f(x) = x + 2
g(x) = 3x² - 5
Find (f.g)(x).
OA. (f g)(x) = 3x³ - 10
OB. (f g)(x) = 3x³ + 6x² - 5x - 10
OC. (f. g)(x) = 3x³ + 10
OD. (f g)(x) = 3x³ + 6x² + 5x + 10
SUBMIT
Answers
Answer:
It's option B, (f • g)(x) = 3x^3 + 6x^2 - 5x - 10
Step-by-step explanation:
In this problem, we are dealing with a branch of functions called composite functions. What the difference is between normal and composite functions is that we instead of defining a value for f(x), take two functions, f(x) and g(x), in the form of f and g. For instance, h(x) = g.
• Take the products of both functions.
f(x)g(x) = 3x²+5 • x-2
• Next, expand the functions. We expand by combining like terms.
= 3x^3 - 6x^2 + 5x - 10
Since the function cannot be simplified further, this leads to option B being our answer.
Hope this helps!
Related Questions
What is the value of x?
Answers
Answer:
x = 62
Step-by-step explanation:
40 + (x + 16) + x = 180 (sum of angles in a triangle=180)
2x + 56 = 180
2x = 124
x = 62
Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus
Answers
The equation of the line in the graph is y = 4x - 9..
How to find the equation of a line?The equation of a line in slope intercept form can be represented as follows:
The line forms a linear equation.
Therefore,
y = mx + b
where
m = slopeb = y-interceptTherefore, using (0, -9)(3, 3) let's find the slope
m = 3 + 9 / 3 - 0
m = 12 / 3
m = 4
Therefore, let's find the y-intercept using (0, -9).
-9 = 4(0) + b
b = -9
Therefore, the equation is y = 4x - 9.
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Your friend uses the figure to say that all the exterior angles of any isosceles triangle are congruent. Is your friend correct? Explain your reasoning
Answers
Answer:
All the exterior angles of any isosceles triangle are congruent - FALSE statementStep-by-step explanation:
We know that the exterior angle of a triangle is the sum of remote interior angles.
If the triangle is equilateral then the sum of any two interior angles is same otherwise, with any isosceles triangle, we get different sums and therefore the friend is wrong.
Answer:
No.
Step-by-step explanation:
An isosceles triangle has two sides of equal length. Therefore, only two of its interior angles are congruent.
The exterior angle of a triangle is equal to the sum of the two opposite interior angles (remote interior angles). Therefore, as not all of the three interior angles of an isosceles triangle are congruent, all the exterior angles will also not be congruent.
Solve for d. 3 + d < 3 −d
d < −6
d < 6
d < 0
d < −3
Answers
Answer:
d is great than -3
Step-by-step explanation:
because negative numbers are less than whole numbers
Use the graph below to answer the following questions.
⦁ Estimate the available territory at 20 years
⦁ Estimate the available territory at 15 years
⦁ Does this graph represent exponential growth or decay?
⦁ As the time decreases the available territory _______________
Answers
Answer:
a) about 190 acres
b) around 240 acres
c) exponential decay because the amount of land available is decreasing at an increasingly rapid rate over time.
The pH of solution measures its acidity and can be determined using the formula pH= -log(base of 10 )C, where is the concentration of hydronium ions in the solution. measured in moles per litre .A lower pH indicates a more acidic solution.
The concentration of Hydronium ions type of coffes is 1.3 x 10above-5 moles per liter .
Calculate the pH of the coffee.
Answers
The value of pH of the coffee is 4.89
How to determine the pH of the coffee?pH is a measure of hydrogen ion concentration, a measure of the acidity or alkalinity of a solution
Given: The formula pH= -log₁₀ C,
where is the concentration of hydronium ions in the solution measured in moles per litre
The concentration(C) of Hydronium ions type of coffee is 1.3 x 10⁻⁵ moles per liter
To calculate the pH, we will substitute the value of the concentration (C) into the given formula:
pH= -log₁₀ C (C = 1.3 x 10⁻⁵ moles per liter)
pH = -log₁₀(1.3 x 10⁻⁵) = 4.89
Therefore, the pH of the coffee is 4.89
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Alan has 229 songs on a playlist. He's categorized them in the following manner: 11 rock, 21 Latin American, 46 gospel, 30 country, 39 rap, 25 classical, and 57 pop. If Alan begins listening to his playlist on shuffle, what is the probability that the first song played is a rock song?
Answers
=================================================
Work Shown:
11 rock songs
229 total
11/229 is the probability of randomly selecting a rock song. The fraction doesn't reduce since 11 and 229 have no factors in common (other than 1).
