Answers
You may be asked to "determine algebraically" whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (–x) = f (x), so all of the signs are the same), then the function is even. If you end up with the exact opposite of what you started with (that is, if f (–x) = –f (x), so all of the signs are switched), then the function is odd.
In all other cases, the function is "neither even nor odd".
Let's see what this looks like in action:
Determine algebraically whether f (x) = –3x2 + 4 is even, odd, or neither.
If I graph this, I will see that this is "symmetric about the y-axis"; in other words, whatever the graph is doing on one side of the y-axis is mirrored on the other side:
graph of y = –3x^2 + 4
This mirroring about the y-axis is a hallmark of even functions.
Also, I note that the exponents on all of the terms are even — the exponent on the constant term being zero: 4x0 = 4 × 1 = 4. These are helpful clues that strongly suggest to me that I've got an even function here.
But the question asks me to make the determination algebraically, which means that I need to do the algebra.
So I'll plug –x in for x, and simplify:
f (–x) = –3(–x)2 + 4
= –3(x2) + 4
= –3x2 + 4
I can see, by comparing the original function with my final result above, that I've got a match, which means that:
f (x) is even
Related Questions
A manufacturer of household washing machines wants to determine the effectiveness of the type of detergent used (three brands – A, B, and C) and the length of time for the washing cycle (18, 20, and 22 minutes). The manufacturer prepared 18 standard household laundry loads (having equal amounts of dirt and the same total weight) to conduct the study. The manufacturer randomly assigned two loads to each type of detergent, time combination. The researcher recorded the amount of dirt removed. Use a 5% significance level, for all hypothesis tests and confidence intervals. What is the alternative hypothesis for testing the interaction?
Answers
Answer:
Two-Factor ANOVA with replication
Step-by-step explanation:
Types of detergent used ( A,B,C ) = 3
Length of time for the washing cycle : A = 18 mins, B = 20 mins, C = 22 mins
number of laundry loads = 18
significance level = 5%
The alternative hypothesis for testing the interaction is a Two-Factor ANOVA with replication this is because the factors that have variations are the : The type of detergent and the length of time for a washing cycle while the load is constant for all.
i rly have no idea what this one is
Answers
Answer:
x = 11, y = 17
Step-by-step explanation:
Set the equations equal to each other. Since the vertical angles are congruent, 8x + 7 = 9x - 4 and 5y = 7y - 34. Now, solve your equations for the x and y values.
8x + 7 = 9x - 4
x = 11
5y = 7y - 34
2y = 34
y = 17
You deposit $800 in an account that earns simple interest at an annual rate of 5%. How many years must you leave the money in the account to earn $100 in interest?
Answer value
Answers
Answer:
yduhegeggegeheygegeveheyegeveheuegeveve
Step-by-step explanation:
your very welcome
Find the common ratio of the geometric sequence 18,-90,450,...
Answers
Answer:
try looking it up on socratic
Answer:
-5
Step-by-step explanation:
The common ratio is what you have to multiply one term by to get the next term.
so:
[tex]18 \times r = -90\\-90 \times r = 450[/tex]
where r is the common ratio
We can solve these equations:
-90 / 18 = -5
450/-90 = -5
therefore the common ratio is -5
Currently bank customers wait approximately 7.5 minutes during peak hours to be served by a teller. Suppose the bank manager hires another teller and wants to show that the wait time has now decreased. She takes a random sample of 50 customers during peak time and finds that the average wait time is 9.3 minutes. Which of the following statements is the correct alternative hypothesis?a) H1: µ < 7.5b) H1: µ ≠ 7.5c) H1: µ > 7.5d) H1: µ > 9.3e) H1: µ < 9.3
Answers
Answer:
a) H1: µ < 7.5
Step-by-step explanation:
From the given information:
mean = 7.5
sample size = 50
sample mean = 9.3
The main task we are to carry out is to identify the correct alternative hypothesis:
Now to do that, let's state the null and the alternative hypothesis from the given study.
The null hypothesis can be computed as:
[tex]\mathbf{H_o: \mu \geq 7.5}[/tex]
The alternative hypothesis can be computed as:
[tex]\mathbf{H_1: \mu < 7.5}[/tex]
Thus, this test hypothesis is a one-tailed test (left tailed).
Adding/Subtracting Rational Expressions
Answers
9514 1404 393
Answer:
(4x^2 +21x +18)/(3x^2 +34x -24)
Step-by-step explanation:
I find it helpful to keep in mind the form ...
a/b + c/d = (ad +bc)/(bd)
When we apply that to this case, we get ...
