The resulting function is (f-g)(x) = 5 · x⁴ + 3 · x² + 10.
The resulting function is (f • g) (x) = 3 · (3 · x⁵ - 5 · x⁴ + 3 · x² - 15)⁵ + 6 · (3 · x⁵ - 5 · x⁴ + 3 · x² -15)² - 5.
How to apply subtraction between two functionsLet be [tex]f(x)[/tex] and [tex]g(x)[/tex] polynomial functions, the subtraction between between the two functions implies the subtraction of similar terms. If we know that [tex]f(x) = 3\cdot x^{5}+6\cdot x^{2}-5[/tex] and [tex]g(x) = 3\cdot x^{5}-5\cdot x^{4}+3\cdot x^{2}-15[/tex], then the subtraction between the two functions:
[tex](f-g)(x) = (3\cdot x^{5}+6\cdot x^{2}-5)-(3\cdot x^{5}-5\cdot x^{4}+3\cdot x^{2}-15)[/tex]
[tex](f-g)(x) = 5\cdot x^{4}+3\cdot x^{2}+10[/tex]
The resulting function is (f-g)(x) = 5 · x⁴ + 3 · x² + 10. [tex]\blacksquare[/tex]
How to apply composition between two functionsThe composition between two functions, the independent variable of the former function by the latter function. If we know that [tex]f(x) = 3\cdot x^{5}+6\cdot x^{2}-5[/tex] and [tex]g(x) = 3\cdot x^{5}-5\cdot x^{4}+3\cdot x^{2}-15[/tex], then the composition between the two functions:
[tex]f\,\circ\,g\,(x) = 3\cdot (3\cdot x^{5}-5\cdot x^{4}+3\cdot x^{2}-15)^{5}+6\cdot (3\cdot x^{5}-5\cdot x^{4}+3\cdot x^{2}-15)^{2}-5[/tex]
(f • g) (x) = 3 · (3 · x⁵ - 5 · x⁴ + 3 · x² - 15)⁵ + 6 · (3 · x⁵ - 5 · x⁴ + 3 · x² -15)² - 5. [tex]\blacksquare[/tex]
To learn more on functions, we kindly invite to check this verified question: https://brainly.com/question/5245372
A one-celled, aquatic organism called a dinoflagellate is 1000 micrometers long. A microscope magnifies the dinoflagellate 100 times. What is the magnified length of the dinoflagellate in meters? (1 micrometer is 10^-6 meter) Write your answer as a power
A colored chip is yellow on one side and red on the other. The chip was flipped 50 times and landed up 29 times. What is the relative frequency of the chip landing with the yellow side facing up?
A.38%
B.42%
C.56%
D.58%
Answer:
56%
Step-by-step explanation:
Answer:
ur mom
Step-by-step explanation:
Find the value of 2x – 4 given that -5x – 1=4. Simplify your answer as much as possible
Answer:
-6
Step-by-step explanation:
To solve: -5x=5
x=(-1)
{2(-1)-4}
-2-4
-6
whats going on in this attachment help thanks xD
Ratio remains same
[tex]\\ \rm\Rrightarrow \dfrac{4}{6x-3}=\dfrac{3}{2}[/tex]
[tex]\\ \rm\Rrightarrow 8=3(6x-3)[/tex]
[tex]\\ \rm\Rrightarrow 8=18x-9[/tex]
[tex]\\ \rm\Rrightarrow 18x=17[/tex]
[tex]\\ \rm\Rrightarrow x=17/18[/tex]
For what value of y does
25-()
25
?
Answer: his is a simple as well as an interesting question. CASE I: y = 25. Consider this a² = |a|. Given y = 25, we can write like this way,. y = -5/2.
