The distribution of heights of adult men in the U.S. is approximately normal with mean 69 inches and standard deviation 2.5 inches. Use what you know about a normal distribution and the 68-95-99.7 rule to answer the following. (a) About what percent of men are between 69 and 74 inches? (b) About 2.5 percent of all men are shorter than?(c) About what percent of men are between 64 and 66.5 inches?
Answers
The 68-95-99.7 rule let us draw some conclusions about a normally distributed population, knowing only the mean and standard deviation.
For example, 68% of the data falls within one standard deviation from the mean. In this case, with mean 69 and standard deviation of 2.5, 68% of the data is between 69-2.5=66.5 and 69+2.5=71.5.
The same can be written for 95% and 2 standards deviation from the mean and 99.7% and 3 standard deviations from the mean.
(a) We have to calculate what percent of men are between 69 and 74.
69 is the mean and 74 is 2 times the standard deviation from the mean:
[tex]\frac{74-\mu}{\sigma}=\frac{74-69}{2.5}=\frac{5}{2.5}=2[/tex]For 74, we apply the 95% rule, but split in half, as we are measuring from the mean and not -2 standard deviation.
The percent of men between 69 and 74 is 95%/2 = 47.5%.
Answer: 47.5%.
b) We have to find the height for which only 2.5% of the men are below.
To calculate this we can use the 95% rule, for which we know that 2.5% of the data are in each of the tails.
Then, we know that the shorter 2.5% is below a height that is equal to the mean less 2 times the standard deviation.
[tex]H=\mu-2\sigma=69-2\cdot2.5=69-5=64[/tex]Then, 2.5% of the men are shorter than 64 inches.
Answer: 64 in.
c) The percent of men that are between 64 (2 times the standard deviation below the mean) and 66.5 (one time the standard deviation below the mean) can be calculated using both the 68% rule and the 95% rule.
We know that 47.5% of the data is between 64 and 69 (half of 95%).
We also know that 34% of the data is between 66.5 and 69 (half of 68%).
Then, between 64 and 66.5 there is 47.5%-34%=13.5% of the data.
The percent of men that are between 64 and 66.5 inches is expected to be 13.5%.
Answer: 13.5%.
Related Questions
5. The point (-4,1) falls in which quadrant?O Quadrant IO Quadrant IIQuadrant IIIQuadrant IV
Answers
We are given the following point
(-4, 1)
We are asked to determine in which quadrant does the point lies.
As you can see, the x-coordinate (x = -4) of the point is negative and the y-coordinate (y = 1) of the point is positive.
Let us sketch a diagram to better understand the problem
The point falls in Quadrant II since the x-coordinate is negative and y-coordinate is positive,
7 singles, 12 fives, 5 twenties, and 2 hundred dollar bills are all placed in a hat. If a player is to reach into the hat and randomly choose one bill, what is the fair price to play this game?
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Okay, here we have this:
Considering the provided information we obtain the following:
7 singles P(1)=7/26
12 fives P(5)=12/26
5 twenties P(20)=5/26
2 hundreds P(100)=2/26
E(X)=1*7/26+5*12/26+20*5/26+100*2/26
E(X)≈14.115
Finally we obtain that the approximately fair price is $14.115.
Maia can run 4/5 of a mile in 5/3 of an hour. How far can she run in 1 hour? * 1 point O 12/15 mile O 15/20 mile 4/3 mile O 12/25 mile
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Answer:
Explanation:
Maia can run 4/5 of a mile in 5/3 of an hour.
Let the mile run in 1 hour = x
We therefore have that:
[tex]\frac{\frac{4}{5}}{\frac{5}{3}}=\frac{x}{1}[/tex]determine if the given triangles are similar if they are select the option that includes a similarity statement with the justifying prostulaye or theorem them they are not select option states such
Answers
We are asked to determine if the given triangles are similar or not.
Let us find the rato of the corresponding sides
[tex]\begin{gathered} \frac{GA}{BE}=\frac{GU}{EF} \\ \frac{12}{15}=\frac{16}{20} \\ \frac{4}{5}=\frac{4}{5} \end{gathered}[/tex]So, △GUA and △EFB have two equal sides since the ratio of the two corresponding sides is equal.
[tex]\begin{gathered} GA\sim BE \\ GU\sim EF \end{gathered}[/tex]Also, notice that the one corresponding angle is equal
[tex]\angle G\cong\angle E[/tex]Hence, the triangles △GUA and △EFB are similar by SAS theorem since the ratio of two corresponding sides is equal and one included angle is also equal.
