Answers
Answer:
h(x) = (x + 4)^2 - 2
Step-by-step explanation:
Start with the red graph: f(x) = x^2
First we move the entire graph 4 units to the left. The resultant function is g(x) = (x + 4)^2.
Next, we move this latest graph 2 units down. The resultant function (and answer to this question) is h(x) = (x + 4)^2 - 2
Related Questions
Working together, two ants named Aran and Beatrice can build an ant hill in 10 hours. Aran and Charlie can build the ant hill in 12 hours. Beatrice and Charlie can build the ant hill in 15 hours. How long, in hours, will it take to build the ant hill if Aran, Beatrice, and Charlie work together?
Answers
Answer:
They complete the hill in 8 hours
Step-by-step explanation:
Equations:
Let's call the variables:
Aran can make build the ant hill in A hours
Beatrice can make build the ant hill in B hours
Charlie can make build the ant hill in C hours
In one hour, Aran makes 1/A of the ant hill.
In one hour, Beatrice makes 1/B of the ant hill.
In one hour, Charlie makes 1/C of the ant hill.
Aran and Beatrice build it in 10 hours, thus:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}=\frac{1}{10}\qquad\qquad[1][/tex]
Similarly:
[tex]\displaystyle \frac{1}{A}+\frac{1}{C}=\frac{1}{12}\qquad\qquad[2][/tex]
[tex]\displaystyle \frac{1}{B}+\frac{1}{C}=\frac{1}{15}\qquad\qquad[3][/tex]
We need to find the time taken for the three ants to build the anthill:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=[/tex]
Adding [1], [2], and [3]:
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{1}{10}+\frac{1}{12}+\frac{1}{15}[/tex]
Adding the fractions (LCM=60):
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{6}{60}+\frac{5}{60}+\frac{4}{60}[/tex]
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{6+5+4}{60}=\frac{15}{60}=\frac{1}{4}[/tex]
Dividing by 2:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{8}[/tex]
All ants together make 1/8 of the hill, thus they complete the hill in 8 hours
The function d = 16t2 models the distance d, in feet, that an object falls in t seconds. Find the inverse function and use the inverse function
o estimate the time it takes an object to fall 100 feet. (1 point)
Answers
Answer:
[tex]t = \frac{1}{4}\sqrt d[/tex]
Time to reach 100ft is 2.5 seconds
Step-by-step explanation:
Given
[tex]d = 16t^2[/tex]
Solving (a): Determine the inverse function
[tex]d = 16t^2[/tex]
Swap the positions of d and t
[tex]t = 16d^2[/tex]
Make d the subject
[tex]\frac{t}{16} = d^2[/tex]
Take positive square root of both sides
[tex]\sqrt{\frac{t}{16}} = d[/tex]
[tex]d = \sqrt{\frac{t}{16}}[/tex]
[tex]d = \frac{1}{4}\sqrt t[/tex]
Swap the positions of d and t
[tex]t = \frac{1}{4}\sqrt d[/tex] --- The inverse function
Solving (b): Find t when d =100
Substitute 100 for d in [tex]t = \frac{1}{4}\sqrt d[/tex]
[tex]t = \frac{1}{4}\sqrt {100[/tex]
[tex]t = \frac{1}{4}* 10[/tex]
[tex]t = \frac{1* 10}{4}[/tex]
[tex]t = \frac{10}{4}[/tex]
[tex]t = 2.5[/tex]
How can this expression be written another way?
60x - 24
Factor using the distributive property and the greatest common factor to write an equivalent expression
Enter your answer by filling in the boxes.
Answers
Answer:
factor using 12 (gcf)
12(5x-2)
Solve and graph the inequality |4 – v| < 5.
a. Write the inequality as two inequalities without absolute value.
b. Solve the inequality and write the solution set.
c. Graph the solution on a number line.
50 points !!!!!
