Answers
(fg)(x) = (x^2 + 4x − 1)(5x − 7)
(fg)(x) = 5x^3 + 20x^2 - 5x - 7x^2 - 28x + 7
(fg)(x) = 5x^3 + 13x^2 - 33x + 7
answer is C. third choice
(fg)(x) = 5x^3 + 13x^2 - 33x + 7
The product of the functions[tex]\( f(x) = x^2 + 4x - 1 \) and \( g(x) = 5x - 7 \) is \( 5x^3 + 13x^2 - 33x + 7 \).[/tex]
The correct answer is indeed [tex]{C} \),[/tex] which matches [tex]\( 5x^3 + 13x^2 - 33x + 7 \).[/tex]
To find the product[tex]\( (f \cdot g)(x) \)[/tex], where [tex]\( f(x) = x^2 + 4x - 1 \)[/tex] and [tex]\( g(x) = 5x - 7 \),[/tex]we need to perform the multiplication of these two functions.
Start by expanding [tex]\( f(x) \cdot g(x) \):[/tex]
1. Write down ( f(x) ):
[tex]\[ f(x) = x^2 + 4x - 1 \][/tex]
2. Write down ( g(x) ):
[tex]\[ g(x) = 5x - 7 \][/tex]
3. Perform the multiplication [tex]\( f(x) \cdot g(x) \)[/tex]:
[tex]\[ f(x) \cdot g(x) = (x^2 + 4x - 1)(5x - 7) \][/tex]
4. Distribute [tex]\( x^2 + 4x - 1 \)[/tex] across ( 5x - 7 ):
[tex]\[ f(x) \cdot g(x) = x^2 \cdot (5x - 7) + 4x \cdot (5x - 7) - 1 \cdot (5x - 7) \][/tex]
5. Perform the multiplications:
[tex]\[ x^2 \cdot (5x - 7) = 5x^3 - 7x^2 \][/tex]
[tex]\[ 4x \cdot (5x - 7) = 20x^2 - 28x \][/tex]
[tex]\[ -1 \cdot (5x - 7) = -5x + 7 \][/tex]
6. Combine all the terms:
[tex]\[ f(x) \cdot g(x) = 5x^3 - 7x^2 + 20x^2 - 28x - 5x + 7 \][/tex]
7. Simplify by combining like terms:
[tex]\[ f(x) \cdot g(x) = 5x^3 + (20x^2 - 7x^2) + (-28x - 5x) + 7 \][/tex]
[tex]\[ f(x) \cdot g(x) = 5x^3 + 13x^2 - 33x + 7 \][/tex]
Therefore, the product [tex]\( (f \cdot g)(x) \) is \( 5x^3 + 13x^2 - 33x + 7 \).[/tex]
The correct answer is indeed [tex]{C} \),[/tex] which matches [tex]\( 5x^3 + 13x^2 - 33x + 7 \).[/tex]
Related Questions
Solve the quadratic equation by completing the square.
x^2-10x+15=0
First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Form:
( x + _ )^2 = _
or
( x - _ )^2 = _
Solution:
x = _
Answers
[tex](x-h) ^{2} +k=y[/tex]
When you complete the square the steps are these:
[tex] x^{2} -10x=-15[/tex]
[tex] x^{2} -10x+25=-15+25[/tex]
[tex](x-5) ^{2} =10[/tex]
and x = 5
Solve :
3x − 6 = 2x − 1
Answers
3x - 6 = 2x - 1
This is a basic algebra problem - our goal is to solve for x.
First, we need to get x on one side of the equation.
3x - 6 = 2x - 1
Subtract 2x from both sides.
x - 6 = -1
Now, we must isolate x.
Add 6 to both sides.
x = 5
I hope this helps!
What is the sum of the measures of the exterior angles in a heptagon? Explain
Answers
If only 4.5% of the non- historically protected have a field stone and mortar foundation, how many homes is this?
Answers
0.045(134) = 6.03 which rounds to 6 <=
1) What kind of figure is formed by the cross section below?
square
rectangle
circle
ellipse that is not a circle
Answers
Allen bought 1,350 shares of stock for $12 per share. If he sold all his shares for $27,000, how much profit on each share did he make?
