The expression (fg)(x) is equal to 16x^4 + 72x^3 - 39x^2 + 5x.
To find (fg)(x), we need to evaluate the product of f(x) and g(x).
First, let's express f(x) and g(x) explicitly:
f(x) = 4x^2 + 19x - 5
g(x) = 4x^2 - x
Now, we can calculate their product:
(fg)(x) = f(x) * g(x)
= (4x^2 + 19x - 5) * (4x^2 - x)
To simplify the expression, we can use the distributive property and combine like terms:
(fg)(x) = 4x^2 * 4x^2 + 4x^2 * (-x) + 19x * 4x^2 + 19x * (-x) - 5 * 4x^2 - 5 * (-x)
Expanding and collecting like terms:
(fg)(x) = 16x^4 - 4x^3 + 76x^3 - 19x^2 - 20x^2 + 5x
Combining like terms:
(fg)(x) = 16x^4 + 72x^3 - 39x^2 + 5x.
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how do you solve 3/(n-1) = 2n/(n+4)
Step-by-step explanation:
To solve the equation 3/(n-1) = 2n/(n+4), follow these steps:
Step 1: Cross-multiply to eliminate the fractions.
3 * (n + 4) = 2n * (n - 1)
Step 2: Distribute the terms on both sides.
3n + 12 = 2n^2 - 2n
Step 3: Move all terms to one side and set the equation to zero.
2n^2 - 5n - 12 = 0
Step 4: Factor the quadratic equation, if possible. In this case, we can factor by finding two numbers that multiply to -24 and add to -5.
(2n + 3)(n - 4) = 0
Step 5: Use the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
2n + 3 = 0 or n - 4 = 0
Step 6: Solve for 'n' in each equation.
2n + 3 = 0 => n = -3/2
n - 4 = 0 => n = 4
So, there are two possible solutions for 'n': -3/2 and 4.
Answer: n= 4 , (-3/2)
Step-by-step explanation:
Your goal is to isolate n by getting it by itself
Multiply both sides by (n-1) to get 3 = ((2n)(n-1))/(n+4)
Use distributive property on the 2n * (n-1) to get 3 = (2n^2 - 2n)/(n+4)
Multiply both sides by (n+4) to get 3n + 12 = 2n^2 - 2n
Subtract 12 and 3n from both sides to get 2n^2 - 5n -12 = 0
Solve the quadratic using any method you like
Factoring would give you (n - 4)(2n + 3) = 0
So n= 4 and -3/2
name the leading coefficient and degree of the polynomial 12+5x^y+4x
Answer:
The leading coefficient is 5, the degree is y+1
Step-by-step explanation:
The polynomial 12+5x^y+4x has two terms, 12 and 5x^y+4x. The leading coefficient of the polynomial is 5, which is the coefficient of the term with the highest degree. The degree of the polynomial is y+1, which is the highest power of x in any term of the polynomial after like terms have been combined. The degree is determined by adding the exponents of the variables in the term with the highest degree, which is 5x^y in this case. The exponent of x is 1 and the exponent of y is y, so the degree is y+1. Therefore, the leading coefficient is 5 and the degree is y+1.
HI PLEASE HELPP REFER TO PICTURE STATISTICS
We are 95% confident that the true mean incubation period of the SARS virus lies between 2.79 and 9.01 days.
This means that if we were to sample many times from the same population, 95% of the intervals we construct would contain the true mean value.
Hence, Using a t-distribution with 86 degrees of freedom (n-1), and a 95% confidence level (α=0.05), the critical value for the two-tailed test is 1.992.
The standard error can be calculated as:
SE = SD / √n = 15.6 / √100 ≈ 1.56
The margin of error (ME) can be calculated as:
ME = t x SE = 1.992 x 1.56 ≈ 3.11
The 95% confidence interval (CI) is then:
CI = mean ± ME = 5.9 ± 3.11 = (2.79, 9.01)
Therefore, we are 95% confident that the true mean incubation period of the SARS virus lies between 2.79 and 9.01 days.
This means that if we were to sample many times from the same population, 95% of the intervals we construct would contain the true mean value.
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Two lines AB and CD intersect each other at O.If angle AOD = 120 deg . BOC=3y. < BOD = 2x then find (x + y)
The value of x + y = 70 when 2 lines AB and CD intersect each other at O. If angle ∠AOD = 120 degree, ∠BOC=3y and ∠BOD = 2x.
Given that,
AB and CD 2 lines intersect each other at O. If angle ∠AOD = 120 degree, ∠BOC=3y and ∠BOD = 2x.
We have to determine the value of (x + y).
We know that,
In the picture we can see the two lines AB and CD intersect each other at O.
