Answer:
[tex]f(x) = 3x^2[/tex] and [tex]g(x) = x + 2[/tex]
Step-by-step explanation:
Given
[tex]h(x) = 3(x+2)^2[/tex]
[tex]h(x) = (fog)(x)[/tex]
Required
Find possible expressions for f(x) and g(x)
[tex]h(x) = (fog)(x)[/tex]
This can be rewritten as:
[tex]h(x) = f(g(x))[/tex]
Recall that [tex]h(x) = 3(x+2)^2[/tex]
So;
[tex]h(x) = f(g(x)) = 3(x+2)^2[/tex]
[tex]f(g(x)) = 3(x+2)^2[/tex]
By comparison, the expression in bracket represents g(x);
Hence;
[tex]g(x) = x + 2[/tex]
Replace g(x) with x
[tex]f(x) = 3(x)^2[/tex]
[tex]f(x) = 3x^2[/tex]
Hence, the possible expressions of f(x) and g(x) are:
[tex]f(x) = 3x^2[/tex] and [tex]g(x) = x + 2[/tex]
Based on the following set of data, which of the statements shown is true? 11, 11, 12, 13 mean < median mean = median mean > median
mean>median
mean=11.75
median=11.5
Please help its eighth math!
Answer:
t and u are parallel lines
s and t are also parallel lines
Step-by-step explanation:
If two parallel lines are cut by a transversal ,
then in it
pair of alternate angle are equals, similarly vice versa
if pair of alternate angle are equals then lines are parallel
pair of corresponding angles are equal and vice-versa
for example
in the given problem
if line t and u are parallel (note we have assumed this to give example of parallel lines)
then angle 7 and 9 are called alternate angles
pair of angles 5 and 9 are corresponding angles.
________________________________________________
given
∠8 = ∠10 which are alternate angles for line t and u and s is transversal for it,
thus t and u are parallel lines
___________________________
∠1 = ∠3 as they vertically opposite angles
and we know that pair of vertically opposite angles are equal
given
∠1 = ∠7
thus
∠3 = ∠7
as pair of angles ∠3 and ∠7 are corresponding angles. and are equal and hence line s and t are also parallel.
plz help
urgent !!!!
will give the brainliest !!
Answer:
[tex]X = \begin{bmatrix}1&3\\ 2&4\end{bmatrix}[/tex]
Step-by-step explanation:
The question we have at hand is, in other words,
[tex]\begin{bmatrix}4&2\\ \:1&1\end{bmatrix}\left(X\right)=\begin{bmatrix}8&20\\ \:3&7\end{bmatrix}[/tex] - where we have to solve for the value of [tex]X[/tex]
If we have to isolate [tex]X[/tex] here, then we would have to take the inverse of the following matrix ...
[tex]\begin{bmatrix}4&2\\ \:1&1\end{bmatrix}[/tex] ... so that it should be as follows ... [tex]\begin{bmatrix}4&2\\ \:1&1\end{bmatrix}^{-1}[/tex]
Therefore, we can conclude that the equation as to solve for " [tex]X[/tex] " will be the following,
[tex]X=\begin{bmatrix}4&2\\ 1&1\end{bmatrix}^{-1}\begin{bmatrix}8&20\\ 3&7\end{bmatrix}[/tex] - First find the 2 x 2 matrix inverse of the first portion,
[tex]\begin{bmatrix}4&2\\ 1&1\end{bmatrix}^{-1}[/tex] = [tex]\frac{1}{\det \begin{pmatrix}4&2\\ 1&1\end{pmatrix}}\begin{pmatrix}1&-2\\ -1&4\end{pmatrix}[/tex]= [tex]\frac{1}{2}\begin{bmatrix}1&-2\\ -1&4\end{bmatrix}[/tex] = [tex]\begin{bmatrix}\frac{1}{2}&-1\\ -\frac{1}{2}&2\end{bmatrix}[/tex]
At this point we have to multiply the rows of the first matrix by the rows of the second matrix,
[tex]X = \begin{bmatrix}\frac{1}{2}&-1\\ -\frac{1}{2}&2\end{bmatrix}\begin{bmatrix}8&20\\ 3&7\end{bmatrix}[/tex] ,
[tex]X = \begin{pmatrix}\frac{1}{2}\cdot \:8+\left(-1\right)\cdot \:3&\frac{1}{2}\cdot \:20+\left(-1\right)\cdot \:7\\ \left(-\frac{1}{2}\right)\cdot \:8+2\cdot \:3&\left(-\frac{1}{2}\right)\cdot \:20+2\cdot \:7\end{pmatrix}[/tex] - Simplifying this, we should get ...
