Write the given function as the composition of two functions.y=√15 + 6xChoose the correct answer below.OA. If f(x) = -√x and g(x) = 15+ 6x, then y = f(g(x)].1B. If f(x)=√x and g(x) = -OC. If f(x) =³√xCOD. If f(x) = -115+ 6x'then y = f[g(x)].and g(x)= 15+ 6x, then y = f[g(x)].and g(x) = 15+ 6x, then y = f[g(x)]....
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Given:
[tex]y\text{ = -}\sqrt[3]{15+6x}[/tex]To find:
the functions that give the above composite function
f(g(x)): substitute x in f(x) with g(x)
This means g(x) will be 15 + 6x which will be substituted into function f(x)
[tex]\begin{gathered} f(x)\text{ = -}\sqrt[3]{x} \\ g(x)\text{ = 15 + 6x} \\ \\ Check: \\ f(g(x)):\text{ substitute x in g\lparen x\rparen with f\lparen x\rparen} \\ f(g(x))\text{ = -}\sqrt[3]{15\text{ + 6x}} \end{gathered}[/tex]Related Questions
Solve the radical equation.9-6=27-29What is the extraneous solution to the radical equation?O 1O 9Both 1 and 9 are extraneous solutions to the equation.O There are no extraneous solutions to the equation.
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Given the radical equation:
[tex]q-6=\sqrt[]{27-2q}[/tex]Squaring both sides to eliminate the root.
[tex]\begin{gathered} (q-6)^2=27-2q \\ q^2-12q+36=27-2q \\ q^2-12q+2q+36-27=0 \\ q^2-10q+9=0 \end{gathered}[/tex]Factor the equation to find the roots:
[tex]\begin{gathered} (q-1)(q-9)=0 \\ q-1=0\rightarrow q=1 \\ q-9=0\rightarrow q=9 \end{gathered}[/tex]we will check ( q = 1 and q = 9 ) by substitution into the given equation:
When q = 1
[tex]\begin{gathered} q-6=1-6=-5 \\ \sqrt[]{27-2q}=\sqrt[]{27-2}=\sqrt[]{25}=5 \end{gathered}[/tex]So, ( q = 1 ) is an extraneous solution.
When q = 9
[tex]\begin{gathered} q-6=9-6=3 \\ \sqrt[]{27-2q}=\sqrt[]{27-18}=\sqrt[]{9}=3 \end{gathered}[/tex]So, ( q = 9 ) is the solution of the given equation.
So, the answer will be:
The extraneous solution to the radical equation is 1
Relationship A has a greater rate than Relationship B. This table represents Relationship B.Hours worked2458Amount paid30.4060.8076121.60Which equation could represent Relationship A?Hours worked is represented by x and Amount paid is represented by y.Select each correct answer.y = 15.4xy = 15.2xy = 16.4xy = 14.9x
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ANSWER:
[tex]\begin{gathered} y=15.4x \\ y=16.4x \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We can calculate the equation that represents relationship B, calculating the slope using the data from the table, like this:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{replacing} \\ m=\frac{121.60-30.40}{8-2} \\ m=\frac{91.2}{6} \\ m=15.2 \end{gathered}[/tex]Therefore, the equation of relationship B is:
[tex]y=15.2x[/tex]Therefore, the relationship A, having a greater rate, could be the following:
[tex]\begin{gathered} y=15.4x \\ y=16.4x \end{gathered}[/tex]find x=, if x-3=13 please
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Answer:
[tex]x - 3 = 13 \\ \\ x = 13 + 3 \\ \\ x = 16[/tex]
-3 goes to other side and changes into +3
At t seconds after launch is given by the function… how long will it take the rocket to reach its maximum height? What is the maximum height?
Answers
Given:
The height equation is,
[tex]h(t)=-16t^2+144t+6[/tex]Explanation:
For maximum/minimum of a function, the first derivative of function is 0.
Differentiate the function with respect to x.
