If f(x) = 5x - 2 and g(x) = 1 - 2x, find (fg)(x).I am not sure if my answer is right please help me
Given:
f(x) = 5x - 2
g(x) = 1 - 2x
Let's find (fg)(x).
To solve the function operation, we have:
(fg)(x) = f(x) * g(x)
Thus, we have:
[tex](fg)(x)=(5x-2)(1-2x)[/tex]Solving further:
Expand using FOIL method, then apply distributive property
[tex]\begin{gathered} (fg)(x)=5x(1-2x)-2(1-2x) \\ \\ (fg)(x)=5x(1)+5x(-2x)-2(1)-2(-2x)_{} \\ \\ (fg)(x)=5x-10x^2-2+4x \\ \\ (fg)(x)=+5x+4x-10x^2-2 \\ \\ (fg)(x)=9x-10x^2-2^{} \end{gathered}[/tex]ANSWER:
[tex]9x-10x^2-2^{}[/tex]Identify the equation without applying a rotation of axes.x squared +10xy+25y squared-2x-4y+10=0a. parabolab. ellipsec. hyperbolad. circle
Solution
We are given the equation
[tex]x^2+10xy+25y^2-2x-4y+10=0[/tex]We will first simplify the equation
[tex]\begin{gathered} x^{2}+10xy+25y^{2}-2x-4y+10=0 \\ \left(x+5y\right)^2-2\left(x+y\right)+10=0 \\ (x+5y)^2=2(x+y)-10 \end{gathered}[/tex]We draw the graph
From the graph, one can see that this is a rotated parabola
Correct answer is a Parabola
Option A
xy12364468710 a. Construct a scatterplot. b. Is there a linear association, nonlinear association, or no association? c. Compute r. d. On the basis of the scatterplot and r, determine the strength of the association? Explain.
SOLUTION:
(a) From the given table, we are to construct a scatterplot.
(b) There is a strong linear association because all the points align themselves in a near perfect straight line.
(c) To Compute r;
(d) We are to determine the strength of the association;
Because r = 0.9934 which is very close to 1.0, so we conclude that the strength of the association is very strong.
What is the mode of the following numbers?8, 1, 2, 6, 1, 4
Adams house, the local park, and the nearest hospital are mapped on a coordinate plane. what's the distance between Adams house and the hospital?
The distance between two points is given by:
[tex]d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]From the plane we notice that Adam's house is located in the point (-4,2) and the hospital in the point (5,7).
Plugging this values in the formula we get:
[tex]\begin{gathered} d(A,H)=\sqrt[]{(7-2)^2+(5-(-4))^2} \\ =\sqrt[]{(5)^2+(9)^2} \\ =\sqrt[]{25+81} \\ =\sqrt[]{106} \end{gathered}[/tex]Therefore the distance between Adam's house and the hospital is the square root of 106 and the answer is D.
Corresponding Angles are congruent.Which angle corresponds with « 2?756 4.36.268 21152414.14 [?]A
Corresponding angles are a pair of equal angles that are found in the same relative positions of the intersection of a transversal and a pair of parallel lines.
Based on this definition, <2 is corresponding/congruent with <6
In the same vein, <3 = <7, <8 = <4, <5 = <1.
as shown above a classic deck of card is made up of 52 cards suppose one card is selected at random and calculate the following probability
Given a classic deck of cards made up of 52 cards
Made up of 13 spades, hearts, diamonds and clubs each,
The formula of Probabaility is given below as,
[tex]\text{Probabilty}=\frac{\operatorname{Re}quired\text{ outcome}}{Possible\text{ outcome}}[/tex]Where the Possible outcome = 52
The probability that a 6 of diamonds is selected is,
[tex]\begin{gathered} \text{required outcome = 1} \\ \text{Probability of a 6 of diamonds=}\frac{1}{52} \end{gathered}[/tex]Probability that a 6 of diamonds is selected is 1/52
The probability that a heart or a diamond is selected,
[tex]\begin{gathered} Probabilty\text{ of a heart P}(H)\text{=}\frac{13}{52} \\ \text{Probability of a diamond=}\frac{13}{52} \\ \text{Probability of a heart or a diamond=}\frac{13}{52}+\frac{13}{52}=\frac{1}{4}+\frac{1}{4}=\frac{1}{2} \end{gathered}[/tex]Probability that a heart or a diamond is selected is 1/2
Probability that a number smaller than 4 (counting the ace as 1) is selected is,
[tex]\begin{gathered} \text{Probability of picking a ace=}\frac{4}{52} \\ \text{Probability of picking a 2=}\frac{4}{52} \\ \text{Probability of picking a 3=}\frac{4}{52} \\ \text{Probability of picking a number smaller than 4=}\frac{4}{52}+\frac{4}{52}+\frac{4}{52}=\frac{3}{13} \end{gathered}[/tex]Probability that a number smaller than 4 (counting the ace as 1) is selected is 3/13
Select the correct answer.What is the area of STR?A. 30 square feetB. 34.5 square feetC. 57.5 square feetD. 60 square feet
Hello!
