equation is:
[tex] f(x) = \frac{x}{ {x}^{2} - 1 } [/tex]
so if its even f(-x) should be equal to f(x)
that means
[tex]f( - x) = \frac{ - x}{ {( - x)}^{2} - 1} \\ \\ f( - x) = - \frac{ x}{ {x}^{2} - 1} [/tex]
so f(x) is not equal to f(-x) so its not even
If its odd than f(-x) should be equal to -f(x)
[tex] - f(x) = - ( \frac{ x}{ { x}^{2} - 1 } ) \\ - f(x) = - \frac{ x}{ {x}^{2} - 1 } [/tex]
so as we can see f(-x)= - f(x)
so the function is odd
Ans:function is odd and not even
By replacing x with -x in the given function X/(x^2-1), we find that it doesn't fulfill the criteria for even or odd functions. Therefore, the function is neither odd nor even.
Explanation:To determine whether the function X/(x^2-1) is odd, even or neither, you can plug in -x into the function and simplify. For a function to be considered even, f(x) should be equal to f(-x). For a function to be considered odd, f(-x) should be equal to -f(x).
For the given function X/(x^2-1), after replacing x with -x, we get -X/((-x)^2 - 1) which simplifies to -X/(x^2 - 1). Since f(-x) is not equal to f(x) or -f(x), the function is neither odd nor even.
Generally, an even function is symmetrical around the y-axis. That is, if you fold the graph of the function over the y-axis, both halves align. On the other hand, an odd function is symmetric about the origin. That is when the graph is rotated 180 degrees about the origin, the graph remains unchanged.
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7 POINTS!!! ~ A 6 foot tall man casts a shadow that is 4.5 feet long. A telephone pole casts a shadow that is 15.6 feet long. Two similar triangles are created. How tall is the telephone pole?
The answer is:
The telephone pole is 20.8 foot tall.
Why?Since it's not mentioned, we can assume that both, man and the telephone pole are close, so, if two similar triangles are created, we know that both shadows are proportional and we can find the telephone pole height creating a proportionality relationship.
We can find the telephone pole height using the following equation,
[tex]\frac{ManHeight}{ManShadow}=\frac{PoleHeight}{PoleShadow}[/tex]
Were,
Man height is 6 foot
Man shadow is 4.5 feet long
Telephone pole shadow is 15.6 feet long.
So, substituting we have:
[tex]\frac{6}{4.5}=\frac{PoleHeight}{15.6}[/tex]
[tex]PoleHeight=15.6*\frac{6}{1.5}=20.8ft[/tex]
So, the telephone pole is 20.8 foot tall.
Have a nice day!
Choose the constant term that completes the perfect square trinomial.
y 2 + 8y
8 divided by 2=4 then square the 4
16
Answer:
16
Step-by-step explanation:
A perfect square trinomial is a three-term polynomial (also called a trinomial) that results from squareing a binomial. Every trinomial of the form: [tex]a^{2} +2ab+b^{2}[/tex], It is a perfect square trinomial.
In this case, it is necessary to divide the intermediate value of 8 by 2, and then square it, obtaining the result.
If f(x)= (1/7)(7^x) what is f(3)
subsitute 3 as x
f(3) = (1/7) × (7^3)
f(3) = 1/7 × 343
f(3) = 343 ÷ 7
f(3) = 49
The required value of f(3) = 49.
f(x)= (1/7)(7^x)
what is exponential function?The function which is in format f(x) = where, a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
f(x)= (1/7)(7^x)
f(3) = 1/7(7^3)
f(3) = 1/7 x 7³
f(3) = 7² = 49
Thus the required value for f(3) = 49
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Sandi lives 5 miles from her school. One day, she took the bus from her house to school. After school, she went to the library to pick out a book. Then she went to the park to read. If sandi traveled along the route shown, how far did she travel.
Her house to school is 5 miles.
The distance on the map is 2.5 inches, so we know 2.5 inches equals 5 miles.
Divide 5 miles by 2.5 inches to find miles per inch:
5 / 2.5 = 2 miles per inch.
Now you can multiply the other dimensions on the map by 2 to find total miles:
School to Library = 3 x 2 = 6 miles.
Library to Park = 1.5 x 2 = 3 miles.
Total distance traveled: 5 + 6 + 3 = 14 miles.