[tex]\begin{gathered} \frac{d}{dt}h(t)=\frac{d}{dt}(-16t^2+144t+6) \\ =-32t+144 \end{gathered}[/tex]For maximum and minimum,
[tex]\begin{gathered} -32t+144=0 \\ t=\frac{144}{32} \\ =4.5 \end{gathered}[/tex]So rocket reach it maximum height after 4.5 seconds of launch.
Substitute 4.5 for t in the equation to determine the maximum reached by rocket.
[tex]\begin{gathered} h(4.5)=-16(4.5)^2+144\cdot4.5+6 \\ =-324+648+6 \\ =330 \end{gathered}[/tex]So maximum height of rocket is 330 feet.
14. John rides his motorcycle for 0.2 hours with a constant speed of 68 km/h and then foranother 13 minutes with a constant speed of 102 km/h. What is his average speed for thetotal trip?
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We must calculate the weighted average as follows:
[tex]\begin{gathered} \frac{68\cdot0.2+102\cdot\frac{13}{60}}{0.2+\frac{13}{60}} \\ \frac{13.6+22.1}{0.416}=85.68 \\ \end{gathered}[/tex]Therefore, the average speed is 85.68 km/h
The graph of f(x) = x² is translated to formg(x) = (x-2)2-3.--5-4-3-2-1-2+Which graph represents g(x)?#
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Step 1
Plot the graph of f(x)
[tex]f(x)=x^2[/tex]Step 2
The function of g(x) suggests that f(x);
[tex]\begin{gathered} 1)\text{ it was moved 2 units towards the right} \\ 2)\text{ It was then moved 3 units down} \end{gathered}[/tex]Thus, the graph of g(x) will look like this;
Answer;
How do I get to the answer of this question?
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Okay, here we have this:
Considering the provided information, and that we must identify which of the provided options allow us to determine that the two triangles are similar, we obtain the following:
As the angle-angle similarity says that if two angles of one triangle are congruent with two angles of another triangle, then the triangles are similar.
Finally, we see that the only option that satisfies this statement is option D, since it indicates that two angles of the triangles are congruent. Therefore the correct option is D.
The sum of two numbers is 200 and their difference is 28.What are the two numbers?
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Let us assume the numbers are x and y.
The first part of the question can be written as
[tex]x+y=200\text{ ---------------(1)}[/tex]and the second part can be written as
[tex]x-y=28\text{ --------------(2)}[/tex]From equation 1, we can get a value for y as
[tex]y=200-x\text{ -------------(3)}[/tex]Substitute for y in equation 3 into equation 2:
[tex]x-(200-x)=28[/tex]Expanding and solving, we get
[tex]\begin{gathered} x-200+x=28 \\ 2x=200+28 \\ 2x=228 \\ \therefore \\ x=\frac{228}{2} \\ x=114 \end{gathered}[/tex]Next, we substitute for the value of x into equation 3:
[tex]\begin{gathered} y=200-114 \\ y=86 \end{gathered}[/tex]Therefore, the two numbers are 114 and 86
1. Find the surface area and volume of box where: L = 31.59ft, W = 24.98ft and H = 43.23ft.
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ANSWER
[tex]\begin{gathered} A=6469.28ft^2 \\ V=34113.58ft^3 \end{gathered}[/tex]EXPLANATION
The surface area of the box (rectangular prism) is:
[tex]A=2(LW+WH+LH)[/tex]where L = length; W = width; H= height
Therefore, we have that the surface area of the box is:
[tex]\begin{gathered} A=2\lbrack(31.59\cdot24.98)+(24.98\cdot43.23)+(31.59\cdot43.23)\rbrack \\ A=2\lbrack(789.1182)+(1079.8854)+(1365.6357)\rbrack \\ A=2(3234.6393) \\ A\approx6469.28ft^2 \end{gathered}[/tex]The volume of the box is:
[tex]V=L\cdot W\cdot H[/tex]Therefore, the volume of the box is:
[tex]\begin{gathered} V=31.59\cdot24.98\cdot43.23 \\ V\approx34113.58ft^3 \end{gathered}[/tex]Given Point A, what is the coordinate for A' after the following transformation has occurred?LaTeX: \left(x,y\right)\rightarrow\left(x-5,\:-y+2\right)A (5, 7)Al.