[tex]\begin{bmatrix}1&3\\ 2&4\end{bmatrix}[/tex] ... which is our solution.
Can you please say if the point is on the line?
How many different "words" can be made from the given word by rearranging the letters? DIGIT I don't need the word themselves I just need the amount
Answer:
60 words
Step-by-step explanation:
Find the number of 4-digit numbers that contain at least three even digits.
Answer:
4625 numbers
Step-by-step explanation:
To solve this problem we can separate it in different cases, and then we sum the amount of numbers of each case to find our final result.
The first case is: all four numbers are even.
We have 5 even digits, and the first digit of the 4-digit number can't be zero, so for the first digit we have 4 possible values, and for the other 3 digits we have 5 possible values, then the amount of numbers with this condition is:
[tex]N_1 = 4 * 5 * 5 * 5 = 500\ numbers[/tex]
The second case is the number having three even digits and one odd digit, and the first digit is the odd digit.
In this case, the first digit has 9 possible values (all digits but zero) and the other 3 digits have 5 possible values (even digits):
[tex]N_2 = 9 * 5 * 5 * 5 = 1125\ numbers[/tex]
The third case is the number having three even digits and one odd digit, and the first digit is not the odd digit.
In this case, the first digit has 4 possible values, the odd digit has 10 possible values and the other two digits have 5 possible values. The odd digit can be the second, the third or the fourth digit, so we multiply our result by 3 (because we will find the same result if we choose the odd digit to be the second, third or fourth):
[tex]N_3 = 3 * 4 * 10 * 5 * 5 = 3000\ numbers[/tex]
So the final result is the sum of these cases:
[tex]N = N_1 + N_2 + N_3[/tex]
[tex]N = 500 + 1125 + 3000 = 4625\ numbers[/tex]
Given the following function, find f(-5), f(0), and f(2).
f(x) = - 3x-5
f(-5) =
Answer:
10, -5, -11
Step-by-step explanation:
f(x) = - 3x-5
f(-5) = -3(-5) - 5 => 15 - 5 => 10
f(0) = -3(0) - 5 => 0 - 5 => -5
f(2) = -3(2) - 5 => -6 - 5 => -11
The value of the function at x = –5, 0, 2 will be 10, –5, and –11.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The function is given below.
f(x) = –3x – 5
The value of the function at x = –5, 0, 2 will be
f(–5) = –3(–5) – 5
f(–5) = 15 – 5
f(–5) = 10
f(0) = –3(0) – 5
f(0) = 0 – 5
f(0) = –5
f(2) = –3(2) – 5
f(2) = –6 – 5
f(2) = –11
More about the function link is given below.
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How many ways can you distribute 4 different balls among 4 different boxes?
Answer:
16?? not sure.......
Gale buys 12 bags of mulch. Each bag contains two cubic feet of mulch. What part of a cubic yard are the 12 bags of mulch in total? Express your answer as a common fraction.
Answer:
8 cubic yards
Step-by-step explanation:
An ant needs to travel along a 20cm × 20cm cube to get from point A to point B. What is the shortest path he can take, and how long will it be (in cm)?
