Answer:
distributive property
9x+15
Step-by-step explanation:
The distributive property is whenever you have () and distribute until you have zero of these ()
The equivalent expression simply means write this equation differently.
The Venn diagram represents the results of a survey that asked participants whether they would want a dog or a cat as a pet. Enter your answers in the boxes to complete the two-way table based on the given data.
The complete table is
Dog Not Dog Total
Cat 31 10 41
Not cat 24 7 31
Total 55 17 72
Given a venn diagram represents the results of a survey that asked participants whether they would want a dog or a cat as a pet as shown in figure which is attached below.
In the figure cat and dog are overlapping which means 31 people like both.
The people that like only dog but not cat are 24 and the people that like only car but not dog is 10.
The people that like not cat not dog is 31-24=7.
The total people that like cats are 31+10=41 and the total people that dont like cat is 24+7=31
The total people that like dogs are 31+24=55 and the people that didn't like dogs are 31+10-24=17 and the total people that like both dog and not dog and also like cat and not cat is 55+17=41+31=72.
Hence, the complete table is shown in attached figure for the given venn diagram.
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can you please help me too
(a) The sample mean for:
Sample 1 is 3.4, Sample 2 is 3.4, Sample 3 is 3.6, and Sample 4 is 3.8.
(b) The range of the sample means is 0.4.
(c) The true statement from the given statements are:
The mean of the sample means will tend to be a worse estimate than a single sample mean, andThe closer the range of the sample means is to 0, the more confident they can be in their estimate.The sample mean, [tex]\bar{x}[/tex], is calculated using the formula, [tex]\bar{x} = \frac{\sum x}{N}[/tex], where N is the sample size.
The range of a data is the difference between the greatest data point and the smallest data point.
(a) Thus, the sample mean for:-
Sample 1:
= (3 + 2 + 6 + 4 + 2)/5 = 17/5 = 3.4.
Sample 2:
= (2 + 2 + 3 + 7 + 3)/5 = 17/5 = 3.4.
Sample 3:
= (6 + 4 + 2 + 2 + 4)/5 = 18/5 = 3.6.
Sample 4:
= (5 + 3 + 2 + 5 + 4)/5 = 19/5 = 3.8.
(b) The range of the sample means is 3.8 - 3.4 = 0.4.
(c) The true statement from the given statements are:
The mean of the sample means will tend to be a worse estimate than a single sample mean, andThe closer the range of the sample means is to 0, the more confident they can be in their estimate.Learn more about means and estimates at
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A rectangular prism measures 8 m by 4 m by 5 m. What is its volume?
Answer:
160 m³
Step-by-step explanation:
the volume of a rectangular prism is equal to :
= Base × height
= length × width × height
………………………………………
= 8 × 4 × 5
= 160
Note : the length can be 8 or 5
and the width can be 4 or 5
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite
direction. The number b varies directly with the number a. For example b = 22 when a = -22. Which
equation represents this direct variation between a and b?
b=-a
-b=-a
b-a=0
b(-a) = 0
Answer:
b = -a
Step-by-step explanation:
Since a and b are equally distant to zero but in opposite directions, a and b are opposites, or additive inverses.
The sum of additive inverses is zero.
a + b = 0
b = -a
Derek wants to determine the height of the top of the backbpard on the basketball goal at the playground. He places a standard 12-
inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 11 inches and
the backboard has a shadow of 7.5 feet, then about how high is the top of the backboard?
the actual height of the backboard is 8.18 feet.
What is proportion?A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
Given
We have been given that Derek places a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 10 inches. We are asked t find the height of the backboard, if the backboard has a shadow of 8.5 feet.
We will use proportions to solve our given problem as ratio between sides ruler will be equal to ratio of sides of background.
[tex]\frac{Actual height of ruler}{Shadow of ruler} = \frac{Actual height of black board}{Shadow of black board} \\\\\frac{12}{11} =\frac{Actual height of black board}{7.5} \\\\Actual height of black board = \frac{12}{11} * 7.5 = 8.18\\[/tex]
Therefore, the actual height of the back-board is 8.18 feet.
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Drag the tiles to the correct boxes to complete the pairs. Match the systems of equations with their solutions.
