You have the following data set:
x 1 0 -3
y 5 4 1
Where y is a function of x. In order to translate the previous function 2 unitd downward, you take into account that you subtract 2 units to the given values for y. Then, you have:
y (5-2) (4-2) (1-2)
which becomes:
y 3 2 -1
Finally, the given table becomes:
x 1 0 -3
y 2 2 -1
Composition of Functions and Inverses:Question 7Which expression represents f(f(x)) if f(x) = x2 – 1? A. 2x ^2-2 B. X^4-2x^2+1C. XD. X^4-2x^2
To solve the question, we will follow the steps below:
[tex]f(x)=x^2-1[/tex]To find f(f(x)), we will simply replace x by x² - 1 in the function x² - 1
That is:
f((fx)) = (x²-1)² - 1
Then we open the parenthesis
f(f(x)) = (x² - 1)(x² -1) - 1
=x²(x²-1)-1(x²-1) - 1
= x⁴ - x² - x² + 1 - 1
= x⁴ - 2x²
So the correct option is option D. which is x⁴ - 2x²
A test requires that you answer either part A or part B. Part A consists of 6 true-false questions, and part B consists of 6 multiple-choice questions with one correct answer out of six. How many different completed answer sheets are possible?
If a test requires that you answer either part A or part B. Part A consists of 6 true-false questions, and part B consists of 6 multiple-choice questions with one correct answer out of six. 46720 different completed answer sheets are possible.
What is Combination?A combination is a mathematical technique that determines the number of possible arrangements in a collection of items.
A test requires that you answer either part A or part B.
Part A consists of 6 true-false questions.
i.e. there are 2 choices to answer each question
Now, the number of ways to answer Part A : 2⁶=64 (1)
Part B consists of 6 multiple-choice questions with one correct answer out of five.
i.e. there are 6 choices to answer each question.
Now, the number of ways to answer Part B : 6⁶=46656
Now, the number of different ways to completed answer sheets are possible= 46656+64
=46720
Hence 46720 different completed answer sheets are possible.
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Rewrite the expression 26 + 8 as the product of the GCF (greatest common factor) and a sum. Then, simplify the expression. Show all of your steps.
The expression 26+8 as the product of the GCF and a sum will be; 2(13+4).
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that we have the expression as 26+8
We have to find the greatest common factor of the numbers 26 and 8.
26 = 2 × 13
8 = 2 × 2 × 2
Then Multiply all the prime factors, both numbers share in order to determine the GCF:
Therefore, GCF = 2
Now we can write the expression as;
26 + 8
=2(13 + 4)
=2×17
=34
Hence. the required expression will be; 2(13 + 4).
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The ratio of children to teachers at a preeschool is 14:5 .How many children are there at the preschool if there are 30 teachers
Answer:
84
Step-by-step explanation:
5*6=30
14*6=84
If you need further explanation just tell me!
Work Shown:
(14 children)/(5 teachers) = (x children)/(30 teachers)
14/5 = x/30
14*30 = 5*x
420 = 5x
5x = 420
x = 420/5
x = 84
Solve for xF(x)=2x+10
So:
f(x) = 2x + 10
To solve for x, we are going to subtract 10 on both sides of the equation:
f(x) - 10 = 2x + 10 - 10
f(x) - 10 = 2x
Then, dividing by 2, we get:
[tex]\begin{gathered} \frac{f(x)-10}{2}=\frac{2x}{2} \\ \frac{1}{2}f(x)-5=x \end{gathered}[/tex]Answer:
[tex]x=\frac{1}{2}f(x)-5[/tex]
Bharat types 20 words/min. How many words can he type in each length of time? a) 5 min b) 30 min c) 23 min
Bharat can type words in lengths of time as 100 words, 600 words, and 460 words in 5 minutes, 30 minutes, and 23 minutes respectively.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
* Multiplication operation: Multiplies values on either side of the operator
For example 12×2 = 24
Bharat types 20 words per minute which are given in the question.