So,
From line AB a straight line has 180°.
Then ∠AOD + ∠DOB = 180°
120° + 2x = 180°
2x = 180° - 120°
2x = 60
x = [tex]\frac{60}{2}[/tex]
x = 30°
Then ∠DOB = 2x = 2(30) = 60°
And by vertically opposite angles ∠AOD = ∠COB
120° = 3y
3y = 120°
y = [tex]\frac{120}{3}[/tex]
y = 40°
Then ∠COB = 120°
So,
Now, x + y = 30 + 40 = 70
Therefore, The value of x + y = 70
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What is the function equation for the graph below?
Answer:
f(x)= - [x] + 3
Step-by-step explanation:
because it describes a negative slope and 3 units up from the origin
Find the volume of this rectangular pyramid. Be sure to include the correct unit in your answer. If necessary, refer to the list of geometry formulas. 8 m 9 m 8 m 0|0 E 08 m² G m3
The value of the volume of this rectangular pyramid is,
⇒ V = 192 m³
We have to given that;
In rectangular pyramid,
Lenght = 8 m
Width = 9 m
Height = 8 m
Hence, The volume of this rectangular pyramid is,
⇒ V = 1/3 x Length x width x height
⇒ V = 1/3 × 8 × 9 × 8
⇒ V = 192 m³
Thus, The value of the volume of this rectangular pyramid is,
⇒ V = 192 m³
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what should be subtracted from -5/12 to get 1
Answer=
-17/12 should be subtracted from-5/12 to get the answer 1
Mark me as brainlist pls...
4(x - 7) in.
2(10 - x) in.
What is the value of x?
3 in. What is the value of X
The value of x, considering the rectangle given at the end of the answer, is given as follows:
x = 8.
How to obtain the value of x?From the rectangle given at the end of the answer, the bases are given as follows:
4(x - 7)2(10 - x).For a rectangle, the bases are congruent, meaning that they have the same measure.
Considering that the bases are congruent, the value of x is obtained as follows:
4(x - 7) = 2(10 - x)
4x - 28 = 20 - 2x
6x = 48
x = 48/6.
x = 8.
Missing InformationThe rectangle is given by the image presented at the end of the answer.
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Geoff sold his handknit hats for
$15 each at the farmers' market. He
bought $45 of yarn to make the hats.
If x represents the number of hats
sold, which expression represents
Geoff's earnings?
If x represents the number of hats sold, the expression representing Geoff's earnings is 15x.
What is an expression?An algebraic expression is a mathematical statement that combines variables, constants, values, numbers, and other quantities based on mathematical operands but without using equal symbols (=).
The selling price per handknit hat = $15
The total cost of materials (yarn) for making the hats = $45.
Let the number of hats sold = x
Expressions:Total earnings from the sales = 15x
Total cost = $45
Net earnings = 15x - 45
Thus, the expression that represents Goefft's earnings from the sale of handknit hats is 15x.
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A geometric pattern is made using 17 triangles and squares. If the triangles and squares have a total of 64 sides how many triangles were used
Answer:
Let s be the number of squares and t be the number of triangles.
s + t = 17---->4s + 4t = 68
4s + 3t = 64---->4s + 3t = 64
----------------- -----------------
t = 4, s = 13
4 triangles, 13 squares
The area of a circle is 81л m². What is the circumference, in meters? Express your
answer in terms of π.
Answer:
Step-by-step explanation:
Formulas:
A = (pi)(radius^2)
C = (pi)(Diameter)
Find the radius
81pi = pi * (r)^2
r^2 = 81
r = 9
Use radius to find diameter
D= 2r
D = 18
Use circumference formula
C = 18π
Advanced algebra please help!!
A real estate sells houses for Birr 200,000 plus Birr 400 per one square metre. a Find the function that represents the cost of the house that has an area of x m². Calculate the cost of the house that has an area of 80 m².
Step-by-step explanation:
Cost of house = Birr ( 200 000 + 400 x ) where x is square meters
for 80 m^2 cost = Birr ( 200 000 + 400(80)) = Birr 232000
What is the interval in which both f (x) and g(x) are positive?
The interval in which both functions are positive is the one in option C.
(3, ∞)
In which interval are the two functions positive?First, when we have a graph, to identify when the function is positive we need to see when the graph of the function is above the horizontal axis.
So here we just need to see in which interval are both curves (orange one and blue one) are above the horizontal axis.
We can see that from x = 3 and above, both of the curves are above the horizontal axis, then the interval in which both functions are positive is:
(3, ∞)
So the correct option is C.