The systems of linear equations have been matched with their respective solutions as shown in the image attached below.
What is a system of linear equations?A system of linear equations can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).
In this exercise, you're required to match the systems of linear equations with their respective solutions as shown in the image attached below.
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An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform. The equation for the object's height s at time t seconds after launch is s(t) = -4.9t2 +19.6t + 58.8, where s is in meters. How high will the object be after 3 seconds?
A)73.5 feet
B)98.49 feet
C)333.69 feet
D)161. 7 feet
The ball will be 73.5 meters above the ground after a time of 3 seconds. (Correct choice: A)
What is the height of the object after launch?
Herein we have an equation that models the height of the ball as function of time, we need to evaluate the expression for t = 3 s to find the required height:
s(3) = - 4.9 · (3 s)² + 19.6 · (3 s) + 58.8
s(3) = 73.5 m
The ball will be 73.5 meters above the ground after a time of 3 seconds. (Correct choice: A)
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20 POINTS TO WHOEVER SOLVE THIS !
Applying the linear pair theorem and the sum of interior angles of hexagon, we have:
Angle 7 = 92°
Angle 1 = 107°
What is the Linear Pair Theorem?According to the linear pair theorem/postulate, when two angles lie on a straight line, the sum of their measures equals 180 degrees.
Angle 7 lie on a straight line with 88°, therefore, applying the linear pair theorem, we have:
Angle 7 + 88 = 180
Subtract both sides by 88
Angle 7 + 88 - 88 = 180 - 88
Angle 7 = 92°
Also, using the linear pair theorem, we have:
Angle 5 = 180 - 64
Angle 5 = 116°
Angle 3 = 180 - 57
Angle 3 = 123°
Sum of interior angles of hexagon equals 720°, therefore:
Angle 1 + angle 3 + angle 5 + angle 7 + 118 + 164 = 720°
Plug in the known values
Angle 1 + 123 + 116 + 92 + 118 + 164 = 720
Angle 1 + 613 = 720
Subtract both sides by 613
Angle 1 + 613 - 613 = 720 - 613
Angle 1 = 107°
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PLEASE HELP 50 POINTS
Step-by-step explanation:
The initial velocity of a particle moving along x−axis is u (at t=0 and x=0) and its acceleration a is given by a=kx.If both cars in Exercise 62 are on one side of the plane and if the angle of depression to one car is 38∘ and that to the other car is 52∘, how far apart are the cars?
The two cars lying on one side of the plane are 50 meters apart.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
let us assume that the height is 100 m. Let d represent the horizontal distance. For depression of 38°, Ф = 90 - 38 = 52°, hence:
tan(52°) = d / 100
d = 128 m
For depression of 52°, Ф = 90 - 52 = 38°, hence:
tan(38°) = d / 100
d = 78 m
Distance apart = 128 - 78 = 50 m.
The two cars lying on one side of the plane are 50 meters apart.
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PLEASE HELP!! ILL GIVE BRAINLESS!!
Question 7(Multiple Choice Worth 5 points)
(05.01 MC)
An architect is creating a scale drawing of a school computer lab. The length of the lab is 36 feet and the width of the lab is 48 feet. If each 12 feet of the lab equals 2 centimeters on a scale drawing, which of the following drawings is the scale drawing of the computer lab?
A) A rectangle is shown. The length of the rectangle is labeled as length equal to 6 cm and the width is labeled as width equal to 8 cm.
B) A rectangle is shown. The length of the rectangle is labeled as length equal to 3 cm and the width is labeled as width equal to 4 cm.
C) A rectangle is shown. The length of the rectangle is labeled as length equal to 12 cm and the width is labeled as width equal to 24 cm.
D) A rectangle is shown. The length of the rectangle is labeled as length equal to 24 cm and the width is labeled as width equal to 36 cm.
Answer:
A.
