Answers
Answer:
the function is odd
Step-by-step explanation:
A function f(x) is said to be even if f(-x) = f(x)
On the other hand, f(x) is said to be odd if f(-x)≠ f(x).
We plug in -x in place of x in the given function and simplify;
f(-x) = 3(-x-1)^4
f(-x) = 3[-1(x+1)]^4
f(-x) = 3 *(-1)^4 * (x+1)^4
f(-x) = 3(x+1)^4 ≠ f(x)
Therefore, the function given is odd
Answer:
The given function is odd
Step-by-step explanation:
we need to determine the function [tex]f(x)=3(x-1)^{4}[/tex] is odd or even
Since, A function f(x) is said to be even if [tex]f(-x) = f(x)[/tex]
and f(x) is said to be odd if [tex]f(-x)= - f(x)[/tex] and [tex]f(-x) \neq f(x)[/tex]
We Replace x with -x in the given function and solve;
[tex]f(x)=3(x-1)^{4}[/tex]
[tex]f(-x)=3(-x-1)^{4}[/tex]
take out the negative common,
[tex]f(-x)=3[-(x+1)]^{4}[/tex]
Since [tex](-1)^{4}=1[/tex]
[tex]f(-x)=3(x+1)^{4}[/tex]
[tex]f(-x) \neq f(x)[/tex]
Hence, the given function is odd
Related Questions
Will vote brainliest.
Answers
Answer:
The last choice availablle
Step-by-step explanation:
The way you can tell the points the function has in common with the x-axis (also known as the solutions, roots, or zeros of the functiion) you have to factor it to solve for x. When you throw this into the quadratic formula you get that there is a negative under the square root sign, which is indicative of imaginary solutions. Imaginary solutions do NOT cross the x-axis. So the answer to your problem is the last choice.
Answer:
21 jk
Step-by-step explanation:
In a week, a light bulb factory produces 12,500 light bulbs. The ratio of light emitting diodes (LED bulbs) to compact fluorescent lamps (CFL bulbs) is 2:3. Of the LED bulbs produced, 3% were defective. How many LED bulbs were not defective?
A) 150
B) 2,425
C) 4,850
D) 7,275
Answers
Answer:
C) 4,850
Step-by-step explanation:
No. of
LED bulbs : CFL bulbs : Total
2 : 3 : 5
5000 : 7500 : 12 500
Percentage of non-defective LED bulbs = 100% - 3% = 97%
No. of non-defective LED bulbs = 97% x 5000 = 4850
please help asap reward
Answers
Hello There!
-The Numbers Ordered From Least To Greatest-
-59 -41 -23 -11
The closer the number is to zero, it is going to be a bigger number than a number far away from zero.
From least to greatest it would be:
-59, -41, -23, -11
Which one of the following is an example of deductive reasoning?
A) The first term of a sequence of numbers is 1, the second term is 3, and the third term is 5. Thus, the nth term is 2n-1.
B) The sum of the angles in Which one of the following is an example of deduct and in Which one of the following is an example of deduct is 180 degrees. Therefore, the sum of the angles in any trianlge is 180 degrees.
C) All rectangles have four right angles. Since ABCD is a rectangle, it must have four right angles.
D) Line l1 has a slope of 5 and line l2 has a slope of 4. Line l1 is closer to the appearance of a vertical line than l2. Thus, the larger the slope of a line, the more vertical the line will appear.
Answers
Answer:
I want to say that the answer is C.
Hope this helps!
What is the inverse of the function f(x) = x + 2?
h(x) = 18x – 2
h(x) = 9x – 18
h(x) = 9x + 18
h(x) = 18x + 2
Answers
The inverse of the function f(x) = x + 2 is found by swapping the variables and solving for y, resulting in f^-1(x) = x - 2.
Explanation:The function f(x) = x + 2 is a simple linear function in Mathematics. The inverse of any function can be found by swapping the x and the y, and then solving for y. In this case, step-by-step, it would work like this:
Swap x and y to get x = y + 2.Solve for y by subtracting 2 from both sides to get y = x - 2.So the inverse of the function f(x) = x + 2 is f^-1(x) = x - 2.