How to do this ?? How
Answer:
The answer in the procedure
Step-by-step explanation:
we have
x+2y > 6
Isolate the variable y
y > -0.5x+3
The solution of this inequality is the shaded area above the dashed line
The equation of the dashed line is y=-0.5x+3
The slope of the dashed line is negative (m=-0.5)
The y-intercept of the dashed line is 3 (value of y when the value of x is equal to zero)
The x-intercept of the dashed line is 6 (value of x when the value of y is equal to zero)
Plot the intercepts to draw the dashed line and shaded the area above the dashed line
see the attached figure
n edge of Cube A is 8 inches, and an edge of Cube B is 5 inches. To the nearest tenth, how many times greater is the volume of Cube A than Cube B?
Answer:
4.1 times greaterStep-by-step explanation:
The formula of a volume of a cube:
[tex]V=a^3[/tex]
a - edge
Cube A:
a = 8in. Substitute:
[tex]V_A=8^3=512\ in^3[/tex]
Cube B:
a = 5in. Substitute:
[tex]V=5^3=125\ in^3[/tex]
[tex]\dfrac{V_A}{V_B}=\dfrac{512}{125}=4.096\approx4.1[/tex]
solve x^2+10x=24 by completing the sqaure. which is the solution set of the equation
Answer:
{-12, 2}
Step-by-step explanation:
x^2 + 10x = 24
Take half of the x-term coefficient and square it. Add that to both sides.
Half of 10 is 5. 5^2 = 25.
x^2 + 10x + 25 = 24 + 25
(x + 5)^2 = 49
x + 5 = +/-sqrt(49)
x + 5 = 7 or x + 5 = -7
x = 2 or x = -12
{-12, 2}
A sandwich shop loses $1.20 every time somebody buys a sandwich, but makes $1.80 every time somebody buys a drink. One day, the shop sells 100 drinks, and makes a profit of over $100. Which are possible numbers of sandwiches the shop could have sold? Check all that apply.
A. 0 sandwiches
B. 40 sandwiches
C. 60 sandwiches
D. 70 sandwiches
E. 80 sandwiches
Answer:
A, B, and C
I think. Please let me know if wrong.
Heres what i did:
1.8 x 100 = 180.
180 - 80 = 100
(they made over 10 in profit)
A. 1.2 x 0 = 0
B. 1.2 x 40 - 48
C. 1.2 x 60 = 72
D. 1.2 x 70 = 84
E. 1.2 x 80 =96
D and E bot Exceed 80 so it has to be AB and C
Hope this Helps ☺
Answer:
A,b,c
Step-by-step explanation:
P=1.8d-1.2s
P=180-1.2s
100=180-1.2s
-80=-1.2s
66.7=s
If they sold ≥67 sandwiches, p<100
If they sold ≤66 sandwiches, p>100
Therefore A, B and C are correct
What are the factors of the square root of 329
Answer: [tex]x=-\dfrac{3}{2}, 7[/tex]
Step-by-step explanation:
[tex]2x^2-10x-26=x-5[/tex]
[tex]2x^2-10x-26-x+5=0[/tex] Move all terms to one side
[tex]2x^2-11x-21=0[/tex] Simplify [tex]2{x}^{2}-10x-26-x+5[/tex]
[tex]2x^2+3x-14x-21=0[/tex] Split the second term
[tex]x(2x+3)-7(2x+3)=0[/tex] Factor out common terms in the first two terms, then in the last two terms.
[tex](2x+3)(x-7)=0[/tex] Factor out the common term [tex]2x+3[/tex]
[tex]x=-\dfrac{3}{2}, 7[/tex]
Answer:
x = -3/4 and 7/2 will be your final answer, but check below for a correction on your work
Step-by-step explanation:
***Your work is incorrect, it should be
2x² - 11x - 21 = 0
you need to subtract an 'x' from both sides, and add 5 to both sides...you added an x to the left side and subtracted a 5 from the left side instead***
I'll solve this so in case you will need help on it too.
Now you'll have
x = (11 ± √[(-11²) - 4(2)(-21)])/([4(2)]
x = (11 ± √289)/8
x = (11 ± 17)/8
x = (11 + 17)/8 = 28/8 = 7/2
or
x = (11 - 17)/8 = -6/8 = -3/4
In a 30-60-90 triangle, the length of the long leg is 8. Find the length of the hypotenuse.