Step-by-step explanation:
36/12 = 3
3*2 = 6 cm
48/12 = 4
4*2 = 8 cm
Tumbleweed, commonly found in the western united states, is the dried structure of certain plants that are blown by the wind, kochia, a type of plant that turns into tumbleweed at the end of the summer is a problem for farmers because it takes nutrients away from soil that would otherwise go to more beneficial plants. scientists are concerned that ko:hia plants are becoming resistant to the most commonly used herbicide, glyphosate. in 2014, 19.7 percent of 61 randomly selected kochia plants were resistant to glyphosate. in 2017, 38.5 percent of 52 randomly selecteikochia plants were resistant to glyphosate. do the data provide convincing statistical evidence, at the leve of 0.05, that there has been an increase in the proportion of all kochia plants that are resistant to glyphosale?
Since we are dealing with a proportion, it is determined by using the z-distribution that there is insufficient evidence to draw the conclusion that the proportion of all kochia plants that are resistant to glyphosate has increased because the test statistic is less than the critical value for the right-tailed test.
In this problem, we consider that:
[tex]p_{1}[/tex] is the proportion in 2014.[tex]p_{2}[/tex] is the proportion is 2017.What are the hypothesis tested?At the null hypothesis, we test if there has been no increase, that is, the subtraction is of 0.[tex]$H_{0}: p_{2}-p_{1}=0$[/tex]
At the alternative hypothesis, we test if there has been an increase, hence:[tex]$H_{1}: p_{2}-p_{1} \neq 0$[/tex]
What is the distribution of the difference of sample proportions?The proportions and standard errors are given by:
[tex]p_{1}=0.197, s_{1}=\sqrt{\frac{0.197(0.803)}{61}}=0.0509\\p_{2}=0.385, s_{2}=\sqrt{\frac{0.385(0.615)}{52}}=0.0675[/tex]
Hence, the distribution has mean and standard error given by:
[tex]\bar{p}=p_{2}-p_{1}=0.0675-0.0509=0.0166\\s=\sqrt{s_{1}^{2}+s_{2}^{2}}=\sqrt{0.0509^{2}+0.0675^{2}}=0.0845[/tex]
What is the test statistic?It is given by:
[tex]$z=\frac{\bar{p}-p}{s}$[/tex]
In which p = 0 is the value tested at the null hypothesis, hence:
[tex]z=\frac{0.0166}{0.0845}\\$z=0.2$[/tex]
What is the decision?Considering a right-tailed test, as we are testing if the proportion is greater than a value, with a significance level of 0.05, the critical value is of [tex]$z^{*}=1.645$[/tex]There is insufficient information to establish that the fraction of all kochia plants that are resistant to glyphosate has increased because the test statistic is smaller than the crucial value for the right-tailed test.Learn More about the z-distribution here: brainly.com/question/26454209
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Find the common ratio for 0.1,0.01,0.001
The common ratio of the set of data is 0. 1
How to determine the common ratio
To determine the common ratio of a set of data, we have to
Divide the second term by the first term orDivide the third term by the second termFor the given set of data
0.1,0.01,0.001
Let's divide the second term by the first term
= 0. 01/ 0. 1
= 0. 1
Thus, the common ratio of the set of data is 0. 1
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Use the image below to describe at least three different ratios, written in simplest form. Include at least one part-to-part ratio and one part-to-whole ratio.
8 out of 36 squares unfilled*
HELP ASAP!!!!!!!!!!!!
The different ratios are 2 : 7, 2 : 9 and 7 : 9
How to determine the ratio?The statement is given as:
8 out of 36 squares unfilled
This means that:
There are 36 squares8 are unfilled28 are filledThe part-to-part ratio is represented as:
Ratio = Unfilled : Filled
This gives
Unfilled : Filled = 8 : 28
Simplify
Unfilled : Filled = 2 : 7
The part-to-whole ratios are represented as:
Ratio = Unfilled : Total
Ratio = Filled : Total
So, we have:
Unfilled : Total = 8 : 36
Filled : Total = 28 : 36
Simplify
Unfilled : Total = 2 : 9
Filled : Total = 7 : 9
Hence, the different ratios are 2 : 7, 2 : 9 and 7 : 9
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Which number is a perfect cube?
21
49
343
600
Answer:
343
Step-by-step explanation:
7 cubed = 7 x 7 x 7 = 343
so, 343 is a perfect cube.
Answer:
C
Step-by-step explanation:
Find the value of f(4)?
