=15x2 + 46x + 16 units
Can I Get Help Pls Damon drew a scale drawing of a swimming pool. The scale he used was 1 inch : 9 feet. The diving board is 2 inches long in the drawing. How long is the actual diving board?
Answer: 18 ft
Step-by-step explanation:
Given
Scale is 1inch:9 feet
1 feet= 12 inch
The dividing board is 2 inches long
Suppose the actual length of the diving board is x
[tex]\therefore \dfrac{1}{9\times 12}=\dfrac{2}{x}\\\\\Rightarrow x=\dfrac{9\times 12\times 2}{1}\\\\\Rightarrow x=216\ inch\ \text{or}\ 18\ ft[/tex]
please answer homework please answer all 3
Answer:
Question 1: 4 x 11
Question 2: x = 7
Question 3: 32x
Step-by-step explanation:
What is the square root of my juicy as.s
A.1000000000000
B.10
C.1
D.1000000000000000000000000000000000000000000000000000000
Answer:
Hi! The answer to your question is C. 1 But im pretty sure to have a square root...you have to have a square butt..
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
Stay Safe!!
- Brooklynn Deka
Answer:
The answer is E.) 0
Step-by-step explanation:
Please, touch some grass.
4x^2=20x
factor step by step please?
Answer: look at the picture
Step-by-step explanation: Hope this help :D
Music
Read aloud
1) Sound effects
Answer:
Step-by-step explanation:
What am I supposed to do? If you don’t mind me asking. Like I’m not trying to waste your points at all just I’m confused I can def help tho if you tell me what I need to do
Answer:
Huh-?
Step-by-step explanation:
please help me please will give brainliest
Answer:
[tex]16\sqrt{17}[/tex]
Step-by-step explanation:
The perimeter is two times width plus two times length:
[tex]2\sqrt{17} + 2\cdot 7\sqrt{17} = 2\sqrt{17} + 14\sqrt{17} = 16\sqrt{17}[/tex]
There is no way to simplify further.
i need help on my math test im not sure how to find the GCF of an equation so please help me
Answer:
2x^3
[tex]2x^{3}[/tex]
thomas sold 412 boxes of cookies at a cost of 1175 what is an estimate closest to the cost of a box of cookies
Answer:
285
Step-by-step explanation:
1175 divided by 412 = 2.85194174757
that would be around 2.85
1. Mr. Jackson took a cab from school to JFK Airport. The taxi fare was d dollars and he gave the
driver a 15% tip. Which of the following expressions can be used to describe the total fair? Select all
that apply.
Help me ASAP!!!!!!!
See pic attached
friend request me and I'll accept thanks xx
Step-by-step explanation:
cosA=b/h
cos41°=y/30
0.754=y/30
y=0.754×30
y=22.64
Answer:
y = x + 4
-3x + y = 2
x = -2y - 2
Step-by-step explanation:
PLSSSS HELPPP ILL GIVEE COOKIE
Answer:
Sorry. It is 4.
Step-by-step explanation:
Again, where is my cookie?
whats the distributive property
Answer:
5n + 5a
Step-by-step explanation:
This would be your simplified algebra expression.
Answer:
The distributive property tells us how to solve equations in the form of a(b + c). The distributive property is sometimes called the distributive law of multiplication and division. Normally when we see an equation like this … 4(8+3) distributive property format 4(8+3) -> 4(11) -> 44 we just evaluate what’s in the parentheses first, then solve it: 4(8+3)=4x8 + 4x3=44 These are the 2 methods
Step-by-step explanation:
how do we find the angles for an irregular trapezoid?
Answer:
all angles must add up to 180 to be a trapizoid so if they dont add up then its irregular
Step-by-step explanation:
Please Helppp pleaseeeeeeee pleaseeee
Answer:
Step-by-step explanation:
I can't see the screenshot
so like yeah
Round to the nearest tenth for the right triangle, wouldn't it be 20 or am I wrong?
A ringtoss toy is composed of a rectangular prism on top of a cylinder. The rectangular prism is completely filled with water. The dimensions of the rectangular prism are shown in the diagram.
What is the volume of the rectangular prism in cubic centimeters?
165 cm3
270 cm3
348 cm3
26 cm3
Answer:
270 cm3
Step-by-step explanation:
The volume of the given rectangular prism is 270 cm³.
What is Volume?Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill.
Volume is defined as the space occupied by an object inside the confines of three-dimensional space. It is also known as the object's capacity.
