The translation of the function 2 | x | - 9 when translated 6 units up gives the function as 2 | x | - 3.
We are given a function:
2 | x | - 9.
A function from a set X to a set Y assigns to each element of X exactly one element of Y.
We are asked to translate the function 6 units up.
This means that we have to add 6 units to the function.
A function has been “translated” when it has been moved in a way that does not change its shape or rotate it in any way.
So, we get that:
f(x) = 2 | x | - 9 + 6
f(x) = 2 | x | - 3
Therefore, the translation of the function 2 | x | - 9 when translated 6 units up gives the function as 2 | x | - 3.
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A direct, consistent relationship between the independent variable and the dependent variable?
A direct, consistent relationship between the independent variable and the dependent variable is called "dose-response relationship."
What is a dose-response relationship?The effect on an organism and, more specifically, the risk of a defined outcome caused by a set quantity of an agent or level of exposure.
Some key features regarding the dose-response relationship are-
A dose-response relationship is considered the strongest proof for a causal relationship between exposure and outcome. Even in the absence of a dose-response relationship, the possibility of a causal relationship can not be discounted. Time can have a significant impact on dose-response relationships. For example, when examining the relationship between exposure and outcome, the time to response can be impacted by a latent period between outcome and exposure. If the effects have been measured too shortly after the exposed, no effect is seen, even if the exposure is the cause of the outcome.To know more about dose-response relationship, here
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Find the area of the region inside the circle r=4cos(theta) and outside the circle r=2.
Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3
What is the polar curve?A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.
r = 1 − cosθsin3θ
Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.
The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.
The figure attached shows the bounded region of the two graphs. The red curve is r=4cos(θ) and the blue curve is r=2.
The points of intersection of the two curves are
θ = π/3 and 5π/3
The area is calculated as follows:
Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.
A = 2 [tex]\(\int_{0}^{\pi /3}[/tex] ½ (4 cos (θ)² − ½ (2)² dθ
= [tex]\(\int_{0}^{\pi /3}[/tex] 16 cos2 (θ) − 4dθ
= [tex]\(\int_{0}^{\pi /3}[/tex] 8 (1+cos(2θ)) − 4dθ
=[tex]\(\int_{0}^{\pi /3}[/tex] 4 + 8 cos (2θ) dθ
= [4θ + 4sin (2θ)] [tex]\(\int_{0}^{\pi /3}[/tex]
= 4π/3 + 2√3
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(3-x)² what is the standard form
Answer:
here is my answer........
Step-by-step explanation:
(3-x)^2 = 9 - 3x - 3x + X2
= X2 - 6x +9
11. A population of bacteria triples every week in a laboratory. The number of
bacteria is modeled by the expression 900 3*, where x is the number of weeks
after a scientist measures the population size. When x = -2, what does the value
of the expression represent?
Answer:
Step-by-step explanation:
Let x represent the number of weeks a population of the bacteria increases. Then, we have the number of bacteria is molded by the expression of 900*3^x. By, the given expression and when we assigned a value of x=2. Then we have 900*3² .
what is the least number that must be subtracted from 3793 for getting a perfect square
Answer:
Step-by-step explanation:
So the nearest perfect square to 3793 is 3721. Hence, the least number that must be subtracted from 3793 to get a perfect square = 3793 - 3721 = 72.
Answer:
ABBCBAAHSHSHDHEEHDHSHHH74737477382
Find the value of x such that the data set has the given mean.
100, 122, 107, 115, 107, x; mean 108
X=
(Type an integer or a decimal.)
Sh
The value of x is 108. If the mean of the data set 100, 122, 107, 115, 107, x is 108.
According to the given question.
We have a data set 100, 122, 105, 115, 107, x .
Also, the mean of the data set is 108.
As we know that, mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Therefore, the mean of the data set 100, 122, 105, 115, 107, x is given by
Mean = [100 + 122 + 107 + 115+ 107 + x]/6
⇒ 108 × 6 = (551 + x)
⇒ 648 = 551 + x
⇒ x = 648 - 551
⇒ x = 97
Hence,the value of x is 108. If the mean of the data set 100, 122, 107, 115, 107, x is 108.
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an amusement park charges 18 dollars for 4 rides. how much will 7 rides cost
1. true or false. if false, correct the statement to make it true. explain ur reasoning
If f(x) = x³, then -4f(x - 1) + 2 can be written as -4(x3 − 1) + 2
pls!!!! asap!!!
