Answer: f(x) = |x|
Step-by-step explanation:
A function is even if for every real N, f(N) = f(-N)
As you know, the module of a function always returns the positive value of a number, so I-3I = 3 = I3I (and that for every number)
So the function f(x) = IxI is an even function.
Functions with odd powers can not be even functions, so the second and tird options are discarded.
the fourth functions seems to be:
f(x) =∛x = (x)1/3 which is not even, because if x = 1, f(1) = 1, and if x=-1, f(-1) = -1
In the given functions, an even function is [tex]f(x)=|x|[/tex]. Therefore, the correct answer is option A.
A function's even, odd, or neither properties can be expressed algebraically or graphically in a variety of ways. If a function's graph remains unchanged when reflected in the y-axis, it is said to be an even function. Consider a function f(x) that is considered an even function if f(-x) equals f(x).
1) [tex]f(x)=|x|[/tex]
Let [tex]x = -3[/tex], we get
[tex]f(-3)=|-3|[/tex]
[tex]f(-3)=3[/tex]
[tex]f(-x)= f(x)[/tex]
2) [tex]f(x)=x^3-1[/tex]
Let [tex]x = -1[/tex], we get
[tex]f(-1)=(-1)^3-1[/tex]
[tex]f(-1)=-1-1[/tex]
[tex]f(-1)=-2[/tex]
[tex]f(-x)\neq f(x)[/tex]
3) [tex]f(x)=-3x[/tex]
Let [tex]x = -1[/tex], we get
[tex]f(-1)=-3(-1)[/tex]
[tex]f(-1)=3[/tex]
[tex]f(-x)\neq f(x)[/tex]
4) [tex]f(x)=\sqrt[3]{x}[/tex]
Let [tex]x = -1[/tex], we get
[tex]f(-1)=\sqrt[3]{(-1)}[/tex]
[tex]f(-x)\neq f(x)[/tex]
Therefore, the correct answer is option A.
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What is the slope of the line containing the points (3,4) and (-6,10)
Answer:-.6666666667x +6
Step-by-step explanation:
I have a school calculator
Answer:
-2/3 is the slope
Step-by-step explanation:
Slope = y2 - y1/x2 - x1
= 10 - 4/-6 - 3
= 6/-9
=-2/3
A triangle with the coordinates (6,4), (2,-1), and (-3,5) is translated 4 Units left and rotate 180 degrees about the origin. What are the coordinates of the image.
Answer:
(-2,-4),(2,1), and (7,-5)
Step-by-step explanation:
The given triangle has coordinates (6,4), (2,-1), and (-3,5).
When we translate 4 units left, the we obtain:
(6,4)------>(6-4,4)=(2,4)
(2,-1)----->(2-4,-1)=(-2,-1)
(-3,5)----->(-3-4,5)=(-7,5)
When the resulting figure is rotated 180° about the origin, the coordinates of the final figure becomes
(2,4)------>(-2,-4)
(-2,-1)----->(2,1)
(-7,5)------->(7,-5)
NB: The mapping for 180° rotation is:
(x,y)----->(-x,-y)
Simplify: (m – 3n)2
m2 – 9n2
m2 + 9n2
m2 – 3mn + 9n2
m2 – 6mn + 9n2
(m - 3m)^2
(m - 3n)(m - 3n)
Use the FOIL method.
First m^2
Outer -3mn
Inner -3mn
Last 9n^2
Equation form:
m^2 - 3mn - 3mn + 9n^2
Simplify terms to get...
m^2 - 6mn + 9n^2
The answer is answer D, m^2 - 6mn + 9n^2.
⭐ Answered by Hyperrspace (Ace) ⭐
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Find the balance in the account after the given period.
