The function (fg)(x) is a composite function
The value of the function (fg)(x) is 2x^3 + 7x^2 - 19x - 20
How to determine the function (fg)(x)?The functions are given as:
f(x) = 2x^2 - 3x - 4 and g(x) = x + 5.
To calculate (fg)(x), we make use of
(fg)(x) = f(x) * g(x)
So, we have:
(fg)(x) = (2x^2 - 3x - 4) * (x + 5)
Expand
(fg)(x) = 2x^3 - 3x^2 - 4x + 10x^2 - 15x - 20
Collect like terms
(fg)(x) = 2x^3 - 3x^2 + 10x^2 - 4x - 15x - 20
Evaluate
(fg)(x) = 2x^3 + 7x^2 - 19x - 20
Hence, the function (fg)(x) is 2x^3 + 7x^2 - 19x - 20
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PU
The data set below represents the different costs of a refrigerator at a local home improvement store.
$777, $498, $619. $379. $895, $1,256, $1,052
b. What is the median of the second half of the data? (third quartile) 379
T
Using the median concept, it is found that the third quartile is of is of $1,052.
What is the median of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
In this problem, the ordered data-set is:
$379, $498, $619, $777, $895, $1,052, $1,256.
Hence, the median of $777 divides the data-set into two halfs:
The first half is: $379, $498, $619.The second half is: $895, $1,052, $1,256.Hence, the third quartile, which is the median of the second half, is of $1,052.
More can be learned about the median concept at https://brainly.com/question/25215461
Which of the following binomials is a factor of the trinomial below?
x^2-5x-24
Answer:
(x-8) and (x+3)
Step-by-step explanation:
To find the binomials of the trinomial, we just need to factor in the trinomial.
First,
x² -5x - 24
Then split it, so the terms add to -5 and multiply to -24
x² +3x -8x - 24
Then factor x in the first part, and -8 in the second part.
x(x+3) - 8(x+3)
Factor again
(x-8)(x+3)
Answer:
Step-by-step explanation:
Factorize 24. When we add the factors, we have to get (-5) and we multiply we have to get (-24).
So, the factors are 3 and (-8)
When we add 3 +(-8) = -5 ; we multiply we get (-8)*3 =(-24)
Replace the middle terms with the factors.
x² - 5x - 24 = x² - 8x + 3x - 24
= x(x - 8) + 3(x - 8)
= (x - 8)(x+3)
A private club grew by 7 members each week for 63 weeks. What was the total change in the club's size? members
Answer:
The answer is 441
Step-by-step explanation:
7 x 63 = 441
Calculate the perimeter of the semi-circle below. Use 3.14 to approximate π.
12 cm
37.902
Step-by-step explanation:
3.14x12+12
Which number line shows the solution set for l s/2 +4 l <2
Step-by-step explanation:
Hopefully this was helpful!
if the length of a rectangle is 3 times of its breadth and perimeter is 96cm find the length and breadth of rectangle
Write the recursive definition for the geometric sequence. Then write the exponential equation using regression
-
128,32,8,2
The geometric sequence 128,32,8,2 has a common ratio
The recursive definition of the geometric sequence is [tex]a_n = 4a_{n-1}[/tex] where a1 = 128
How to determine the recursive definition?The geometric sequence is given as:
128,32,8,2
Start by calculating the common ratio (r)
[tex]r = \frac{a_{n}}{a_{n-1}}[/tex]
Substitute 2 for n
[tex]r = \frac{a_2}{a_1}[/tex]
Substitute known values
[tex]r = \frac{128}{32}[/tex]
Evaluate the quotient
[tex]r = 4[/tex]
Substitute 4 for r in [tex]r = \frac{a_{n}}{a_{n-1}}[/tex]
[tex]4 = \frac{a_{n}}{a_{n-1}}[/tex]
Cross multiply
[tex]a_n = 4a_{n-1}[/tex]
Hence, the recursive definition of the geometric sequence is [tex]a_n = 4a_{n-1}[/tex] where a1 = 128
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Choose an appropriate metric unit for the mass of bowling ball
A)
kilogram
B)
milligram
C)
meter
D)
gram
Answer:
i think that the correct answer would A
Step-by-step explanation:
hope this helps
99 PTS PLS HELP! Community volunteers helped clean 7 local parks. They each recorded the number of garbage bags they filled and arranged their data from least to greatest. The number of bags filled was 1, 2, 2, 3, 4, 4, and 5. The mean number of garbage bags filled was 3.
What is the MAD (mean absolute deviation) rounded to the nearest tenth?