Answers
Andrea and raleigh are each rolling a fair, six-sided die. they roll their dice simultaneously, individually keeping a sum until someone reaches 100; whoever reaches 100 first wins. (if they reach 100 on the same roll, it's a tie.) andrea's die has sides 1, 2, 3, 4, 5, and 6. raleigh's has sides 1, 1, 1, 6, 6, and 6. who is more likely to win?
Answers
Let An be the likely number of rolls for Andrea to arrive at 100 or more, given that she is n away from the target of 100 (which means her current total is 100 - n ). Then we get the recurrence relation
An = 1 + (1/6) (An-1 + An-2 + An-3 + An-4 + An-5 + An – 6)
and the initial conditions A0 = A-1 = A-2 = A-3 = A-4 = A-5 = 0. This results in A100 = 29.0476 as the amount of expected rolls that Andrea has to make.
Now let Rn to be expected amount of rolls for Raleigh to arrive at 100 or more, given than he is also n away from the target of 100. Now the recurrence relation is:
Rn = 1 + (1/2) (Rn-1 + Rn-6)
with the initial conditions R0 = R-1 = R-2 = R-3 = R-4 = R-5 = 0. This gives us R100 = 29.1837 as the expected amount of rolls for Raleigh.
Therefore Andrea has to make less number of rolls thus she is expected to win.
Winner: Andrea
A mother has 3 kids. Kid A is half the mother's current age. Kid B is 4 years younger than Kid A. In 3 years, Kid C will be 1/5 of his mother's age (not her current age). The sum of all their current ages is the mother's current age.
How old is the mother currently?
How old is each of her kids?
Answers
i)
"Kid A is half the mother's current age."
thus, the age of Kid A is G/2
ii)
"Kid B is 4 years younger than Kid A."
this means, the age of Kid B is the age of Kid A - 4 = G/2 - 4
iii)
"In 3 years, Kid C will be 1/5 of his mother's age (not her current age). "
thus, in 3 years the age of Kid C will be 1/5(G+3)=1/5G+3/5
this means that the current age of Kid C is
1/5G+3/5-3=1/5G+3/5-15/5=1/5G-12/5 = (G-12)/5
The ages of the Kids A, B and C are:
G/2 , G/2 - 4, (G-12)/5
From the smallest Child's age (G-12)/5 we understand that G-12 is a multiple of 5,
so G-12 ∈{5, 10, 15, 20, 25, ....}
which means G∈{17, 22, 27, 32, 37, 42, 47, 51, 56, 61... }
From the age of the oldest child G/2, we understand that G must be an even number (so that G/2 is a whole number).
This means that G∈{22, 32, 42, 56,...}
If G was 22, the oldest child would be 11, which makes no sense
If G is 32, the oldest child is 16, which means the woman became a mother at the age of 16, which is rare, but possible.
then G/2=16 , G/2 - 4=12, (G-12)/5=(32-12)/5=20/5=4
If G is 42, her oldest child is 21, no more a "kid", but still, lets consider this case:
the age of the second child is 21-4=17, and the youngest (42-12)/5=6
Answer:
The Plausible cases are :
i) mother: 32, children 16, 12, 4
ii) mother: 42, children : 21, 17, 6
Final answer:
The mother is currently 40 years old. Kid A is 20 years old, Kid B is 16 years old, and Kid C is 36 years old.
Explanation:
Let's denote the mother's current age as M. Kid A's age is A = M/2. Kid B is 4 years younger than Kid A, so B = A - 4 = M/2 - 4. Kid C will be 1/5 of his mother's age in 3 years, so if we denote Kid C's current age as C, we have C + 3 = 1/5(M + 3). The sum of all their current ages is the mother's current age, so M = A + B + C. With these equations, we can solve for M, A, B, and C.
We substitute A and B into the mother's age equation: M = M/2 + M/2 - 4 + C. Rearranging terms, we get M - 4 = C. Now we have two expressions for C: M - 4 and 1/5(M + 3) - 3. Setting them equal to each other, we get M - 4 = 1/5(M + 3) - 3. Solving for M, we find that M = 40 years old.
Now we can find Kid A, B, and C's ages using the mother's age. Kid A is half the mother's age, A = M/2 = 20 years old. Kid B is 4 years younger than Kid A, B = A - 4 = 16 years old. Kid C's age can be found by the substitution, C = M - 4 = 36 years old. So the mother is 40 years old, Kid A is 20 years old, Kid B is 16 years old, and Kid C is 36 years old.