To determine the number of words can he type in each length of time
We have to multiply the time by his typing speed.
The number of words that can be typed by Bharat in 5 minutes :
⇒ 20 × 5
⇒ 100
The number of words that can be typed by Bharat in 30 minutes :
⇒ 20 × 30
⇒ 600
The number of words that can be typed by Bharat in 23 minutes :
⇒ 20 × 23
⇒ 460
Therefore, He can type words in lengths of time as 100 words, 600 words, and 460 words in 5 minutes, 30 minutes, and 23 minutes respectively.
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Reduce the vector shown to its (X) horizontal component. (Round your final answer to two decimal places.)
The horizontal component of the provided vector is 100cos35 or 8.19 after reducing.
What is a vector?It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.
It is given that:
The vector is shown in the picture.
Let's draw an imaginary line from the tail of the vector and it makes the angle between the imaginary line and the vector 35 degrees.
The horizontal component of the vector:
H = 100cos35
The value of the cos35 is 0.819
H = 10(0.819)
H = 8.19
Thus, the horizontal component of the provided vector is 100cos35 or 8.19 after reducing.
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Determine whether the values in the table
are best modeled by a linear or nonlinear
function. (Lesson 2-2)
X
-2
0
2
4
6
y
6555o
Answer: nonlinear function
Step-by-step explanation:
The rate at which y increases is not constant with respect to x.
- A fireworks show starts at 9:00 P.M.
Orange rockets burst every 1.5 minutes,
green rockets burst every 30 seconds,
and silver showers burst every minute. [
What time is it when all three burst at
the same time?
A. 9:03 P.M.
C. 9:10 P.M.
BLcatc21
B. 9:05 P.M.
D. 9:25 P.M.
what 3 factors were used to create this product game board with the numbers 4 6 9 14 49?
What product is missing?
By using 3 factors 2, 3, and 7, if we create a product game board with the numbers 4 6 9 14 49 then the missing product is 21.
To solve this problem we have to follow a few steps. First, we should know about factors.
What are the factors?
Factors of a number are such numbers as they can divide the whole number without remaining.
Example: The factors of 24 are 1, 2, 3, 4, 6, 8, and 12.
Now we have to analyze the given numbers,
4 = 2× 2
6 = 2× 3
9 = 3× 3
14 = 2× 7
49 = 7× 7
The factors are 2, 3, and 7. Therefore, the missing product is, 3× 7= 21
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What is the equation of this line?
The equation of this line is y =4.
What is the Equation of line?The equation y = mx + c, where m is the gradient of the line (how steep the line is), and c is the y-intercept, is the universal equation of any straight line (the point in which the line crosses the y-axis).In the linear equation y = mx + c, the variables x and y correspond to points on the line.We get a result for y when we enter a value for x into the equation y = mx + c.In light of the fact that y depends on the value of x, x is an independent variable and y is a dependent variable.From the given graph we can infer that line A is a horizontal line
It can be expressed in the form y = constant
Hence the equation of this line is y = 4
Similarly, from the given graph we can infer that line B is a vertical line
It can be expressed in the form x = constant
Hence the equation of this line is x = 8
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A clothing designer is selecting models to walk the runway for her fashion show.
The designer prefers models that are no more than 3 inches away from being 5'10".
Since 5'10" is the same as 70 inches, write an inequality - in terms of inches - that
could be used to determine if a model's height is within the designer's preferred height
range.
Using proportions, the inequality that could be used to determine if a model's height is within the designer's preferred height range is of:
67 inches ≤ Height ≤ 73 inches.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication and division, from the unit rates in the context of the problem.
One example of application of proportions is for conversion of units, as there are rates for each unit.
In the context of this problem, the rate used is:
1 feet = 12 inches.
Hence the measure of 5'10" = 5 feet and 10 inches is given by:
5 x 12 + 10 = 60 + 10 = 70 inches.
The heights that are within 3 inches of 70 inches are given by:
70 - 3 = 67 inches.70 + 3 = 73 inches.Hence the inequality that models the situation is:
67 inches ≤ Height ≤ 73 inches.