$2,200 deposit earning 4.2% compounded monthly, after 1 year
Answer:
2294.20
Step-by-step explanation:
the formula [tex]A = P (1+\frac{r}{n}) ^{nt}[/tex] will show the exponential growth in the account
A = amount in account (how much you'll have after earning interest)
P = the initial amount (how much YOU put in the account)
r = interest rate (in decimal form)
n = the number of times the interests in compounded in one year
t = number of years
plug in numbers into formula
(4.2 will become 0.042 because we need it as a decimal)
(n = 12 because monthly means every month and there is 12 months in a year)
formula will look like [tex]A = 2200 (1+\frac{0.042}{12})^{12(1)}[/tex]
once solved you will get 2294.199616 *round as needed
Can you explained this and give the answer
Answer:
[tex]x^{\frac{3}{7}}[/tex]
Step-by-step explanation:
What is the simplified form of
[tex](\sqrt[7]{x})(\sqrt[7]{x})(\sqrt[7]{x})[/tex]
Applying property of exponents
Remember that
[tex]\sqrt[n]{x^{m}} =x^{\frac{m}{n}}[/tex]
[tex]x^{m}x^{n}=x^{m+n}[/tex]
so
[tex](\sqrt[7]{x})(\sqrt[7]{x})(\sqrt[7]{x})=(x^{\frac{1}{7}})(x^{\frac{1}{7}})(x^{\frac{1}{7}})=x^{(\frac{1}{7}+\frac{1}{7}+\frac{1}{7})}=x^{\frac{3}{7}}[/tex]
Rectangle M was dilated to form rectangle M'.
What ratio is the scale factor?
Answer:
The scale factor is the ratio 3/2
Step-by-step explanation:
The picture of the question in the attached image
we know that
A dilation is a non rigid transformation that produce similar figures
If two figures are similar, then the ratio of its corresponding sides is proportional
In this problem rectangle M and rectangle M' are similar
so
The scale factor is equal to
[tex]\frac{6}{4}=\frac{3}{2}[/tex]
The scale factor is greater than 1
so
The dilation is an enlargement
Good morning,
which of the following rational functions is graphed below? thanks
Answer:
C.x/(x+5)(x-2)
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
What is 3.68328446 rounded to the nearest hundredths
Answer:
3.68
Step-by-step explanation:
Bela started studying how the number of branches on her tree grows over time. Every 2.9 years, the number of
branches increases by an additional 83%, and can be modeled by a function, which depends on the amount
of time, t (in years).
When Bela began the study, her tree had 60 branches.
Write a function that models the number of branches t years since Bela began studying her tree.
Answer:
The required function that models the number of branches t years since Bela began studying her tree is
number of branches = [tex]60(1.83)^{\frac{t}{2.9} }[/tex]
Step-by-step explanation:
Let t be the time in years
Initially Bela's tree had 60 branches.
therefore the function that can be used to model the number of branches after t years will be given by
number of branches( after t years) [tex]= 60\times(1 + \frac{83}{100})^{\frac{t}{2.9} } = 60(1.83)^{\frac{t}{2.9} }[/tex]
The function model is [tex]B(t) = 60 * (1.83)^{\frac{t}{2.9}}[/tex].
To model the growth of branches on Bela's tree over time, we can use an exponential growth function. Given that the number of branches increases by 83% every 2.9 years, and the initial number of branches is 60, the function can be derived as follows:
The growth factor after each period of 2.9 years can be expressed as 1 + 0.83 = 1.83. If we let t represent the time in years, we need to determine how many 2.9-year periods have passed. This is given by [tex]\frac{t}{2.9}[/tex].
Thus, the function modeling the number of branches, B(t), after t years is:
[tex]B(t) = 60 * (1.83)^{\frac{t}{2.9}}[/tex]
This function accounts for the exponential growth of the number of branches on Bela's tree over time.
5. What value of x makes the equation true?
3(x - 2) = 3x + 7
Answer:
There are no values of x that make the equation true.
Step-by-step explanation:
3(x-2)=3x+7
3x-6=3x+7
3x-6+6=3x+7+6
3x=3x+13
Dviding 3x by 3x will equal 1, and 1 does not equal 13.
Answer:
There are no value of x
Step-by-step explanation:
3(x-2) = 3x+7
3x-6 = 3x+7
-6= 7
=7 +6
=13
so we can say that,There are no value of x
Solve the system of linear equations by graphing.
y = 2x
2x + y = - 4
In graph form
Answer:
2x + 2x = 4
4x = 4
x = 1
y = 2(1)
y = 2
(1,2)
Describe the end behavior of the following function:F(x)=2x^4+x^3
A.The graph of the function starts low and ends high.
B.The graph of the function starts high and ends high.
C.The graph of the function starts low and ends low.
D.The graph of the function starts high and ends low.
The graph of the function starts high and ends high.
Answer: Option B.
Explanation:
The end conduct of a graph is characterized as what is happening at the parts of the bargains. As the capacity approaches positive or negative infinity, the main term figures out what the diagram resembles as it moves towards vastness.