From the given graph, we can see by tracing that f(4) is -3.5
Graph of a quadratic functionThe given graph is a graph of a quadratic function with a parabola opening upwards.
According to the question, we are to find the value of y where the value of x is 4. From the given graph, we can see by tracing that f(4) is -3.5
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What is the net force acting on the crate? 352 n to the left 176 n to the left 528 n to the right 440 n to the right
The net force acting on the crate is the sum of all the forces acting in the different directions on the crate, which is 176 N to the left.
What is net force?The net force is defined as the sum of all the forces acting on an object.
From the figure given that,
Upward force = 440 N
Downward force = - 440 N
Rightward force = 176 N
Leftward Force = - 352 N
The net vertical force acting on the crate = Upward force + Downward force
= 440 N + (-440 N)
= 0 N
The net horizontal force acting on the crate = Rightward force + Leftward force
=176 N + (- 352 N)
= - 176 N
Hence, the net force acting on the crate is - 176 N, which is 176 N to the left.
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Answer:
175N to the left
Step-by-step explanation:
Jorge wrote the equation negative 6 x 4 x = 8. what is the value of x? –4 –2 2 4
Option (A) - 4 is the correct answer.
The value of x for linear equation -6x + 4x = 8 is - 4.
What is linear equations in one variable?If a variable's maximum power constantly equals 1, the equation is considered linear equation. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. Here, A is a coefficient, B is a constant, and x is a variable.
The given equation is -6x + 4x = 8.
Simplifying the above equation.
-2x = 8
Now, dividing both sides by -2.
x = -4
Therefore the value of x in equation -6x + 4x = 8 is -4.
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I understand that the question you are looking for is " Jorge wrote the equation -6x + 4x = 8. What is the value of x?
(A) –4
(B) –2
(C) 2
(D) 4 "
Answer: (A): -4
Step-by-step explanation:
It's the correct option.
Direct to Coordinates
plot the point A (2, 3) then, plot point b that is 4 right and 5 up from point A.
Plot the point C (9, 7). Then, plot another point D that is 8 left and 2 down from point C.
Point A is at A(2, 3) while point B is 4 right and 5 up from point A. Point B is at B(6, 8). Also, point C is at C(9, 7). Point D is 8 left and 2 down from point C which is at D(1, 5).
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Point A is at A(2, 3) while point B is 4 right and 5 up from point A. Point B is at B(6, 8). Also, point C is at C(9, 7). Point D is 8 left and 2 down from point C which is at D(1, 5).
The location of point A, B, C and D is located on the graph.
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i would appreciate it sm if u anyone responded
x-2(x+1)+3(x-2)+2(x-6)=0
Answer:
x = 5
Step-by-step explanation:
Simplifying the expression:x - 2(x +1) + 3(x -2) + 2(x - 6) = 0
x + (-2)*x + (-2)*1 + 3*x +3*(-2) + 2*x + 2*(-6) = 0
x - 2x -2 + 3x - 6 + 2x - 12 = 0
x - 2x + 3x + 2x - 2 - 6 - 12 = 0
Combine like terms. Like terms have same variable with same power.
4x - 20 = 0
Add 20 to both sides.
4x = 20
Divide both sides by 4
x = 20/4
x = 5
Answer:
x = 5
Step-by-step explanation:
x -2(x+1) + 3(x-2) + 2(x-6) = 0
here, we need to distribute the numbers on the outside of the parentheses to the inside numbers.
As you may know, when two numbers are in parentheses, they are to be multiplied--and it is the same idea here.
When we have a number, say 3, multiplied by parentheses, say (x - 2), we multiply all inside numbers by the outside number, which is called distributing.
