Answer:
We know that:
H(x) = |1 - x^3|
and:
We want to write H(x) as f( g(x) ) , such that for two functions:
So we want to find two functions f(x) and g(x) such that:
f( g(x) ) = |1 - x^3|
Where neither of these functions can be an identity function.
Let's define g(x) as:
g(x) = x^3 + 2
And f(x) as:
f(x) = | A - x|
Where A can be a real number, we need to find the value of A.
Then:
f(g(x)) = |A - g(x)|
and remember that g(x) = x^3 + 2
then:
f(g(x)) = |A - g(x)| = |A - x^3 - 2|
And this must be equal to:
|A - x^3 - 2| = |1 - x^3|
Then:
A = 3
The functions are then:
f(x) = | 3 - x|
g(x) = x^3 + 2
And H(x) = f( g(x) )
How to solve this?!?!? (5x+24)(9x+12) + (3x+9)(8x+6)(2x+7)
Answer and Step-by-step explanation:
First, multiply the parentheses, then add everything together.
-- (5x + 24)(9x + 12)
-- 45[tex]x^2\\[/tex] + 60x + 216x + 288 (Simplify)
-- 45[tex]x^2\\[/tex] + 276x + 288
--- (3x + 9)(8x + 6)
--- 24[tex]x^2\\[/tex] + 18x + 72x + 54 (Simplify)
--- 24[tex]x^2\\[/tex] + 90x + 54
---- (2x + 7)(24[tex]x^2\\[/tex] + 90x + 54)
---- 48[tex]x^{3}[/tex] + 180[tex]x^2\\[/tex] + 108x + 168[tex]x^2\\[/tex] + 630x + 378 (Simplify)
---- 48[tex]x^{3}[/tex] + 348[tex]x^2\\[/tex] + 738x + 378
----- 45[tex]x^2\\[/tex] + 276x + 288 + 48[tex]x^{3}[/tex] + 348[tex]x^2\\[/tex] + 738x + 378
----- 48[tex]x^{3}[/tex] + 393[tex]x^2\\[/tex] + 1014x + 666
48[tex]x^{3}[/tex] + 393[tex]x^2\\[/tex] + 1014x + 666 is the final answer.
#teamtrees #PAW (Plant And Water)
Answer:
[tex] \rm \displaystyle {48x}^{3} + 393 {x}^{2} +1014x + 660[/tex]
Step-by-step explanation:
we would like to simplify the following:
[tex] \rm \displaystyle (5x + 24)(9x + 12) + (3x + 9)(8x + 6)(2x + 7)[/tex]
there're two parts the multiplication the whole part to solve the multiplication part we can consider FOIL and for the whole, PEMDAS which can be represented as
[tex] \rm\displaystyle \rm \displaystyle \underbrace{\underbrace{(5x + 24)(9x + 12) } _{ \text{FOIL - 1}}+ \underbrace{ (3x + 9)(8x + 6)(2x + 7)} _{ \text{FOIL - 2}}} _{ \text{PEMDAS}}[/tex]
let's figure out FOIL-1 part
By FOIL we obtain:
[tex] \displaystyle {45x}^{2} + 60x + 216x + 288[/tex]
simplify addition:
[tex] \displaystyle {45x}^{2} + 276x+ 288[/tex]
let's figure out FOIL-2:
By FOIL and PEMDAS we acquire:
[tex] \rm \displaystyle {48x}^{3 } + {348x}^{2} + 738x + 378[/tex]
finally the whole part
[tex] \rm \displaystyle {45x}^{2} + 60x + 216x + 288+ {48x}^{3 } + {348x}^{2} + 738x + 378[/tex]
combine like terms:
[tex] \rm \displaystyle {48x}^{3} + 393 {x}^{2} +1014x + 660[/tex]
and we are done!
Which one of these polls is the correct answer? Please help.
Guys what is the answer
150°
Step-by-step explanation:
360° - 210° = 150° .......
Find the area of the figure below
Options
360 ft²
240 ft²
275 ft²
300 ft²
Answer:
The total area is 300 ft^2
Step-by-step explanation:
First find the area of the rectangle
A = l*w = 24*10 = 240
Then find the area of the triangle on the top
A = 1/2 bh
The base is 24 and the height is 15-10 = 5
A = 1/2 (24)*5 = 60
Add them together
240+60 = 300
The total area is 300 ft^2
Answer:
Total area of figure is 300 ft ²
Step-by-step explanation:
Finding the area of rectangle
We know that
Area of rectangle = length × widthWhere,
length of rectangle = 10 ftwidth of rectangle = 24 ftSubstitute the values into the formula
Area = 10 ft × 24 ft
multiply ✖ , we get
Area of rectangle = 240 ft ²
Similarly, Finding the area of triangle
We know
Area of triangle = 1 /2 × Base × HeightWhere,
Base of triangle = 24 ftHeight of triangle = 15 - 10 = 5 ftSubstitute the values
Area of triangle = 1 /2 × 24 ft × 5 ft
multiply
Area of triangle = 1/2 × 120 ft ².
divide , we get
Area of triangle = 60 ft ².