The end conduct of a chart is the way our capacity carries on for extremely huge and tiny info esteems. For exponential capacities, we see that our end conduct goes to endlessness as our information esteems get bigger. The bigger the base of our exponential capacity, the quicker the development.
The end behavior of the function F(x) = 2x^4 + x^3 is determined by the term 2x^4. As x tends toward both positive and negative infinity, this term causes the function to increase towards infinity, meaning the graph starts low and ends high.
The question asks about the end behavior of the polynomial function F(x) = 2x^4 + x^3. To determine this, we look at the highest degree term, which dominates the end behavior. In this case, that term is 2x^4.
As x approaches positive infinity, 2x^4 will grow very large, so the function will also go towards infinity. Similarly, as x approaches negative infinity, 2x^4 will still grow very large (since an even power of a negative number is positive), and the function will go towards infinity as well. Thus, the graph of the function starts low when x is very negative and ends high as x becomes very positive.
Therefore, the correct answer to the student's question is Option A: The graph of the function starts low and ends high.
a number times 45 decreased by 12 is no more than 117
Answer: n*4512 is less than or equal to 117
Step-by-step explanation: n=number N*45=X X=Number more than 117. X decreased by 12 is less than or equal to 117.
How many times does seven go into 52
49 remainder of 3
Step-by-step explanation:
52 divided by 7 is 49 R 3
Answer:
7.42857142857
Step-by-step explanation:
divide 7 into 52 and you will get 7.42857142857
Kiran wrote the expression x-10 for this number puzzle: "Pick a number, add -2, and multiply by 5."
Lin thinks Kiran made a mistake.
How can she convince Kiran he made a mistake?
Answer:
Step-by-step explanation:5(x-2)
The correct expression Kiran is trying to write is 5x - 10
How to write expressionKiran:
x - 10
let x = the unknown numberAdd - 2
= x + (-2)
= x - 2
multiply by 5(x - 2)5
5x - 10
Therefore, the correct expression Kiran is trying to write is 5x - 10
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What is the exponents to write the expression of 6×6?
Answer:
6 to the power of 2 or 6 squared
Answer:
6 to the power of 2 or 6 squared
Step-by-step explanation:
Find the length of the missing side of the triangle below
PLEASE HELPP!!
To find the length of the missing side, you can use the Pythagorean Theorem, which you can only use for right triangles.
Pythagorean Theorem: a² + b² = c²
[ c is the hypotenuse or the longest side of the triangle, and a and b are the other sides, I think it doesn't matter which side ]
Plug in what you know:
b = 8
c = 14
a² + b² = c²
a² + (8)² = (14)²
a² + 64 = 196 Subtract 64 on both sides
a² = 132 Square root both sides to get "a" by itself
[tex]\sqrt{a^2} =\sqrt{132}[/tex]
a = [tex]\sqrt{132}[/tex] inches
If you need to simplify more, you need to find two numbers that multiply to = 132 where one of them can be square rooted, to do so you can list the greatest common factors of 132
132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
The only number that can be square rooted is 4, so you can do:
[tex]a=\sqrt{4*33}[/tex]
[tex]a=\sqrt{4} *\sqrt{33}[/tex]
[tex]a=2\sqrt{33}[/tex]
what is equivalent to (4xy-3z)^2 and
what type of special product is it?
Answer:
16x2y2 + 9z2 (They are a perfect square trinomial.
Step-by-step explanation:
Explain when you must write the number 1, and when you do not need to.
Answer:
The number 1 is not necessary when expressing powers of one. For example, you needn't write "5" as [tex]5^{1}[/tex].
Step-by-step explanation:
The number 1 is written when it is part of a larger number, as it is significant. It is not necessary to write leading zeros. In scientific notation, trailing zeros are excluded, and the number is written in a form where only non-zero digits appear before the decimal.
Explanation:Understanding when to write the number 1 and when it's not needed depends on the context in mathematics, especially when dealing with significant figures and scientific notation. Generally, all non-zero numbers are considered significant (rule 1), which means that when a value like 1 is part of a larger number, it contributes to the meaning of that number. However, leading zeros do not count as significant (rule 3).
In the case of multiplication by units, like converting from kilograms to grams, we utilize the concept of multiplying by the number 1 to affect the units without changing the value. For example 0.7 kg can be multiplied by 1000/1 (1000 g / 1 kg) to convert to grams. This is because 1000/1 is equal to 1000, indicating multiplication by one does not change the value.
