The translation of the parent function is:
g(x) = ∛(x + 6) + 1
How do translations work?There are two types of translations, these are:
Horizontal translation:
For a function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
If N is positive, the translation is to the left.If N is negative, the translation is to the right.Vertical translation:
For a function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N
If N is positive the translation is upwards.If N is negative the translation is downwards.Here we start with the parent function:
f(x) = ∛x
And we apply two translations such that:
g(x) = ∛(x + a) + b
Such that:
g(-7) = 0
g(2) = 3
Then we have the system of equations:
∛(-7 + a) + b = 0
∛(2 + a) + b = 3
From the options, the only ones that make the first option true are:
g(x) = ∛(x + 6) + 1
Such that when evaluated in x = -7 we get:
g(-7) = ∛(-7 + 6) + 1 = ∛(-1) + 1 = 0
When evaluated in x = 2 it gives:
∛(2 + 6) + 1 = ∛(8) + 1 = 2+ 1 = 3
So the only option that meets these conditions is:
g(x) = ∛(x + 6) + 1
Which is a translation to the left of 6 units and up 1 unit.
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Answer:
A) f(x) = RootIndex 3 StartRoot x + 6 EndRoot + 1
Step-by-step explanation:
I Just take the test
Keenan hiked 15 times as far as Margot. How far did Keenan hike? Let m = the total number of miles
Keenan hiked 15 times as far as Margot. How far did Keenan hike? the total number of miles be m
The Keenan hike is measured in m is [tex]\frac{15m}{16}[/tex]miles.
The given parameters;
Keenan and Margot hiked m miles altogether.
Let the distance Margot hiked = n
Then, the distance Keenan hiked = 15n
The combined distance both hiked: m = n + 15n
Calculating Margot's hiked distance in terms of m is as follows:
m = n + 15n
m = 16n
n=[tex]\frac{m}{16}[/tex]
The calculation for Keenan's hike in terms of miles is
= 15(n)
=15[tex]\frac{m}{16}[/tex]
=[tex]\frac{15m}{16}[/tex]
Thus, the distance hiked by Keenan in terms of m is [tex]\frac{15m}{16}[/tex]miles.
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In a high school, 28% of the school’s population is seventeen years old. Of the students who are seventeen years old, 44% play a sport. One student at the high school is chosen at random to represent the school at a community event. What is the probability that the selected student will be seventeen years old and not play a sport?
Answer:
15.68%
Step-by-step
Since 44% of the 28% play sport subtract 44 from 100 to see how many of the 28% do not play sports and you get 56%. So multiply 56% and 28% and you get 15.68%.
The circle graph shows the number of cell phones sold at a local store. The darker shaded portion shows the number of cell phones that were sold with an unlimited data plan. A total of 2,712 cell phones were sold. Using the circle graph, approximately how many cell phones were sold with an unlimited data plan?
Answer:
1,153
Step-by-step explanation:
5. Which image in the collage to the right is an
example of an object not doing work?
O A. climbing a rock wall
B. a water wheel in a dry river
C. kicking a soccer ball
D. carrying a bicycle down the stairs
Answer:
B. A water wheel in a dry river
Step-by-step explanation:
Work is said to be done when a force moves a body or an object through a certain distance in the direction of the force. Thus for work to be done, force and distance are required.
i.e Work done = Force x distance
It is measured in Joules.
Also, the work done by an object could be a measured of potential energy.
So that,
Work done = potential energy = mass x gravitational force x height
Considering the collage in the question, since the water wheel is in a dry river no work is done. Water wheel is a device that functions through the flow of water body, thus causing its rotation.
How many solutions does this linear system have?
y= 5a-1
-15
3y = 3
Answer:
The answer would be B one solution
Hope this helps
* 16 points *. can somebody help me thanks
Answer:
b) [tex]\sqrt{10\\}[/tex]
Step-by-step explanation:
use law of sines to find all the sides and angles
URGENT!! Please i need to be done with this class by midnight!!
Pablo is riding his bike. The number of revolutions (turns) his wheels make varies directly with the distance he travels. See the graph below.(a) How many revolutions does Pablo make per foot of distance traveled? (b) What is the slope of the graph?