Therefore, the last option is the correct answer.
lYou invested S8000 between two accounts paying 4% and 8% annual interest, respectively if the total interest earned for the year was $520, how much was invested at each ratė? was invested at 4% and was invested at 8% Enter your answer in the edit fields and then click Check Answer All parts showing Clear All Check Answer
Answers
Answer:
$3000 was invested at 4% and was $5000 invested at 8%
Explanation:
The formula for calculating simple interest id expressed as;
I = I1+I2
I1 and I2 are the interest earned on both accounts'
Since I =PRT/100
520 = P1R1T1/100 + P2R2T2/100
P is the principal
R is the rate
T is the time
520 = P1(4)(1)/100 + P2(8)(1/100)
520 = (4P1+8P2)/100
4P1+8P2 = 520 *100
4P1+8P2 = 52,000 ......1
SInce the total amount invested is $8,000, hence;
P1 + P2 = 8000 .... 2
Solve 1 and 2 simultaneously;
4P1+8P2 = 52,000 ......1 ..... * 1
P1 + P2 = 8000 .... 2 .... * 4
____________________________]
4P1+8P2 = 52,000
4P1 + 4P2 = 32000
Subtract both equatons;
8P2 - 4P2 = 52000 - 32000
4P2 = 20000
P2 = 20000/4
P2 = 5000
Recall that P1 + P2 = 8000
P1 = 8000 - P2
P1 = 8000 - 5000
P1 = 3000
Hence $3000 was invested at 4% and was $5000 invested at 8%
The UN's measures gender equality. The mean number of hours spent on household chores is another measure of gender equality for a nation. Suppose that a UN study aims to estimate the mean hours spent on household chores by adults 15 years and older for a particular country within 0.2 hour. The desired level of confidence is 96%. From the previous studies, the the population standard deviation is 0.8 hours.What is the necessary sample size to achieve the above margin of error?
Answers
We have to find the minimum sample size.
The margin of error that it is aimed is ±0.2 hours from the real mean.
The population standard deviation is 0.8 hours.
The desired level of confidence is 96%. This corresponds to a z-score of 2.054.
We can relate sample size with the given information as:
[tex]\begin{gathered} e=\frac{\sigma}{\sqrt{n}}\cdot z \\ \sqrt{n}=\frac{\sigma}{e}\cdot z \\ n=(\frac{\sigma\cdot z}{e})^2 \end{gathered}[/tex]If we replace e = 0.2, σ = 0.8 and z = 2.054 we can calculate the sample size n as:
[tex]\begin{gathered} n=(\frac{0.8*2.054}{0.2})^2 \\ \\ n=(8.216)^2 \\ n\approx67.5 \\ n\approx68 \end{gathered}[/tex]Answer: the sample size has to be at least 68 people.
W
Identify the type of sampling method used.A trucking company places their office phone number on the back of all of their vehicles to receive comments on how well their employees are driving.
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Explanation
In this sample, people elect to participate or self-select to do the survey. Often, these folks have a strong interest in the main topic of the survey.
In essence, they volunteer to inform the trucking company about the activities of their drivers. That makes this a voluntary sample.
Answer: Voluntary Sampling Method
If sin(0)1213and O is in Quadrant III, then what is coss)
Answers
Answer:
cos(θ/2) = -2(√2)/13
Explanation:
To find cos(θ/2), we will use the following trigonometric identity
[tex]\cos (\frac{\theta}{2})=\pm\sqrt[]{\frac{1+\cos\theta}{2}}[/tex]Now, we know that sin(θ) = -12/13 and sin(θ) is also equal to the opposite side over the hypotenuse, so we can represent the angle with the following triangle
Then, using the Pythagorean theorem, we can find the value of the adjacent side x, so
[tex]\begin{gathered} x=\sqrt[]{13^2-(-12)^2} \\ x=\sqrt[]{169-144} \\ x=\sqrt[]{25}=5 \end{gathered}[/tex]Therefore, cos(θ) will be equal to:
[tex]\cos (\theta)=\frac{\text{Adjacent}}{\text{Hypotenusa}}=\frac{-5}{13}[/tex]Where we use the negative sign because θ is in quadrant III. Now, we can use the trigonometric identity
[tex]\begin{gathered} \cos (\frac{\theta}{2})=\pm\sqrt[]{\frac{1+\cos\theta}{2}}_{} \\ \cos (\frac{\theta}{2}_{})=\pm\sqrt[]{\frac{1-\frac{5}{13}}{13}} \\ \cos (\frac{\theta}{2})=\pm\sqrt[]{\frac{8}{169}} \\ \cos (\frac{\theta}{2})=\pm\frac{2\sqrt[]{2}}{13} \end{gathered}[/tex]Since θ is in quadrant III, θ/2 should be in quadrant II, so cos(θ/2) is negative. then, the answer is
[tex]\cos (\frac{\theta}{2}_{})=-\frac{2\sqrt[]{2}}{13}[/tex]At what x-values do the graphs of the functions y = cos 2x and y =3cos^2x-sin^2x intersect over the interval -pi
Answers
To find:
The x-values at the intersection of the graphs of two functions.