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Solve the following equation:
4x - 3 = 12 + x
A x = 45
B x = 15
C x = 5
D x = 3
Answer:
C x = 5
Step-by-step explanation:
4x - 3 = 12 + x
Add 3 on both sides:
4x - 3 + 3 = 12 + 3 + x
4x = 15 + x
Subtract x from both sides:
4x - x = 15 + x - x
3x = 15
x = 15/3
or
x = 5
Answer:
[tex]4x - 3 = 12 + x \\ \\ ➪4x - x = 12 + 3 \\ \\ ➪3x = 15 \\ \\ ➪x = \frac{15}{3} = 5[/tex]
C] x = 5 Is ᴛʜᴇ ʀɪɢʜᴛ ᴀɴsᴡᴇʀ.
Find the expected value of the winningsfrom a game that has the followingpayout probability distribution:Payout ($) 1 2 5 8 10Probability 0.35 0.2 0.1 0.2 0.15Expected Value = [?]Round to the nearest hundredth.
On the frequency table, you can see the payouts of the lottery and the corresponding probabilities for every payout. To determine the expected payout, you have to multiply each possible price by its corresponding probability and add the results, following the formula:
[tex]E(X)=\sum ^{10}_{n\mathop=1}x_i\cdot P(x_i)[/tex][tex]\begin{gathered} E(X)=(1\cdot0.35)+(2\cdot0.20)+(5\cdot0.10)+(8\cdot0.20)+(10\cdot0.15) \\ E(X)=0.35+0.4+0.5+1.6+1.5 \\ E(X)=4.35 \end{gathered}[/tex]The expected payout for the lottery is $4.35
Consider parallelogram VWXY below.Use the information given in the figure to find mZY, mZYVX, and x.म7503903xmZY - •mZYVX - _х$12
In a parallelogram, opposite angles are congruent, this means that,
[tex]\begin{gathered} m\angle Y=m\angle W \\ m\angle Y=75 \end{gathered}[/tex]Similarly, in a parallelogram, we have that angles in green are congruent because they are alternate interior angles:
This implies that
[tex]m\angle YVX=39[/tex]On the other hand, opposite sides are congruent, this implies that
[tex]3x=12[/tex]Then, by moving 3 to the right hand side, we get
[tex]\begin{gathered} x=\frac{12}{3} \\ x=4 \end{gathered}[/tex]Therefore, the answers are
[tex]\begin{gathered} m\angle Y=75 \\ m\angle YVX=39 \\ x=4 \end{gathered}[/tex]Write the equation of the line with a slopeof -3 that passes through (-5,20)
The equation of the line which passes through point (-5,20), with a slope of -3 is y = -3x + 5.
How yo determine the equation of line from a point and slope?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Slope m = -3Point ( -5,20 )
x = -5y = 20First, we find the y-intercept 'b', by plug the slope m ( -3 ) and point ( -5,20 ) into the equation of line formula and solving for b.
y = mx + b
20 = (-3)(-5) + b
20 = 15 + b
b = 20 - 15
b = 5
Now that both the slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = (-3)x + 5
y = -3x + 5
Therefore, the linear equation of the line is y = -3x + 5.
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What type of chart did we use to build a tornado chart?
Bar chart
For 20 charterers
If PQ = 6x - q and PR = 15x - 29, then QR =?
I need help figuring out the measures of the missing sides
Given:
• c = 20
,• h = 15
,• j = 12
,• k = 16
Let's find the measures of the mssing sides if triangle ABC is similar to triangle JKH.
Here, the missing sides are:
Side a and Side b
Since both triangles are similar, the corresponding sides will be proportional.