We know that 3(x) = 3x, and that 3(-2) = -6, so we distribute
3(x - 2) to be 3x - 6
let's do that for all of our parentheses:
x -2(x+1) + 3(x-2) + 2(x-6) = 0
-2( x + 1 )
-2x - 2
3(x - 2)
3x - 6
2( x - 6)
2x - 12
Now, let's rewrite our problem:
x -2(x+1) + 3(x-2) + 2(x-6) = 0
x - 2x - 2 + 3x -6 + 2x - 12 = 0
First, we should combine like terms:
x - 2x + 3x + 2x - 2 - 6 - 12 = 0
(x - 2x = -x; -x + 3x = 2x; 2x + 2x = 4x)
( - 2 - 6 = -8; -8 - 12 = -20
So, we are left with:
4x - 20 = 0
At this point, we want to get x alone (so that we can find what "x" is)
4x - 20 = 0
+ 20 + 20 ( add 20 to both sides of the equation to isolate x )
4x = 20
÷ 4 ÷ 4 (divide both sides by 4 to find "1"x)
x = 5
So, we know that the value of x is 5, or x = 5
hope this helps! let me know if you need clarification on anything :)
HELP ASAP
x =x=x, equals
^\circ
∘
Answer:
[tex]\huge\boxed{\sf x = 55\°}[/tex]
Step-by-step explanation:
Given that,
x° + 35° = 90° (complementary angles)
Subtract 35 to both sides
x = 90 - 35
x = 55°
[tex]\rule[225]{225}{2}[/tex]
ƒ(1) = −16 [ƒ(1)
f(n) = -29 - f(n-1)
what is f(2)=
Answer:
f(2) = -13
Step-by-step explanation:
Evaluate the given formula with the given value of the variable.
Applicationf(1) = -16 . . . . . . . . . . given
f(n) = -29 -f(n-1) . . . . given
For n = 2, we have ...
f(2) = -29 -f(2-1) = -29 -f(1) = -29 -(-16) . . . . put 2 in place of n and evaluate
f(2) = -13
i need help!!!!!!!!!!!!!! how many pound are in 40 ounces. this is off or i ready. please help me!!!
Answer:
2.5 pounds
Step-by-step explanation:
A $6$-sided die is weighted so that the probability of any number being rolled is proportional to the value of the roll. (So, for example, the probability of a $2$ being rolled is twice that of a $1$ being rolled.) What is the expected value of a roll of this weighted die
The expected value of a roll of this weighted die is; 13/3 or 4.33
How to find the Expected Value?We are given that;
A $6 sided die is weighted.
Probability of any number being rolled is proportional to the value of the roll.
Probability of a $2 being rolled is twice that of a $1 being rolled.
Thus, the expected Value is;
E(x) = (1*1 + 2*2 + 3*3 + 4*4 + 5*5 + 6*6)/(1 + 2 + 3 + 4 + 5 + 6)
E(x) = 13/3 = 4.33
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determine which two of the three given triangles are similar. Find the scale factor for the pair.
pls help me w this, i need it answred asap
Answer:
A
Step-by-step explanation:
As angles in a triangle add to 180 degrees, angle C measures 35 degrees.
Therefore, the answer is A, since thr triangles will be similar by AA.
MATH HELP!!! 100PTS plus BRAINLIEST!!!!
The formula C=59(F−32), where F≥−459.67 expresses the Celsius temperature C as a function of Fahrenheit temperature F.
1. Find the formula for the inverse function.
Answer: C^−1(F)=
9F/5+32 (I'm right about this one)
2. What is the domain of the inverse function C^−1 ?
Answer (in interval notation):(for some reason it keep telling me wrong :( )
Answer:
[tex]\textsf{1.} \quad C^{-1}(F)=\dfrac{9}{5}F+32[/tex]
2. [-273.15, ∞)
Step-by-step explanation:
Given:
[tex]C=\dfrac{5}{9}(F-32), \quad \text{where }F \geq -459.67[/tex]
To find the inverse of the given function, make F the subject:
[tex]\begin{aligned}C & =\dfrac{5}{9}(F-32)\\\implies \dfrac{9}{5}C & =F-32\\\implies F & = \dfrac{9}{5}C+32 \end{aligned}[/tex]
[tex]\textsf{Replace the } F \textsf{ with }C^{-1}(F)\textsf{ and the }C \textsf{ with } F:[/tex] :
[tex]\implies C^{-1}(F)=\dfrac{9}{5}F+32[/tex]
Domain: set of all possible input values (x-values)
Range: set of all possible output values (y-values)
The given domain of the function C(F) is F ≥ -459.67
Therefore, the minimum value of the function is:
[tex]\implies C(-459.67)=\dffrac{5}{9}(-459.67-32)=-273.15[/tex]
This means the range of the function C(F) is C(F) ≥ -273.15
The domain of the inverse function is the range of the function.