When expressing numbers in scientific notation, it's important to include the non-zero digits only before the decimal point, excluding any trailing zeros. Thus, 1,500,000 would be written as 1.5 x 106, with the power indicating the necessary number of decimal point movements to place it after the first significant digit.
The dimensions of a rectangular monitor screen are such that it’s length is 4 in. more than it’s width. If the length were doubled and if the width were decreased by 1 in., the area would be increased by 216 in^2. What are the length and width of the screen?
Answer:
14 inches by 18 inches
Step-by-step explanation:
Old rectangular monitor screen:
Width = x in
Length = x + 4 in
Area [tex]=x(x+4)\ in^2[/tex]
New rectangular monitor screen:
Width = x - 1 in
Length = 2(x + 4) in
Area [tex]=(x-1)(2(x+4))=2(x-1)(x+4)\ in^2[/tex]
This area would be increased by [tex]216\ in^2,[/tex] so the area would be equal to [tex]x(x+4)+216\ in^2[/tex]. Hence,
[tex]2(x-1)(x+4)=x(x+4)+216\\ \\2(x^2+4x-x-4)=x^2+4x+216\\ \\2x^2+6x-8-x^2-4x-216=0\\ \\x^2+2x-224=0\\ \\D=2^2-4\cdot (-224)=4+896=900\\ \\x_{1,2}=\dfrac{-2\pm \sqrt{900}}{2}=\dfrac{-2\pm 30}{2}=-16,\ 14[/tex]
The width cannot be negative, so
Width = 14 in
Length = 14 + 4 = 18 in
Slope is -3 and a y-intercept of 7
Answer:
y = -3x + 7
Step-by-step explanation:
Answer: y=-3x+7
Step-by-step explanation:
The formula is y=mx+b. M is the equal to the slope and b is equal to the y-intercept. Since they are both given to you, you just fill them in for the variables and it is your answer
What type of association does the graph show between X and Y? A. Linear positive association B.NoNlinear Positive association C.Linear negative association D.Nonlinear negative association?
Answer: A. Linear positive association
Step-by-step explanation:
As the x values increase, so do the y values. this makes the association to be positive because they are both increasing. Additionally if you were to connect all the data points together you would get a straight line, which makes it linear.
What 48 divide by 879
an otterbox was on sale 20% off. if the sale price was $47.99, what was the original price?
Answer:$38.39
Step-by-step explanation:
Original price: $
47.99
Discount percentage:
20
%
Results
Discount:
$9.60
Final Price:
$38.39
Answer:
$59.99
Step-by-step explanation:
"20% off" translates into "80% of original price."
Thus, 0.80p = $47.99, where p is the original price.
Dividing both sides by 0.80 yields:
p = $59.99
Solve.
fy=z -8
122+3y=1
Use the substitution method.
०(5, -3)
0 (0, -8)
10 (2, -6)
(4, -4)
Answer: Answer is x = 5, y = -3
(5, -3)
Step-by-step explanation: The instruction is to use the substitution method, and from the first equation,
y = x - 8
This means we replace the value of y in the second equation with x - 8. Hence;
2x + 3y = 1 can now be re-written as
2x + 3(x - 8) = 1
2x + 3x - 24) = 1
5x - 24 = 1
Add 24 to both sides of the equation
5x -24 + 24 = 1 + 24
5x = 25
Divide both sides of the equation by 5
x = 5
Having calculated x as 5, we can now substitute for the value of x in the first equation
y = x - 8 now becomes
y = 5 -8
y = -3
Using the substitution method, we found the solution to be (5, -3), which matches option a.
To solve the system of equations using the substitution method, we'll first solve one equation for one variable and then substitute it into the other equation.
Given:
1. [tex]\( y = x - 8 \)[/tex] (Equation 1)
2. [tex]\( 2x + 3y = 1 \)[/tex] (Equation 2)
From Equation 1, we can solve for y:
[tex]\[ y = x - 8 \][/tex]
[tex]\[ x = y + 8 \][/tex] (Re-arranging)
Now, substitute [tex]\( x = y + 8 \)[/tex] into Equation 2:
[tex]\[ 2(y + 8) + 3y = 1 \][/tex]
Simplify and solve for y:
[tex]\[ 2y + 16 + 3y = 1 \][/tex]
[tex]\[ 5y + 16 = 1 \][/tex]
[tex]\[ 5y = 1 - 16 \][/tex]
[tex]\[ 5y = -15 \][/tex]
[tex]\[ y = -3 \][/tex]
Now, substitute [tex]\( y = -3 \)[/tex] into Equation 1 to find [tex]\( x \)[/tex]:
[tex]\[ x = (-3) + 8 \][/tex]
[tex]\[ x = 5 \][/tex]
So, the solution to the system of equations is [tex]\( (x, y) = (5, -3) \)[/tex].
