it was 1091227 on APEX
Given f(x) = x2 + 4x − 1 and g(x) = 5x − 7, identify (fg)(x).
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]
What is the solution of sqrt 2x + 4 = 16 ? x = 6 x = 72 x = 126 no solution
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
[tex]\sqrt{2x+4}=16[/tex]
We need to find the value of 'x'.
First we squaring the both sides:
[tex](\sqrt{2x+4})^2=16^2\\\\2x+4=256\\\\2x=256-4\\\\2x=252\\\\x=\dfrac{252}{2}\\\\x=126[/tex]
Hence, the value of x is 126.
Therefore, Third option is correct.
Answer:
C on Edge
Step-by-step explanation:
Received a 100% on the quiz.
Find PS if ABC=PQR, AD is an altitude of ABC, PS is an altitude of PQR, AD=12, AC=16 and PR=10
a. 7.5
b. 19.2
c. 4.62
d. 19.5
The expression 9n is also considered a _____.
constant
variable
term
Answer:
Term
Step-by-step explanation:
hope this helps
How to find the x intersept
Consider the relation y = 4|x + 2| + 7. What are the coordinates of the vertex?
(7, −2)
(2, 7)
(4, −2)
(−2, 7)
Barry’s Bagel Emporium sells a dozen bagels for $5.00. This price is no longer high enough to create a profit. The owner decides to raise the price. He does not want to alarm his customers with too large of an increase. He is considering four different plans. Plan A: Raise the price by $0.05 each week until the price reaches $8.00. Plan B: Raise the price by 10 percent each week until the price reaches $8.00. Plan C: Raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00. Plan D: Raise the price by $0.25 each week until the price reaches $8.00. Which plan will result in the price of the bagels reaching $8.00 fastest? plan A plan B plan C
Answer:
Plan B is correct answer.
Step-by-step explanation:
Raise the price by 10 percent each week until the price reaches $8.00.
Week 1. Starting price $5
[tex]0.1\times5=0.5[/tex]
price becomes = [tex]5+0.5=5.5[/tex]
Week 2.
[tex]0.1\times5.5=0.55[/tex]
Price becomes = [tex]5.5+0.55=6.05[/tex]
Week 3.
[tex]0.1\times6.05=0.605[/tex]
Price become = [tex]6.05+0.605=6.655[/tex]
Week 4.
[tex]0.1\times6.655=0.6655[/tex]
Price becomes = [tex]6.655+0.6655=7.320[/tex]
Week 5.
[tex]0.1\times7.320=0.732[/tex]
Price becomes = [tex]7.320+0.732=8.052[/tex]
So, we can see that in 5 weeks the price becomes $8 from $5. Therefore, plan B is the best plan.
John is participating in a marathon that is 26.2 miles. His distance (d, in miles) depends on his time (t, in hours). Which is an appropriate range for this situation?
The appropriate range for John's distance in miles (d) during the marathon is A. [tex]$0 \leq d \leq 26.2$[/tex].
In a marathon, the distance (d) John covers depends on the time (t) he spends running. The distance is fixed at 26.2 miles, so we need to find the appropriate range for the time (t) he spends running.
Let's calculate John's average speed (v) during the marathon. We know that speed is given by:
[tex]\[ v = \frac{d}{t} \][/tex]
Where:
- v = average speed (miles per hour)
- d = distance covered (miles)
- t = time spent running (hours)
Given that John's distance is 26.2 miles, and the marathon covers this distance, we have:
[tex]\[ 26.2 = \frac{26.2}{t} \][/tex]
Solving for t:
[tex]\[ t = \frac{26.2}{26.2} = 1 \][/tex]
So, John takes 1 hour to cover the 26.2 miles.
Now, let's consider the maximum and minimum possible times for John to complete the marathon:
- Minimum time: John completes the marathon in the fastest time possible. Let's say this is 0. This implies he runs the marathon in 0 hours.
- Maximum time: John takes his time and completes the marathon at the slowest pace possible. Let's use the average time for a marathon, which is around 4.5 hours.
Thus, the appropriate range for the time (t) is:
[tex]\[ 0 \leq t \leq 4.5 \][/tex]
This corresponds to option C: [tex]$0 \leq t \leq 4.5$[/tex].