Therefore, the domain of the inverse function in interval notation is: [-273.15, ∞)
Answer: -273.15
Step-by-step explanation:
Visual Description for Figure 1
Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.
1. What transformations would you use on the blue segment CD to get it to match with the red segment C2D2? Explain your movement using the coordinates of the vertices.
2.
What transformations would you use on the blue triangle to get it to match with the red triangle? Explain your movement using the coordinates of the vertices.
3.
Which line segments on the boat are parallel? Explain your answer.
4.
Which line segments on the boat are perpendicular? Explain your answer.
5.
Which line segments on the boat have a slope of 0? Explain your answer.
6.
Which line segments on the boat have an undefined slope? Explain your answer.
7.
What is the slope of ED? Explain your answer using the change in coordinates given that E is at (−11,4) and D is at (−10,5).
A) Rotate by 90° counterclockwise.
B) Reflection transformation about the line y = 5.
C) Parallel Lines are C₂D₂ and A₂B₂; EF and E₁F₁.
D) Perpendicular lines are; D₁F₁ and E₁F₁; DF and EF; DC and AB.
E) Line segments with slope of 0 are; AB, C₂D₂, A₂B₂, EF and E₁F₁
F) Line segments on the boat that have an undefined slope are; Lines A₁B₁, DF and DC.
G) Slope of Line ED = 1
How to carry out Transformations?A) The blue segment CD is seen on the graph as a perpendicular line with 2 units while the line segment C₂D₂ is seen as a horizontal line. Thus, to match CD with C₂D₂, we will rotate by 90° counterclockwise.
B) The transformations that would be used on the blue triangle to get it to match with the red triangle is a reflection transformation about the line y = 5.
C) The line segments that are parallel to each other are; C₂D₂ and A₂B₂; EF and E₁F₁.
D) The line segments that are perpendicular are; D₁F₁ and E₁F₁; DF and EF; DC and AB.
E) Horizontal lines that are parallel to the x-axis have zero slope. Thus, AB, C₂D₂, A₂B₂, EF and E₁F₁ all have zero slopes.
F) Undefined slope is the slope of a vertical line. Thus, Lines A₁B₁, DF and DC have undefined slopes.
G) Slope of ED = (5 - 4)/(-10 - (-11))
Slope of ED = 1/1
Slope = 1
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If tanA+cotA=2, then find the value of tan^2A+cot^2A.
tan45° = cot45° = 1
---> If tanA + cotA = 2, then A is 45°.
---> tan²A + cot²A = 1² + 1² = 2
The correct answer is 2
Select all the correct answers.
Consider functions f and g.
f(x) = - 2 cos (x - 1) + 3
g(x) = 2 cos (x + 3) - 3
Which statements describe transformations of the graph of fresulting in the graph of function g?
A. The graph of function f has been vertically stretched by a factor of 4.
B. The graph of function fhas been reflected over the y-axis.
C. The graph of function fhas been reflected over the x-axis.
D. The graph of function fhas been translated 3 units down.
D. The graph of function fhas been translated 4 units left.
E. The graph of function fhas been translated 3 units left.
((More than one))
The function g(x) is created by applying an horizontal translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)
How to determine the characteristics of rigid transformations by comparing two functions
In this problem we have two functions related to each other because of the existence of rigid transformations. Rigid transformations are transformations applied to geometric loci such that Euclidean distance is conserved at every point of the geometric locus.
Let be f(x) = - 2 · cos (x - 1) + 3, then we use the concept of horizontal translation 4 units in the + x direction:
f'(x) = - 2 · cos (x - 1 + 4) + 3
f'(x) = - 2 · cos (x + 3) + 3 (1)
Now we apply a reflection over the x-axis:
g(x) = - [- 2 · cos (x + 3) + 3]
g(x) = 2 · cos (x + 3) - 3
Therefore, the function g(x) is created by applying an horizontal translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)
To learn more on rigid transformations: https://brainly.com/question/1761538
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