1.1
1.3
2.3
3.0
Answer: 1.1
Step-by-step explanation:
To find the MAD (mean absolute deviation) we subtract the mean from each data value, and take the absolute value. Then we take the average of all the values. It looks like this:
1 - 3 = -2 -> |-2| = 2
2 - 3 = -1 -> |-1| = 1
2 - 3 = -1 -> |-1| = 1
3 - 3 = 0
4 - 3 = 1
4 - 3 = 1
5 - 3 = 2
-
[tex]\frac{2+1+1+0+1+1+2}{7}[/tex]
[tex]\frac{8}{7}[/tex]
1.14
The mean absolute deviation is about 1.1
After plotting the data where x=the side of a polygon, and f(x) = the area of the polygon, Jack used technology and
determined the appropriate model to approximate the area of the polygon, F(x) = x^2 + 3x + 2. Use the model Jack
created to predict the area of a polygon that has a side length of 3.
10
18
19
020
Answer: 19
Step-by-step explanation:
As per the model created by Jack; f(x) determines the area and x represents length so f(3) = 9+9+1
Therefore, f(3) = 19
Hooray! Poplin Elementary collected 1,224 Box Tops! The 8 volunteer moms will have to tape them to the turn-in sheet. If they share the work equally, how many will each mom need to do?
A bag of fruit contains 3 apples, 2 oranges, 1 banana, and 4 pears, Gerald will randomly select two pieces of fruit
one at a time from the bag and not put them back. What is the probability that the first piece of fruit Gerald selects will be a banana and the second piece of fruit will be a pear?
Answer:
2/45
Step-by-step explanation:
The probability that a banana is picked for the first one is:
1/10
because there are 10 fruits and one of them is a banana,
Then, the second piece has to be a pear.
For this we have already picked one fruit out of the bag, which leaves 9 fruits in the bag.
There are 4 pears so the probability of picking a pear second is
4/9
To find the probability of a banana and then a pear, you want to multiply these values together
So:
1/10 x 4/9 = 4/90 = 2/45
So the probability is 2/45
the length of a rectagle is 5 in longer than its width. if the perimeter of the rectangle is 58 in, find its length and width
Answer:
Width = 12in, Length = 17in
Step-by-step explanation:
We can create two expressions from the given statements:
1) L (length) = 5 + W (width)
and
2) 58 = 2L + 2W (the equation for rectangular perimeter)
Substituting L from the first equation into the second equation yields:
58 = 2(5+W) + 2W
Distributing the 2 and solving for W yields:
12in = W
Plug this back into the first expression,
L = 5 + 12
L = 17in
Answer:
width = 12 in
length = 17 in
Step-by-step explanation:
Let width of rectangle = x
⇒ length of rectangle = x + 5
Given:
Perimeter = 58 inPerimeter = 2 × width + 2 × length
⇒ 58 = 2x + 2(x + 5)
⇒ 58 = 2x + 2x + 10
⇒ 58 = 4x + 10
⇒ 48 = 4x
⇒ x = 12
Therefore,
width = x = 12 in
length = x + 5 = 12 + 5 = 17 in
what is the percentage of this
Answer:
69%
Step-by-step explanation:
10×10 table, 69 cells are orange. Therefore the fraction 69/100 as a percentage is 69%.
Fourth Grade
Memory Jogger Week 5 I need helppppp
Answer:
I can help you what you need help with
Step-by-step explanation:
210 cartons is __% of 60 cartons
Answer:
should definitely be 28.56
What is the value of x? 1/6 (3 - 2x) < 1/3 x
Step-by-step explanation:
1/6 (3 - 2x) < 1/3 x
let's multiply everything by 6
3 - 2x < 6/3 x
3 - 2x < 2x
3 < 4x
3/4 < x
so, x > 3/4
since 3/4 is never equal to x but is purely smaller than x, the interval of valid x values starts right after 3/4 and goes to infinity.
x = 3/4 is not valid, because 3/4 is not smaller than 3/4 (it is equal to) ...
the graph of f x shown below resembles the graph of g =x2 but it has been stretched somewhat and shifted which of the following could be the equation of f
The graph of the function g(x) is a quadratic equation
The possible equation of the function f(x) is f(x) = 2(x - 3)^2 + 3
How to determine the possible equation of f(x)?From the question, we have:
g(x) = x^2 --- the equation of the graph
The function f(x) is in the first quadrant.
This means that the function g(x) is shifted right and up.
This is represented as:
f(x) = (x - h)^2 + k
When stretched, the function becomes
f(x) = a(x - h)^2 + k
Where:
a > 0
From the list of given options;
The equation that has the form f(x) = a(x - h)^2 + k is
f(x) = 2(x - 3)^2 + 3
Hence, the possible equation of the function f(x) is f(x) = 2(x - 3)^2 + 3
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Please help this is due
[tex]\text{Area of equilateral triangle ABC}\\ \\=\dfrac{\sqrt 3}{4} BC^2\\\\=\dfrac{\sqrt 3}4 \cdot 12^2\\\\=\dfrac{144\sqrt 3}{4}\\\\=36\sqrt 3[/tex]
one way to test if a graph is a function or not is by doing a?