And Finally, Finding the total area
Total area of figure = Area of rectangle + Area of triangle
Total Area = 240 ft ² + 60 ft ²
➛ Total area of figure = 300 ft ²
Help plz I’m confused
Answer:
C.
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] is between 0 and 1
Only 1 point is between 0 and 1
C.
Given that A=1/2πrh, make r the subject of the formula?
Answer:
r=1/2πhA
Step-by-step explanation:
..................
Therefore, the formula of [tex]r[/tex] is [tex]2A(\pi h)^{-1}[/tex].
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given equation is
[tex]A=\frac{1}{2}\pi rh[/tex]
So,
[tex]A=\frac{1}{2}\pi rh\\\\r=2A(\frac{1}{\pi h})\\\\r=2A(\pi h)^{-1}[/tex]
Hence, the formula of [tex]r[/tex] is [tex]2A(\pi h)^{-1}[/tex].
To know more about the equation
https://brainly.com/question/12788590
#SPJ2
A basketball player scored 14 times during one game. She scored a total of 15 points, two for each two-point shot and one for each free throw. How many two-point shots did she make? How many free throws?
She made ____ two-point shots
Answer:
The player made one two-point shot and 13 free throws.
Step-by-step explanation:
We can write a system of equations to model the situation.
Let t represent the number of two-point shots and let f represent the number of free throws made.
Since she scored a total of 14 times, the sum of two-pointers and free throws must equal 14. Hence:
[tex]t+f=14[/tex]
And since she scored a total of 15 points and each two-pointers is worth two points and every free throw is worth one:
[tex]2t+f=15[/tex]
Solve the system. We can use elimination. From the first equation, multiply both sides by negative one:
[tex]-t-f=-14[/tex]
We can add this to the second equation:
[tex](2t+f)+(-t-f)=(15)+(-14)[/tex]
Simplify:
[tex]t=1[/tex]
So, the player made only one two-point shot.
Using the first equation again, substitute one for t and solve for f:
[tex](1)+f=14\Rightarrow f=13[/tex]
Therefore, the player made one two-point shot and 13 free throws.
Answer:
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.
Step-by-step explanation:
Please help immediately! In desperate need!
9514 1404 393
Answer:
see attached
Step-by-step explanation:
You know that f(0) = 2^0 = 1, so g(0) = -11 has been shifted down 12 units from f(x). A shift of half as much will be a shift down 6 units from f(x), or up 6 units from g(x).
In the attached, we have named the new function h(x). It is equivalent to g(x)+6. That is, you can add 6 to each of the g(x) table values to get the corresponding values for h(x).
Find the volume of each shape. Round your answer to two decimal places.with clear explanation.
Answer:
Volume = 111.33 in.³
Step-by-step explanation:
The volume of the shape = volume of the rectangular prism part + volume of the triangular prism part
✔️volume of the rectangular prism part:
V = L*W*H
Where,
L = 5.1 in.
W = 3.4 in.
H = 5.9 in.
V = 5.1*3.4*5.9
V = 102.306 in.³
✔️volume of the triangular prism part:
V = ½*b*h*l
b = 6 - 5.1 = 0.9 in.
h = 5.9 in.
l = 3.4 in.
V = ½*0.9*5.9*3.4
V = 9.027 in.³
✅Volume of the shape = 102.306 + 9.027
= 111.333 in.³
≈ 111.33 in.³ (approximated to 2 decimal places)
On Tuesday, a local hamburger shop sold a combined total of 576 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Tuesday?
Answer:
check the picture
Step-by-step explanation:
I hope this helps
I need help with this problem
Step-by-step explanation:
y=sin ^-1(9/14) =44,27 degree
X= by pythegoras) =14 square - 9 square
= root 115
A pizza has a radius of 7 inches. If it is cut into 6 equal slices, what is the area of each slice?
answer: each slide would be one sixth of the entire area; the entire area is (pi)(72).
Do not use pi = 22/7 because that's untrue. It's approximately 3.1416; round off later!
hope this helps
The interior angle of a polygon is 100 . The other interior angle are all equal to 110. how many sides has the polygon?
There is a formula for the total interior angles of a polygon:
180(sides−2)=total interior angles
One of the angles is 100 and all the others are 110.
We can rewrite the equation.
Assume there is x number of sides.