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Given:
The point A(5, 7).
To given transformation is (x-5, -y+2).
So,
The new point is,
[tex]A^{\prime}(5-5,-7+2)=A^{\prime}(0,-5)[/tex]Therefore, the coordinate for A' after the given transformation has occured is A'(0,-5).
Is the expression 4sr2(2rs + 3s) completely factored? Complete the sentence with the correct explanation.
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The expression 4sr²(2rs + 3s) is not completely factored.
How to factor an expression?An algebraic expression consists of unknown variables, numbers and arithmetic operators.
In other words, an expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.
An expression is completely factored when no further factoring is possible.
Therefore, let's check if the expression is completely factored.
4sr²(2rs + 3s)
The expression still have a common factor which is s. This means its not completely factored.
The complete factorisation is as follows;
4sr²(2rs + 3s) = 4s²r²(2r + 3)
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In the diagram below AB⊥CD and bisects ∠MOP.(a) If m∠MOP=130° find m∠POD.(b) If m∠COM=38°, find m∠MOP and m∠POD.
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A
Since AB in perpendicular to CD and bisects mThis can be written as
[tex]m<\text{MOP}+m<\text{COM}+m<\text{DOP}=180\text{ (1)}[/tex]but
[tex]m<\text{COM}=m<\text{DOP}[/tex]then
[tex]m<\text{MOP}+2m<\text{DOP}=180[/tex]pluggin the value of the angle m[tex]\begin{gathered} 130+2m<\text{DOP}=180 \\ 2m<\text{DOP}=180-130 \\ m<\text{DOP}=\frac{50}{2} \\ m<\text{DOP}=25 \end{gathered}[/tex]Therefore the angle m
B
As we mentioned above the angle mthen m
Using equation (1) of part to find the angle m[tex]\begin{gathered} m<\text{MOP}+38+38=180 \\ m<\text{MOP}=180-76 \\ m<\text{MOP}=104 \end{gathered}[/tex]therefore the angle m
A toy factory makes 5.7 x 10³ toys each day.At this rate, how many toys will be made in 9 days?Express the answer in scientific notation.
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First We will put the number of toys per day in simple form:
[tex]5.7\times10^3=5.7\times1000=5700[/tex]Then, to know how many toys will be made in 9 days, let's multiply the number of toys per day by the given number of days:
[tex]5700\times9=51300[/tex]Now We will put the number in scientific notation:
[tex]5.13\times10^4[/tex]Using the slope formula, find the slope of the line through the points (0, 0) and (5, 20).
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The slope formula for 2 points is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(5,20) \end{gathered}[/tex]By substituting these values into the slope formula, we get
[tex]\begin{gathered} m=\frac{20-0}{5-0} \\ m=\frac{20}{5} \\ m=4 \end{gathered}[/tex]therefore, the slope is 4.
find the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval. Leave your answer in terms of n, the number of subintervals.
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Explanation
The area under a curve between two points can be found by doing a definite integral between the two points
Step 1
a) set the intergral
[tex]\begin{gathered} limits:\text{ 1 and 2} \\ function:\text{ f\lparen x\rparen=6-2x} \end{gathered}[/tex]hence
[tex]Area=\int_1^26-2x[/tex]Step 2
evaluate
let ; numbers of intervals
[tex]\begin{gathered} \begin{equation*} \int_1^26-2x \end{equation*} \\ \int_1^26-2x=\lbrack6x-x^2\rbrack=(12-4)-(6-1)=8-5=3 \end{gathered}[/tex]therefore, the area is
[tex]area=3\text{ units }^2[/tex]
I hope this helps you
10. The perimeter of the rectangle to the right is 28 ft. What is the value of x?
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ANSWER
x = 9
EXPLANATION
We have the rectangle with width 3 ft and length (2 + x) ft.
The perimeter of the triangle is 28 ft.
The perimeter of a rectangle is given as:
P = 2(L + W)
where L = length
W = width
Therefore, we have that:
28 = 2[(2 + x) + 3]
28 = 2(2 + x + 3) = 2(x + 5)
28 = 2x + 10
=> 2x = 28 - 10 = 18
Divide through by 2:
2x/2 = 18/2
x = 9
That is the value of x.