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The inverse of the function f(x) = x + 2 is found by switching the roles of x and y and solving for y, resulting in the inverse function h(x) = x - 2. None of the provided options is correct.
Explanation:To determine the inverse of the function f(x) = x + 2, you need to first replace f(x) with y, resulting in the equation y = x + 2. Next, swap x and y to get x = y + 2. Solve for y to find the inverse function: y = x - 2. Therefore, none of the options provided is the correct inverse of the function f(x) = x + 2. The correct inverse is h(x) = x - 2.
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The area of triangle ABC is ____
square units.
Answers
Answer:
A = (1/2)(7 units)(5 units) = (35/2) units^2.
Step-by-step explanation:
Call AB "the base" and recognize that its length is 7 units. Call BC "the height" and recognize that its length is 5 units.
Then apply the area-of-a-triangle formula A = (1/2)(base)(height):
A = (1/2)(7 units)(5 units) = (35/2) units^2.
The area of triangle ABC is A = (1/2)(7 units)(5 units) = (35/2) units^2.
What is area of triangle?Triangle's area is equal to 1/2 (b* h) square units.
where the triangle's base and height, respectively, are denoted by b and h.
Given
Call AB "the base" and recognize that its length is 7 units. Call BC "the height" and recognize that its length is 5 units.
Then apply the area-of-a-triangle formula A = (1/2)(base)(height):
A = (1/2)(7 units)(5 units) = (35/2) units²
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Please help 10points
Answers
Answer:
x = 9
Step-by-step explanation:
Those are chords of a circle, and the theorem to find x is, in this context:
6(3) = 2(x) so
18 = 2x and
x = 9
A bell tower is 17 meters tall. It casts a long shadow on the ground below. The tip of the shadow of the bell tower is 51 meters from the base of the bell tower. At the same time, a tall elm tree casts a shadow that is 63 meters long. If the right triangle formed by the tower and its shadow is similar to the right triangle formed by the elm and its shadow, how tall is the elm to the nearest tenth?
Answers
Check the picture below.
The elm is 21 m tall.
How to find the height is the elm to the nearest tenth?Both the triangles are the same.
To find the height, by similarity we get
17 / h = 51 / 63
h = 63 * 17 / 51 = 21
The answer is 21 m.
If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar. Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.
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A triangle has vertices of (1, 5), (2, 2), and (6, 3). What are the vertices of the image created by applying the translation (x,y) --> (x+6,y-4)?
Answers
Answer:
Step-by-step explanation:
the translation (x,y) --> (x+6,y-4):
(1, 5)--> (1+6,5-4)=(7,1)
(2, 2)--> (2+6,2-4)=(8,- 2)
(6, 3)--> (6+6,3-4)=(12,- 1)
the image of A triangle has vertices of (1, 5), (2, 2), and (6, 3) is :
the triangle has vertices of (7, 1), (8,- 2), and (12, -1)
Jack plays cards with friend each afternoon here are his scores from the last 5 games 8,-6,-3,4,7 which is the least of his scores
Answers
Answer:
-6
Step-by-step explanation:
8,-6,-3,4,7 rearranged in ascending order produces -6, -3, 4, 7, 8.
-6 is the least of these scores (i. e., -6 is the lowest score).
Final answer:
Jack's least score from his last 5 card games is -6, as it is the smallest number in the set of his scores.
Explanation:
The question involves identifying the least score from a set of given numbers. To find the least score, Jack's scores from the last 5 card games are considered: 8, -6, -3, 4, 7.
Upon reviewing these numbers, it can be determined that -6 is the least because it is the smallest number and also it has a negative value, which makes it less than all the positive scores or any potential zero scores. Thus, the least of Jack’s scores is -6.
Find an equation for the nth term of the arithmetic sequence.
a14 = -33, a15 = 9
HELP ASAP!! THANK YOU!