There are x−1 number of angles, 110 degrees
180(x−2)=100+110(x−1)
180x−360=100+110x−110
70x−360=100−110
70x−360=−10
70x=3507x=35
x=5
There are 5 sides to the polygon.
We can check our answer:
180(sides−2)=total interior angles
Therefore it is true:
The polygon has 5 sides
I HOPE IT HELPS
HAVE A GREAT DAY
#Liliflim
PLEASE HELP ASAPPPPP!!!!!!
You have 2 spreads, 3 meats, and 4 kinds of bread. How many different sandwiches can you make using one of each ingredient?
The total combinations are found by multiplying each option by each other.
2 spreads x 3 meats x 4 breads = 24 different combinations.
Answer : 24
The denominator of a fraction is twice the numerator. If 3 is added to the numerator and 3 is subtracted from the denominator, the new fraction is 7/5. Find the original fraction.
Answer:
4/8
Step-by-step explanation:
d = 2n
n+3 = 7
d-3 = 5
substitute '2n' for 'd' in d-3=5
2n-3 = 5
2n = 8
n = 4
d = 2(4)
4/8
Solve P = 8/3 R + 30 for R.
Answer:
R = (3P-30)/8
Step-by-step explanation:
subtract 30 from each side to get:
P-30 = [tex]\frac{8}{3}[/tex]R
multiply each side by [tex]\frac{3}{8}[/tex] to get:
[tex]\frac{3}{8}[/tex] · P - 30 = R
R = (3P-30)/8
At Bill’s Burger Barn, every time you buy a burger there is a one in eight chance of winning a free burger. Nicholas bought a hamburger every day for five days. What is the probability that Nicholas wins 1 free hamburger this week?
Answer:
im not sure about this one but my answer is 0.025.
Step-by-step explanation:
if there is a 1 out of 8 chance of getting a free burger, convert that into 1/8. divide that by 5 and you get 0.025.
what is the product of -8 1/3 and 3 2/5
Answer:
-28 1/3
Step-by-step explanation:
-8 1/3= -25/3
3 2/5= 17/5
-25/3*17/5= -28 1/3
20 5 4 2 X 2.5 12 1.5 3
Answer:
x = 10
Step-by-step explanation:
if two prisms are similar then the side lengths are proportional
2/4 = x/20 cross multiply expressions
40 = 4x divide both sides by 4
10 = x
A pair of elephants walk 26 meters on a straight slope. The height of the slope is 12 meters. Find the angle between ground and the top of the hill.
Answer:
36
Step-by-step explanation:
what is the common difference of the following sequence?
3,5,7,9,11___
16,19,22,25___
Answer:
the first one goes by 4n-1
the Second sequence goes by 3n + 13
Step-by-step explanation:
using the formula an=a1+d(n-1)
x2 + y2 − 4x + 12y − 20 = 0
(x − 6)2 + (y − 4)2 = 56
x2 + y2 + 6x − 8y − 10 = 0
(x − 2)2 + (y + 6)2 = 60
3x2 + 3y2 + 12x + 18y − 15 = 0
(x + 2)2 + (y + 3)2 = 18
5x2 + 5y2 − 10x + 20y − 30 = 0
(x + 1)2 + (y − 6)2 = 46
2x2 + 2y2 − 24x − 16y − 8 = 0
x2 + y2 + 2x − 12y − 9 = 0
Answer:
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Step-by-step explanation:
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Can y’all help me on question 6?!
Answer:
B
Step-by-step explanation:
To find the area of a parallelogram you do A=(b)(h) so 20x8=160. It's 160ft^2 because area is measured in square units.
Which statement is true?
Can someone help me again with these math work?
Watch help video
Solve for 2. Round to the nearest tenth, if necessary.
5-3
O
52
х
N
Answer:
x = 3.3
Step-by-step explanation:
Reference angle = 51°
Hypotenuse = x
Adjacent = 5.3
Apply trigonometric function CAH, which is:
Cos 51° = Adj/Hyp
Cos 51° = 5.3/x
x*Cos 51° = 5.3
x = 5.3/Cos 51°
x = 3.3 (nearest tenth)
If anybody needs gauthmath code for homework this is my code = ER326P
...help please I would appreciate it
No link please
Answer:
B
Step-by-step explanation:
Answer:
it's B. pa brainliest nalang po thanks
Step-by-step explanation:
B.
Which of the following values could be an absolute value?
Answer:
Step-by-step explanation: It could be 8,7, or 2. Because these are all positive
:)
16. Subtract: 5 - 3 1/3
Answer:
1 2/3 ( d is the answer)
Step-by-step explanation:
See image below:) I know it says 5/3 but where it says alternative form it says 1 2/3