Step-by-step explanation:
Answer:
-1/2
Step-by-step explanation:
We are given the exponential equation:—
[tex]\displaystyle \large{125=(\frac{1}{25})^{y-1}}[/tex]
First, use a law of exponent [Quotient Rules] to convert RHS:—
[tex]\displaystyle \large{125=(25^{-1})^{y-1}}[/tex]
Then convert both bases to base 5:—
[tex]\displaystyle \large{5^3 = (5^{-2})^{y-1}}[/tex]
Use another law of exponent [Power] to multiply the exponent of RHS:—
[tex]\displaystyle \large{5^3 = 5^{-2y+2}}[/tex]
Now that both sides have same base, solve the equations with exponent:—
[tex]\displaystyle \large{3=-2y+2}\\\displaystyle \large{1=-2y}\\\displaystyle \large{y=-\frac{1}{2}}[/tex]
Therefore, the value of y is:—
[tex]\displaystyle \large{\boxed{-\frac{1}{2}}}[/tex]
__________________________________________________________
Summary
This section includes an important or necessary explanation, summary or formulas that was used in the explanation above.
Laws of Exponent
Power of Power Rules:—
[tex]\displaystyle \large{(a^m)^n = a^{mn}}[/tex]
Quotient Rules:—
[tex]\displaystyle \large{a^{-n}=\frac{1}{a^n}}[/tex]
Note that the above, Quotient Rules, is derived from:—
[tex]\displaystyle \large{\frac{a^m}{a^n} = a^m \div a^n = a^{m-n}[/tex]
But when m = 0 the numerator becomes 1.
Exponential Equation
When solving an Exponential Equation, the goal is to convert both sides having the same base.
When both sides have same base, take both exponents of both sides to solve the equation.
__________________________________________________________
If you have any questions regarding this problem or need clarification, do not hesitate to ask in comment! Good luck on your assignment and have a nice day!
Which of the following is the correct way to write the amount $73.78 on a check?
Answer:seventy-three and 78/100 dollars
Step-by-step explanation:hope that helps
One angle in a right triangle measures 57°. What is the measure of the other acute angle?
43°
123°
90°
33°
HELP ME OUT PLS!!!!!
2) Find the value of a.
A) 3
B) 4
C) 6
D) 9
Plot the following points to create
a rectangle. Find the missing
vertex.
(1,5); (-1,5); (-1,-5); ?
Answer:
(1, -5)
Step-by-step explanation:
From the information that is given (1, -5) seems to be the logical answer since we have (1, 5), (-1, 5), and (-1, -5). 1 has been negative twice, 5 has been positive twice so to make things right add a positive +1 and a negative -5
I hope this helps!
(50 POINTS AND WILL MARK BRAINLIEST PLS HELP)What is the slope of the line that passes through the points (-2, 2), and (-4, -2)?
A. 1/2
B. 2
C. -2
D. - 1/2
Answer:
2
Step-by-step explanation:
x1, y1. x2, y2
(-2,2) (-4,-2)
Divide y2-y1 and x2-x1:
-2-2÷ -4-(-2)= -4/-2
Simply. (A negative divided by a negative is a positive.)
-4/-2=2
What is the equation of the line in slope-intercept form?
Answer:
y=4/3x+4
Step-by-step explanation:
Find the degree measure of each triangle?
Answer:
M= 90 degrees
L= 47 degrees
K = 43 degrees
Step-by-step explanation:
90+3x+28+2x+37=180
simplify and place x by itself to get
x= 5
input x into both angle equations
and it already tells you M is equal to 90 degrees due to the box symbol.
What present is 40% of 120% of x
Answer:
0.48x
Step-by-step explanation:
x times 120% = 1.2x
1.2x times 40% is 0.48x
Brainliest if correct
Answer:
9 over 0 = 9/0 also - 9
Step-by-step explanation:
Emma has a coupon for $5.25 off a frame that normally costs $15.00. What percent discount did she receive on the frame? Show your work in arriving at your answer.
Emma has received a 35 percent discount on the frame
What is a discount?A discount is a reduction in price of an item usually for promotion or marketing purposes.
A discount could be in the form of a percentage off the price of the item or a fixed amount(say $7) off the price of the item
In the case of Emma, he got a fixed amount off the price which we converted to percentage to determine the amount off. This is calculated thus:
discount price/price of item ×100/1
5.25/15×100/1= 0.35(35%)
If a percentage is used, a variable( can change)amount in the form of a discount is possible otherwise not.