To calculate the area of a triangle, we must use the formula below:
[tex]\mathrm{Area=\dfrac{base\times height}{2}}[/tex]In this triangle, we have:
• base,: 6 feet
,• height,: 10 feet
Knowing it, let's replace the formula with the values:
[tex]\mathrm{Area=\dfrac{6\times10}{2}}=\frac{60}{2}=30\text{ }\mathrm{feet^2}[/tex]Answer:A. 30 square feet
Vanessa cycled from her home to the beach at a speed of 18 meters per second The distance between her home and the beach is 1,350 m. How long did she ta to cycle from her home to the beach? speed + distance=time
Vanessa took 75 sec time to cycle from her home to the beach
What is Speed?Speed is the time rate at which an object is moving along a path
Speed =Distance/time
Given,
Vanessa cycled from her home to the beach at a speed of 18 meters per second
Speed=18 m/s
The distance between her home and the beach is 1,350 m.
Distance=1,350 m
Now we need to find the time for Vanessa to cycle from her home to the beach
Time=?
We have formula of speed
speed=Distance/time
Time=Distance/speed
Time=1350/18
=75 sec
Hence Vanessa took 75 sec to cycle from her home to the beach
To learn more on Speed click:
https://brainly.com/question/28224010
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Three Turtles are racing . Abe the turtle's distance is represented by the green line, Benji the turtle's distance is represented by the red line, and Carter the turtle's distance is represented by the bule line. Use the graph to answer the following questions.
Using the graph we can see that Benji (the red line) goes 50 feet far, also by looking at the graph we see tht Carter (the blue line) takes 240 seconds to travel 80 feet.
If they are racing I would pick the one who takes less time to travel more distance, by the graph we see that Carter is faster than Benji and Abe.
Solve the equation. 1 / 3X - 9 = -12
x=-9
Explanation
[tex]\frac{1}{3}x-9=-12[/tex]
Step 1
add 9 in both sides
[tex]\begin{gathered} \frac{1}{3}x-9=-12 \\ \frac{1}{3}x-9+9=-12+9 \\ \frac{1}{3}x=-3 \end{gathered}[/tex]Step 2
multiply both sides by 3
[tex]\begin{gathered} \frac{1}{3}x=-3 \\ \frac{1}{3}x\cdot3=-3\cdot3 \\ x=-9 \end{gathered}[/tex]I hope this helps you
Answer:
x=-9
Step-by-step explanation:
Solve for X by simplifying both sides of the equation, then isolating the variable. So, pretty much the other dude is right.
What is the type of dilation and what is the scale factor?
We have that in the first one the dilation is a reduction and the scale factor is 1/2 with the scale factor we prove that the dilation is a reduction.
In the second one we have that the dilation is an enlargement and the sclae factor is 3 with the scale factor we prove that the dilation is an enlargement.
We can find the sacle factor with the next equation
[tex]scale\text{ factor = }\frac{image}{preimage}[/tex]you can take a side or the area of the figures and find the scale factor, for example in the first one we can do with one side od the triangle
[tex]\frac{image}{preimage}=\frac{4}{8}=\frac{1}{2}\text{.}[/tex](B) How many participants selected an image that is associated with being indeclsive
Answer:
8
Explanation:
The images that are associated with the trait 'indecisive' are 3 and 5.
• The frequency of the image 3 = 5
,• The frequency of the image 5 = 3
Add the two:
[tex]5+3=8[/tex]Therefore, the number of participants that selected an image that is associated with being indecisive is 8.
Hello! I'm feeling unsure on this answer. Can we please review?
From the given graph, let's identify the solution.
The solution will be the point(s) where both lines meet.
In this given graph, the lines meet at one point.
So we have just one solution.
From the graph, the point of intersection(point where both line meet) is:
(x, y) ==> (-1, -2)
Therefore, the solution of the graphed system is:
(-1, -2)
ANSWER:
(-1, -2)
it's easier if I show you the question I'm not good with math
Find the value of f(-2);
[tex]\begin{gathered} f(x)=\frac{1}{2}x^2 \\ f(-2)=\frac{1}{2}(-2)^2 \\ f(-2)=\frac{1}{2}(4) \\ f(-2)=2 \end{gathered}[/tex]The answer is 2
f(-2) = 2
Find the formula for the geometric sequence 1, 5, 25, 125,...OA4, = 5-1OB. 0,= 5.50-1OC. a, = (-2)"-1D. 0,= -2"-1Reset Selection
Given: geometric series 1 , 5, 25 , 125,.................