Answer:
Step-by-step explanation:
In a 30-60-90 triangle, the ratio of the lengths of the angles' opposite sides are 1-√3-2.
If the long leg is 8, then the short one is 8/√3, or 8√3/3.
Therefore, the hypotenuse, which is double the short leg, is 16√3/3.
In a 30-60-90 triangle, the long leg is √3 times the short leg and the hypotenuse is twice the short leg. By knowing the long leg and using these relationships, we can work out the short leg and then the hypotenuse. In this specific problem, the hypotenuse of the triangle is approximately 9.24.
Explanation:
In a 30-60-90 triangle, the ratio of the side lengths is consistent. The length of the long leg is always √3 times the length of the short leg. The hypotenuse, which is the longest side of the triangle, is always twice the length of the short leg. If the length of the long leg is 8, the formula of this triangle can be used to find the length of the hypotenuse.
However, in your question, the length of the short leg isn't given. But based on the formulas for a 30-60-90 triangle, we can work it out. As long as we know that the long leg is √3 times the short leg, we can solve for the short leg, hence it's 8/√3.
Then, as the hypotenuse is twice the short leg, so hypotenuse = 2 * (8/√3) = 16/√3 ≈ 9.24.
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Given f(x) = 10 -2xfind f(7). –4 3 7 56
Answer: [tex]f(7)=-4[/tex]
Step-by-step explanation:
1. You have the following function given in the problem:
[tex]f(x)=10-2x[/tex]
2. Then, to find [tex]f(7)[/tex] asked in the exercise, you only need to substitute [tex]x=7[/tex] (which is the input value) into the given function.
3. Therefore, keeping the above on mind, you obtain that [tex]f(7)[/tex] is:
[tex]x=7[/tex]
[tex]f(7)=10-2(7)[/tex]
[tex]f(7)=10-14[/tex]
[tex]f(7)=-4[/tex]
Answer:
The correct answer is,
f(7) -4
Step-by-step explanation:
It is given that,
f(x) = 10 - 2x
To find f(7)
To find f(7) we have to put 7 instead of x in f(x).
Here f(x) = 10 - 2x,
Step 1: substitute the value x = 7 we get ,
f(7) = 10 - (2 * 7)
= 10 - 14 = -4
Therefore we get the answer f(7) = -4
The correct answer is first option.
The table represents a bicycle rental cost in dollars as a function of time in hours.
which explains weather or not the function represents a direct variation ?
a.would be the best answer to me because base in the table is you look carefully.you would see that it is double by yen and it is a constant. rate of change a linear function. that is why I think it's the best answer.
Answer:
A
Step-by-step explanation:
It can not be B, because the statement in the reasoning is false.
Nor can it be C, the statement is irrelevant and unnecessary.
Nor D, it makes no sense.
It's A because it is true and makes sense.
Please can someone help me I’ve been stuck in this for a while and I don’t get it, help please?
C . Permutation number of ways = 1
What is 3m in cm
?????
Answer:
300 cm
Step-by-step explanation:
What is the volume of the composite figure?
A sphere and a cylinder have the same radius, and the height of the cylinder is equal to its radius; which figure has the greater volume?
Given a sphere and a cylinder with the same radius, r, and the height of the cylinder equal to the radius, the sphere has a greater volume. This is concluded by comparing the volume formulas for a sphere (4/3πr³) and a cylinder (πr³).
Explanation:The sphere and cylinder have the same radius, r, and the height of the cylinder, h, is equal to its radius, r. We'll calculate the volumes of both an apply our given conditions to see which figure has a greater volume.
The formula for the volume of a cylinder is Vcylinder = πr²h. In this case given that h=r, it becomes Vcylinder = πr³.
The formula for the volume of a sphere is Vsphere = 4/3πr³.
Comparing both, we definitely see that the sphere with a volume of 4/3πr³ is greater than the cylinder with a volume of πr³
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Can you help me with 4? Can you give me a rule to follow when naming these?
Answer:
2,2 dimethyl propane
Step-by-step explanation:
To name such an organic compound, first identify the longest carbon chain in the provided table, the fourth compound, its longest carbon chain has three carbon atoms thus, the prefix prop-
Then we find the other substituents attached to the carbon chain. In the given compound it has two methyl (CH₃) groups attached to the second carbon atom.
thus 2,2 since there are two attached.
Bill drew each face of an ice cube below.