To solve for the length of side a, apply the proportionality equation:
[tex]\frac{c}{h}=\frac{a}{j}[/tex]Plug in values and solve for a:
[tex]\begin{gathered} \frac{20}{15}=\frac{a}{12} \\ \\ \text{ Cross multiply:} \\ 15a=20*12 \\ \\ 15a=240 \\ \text{ } \\ \text{ Divide both sides by 15:} \\ \frac{15a}{15}=\frac{240}{15} \\ \\ a=16 \end{gathered}[/tex]Thereofore, the length of side a = 16
To solve for the length of side b, apply the equation:
[tex]\frac{c}{h}=\frac{b}{k}[/tex]Plug in the values for the variables and solve for b:
[tex]\begin{gathered} \frac{20}{15}=\frac{b}{16} \\ \\ 15b=20*16 \\ \\ 15b=320 \\ \\ b=\frac{320}{15} \\ \\ b=21.3 \end{gathered}[/tex]The length of b is 21.3
ANSWER:
• a = 16
,• b = 21.3
Use the square root property to solve the equation.x² = 36Select one:O A. (18)O B. {16}O C. {±6i}O D. {6}
Given the equation
[tex]x^2=36[/tex][tex]x=\sqrt{36}[/tex][tex]x=\pm6[/tex]Then
The Correct answer is
Option D 6
PLEASE HELP! Sharel received a bank account statement report the recent changes to her account. The statement showed an overall increase in the account balance of $4,317.59. During the time shown on the statement, Sharel was paid three times and withdrew a total of $1,230.67 to cover all her bills and expenses. How much (x) is each of Sharel's paychecks? Write an equation to represent this situation.
Cars enter a car wash at a mean rate of 4 cars per half an hour. What is the probability that, in any hour, exactly 4 cars will enter the car wash? Round your answer to four decimal places.
The probability that, in any hour, exactly 5 cars will enter the car wash is P(x = 5) = 0.0920.
This can be modeled as a Poisson random variable.
The mean rate is the parameter of the Poisson distribution:
λ = 4 cars/30 mins
λ = 8 cars/hr
The probability that exactly k cars will enter the car wash can be calculated as:
P(x = k) = ([tex]8^{k}[/tex] × [tex]e^{-8}[/tex]) ÷ k!
Then, the probability that exactly 5 cars will enter the car wash for k=5 is:
P(5) = ([tex]8^{5}[/tex] × [tex]e^{-8}[/tex]) ÷ 5!
P(5) = (32768 × 0.0003) ÷ 120
P(5) = 0.0920
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HELP PLEASE
thank youuu
Answer:
a/c
Step-by-step explanation:
Sine is always the side opposite the angle and the hypotenuse
Answer:
[tex]\large \text{Second Choice: $\dfrac{a}{c}$}[/tex]
Step-by-step explanation:
For any given triangle, the Law Of Sines states that the ratio of each side to the sine of the angle opposite that side is the same
So we have
[tex]\dfrac{a}{\sin \angle F} = \dfrac{c}{\sin \angle 90} = \dfrac{b}{\sin \angle G} \\\\[/tex]
[tex]\sin \angle 90 = 1[/tex]
So we get from the first two ratio equality,
[tex]\dfrac{a}{\sin \angle F} = \dfrac{c}{1} \\\\\\\dfrac{a}{\sin \angle F} = c\\\\\\\dfrac{a}{c} = sin \angle F\\\\[/tex]
Or, in other words,
[tex]\sin \angle F = \dfrac{a}{c}[/tex]
What is the slope of the line?
*2
*1/2
*-1/2
*-2
The answer is 2 m = -4 / -2 = -2 / -1 = 2
I need help with this!!
Answer:
Step-by-step explanation:
The Lawrence family needed to cut expenses on their cell and landline phone service, cable television service, and Internet service. Here are the best prices they found forbasic service, using different service providers: Cell Phone Service: $36.45 per month Landline Phone Service: $30.11 per month Cable TV Service: $57.43 per monthInternet Service: $37.32 per month They found a company with a package deal with all 4 services for $131.59. What is the percentage decrease by purchasing the packagedeal?15.8%16.5%17.7%18.4%None of these choices are correct
Given:
Cell Phone Service, x=$36.45 per month
Landline Phone Service, y= $30.11 per month
Cable TV Service, z=$57.43 per month
Internet Service, p= $37.32 per month
The price for a package of all services, P=$131.59.