Please read more on discounts and percentages here:
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these numbers form an addition and subtraction fact family 6,7,13 what is the correct answer
Answer:
6 + 7 = 13
13 - 7 = 6
13 - 6 = 7
7 + 6 = 13
Step-by-step explanation:
if f(5x)=f(5)+f(x) then prove f(1)=0
Answer:
2&4+44-24÷333×6385
Step-by-step explanation:
so it can be a cardinal product
If functions f(5x)=f(5)+f(x) then f(1)=0.
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that f(5x)=f(5)+f(x)
f of five times of x equal to f of five plus f of x.
We need to prove f(1) is equal to zero.
f(5x)=f(5)+f(x)
Let plug in x value as one
f(5×1)=f(5)+f(1)
f(5)=f(5)+f(1)
Subtract f(5) from both sides
f(1)=0
Hence, if functions f(5x)=f(5)+f(x) then f(1)=0.
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HELP PLSSS
max is m years old. His sister is twice as old as he is. The sum of their ages is 27. How old is Ahmed and his sister?
Answer:
Given ,
Ahmed's age = " m " years.
Also ,
age of Ahmed's sister = 2 × m = 2m years
According to Question ,
age of ahmed + age of his sister = 27
[tex]\bold{m + 2m = 27 }\\ \bold{3m = 27 }\\ \bold{m = \cancel{\frac{27}{3} }} \\ \\ \fbox\blue{m = 9}[/tex]
therefore ,
age of Ahmed = 9 years.
age of Ahmed's sister = 2m = 2 ( 9 ) = 18 years.
hope helpful~
Age of Ahmed is 9 years
Age of Ahmad's sister is 18 years
Explaination :In the question it is given that Ahmed is of m years.
Age of Ahmed = m yearsHer sister is twice as old as he.
Age of Ahmad's sister = 2 × m = 2m yearsNow in the question it is given that sum of their ages is 27. So lets add the age of Ahmed and his sister and keep it equal to 27 inorder to get the value of m.
Age of Ahmed + Age of his sister = 27
m + 2m = 27
3m = 27
m = 27 / 3
m = 9
Therefore, value of m is 9..!!★ Age of Ahmed:-
Age of Ahmed = m
Age of Ahmed = 9 years
★ Age of his sister:-
Age of Ahmad's sister = 2m
Age of Ahmad's sister = 2 × 9
Age of Ahmad's sister = 18 years
a Japanese giant salamander can weigh 140 lb what is the weight in ounces
Which of the following equations represents a line that passes through the points (6,-16) and (-3,2)
Answer:
y=-2x-4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(2-(-16))/(-3-6)
m=(2+16)/-9
m=18/-9
m=-2
y-y1=m(x-x1)
y-(-16)=-2(x-6)
y+16=-2(x-6)
y=-2x+12-16
y=-2x-4
Answer:
Neither
Step-by-step explanation:
y2 - y1 -16 - 2 -18
---------- = ----------- = -------- = 2
x2 - x1 -3 - 6 -9
y = mx + b
-16 = 2(6) + b
-16 = 12 + b
-12 -12
-28 = b
y = 2x - 28
y = mx + b
2 = 2(-3) + b
2 = -6 + b
+6 +6
8 = b
y = 2x + 8
I hope this helps!
50 PTS. Solve the given equation by completing the square.
r2 + 8 = 38
Fill in the values of a, b, and c to complete the solutions.
Answer:
r = 15
Step-by-step explanation:
That's my answer hope it helps brainliest my answer please that's correct
Answer:
r=15
Step-by-step explanation:
hope it helps you bro
lionfish are considered an invasive species, with an annual growth rate of 67%. A scientist estimates there are 8,000 lionfish in a certain bay after the first year.
Part A: Write the explicit equation for f (n) that represents the number of lionfish in the bay after n years. Show all necessary math work.
Part B: How many lionfish will be in the bay after 6 years? Round to the nearest whole number and show all necessary math work.
Part C: If scientists remove 1,200 fish per year from the bay after the first year, what is the recursive equation for f (n)? Show all necessary math work.