Answer:
A general line can be written as:
y = a*x + b
Where a is the slope, and b is the y-intercept.
if we know that the line passes through the points (x1, y1) and (x2, y2), the slope will be:
a = (y2 - y1)/(x2 - x1)
In this case, we can see that the line passes through the points (0,0) and (4,2) then the slope will be:
a = (2 - 0)/(4 - 0) = 2
Then the equation is:
y = 2*x + b
And because we have the point (0, 0), we know that the y-intercept is equal to zero, then the equation is:
y = 2*x
This means that Pablo does 2 revolutions per feet, and we already found that the slope of the equation is 2.
solve by factoring
[tex]x^{4}+x^{3}-6x^{2}[/tex]
Benny wants to buy a new video game that costs $49.95. He already saved $24.65, and his aunt gave him $15 for mowing her lawn. How much more money does Benny need to buy the video game?
Answer:
$10.30
Step-by-step explanation:
X = 49.95 - (24.65 + 15)
x = 49.95 - 39.65
x = 10.30
The amount of calories you consume after eating x pieces of candy is represented by the function. y=135x. Find the domain of the function and determine whether it is discrete or continuous.
Answer:
The function is:
y = 150*x
where y is the number of calories consumed, and x is the number of pieces of candy consumed.
Now, the domain of a function is the possible values of x that you can input in the function.
For this particular case you can have:
x = 0 (no pieces candy)
x = 1 (one piece of candy)
x = 2 (two pieces of candy)
Notice that x can be only whole numbers because, in principle, you can't eat a fraction of a piece of candy.
So we only use x = whole numbers.
Then the domain of the function is equal to all the natural numbers plus the zero, or:
D = {x ∈ N ∪ {0}}
"x belongs to the union between the set of the natural numbers and the zero"
Step-by-step explanation:
help!! A group of friends receives a dinner bill for $87.50. The sales tax rate is 5%.
How much is the bill with tax? Round to the nearest dollar. *
Answer:
$91.88
Step-by-step explanation:
$87.50 x 1.05 = $91.88
Answer:
87.50*1.05=91.875 simplify to nearest dollar. The answer is $92
Step-by-step explanation:
explain the difference in meaning between |-3| and -3
giving brainliest to whoever answers first
HELPPP DUE AT 10:45 ???
Find the angle between the vectors (5,-4) and (-7,3).
Round final answer to the nearest whole degree.
Angle =
Answer:
α = 164.5387822595581°
Step-by-step explanation:
Calculate dot product:
a · b = ax · bx + ay · by = 5 · (-7) + (-4) · 3 = - 35 - 12 = -47
Calculate magnitude of a vector:
|a| = ax2 + ay2 = 52 + (-4)2 = 25 + 16 = 41
|b| = bx2 + by2 = (-7)2 + 32 = 49 + 9 = 58
Calculate angle between vectors:
cos α = a · b
|a|·|b|
cos α = -47
41 · 58
= - 47
2378
√2378 ≈ -0.9638111202541978
α = 164.5387822595581°
Please help! Almost done! thx
Answer:
c^2 = a^2 + b^2 - 2ab cos(C)
Step-by-step explanation:
The angle at A is named A, the angle at B is named B, and the angle at C is named C
Is y=3 proportional?
wait it is proportional
The cost y (in dollars) to rent a pickup truck is proportional to the number x of hours that the pickup truck is rented. It costs $100 to rent the truck for 4 hours. Write an equation that represents the cost to rent a pickup truck for x hours?
Answer:
Step-by-step explanation:D∧M a\\
Find the total cost of a pair of shoes for $57 with a sales tax of 2%
Answer:
58.14
Step-by-step explanation:
57x.02=1.14
add that to 57 and get 58.14
PLEASE HELP FAST ILL GIVE BRAINLIST
At 10 m tall farmhouse is located 28.0 metres away from a tree with a an Eagles nest. The angle of the elevation from the roof of the farmhouse to the Eagles nest is 30
What is the height of the Eagles nest?