Find the value of f(-8) if:f(x)=12x-29
Answer:
f=41, 41×(-8)=-328(not so sure so you might want so check with other people again)
Step-by-step explanation:
f(x)=12x-29
Step 1, u bring the x terms over to one side, in this case on the left side. So it becomes:
f(x)-12x=29
Next step is to find the common factor of the x terms
f(x)-12(x)=29
f-12=29
bring the numbers to the right side
f=29+12
so f=41
Ilana drew a marble at random from a bag containing 4 blue, 3 red, 2 yellow, and 5 green marbles. What is the probability that she picked a marble that is not red?
20 points for best answer
Answer:
[tex]\frac{11}{14}[/tex]
Step-by-step explanation:
Total number of marbles = 4+3+2+5=14
number of not red marbles = 4+2+5=11
then
the probability that she picked a marble that is not red = 11/14
Look at the pic and answer
Answer:
Step-by-step explanation:
To find the length of LK, we can use the triangle similarity concept. First, let's compare triangles LJK and LMK. We can see that they share angle L, and we know that LJ = 10 and KM = 7. By comparing the corresponding sides, we can set up the proportion: LK / LJ = KM / KJ Substituting the given values, we have: LK / 10 = 7 / 11 To solve for LK, we can cross multiply and then divide: LK * 11 = 10 * 7 LK * 11 = 70 LK = 70 / 11 So, LK = 6.36 (rounded to two decimal places). Therefore, the answer is not provided in the answer choices.
From the answer choices, we can conclude that LK = d. 70/11.
What is the value?From the figure we are given, we can use the property of corresponding angles to determine the probable value of LK. From the corresponding sides, LK/LJ is equal to KM/KJ. Now, we substitute the given values to have the following:
LK / 10 = 7 / 11
To get the exact value of LK, we cross-multiply as follows:
LK * 11 = 10 * 7
LK * 11 = 70
LK = 70 / 11
So, the value of LK = 70/11.
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HELP Write a proportion that could be used to solve for each variable. Then solve. 16 walls in 40 hours 3 walls in h hours a. 16/40 = h/3; h = 1.2 c. 16/h = 3/40; h = 213.3 b. 16/40 = 3/h; h = 7.5 d. 16/40 = 3/h; h = 8.5
The proportion that could be used to solve for the variable is:
[tex]\frac{16}{40} = \frac{3}{h}[/tex]
h = 7.5
Solution:
Given that,
16 walls in 40 hours 3 walls in h hours
Which means,
16 walls build in 40 hours
Then 3 walls in h hours
We have to write a proportion
The number of walls and the number of hours are proportion
Therefore, we get,
[tex]\frac{16}{40} = \frac{3}{h}[/tex]
Cross multiply and solve for h
[tex]16 \times h = 3 \times 40\\\\16h = 120\\\\h = \frac{120}{16}\\\\h = 7.5[/tex]
Thus the proportion is solved
after 2/5 of the kittens were given away, there was k kittens and p puppies left in the pet store. write and algebraic expression in terms of k
Answer:
Algebraic expression in terms of k
k= T- p
Step-by-step explanation:
As
no of kittens left = k
no of puppies left =p
If total left after giving away kittens =T
T = p + k
In terms of k the expression will be
k= T- p
Keywords: Algebra
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Final answer:
To write an algebraic expression in terms of k, subtract the number of kittens given away from the initial number of kittens. The algebraic expression in terms of k is (3/5)x.
Explanation:
To write an algebraic expression in terms of k, we need to determine the initial number of kittens before any were given away. Let's call this number 'x'. According to the problem, 2/5 of the kittens were given away. This means that (2/5)x kittens were given away, leaving k kittens remaining.
To find the algebraic expression in terms of k, we subtract the number of kittens given away from the initial number of kittens. So the expression is x - (2/5)x = k.
We can simplify this expression by finding a common denominator for the fractions. In this case, the common denominator is 5. So the expression becomes 5x/5 - (2/5)x = k. Simplifying further, we have (3/5)x = k. Therefore, the algebraic expression in terms of k is (3/5)x.