Solution:
Two functions are:
[tex]y=\cos2x\text{ and }y=3\cos^2x-\sin^2x[/tex]The functions are equal at the intersection. So,
[tex]\cos2x=3\cos^2x-\sin^2x[/tex]The solutions of the above equation are the x-values of the intersection.
[tex]\begin{gathered} \cos2x=3\cos^2x-\sin^2x \\ \cos^2x-\sin^2x=3\cos^2x-\sin^2x \\ 2\cos^2x=0 \\ \cos^2x=0 \\ \cos x=0 \end{gathered}[/tex]The solution to the above equation is:
[tex]x=\frac{\pi}{2}+2\pi n\text{ and }x=\frac{3\pi}{2}+2\pi n[/tex]It is given that x lies between -pi and pi. So, the value of n = 0 for the first solution and n = 1 for the second solution. Therefore,
[tex]x=\frac{\pi}{2}\text{ and }x=-\frac{\pi}{2}[/tex]Thus, options A and B are correct.
I was supposed to simplify 3x (x² - x - 2) + 2x (3 - x) - 7x, I had trouble and asked tutor who gave me 3x³ - 5x² - 7x. Then I went back to answer the question and the answer choices were:x² - 12x - 6x² - 4x - 69x² - 12x - 69x² - 4x - 6I'm wondering if maybe 3x³ - 5x² - 7x simplifies somehow into one these choices or if there was mistake.
Answers
Let's simplify the expression:
3x (x² - x - 2) + 2x (3 - x) - 7x=
3x³ - 3x² -6x +6x -2x² -7x =
3x³ -5x²-7x.
What amount of money will accumulate to $192,400 in 6 years and 11 months at the interest rate of 5.36% compounded semi-annually? $_______
Answers
We will have the following:
[tex]\begin{gathered} 192400=A(1+\frac{0.0536}{2})^{(11/12)(2)}\Rightarrow A=\frac{192400}{(1+0.0536/2)^{(11/12)(2)}} \\ \\ \Rightarrow A=183293.7505...\Rightarrow A\approx18329375 \end{gathered}[/tex]So, the original quantity was approximately $183 293.75.
Add polynomials (intro) Add. Your answer should be an expanded polynomial in standard form. (3x^3 + 4x²) + (3x^3 – 4x^2 – 9x) =
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(3x^3 + 4x²) + (3x^3 – 4x^2 – 9x) =
We have to combine like terms, terms that have x raised to the same power:
First, eliminate the parenthesis:
3x^3 + 4x² + 3x^3 – 4x^2 – 9x =
We have 2 terms raised to the second power (4x^2 and -4 x^2) simply add and subtract.