Find: formula for the geometric series
Explanation: the general formula for the series is
[tex]\begin{gathered} ar^{n-1} \\ 1.5^{n-1} \\ 5^{n-1} \end{gathered}[/tex]Final answer:
[tex]a_n=5^{n-1}[/tex]I need help seeing how this works out because what I am doing is not right
We will have the following:
AB and CD related in terms of x and y will be:
[tex]\begin{gathered} AB=CD\Rightarrow x+y=2x-y-2 \\ \\ \Rightarrow2y=x-2\Rightarrow y=\frac{x}{2}-1 \end{gathered}[/tex]So, the equation that relates AB and CD is:
[tex]y=\frac{x}{2}-1[/tex]BC and DA in terms of x and y is:
[tex]\begin{gathered} BC=DA\Rightarrow x+2y=3x-3y+2 \\ \\ \Rightarrow5y=2x+2\Rightarrow y=\frac{2}{5}x+\frac{2}{5} \end{gathered}[/tex]So, the equation that relates BC and DA is:
[tex]y=\frac{2}{5}x+\frac{2}{5}[/tex]Now; we determine the values of x & y as follows:
[tex]\begin{gathered} \frac{x}{2}-1=\frac{2}{5}x+\frac{2}{5}\Rightarrow\frac{1}{10}x=\frac{7}{5} \\ \\ \Rightarrow x=14 \end{gathered}[/tex]Then:
[tex]y=\frac{(14)}{2}-1\Rightarrow y=6[/tex]So, the values are:
[tex]\begin{gathered} x=14 \\ \\ y=6 \end{gathered}[/tex]Gillian works from 23 to 33 hours per week during the summer. She earns $12.50 per hour. Her friendEmily also has a job. Her pay for t hours each given is given by the function e(t) = 13t, where 18 st 3 28.Find the domain and range of each function. Then compare their hourly wages and the amount they earnper week.
The domain for g(t) is [23,33]
The domain for e(t) is [18,28]
The range for g(t) is [287.5,412.5]
The range for e(t) is [234,364]
f(x)=4x^2-17x + 3What is the value the discriminant F?How many distinct real numbers zeros does F have?
Answer:
• D=249
,• Two real numbers zeros
Explanation:
Given the quadratic function:
[tex]f\mleft(x\mright)=4x^2-17x+3[/tex]a=4, b=-17, c=3
The discriminant is obtained using the formula:
[tex]\begin{gathered} D=b^2-4ac \\ =(-17)^2-4(4)(3) \\ =289-48 \\ =249 \end{gathered}[/tex]Since the discriminant is greater than 0, the equation has 2 real solutions (or zeros).
Note:
• If D<0, the equation has 0 real solutions.
,• If D=0, the equation has 1 real solution.
Monica wants to know how many students take the bus home from Morton Middle School. She handed out 100 surveys and 86 said they take the bus home and rest were car-riders. If 1200 students attend Morton Middle School, what is Monica's estimate for the number of students who take the bushome? How many students take the bus home?
Let the number of students who take the bus home be x.
Determine the value of x as ratio of number of students who take the bus home to total number of student is equal.
[tex]\begin{gathered} \frac{86}{100}=\frac{x}{1200} \\ x=\frac{86\cdot1200}{100} \\ =1032 \end{gathered}[/tex]Answer: 1032 students.
Find the volume of this object.Use 3 for π.Volume of a CylinderV= πr²h6 in8 in12 in V[?]in³310 in
ANSWER
V = 366 in³
EXPLANATION
This object is composed of two cylinders. The total volume of the object is the sum of the volumes of the cylinders.
As stated in the problem, the volume of a cylinder is given by,
[tex]V=\pi r^2h[/tex]Where r is the radius of the base and h is the height of the cylinder.
For the tallest cylinder, the diameter is 6 in - so the radius is 3 in, and the height is 8 in. Using 3 for π, the volume is,
[tex]V_1=3\cdot3^2in^2\cdot8in=216in^3[/tex]For the shortest cylinder, the diameter is 10 in, so the radius is 5 in, and the height is 2 in. The volume of this cylinder is,
[tex]V_2=3\cdot5^2in^2\cdot2in=150in^3[/tex]And the total volume of the object is,
[tex]V=V_1+V_2=216in^3+150in^3=366in^3[/tex]Hence, the volume of the object is 366 cubic inches.
I need help with this question... which one is the correct choice
Given:
The image of the point (-2, 3) under translation T is (3, -1)
So, we will find the rule of the translation T
[tex]\begin{gathered} (-2+h,3+k)=(3,-1) \\ -2+h=3\rightarrow h=5 \\ 3+k=-1\rightarrow k=-4 \end{gathered}[/tex]so, the rule of translation is: shift 5 units right and 4 units down
[tex](x,y)\rightarrow(x+5,y-4)[/tex]Now, we will find the image of the point (4, 2)
So,
[tex](4,2)\rightarrow(4+5,2-4)=(9,-2)[/tex]So, the answer will be (9, -2)
I need help on this problem getting the answers do you know what they are ??????????