Complete Question:
John is participating in a marathon that is 26.2 miles. His distance (d, in miles) depends on his time (t, in hours) Which is an appropriate range for this situation?
A. [tex]$0 \leq d \leq 26.2$[/tex]
B. [tex]$0 \leq d \leq 4.5$[/tex]
c. [tex]$0 \leq t \leq 4.5$[/tex]
D. [tex]$0 \leq t \leq 26.2$[/tex]
[tex] \frac{x}{5}+\frac{3x}{15}=\frac{2x}{3} } [/tex]+2 Answer plz math help
Which function below is the inverse of f(x) = The quantity of four x minus three, over two.?
Which of the following points lie in the solution set to the following system of inequalities?
y ≤ x − 5
y ≥ −x − 4
(−5, 2)
(5, −2)
(−5, −2)
(5, 2)
Answer: Second option : (5, −2)
Step-by-step explanation: Given system of inequalities
y ≤ x − 5
y ≥ −x − 4
Plugging x=5 and y=-2 in first inequality
-2 ≤ 5 − 5
-2 ≤ 0 : True.
Plugging x=5 and y=-2 in second inequality
-2 ≥ −5 − 4
-2 ≥ -9 : Also true.
Point (5, −2) satisfied both of the given inequalities in the system.
Therefore, (5,-2) is correct option.
75% of our 1000 products are shipped on time each month the remainder have defects that take two weeks to fix and ship our clients complain about 10% of the anti-products are defective and 5% of the product shipped late or defective what is the overall percentage of defective products
Final answer:
Calculating the overall percentage of defective products from the given data, we find that 150 out of 1000 products are defective, leading to an overall defect rate of 15%.
Explanation:
The question asks us to calculate the overall percentage of defective products based on the given scenarios. Firstly, it's mentioned that 75% of 1000 products are shipped on time, which means 750 are shipped on time and 250 are initially defective.
Since clients complain that 10% of the products are defective and 5% of the products are shipped late or are defective, we need to consider these percentages in our calculations.
To find the number of defective products, we can assume the 10% complaint rate on the entire batch of products which would lead to 100 out of 1000 products being defective. This is the initial estimated number of defective products.
To address the 5% of the products that are both shipped late and are defective, we consider this as an additional defect rate on top of the existing one, which would be another 50 products.
Total defects would then be the sum of defects from the complaints about defects and the defects because of shipping delay, which amounts to 100 + 50 = 150 defective products. To find the overall percentage, we divide 150 by 1000 and multiply by 100, giving us an overall defect rate of 15%.
A drawer contains five pairs of socks that are brown, black, white, red, and blue. Claude takes the red socks out of the drawer. What is the probability of Claude choosing the red socks on his first pick?
A drawer contains five pairs of socks that are brown, black, white, red, and blue. Claude takes the red socks out of the drawer. What is the probability of Claude choosing the red socks on his first pick?
Answer: 1/25
Answer:
The answer would be 1/25 Hopefully this any T4L students!
The length of a rectangle is 2 yd longer than its width. if the perimeter of the rectangle is 40 yd , find its area.
perimeter = 2L+2W
L=2+w
40 = 2L+2W
40= 2(2+w)+2W
40=4+2w+2w
36=4w
w=9
L=9+2=11
2(9) = 18, 2(11) = 22, 22+18 = 40
L=11
W=9
Area = L x w
area = 11x9= 99 square yards
The best approximation for the square root of 10 is.. A).5 B).100 C).3.1 D).25
Answer:
It is approximately 3.1
Step-by-step explanation:
Assume that y varies inversely with x. If y=7 when x=2/3, find y when x=7/3
what is the inverse of the function f(x)=1/9x+2
What is the answer? (Tip- to undo multiply both sides by 4/7)
x|4/7 = 28
x / |4/7| = 28
Multiply by |4/7|
x = |4/7| x 28
Ignore the absolute for a second and note 4/7 x 28 is 16 because...
28 / 7 = 4
4 x 4 = 16
x = |16|
Which of the following is a solution of x2 + 4x + 10?
