The values of the composite functions are (f.g)(x) = 2x^3 - 19x^2 + 40x + 25 and (f/g)(x) = 2x + 1
How to evaluate the composite functions?The functions are given as:
f(x) = 2x^2 - 9x - 5
g(x) = x - 5
The composite function (f.g)(x) is calculated as
(f.g)(x) = f(x) * g(x)
This gives
(f.g)(x) = (2x^2 - 9x - 5) * (x - 5)
Evaluate the product
(f.g)(x) = 2x^3 - 9x^2 - 5x - 10x^2 + 45x + 25
Evaluate the like terms
(f.g)(x) = 2x^3 - 19x^2 + 40x + 25
The composite function (f/g)(x) is calculated as
(f/g)(x) = f(x)/g(x)
This gives
(f/g)(x) = (2x^2 - 9x - 5)/(x - 5)
Factorize the numerator
(f/g)(x) = (2x + 1)(x - 5)/(x - 5)
Evaluate the quotient
(f/g)(x) = 2x + 1
Hence, the values of the composite functions are (f.g)(x) = 2x^3 - 19x^2 + 40x + 25 and (f/g)(x) = 2x + 1
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Q.5 - Solve the equation 3(2x - 4) = 8 + 2x + 6. Show your work.
Answer: x=6.5
Step-by-step explanation:
3(2x - 4) = 8 + 2x + 6
6x-12=14+2x
4x-12=14
4x=26
x=26/4
x=6.5
Complete each function table,then graph the function
The y values from:
1. ₋6
2. ₋3
3. 0
4. 3
Given the x values and y value as y = 3x
1. when x = ₋2 then y = 3x
y = 3(₋2)
y = ₋6
2. when x = ₋1 then y = 3x
y = 3(₋1)
y = ₋3
3. when x = 0 then y = 3x
y = 3(0)
y = 0
4. when x = 1 then y = 3x
y = 3(1)
y = 3
therefore we get the points as (₋2 , ₋6) (₋1 , ₋3) (0,0) (1 , 3).The graph is pltted and attached.
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1/4 g(x)=-4x-8 if g (-3)
Answer:
16
Step-by-step explanation:
x=-3
g(x)=4(-4(-3)-8)
g(x)=4(4)
g(x)=16
Write a linear equation for the graph in point-slope form. Show your work.
Answer:
y-20=0.75(x-4)
Step-by-step explanation:
First, use slope formula to find the slope.
The points I will use are (4, 20) and (8, 23).
Formula:
y2-y1/x2-x1
23-20/8-4=
=3/4
The slope in decimal form is 0.75.
Now you put the linear equation in point-slope form.
m=0.75
Use the point (4, 20).
y-y1=m(x-x1)
y-20=0.75(x-4)
The linear equation is point-slope form is y-20=0.75(x-4).
Hope this helps!
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Find the difference between simple interest and annual compound interest on Rs 9,600 for 2 yers at the rate of 5 % per annum.
Answer:
Rs 984
Step-by-step explanation:
Principal (P) = Rs 9,600
Time (T) = 2 years
Rate (R) = 5%
Simple Interest (SI) = [tex]\frac{PTR}{100}[/tex]
SI = [tex]\frac{9600*2*5}{100}[/tex]
SI = [tex]\frac{9600}{10} = Rs 960[/tex]
Compound Interest (CI) = 9600 * [tex]\frac{41}{100} = 24*41 = Rs 984[/tex]
What if? if the height of the pyramid were increased to 563 ft and the height to base area ratio of the pyramid were kept constant, by what percentage would the volume of the pyramid increas
The pyramid's volume will increase by 11.79%.