Answer: False
The correct expression is -4(x-1)^3+2
====================================================
Work Shown:
[tex]f(x) = x^3\\\\f(x-1) = (x-1)^3\\\\-4f(x-1) = -4(x-1)^3\\\\-4f(x-1)+2 = \boldsymbol{-4(x-1)^3+2}\\\\[/tex]
So the error is with the stuff in the parenthesis. Instead of (x^3-1) it should be (x-1)^3
Side note: (x-1)^3 expands to x^3-3x^2+3x-1
Find the volume of a cube with a side that measures 0.01 cm. (Hint: V = s ³).
Answer: V=[tex]\frac{1}{1000000}[/tex] cm^3
Step-by-step explanation:
V = s³
V = (0.01)³
V=(1/100)³
V=[tex]\frac{1}{1000000}[/tex] cm^3
the volume of cube with a side that measures 0.01 cm is answer v = a3
if LM=MP, then M must be the midpoint of LP.
True or False?
Answer:
True
Step-by-step explanation:
dividing both sides by M you are left with L=P
How would you write .8% as a decimal? Remember DP!
Answer:
0.08
Step-by-step explanation:
0.8% as a decimal is 0.08.
Hope this helps!
Please mark as brainliest if correct!
Answer:
.8% = 0.08
Imagine the hundredths place(2 DP) as the ones place, and the tenths place as the tens place like in 57%, that would be 0.57 because it's double digit.
Hope this helps.
Jenna works in an ice cream shop. When she starts her shift, the tub of chocolate ice cream is 23 full. When she finishes her shift 612 hours later, there is only 16 of the tub left. What was the average hourly change in tub fullness?
The average hourly change in tub fullness is ₋1/13.
Jenna she starts her shift, the tub of chocolate ice cream is 2/3 full.
After she finishes her shift 6 1/2 hours , there is only 1/6 of tub left.
the average hourly change in tub fullness = ?
subtract the initial quantity from the quantity left after 6 1/2 hours.
⇒ 2/3 ₋ 1/6
= 1/2
Divide the quantity by 6 1/2 hours.
time is represented in improper fraction, convert it into proper fraction.
6 1/2 = 12 ₊ 1/2
= 13/2
⇒ 1/2 ÷ 13/2
= 1/13
the statement says the quantity decreases,
so ₋1/13
therefore the average hourly change in tub fullness is ₋1/13
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Evaluate the function.
f(x) = -4x² + 7x
Find f(5)
Answer:
-65
Step-by-step explanation:
Given ~
[tex] \tt \: f(x) = - 4 {x}^{2} + 7x[/tex]
[tex] \: [/tex]
put x=5 in given function ~
[tex] \: [/tex]
[tex] \tt \: f(5) = - 4(5) ^{2} + 7(5)[/tex]
[tex] \: [/tex]
[tex] \tt \: f(5) = - 4(25) + 7(5)[/tex]
[tex] \: [/tex]
[tex] \tt \: f(5) = -100 + 35 [/tex]
[tex] \: [/tex]
[tex] \underline{\boxed{\red{ \tt f(5) = - 65}}}{\green✓}[/tex]
[tex] \: [/tex]
hope helps ~
I need help fast please and thank you
Answer:
Option a 340 cm²
Area= bxh
20x17=340 cm²
Seventh grade > Z.2 Scale drawings: word problems 84H
Carmen drew a scale drawing of a house and its lot. In real life, the lawn in the backyard is
72 meters long. It is 24 millimeters long in the drawing. What is the scale of the drawing?
1 millimeter :
Submit
You've won a new
meters
Tutorial
Qu
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The scale of the drawing is in the ratio of 1 millimeter : 3 meter
In this, we need to find the ratio that is 1millimeter:x meter where x is the original scaling of the plot.
We have been given that
24 millimeters = 72 meters
Now we have to find how many meters is equal to 1 millimeter which will find out by the unitary method.