If you wanted to convert to decimal form, then 11/229 = 0.04803 approximately. This converts to about 4.803%
Juan has a sandbox and wants to double the length, width and height. if the original box holds 1 cubic foot of sand, how many more cubic feet of sand must be added to fill the box
Answers
The box must be added with 7 cubic feet of sand
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also be defined as the capacity of an object.
It is measured in cubic units.
The volume of a box is length × width × height
represent the original length, width and height by x ,y ,z respectively
This shows that the volume of the original box= x× y× z = 1cubic foot
when the original length, width and height are doubled to give the new dimensions
Therefore the new length,width and height will be 2x, 2y and 2z
the volume of the new formed box = 2x×2y×2z
= 8xyz
XYZ= 1cubic foot
therefore 8xyz = 8cubic feet
since there is 1 cubic foot of sand in the box already,
then( 8-1)cubic feet = 7cubic feet will be added.
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It takes a word processor 45 minutes to word process and spell check 12 pages. Find how long it takes her to word process and
spell check 40 pages.
It takes the word processor
minutes.
Answers
Answer: the correct answer is 150 minutes for 40 pages.
Step-by-step explanation:
It takes a word processor 45 minutes to word process and spell check 12 pages.
45 minutes / 12 pages = 3.75 minutes per page
3.75 min/page x 40 pages = 150 minutes
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The operation * is defined as a*b=a+b-2ab
Evaluate 2* (3*5)
(2*3)*5
Answers
The value of 2*(3*5) = 68.
The value of (2*3)*5 = 68.
What is multiplication?
A mathematical formula that specifies the objects to be multiplied, known as a factor, produces a product. For instance, the product of 6 and 5 is 30.
Given: The operation * is defined as,
a*b = a + b - 2ab
We have to find the value of 2*(3*5) and (2*3)*5
First to find the value of 2*(3*5).
2*(3*5) = 2*(3 + 5 - 30) = 2*(-22) = 2 + (-22) - 2(-22)(2) = 68.
Now to find the value of (2*3)*5.
(2*3)*5 = (2 + 3 - 12)*5 = -7*5 = (-7) + 5 - 2(-7)(5) = -2 + 70 = 68.
Therefore, 2* (3*5) = 68 and (2*3)*5 = 68.
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5 pounds=______ounces
Answers
Answer:
Step-by-step explanation:
1. Basic systems in fluids: 1 pound equals 16 ounces.
2. Multiply 16 ounces by 5 to become equivalent!
16 ounces*5= 80 ounces!
3. Always double check
80 ounces/16=5 pounds
Answer: 80 ounces
what kind of transformation converts the graph of f(x)= -10(x-2)^2 into the graph of g(x)= -2(x-2)^2
Answers
The transformation that converts f(x) to g(x), f(x) is contraction by 5 units
What are transformations?Transformations are mathematical operations which change the shape and orientation of an object or function.
The types of transformations include
Dilation, Reflection, translationcontraction and rotationHow to find what kind of transformation converts f(x) to g(x)?Since we have the graph of f(x) = -10(x - 2)² into the graph of g(x)= -2(x - 2)².
We see that f(x) = -10(x - 2)²
= 5 × -2(x - 2)²
= 5g(x)
Since f(x) = 5g(x)
⇒g(x) = f(x)/5
So, we converts f(x) to g(x), f(x) is contraction by 5 units
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What is the y-intercept of the function f(x) = 2 ^x?
A.27
B.2
C. 6
D. 1
Answers
Answer:
D
Step-by-step explanation:
the y- intercept is the value of y on the y- axis where the function crosses.
the function crosses the y - axis when x = 0
substitute x = 0 into f(x)
f(0) = [tex]2^{0}[/tex] = 1
y- intercept is 1
Please Help 2
find (f/g)(m)iff(m)=8m3+5m2-32m-20 and g(m)=8m+5
Answers
Diving the polynomial expression f(m) = 8m^3 + 5m^2 - 32m - 20 and g(m) = 8m + 5, as (f/g)(m) using long division gives m^2 - 4
What is long division ?Long division refers to a way of dividing large numbers including polynomials
performing the long division (f/g)(m) gives
divisor 8m + 5
dividend 8m^3 + 5m^2 - 32m - 20
quotient m^2
multiplication (quotient and divisor) = 8m^3 + 5m^2
subtraction (dividend - result of multiplication) = - 32m - 20 new dividend = - 32m - 20
divisor 8m + 5
dividend - 32m - 20
quotient -4
multiplication (quotient and divisor) = - 32m - 20
subtraction (dividend - result of multiplication) = 0
new dividend = 0
The quotient is then added as
m^2 - 4
The second option is the correct option
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helppppppppppppppppppppppppp
Answers
Answer:
E
Step-by-step explanation:
I am a line & domain is -7
Help quick please this is hard for me
Answers
Answer:
525 cm
Step-by-step explanation:
a heptagon has 7 sides and it can be split into 7 different equal triangles and one already has the side so we just find the area of the triangle.