What is a pyramid?It has a polygonal base.A pyramid has n + 1 vertices, n + 1 faces, and 2n edges with an n-sided base.A Pyramid's volume is calculated as:
[tex]V=\frac{B h}{3}[/tex]
Where:
B denotes the base area.h stands for height.When the height increases from 458 to 512, the initial and final volumes are as follows:
[tex]\begin{aligned}&V_1=\frac{458}{3} b \\&V_2=\frac{512}{3} b\end{aligned}[/tex]
The percentage difference is then calculated as follows:
[tex]\% \text { Change }=\frac{V_2-V_1}{V_1} \times 100 \%[/tex]
We obtain:
[tex]\% \text { Change }=\frac{512 b / 3-458 b / 3}{4586 / 3} \times 100 \%\\\% \text { Change }=\frac{54 b / 3}{4586 / 3} \times 100 \%\\\% \text { Change }=0.1179 \times 100 \%\\\% \text { Change }=11.79 \%[/tex]
Therefore, the pyramid's volume will increase by 11.79%.
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The correct question is given below;
If the height of the pyramid were increased to 512 ft and the height to base area ratio of the pyramid were kept constant, by what percentage would the volume of the pyramid increase
maritza compro 1.5 litros de pintura azul. si empleo 1/2 del contenido de esa lata para pintar un mural
¿cuantos litros de pintura azul uso en este?
The fraction of 1/2 of the number of liters of blue paint is 3/4 therefore 3/4 liters of blue paint must be used to draw that painting.
What is a fraction?If we divide two numbers by each other then the upper word is called the numerator, a lower word is called the denominator, and the representation is known as the fraction.
Given that,
Maritza bought 1.5 liters of blue paint.
The given painting is going to be used 1/2 fraction of the total liters of blue paint.
1/2 of the blue paint ⇒
(1/2)1.5
⇒ (1/2)15/10
⇒ (1/2)3/2
⇒ 3/4 liters of blue paint.
Hence "The fraction of 1/2 of the number of liters of blue paint is 3/4 therefore 3/4 liters of blue paint must be used to draw that painting".
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The given question is in another language the translation in English is as follows;
Maritza bought 1.5 liters of blue paint. if I use 1/2 of the contents of that can to paint a mural
How many liters of blue paint do I use on this?
If a leinear system has more unknowns equations then it must hav einfinitely many solutions.
a. true
b. false
If a linear system has more unknown equations then it must have infinitely many solutions, which is true.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
If there is only one equation with more than one parameter, then the number of the solution will be infinite.
If a linear system has more unknown equations then it must have infinitely many solutions, which is true.
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Miguel is asked to solve the problem below and wants to convert the values to the same form. Which form would you encourage Miguel to choose?
-0.6(⅚)
Group of answer choices
No answer text provided.
Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions.
Since 5/6 is a repeating decimal, Miguel should convert the fraction 5/6 to a decimal and multiply decimals.
Since 5/6 is a terminating decimal, Miguel should convert 5/6 to a decimal and multiply the decimals.
the correct option is:
"Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions."
Which form would you encourage Miguel to choose?
Miguel wants to do the product below:
-0.6*(5/6)
And he know that to do it, he should convert both numbers to the same form, only that he does not know if he should transform the decimal number into a fraction or the fraction into a decimal.
It is always easier to work with fractions, so the blind answer is to go with the fraction, but let's see why this is the best option.
5/6 written as a decimal will give:
5/6 = 0.833....
It is a repeating decimal number, so taking the exact product would be impossible to do by hand if we used both numbers in decimal form.
While -0.6 written as a fraction is really trivial, just multiply it and divide it by 10, it becomes:
-0.6 = -6/10
Then the product is:
(-6/10)*(5/6) = -5/10 = -1/2
Then the correct option is:
"Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions."
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Dyani began solving the equation g = x-1/k for x by using the addition property of equality. explain dyani's error. then describe how to solve for x
Given equation g = x-1/k in terms of x would be x = 1 + gk
for given question,
we have been given an equation g = x-1/k
Dyani began solving the equation g = x-1/k for x by using the addition property of equality.
We solve given equation for x.