Construct triangle ABC if AB = 5cm, BC=5cm and AC=3cm. What type if triangle does this create
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The type of triangle is isosceles.
Picture
the circumference of a circular garden is 109.9 feet. what is diameter of the garden? use 3.14 and do not round your answer.
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The circumference of a circle is given by the formula:
[tex]C=\pi d[/tex]Where d is the diameter of the circle.
If the circumference is 109.9 ft, we have:
[tex]\begin{gathered} 109.9=3.14\cdot d \\ d=\frac{109.9}{3.14} \\ d=35\text{ ft} \end{gathered}[/tex]So the diameter of the garden is 35 feet.
Using the figure below as a starting point, identify the figure in which lines to l are drawn through points A, B, C, and D.
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SOLUTION
We want to find the figure in which lines perpendicular to l are drawn through points A, B, C, and D
The correct figure will be the one in which a vertical line is drawn across each of points A, B, C and D.
Looking at this, we can see that the correct answer is the first option
Answer:
a
Step-by-step explanation:
a right triangle is shownwhich angle measure is closet to x
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We know that
[tex]\cos (x)=\frac{20}{24}[/tex]Solving for x,
[tex]\begin{gathered} x=\cos ^{-1}(\frac{20}{24}) \\ \Rightarrow x=33.56 \end{gathered}[/tex]x is aproximately 33.56
The graph of a quadratic function with vertex (-1,4) is shown in the figure below. Write the domain and range in interval notation.
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Background:
• Domain,: a set of all possible values of the independent variable (,x,, in this case).
,• Range,: a set of all possible values of the dependent variable (,y,, in this case), after substituting the domain.
Based on the arrows of the function, we can conclude that those extend to infinity (negative and positive).
Also, based on the coordinates of the vertex given we can see that the first value of y is 4.
Answer:
• Domain
[tex](-\infty,\infty)[/tex]• Range
[tex](4,\infty)[/tex]A certain loan program offers an interest rate of 4%, compounded continuously. Assuming no payments are made, how much would be owed after six yearson a loan of I300Do not round any intermediate computations, and round your answer to the nearest cent
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In order to calculate how much will be owed, we can use the formula below for interest compounded continuously:
[tex]A=P\cdot e^{rt}[/tex]Where A is the final amount after t years, P is the initial amount and r is the interest rate.
So, using P = 1300, r = 0.04 and t = 6, we have:
[tex]\begin{gathered} A=1300\cdot e^{0.04\cdot6}\\ \\ A=1300\cdot e^{0.24}\\ \\ A=1652.62 \end{gathered}[/tex]Therefore the amount owed after 6 years is $1652.62.
write a function to describe the following scenario.a garden watering bucket has 3,000 mm of water in it but there is a hole that is leaking 18 mm every minute how much water remains in the container after certain number of minutes? y= ? - __x
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The bucket has 3000 milliliters of water.
It leaks 18ml per minute.
Let "y" represent the remaining water after a certain number of minutes and "x" represent the number of minutes passed.
"3000ml" represents the y-intercept of the function (the amount of water in the bucket at x=0 minutes)
and "-18ml" represents the amount of water that has leaked after a certain amount of time, and is the slope of the function. The value is negative because the volume of the bucket is decreasing as time passes.
Then the function will be
[tex]y=3000-18x[/tex]I tested positive for covid yesterday so i have no motivation to do this problem. Please don’t be slow when answering, I am every tired.
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The value of sector KL is 52
If JM and KN are two diamters of the circle,
then they intersect at the center
The sector JK and NM are equal
Thus,
The sector JN and KM are also equal
sector KM = sector KL + sector LM
Sector JN = Sector KM
sector JN = sector KL + sector LM
125 = 6x + 4 + 8x + 9
125 = 14x + 13
14x = 125 - 13
14x = 112
x = 8
sector KL = 6x + 4
= 6(8) + 4 = 48 + 4 = 52
Therefore, the sector KL is 52
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I need help with this problem if anyone want to help me please do thanks
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Solve e from the equation by substraction 96 to both sides of the equal sign:
[tex]undefined[/tex]help me please!! (10 pts)
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(2,3) (4,6) (6,9) (8,12) is the set of ordered pair lie on the function that is direct proportion.