3x^3+3x^3+4x^2-4x^2-9x
6x^3-9x
help.................solve for z:11z=-110
Answers
Given the following equation:
[tex]11z=-110[/tex]Since we want to solve for 'z', we want to leave the variable z alone on one side of the equation. In this case, we can do this easily by dividing both sides of the equation by 11, since it is the coefficient of the term 11z. Then, we would have the following:
[tex]\begin{gathered} (11z=-110)(\frac{1}{11}) \\ \Rightarrow\frac{11z}{11}=\frac{-110}{11} \\ \Rightarrow z=\frac{-110}{11} \end{gathered}[/tex]now, notice that on the right side we have a positive number dividing a negative number, then, by the laws of signs, the result will be a negative number. Thus, we have:
[tex]\begin{gathered} z=\frac{-110}{11}=-10 \\ \Rightarrow z=-10 \end{gathered}[/tex]therefore, the solution for z is -10
1. Simplify 62 x 6-4
Answers
hello
what i presume your question is asking is
[tex]62\times6-4[/tex]well, to solve this question, we can simply apply BODMAS
[tex]\begin{gathered} \text{BODMAS} \\ B=\text{bracket} \\ O=\text{order} \\ D=\text{division} \\ M=\text{ multiplication} \\ A=\text{addition} \\ S=\text{subtraction} \end{gathered}[/tex]step 1
multiplication comes first and we'll do that operation
[tex]62\times6-4=372-4[/tex]step 2
subtract 4 from 372 since subtraction is the last operation here
[tex]372-4=368[/tex]P'Q' is a translation of PQ. Write the translation rule.(x, y) -> (____,____)
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Let:
[tex]\begin{gathered} P=(-2,-9) \\ Q=(-7,-4) \\ P^{\prime}=(9,2) \\ Q^{\prime}=(4,7) \end{gathered}[/tex]so:
[tex]\begin{gathered} P\to(x,y)\to P^{\prime} \\ -2+x=9 \\ so\colon \\ x=11 \\ ----- \\ -9+y=2 \\ y=11 \end{gathered}[/tex]Therefore:
[tex](x,y)\to(11,11)[/tex]wwmuch money, in dollars, does each person earn per lawn hard earns per lawn. omanas per lawn
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Both are proportional functions.
Divide the earnings by the number of lawns in each case, pick one point.
Richard: 40 / 5 = $8 per lawn
Tom = 22.50 / 3 = $7.5 per lawn
Which data are represented by this dot plot? Student Absences in Mrs. Li's Class 0 1 2 3 4 5 6 7 8 Days O A. 2, 4, 0, 2, 4, 6, 3, 0, 7, 1, 2, 7, 8, 1, 1 O B. 0, 1, 2, 3, 4, 5, 6, 7, 8,0, 1, 2, 4, 6, 7 O C. 0, 2, 3, 0, 2, 4, 4, 5, 7, 8, 7, 2, 0, 2, 7 O D. 1, 2, 6, 4, 6, 7, 7, 2, 2, 0, 1, 0, 1
Answers
The number of dots gives the frequency of each number over which the dots appear.
The tabular representation of the dot plot is as shown below
Number | Frequency
-------------------------------------------
0 | 2
-------------------------------------------
1 | 3
-------------------------------------------
2 | 3
-------------------------------------------
3 | 1
-------------------------------------------
4 | 2
-------------------------------------------
6 | 1
-------------------------------------------
7 | 2
-------------------------------------------
8 | 1
-------------------------------------------
The only option that matches the table is option A
From the table 0 appears twice, 1 three times, 2 three times, 3 once, 4 twice, 6 once
Select the values of r that make the inequality true. Choose 2 answers.
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if x > -3, then the values which satisfy the inequalities can be represented on a number line as shown
Then the range of values that satisfies the inequalities are numbers to the right of -3 which are: -2, -1, 0, 1, 2, 3,4, 5 --- up to positive infinity
From the options provided only 0 and -1 satisfies the range
options C and D are correct
45. A tree casts a shadow that is 80 ft. long when the angle of elevation of the sun is 27º. Find the height of the tree.Round your answer to the nearest tenth.Height = ft.
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To properly answer the problem, it is best that we draw an illustration representing the problem in order for us to understand the problem, according to the problem, we have a tree facing the sun thus creating a shadow on the gorund.
In our problem it is stated that the tree cast a SHADOW of 80ft long, and has an Angle of Elevation of 27°. Therefore we can add measurements to our drawing, giving us;
Notice that the TREE, THE SHADOW, and THE LINE FORMED BY THE ANGLE OF ELEVATION creates a shape called a RIGHT TRIANGLE with a measurements of;
Since we have a right triangle we can now use the SOHCAHTOA properties of a right triangle, and SOHCAHTOA means;
(SOH) Sine of an Angle = Opposite side / Hypotheneus
(CAH) Cosine of an Angle = Adjacent side / Hypotheneus
(TOA) Tangent of an Angle = Opposite side / Adjacent side
An for our problem, the angle 27° has an opposite side which is the TREE (a), it has an adjacent side which is the SHADOW (b), and its Hypotheneus which is the Line formed by the angle of elevation (c).
Therefore in order to find the height of the TREE, we can use the CAH property since our Adjacent side is given while the Hypotheneus remains unknown. So we have;
[tex]\begin{gathered} Tangent\text{ of an Angle = }\frac{Opposite\text{ Side}}{\text{Adjacent Side}} \\ Tan27^{\circ}=\frac{Tree}{\text{Shadow}} \\ \text{Tan 27}^{\circ}=\frac{Tree}{80\text{ ft}} \\ \text{Tre}e=(Tan27)(80ft) \\ \text{Tre}e=(0.5095)(80ft) \\ \text{Tre}e=40.7620ft \\ \text{Tre}e=40.8ft \end{gathered}[/tex]Therefore by using the SOHCAHTOA property of a right triangle we found that the height of the TREE is 40.8 ft.