Anita and Joelle bowled together and their combined total score for one game was 425 points. Anita’s score was 40 less than twice Joelle’s. What were their scores? Write a system of equations to model the problem if x represents Joelle’s score and y represents Anita’s score.
Answers
y=2x-40
Use substitution.
x+(2x-40)=425
3x-40=425
3x= 465
x=155
Plug in x value
y= 2(155)-40
y= 310-40
y= 270
Final answer: Anita-270, Joelle-155
The area of an artist's square canvas can hold 113 square inches of paint. What is the approximate length of one side of the canvas? (Approximate to the nearest hundredth inch.)
10.62 inches
10.63 inches
10.64 inches
10.65 inches
Answers
A=xy, and a square is just a special rectangle where the two dimensions are equal. x=y=s, where s is the side length so the area of a square is:
A=s^2 we want to solve for s so
s^2=A
s=√A, and we are told that the area is 113 in^2
s=√113 in
s≈10.63 in (to nearest hundredth of an inch)
The area of the square canvas is the square of its side length
The length of the side of the square canvas is 10.63 inches
The area the square canvas can hold is given as:
[tex]Area=113in^2[/tex]
The canvas has a square as its shape, and the area of a square is:
[tex]Area = L^2[/tex]
Where:
L represents the length of the shape (i.e. the square canvas)
So, we have:
[tex]L^2 = 113[/tex]
Take square roots of both sides
[tex]L = \sqrt{113[/tex]
Take the square root of 113
[tex]L = 10.63[/tex]
Hence, the length of the side is 10.63 inches
Read more about areas at:
https://brainly.com/question/24487155
Which of the following questions describes the equation w + 9 = -17? What number, A. when decreased by nine, is equal to negative seventeen?
B. What number, when added to negative seventeen, equals nine?
C. What number, when increased by nine, results in negative seventeen?
D. What number, when subtracted from nine, equals negative seventeen?
Answers
First, let's write our equation.
w + 9 = -17
We have "w + 9", which means "a number, w, is added to 9", and we have "= -17", which means "is equal to negative 17".
To solve for this, let's rewrite what's in quotation marks.
w + 9. A number, w, is added to 9 is equal to negative 17.
The answer choice that best matches this is "C.)", as it increases our number by 9 and is equal to negative 17.
I hope this helps!
A box contains 13 red hats, 15 white hats, 18 blue hats, and 14 brown hats. Nina randomly chooses a hat from the box.
What is the probability that it will NOT be white? Write your answer as a decimal.
Answers
13 + 15 + 18 +14 = 60 total hats
15 are white
60-15 = 45 hats that are not white
45/60 reduces to 3/4
3/4 =0.75 probability the hat will not be white
a randomly generated list of numbers from 0 to 4 is being used to simulate an event with numbers 3 and 4 representing a success. what is the estimated probability of a success
A. 75%
B. 60%
C. 25%
D. 40%
Answers
Answer: 40% appex
Step-by-step explanation:
The probability of success, where success is defined as generating a 3 or 4 in a random list of numbers from 0 to 4, is 40%.
To calculate the probability of success in a random number generation scenario. The numbers 0 to 4 are possible outcomes, with 3 and 4 being defined as success. There are 5 equally likely outcomes in total, and 2 of these (3 and 4) represent success. Hence, the probability of success (P(success)) is calculated as the number of successful outcomes divided by the total number of possible outcomes.
P(success) = Number of successful outcomes / Total number of outcomes
P(success) = 2/5
This fraction simplifies equals 0.4, which, when converted into a percentage, results in a 40% chance of success. Therefore, the correct answer is D. 40%.
Which transformations can be used to map a triangle with vertices A(2, 2), B(4, 1), C(4, 5) to A’(–2, –2), B’(–1, –4), C’(–5, –4)? a 180 rotation about the origin a 90 counterclockwise rotation about the origin and a translation down 4 units a 90 clockwise rotation about the origin and a reflection over the y-axis a reflection over the y-axis and then a 90 clockwise rotation about the origin
Answers
Let ABC be first transformed onto A"B"C" by a 90° clockwise rotation.