Answer:
There would be 173,535 lionfish after 6 years.
Step-by-step explanation:
Since lionfish are considered an invasive species, with an annual growth rate of 67%, ya scientist estimates there are 8,000 lionfish in a certain bay after the first year, A) to write the explicit equation for f (n) that represents the number of lionfish in the bay after n years; B) determine how many lionfish will be in the bay after 6 years; and C) if scientists remove 1,200 fish per year from the bay after the first year, determine what is the recursive equation for f (n); the following calculations must be performed:
A)
8000 x 1.67 ^ n = f
B)
8000 x 1.67 ^ 6 = X
8000 x 21.691961596369 = X
173,535.692770952 = X
C)
(8000 - 1200 x 1 ^ n) x 1.67 ^ n = f
Therefore, there would be 173,535 lionfish after 6 years.
bob the builder is making 480kg of concrete mix
concrete is made by mixing cement, sand and gravel in the ratio 1:3:4
Answer:
60 kg of cement, 180 kg of sand and 240 kg of gravel
Step-by-step explanation:
x : 3x : 4x
If you turn this into an equation, it becomes x + 3x + 4x = 480
8x = 480
x = 60
60 is the amount for the cement, for the sand and gravel multiply this answer by 3 and the other by 4, you should get 180 and 240
Sorry if this was not clear
Which statement best describes the expression - x (14 - 6) x 6 + 4?
17/
Find half the product of 6 and 4, then subtract the difference between 14 and 6.
Find half the difference of 14 and 6, multiply by 6, then add 4.
Find the product of 14 and 6, add the product of 6 and 4, then divide by 2.
Find the product of 6 and 4, subtract the difference between 14 and 6, then multiply by
1/2
Answer:
B
Step-by-step explanation:
Find half the difference of 14 and 6, multiply by 6, then add 4.
Answer:
B
Step-by-step explanation:
an i got 2 points on the test trust me
what is the answer??
Answer:
276 square inches
Step-by-step explanation:
The area can be decomposed as a square of side length 14 in, having a surface of area of [tex]14^2 = 196 in^2[/tex], and a triangle of base 14 and height 12, giving an area of [tex]\frac12\times 12\times14 =84 in^2[/tex]. Added them together we get a grand total of [tex]196+84=280 in^2[/tex]
Answer:
280 in²
Step-by-step explanation:
This is a composite figure composed of a triangle and a square. Let's find the area of each and add them up.
The area of the square is 196 square inches. The area of the triangle is 84 square inches. Add those two together, and you have 280 square inches.
Question 2
Work out -9--3
What makes Europa a potential home to extraterrestrial life? *
Europa is the sixth closest moon of the planet Jupiter, and one of the largest moons in the solar system. Europa is slightly smaller than the Earth’s moon and has a tenuous atmosphere compared primarily to oxygen. The surface of Europa is composed of water and is one of the smoothest in the solar system. Scientists suggest that it is possible Europa has an ocean of liquid water beneath its surface, making it a strong candidate for extraterrestrial life. It is also predicted that heat energy from tidal flexing may cause oceans to remain liquid and drives geological activity similar to plate tectonics on Earth.
simplify 4a^2b^-2/16a^-3b
Answer : 1/4ab
◊ YusuCr ◊
It is 4 kilometers from Ravi's house to the nearest mallbox. How far is it in meters
Be sure to Include the correct unit in your answer,
Answer:
4,000 meters
Step-by-step explanation:
The conversion from kilometers to meters is 1 kilometer equals 1,000 meters. So times the conversion by 4 to get 4,000 meters.
If I have a 97% in one of my classes what do I have to get on my final project, which is 30% of my grade, to pass with at least a C or 70%.
Answer:
you will need at least a 94 on your final project
Step-by-step explanation:
hope it helps!
1 point
A grid shows the positions of a subway stop and your house. The subway
stop is located at (0.-1), and your house is located at (-7.-4). What is the
distance, to the nearest unit, between your house and the subway stop?
Answer:
8 units.
Step-by-step explanation:
Use the distance formula.