Answer:
1. Along a diagonal, and then along an edge.
2. 48.28 cm.
Step-by-step explanation:
Assume points A and B are at diagonally opposite corners, as in the diagram below.
1. Shortest path
The shortest path is to go along the diagonal AC and continue along the edge CB.
2. Distance
The distance travelled is
d = AC + CB
According to Pythagoras,
AC² = AD² + CD² = 20² + 20² = 400 + 400 = 800
AC = √800 = 20√2
d = AC + CB = 20√ 2+ 20 ≈ 2 × 1.414 + 20 = 48.28 cm
The ant travels 48.28 cm.
There are about 3.5725 * 10^4 grains of sand in an 8-ounce cup. Based on this, about how many grains of sand would there be in a 5-gallon container (note: 1 gallon = 16 cups). Write the result in scientific notation.
Answer:
[tex]3.5725 * 10^5[/tex]
Step-by-step explanation:
Given
There are about 3.5725 * 10^4 grains of sand in an 8-ounce cup.
Required
How many grains of sand would there be in a 5-gallon container?
Let x represent the number of grains in 5 gallon; So, From the question, we have that;
8 cups = 3.5725 * 10^4
5 gallon = x
Cross Multiply
x * 8 cups = 5 gallon * 3.5725 * 10^4
Recall that 1 gallon = 16 cups
[tex]x * 8\ cups = 5 * 16\ cups * 3.5725 * 10^4[/tex]
[tex]x * 8 = 5 * 16 * 3.5725 * 10^4[/tex]
Divide both sides by 8
[tex]\frac{x * 8}{8} = \frac{5 * 16 * 3.5725 * 10^4}{8}[/tex]
[tex]x = \frac{5 * 16 * 3.5725 * 10^4}{8}[/tex]
[tex]x = 5 * 2 * 3.5725 * 10^4[/tex]
[tex]x = 10 * 3.5725 * 10^4[/tex]
[tex]x = 3.5725 * 10^5[/tex]
Hence, the number of grains of sand in 5 gallon is [tex]3.5725 * 10^5[/tex]
rewrite the polynomial in the form ax^2+bx+c and then identify the values of a, b, and c. 6+9x^2
Answer:
see below
Step-by-step explanation:
6+9x^2
Rewriting in decreasing powers of x
9x^2 +0x + 6
ax^2+bx+c
a = 9
b =0
c = 6
a+2=6 explain pkleaseeeeeeeeeeeeeeee
━━━━━━━☆☆━━━━━━━
▹ Answer
a = 4
▹ Step-by-Step Explanation
a + 2 = 6
Subtract 2 from both sides
2 - 2 = crossed out
6 - 2 = 4
Final Answer
a = 4
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
a=4
Step-by-step explanation:
If you are trying to find the value of a, it is simply 6-2. You can also check your answer by seeing if 4, the answer you found can be substituted into the equation while keeping the equation true. 4+2 does equal 6 so you know your right. Hope this helps!! :)
Which solid has a greater volume?
O A. Figure A has a greater volume.
75
O B. Figure B has a greater volume.
O C. They are equal.
OD. It cannot be determined.
SUBME
Answer:
C. they are eqwal
Step-by-step explanation:
I took the APE_X quiz
The volume of cone and cylinder are same or equal, so they are equal is correct.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
There are two figures one is cone and other is Cylinder.
The volume of cone can be find by using πr²h/3
r=5, h=6
Volume = π(25)(6)/3
=50π
Now to find volume of cylinder.
h=50 and r=1
Volume = πr²h
=50π
the volumes are same for both cylinder and cone.
Hence, the volume of cone and cylinder are same or equal, so they are equal is correct.