Notice that B(4, 1) is mapped onto B''(1, -4). So the rule mapping ABC to A"B"C" is (x, y)→(y, -x)
so we are very close to (-y, -x).
The transformation that maps (y, -x) to (-y, -x) is a reflection with respect to the y-axis. Notice that the 2. coordinate is same, but the first coordinates are opposite.
ANSWER:
"a 90 clockwise rotation about the origin and a reflection over the y-axis"
Answer:
C. a 90 clockwise rotation about the origin and a reflection over the y-axis
Step-by-step explanation:
given the polynomail function below, find f(-5) f(x)=x^2-2x-7
Answers
Eight less than a number is seventy-five. What is the number? -67 67 83
Answers
8-75 = x
x=8+75
x= 83
the number is 83
The sum of the roots of 5 - 2m - 3m2 = 0 is:
Answers
[tex]\displaystyle m_1 +m_2 = - \frac{b}{a}= \frac{2}{3} [/tex]
A + B = -b/a = -(-2) / -3 = -2/3
Angle c and angle d are supplementary, the measure of angle d is eight times the measure of angle
c. find measure of angle c and measure of angle d
Answers
d = 180 - c
and
d = 8c (given)
8c = 180 - с
8с + с = 180
9с = 180
с = 180/9
m∠с = 20°
m∠d = 8c = 8*20 = 160°
Answer:
160
Step-by-step explanation:
What is the equation in point−slope form of the line passing through (−2, −5) and (2, 3)?
a) (y + 2) = −2(x + 5)
b) (y − 2) = 2(x − 3)
c) (y − 3) = 2(x − 2)
d) (y + 3) = −2(x + 2)
Answers
Now plug in y - 3 = 2( x - 2) Answer is c.
y varies inversely with x
k = 0.6
What is the value of x when y is 0.6?
Answers
to find X when K is known
divide K by Y
0.6/0.6 = 1
X = 1
How do we refer to self-contained state actions: monadic. dyadic. triadic. k-adic?
Answers
In mathematics, self-contained state actions are known as k-adic. Monadic, dyadic, and triadic are specific cases of k-adic functions.
Explanation:In mathematics, self-contained state actions are known as k-adic. The term 'k-adic' refers to functions that take k inputs and produce a single output. Monadic, dyadic, and triadic are specific cases of k-adic functions, where k is 1, 2, and 3, respectively. Thus, it typically refers to a numeral or number system that is based on the value of k, which can be any positive integer.
In such systems, numbers are represented using a base of k, and each digit holds its own place value. K-adic expansions are useful in number theory and algebraic number theory, providing insights into number properties and relationships in various mathematical contexts.
Learn more about Self-contained state actions here:https://brainly.com/question/4437329
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At what value of x does the graph of the function f(x) have a vertical asymptote?
F(x) = 5X/ 2X-6
Answers
2x-6=0
2x=6
x=3
So the vertical asymptote is the vertical line x=3
A bus averages 60 mi/h traveling to its destination in the first half of its trip through an expressway and 72 mi/h in the second half traveling through a motorway. What is the bus's average speed for the entire trip rounded to the nearest tenth?
A) 64.2 mi/h
B) 63.0 mi/h
C) 65.5 mi/h
D) 66.0 mi/h
Answers
Answer:
The correct answer is 65.5 mi/h
Hope this helps :)
Derive the equation of the parabola with a focus at (−2, 4) and a directrix of y = 6. Put the equation in standard form.
Answers
My formula is (x-h)^2=4p(y-k), now just plug in numbers. You should end up with (x+2)^2=-4(y-5).
Some instructors want you to write (y-k)=1/(4p)(x-h)^2 which is the same thing, so check to see which one you should be using.
Answer: f(x) = -1/4x² -x + 4
Iodine-123 is a radioactive substance used in medicine. It has a half-life of 13 hours. A nurse received a solution that initially contained 48 grams of iodine-123. Now only 12 grams of the iodine-123 remain. How many hours have passed since the nurse received the solution?
Answers
A=P(1/2)^(t/h)
A=amount final
P=initial amount
t=time elapsed
h=time of half life
so
given h=13
and initial =48g
and final is 12g
12=48(1/2)^(t/13)
divide both sides by 48
1/4=(1/2)^(t/13)
what a coincidence
(1/2)^2=(1/2)^(t/13)
so
2=t/13
26=t
26 hours have passed
In triangle ∆PQR, C is the centroid.
a. If CY = 10, find PC and PY
b. If QC = 10, find ZC and ZQ
c. If PX = 20, find PQ
Answers
Because C is the centroid, therefore:
Segments PZ = ZR; RY = YQ; QX = XP
A.