Answers
Answer:
-1 < v < 9Step-by-step explanation:
Given inequality
|4 - v| < 5a. The two inequalities:
1. 4 - v < 5
v > 4 - 5v > -12. 4 - v > -5
v < 4 - (-5)v < 9b. Solution is the combination of the above two:
-1 < v < 9c. The graph is attached
What is the equation of the line going through the points (2, 4) and (4, 12)
Answers
Answer:
m= 4
b= -12
( 4, -12)
Step-by-step explanation:
m= y2- y1/ x2-x1
m= 12 - 4/ 4 - 2
m= 8/ 2
m= 4
y= 4x + b
(2,4)
4= 4(4) + b
4= 16 + b
-16+4= b
-12= b
b= -12
Find the 15th term of the geometric sequence 1, -4, 16, ...
Answers
Answer:
Answer is 268435456
Step-by-step explanation:
use an = a × ^r n-1 to find the sequence
The 15th term of the given geometric progression sequence 1, -4, 16, ... will be 268435456.
What is geometrical progression series?A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.
For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.
As per the given sequence,
1, -4, 16, ...
First term a = 1
Common ratio r = -4/1 = -4
The nth term is given as ar^(n - 1)
Therefore, the 15th term will be as,
a₁₅ = 1(-4)¹⁵⁻¹
a₁₅ = -4¹⁴ = 268435456
Hence "The 15th term of the given geometric progression sequence 1, -4, 16, ... will be 268435456".
For more information about the geometrical progression,
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Find the radius of the circle. The center of the circle is (2, -3) and a point that lies on the circle is (-1, -2).
Answers
Answer:
[tex]\displaystyle r = \sqrt{10}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Geometry
Definition of a radius - the center of a circle to any point to the circumferenceAlgebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Center (2, -3) → x₁ = 2, y₁ = -3
Circumference point (-1, -2) → x₂ = -1, y₂ = -2
In this case, the distance d from the center to the circumference point would be the radius r of the circle.
Step 2: Find Radius r
[Distance Formula] Define equation [Radius]: [tex]\displaystyle r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute in points [Radius]: [tex]\displaystyle r = \sqrt{(-1-2)^2+(-2--3)^2}[/tex][Radius] [√Radical] (Parenthesis) Simplify: [tex]\displaystyle r = \sqrt{(-1-2)^2+(-2+3)^2}[/tex][Radius] [√Radical] (Parenthesis) Subtract/Add: [tex]\displaystyle r = \sqrt{(-3)^2+(1)^2}[/tex][Radius] [√Radical] Evaluate exponents: [tex]\displaystyle r = \sqrt{9+1}[/tex][Radius] [√Radical] Add: [tex]\displaystyle r = \sqrt{10}[/tex]A light bulb consumes 1800 watt-hour per day. How long does it take to consume 8550 watt-hours
Answers
Answer:
4 hours and 45 minutes
Step-by-step explanation:
8550 ÷ 1800 equals 4.75 which should translate into 4 hours and 45 minutes
4(2x - y) - 3x + 2y
Answers
Answer:
5x - 2y
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
4(2x - y) - 3x + 2y
Step 2: Simplify
Distribute 4: 8x - 4y - 3x + 2yCombine like terms (x): 5x - 4y + 2yCombine like terms (y): 5x - 2y8x + 3 – 13
31 - 21 - 11
Answers
Answer: 8x+10
-1
Step-by-step explanation:
1over 4 power negative 5
Answers
Answer:
4 to the 5th power (4^5)
Y is directly proportional to x squared if y=20 when x=2 find y when x= 5
Answers
Answer:
y = 125
Step-by-step explanation:
Given that,
y is directly proportional to x² i.e.
[tex]y=kx^2[/tex]
k is a constant of proportionality
Put y = 20 and x = 2 in the given equation to find k.
[tex]k=\dfrac{y}{x^2}\\\\k=\dfrac{20}{(2)^2}\\\\k=5[/tex]
Now put k = 5 and x = 5 in the given equation to find y.
[tex]y=5\times (5)^2\\\\y=125[/tex]
So, the value of y is equal to 125.
Make P the subject of the formula
pliz pliz ans this
A= P(1+(r/100))^t
Answers
Answer:
P = A / (1 + r/100)ᵗ
Step-by-step explanation:
A = P(1 + r/100)ᵗ
We can make P the subject of the above expression as follow:
A = P(1 + r/100)ᵗ
Divide both side by (1 + r/100)ᵗ
P = A / (1 + r/100)ᵗ
Therefore, making P the subject of
A = P(1 + r/100)ᵗ, we have
P = A / (1 + r/100)ᵗ
find the graph below, find the slope of the line. Write your answer as a decimal.