• 16.
Common difeference:
Is the difference between consecutive numbers in an arithematic sequence
18 -20 = -2
16-18 = -2
14-16 = -2
Common difference = -2
• 17.
Explicit rule: Use the arithematic sequence formula
an = a1 +(n-1 ) d
Where:
a1 = first term = 20
d= common difference = -2
Replacing:
an = 20 + (n-1)-2
• 18.
Replace n by 11
an = 20 + (11-1 ) -2
an = 20 + (10)-2
an= 20 - 20
an = 0
Amount to be paid = 0 (zero)
How many square feet are there in 288 square inches (1 foot=12 inches)
Given:
1 foot = 12 inches
So, 288 square inches are:
[tex]288\text{ in}^2=288\text{ in}^2\times(\frac{1\text{ ft}}{12\text{ in}})^2[/tex]Solve:
[tex]288\text{ in}^2\times\frac{1^2\text{ ft}^2}{12^2\text{ in}^2}=288\text{ in}^2\times\frac{1\text{ ft}^2}{144\text{ in}^2}[/tex]Simplify:
[tex]2\text{ ft}^2[/tex]Answer: 2 square feet
Question 3 of 10
Which of the following is equal to 7%?
O A. 17
OB. 17.3
O C. 73
OD. 17
Since the exponent of 7 is 1/3, when this is converted to radical expression, the denominator of the exponent becomes the root of the radical. Hence,
[tex]7^{\frac{1}{3}}\Leftrightarrow\sqrt[3]{7}[/tex]Therefore, 7^1/3 is equivalent to the cube root of 7. (Option A)
Find the equation in slope-intercept form of the line passing through the points with the given coordinates.(5,2), (5,6)
Given,
The line is passing through the points (5,2), (5,6).
The standard equation of line passing through two points is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Substituting the values of coordinates then,
[tex]\begin{gathered} y-2_{}=\frac{6_{}-2_{}}{5_{}-5_{}}(x-5) \\ y-2=\frac{4_{}}{0_{}} \\ y-2=\infty\mleft(x-5\mright) \\ \frac{y-2}{\infty}=x-5 \\ 0=x-5 \\ x=5 \end{gathered}[/tex]Hence, the equation of line passing through point (5,2) and (5,6) is x=5.
How to find the value of x so that the function has a given value
we have the function
f(x)=6x
f(x)=-24
substitute the given value of f(x)
-24=6x
solve for x
divide both sides by 6
-24/6=6x/6
simplify
-4=x
rewrite
x=-4a rectangular Park is 172 yards long and 92 yd wide. what is its perimeter?
A rectangular Park is 172 yards long and 92 yd wide :
The general expression for the perimeter of the rectangle = 2( Length + Breadth)
In the given rectangular park :
Length = 172 yd
Breadth = 92 yd
[tex]\begin{gathered} \text{ Perimeter of rectangle = 2(Length + Breadth)} \\ \text{ Perimeter of rectangle = 2(172+92)} \\ \text{ Perimeter of rectangle = }2(264) \\ \text{ Perimeter of rectangle = }528yards^2 \end{gathered}[/tex]The perimeter of rectangular park is 528 yards²
Answer : 528 yards²
solve quadratic by completing the squarex^2 + 12x + 23 = 0which form do i use and solve(x+___)^2(x - ___) ^2solutionx = ___
Quadratics are in the general form:
[tex]ax^2+bx+c[/tex]For completing the square, we use:
[tex](x+\frac{b}{2})^2=c+(\frac{b}{2})^2[/tex]Now, we have:
[tex]\begin{gathered} (x+\frac{12}{2})^2=-23+(\frac{12}{2})^2 \\ (x+6)^2=-23+(6)^2 \\ (x+6)^2=13 \end{gathered}[/tex]From here, we can easily solve for x with a little algebra. Shown below:
[tex]\begin{gathered} \sqrt[]{(x+6)^2}=\pm\sqrt[]{13} \\ x+6=\pm\sqrt[]{13} \\ x=-6\pm\sqrt[]{13} \end{gathered}[/tex]The answer(s) are:
[tex]\begin{gathered} x=-6+\sqrt[]{13} \\ x=-6-\sqrt[]{13} \end{gathered}[/tex]For further clarification
Form:
[tex](x+\frac{12}{2})^2=13[/tex]F(x) = (x + 3)^2 Graphing
Explanation:
F(x) = (x + 3)^2
let y = F(x)
y = (x + 3)^2
Graphing the function:
we need to set values for x and get corresponding values of y
Assigned values:
x =