Note: Figure is not drawn to scale.
He measured the length of each edge to be 2.5 cm. What is the surface area of the ice cube?
A.
37.5 sq cm
B.
15 sq cm
C.
13.5 sq cm
D.
27 sq cm
Answer:
Option A. [tex]37.5\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of a cube is equal to
[tex]SA=6(b)^{2}[/tex]
where
b is the length side of the cube
In this problem we have
[tex]b=2.5\ cm[/tex]
substitute the value in the formula
[tex]SA=6(2.5)^{2}=37.5\ cm^{2}[/tex]
Answer:
if i had to say i would say B. 15 sq cm
Step-by-step explanation:
What is 0.888 into a fraction, is it over 100ths or 1,000's?
Thanks for using Brainly!
[tex]0.888 = 111/125 = 88.8percent[/tex]
I just gave you 0.888 is it's fraction and percentage.
First, 111/125 is the simplified answer and is over the 100th and is not big enough for the 1,000's.
Second, 111/125 as a percentage is 88.8%.
Have a great day.
Calculate the amount of money you'll have at the end of the indicated time period. You invest $2000 in an account that pays simple of 3% for 20 years. The amount of money you'll have at the end of 20 years is?
Answer:
compound interest
Step-by-step explanation:
2000 * 20 to power of 3
plz answer DDDDDDDDDDDDDDDDDD! using the line plot
Answer:
a. 6
b. 9
c. 4
Step-by-step explanation:
a.
Range = greatest - smallest
Range = 85 - 79
Range = 6
b.
b > 81
82, 83, 84...
3 82s
4 83s
2 85s
3 + 4 + 2 = 9
c.
b = 83
4 83s
4
Abby caught a fish that was 10 3/8 inches long. Brandon caught a fish that was 8 5/8 inches long. How much longer was Abby's fish than Brandon's fish?
what you do is take 5 away from 3. No! Borrow 1 Whole (9) and makes it 9 13/8 - 8 5/8 then subtract the 2 fractions
[tex] \frac{13}{8} - \frac{5}{8} ...[/tex]
and that is
[tex] \frac{8}{8} [/tex]
then convert that into 1 whole. Now add the whole to the 9 and thats 10. Now, subtract the 2 whole numbers. 10-8=2 so the answer is 2
Solve the equation.
3p/8-13=-25
3p/8 - 13 = -25
3p/8 = -12 | * 8
3p = -96 | : 3
P = -32
The value of p is -32
Step-by-step explanation:see the image
the diagram show the approximate length and width of Nevada. Estimate the area of the state
Area of a triangle is 0.5(base x height)
Base = 320mi
Height= 270+210= 480mi
0.5(480 x 320) = 76,800 miles squared
I NEED HELP PLEASE PLEASE PLEASE (35 POINTS)
Answer:
a
Step-by-step explanation:
Kay was walking along the bridge above the river. She accidentally lost her grip on her camera when she was trying to get it out to photograph massive birds nest in the trees.The height of the camera above the water can be modeled by the equation y=-16t^2+400, where t represents the seconds after the camera is dropped. How long will it take before Kay sees the splash from the camera hitting the water.
Answer:
5 seconds it will hit the water.
Step-by-step explanation:
y=-16t²+400
add -16t² to both sides
-16t²=-400
divide both sides by 16
t²=-25
t=√25
t=5
Answer:
t=5
Step-by-step explanation:
t=√25=t=5
■ ■I_____I8..................................
Answer:
The answer is [tex]2x^{3}y^{-2}\sqrt{6}[/tex]
Step-by-step explanation:
∵ √24 = 2√6
∵ [tex]\sqrt{x^{6}}=(x^{\frac{1}{2}})^{6}=x^{3}[/tex]
∵ [tex]\sqrt{y^{-4}}=(y^{\frac{1}{2}})^{-4}=y^{-2}[/tex]
∴ [tex]\sqrt{24x^{6}y^{-4}}=2x^{3}y^{-2}\sqrt{6}[/tex]
5–(6+9x)=9–(4x–1) evaluate the problem
the answer will be -11/5. i
Answer:
x= - 2 and 1/5
Step-by-step explanation:
jamal wrote the inequality x/16_<66. witch situation best represented by this inequality?
the number of candy bars (x) divided by 16 kids is less than or equal to 66 canyldy bars
PLS HELP ASAP. IM TIMED