1/2(12)(12.5)
6(12.5)
75
75 is the area of the triangle so now we multiply by 7
75x7=525 cm
Hopes this helps please mark brainliest
Answer: 525 cm squared
Step-by-step explanation:
Find the area of 1 of the Isoceles triangle and then multiply it by 7, because there are 7 Isoceles triangles in the heptagon. Area= 1/2 base x height = 1/2 x 12cm x12.5cm = 75cm squared. Now 75 cm squared x 7 = 525 cm squared
(Lesson 22)
P=L(+)
a. Find the monthly payment P on a $75,000 loan with an
annual interest rate of 4% (let r= .9967) and a term of
20 years (n = 240 months). Show your work below and
circle your final answer.
Answers
The monthly payment is 38455 when the P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4%.
Given that,
We have to calculate the monthly payment P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4% (let r=.9967).
We know that,
Formula for monthly payment is P(i(1+i)ⁿ/(1+i)ⁿ-1)
Here,
P is principal amount $75,000
n is number of months 240 months
i is interest rate 4% is 0.04
=P(i(1+i)ⁿ/(1+i)ⁿ-1)
=75,000(0.04(1+0.04)²⁴⁰/(1+0.04)²⁴⁰-1)
=75,000(0.04(1.04)²⁴⁰/(1.04)²⁴⁰-1)
=75,000(0.04(12246.20236)/(12245.20236)
=75,000(0.04×1.000081665)
=38455
Therefore, The monthly payment is 38455 when the P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4%.
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See question in screenshot below.
Answers
The equation of the transformation of the exponential function y = 2ˣ in the form y = A·2ˣ + k, obtained from the simultaneous found using the points on the graph is y = (-2)·2ˣ + 3
What is an exponential equation?An exponential equation is an equation that has exponents that consists of variables.
The given equation is y = 2ˣ
The equation for the transformation is; y = A·2ˣ + k
The points on the graphs are;
(0, 1), (1, -1) and (2, -5)
Plugging the x and y-values to find the value A and k gives the following simultaneous equations;
When x = 0, y = 1, therefore;
1 = A·2⁰ + k = A + k
1 = A + k...(1)
When x = 1, y = -1, which gives;
-1 = A·2¹ + k
-1 = 2·A + k...(2)
Subtracting equation (1) from equation (2) gives;
-1 - 1 = 2·A - A + k - k
-2 = A
1 = A + k, therefore;
1 = -2 + k
k = 2 + 1 = 3
k = 3
Which gives;
y = -2·2ˣ + 3 = 3 - 2·2ˣ
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Bahir is h cm tall. Sienna is 4 cm taller than Bahir.
Write down an expression, in terms of h, for Sienna’s height.
Answers
Answer:
.
Step-by-step explanation:
Simplify completely. 3x+18 divided 18
Answers
solution
3x+18/18
ans4
Exercises 12 -15, decide whether the statement is correct or incorrect. Explain your reasoning in words or by drawing pictures. 12. 1/3 equal to 4/12 13. 4/6 equal to 2/3 14. 2/5 equal to 1/3 15. 2/5 equal to 5/10.
Answers
The correct statement:
1/3 equal to 4/12; 4/6 equal to 2/3; 2/5 equal to 5/10
incorrect statement: 2/5 equal to 1/3
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
a) 4/12
Writing into Simplest form
4/12 = 1/3
b) 4/6
Writing into Simplest form
4/6 = 2/3
c) 2/5 cannot be simplified to 1/5
d) 5/10
Writing into Simplest form
5/10= 1/2
Hence, The correct statement: 1/3 equal to 4/12; 4/6 equal to 2/3; 2/5 equal to 5/10 and incorrect statement: 2/5 equal to 1/3.
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The graph shows Derek’s pay compared to the hours he has worked.
What is Derek’s hourly rate of pay?
Charlie earns $52.25 in 5 hours of work. What is Charlie’s hourly rate of pay?
Who gets paid more per hour? How much more?
Answers
Answer:
Charlie gets paid more then Derek. Charlie gets paid per hour $52.25
What is the next fraction in this sequence? Simplify your answer.