Answers
Answer:
The equation of the nth term is an = -621 + 42n
Step-by-step explanation:
* Lets revise the arithmetic sequence
- There is a constant difference between each two consecutive numbers
- Ex:
# 2 , 5 , 8 , 11 , ……………………….
# 5 , 10 , 15 , 20 , …………………………
# 12 , 10 , 8 , 6 , ……………………………
* General term (nth term) of an Arithmetic sequence:
- U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d
- Un = a + (n – 1)d, where a is the first term , d is the difference
between each two consecutive terms
, n is the position of the term
* Lets solve the problem
∵ an = a + (n - 1)d
∴ a14 = a + (14 - 1)d
∴ a14 = a + 13d
∵ a14 = -33
∴ a + 13d = -33 ⇒ (1)
- Similar we can find another equation from a15
∵ a15 = a + (15 - 1)d
∴ a15 = a + 14d
∵ a15 = 9
∴ a + 14d = 9 ⇒ (2)
- We will solve equations (1) and (2) to find a and d
* Lets subtract equation (2) from equation (1)
∴ (a - a) + (13 - 14)d = (-33 - 9)
∴ -d = -42 ⇒ × both sides by -1
∴ d = 42
- Substitute this value of d in equation (1) or (2)
∵ a + 13d = -33
∵ d = 42
∴ a + 13(42) = -33
∴ a + 546 = -33 ⇒ subtract 546 from both sides
∴ a = -579
* Now lets write the equation of the nth term
∵ an = a + (n - 1)d
∵ a = -579 and d = 42
∴ an = -579 + (n - 1) 42 ⇒ open the bracket
∴ an = -579 + 42n - 42
∴ an = -621 + 42n
* The equation of the nth term is an = -621 + 42n
Given the exponential function f(x) = 54(0.45)x, classify the function as exponential growth or decay and determine the percent rate of growth or decay.
A.Exponential decay, 55% decrease
B.Exponential growth, 45% increase
C.Exponential decay, 45% decrease
D.Exponential growth, 55% increase
Answers
Answer:
Option A.Exponential decay, 55% decrease
Step-by-step explanation:
we have
[tex]f(x)=54(0.45)^{x}[/tex]
This is a exponential function of the form
[tex]f(x)=a(b)^{x}[/tex]
where
a is the initial value
b is the base
b=(1+r)
r is the rate of change
In this problem
a=54
b=0.45
so
0.45=1+r
r=0.45-1
r=-0.55
Convert to percentage
r=-55% ------> is negative because is a exponential decay
Answer:
Exponential decay, 55% decrease
Step-by-step explanation:
[tex]f(x) = 54(0.45)^x[/tex]
General exponential growth function is [tex]y=a(1+r)^x[/tex]
exponential growth function is [tex]y=a(1-r)^x[/tex]
The value of 1-r is less than 1 then it is exponential decay
In the given f(x) , the 1-r is 0.45 that is less than 1
So it is exponential decay.
[tex]1-r= 0.45[/tex]
Subtract 1 on both sides
[tex]r=0.55[/tex]
Multiply by 100 to get %
r= 55%
Exponential decay, 55% decrease
A party store has 54 packs of plates in stock. The packs are either sets of 8 or sets of 12. If the store has 496 total plates in stock, how many plates would the customer buy if he or she buys all of the 12 that the store has in stock?
A) 16
B) 38
C) 192
D) 304
Answers
Answer:
a 16
Step-by-step explanation:
16 x 12 = 192 plates
496 total plates - 192 = 304
304 packages of 8 plates
304 / 8 = 38 sets of 8 plates
38 + 16 = 54 packs of plates
What is the surface area of this rectangular prism
Answers
Answer:
C. [tex]490 \textrm{ units}^{2}[/tex]
Step-by-step explanation:
The formula for surface area is
LA + 2B
LA indicated Lateral Area and can be found multiplying perimeter of base by the height.
7 + 7 + 14 + 14 = 42 * 7 = 294
Multiply the LA from above with the area of base times 2.
98 * 2 = 196
294 + 196 = 490, so the surface area of the rectangular prism is 490 units.
To find the surface area of a rectangular prism, add up the areas of all six faces by multiplying length by width.
Explanation:To find the surface area of a rectangular prism, you need to add up the areas of all six faces. Each face is a rectangle, so to find the area, you multiply the length by the width. Then, you add up the areas of all the faces to get the total surface area.