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Y-3=2(x-6) what point does this line pass through? What is the slope of this line ? Rewrite the equation in slope intercept form
Answer:
This line passes through (0, -9)
Slope = 2
y = 2x-9
Step-by-step explanation:
Slope intercept form is : y=mx+b (m = slope, b= y-intercept)
First, let's distribute the 2 to the (x-6).
y-3 = 2x-12
Second, set it into slope intercept form (y = mx+b) by adding 3 to both sides.
y = 2x-9
This will be the equation in slope intercept form.
After looking at the the slope intercept form, we know that m = the slope. So the since the 2 is in the place of m when in slope intercept form, m=2. this would mean that the slope = 2.
Y-intercept is the point when the line touches the y-axis. To find the y-intercept, x would have to equal 0. This would mean that the point would have to be (0, y). After looking at the slope intercept form, and comparing it with our equation in slope intercept form, we know that -9 is in the place of b. This would mean that b = -9. This would also mean that the y-intercept is equal to -9. Therefore, the point would be (0, -9).
To the nearest tenth, what is the value of x?
Answer:
34.1
Step-by-step explanation:
In this case we have supplementary information that is not required to find the length of [tex]x[/tex].
A screenshot is provided below with the other values.
Express 0.01430 in Standard form
Answer:
1.430
Step-by-step explanation:
1.430 x 10^-2
On average, Americans consume 13.9 pounds of ice cream per person over an entire year. Ben loves ice cream, but limits himself to one 3-ounce (oz) serving each week. Find the difference between the amount of ice cream that Ben consumes compared to the national average. (1 pound equals to 16 ounces and there are 52 weeks in a year.)
All points of the step function f(x) are graphed. What is the domain of f(x)?
The domain of the step function f(x) is given as follows:
{x | -4 < x ≤ 4}.
How to define the domain and range of a function?The domain of a function is defined as the set containing all possible input values of the function, that is, all the values assumed by the independent variable x in the context of the function.The range of a function is defined as the set containing all possible output values of the function, that is, all the values assumed by the dependent variable y in the context of the function.For the function graphed at the end of the answer, we have that:
The lowest value of x is the open circle at x = -4.The highest value of x is the closed circle at x = 4.Hence the domain of the step function f(x) is given as follows:
{x | -4 < x ≤ 4}.
Missing InformationThe function is given by the image presented at the end of the answer.
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please help me with my geometry i cant fail this class or i’ll have to move out of my parents house :(
The values of all the solutions are,
16) m QT = 142 deg
17) m ∠STR = 23 deg
18) m ∠RSQ = 19 deg
Given that;
A circle is shown.
Now, We can formulate;
16|) The value of m QT is,
m QT = 2 ∠QST
= 2 × 71
= 142 degree
17) The value of m ∠STR is,
m ∠STR = 1/2 m ∠SXR
= 1/2 × 46
= 23 deg
17) Since, ∠ RST = 90°
Then, We get;
m ∠RSQ = 90 - ∠QST
= 90 - 71
= 19 degree
Thus, The values of all the solutions are,
16) m QT = 142 deg
17) m ∠STR = 23 deg
18) m ∠RSQ = 19 deg
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Determine the number of real solutions:
1. y=-3x^2+x+12
Answer:
2
Step-by-step explanation:
To determine the number of real solutions of the quadratic equation `y = -3x^2 + x + 12`, we can use the discriminant formula `b^2 - 4ac`.
First, we identify the values of a, b, and c:
a = -3
b = 1
c = 12
Next, we substitute these values into the discriminant formula:
b^2 - 4ac = (1)^2 - 4(-3)(12) = 145
Since the discriminant is positive (and not equal to zero), the quadratic equation has two distinct real roots. Therefore, the number of real solutions is 2.
The area of the object nelow
[tex] {77.05 \: m}^{2} [/tex]
hope this is correct
You are standing 190 meters away from the base of a building. The angle of elevation to the top of the
building is 25°. What is the height of the building?
Answer:
Step-by-step explanation:here it is. you did not say which grade ...
but hoping ok method .
Determine sin (A) and sin (B)
The values of sin (A) and sin (B) are sin(A) = 7/25 and sin(B) = 24/25
Determining the values of sin (A) and sin (B)From the question, we have the following parameters that can be used in our computation:
The right triangle
The values of sin (A) and sin (B) can be calculated using
sin = opposite/hypotenuse
Using the above as a guide, we have the following:
sin(A) = 14/50
sin(B) = 48/50
Simplify the equations
sin(A) = 7/25
sin(B) = 24/25
Hence, the values of sin (A) and sin (B) are sin(A) = 7/25 and sin(B) = 24/25
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Which measurement is the same for Charles and Jermod?
O median
Orange
Olower quartile
Oupper quartile
1
These dot plots show how many refutes Charles and Jermod spent on homework per day
for three weeks.