9
14
,
4
7
,
1
2
,
3
7
,
Answers
Answer:
5/14
Step-by-step explanation:
they subtract 1/14th each time
(You cant simplify)
A person needs to borrow $10,000 for 240 days. A lender offers a 9% simple discount note/loan. Determine the amount of interest for the loan and the proceeds of the discounted note. Label each. (Use 365 days)
Answers
The simple interest on a $10000 loan offered at a rate of 9% over 240 days is $10591.78
Simple InterestSimple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
The formula is given as
S.I = p(1 + rt)
S.I = simple interestp = principalr = ratet = timeSubstituting the values into the equation,
S.I = 10000(1 + 0.09 * 240)
S.I = 10591.78
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3x ≥5 or -3/5x-3>7 solve the compound inequality
Answers
By using the concept of linear inequation, the required solution is
[tex]x > \frac{5}{3} \ or \ x < -\frac{50}{3}[/tex]
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]> , < . \geq, \leq[/tex]
A one degree inequation is known as linear inequation.
Here the given linear inequation is
[tex]3x \geq 5 \ or \ \frac{-3}{5}x -3 > 7[/tex]
Now
[tex]3x \geq 5 \ or \ \frac{-3}{5}x -3 > 7\\\\x \geq \frac{5}{3} \ or \ \frac{-3}{5} x > 7 + 3\\\\x \geq \frac{5}{3} \ or \ \frac{-3}{5}x > 10\\\\x > \frac{5}{3} \ or \ x < \frac{10 \times 5}{-3}\\\\x > \frac{5}{3} \ or \ x < -\frac{50}{3}[/tex]
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what is 2 +2
4+5
0+9
Answers
Answer:
Step-by-step explanation:
2+2=4
4+5=9
0+9=9
Answer:
4, 9 , 9 OR 4 + 9 + 9 = 22
Step-by-step explanation:
Oliver saves 10% of his weekly earnings for living expenses. He usually makes $520 each week. This week he made 10% more. Oliver incorrectly claims that he has $520 left for spending money this week.
Answers
Answer:
10% of $520
=$52
Money made this week :
$520+$52=$572
Saving:
10% of $572
=$57.2
Money left:
$572-$57.2=$514.8
Please mark as brainliest
Answer: We have been given that,
Oliver's weekly earnings = $520
His earnings this week = 10% of $520 +$520
= $520+$52= $572
As he saves 10% of his weekly earnings so he would have been left with
= 10% of $572
= $57.2
So, he only has $52.7 left for spending money this week
Step-by-step explanation:
A local grocery store offers 3 brands of laundry detergent. Brand A costs $14.99 and contains 40 fluid ounces of detergent. Brand B costs $19.99 and contains 50 fluid ounces of detergent. Brand C costs $21.99 and contains a half-gallon of detergent. Which of the detergents has the best value?
Answers
Answer:
$ 52.63
Step-by-step explanation:
The brand C detergent has the best value.
What is Arithmetic?The mathematical branch known as arithmetic deals with the study and application of numbers, their relationships, and mathematical observations.
As per the given data in the question:
The information regarding the quantity and cost of 3 detergents is given in the question.
We have to find out which detergent is the most economical.
The detergent with the lowest cost/quantity will be the most economical.
For Brand A
Cost = $14.99
Quantity = 40 ounces
cost/quantity = 14.99/40 = 0.374 dollar/ounce
For Brand B
Cost = $19.99
Quantity = 50 ounces
cost/quantity = 19.99/50 = 0.399 dollar/ounce
For Brand C
Cost = $21.99
Quantity = 1/2 gallon = 64 ounces
cost/quantity = 21.99/64 = 0.343 dollar/ounce
The brand C detergent has the best value.
Hence, The brand C detergent has the best value.
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1. What is the result if you divide -12x8y8 by 3x4y ²?
O A. 4x4yê
O B. 4x²y
O C.-4x²yA
O D. -4x^y6
Please look at photo, it didn’t type correctly.
Answers
Divide -12/3 = -4
Then subtract the exponents for x and y
x^8-4 = x^4
y^8-2 = x^6
Adam has 6 cookies less than
Tony, there are a total of 15 cookies between both of them.
How many cookies does Tony
have?
Answers
Tony has 10.5 cookies.
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order term, where m is the slope and b is the y-intercept.
Given that, Adam has 6 cookies less than Tony, there are a total of 15 cookies between both of them.
Let the number of cookies Tony has be x,
x+x-6 = 15
2x - 6 = 15
2x = 21
x = 21/2 = 10.5
Hence, Tony has 10.5 cookies.
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