For example, if the length of one side is 4 units, the width is 2 units, and the height is 3 units, the surface area would be:
Face 1: 4 units x 2 units = 8 square units
Face 2: 4 units x 2 units = 8 square units
Face 3: 4 units x 3 units = 12 square units
Face 4: 4 units x 3 units = 12 square units
Face 5: 2 units x 3 units = 6 square units
Face 6: 2 units x 3 units = 6 square units
Total surface area: 8 + 8 + 12 + 12 + 6 + 6 = 52 square units.
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If the graphs of the lines in the system of equations above the intersect at (-3,1), what is the value of K/H?
A) 3/2
B) 2
C) 3
D) 6
Answers
Answer:
h = 2 and k = 6
Step-by-step explanation:
Since the lines intersect at (- 3, 1) then this is the solution to the system of equations.
That is x = - 3 and y = 1
Substitute these values into the equations and solve for h and k
hx - 4y = - 10
- 3h - 4 = - 10 ( add 4 to both sides )
- 3h = - 6 ( divide both sides by - 3 )
h = 2
Similarly
kx + 3y = - 15
- 3k + 3 = - 15 ( subtract 3 from both sides )
- 3k = - 18 ( divide both sides by - 3 )
k = 6
If log(a) = 1.2 and log(b)= 5.6, what is log(a/b)?
a. 4.4
b. 6.8
c. not enough information
d. -4.4
Answers
Answer:
d. -4.4
Step-by-step explanation:
We know that log (a/b) = log a - log b
Since log a = 1.2 and log b = 5.6 , we can substitute these values into the equation.
log (a/b) = 1.2 - 5.6
= -4.4
What do you know to be true about values of p and q?
Answers
Answer:
p = q
Step-by-step explanation:
There are 180 degrees in a triangle. If you subtract 50 and 60 from 180, you get 70. If you subtract 30 an 80 from 180, you get 70. therefore p = q.
How many solutions does the nonlinear system of equations graphed below have?
Answers
Answer:
its one
Step-by-step explanation:
ape x legends
A pizza shop offers the toppings shown below how many different three topping pizzas can you make ?
Pepperoni
Mushrooms
Sausage
Onion
Ham
A. 6
B. 10
C. 4
D. 5
Answers
Answer:
B. 10.
Step-by-step explanation:
This is the number of combinations of 3 from 5.
5C3 = 5! / 3! (5-3)!
= 5*4*3*2*1 / 3*2*1 * 2*1
= 5*4/2*1
= 10.
Answer: 10 i think
Step-by-step explanation:
please help asap will mark brainliest
Answers
Answer:
10x
Step-by-step explanation:
Note the place values of the value 3 in both of the decimals.
The value of the 3 in 46.132 is in the hundredths place.
The value of the 3 in 8.553 is in the thousandths place.
Divide thousands with hundreds: 1000/100 = 10
The value of the 3 in 46.132 is 10x larger than the value of 3 in 8.553
~
Use the graph of each polynomial function to find the factored form of the related polynomial. Assume the polynomial has no constant factor.
What are the zeros of this function? (2 points) _______, _______
What is the factorization of the polynomial? (2 points)
Answers
Answer:
zeros: x = -2; x = +4factorization: y = (x +2)(x -4)Step-by-step explanation:
The zeros are where the graph crosses the x-axis (y=0). They are x=-2 and x=4.
The factors are the binomials that are zero when x has the value of a zero:
y = (x +2)(x -4)
A deposit of $10,000.00 was made to an account the year you were born. After 12 years, the account had earned $6,600.00 in interest. What simple interest rate did the account earn?
Answers
Answer:
5.5% per year
Step-by-step explanation:
Using Formula A = P (1 + rt)
Where
A = Final amount = $10,000 + $6,600 = $16,600
P = Principal = Beginning Amount = $10,000
t = time = 12 years
r = rate in $/year (which we need to find)
Assembling the formula
A = P (1 + rt)
16,600 = 10,000 (1 + 12r)
[tex]\frac{16,600}{10,000}[/tex] = 1 + 12r
1.66 = 1 + 12r
1.66 - 1 = 12r
0.66 = 12 r
r = 0.055 = 5.5%
Mary wants to fill in a cylinder vase. At the flower store they told her that the vase should be filled 3/4 for the flowers to last yhe longest. Her cylinder vase has a radius of 2 in and a height of 9 in how much water should mary pour into the vase?