Answers
Slope = (0-2)/(4-0) =-½
Which subject is used most heavily in game design?
a.
Science
c.
Social studies
b.
Language arts
d.
Math
Answers
Answer:
nose
Step-by-step explanation:
perdno
Answer:
Language arts
Step-by-step explanation:
carmen is taller than ramon but shorter than ricardo. carmen is shorter than ryan who is taller than ricardo. who is the tallest? who is the shortest?
Answers
Answer:
ramon is the shortest
ryan is the tallest
carmen is taller than ramon
carmen is shorter than ricardo
carmen is shorter than ryan
ryan is taller than ricardo
Sam invested $7500, some at 7% interest and the rest at 10%. How much did he invest at each rate if he received $570.00 in interest in one year?
Answers
Answer:
.
Step-by-step explanation:
If the root of x2-7x+k=0, m=1, find the value of the constant k
Answers
Answer:
hfrhghubifhvfuovhtjopugjob
Step-by-step explanation:
The expression (2x + 6) + x represents the perimeter of an isosceles triangle. If x represents the length of one side of the triangle, explain how you can use Distributive Property to find the length of each of the two equivalent sides?
Answers
Answer:
x+3
Step-by-step explanation:
x= one side of the triangle
(2x+6)=two sides of the isosceles triangle
Factor (2x+6) which is 2(x+3)
So, the length of each side is x+3.
Please help with explanation
1/3 of Cheryl’s savings was the same as 3/4 of Hilda’s savings.Cheryl saved $36.
(a) Find the ratio of Cheryl’s savings to Hilda’s savings.
(b) How much did Hilda save?
Answers
Answer:
a) the ratio is 9:4
b) Hilda did save $16.
Step-by-step explanation:
Let's define the variables:
C = Cheryl's savings.
H = Hilda's savings.
We know that:
(1/3)*C = (3/4)*H
We also know that Cheryl saved $36, then we have:
C = $36
Now we can replace that in the above equation to get:
(1/3)*$36 = (3/4)*H
$12 = (3/4)*H
$12*(4/3) = H = $16
Then Hilda did save $16.
And the ratio between of Cheryl's savings to Hilda's savings is:
36 : 16
We can simplify this if we divide both by 2.
(36/2) : 16/2
18 : 8
Again, we can divide both by 2:
(18/2) : (8/2)
9 : 4
Then the ratio is 9 : 4
Hello! I'm having a problem figuring out this problem: 6c-9d=111 5c-9d=103
I've been looking at different ways to solve it, but I'm not sure how to do it. Please, help give me a step-by-step instruction on how to figure it out. (I'll make you the most Brainliest answer.) (And, you'll get a good amount of points.)
Answers
Answer:
C=8
Step-by-step explanation:
6c-9d=111
-) 5c-9d=103
6c-5c=c
-9c+9c=0
111-103=8
(Negative+Negative=Positive)
C=8
I need Brainliest!
what is 1+1?
(serious question)
Answers
Answer:
2
Step-by-step explanation:
What procedure can be used to solve the equation StartFraction x Over 19.3 EndFraction = 38.6, and what is the solution?
Answers
Answer: it’s number D I think let me know if I’m wrong
Step-by-step explanation:
Answer:
the answer is d.Multiply both sides by 19.3; the solution is 744.98.
Step-by-step explanation:
got it right on edge.
A strawberry farmer will receive 37 per bushel of strawberries during the first week of harvesting each week after that the value will drop 0.8 per bushel the farmer estimates that there are approxiamately 129 of strawberries int he fieldsand that the crop is increasing at a rate of four bushels per week when should the farmer harvest the strawberries to maximize their value? (Assume that "during the first week of harvesting" here means week 1. How many bushels of strawberries will yield the maximum value? (Round your answer to the nearest integer.)
bushels
2. What is the maximum value of the strawberries? (Round your answer to two decimal places.)
$
Answers
Answer:
a.)
Number of bushes = b = 129 + 4(7) = 129 + 28 = 157 bushes
b.)