W
15 20 25 30 35 40 45 50 55 60
Charles's Homework (minutes per day)
..
15 20 25 30 35 40 45 50 55 60
Jermod's Homework (minutes per day)
Which measurement is the same for Charles and Jermod?
The measurement that is the same for Charles and Jermod is the median
How to find the Which measurement is the same for Charles and Jermod?The dot plots show the distribution of the number of minutes that Charles and Jermod spent on homework per day for three weeks. To determine which measurement is the same for both of them, we need to compare the dot plots.
Looking at the dot plots, we can see that both Charles and Jermod have a dot at 35 minutes, indicating that they both spent 35 minutes on homework on at least one day.
Therefore, the measurement that is the same for Charles and Jermod is the median, since it is the middle value of the data when arranged in order. In this case, the median is not clearly identifiable from the dot plots
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URGENT
A pyramid is
Group of answer choices
the total area of the surface of a solid figure.
a pattern of two-dimensional shapes that can be folded to make a model of a solid figure.
a solid figure with a base that is a polygon and sides that are triangles that meet at the top.
any one of the individual surfaces of a solid object.
A pyramid is a solid figure with a base that is a polygon and sides that are triangles that meet at the top.
Answer: A solid figure with a base that is a polygon and sides that are triangles that meet at the top.
Step-by-step explanation: A pyramid consists of a polygonal base and sides that are triangles. A polygon is a 2D shape that only has straight lines that enclose an area.
Helppppp pleaseeeeee
The reduced row echelon form of the matrix is given as follows:
[tex]\left[\begin{array}{cccc}1&0&0&-7\\0&1&0&2\\0&0&1&4\end{array}\right][/tex]
How to obtain the reduced row echelon form?The row echelon form of a matrix contains the entire matrix except the last column in the format of an identity matrix, with the last column containing the solution to the system of equations represented by the matrix.
Considering the matrix, the system of equations is given as follows:
7x - y - 3z = -63.-6y - 2z = -20.y + z = 6.Multiplying the last equation by 2 and adding with the second equation, the value of y is obtained as follows:
-4y = -8
4y = 8
y = 2.
The value of z is given as follows:
z = 6 - y
z = 4.
The value of x is given as follows:
7x = -63 + y + 3z
7x = -63 + 2 + 14
7x = -49
x = -7.
Hence the row-echelon form of the matrix is given as follows:
[tex]\left[\begin{array}{cccc}1&0&0&-7\\0&1&0&2\\0&0&1&4\end{array}\right][/tex]
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Solve using long division. 142/6 =
Answer: 23.666
(if you would like an explanation please let me know)
A class is presented with the following problem.
In a bag of marbles, the ratio of white marbles to red marbles is 2:3 and the ratio of red to black marbles is 6:11. What is the ratio of white to black marbles?
Connor, who likes using fractions, writes 2/3 *6/11 = 4/11 announces, without explanation, that the ratio of white to black marbles is 4:11. Explain why he is right. (Hint: taking the number of black marbles to be the whole unit, what fraction are red, and then what fraction are white?)
Answer:
Therefore, Connor is correct in his explanation that the ratio of white to black marbles is 4:11.
Step-by-step explanation:
Connor is correct in his reasoning. Let's break down the problem step by step to understand why.
Given:
Ratio of white marbles to red marbles = 2:3
Ratio of red marbles to black marbles = 6:11
To find the ratio of white to black marbles, we can follow these steps:
Step 1: Consider the black marbles as the whole unit.
Let's assume there are 11 black marbles (since the ratio of red to black marbles is 6:11).
Step 2: Determine the number of red marbles.
Since the ratio of red marbles to black marbles is 6:11, out of the assumed 11 black marbles, there are (6/11) * 11 = 6 red marbles.
Step 3: Determine the number of white marbles.
Using the ratio of white marbles to red marbles (2:3), we can find the number of white marbles. Since the ratio is 2:3, the number of white marbles would be (2/3) * 6 = 4.
Step 4: Find the ratio of white to black marbles.
Now that we have determined there are 4 white marbles and 11 black marbles, the ratio of white to black marbles is indeed 4:11.
Please help on question! If answers correct I'll reward with five stars , a thanks and maybe even brainliest!
Bob the builder is making 480kg of a concrete mix. Concrete is made by mixing cement , said and gravel in ratio 1:3:4.
How much sand does he need?
Answer:
x = the number of kg of cement
3x = number of kg of sand
4x = number of kg of gravel
x + 3x + 4x = 480
8x = 480, so x = 60
60 kg of cement
3(60) = 180 kg of sand
4(60) = 240 kg of gravel
Bob will need 180 kg of sand.