Thus, 24 millimeters = 72 meters
1 millimeter = 72/24 meter
1 millimeter = 3 meter
Hence the scale of the drawing is 1 millimeter : 3 meter
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∠ABC and ∠DEF are complementary. If m∠ABC = (2x+4)∘ and m∠DEF = (3x−5)∘, find the measure of each angle.
m∠ABC =
m∠DEF =
The measure of each angle are m∠ABC = 40.4 and m∠DEF = 49.6
How to determine the measure of each angle?The given parameters are
m∠ABC = (2x+4)∘ and m∠DEF = (3x−5)∘,
Complementary angles add up to 90 degrees
So, we have
2x + 4 + 3x - 5 = 90
Evaluate the like terms
5x = 91
Divide by 5
x = 18.2
Substitute x = 18.2 in m∠ABC = (2x+4)∘ and m∠DEF = (3x−5)∘,
m∠ABC = (2 x 18.2 + 4) = 40.4
m∠DEF = (3 x 18.2 − 5)∘ = 49.6
Hence, the measure of each angle are m∠ABC = 40.4 and m∠DEF = 49.6
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The graph of y=
-2x²5x+2 is drawn below
Draw a suitable line to solve -2x² - 5x + 2 = -5
Answer:
x = 1 and x = -3.5
Step-by-step explanation:
y = -2x² -5x + 2
-2x² -5x + 2 = -5
which means y = -5
Draw the line on y = -5 like the green line in the attached file
and see where this line intersects with the graph
the values are:
x = 1 and x = -3.5
Answer:
Draw a line at y = -5.
x ≈ -3.5
x ≈ 1
Step-by-step explanation:
Given equation:
[tex]y = -2x^2 - 5x + 2[/tex]
This is the equation of the graphed parabola.
To solve the equation [tex]-2x^2 - 5x + 2 = -5[/tex] draw a line at y = -5 and find the points of intersection of the two graphed equations.
From inspection of the graph, the x-values of the points of intersection are:
x ≈ -3.5x ≈ 1Solving algebraically
Add 5 to both sides of the equation:
[tex]\implies -2x^2-5x+2+5=-5+5[/tex]
[tex]\implies -2x^2-5x+7=0[/tex]
Factor out -1 from the left side:
[tex]\implies -1(2x^2+5x-7)=0[/tex]
Divide both sides by -1:
[tex]\implies 2x^2+5x-7=0[/tex]
Find two numbers that multiply to -14 and sum to 5: 7 and -2
Rewrite b as the sum of these two numbers:
[tex]\implies 2x^2+7x-2x-7=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(2x+7)-1(2x+7)=0[/tex]
Factor out the common term (2x + 7):
[tex]\implies (x-1)(2x+7)=0[/tex]
Apply the zero-product property:
[tex](x-1)=0 \implies x=1[/tex]
[tex](2x+7)=0 \implies x=-\dfrac{7}{2}=-3.5[/tex]
There are a total of 463,100 books in a library. What is the value of the exponet when this number is written in scientific notation?
Answer: 4.631*10^5
Step-by-step explanation:
463,100=
400,000+63,100=
4*100,000+(63,100/100,000)*100,000=
4*10^5+(631/1000)*10^5=
4*10^5+0.631*10^5=
(4+0.631)*10^5=4.631*10^5
Solve for x when g=x-c/x
Answer:
x= -3/g -1
Step-by-step explanation:
tyler wants to buy a new game system that costs $240 tyler has already saved $32 but he needs to make a plan so he can save the rest of the money he needs he decided to save the same amount of money x dollars each month for the next four months, write an equation that helps tyler determine the amount of money he must save each month, solve the equation to find the amount of money he must save each month to meet his goal of buying a new game system
Answer: He must save $52 per month
Step-by-step explanation: 240-32= 208/4= 52
a sequence of natural numbers is constructed by listing the first 4, then skipping the next 5, skipping 2 listing 6, skipping 3, and, on the nth iteration, listing n 3 and skipping n. the sequence begins 1,2,3,4,6,7,8,9,10,13. what is the 500,00th number in the sequence?
The 500,00th number in the sequence = 98828
What is sequence?A sequence is a numbered collection of objects where repeats are permitted and order is important. It has members, just like a set. The length of something like the sequence is defined as the number of items.
According to the given data:here n^th iteration n+3 element are listed and n element are skipped.
now before nth iteration total skipped natural number : 1+2+3+.........n-1
= n(n-1)/2
now after completion of nth iteration total listed natural number = 4+5+6+.....n+3
= ((n+3)(n+4)/2)-6
to find 50000th number total listed element must be greater than or equal to 50000.