If CY = 10, then
PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answer: PC = 20 PY = 30
B.
If QC = 10, then
ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answer: ZC = 5 ZQ = 15
C.
If PX = 20
Because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer: PQ = 40
Which function is shown in the graph below?
Answers
Answer: The correct option is 2.
Explanation:
From the given figure it is easily noticed that the graph intersect the y-axis at y=9 , therefore the y-intercept is (0,9).
To find the equation of the curve put x=0 in each option, If we get y=9 then that option is true.
Option 1:
[tex]y=(\frac{1}{2})^{(x+3)}-1[/tex]
[tex]y=(\frac{1}{2})^{(0+3)}-1=\frac{1}{8}-1=\frac{-7}{8}[/tex]
Option 2:
[tex]y=(\frac{1}{2})^{(x-3)}+1[/tex]
[tex]y=(\frac{1}{2})^{(0-3)}+1=8+1=9[/tex]
Option 3:
[tex]y=(\frac{1}{2})^{(x-1)}+3[/tex]
[tex]y=(\frac{1}{2})^{(0-1)}+3=2+3=5[/tex]
Option 4:
[tex]y=(\frac{1}{2})^{(x+1)}-3[/tex]
[tex]y=(\frac{1}{2})^{(0+1)}-3=\frac{1}{2}-3=\frac{-5}{2}[/tex]
Only the equation in option 2 have the y-intercept (0,9), therefore the correct answer is option second.
Answer:
Its B
Step-by-step explanation:
an article with a net weight of 10 lb (pounds) is packaged in a box that weighs 1/2 lb. If 20 of these boxed articles are put into a freight container 15 lb, what is the gross weight?
Answers
the box is 1/2 lb....so 20 of them = (1/2 * 20) = 10 lbs
the freight container is 15 lbs
for a total of : 200 + 10 + 15 = 225 lbs <==
Final answer:
The gross weight of the freight container with 20 boxed articles inside is 225 lb, calculated by adding the total weight of all the boxed articles (210 lb) to the weight of the container (15 lb).
Explanation:
To calculate the gross weight of the freight container with the packaged articles inside, we need to add the weight of the articles, the boxes, and the container itself.
First, we calculate the weight of one boxed article. Since the net weight of the article is 10 lb and the box weighs 0.5 lb, the total weight for one boxed article is 10 lb + 0.5 lb = 10.5 lb.
Next, we multiply the weight of one boxed article by the number of articles to find the total weight of all the boxed articles. For 20 articles, this is 20 imes 10.5 lb = 210 lb.
Finally, we add the weight of the freight container. The container weighs 15 lb, so the gross weight of the container with the articles is 210 lb + 15 lb = 225 lb.
Therefore, the gross weight of the freight container with 20 boxed articles inside is 225 lb.
Which of the following is equivalent to 36^1/2?
A) –18
B) –6
C) 1/18
D) 1/6
Answers
Thus, it is (B)
√36=±6
So the square root of 36 is 6 and -6, and only -6 is among your choices.
Pedro has created the function f(x)= 4x-3/2 to represent the number of assingments he has completed where x represents the number of weeks in the course Person discovers that using the inverse function to solve for x=30, he can predict when he will have 30 assignments completed explain to Pedro how to accomplish this using complete sentences
Answers
f(x) = 4x - 3/2
where
f(x) = number of assignments completed
x = number of weeks required to complete the assignments
We want to find f⁻¹ (30) as an estimate of the number of weeks required to complete 30 assignments.
The procedure is as follows:
1. Set y = f(x)
y = 4x - 3/2
2. Exchange x and y
x = 4y - 3/2
3. Solve for y
4y = x + 3/2
y = (x +3/2)/4
4. Set y equal to f⁻¹ (x)
f⁻¹ (x) = (x + 3/2)/4
5. Find f⁻¹ (30)
f⁻¹ (30) = (30 + 3/2)/4 = 63/8 = 8 (approxmately)
Answer:
Pedro needs about 8 weeks to complete 30 assignments.