[tex]\dfrac{x+3}{x+12}+\dfrac{x+2}{3x-2}=\dfrac{(x+3)(3x-2)+(x+12)(x+2)}{(x+12)(3x-2)}\\\\=\dfrac{(3x^2+7x-6)+(x^2+14x+24)}{(x+12)(3x-2)}=\boxed{\dfrac{4x^2+21x+18}{3x^2+34x-24}}[/tex]
114 = 3 (y + 18) what is the missing value
Answers
Answer:
y= 20
Step-by-step explanation:
114 = 3y + 54
114 - 54 = 3y
60 = 3y
y = 60 ÷ 3
y = 20
5. If you receive 24% off of a $100.00 item, what is the final price of the item?
A. $0.24
Answers
Answer:
24% of 100 is 24 meaning you subtract 24 to 100. Giving you $76 as the final price.
Step-by-step explanation:
What is the slope-intercept form of the equation of the line that passes through the point (–6, 1) and is perpendicular to the graph of 2x + 3y = –5?
Answers
.
Jamie went shopping for party snacks. He bought 3 bags of chips for $4.00 each, 5 bottles of soda for $2.00 each and an ice cream cake for $20.00. How much did he spend altogether?
Choose the expression that is a correct translation of the problem.
(3 x 4) x (5 x 2) + 20
(3 + 4) + (5 + 2) + 20
(3 x 4) + (5 x 2) + 20
(3 x 4) + (5 x 2) x 20
Answers
Answer:
C (3x4) + (5x2) + 20
Step-by-step explanation:
3 things that cost 4 dollars. 5 things that cost 2 dollars and one that cost 20.
Lin rode her bike 2 miles in 8 minutes. She rode at a constant speed. How far would she travel in 1 minute?
Answers
Answer: She can travel a quarter of a mile in 1 minute.
Step-by-step explanation: In 8 mins she can bike 2 miles and if you split that in half then you can see she can bike 1 mile in 4 min then you can say ok well in 2 mins she can bike half a mile and just split that again and you have a Quarter of a mile in one Minute...
Find the measure of angle 1.
152
115
mZ1 =
Please help mee:(
Answers
Answer:
37°
Step-by-step explanation:
We have been given the diagram of the triangle;
To find the angle I;
We need to apply one of the geometry laws,
The sum of adjacent internal angles of a triangle gives the external angle;
So;
I + 115 = 152
Solve for I;
I = 152 - 115 = 37°
A box has a volume of 30 cubic cm. the box is filled with unit cubes, with no gaps or overlaps. each unit cube measures 1 cm in length, 1 cm in width, and 1 cm in height. how many unit cubes fill the box A:90
B:10
C:30
D:33
Answers
Answer:
C. 30.
Step-by-step explanation:
Each cube has a volume of 1 * 1* 1 = 1 cu cm.
The answer is 30 unit cubes because 30 *1 = 30.
The box is filled with 30 unit cubes.
The formula to calculate the volume of a cube: -For a cube with side length 'a' volume V is,
[tex]V=a^{3}[/tex] cubic units
In this question, a box has a volume of 30 cubic cm.
The box is filled with unit cubes, with each unit cube measures 1 cm in length, 1 cm in width, and 1 cm in height.
Let [tex]V_{s}[/tex] represents the volume of each unit cube and [tex]V[/tex] represent the volume of the box.
The length of each side of a unit cube is 1 cm.
So, [tex]V_{s}=(1)^{3}[/tex]
⇒ [tex]V_{s}=1[/tex] cubic cm
Let there are n unit cubes filled in the box.
⇒ [tex]V=n\times V_{s}[/tex]
⇒ [tex]30=n\times 1[/tex]
⇒[tex]n=30[/tex]
Therefore, 30 unit cubes are filled in the box.
Hence, option C. 30 is the correct answer.
Learn more about cube here:
https://brainly.com/question/11168779
#SPJ2
How is dividing and multiplying with an area model similar and How is it different?
Answers
Answer:
In multiplication the numbers you multiply are called factors; the answer is called the product. In division the number being divided is the dividend, the number that divides it is the divisor, and the answer is the quotient.
Solve the inequality.
negative 2 times left parenthesis 6 plus s right parenthesis is greater than or equal to negative 15 minus 2 s
Answers
We distribute the left side of the inequality.
-12 - 2s >_ -15 - 2s
Add 2s on both sides.
They cancel out, and we’re left with:
-12 >_ -15
This is surprisingly a true statement, so s = 0 in order for us to end up with this again.
Hopefully it’s right. Good luck!
50 POINTS SOLVE !! ::
pls actually solve it thank you <3
k-4 /9 =3
8+b /-4 = -5
Answers
Answer:
k = 31/9b = 12Step-by-step explanation:
k - 4 = 3
9
k/9 = 3(9) + 4
k = 31/9
k = 31/9
8 + b = -5
-4
8 + b = -5 (-4)
8 + b = 20
b = 20 - 8
b = 12
4+7x=-10+5x please answer
Answers
X=-7
---------------------------------------------------------
4+7x=-10+5x
+10 +10
14+7x=5x
-7x -7x
14=-2x
14/-2 -2x/-2
-7=x
The slope of AB is 2/3, A(1,-4) and B(-5,y). Solve for the value of y.
Answers
the difference between the x coordinates of each point is 6. in order for the slope to simplify to 2/3 the difference in y should be 9.
y=9-4(y coordinates of A)
=5
Answer:
y=5
Step-by-step explanation:
the difference between the x coordinates of each point is 6. in order for the slope to simplify to 2/3 the difference in y should be 9.
y=9-4(y coordinates of A)
=5
what is the value of n n+11=13
Answers
Answer:
n = 2
Step-by-step explanation:
[tex]n + 11 = 13[/tex]
Subtract 11 from both sides to isolate n.
[tex]n + 11 - 11 = 13 - 11[/tex]
[tex]n = 2[/tex]
What is the length of the hypotenuse of the triangle?
Answers
Answer:
It depends, you have to use the Pythagorean Theorem
explanation:
Answer:
If you have both legs, then you can use the PYTHAGOREAN THEOREM to find the value of the hypotenuse. a^2 + b^2 = c^2 ( a= leg, b = leg, c = hypotenuse)
Step-by-step explanation:
If you do not have a leg value, but you do have an angle measure, then you can use Sine or Cosine to find the hypotenuse. Sin = opposite/hypotenuse and Cos = adjacent/hypotenuse.
Let me know if you need further explaination!
Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary.
Answers
Write an equation for the line that passes through (4, 5) and (6, 7).
|
Answers
Answer:
y=x+1
Step-by-step explanation:
The first step I took was to find the slope. A slope is equal to the rise over the run. The equation goes up 2 for every 2 it goes over, which means that the slope is 2/2 or 1. Then you need to determine the y intercept. I usually go about this by thinking logically about the problem. Because there is a point at (4,5) and the slope is 1, there must also be a point at (3,4) (2,3) (1,2) and (0,1) Because the x value in (0,1) is 0, we know that the y intercept must be 1, so I added 1 to the equation. The last step is putting it all together. We know that a linear equation is y=mx+b (m being the slope, b being the y-intercept) so the final equation is y=x+1
2. Find the distance between (-2,1) and (3,4).
Answers
Answer:
[tex]\sqrt{34}[/tex] or 5.83095
Step-by-step explanation:
Use the distance formula [tex]\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1} )^2 }[/tex]
Make sure to round the answer appropriately if not asked for in square root form!!
A recipe calls for 4c of flour. You have 20 c of flour. Let r represent the flour you when left after making the recipe. Is the remaining amount of flour 18c?
Answers
Answer:
r=16c
Step-by-step explanation
20-4=r
16=r
Super easy math question pls help
Answers
Answer:
Thanks
Step-by-step explanation
6(9)+6(7)
also, 18(3)+14(3)
Help me?? Anyone I'll vote brainliest and everything 5 stars!! :)
Answers
Answer: y - 3 = -1/5(x+5)
Step-by-step explanation:
Hope this helps
Which expression shows the ASSOCIATIVE PROPERTY?
3 + a + b = a + 3 + b
3(ab) = (3a)b
(3 + a) + b = 3 + (a + b)
3 - a = 3 - b
Answers
Answer:
the first one
Step-by-step explanation:
Use the substitution method to solve the system of equations. Choose the correct ordered pair 2x+y= 10
y=x-5
(a) (5,0)
(b) (7,2)
(c) (9,-8)
(d) (8,-6)
Answers
Answer:
a (5,0)
Step-by-step explanation:
2x + y = 10 substitute y= x - 5 into that first equation
2x+(x-5)=10
2x+x-5=10
3x - 5 = 10
3x = 10 + 5
3x = 15
[tex] \frac{3x}{3} = \frac{15}{3} [/tex]
x=5
substitute the x into either the first or second equation
2(5) +y=10
10 + y = 10
y= 10 - 10
y = 0
therefore
x = 5 and y= 0
Jose and Maris work for different car dealerships. Jose earns a monthly salary of $3,500 plus a 6% commision on his sales, x. Maris earns a monthly salary of $4,000 plus a 4% commission on her sales, x. For what value of sales, x, will Jose's earnings be greater than Maris' earnings?
Answers
Answer:
x>$25000
Step-by-step explanation:
John was gifted a pack of crayons. He gave 13 crayons to his friend Rhea
and was left with 11 crayons. How many crayons did the pack contain?
Answers
Answer:
24
Step-by-step explanation:
13+11=24