A 16m
B 24m
C 26m
D 48m
Answer:
26m
Step-by-step explanation:
opp represents the height of the nest from the angle of elevation,adj represents the distance of the farmhouse from the building . Therefore,according to Tan rule (TOA)
Tan30° = opp/adj
opp= tan30° x adj
opp= tan30° x adj
opp = 0.5774 x 28
0pp= 16.12m
the height of the eagle's nest from the ground = 16m + 10m(since the farm house is 10m tall)
the height ...= 26m
Work out 4/5 - 1/5 9/11 + 5/11 3/4+ 1/8
Decimal: 1.17865691489
Fraction: 97/88
Mixed Fraction: 1 9/88
I hope this helps you
Have an awesome weekend :)
WILL MARK BRAINLIST ASAP Write an equation passing through the point and perpendicular to the given line (-2,-2); y= - 1/5x+9
Answer:
A line that is perpendicular to the x-axis is a vertical like with a slope equal to infinity. A line parallel to it would have the same slope and will also be a vertical line perpendicular to the x-axis. As the line passes through the point (2, -1) its equation is x = 2.
Step-by-step explanation:
please give brianliest
If ray DB If ray DB is an angle bisector of
Answer:
[tex]x = 5[/tex]
Step-by-step explanation:
[tex]m∠ADB = \frac{1}{2} m∠ADC [/tex]
⟹[tex]8x - 3 = \frac{1}{2} \times 74[/tex]
[tex]8x - 3 = 37 ⟹8x = 37 + 3[/tex]
Divide both sides by 8 to find the value of x
[tex]x = \frac{40}{8} [/tex]
Therefore:
[tex]x = 5[/tex]
If you take a number multiply by 7 then takeaway 1. You get the same as if you took the number multiply by 5 then takeaway 8. What is the number?
Answer:
x = -3.5
Step-by-step explanation:
First we create the equation.
Let x = the unknown number
7x-1 = 5x - 8
Add 8 to both sides
7x + 7 = 5x
Subtract 7x
7 = -2x
Divide by 2
-7/2 = x
-3.5 = x
Lin and Han's families provide money for their school lunch accounts.
• Han starts with $100 in his account. He spends $15 each week on lunches.
• Lin starts with $25 in her account and does not spend any of it. Her family adds $10 each
week to her account.
1. At the end of 4 weeks, who has more money in their account?
2. After how many weeks will Han and Lin have the same amount of money in their lunch
accounts?
Answer:
1. Lin
2. 3 weeks
Step-by-step explanation:
Lin has more money in his account, and after 3 weeks Han and Lin will have the same amount of money in their lunch accounts.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
Han starts with $100 in his account. He spends $15 each week on lunches.
Lin starts with $25 in her account and does not spend any of it. Her family adds $10 each week to her account.
For hen:
x be the number of weeks
Total amount left = 100 - 15x
Plug x = 4
Total amount left = $40
For Lin:
y be the number of weeks.
Total amount = 25 + 10y
Plug y = 4
Total amount = 25+40 = $65
Lin has more money in his account.
To have the same amount:
100 - 15x = 25 + 10y
x = y
100 - 15x = 25 + 10x
x = 3 weeks
Thus, Lin has more money in his account, and after 3 weeks Han and Lin will have the same amount of money in their lunch accounts.
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If 3/4 pound of sugar makes 10 cakes, how much sugar, in pounds, is needed to make 1 cake?
Answer:
3/40 or 0.075 pounds
Step-by-step explanation:
If v 1 =(-2,5) and v 2 =(4,-3) , then the angle between the two vectors is Round your answer to two decimal places.
Answer:
-2.5, 4.-3
Step-by-step explanation:
I'm trying I hope this help's??
g(x)=−4x−4, find g(-2)g(−2)
Answer:
g(-2) = 4
Step-by-step explanation:
g(x)=−4x−4
Find g(-2)
This means let x = -2
g(-2)=−4(-2)−4
= 8 -4
= 4
5 +-8f+ -2f + -1 + -8
Answer:
= −10f − 4
Step-by-step explanation:
13 is no more than 5 less than a number. What is the minimum value of the number?
Answer:
18 is the minimum value.
Step-by-step explanation:
Set up an equation:
13 [tex]\leq[/tex] x - 5
Add 5 on both sides to isolate x:
(13) + 5 [tex]\leq[/tex] (x - 5) + 5
18 [tex]\leq[/tex] x
X can be equal to or greater than 18 so the minimum value of the number is 18.
Hope this helps!
7 (n + 4) = 21 Plsss HELP NOW I will try to get u brainliest
Answer:
n = -1
Step-by-step explanation:
please mark me brainliest
Answer:
n = -1
Step-by-step explanation:
7 (n + 4) = 21
28 + 7n = 21
28 + -28 + 7n = 21 - 28
7n = -7
n = -1