2 + i times the square root of 6
−2 + i times the square root of 24
−2 + i times the square root of 6
2 + i times the square root of 24
Answer:
[tex]x=2+-i \sqrt{6}[/tex]
Step-by-step explanation:
[tex]x^2 + 4x + 10[/tex]
To find out the solution we set the expression =0 and solve for x
[tex]x^2 + 4x + 10=0[/tex]
Apply quadratic formula to solve for x
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
a=1, b=4, c=10 plug in the values in the formula
[tex]x=\frac{-4+-\sqrt{4^2-4(1)(10)}}{2a}[/tex]
[tex]x=\frac{-4+-\sqrt{-24}}{2(1)}[/tex]
The value of square root (-1) is 'i'
[tex]x=\frac{-4+-2i\sqrt{6}}{2}[/tex]
Divide each term by 2
[tex]x=2+-i\sqrt{6}[/tex]
99 POINTS!!! Find the equation for an ellipse with vertices at (-6, 0) and (6, 0) and foci at (-4, 0) and (4, 0).
(x^2)/a^2+(y^2)/b^2=1
a>b
a=6, a^2=36
foci=(a^2-b^2)^(1/2)
4=(36-b^2)^(1/2)
16=36-b^2
b^2=36-16
b^2=20
b=2(5)^(1/2) or (20)^(1/2)
1=(x^2/36)+(y^2/20)
last question
help me pls c:
Identify intervals on which the function is increasing, decreasing, or constant. g(x) = 4 - (x - 6)^2 ??
Determine whether the equation represents y as a function of x 16x-y^4=0
Convert this percent into decimal form.
The diffrence between a term and
coefficient
Tell which equation you would use to isolate a variable in order to solve the system using substitution. Explain your reasoning.
2x + y=-10
3x-y=0
The local theater has three types of seats for broadway plays: main floor, balcony, and mezzanine. main floor tickets are $59, balcony tickets are $50, and mezzanine tickets are $40. one particular night, sales totaled $73,785. there were 435 more main floor tickets sold than balcony and mezzanine tickets combined. the number of balcony tickets sold is 78 more than 33 times the number of mezzanine tickets sold. how many of each type of ticket were sold?
Final answer:
10 mezzanine tickets, 408 balcony tickets, and 853 main floor tickets were sold.
Explanation:
Let's solve this problem step-by-step to find out how many of each type of ticket were sold:
Let's assume that the number of mezzanine tickets sold is x. Therefore, the number of balcony tickets sold is 33x + 78 (since it is 78 more than 33 times the number of mezzanine tickets sold).
The number of main floor tickets sold is 435 + (33x + 78) + x = 435 + 34x + 78 = 34x + 513 (since there were 435 more main floor tickets sold than balcony and mezzanine tickets combined).
The total sales amount is $73,785.
Now, we can set up an equation to solve for x:
$40x + $50(33x + 78) + $59(34x + 513) = $73,785
Simplifying the equation:
40x + 1650x + 3900 + 59(34x + 513) = 73785
40x + 1650x + 3900 + 2006x + 30567 = 73785
3696x + 34467 = 73785
3696x = 39318
x = 39318/3696
x = 10.65
Since we can't have a fraction of a ticket, we can round down to the nearest whole number. So, x = 10.
Therefore, 10 mezzanine tickets were sold, 33x + 78 = 408 balcony tickets were sold, and 34x + 513 = 853 main floor tickets were sold.
Conditional probabilities are based on some event occurring given that something else has already occurred?
The answer is true. A conditional probability is a measure of the probability of an event given that (by assumption, presumption, assertion or evidence) another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A in the condition B", is usually written as P (A|B). The conditional probability of A given B is well-defined as the quotient of the probability of the joint of events A and B, and the probability of B.
can you help me????????
Three cities lie along a perfectly linear route: Springfield, Clarksville, and Allentown. Molly lives in Springfield and works in Allentown. She makes it to work using two gallons of gas in her car. Her friend Edgar lives in Allentown and works in Clarksville. It takes Edgar one gallon of gas to get to work. If Molly's car averages 26 miles per gallon, and Edgar's car averages 17 miles per gallon, about how far apart are Springfield and Clarksville?