One way to test if a graph is a function or not is by doing a vertical line test.
The vertical line test is tested by testing if any vertical line is drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function, if there isn't any such line, the graph is a function.
Hope that helps!
Answer:
Vertical line test. (literally what it say)
Step-by-step explanation:
Given a graph, use the vertical line test to determine if the graph represents a function. Inspect the graph to see if any vertical line drawn would intersect the curve more than once.
Therefore you would have x value being the same for several points.
Need some math help 50pts
Answer:
angle 1 and 3 are 127.3 degrees and angle 2 is 52.7 degrees
Step-by-step explanation:
so angle 2 is also 52.7 degrees because angle 2 and 4 are vertical oppostite angles
so we can look at it now that we have to find angle 1. since we know a line is 180 degrees we make angle 1 plus angle 2 equal to 180
let angle 1 be x
x + 52.7 = 180
x = 180 - 52.7
x = 127.3
Answer:
m∠1 = 127.3°
m∠2 = 52.7°
m∠3 = 127.3°
Step-by-step explanation:
Vertical Angle Theorem: When two straight lines intersect, the opposite vertical angles are always equal to each other.
⇒ m∠1 = m∠3 and m∠2 = m∠4
If m∠4 = 52.7° then m∠2 = 52.7°
Linear pair: Two adjacent angles which sum to 180°.
⇒ m∠1 + m∠2 = 180°
⇒ m∠3 + m∠4 = 180°
⇒ m∠3 + 52.7° = 180°
⇒ m∠3 = 180° - 52.7°
⇒ m∠3 = 127.3°
As m∠1 = m∠3 then m∠1 = 127.3° also.
Suppose a math class has 18 females (2 of whom speak French) and 13 males (5 of whom speak French).
Compute the probability that a randomly selected student is male, given that the student speaks French.
Round your answer to three decimal places.
18 females, 13 males, total: 31 students.
•female french students: 2
•male french students: 5
probability: male french = 5/31,
total students
edit: as a percentage, 16.129 %
Becky is jumping on a trampoline. As he lands on the trampoline, his momentum carries him 2 feet below the trampoline, and he returns 0.4 seconds later to flat. What would be the a-value for this quadratic? Show work if possible
Answer:
becky got 2.4 lands and a quadratic is a possible
Step-by-step explanation:
2times 0.4 = 2.4
What is the slope of the line with equation y-3=-1/2 (x-2)?
Hello!
This equation is written in Point-Slope Form (y-y₁=m(x-x₁)
Where
y₁=y-coordinate of the point
m=slope
x₁=x-coordinate of the point
In this case, the slope is
[tex]\boxed{\boxed{\bold{\frac{1}{2}}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#KeepLearning
:-)
Answer:
C) 1/2
Step-by-step explanation:
woof woof
Malcolm draws this map of his neighborhood . Help please and thank you!!!!!
Answer:
Alden, perpendicular, Elm, parallel
Step-by-step explanation:
A fair 6-sided die is rolled five times. What is the probability that the sequence of rolls is 3,4,1,2,6
Answer:
Step-by-step explanation:
probability = number of favorable outcomes/total number of outcomes
To find compound probability multiply all the probabilities together.
p(3) = 1/6
p(4) = 1/6
p(1) = 1/6
p(2) = 1/6
p(6) = 1/6
Multiply all of them together.
1/6 x 1/6 x 1/6 x 1/6 x 1/6 = 1/7,776
or
[tex](\frac{1}{6} )^5 = \frac{1}{7,776}[/tex]
please help
The radius of the base of a right circular cone is 5 times greater than the radius of a second right circular cone. If the heights of both cones are the same, what is the volume of the larger cone divided by the volume of the smaller cone?
A. 5
B. 10
C. 15
D. 25
Answer: its A or B I think its more of B than A
PLEASE HELP I WILL GIVE BRAINLIEST
Step-by-step explanation:
37×2=74
360-74 = 286
286 ÷ 2=143
Of course, if AD and BC , and also BA and CD are even.
What are the y-intercepts of this conic section?
(0, −4) and (0, 4)
(0, −2) and (0, 2)
no y-intercepts
(−2, 0) and (2, 0)
Step-by-step explanation:
the second one, of course.
a y-intercept is a point where x = 0.
the 2 options are clearly having y-values of -2 and +2.
Moose left a $7.50 tip for his waitress on a $50 restaurant bill. What percent of his bill did he leave as a tip?
Answer:
he left 15 % of his bill as a tip
Step-by-step explanation:
7.5/50 x 100
0.15 x 100
15
Percentage
7.5/50×1000.150(100)15.0%