The total price of services before purchasing the package is,
[tex]T=36.45+30.11+57.43+37.32=161.31[/tex]Now, the percentage decrease by purchasing the package is,
[tex]\begin{gathered} \text{Percentage}=\frac{T-P}{T}\times100 \\ =\frac{161.31-131.59}{161.31}\times100 \\ =18.4 \end{gathered}[/tex]Therefore, the percentage decrease by purchasing the package is 18.4%.
A square has an area of 144 ft^2 what is the length of each side
Answer: 12 feet
This is because [tex]12^2 = 12*12 = 144[/tex]
Squaring a number means you multiply it with itself.
The square root goes in reverse to have [tex]\sqrt{144} = 12[/tex]
Answer:
Each side is 12 ft long.
Step-by-step explanation:
So, you have a square, which means all of the sides are going to be the same length. So, you need something times itself that equals 144. Or, you need the square root of 144 (Because when something is squared, it is multiplied by itself). And the square root of 144 is 12.
What is the image of point (-3,-1) under a reflection in the origin?
(1) (3,1)
(3) (1,3)
(2) (-3,1)
(4) (-1,-3)
The image of point (-3,-1) under a reflection in the origin( 3 , 1 )
Point (x, y) is reflected over the line y = x, and the reflection is (y, x)
Find the point of a reflection on a point by what method?
The x-coordinate and y-coordinate of a point change positions when it is reflected across the line y = x. The x- and y-coordinates shift positions and are negated when a point is mirrored across the line y = -x. Therefore, Point (x, y) is reflected over the line y = x, and the reflection is (y, x)
following a reflection, a 3-1 picture Reason: A(3,1) becomes A'(3,3+3(1)), or A', when it is reflected over y=3 (3,7)
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1/3 (x + 5) + x = 4 ( x - 4) -9
Distributing and combining similar terms
[tex]\begin{gathered} \frac{1}{3}\cdot x+\frac{1}{3}\cdot5+x=4\cdot x-4\cdot4-9 \\ \frac{1}{3}x+x+\frac{5}{3}=4x-16-9 \\ \frac{4}{3}x+\frac{5}{3}=4x-25 \end{gathered}[/tex]Subtracting 4/3x at both sides
[tex]\begin{gathered} \frac{4}{3}x+\frac{5}{3}-\frac{4}{3}x=4x-25-\frac{4}{3}x \\ \frac{5}{3}=(4-\frac{4}{3})x-25 \\ \frac{5}{3}=(\frac{4\cdot3-4}{3})x-25 \\ \frac{5}{3}=\frac{8}{3}x-25 \end{gathered}[/tex]Adding 25 at both sides:
[tex]\begin{gathered} \frac{5}{3}+25=\frac{8}{3}x-25+25 \\ \frac{5+25\cdot3}{3}=\frac{8}{3}x \\ \frac{80}{3}=\frac{8}{3}x \end{gathered}[/tex]Multiplying by 3/8 at both sides
[tex]\begin{gathered} \frac{80}{3}\cdot\frac{3}{8}=\frac{8}{3}x\cdot\frac{3}{8} \\ \frac{80}{8}=x \\ 10=x \end{gathered}[/tex]Answer:
x=10 am not sure
Step-by-step explanation:
Circumference =96cm, find radius, diameter and area
The Radius is 15.27 cm and the the Diameter is 30.55 cm
Given
Circumference = 96cm
Circumference is the total arc length of a circle or it is simply the perimeter of a circle.
The formula for circumference is 2πr
where π = Ratio of circumference to the diameter of a circle
π = 3.14
r = Radius of the circle
Substituting the value in the formula we get
2πr = 96 cm
πr = 48 cm
r = 15.27 cm
Diameter (d) = 2 × r
hence d = 2 × 15.27 cm
d = 30.55 cm
Hence the radius = 15.7cm
Diameter = 30.55 cm
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