((n+3)(n+4)/2)-6 ≥ 50000
(n+3)(n+4) ≥ 100012
n = 313
total skipped before 313th iteration
=( 313 * 312)/2
= 48828
total listed before 313th is 48828.
listed after 312th iteration
= ((315)(316))/2)-6
= 49764
total number remaining for 50000
= 50000 - 49764
= 236
total number passed.
skipped+ listed
= 48828 + 49764
= 98592
50000th element = 98592 + 236
= 98828
The 500,00th number in the sequence = 98828
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matt bought 2 packages of gum for 64 cents each he also bought a candy bar for 76 cents write an expression to show the best estimate for how much money matt spent
The expression to show the best estimate is 64 * 2 +76 * 1
How to write an expression to show the best estimate?The given parameters are:
Gum package = 64 cents eachNumber of gum package = 2Candy bar = 76 cents eachNumber of Candy bar = 1The expression to show the best estimate is
Expression = Gum package * Number of package + Candy bar * Number of bars
So, we have
Expression = 64 * 2 +76 * 1
Hence, the expression to show the best estimate is 64 * 2 +76 * 1
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. Which graph has f(x) = 1xI as its parent function?
Answer: Im not sure
Step-by-step explanation:
you didnt list/provide the graphs for me to answer. :I
5. Using the data from question 2, you can compute the mean food and lodging
cost of a 10-day vacation by multiplying the per-day mean by 10. The
standard deviation for the 10-day vacation can be found by multiplying by
10 also.
a. What is the mean for food and lodging for a 10-day vacation?
Multiplying the underlying mean of $247 for a single day by 10 to account for the 10 days, the mean for food and lodging for a 10-day vacation is of $2470.
What is the mean per day cost?This problem is incomplete, but researching it on a search engine, it is found that the mean for a single day was of $247.
What is the mean for the entire trip?The entire trip was of 10 days, hence the mean is given as follows, multiplying the mean by the constant:
247 x 10 = $2,470.
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Can someone give me the answer of D??
Answer:
Corrected - didn't see the 10 to the negative 2 in the denominator at first - sorry)
8000
Step-by-step explanation:
Simplify
5.12 x 10 ^6/ 1.6 X 10 ^5 X (.4 X 10^-2)
Do the math
3.2 x 10/.04 x 1- ^-2)
Simplify
8 X 10^3
Simplify
8000
2: Strategically decompose 1.57 to round to the nearest whole and nearest tenth.
So, the area is square units.
The area of a triangle is 4 square units.
Given that, the coordinates of the triangle ABC are A(4, 3), B(5, 1) and C(1, 1).
We need to find the area of a triangle ABC.
What is the area of a triangle?The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
The base of the triangle = |5-1|=4
From vertices, A(4, 3) to the base the distance is 2 units at the vertice (4, 1)
So, the height of the triangle = 2 units
Now, the area of a triangle ABC = 1/2 × 4 × 2 = 4 square units.
In the given solution the height of a triangle is wrongly calculated.
Therefore, the area of a triangle is 4 square units.
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If f(x) = 24x + 24, find the instantaneous rate of change of f(x) at x = 6
Answer:
168
Step-by-step explanation:
You'd plug 6 in for x
f(x) = 24x + 24
f(6) = 24(6) + 24
f(6) = 144 + 24
f(6) = 168
The kinetic energy k of an object varies jointly with its mass m and its velocity v. The formula to kinetic energy is K = 1/2mv^2. Rearrange the formula to write the mass m in terms of K and v, where v is not equal to 0.
(I will rate brainliest if only right)
The mass m in terms of K and v is expressed as m= 2K/v^2
Subject of formulaThe subject of formula is a way of representing a variable in terms of other variables.
Given the equation below;
K = 1/2mv^2
Make m the subject of the formula
2K = mv^2
Divide both sides by v^22K/v^2 = mv^2/v^2
2K/v^2 = m
Swap
m= 2K/v^2
Hence the mass m in terms of K and v is expressed as m= 2K/v^2
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4a + 2b - 12ax + 15b = -40x - 52. What is a and b
Answer:
a = 10/3 and b = -196/51.
Step-by-step explanation:
4a + 2b - 12ax + 15b = -40x - 52
Equating coefficients of x:
-12ax = -40x
-12a = -40
a = 40/12
= 10/3.
Equating constants:
4a + 2b + 15b = -52
4a + 17b = -52
Substituting a = 10/3:
40/3 + 17b = -52
17b = -52 - 40/3
b = (-52 - 40/3) / 17
= (-156/ 3 - 40/3) / 17
= -196 / 51