To learn more on Three dimensional figure click:
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plz help me do this and i will also help you back
Answer:
2^5 • 3^2 • 7
Answer:
2^5 • 3^2 • 7
Step-by-step explanation:
The value of /42 is rational or irrational numer. It’s value is between 3 and 5/. 5 and7/7and 9
Answer:
irrational
5 and 7
Step-by-step explanation:
sqrt( 42) irrational
it is not a perfect square so it is irrational
Looking at perfect squares
6^2 = 36
7^2 = 49
42 is between 36 and 49
so sqrt(42) is between sqrt(36) and sqrt(49)
sqrt(42) is between 6 and 7
Given the choices, 5 and 7
Answer:
Irrational
5 and 7
Step-by-step explanation:
[tex]\sqrt{42}[/tex] is irrational (Those Roots are usually irrational which cannot be simplified)
=> [tex]\sqrt{42}[/tex] = 6.48 (Between 5 and 7)
Need help finding the missing length to the attached triangle.
Answer:
x = 60
Step-by-step explanation:
All 3 right triangles are similar, thus ratios of corresponding sides are equal.
[tex]\frac{x}{144}[/tex] = [tex]\frac{25}{x}[/tex] ( cross- multiply )
x² = 3600 ( take the square root of both sides )
x = [tex]\sqrt{3600}[/tex] = 60
What are the domain and range of f(x) = 4x – 8? A. domain: {x | x is a real number}; range: {y | y > –8} B. domain: {x | x is a real number}; range: {y | y > 8} C. domain: {x | x > 4}; range: {y | y > –8} D. domain: {x | x > –4}; range: {y | y > 8}
Answer: Non of the options is correct.
Step-by-step explanation:
Domain of a function are the minimum and maximum values of independent variable (x).
You are given the function:
f(x) = 4x – 8
The domain can be any real numbers.
Range is the minimum to maximum value of dependent variable ( y )
From the given equation:
f(x) = 4x – 8
If the value of domain are substituted, the range will also be any real numbers.
Non of the answers is correct because both the domain and the range are all real numbers.
But the best option among the given option is option A:
domain: {x | x is a real number}; range: {y | y > –8}
Answer:
A on edg
Step-by-step explanation:
which number is a solution of the inequality b>11.3
Answer:
You can use any number greater than 11.3 to make this inequality true. Let's go with the number 14.
When we plug this in, this is what we get:
14 > 11.3
Hope this helps! :)
wuudxjwejd unm would iou hx
Answer:
PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Step-by-step explanation:
Help me plz....Thanks
Answer:
it is about 34 days
Step-by-step explanation:
divide the weight by the age for each kitten, you have a number called H
for example: kitten 1 has H1 = 600/50=12, kitten has H2 =340/28=85/7,kitten 3 has H3= 480/42= 80/7,...
find the arithmetic mean K of those number
K = (H1+H2+...+H8)/8 ≈ 13,44
so the age of the abandoned kitten is 460/13,44 ≈ 34,2 days
FOLIUS
Select the two binomials that are factors of 49x2 - 36.
I A. 7x + 6
B. 7x + 12
OC. 7x-6
D. 7x - 3
Answer:(7x - 6)(7x + 6)
Step-by-step explanation:
Answer:
answer is just C and
Step-by-step explanation:
PRE CALC, PLEASE HELP
Answer: 41
Step-by-step explanation:
Plug in 3 into x
Therefore the equation would become
f(3) = 3^3+2(3)^2-3-1 = 41
Answer:
I think it is 41
Step-by-step explanation:
x^3=27
2x^2=18
-x=-3
-1
27+18-3-1=41
Hope this helped
What is the value of s?
Answer:
s = 4
Step-by-step explanation:
x is a supplementary angle or 3d angle of the triangle.
(33s - 38) + x = 180 as supplementary angles.
(4s + 43 )+ 35 + x = 180 as angles of the triangle.
(33s - 38) + x = (4s + 43 )+ 35 +x
33s - 38 = 4s + 43 + 35
33s - 4s = 43 + 35 + 38
29s = 116
s = 4
Miranda has 5 shirts and 4 pairs of pants that she uses for her work clothes. How many different outfits can be assembled using 5 shirts and 4 pair of pants?