We have
Length = 9 cm
Width = 2 cm
Height = 15 cm
Using the formula for volume of the rectangular prism
= length x width x height
= 9 x 2 x 15
= 270 cm³
Thus, the volume of the given rectangular prism is 270 cm³.
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Write this word sentence as an equation. 82 is the difference of a number b and 24
Answer:
106 - 24 = 82
Step-by-step explanation:
b = 106, solve 106 - 24 and you get 82.
Hope this helped.
Answer:
b/24=82
Step-by-step explanation:
Since the difference of an equation is the outcome of division we place 82 as the answer.
Also, since 82 is greater than 24 we can assume that the variable "b" is larger than both 82 and 24.
Describe how you know that (8+9)+3 is equivalent to 8+(9+3). What is the benefit to using this property
Answer:
Associative property of addition
Step-by-step explanation:
The associative property of addition is as follows :
a+(b+c) = (a+b)+c
We have,
a = 8, b = 9 and c = 3
So,
Using above property,
(8+9)+3 = 8+(9+3)
20 = 20
Hence, this is the required solution.
A woodworker wants to cut a board that is 10.016 feet long into 4 equal-length pieces. How long will each of the cut boards be?
Answer:
2.504 feet
Step-by-step explanation:
Find the length by dividing 10.016 by 4
10.016/4
= 2.504
So, each cut board will be 2.504 feet
We have
[tex] \begin{cases} \sf No. \: of \: pieces = \frak{4} \\ \sf Total \: Length = \frak{10.016 \: ft} \end{cases} [/tex]
So,
Length of 1 board = 10.016/4
Length of 1 board = 2.504 ft
So,
The length of 1 board is 2.504 ft.
Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were allergic to penicillin, Nathan has a 75% chance of having the same allergy. The doctor performed a skin test to see whether Nathan would react to it. The test is 98% accurate. What is the probability that Nathan is not allergic to penicillin and the test predicts it?
0.005
0.015
0.245
0.735
Answer:
0.245 because of him having the 75% chance of getting it and the test only being 98%
Step-by-step explanation:
its 0.245
Answer:
its 0.245
Step-by-step explanation:
I used the big fat mega thinking side of meh brain im smart
Use the information from the graphs to write the equation in y=ab*^x
Answer:
1). y = 4(1.75)ˣ
2). y = (2)ˣ
Step-by-step explanation:
1). Let the equation of the given exponential graph is,
y = a(b)ˣ
Graph of the given equation passes through two points (0, 4) and (0+1, 4+3)
For point (0, 4),
4 = a(b)⁰
a = 4
For point (1, 7),
7 = 4(b)¹
b = [tex]\frac{7}{4}[/tex]
b = 1.75
Therefore, equation of the function is,
y = 4(1.75)ˣ
2). Similarly, equation of the second graph will be same in the form of
y = a(b)ˣ
Second graph passes through the points (0, 1) and (2, 4)
For (0, 1),
1 = a(b)⁰
a = 1
For (2, 4),
4 = 1(b)²
b = 2
Therefore, exponential function representing the graph will be,
y = 1(2)ˣ
y = 2ˣ
You charge people $10 per hour to pick fruits and $8 per hour
to water flowers. The equations model the money you earn for
h hours by given as Picking fruits: m = 10h and Watering
flowers: m = 8h. Graph the equations, then see how much more you can earn from picking fruits than from watering flowers after 6 hours.
Can someone help me with this please!!!
Answer:
It's B
Step-by-step explanation:
Jon didn’t follow the order of operations. Explain what he did wrong.
Which are true about the area of a circle? Check all that apply. The diameter is used in the formula The units are always squared. The area can be found when given the diameter by first finding the radius O The area is the distance around the circle. O Circumference can be used to find area.
Answer:
the second one and the first one
Step-by-step explanation:
Diameter is double radius so divide by two for radius then times by pi and you have area and when it comes to area is it always sqaured
The polygons are similar. Find the value of x.
Answer:11
Step-by-step explanation:
hello please help thanks
Answer:
Condensation.
Pls help! giving thanks. What is the slope of the line (picture above)
Answer:
[tex]slope = 1 [/tex]
Step-by-step explanation:
We can see that the graph cuts the x axis at , (-1,0) and y axis at (0,1) . So we can find the slope as ,
[tex]\implies slope = \dfrac{y_2-y_1}{x_2-x_1}\\\\\implies slope = \dfrac{ 1-0}{0+1} \\\\\implies\boxed{\boxed{ slope = 1 }}[/tex]