⇒ g = x-1/k ..........(Given)
⇒ gk = (x - 1/k)k .........(Multiply both the sides by k)
⇒ gk = x - 1
⇒ gk + 1 = x - 1 + 1 .........(Add 1 to each side)
⇒ gk + 1 = x
⇒ x = 1 + gk
Therefore, given equation g = x-1/k in terms of x would be x = 1 + gk
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Rename the fraction as a decimal.
1/50 =
-
Answer:
0.02
Step-by-step explanation:
(5,-4), (1, -7) distance formula
Answer:
The distance between both points is 5 units
Step-by-step explanation:
The distance formula is: d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}
show your work for -4x+3(2x-5)=31
Step-by-step explanation:
[tex] - 4x + 3(2x - 5) = 31 \\ - 4x + 6x - 15 = 31 \\ 2x - 15 = 31 \\ 2x = 31 + 15 \\ 2x = 46 \\ x = 46 \div 2 \\ x = 23[/tex]
a house is drawn to the scale of 1/4in = 5 ft. Its rectangular kitchen measures
4.5 inches by 6.5 inches on the blueprints. What is the actual length and width of the kitchen?
Find the actual area of the kitchen.
Answer:
1 : 4 1/2 :: 8 1/5 : x proportion
x = (4 1/2)(8 1/5) product of means/extremes
x = (9/2)(41/5) change improper fraction
x = 369/10 multiply
x = 36.9 change to decimal
If a number is chosen at random from the set {1, 2, 3, 4, . . ., 18}, what is the probability that the number chosen is a factor of 17?
Pwease help me :0 Thank u!
Answer:
1/2
Step-by-step explanation:
simply divide 3/10 to get 0.3 and then divide 3/5 to get 0.6 then just divide 0.3 to 0.6 to get 0.5 or 1/2
square root 147 simplified
Answer:
7√3
Step-by-step explanation:
9n-22=4n + 3
And please explain how you got your answer, I’ve gotten this far (look at image) but I don’t know what to do now
1. Which one of the following is a solution of 5x + 3y = 11?
A. (-1, 2)
B. (2, -1)
C. (2, 1)
D. (1, 2)
E.(1/5,3)
I cannot figure this out
An advantage of a weighted moving average is that recent actual results can be given more importance than what occurred a while ago. True or false?.
An advantage of a weighted moving average (WMA) is that recent actual results can be given more importance than what occurred a while ago is a "true" statement because "Weighted moving averages could be adjusted to emphasize more recent data in forecasting."
What is moving average?Moving averages are popular tools for measuring momentum among active traders. The formula used to calculate the average is the primary distinction between a simple moving average, a weighted moving average, and an exponential moving average.
Some key features regarding the weighted moving average are-
The SMA calculates the average price above a specific time period, whereas the WMA emphasizes current data.The exponential moving average (EMA) is also weighted to reflect the most recent prices, however the rate of decrease among one price and its previous price is not constant but exponential.Weighted moving averages give more weight to recent data points as they're more relevant than data points from the distant past. The total of the weightings should equal 1 (or 100%). The weightings are distributed equally in the case of the simple moving average.To know more about moving average, here
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sx+tx=r solve the literal equation for x
Answer:
[tex]x = \frac r{s + t}[/tex]
Step-by-step explanation:
Hello!
Solve by isolating the variable.
Solve for x[tex]sx + tx = r[/tex][tex]s(x) + t(x) = r[/tex][tex]x(s + t) = r[/tex][tex]x = \frac r{s + t}[/tex]The solution for x is [tex]x = \frac r{s + t}[/tex].
Find an equation for the perpendicular bisector of the line segment whose endpoints are (−4,−1) and (8,-5)
An equation for the perpendicular bisector of the line segment whose endpoints are (−4,−1) and (8,-5) is [tex]y=-\frac{1}{3} x-\frac{7}{3}[/tex]
Find the line [tex]$y=m x+b$[/tex] passing through [tex]$(-4,-1),(8,-5)$[/tex]
Compute the slope [tex]$(-4,-1),(8,-5): \quad m=-\frac{1}{3}$[/tex]
Compute the [tex]$y$[/tex] intercept: [tex]$\quad b=-\frac{7}{3}$[/tex]
Construct the line equation [tex]$y=m x+b$[/tex] where [tex]$m=-\frac{1}{3}$[/tex] and [tex]$b=-\frac{7}{3}$[/tex]
[tex]y=-\frac{1}{3} x-\frac{7}{3}[/tex]
A perpendicular bisector can be defined as a line that intersects another line segment perpendicularly and divides it into two parts of equal measurement. We can draw a perpendicular bisector using a rule, a compass and a pencil.
Two lines are said to be perpendicular to each other when they intersect each other at 90 degrees or at right angles. And, a bisector is a line that divides a line into two equal halves. Thus, a perpendicular bisector of a line segment AB implies that it intersects AB at 90 degrees and cuts it into two equal halves.
A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other words, a perpendicular bisector divides a line segment into two equal parts by intersecting it at a 90° angle.
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Andrei had cinnamon-scented jar candle that burned for 303030 hours and a berry-scented pillar candle that burned for 888888 hours. relative to its type, which candle burned faster?
The cinnamon-scented jar candle brunt faster.
What does relative speed means ?Relativity means observing some action with different perspective.
Suppose you are moving in a bus at 100 km/hr and you are reading a book.To an observer which you are passing by you and the book he observes moving at a speed of 100 km/hr.But for you the book is not moving at all because both you and the book is moving at a speed of 100 km per hour.
According to the given question Andrei had cinnamon-scented jar candle that burned for 303030 hours and a berry-scented pillar candle that burned for 888888 hours.
From the given data of burning hours we can observe that berry-scented pillar candle that burned for 888888 hours which is more that of Andrei had cinnamon-scented jar candle that brunt for 303030 hours because
30303030 < 888888.
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Is o.227 a rational number explain
Answer: 227 is a rational number because it can be expressed as the quotient of two integers: 227 ÷ 1.
Step-by-step explanation:
lol i still dont get it i need a smartt brainlist help pleaseee
What are the zeros of the expression (x-5)(2x+7)
Answer:
The zeros are x =5, -7/2
Step-by-step explanation:
To find the zeros, set the expression equal to zero
(x-5)(2x+7) =0
Using the zero product property
(x-5)=0 (2x+7)=0
Solve each equation
x=5 2x = -7
x=5 x = -7/2
The zeros are x =5, -7/2
Answer:
5, -7/2
Step-by-step explanation:
[tex]x - 5 = 0 = 5\\\\2x + 7 = 0\\2x + -7 = 0\\\frac{2x}{2} = \frac{-7}{2}\\ x = \frac{-7}{2}\\x = -\frac{7}{2}[/tex]
Thus,
x = 5
x = -7/2
A party of 17 comes in the door. What is the leastnumber of tables needed to seat them together?
Answer: 1
Step-by-step explanation:
How big is the table? 1 table can fit all 17 people if the table is big enough.
Isabella and Tom leave from the same location at
9:45 AM. Isabella drives north at a constant speed of
65 kilometers per hour, and Tom drives south at a
constant speed of 77 kilometers per hour.
25
At what time will Isabella and Tom be 639 km apart?
A) 1:15 PM
B) 2:15 PM
C) 3:30 PM
D) 4:30 PM
In the coordinate plane, the point X (2, 2) is translated to the point X (0, 4). Under the same translation, the points Y(-2, 0) and Z (0, 6) are
translated to Y and Z', respectively. What are the coordinates of Y' and Z?
The points Y and Z after transition are (-4,-2) and (-2,4)
In this case, we are required to find x' and y' to find the direction of transition
x' =x coordinate of point 2 - x coordinate of point 1
= 0-2 = -2
y'= y coordinate of point 2 - y coordinate of point 1
=4-2 = 2
Now we are required to subtract these transition from the points given,
Transition of point Y = (-2-2 ,0-2) =(-4,-2)
Transition of point Z =(0-2,6-2) = (-2,4)
Hence the points after transition are Y as(-4,-2) and Z as (-2,4)
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