Answer:
20
Step-by-step explanation:
lets label each shirt as A, B, C, D, E and each pair of pants as a, b, c, d
combinations include:
Aa, Ab, Ac, Ad, Ba, Bb, Bc, Bd, Ca, Cb, Cc, Cd, Da, Db, Dc, Dd, Ea, Eb, Ec, Ed
however, it isn't necessary to write out all the combinations as you could just do 5*4=20.
Use the data set shown below to complete the sentence.
3, 3, 4, 5, 5,9
The mean
the median. is it greater than, is less than or is equal to
Answer:
is greater than
Step-by-step explanation:
Mean: sum of numbers ÷ how many numbers there are
3 + 3 + 4 + 5 + 5 + 9 = 29
29 ÷ 6 = 4.83333
Median: middle number
3 3 4 5 5 9
4 + 5 = 9
9 ÷ 2 = 4.5
4.83333 > 4.5 so the mean is greater than the median.
Hope that helps. :)
7) Which author's point of view is MOST SUPPORTED in the passage?
A)
The author respects and admires qualities in the
queen.
Eliminate
B)
The author is deeply saddened by the death of the
queen.
Te
The author is heavily critical of the queen's ignorant
politics
D)
The author feels the trip to Ireland contributed to 'her
worsening condition
Answer:
I think A is the MOST supported of all of the options. The author spends the majority of the writing remarking and complimenting the Queen's strength and desire to be concerned with the people of her land.
A) The author respects and admires qualities in the queen.
Step-by-step explanation:
HOPE THIS HELPED!! :)
Please help me I give brainliest when I can
Answer: X=7 y=0
Step-by-step explanation:
first transfer the -6y over than multiply it by 2 so the x's are equal then subtract the bottom equation from top equation and you get y = 0 then solve each equation with y = 0 and you get x = 7
<!> Brainliest is appreciated! <!>
Answer:
y = 0
x = 7
Step-by-step explanation:
First substitute
[tex]First\\ substitute\\\\2(-6y+7)-9y=14\\\\Then \\ distribute\\\\-12y+14-9y=14\\\\Then\\ combine \\like \\terms\\-21y=0\\\\Then\\ divide\\y=0\\\\Then \\substitute\\x=-6(0)+7\\\\Then\\Distribute\\\\x=0+7\\\\Then\\combine\\like\\terms\\\\x=7\\[/tex]
Hope it helps <3
(Please give brainliest, this took forever :) )
How many times will the digit '1' appear if we write all whole numbers from 1 to 99?
Answer:
20 times
Step-by-step explanation:
The digit 1 appear in number from 1 to 99 is 20 times
19 times will the digit '1' appear if we write all whole numbers from 1 to 99.
To determine the digit '1' appear if we write all whole numbers from 1 to 99?
From 1 to 9, there is one 1.
From 10 to 19, there are ten 10.
From 20 to 29, there is one 1.
From 30 to 39, there is one 1.
From 40 to 49, there is one 1.
From 50 to 59, there are ten 1.
From 60 to 69, there is one 1.
From 70 to 79, there is one 1.
From 80 to 89, there is one 1.
From 90 to 99, there is one 1.
So the total number of 1s is 1 + 10 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 19.
Therefore, 19 times will the digit '1' appear if we write all whole numbers from 1 to 99.
Learn more about whole numbers here:
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Sam is rowing a boat away from a dock. The graph shows the relationship
between time and Sam's distance from the dock. Evaluate the function for an
input of 9.
Answer: 100 minutes
Step-by-step explanation:
Distance from Dock
130
100
90
90
20
CO
Distance (meters)
Times (minutes) The answer is 100 minutes
Answer:
B. After 9 minutes, Sam is 80 meters from the dock
Step-by-step explanation:
truss me folks.