Answers
Answer:
84.8 in³
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h
The volume Mary will be filling will be 3/4 of the 9-inch height of the vase, so is ...
V = π(2 in)²(3/4·9 in) = 27π in³ ≈ 84.8 in³
_____
Comment on the answer
In more conventional units of measure, that is very nearly 3 pints of water.
Suppose $r$ and $s$ are the values of $x$ that satisfy the equation
\[x^2 - 2mx + (m^2+2m+3) = 0\]for some real number $m$. Find the minimum real value of $r^2+s^2$.
Answers
Answer:
-8
Step-by-step explanation:
For roots r and s, the quadratic can be factored ...
f(x) = (x -r)(x -s) = x^2 -(r+s)x +rs
Then the value of r^2+s^2 can be determined from the coefficient of x (-(r+s)) and the constant (rs) by ...
r^2 +s^2 = (-(r+s))^2 -2(rs) = (r^2 +2rs +s^2) -2rs = r^2 +s^2
Comparing this to your given equation, we have the coefficient of x as (-2m) and the constant term as (m^2+2m+3). Forming the expression ...
(x-coefficient)^2 -2(constant term)
we get ...
r^2 +s^2 = (-2m)^2 -2(m^2 +2m +3) = 2m^2 -4m -6
r^2 +s^2 = 2(m -1)^2 -8
The minimum value of this quadratic expression is where m=1 and the squared term is zero. That minimum value is -8.
PLS HELP SHOW ALL YOUR WORKING OUT
THANK YOU IN ADVANCE :D
Answers
Answer:
[tex]AB =3 \sqrt{5} = 6.708203932...[/tex]
Step-by-step explanation:
[tex]A( - 1,6) \:,\: B(5,3)\\ AB = \sqrt{{(x1 - x2)}^{2} + {(y1 - y2)}^{2} } \\ AB = \sqrt{ {( - 1 - 5)}^{2} + {(6 - 3)}^{2} } \\ AB = \sqrt{ {( - 6)}^{2} + {(3)}^{2} } \\ AB = \sqrt{36 + 9} \\ AB = \sqrt{45} = 3 \sqrt{5} = 6.708203932...[/tex]
The distance between A and B to 3 significant figure is 6.71
The formula for calculating the distance between two points is expressed as:
[tex]D =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Given the coordinate points (-1, 6) and (5, 3)
Substitute the given coordinates into the formula;
[tex]D =\sqrt{5+1)^2+(3-6)^2}\\D =\sqrt{(6^2+(-3)^2}\\D=\sqrt{36+9}\\D=\sqrt{45}\\D= 6.71\\[/tex]
Hence the distance between A and B to 3 significant figure is 6.71
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In a basketball drill, two players start at the same spot on the court. One player runs 6 feet
down the court and the other player runs 4.5 feet across the court (in a direction perpendicular
to the first player). What is the distance that one player must pass the ball for it to reach the
other?
Answers
Answer:
7.5 ft
Step-by-step explanation:
The distance can be found using the Pythagorean theorem. The given distances form the legs of a right triangle, and the ending distance (d) between the players is its hypotenuse. The Pythagorean theorem tells you ...
d² = (6 ft)² +(4.5 ft)² = 36 ft² +20.25 ft²
d² = 56.25 ft² = (7.5 ft)² . . simplifying and rewriting as a square
d = 7.5 ft . . . . . . . . . . . . . . . taking the positive square root
The ball must be passed a distance of 7.5 ft for it to reach between players.
_____
If you recognize the given numbers as having the ratio 3:4, then you may realize they are the legs of a 3-4-5 right triangle with a scale factor of 1.5. The distance between players will be 1.5×5 = 7.5 feet.