Revenue = bx = (157)(31.4) = $ 4929.8
Step-by-step explanation:
Let number of bushes = b
The price of the bushes = x
The time to harvest = t
The revenue = y
Now given,
Price = x = 37 - (0.8)t
and
Number of bushes = b = 129 + 4t
Also,
The revenue = (Number of bushes)(Price of the bushes)
= bx
= (129 + 4t)[37 - (0.8)t]
= 129×37 - 129× (0.8)t + 4×37t - 4×0.8t²
= 4773 - 103.2t + 148t - 3.2t²
= 4773 + 44.8t - 3.2t²
⇒ y = 4773 + 44.8t - 3.2t²
Now,
[tex]\frac{dy}{dt}[/tex] = 0 + 44.8 - 6.4t
Now,
[tex]\frac{dy}{dt}[/tex] = 0
⇒ 44.8 - 6.4t = 0
⇒ - 6.4t = -44.8
⇒ 6.4t = 44.8
⇒t = [tex]\frac{44.8}{6.4} = 7[/tex]
Now,
[tex]\frac{d^{2}y }{dt^{2} }[/tex] = -6.4
As [tex]\frac{d^{2}y }{dt^{2} }[/tex] < 0 ,
It means at time t = 7 , the revenue is maximum
a.)
Number of bushes = b = 129 + 4(7) = 129 + 28 = 157 bushes
Price = x = 37 - (0.8)(7) = 37 - 5.6 = 31.4
b.)
Revenue = bx = (157)(31.4) = 4929.8
Kevin is driving on a long road trip. He currently has 11 gallons of gas in his car. Each hour that he drives, his car uses up 1.75 gallons of gas. How much gas would be in the tank after driving for 5 hours? How much gas would be left after t hours?
Answers
Answer:
He would have 2.75 gallons left after 5 hours.
Step-by-step explanation:
11. What percent of this circle is shaded if you have 1/3 and 5/12?
Answers
Answer:
Epic
Step-by-step explanation:
you can do it trust me.
Find the volume of the conical paper cup.
3 cm
7 cm
O A. 49 pi cm ^3
B. 7 pi cm^3
C. 21 pi cm ^3
O D. 63 pi cm^3
Answers
Answer:
C. 21π cm³
Step-by-step explanation:
Use volume formula for cone
[tex]V = \pi r^{2} \frac{h}{3}[/tex]
r = 3cm
h = 7cm
[tex]V = \pi (3)^{2} * \frac{7}{3}[/tex]
[tex]V = \pi 9 * \frac{7}{3}[/tex]
[tex]V = \pi \frac{63}{3}[/tex]
[tex]V = 21 \pi[/tex]
Answer:
C
Step-by-step explanation:
credit goes to the person up top
The shape below is a horizontal cross section of a figure. Select all the possible figures that could have this shape as a cross section. A Sphere B Rectangular Prism C Triangular pyramid D Rectangular pyramid
Answers
Answer:
D. Rectangular prism
Step-by-step explanation:
I believe the answer is D. Rectangular prism
A rectangular prism is also called a cuboid. Like cuboid, it also has three dimensions, i.e., length, width and height. So here the horizontal cross section of the figure is rectangular prism. The correct option is B.
What is a rectangular prism?A rectangular prism is defined as a three dimensional shape which has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. A geometrical box, notebooks, rooms, etc. are in the shape of a rectangular prism.
A rectangular prism has 6 faces, 12 edges and has 8 vertices. For a rectangular prism the pairs of opposite faces are identical or congruent. A prism with six faces that are rectangles and all angles are right angles is a right rectangular prism.
Thus the correct option is B.
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find the following (a) 20% of 1 kg in grams
Answers
Answer:
20% of 1kg.(1000g)
20/100×1000g
200g
Determine the interval(s) where f(x) = In (9x - 81) is continuous.
Answers
Answer: (9, ∞)
Step-by-step explanation:
You cant take the natural log of a negative number, and you cant take the natural log of 0. So, to find the intervals where the function is defined, set the inside of the natural to 0.
9x - 81 = 0
x = 9
The intervals where this function is continuous is from 9 --> infinity