Direct proportion is mathematical comparison between two variable
when one increase also increase the other or one decrease also decreases the other then , they are direct proportion.
In direct proportion , the ratio of these variable remains same no matter what.
The following are the set of ordered pair,
a. (2,6) (4,8) (6,10) (8,12)
calculating ratio,
[tex]\frac{2}{6} = \frac{1}{3} \neq \frac{4}{8} = \frac{1}{2}[/tex]
Ratio is changing so, ordered pair are not direct proportion
b. (2,2) (4,2) (6,2) (8,2)
ratios = [tex]\frac{2}{2} =1 \neq \frac {4}{2} = 2[/tex]
Ratio is different
c. (2,1) (4,3) (6,5) (8,7)
Ratio is different , the ordered set is not direct proportion
d. (2,3) (4,6) (6,9) (8,12)
ratios = [tex]\frac{2}{3}=\frac{4}{6}[/tex]
Ratios are same in entire ordered set
Hence , (2,3) (4,6) (6,9) (8,12) is a direct proportion.
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Consider the scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5800. By 2012 the population had dropped to 4,600. Assume the trend continues predict the population in 2016.
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Given:
In 2010 the population was 5800.
2012 the population had dropped to 4,600.
Let 't=0' be the year 2010.
P(t) represents the year population of the town t years after 2010.
Slope of a function P(t) is
[tex]\begin{gathered} m=\frac{4600-5800}{2012-2010} \\ m=-600 \end{gathered}[/tex]Population of town t years after 2010.
[tex]P(t)=-600(t)+5800[/tex]Population in the year 2016 that is t=6
[tex]\begin{gathered} P(6)=-600(6)+5800 \\ =2200 \end{gathered}[/tex]Population in the year 2016 is 2200
WILL GIVE BRAINLEST! I NEED HELP ASAPPP! The highest score on an Algebra test was 40 points more than the lowest. When added together, the lowest and highest score was 152. Write an equation to find the highest score, then solve.
A= x + x + 40 = 152; 56
B= x + x = 152; 76
C= x + x - 40 = 152; 96
D= x + x + 40 = 152; 96
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Answer:
D is correct.
Step-by-step explanation:
Let x be the lowest score. Then x + 40 is the highest score.
[tex]x + x + 40 = 152[/tex]
[tex]2x + 40 = 152[/tex]
[tex]2x = 112[/tex]
[tex]x = 56[/tex]
[tex]x + 40 = 96[/tex]
Lowest score is 56, highest score is 96.
Find a quadratic function of the form y=ax^2 that passes through the point (-2,-8)
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Solution
[tex]\begin{gathered} \text{ since }y=ax^2 \\ \\ \text{ at }(-2,-8) \\ \\ \Rightarrow-8=a(-2)^2 \\ \\ \Rightarrow-8=a(4) \\ \\ \Rightarrow a=-\frac{8}{4}=-2 \\ \\ \Rightarrow y=-2x^2 \end{gathered}[/tex]The quadratic equation is
[tex]y=-2x^2[/tex]Hello I need help with this I’m in a rush thanks
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Recall that:
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)},[/tex]and that the domain of a rational function consists of all real numbers such that the denominator is different from zero.
If f(x)=5x+3 and g(x)=4x-5 we get that:
[tex]\frac{f}{g}(x)=\frac{5x+3}{4x-5}\text{.}[/tex]The domain of the above rational function is:
[tex]\begin{gathered} \mleft\lbrace x|g(x)\ne0\mright\rbrace=\lbrace x|4x-5\ne0\rbrace \\ =\lbrace x|4x\ne5\rbrace=\lbrace x|x\ne\frac{5}{4}\rbrace\text{.} \end{gathered}[/tex]Answer: Last option.