Answer:
[tex]\boxed{\text{7.5 ft}}[/tex]
Step-by-step explanation:
If the players are running perpendicular to each other, we have a right triangle, as in the diagram below.
We can apply Pythagoras' Theorem.
[tex]\begin{array}{rcl}a^{2} & = & b^{2} + c^{2}\\& = & 4.5^{2} + 6^{2}\\& = & 20.25 +36\\& = & 56.25\\a & = & \sqrt{56.25}\\& = & \mathbf{7.5}\\\end{array}\\\text{The distance between the two players will be } \boxed{\textbf{7.5 ft}}[/tex]
The highest elevation in California is 14,494 feet at Mt. Whitney and the lowest elevation is –282 feet at Death Valley. What is the total difference in elevation between these two places
Answers
14,776
/////////////////////////////////////////////////////////////
equation: 14494 + 282 = 14,776
(you convert the negative 282 to positive)
Add the highest elevation with the lowest elevation, to find the total difference. 14494 + 282 = 14,776. You convert the negative 282 to positive. The total difference in elevation between these two places is 14,776.
The length of a rectangular garden ABCD is 9 feet more than its width. It is surrounded by a brick walkway 4 feet wide as shown below. Suppose the total area of the walkway is 400 square feet. 25. What are the dimensions of the garden?
Answers
Answer:
16.5 ft by 25.5 ft
Step-by-step explanation:
Let w represent the width of the garden in feet. Then w+9 is the garden's length, and w(w+9) represents its area.
The surrounding walkway adds 8 feet to each dimension, so the total area of the garden with the walkway is ...
(w+8)(w+9+8) = w^2 +25w +136
If we subtract the area of the garden itself, then the remaining area is that of the walkway:
(w^2 +25w +136) - (w(w+9)) = 400
16w + 136 = 400 . . .simplify
16w = 264 . . . . . . . . subtract 136
264/16 = w = 16.5 . . . . . width of the garden in feet
w+9 = 25.5 . . . . . . . . . . .length of the garden in feet
Please help me with this question, I'm actually sick of people who keep answering dumb things just to get the points. I really need help with this.
Answers
Answer:
see below
Step-by-step explanation:
Events are independent when the probability of one of them does not depend on the other one. That is, P(A|B) = P(A) and P(B|A) = P(B).
They are not independent if the above condition is not met.
A quick assessment of the given table shows ratios of one row to the next are different between columns, and vice versa. Hence the events are not indpendent.
(01.03)
Solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.
square root of the quantity x minus 3 end quantity plus 5 equals x
Answers
Answer:
x=7 satisfy the equation, so it is the solution.
x=4 doesn't satisfy the equation so it is extraneous solution.
Step-by-step explanation:
The equation given is:
[tex]\sqrt{x-3}+5=x[/tex]
Adding -5 on both sides
[tex]\sqrt{x-3}=x-5[/tex]
Taking square on both sides
[tex](\sqrt{x-3})^2=(x-5)^2[/tex]
Now solving
[tex]x-3 = x^2 -10x+25\\Arranging\\x^2-10x-x+3+25=0\\x^2-11x+28=0\\Factorizingx^2-7x-4x+28=0\\\\x(x-7)-4(x-7)=0\\(x-4)(x-7)=0\\x-4=0 \,\,and\,\, x-7=0\\x=4 \,\,and\,\, x=7[/tex]
Verifying solutions:
Putting x=4 in the equation
[tex]\sqrt{x-3}+5=x[/tex]
[tex]\sqrt{4-3}+5=4[/tex]
[tex]\sqrt{1}+5=4[/tex]
[tex]1+5=4[/tex]
[tex]6\neq 4[/tex]
So, x=4 doesn't satisfy the equation so it is extraneous solution.
Now Putting x=7 and verifying
[tex]\sqrt{x-3}+5=x[/tex]
[tex]\sqrt{7-3}+5=7[/tex]
[tex]\sqrt{4}+5=7[/tex]
[tex]2+5=7[/tex]
[tex]7=7[/tex]
x=7 satisfy the equation, so it is the solution.
Answer:
= 7
Step-by-step explanation: