Answers
Answer:
(g ∘ f)(6) = 216
Step-by-step explanation:
Pre-SolvingWe are given the functions f(x) = 2x - 6 and g(x)=x³
We want to find the value of (g∘f)(6), where we first find the value of f(6), and then substitute that value into g(x).
SolvingSubstitute 6 as x in f(x)=2x-6.
f(6)=2(6)-6
Multiply
f(6)=12-6
Subtract
f(6)=6
Now substitute 6, which is the value of f(6) as x in g(x) = x³.
g(6)=6³ = 6 * 6 * 6 = 36 * 6 = 216
The value of g(6) is the same as the value of (g ∘ f)(6), as the 6 that we plugged into g(x) is the value of f(6).
Therefore, (g ∘ f)(6) = 216.
Related Questions
Which IRS form is provided at the end of the year by employers, so employees can use it to file taxes?
Answers
The IRS form is provided at the end of the year by employers, so employees can use it to file taxes is Form W-2.
What is Form W-2?Form W-2 can be described as the form that is been offered from the Internal Revenue Service which can be considered as the (IRS) tax form .
It should be noted that this form is been used in the United States so that the wages that is been paid to employees as well as their taxes can be reported. withheld from them
It should be noted that the form is been provided when the year is coming to an end by employers.
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2. Mr V bought 2 pajama sets for christmas for $25. He realized that he needed 2 more pajama sets. So now he bought 4 pajama sets for $50. Part A: Is this relationship proportional? Explain. *
Answers
We will have that the relationship is proportional because each time he bought more sets they had the same cost, and the total cost added to the sum of the independent cost. And we have the following relationship for the 2 sets and 4 sets:
2 sets:
[tex]\frac{25}{2}=12.5[/tex]So, each individual set is $12.5.
4 sets:
[tex]\frac{50}{4}=12.5[/tex]So, each individual set is $12.5.
So, each individual set for each relationship has the same cost, therefore the relationship is proportional.
PLEASE HELP ME ASAP.
Answers
y value
0,12 goes in the y axis because there is only a y value
4.5, 10.6 goes in quadrant I because all the values in quadrant I must be positive.
3,-7 goes in quadrant IV because values in that quadrant will have a negative y value
-15, 12 goes in quadrant II because in that quadrant all the x values are negative.
- 3/4, -4 1/9 goes in quadrant III because in that quadrant both the x and y values are negative.
I recommend you draw a graph like this in your notes just in case you get another question like this, you could also print one out.
Also I apologize if anything is wrong.
In Exercises 1 and 2, find m/1 and m<2
1.
Answers
Answer:
m/1 = 87
m/2 = 93
Step-by-step explanation:
m1 and m2 need to have an angle of 180
so 180-87 = 93
dentify ALL pairs of parallel and perpendicular lines in the image below.
Answers
Step 1: redraw the figure given
Step 2: State the relationship between the lines
It can be observed that
(i) line XY is perpendicular to line PS
[tex]\text{line XY}\perp line\text{ PS}[/tex](ii) line XY is perpendicular to line QT
[tex]\text{line XY}\perp lineQT[/tex](iii) line PS is parallel to line QT
[tex]\text{line PS}\parallel lineQT[/tex]Hence, XY⊥PS, XY ⊥ QT, PS ║ QT, The Second option.
A triangle with sides 10, 24, and 25 is a right triangle True/ False
Answers
Answer:
False
Step-by-step explanation:
Check using Pythagorean theorem (proof for right triangles)
[tex]10^2+24^2=25^2[/tex]
[tex]100+576=625[/tex]
[tex]676\neq 625[/tex]
False
Evaluate the following quotient. Leave your answer in scientific notation(5.44 x 10-18) + (6.8 x 10-))Answer
Answers
Given:
[tex](5.44\times10^{-18})\div(6.8\times10^{-9})[/tex]It can be written as follows.
[tex](5.44\times10^{-18})\div(6.8\times10^{-9})=\frac{5.44\times10^{-18}}{6.8\times10^{-9}}[/tex][tex]\text{Use }\frac{1}{10^{-9}}=10^9.[/tex][tex]=\frac{5.44\times10^{-18}\times10^9}{6.8^{}}[/tex][tex]=\frac{5.44\times10^{-18+9}^{}}{6.8^{}}[/tex][tex]=\frac{5.44\times10^{-9}}{6.8^{}}[/tex]Dividing 5.44 by 6.8, we get
[tex]=0.8\times10^{-9}^{}[/tex][tex](5.44\times10^{-18})\div(6.8\times10^{-9})=0.8\times10^{-9}[/tex]
Hence the quotient is
[tex]0.8\times10^{-9}[/tex]Simplify by dividing
Answers
Answer: -27/40
Step-by-step explanation:
Point F is located at (-6, -2) on the coordinate plane. Point Fis reflected over the
y-axis to create point F'. What ordered pair describes the location of F'?l
Answers
The ordered pair describes the location of F' is (6, -2) reflected over the
y-axis.
What is meant by the term reflection?A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line. A figure is said to reflect another figure when every point in one figure has been equidistant from every point in another figure. The reflected image should be the same shape and size as the original, but it should face in the opposite direction. Translation can also occur as a result of changes in position.The Y-coordinates of a point remain constant when it is reflected across the Y-axis. However, the X-coordinates are transformed into their inverse signs.
As a result, the Y-axis reflection of a point (x, y) is (-x, y).
For the given question;
Point F (-6, -2) is reflected along the y-axis to form a point F'.
The coordinates of F' becomes (6, -2), negative x axis will becomes positive.
Thus, the ordered pair describes the location of F' is (6, -2) reflected over the
y-axis.
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Jenna bought a new car for $29,000. She paid a 10% down payment and financed
the remaining balance for 48 months with an APR of 4.5%. Determine the monthly
payment that Jenna pays.
Answers
The monthly payment that Jenna pays for the new car is $1279.411 .
What is compound interest and how is it calculated?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Mathematically, A = P (1 + (R/n))^t
Given, total cost of the car = $29,000
Percentage of amount paid while in down payment = 10%
Therefore, amount paid as down payment = (10/100)*29000 = $2900
Now, amount put on loan by Jenna = A = 29000 - 2900 = $26,100
Also, number of years for which amount is loaned = n = 4 years
Annual Percentage Rate of the loan allowed = R = 4.5
Following the formula established in the literature above, we have:
26100 = P (1 + (4.5/4))⁴ ⇒ P = 26100/(1 + (4.5/4))⁴ ⇒ P = 26100/20.4
= 1279.411
The monthly payment that Jenna pays for the new car is $1279.411
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Two cylinders have the same volume. The first has a radius of 5cm and a height of 10 cm. The second has a radius of 10cm. The surface area of the first cylinder is and the surface area of the second i s
Answers
ANSWER
[tex]\begin{gathered} 1)150\pi \\ 2)250\pi \end{gathered}[/tex]EXPLANATION
For the first cylinder;
[tex]\begin{gathered} r=5 \\ h=10 \end{gathered}[/tex]Recall, the formula for calculating the surface area of a cylinder is;
[tex]A=2\pi rh+2\pi r^2[/tex]Now, substitute the values for the first cylinder;
[tex]\begin{gathered} A=2\pi rh+2\pi r^{2} \\ =2\times\pi\times5\times10+2\times\pi\times5^2 \\ =100\pi+50\pi \\ =150\pi \end{gathered}[/tex]The volume of the first cylinder is calculated using the formula;
[tex]\begin{gathered} V=\pi \cdot \:r^2\cdot \:h \\ \end{gathered}[/tex]Substitute the values of r and h for the first cylinder;
[tex]\begin{gathered} V=\pi \cdot \:r^2\cdot \:h \\ =\pi\times5^2\times10 \\ =\pi\times25\times10 \\ =250\pi \end{gathered}[/tex]To get the surface area of the second cylinder, we need to calculate the height (h).
To get the height, we use the volume of the first cylinder to get the height of the second (since they have the same volume).
Hence;
[tex]\begin{gathered} V=250\pi \\ r=10 \\ V=\pi r^{2}h \\ 250\pi=\pi\times10^2\times h \\ h=\frac{V}{\pi \cdot \:r^2} \\ h=\frac{250\pi }{\pi 10^2} \\ =2.5 \end{gathered}[/tex]Substitute the height to calculate the surface area is calculated thus;
[tex]\begin{gathered} A=2\pi rh+2\pi r^{2} \\ =2\times\pi\times10\times2.5+2\times\pi\times10^2 \\ =50\pi+200\pi \\ =250\pi \end{gathered}[/tex]13) Which of the following algebraic representations would result in a reduction dilation?A. (x,y) → x,y)C. (x,y) →x,0.75y)AnswerB. (x,y) → (-2x.-2y)D. (x,y) →x,y)acxiy) (tx, tyTriangles JKN and MKL are shown below.KMN14) Which of the following congruency statements is true about the two triangles?Angwer BA. L and ZN ZM B. ZNZL and ZK-ZK2N and CL areCongruentC. ZNZL and ZMD. UN and ZMZL Eck and Zk aze congruen15) Are triangles JKN and MKL similar?Yes16) If you answered YES for question 15, explain how you know they are similar. If you answered NO forquestion 15, explain how you know they are not similar.
Answers
16) We know that the triangles are similar because the three angles are equal in both triangles:
The angles in K are opposite by the vertex, so they are equal.
We also know that angles L and N are equal too.
By the rule of the sum of the angles in a triangle, we know that the third angle has to be equal.
Also, the side opposite to the angle N and L in each triangle have the same measure, so we can conclude that the triangles are similar.
The amount of money an engineer receives from a bank if he invests $50,000 for 7 years at 11.5% per annum compound interest.
Answers
Answer:
$107125.80
working out:
50000x1.115^7=107125.8 (rounded)
I Need Help Quick!! A recycling machine crushes 175 pounds of cans in 5 minutes.
How many pounds of cans will the machine crush in 16 minutes?
A. 560 pounds
B. 955 pounds
C. 1,925 pounds
D. 2,805 pounds
Answers
Answer:
560 pounds
Step-by-step explanation:
175 pounds divided by 5 minutes.
= 35 pounds per minute
35 pounds per minute multiplied by 16 minutes
= 560 pounds
Please answer the following questions. What is the slope of the line? How much does the distance increase for each hour since Alan crossed the bridge?
Answers
SOLUTION
The slope of the line can be gotten using the formula
[tex]\begin{gathered} \text{Slope =}\frac{change\text{ in distance}}{\text{change in time }}\text{ = }\frac{d2-d1}{t2-t1} \\ \text{Taking two points on along the line we have } \\ \text{Slope = }\frac{350-100}{7-2} \\ \\ \text{Slope =}\frac{250}{50} \\ \\ \text{Slope = 50} \end{gathered}[/tex]The slope is 50. This means the distance increased by 50 miles for every hour.
arrange the numbers in increasing order a. 8.08 8.081 8.09 8.008b. 14.204. 14.200. 14.240 14.210
Answers
Given:
a)
[tex]8.08,8.081,8.09,8.008[/tex]b)
[tex]14.204,14.200,14.240,14.210[/tex]Required:
To arrange in the increasing order.
Explanation:
a)
Here, the first two places' numbers are the same.
Let us check the hundredth decimal place.
The lowest number is 8.008.
The second lowest number is 8.08.
The third lowest number is 8.081
The fourth lowest number is 8.09.
So, the numbers are in ascending order is,
[tex]8.008,8.08,8.081,8.09[/tex]b) Here, the first t places' numbers are the same.
Let us check the hundredth decimal place.
The lowest number is 14.200.
The second lowest number is 14.204.
The third lowest number is 14.210.
The fourth lowest number is 14.240.
So, the numbers ar
the scale of topographical of map is 1:50000.what is the area of a dam which is represented on the map by an area of 3.5 centimeter square
Answers
The scale of a topographical map is 1:50000. This means that 1 cm on the map is 50 000 cm on reality.
[tex]1\operatorname{cm}\rightarrow50000\operatorname{cm}[/tex]Now, we can take the
[tex]x^{2} + 2x _5=0[/tex]
Answers
Step-by-step explanation:
Substitute the values
a
=
1
,
b
=
−
2
, and
c
=
−
5
into the quadratic formula and solve for
x
.
2
±
√
(
−
2
)
2
−
4
⋅
(
1
⋅
−
5
)
2
⋅
1
Simplify.
x
=
1
±
√
6
Simplify the expression to solve for the
+
portion of the
±
.
x
=
1
+
√
6
Simplify the expression to solve for the
−
portion of the
±
.
Determine if the table shows a proportional relationship. x 42.5 29.2 69.4 y 21.25 14.6 34.7 Yes, it is proportional because the ratios for y over x are all equivalent to one half. Yes, it is proportional because the ratios for y over x are all equivalent to one third. No, it is not proportional because 21.25 over 42.5 is not equal to 29.2 over 14.6. No, it is not proportional because 42.5 over 21.25 is not equal to 34.7 over 69.4.
Answers
Yes, it is proportional because the graph of these coordinates is a straight line and the ratios for [y] over [x] are all equivalent to one half.
What is proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. A straight line represents a proportional relationship. Mathematically -
y = kx + c
(y - c)/x = k [k is constant]
or
y = kx
k = y/x [k is constant]
Given is the following data -
[x] 42.5 29.2 69.4
[y] 21.25 14.6 34.7
In order to find if the given coordinates represent proportional relationship, plot these coordinates on graph. If the by joining the coordinate points, we get a straight line, then it represents a proportional relationship. Graph is attached with the answer. It can be seen that its graph is a straight line and hence represents a proportional relationship.
Now, the ratio of [y] by [x] -
m = (21.25 - 14.6)/(42.5 - 29.2) = 6.65/13.3 - 0.5 = 1/2
Therefore, we can say that, Yes, it is proportional because the graph of these coordinates is a straight line and the ratios for [y] over [x] are all equivalent to one half.
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Answer: Yes, it is proportional because the ratios for y over x are all equivalent to one half.
Step-by-step explanation:
I did the test. :)
Which inequality represebts the graph shown below
Answers
The endpoint is a circle so equality is excluded
The arrow points to the right so x is strictly greater than -2
Answer:
x > -2
Step-by-step explanation:
Thelma is a real estate agent negotiating the sale of a property with a listed price of $180,000. The buyer and seller of the property have agreed to a sale price that is 15% lower than the listed price.
If Thelma earns a 6% commission based on the negotiated sale price, how much will she earn for this sale?
Answers
When Thelma earns a 6% commission based on the negotiated sale price, the amount earned is $9180.
How to calculate the value?From the information, Thelma is a real estate agent negotiating the sale of a property with a listed price of $180,000. The buyer and seller of the property have agreed to a sale price that is 15% lower than the listed price.
The sales price will be:
= $180000 - (15% × $180000)
= $180000 - $27000
= $153000
Sine she earns 6% commission, this will be:
= Percentage × Sale price
= 6% × $153000
= 0.06 × $153000
= $9180
The commission is $9180.
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What is the average rate of change of the function x increases from -3 to 5
Answers
The average rate of change when x increases from -3 to 5 is given as follows:
r = (f(5) - f(-3))/8.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the average rate of change is given by the fraction presented as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
In the context of this problem, the input x increases by -3 to 5, hence the change in the input is given as follows:
b - a = 5 - (-3) = 5 + 3 = 8.
The change in the output is given as follows:
f(b) - f(a).
(the problem is incomplete hence the answer is given in general terms).
Then the average rate of change of the function when x increases from -3 to 5 is given as follows:
r = (f(5) - f(-3))/8.
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2) Choose the correct answer.
A given line passes through the points (2, 3) and (2, 3). Determine the equation of the
line that is perpendicular to the given line and passes through the point (1,5).
y = 5
x = -1
x=5
y= -1/2x + 13/3
y = -1
Answers
There is no slope, hence the equation of the line will be in the form y = b. Then the equation of the line that is perpendicular to the given line and passes through the point (1, 5) exists (A) y = 5.
What is meant by equation?The definition of an equation in algebra exists as a mathematical statement that demonstrates the equality of two mathematical expressions.The equation of a perpendicular line to a line in point-slope form is expressed as:
y - y1 = -1/m(x - x1)m is the slope(x1, y1) is any point on the lineDetermine the slope:
Slope = -3-3/2-2y = ∞Since there is no slope, hence the equation of the line will be in the form y = b.
Where b exists the y-coordinate of the point. Hence the required equation of the line is y = 5Therefore, there is no slope, hence the equation of the line will be in the form y = b. Then the equation of the line that is perpendicular to the given line and passes through the point (1, 5) exists (A) y = 5.
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Correct question:
2) Choose the correct answer.
A given line passes through points (2, 3) and (2, 3). Determine the equation of thethe line that is perpendicular to the given line and passes through the point (1,5).
(A) y = 5
(B) x = -1
(C) x=5
(D) y= -1/2x + 13/3
(E) y = -1
Please help *100 POINTS*
New Orleans is 2 feet under seas level.
Salton City has a elevation lower than New Orleans.
What is a possible elevation, in feet of Salton City
With explanation please
Answers
The given elevation of New Orleans of 2 feet below sea level gives the possible elevation of Salton City by using a number line, as 3 feet below sea level.
What is a number line?A number line pictorially presents the set of real numbers, showing their position in order of their magnitude, such that the numbers increases positively as we move from left to right with negative numbers increasing from the zero mark as we move further left.
The given elevation of New Orleans with reference to the sea level = 2 feet below (lower than) sea level
The elevation of Salton City = Lower than the elevation of New Orleans
Required; The possible elevation of Salton City
The elevation of Salton City can be found by presenting the given information on a number line as follows;
Let SL represent the sea level, let N represent New Orleans and let S represent Salton City, we have;
<___|-3______|-2____|0______>
' S. N. SL
A level higher than the elevation of New Orleans is given by a point to the right of the -2 mark on the above number line, while an elevation lower than that of New Orleans is given by a point to the left of -2 on the number line. The location of Salton City should therefore be to the left of -2, which is a point, x < -2 feet
The elevation of Salton City is less than 2 feet below sea level, which is given by the set x < -2 feet
-3 feet is less than -2 feet, therefore, a possible elevation in feet of Salton City is x = 3 feet below sea level, which is less than (<) 2 feet below sea level
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what is the correct ascending order for these numbers1.525/848%
Answers
Given the set of numbers:
[tex]\text{ 1.52, 5/8 and 48\%}[/tex]To be able to determine their correct ascending order, we must first make all the numbers into similar forms.
Let's convert a
10) Find DF if LF = 2X - 8 and LD = X - 3
Answers
Answer:
DF = 4
Step-by-step explanation:
You want DF when L is the midpoint, LD = x-3 and LF = 2x-8.
Congruent segmentsSegments DL and LF are marked the same, so are congruent. Using the given expressions, we have ...
LF = LD
2x -8 = x -3
x = 5 . . . . . . . . add 8-x to both sides
Then the measures of the segments are ...
LF = 2(5) -8 = 2
LD = 5 -3 = 2
DF = DL +LF = 2 +2 = 4
The length of DF is 4 units.
If you vertically compress the absolute value parent function, f(x) = Ixl, by afactor of 4, what is the equation of the new function?A. g(x)=xB. g(x) = 4xC. g(x) = 14x1D. g(x) = |x-41
Answers
Solution:
Given the absolute value parent function below
[tex]f(x)=|x|[/tex]If the function is vertically compressed by a factor of 4, the function becomes
[tex]g(x)=\frac{1}{4}f(x)[/tex]Where
[tex]\begin{gathered} f(x)=|x| \\ g(x)=\frac{1}{4}|x| \end{gathered}[/tex]Hence, the answer is
[tex]g(x)=\frac{1}{4}\lvert x\rvert[/tex]Option A
63 ÷ 5 = 12 R3 solve the problem
Answers
Answer:
12r^3
Step-by-step explanation:
The table shows a proportional relationship.
x 12 8 24
y 3 2 6
Describe what the graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (3, 12).
A line passes through the point (0, 0) and continues through the point (2, 8).
A line passes through the point (0, 0) and continues through the point (6, 24).
A line passes through the point (0, 0) and continues through the point (12, 3).
Answers
A graph which best describes what the proportional relationship would be D. A line that passes through the point (0, 0) and continues through the point (12, 3).
What is a graph?In Mathematics, a graph is used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
Additionally, a graph which shows a proportional relationship between two variables would always have a straight line with its data points passing through the origin (0, 0).
Since the graph represents a proportional relationship we will get;
Constant of proportionality, we get;
k = 12/3 = 8/2 = 24/6
k = 4
Ratio,
24:6
= 12:3.
Therefore, A line that passes through the point (0, 0) and continues through the point (12, 3).
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Which of the following is equivalent to 3/8 A) 0.3 B) 0.45 C) 0.6 D) 0.375
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given fraction
[tex]\frac{3}{8}[/tex]STEP 2: Convert to decimal
[tex]\frac{3}{8}=0.375[/tex]Hence, the equivalent is 0.375