HELP MEEE PLEASEEEEEEEE
Answers
Step-by-step explanation:
The answer is going to be B
Answer:
B
Step-by-step explanation:
0.5x - 18 >= -14
0.5x >= 4
x >= 4/0.5 = 8
so,
x >= 8
therefore, 8 is the smallest number to make that inequality true.
Given h(x) = 2x^2 - 4x + 4, find h ( -4 ).
Answers
Given:
[tex]h\mleft(x\mright)=2x^2-4x+4[/tex]To find h(-4):
Substitute x=-4 in the given equation, we get
[tex]\begin{gathered} h\mleft(-4\mright)=2(-4)^2-4(-4)+4, \\ =2(16)+16+4 \\ =52 \end{gathered}[/tex]Hence, the answer is 52.
what letters do you need to get rid of first to solve the equation [tex] \frac{x}{z } [/tex][tex] - c for x[/tex]
Answers
You have the following equation:
[tex]y=\frac{x}{z}-c[/tex]In order to determine which of the previous letter you need to get rid off, to solve for x, you consider it is necessary to eliminate additional terms in the side of the equation where the variable is.
In this case, such additional term is - c.
Hence, the letter you need to get rid off is letter c.
Elena went to a store where you can scoop your own popcorn and buy as much as you want. She bought 10 ounces of spicy popcorn for $2.50. 1. How much does popcorn cost per ounce? Show your work.
Answers
Okay, here we have this:
Considering that we know that 10 ounces of popcorn cost $2.50, let's calculate how much does popcorn cost per ounce:
Cost of one ounce of popcorn=Cost of 10 ounces/10
Replacing we obtain:
Cost of one ounce of popcorn=$2.50/10
Cost of one ounce of popcorn=$0.25
A triangle has side lengths of (1.2u + 1.8v) centimeters, (6.5u + 8.7w) centimeters, and (5.8W – 6.9v) centimeters. Which expression represents the perimeter, in centimeters, of the triangle? 0 13.5uw + 3.6vw 7.7u + 1.8w + 7.6v -1.lvw + 15.2uw + 3uv 0 14.5w – 5.1v + 7.7u Submit Answer i dont get this?
Answers
1) The Perimeter (2P) is the sum of the side lengths so let's sum those given measures:
2P=(1.2u+1.8v) +(6.5u+8.7w)+(5.8w-6.9v) Combining Like terms
2P=1.2u +6.5u +1.8v -6.9v +8.7w+5.8w
2P= 7.7u-5.1v+14.5w
2) Reordering
2p= 14.5w -5.1v +7.7u
2. Jenny makes $333.75 for 25 hours of work, and Christina makes $505.75 for 35 hours of work.a. How much do Jenny and Christina each make per hour?
Answers
• We know that
,• Jenny makes $333.75 for 25 hours of work.
,• Christina makes $505.75 for 35 hours of work.
To know how much they make per hour, we just need to divide each given relation.
Jenny's earnings per hour:
[tex]J=\frac{333.75}{25}=13.35[/tex]Therefore, Jenny earns $13.35 per hour.
Christina's earnings per hour:
[tex]C=\frac{505.75}{35}=14.45[/tex]Therefore, Christina earns $14.45 per hour.
This means Christina earns more money per hour than Jenny.
If x^3 = 125, what is the value of x?
Answers
Solution:
Given the equation:
[tex]x^3=125[/tex]To find the value of x,
we have
[tex]\begin{gathered} x^3=5^3 \\ since\text{ the powers are equal,} \\ \Rightarrow x=5 \end{gathered}[/tex]Hence, the value of x is
[tex]5[/tex]Given the problem below, what is the maximum number of gallons that the storagetank can hold?The volume of water, V, in a storage tank can be modeled as a function of the number of hours since it was27full by the equation V = 55cos -1 +67, where V represents the number of gallons of water in the tank.
Answers
ANSWER:
122 gallons
STEP-BY-STEP EXPLANATION:We have the following function:
[tex]V=55\cdot\: cos\mleft(\frac{2\pi}{7}t\mright)+67[/tex]The first thing is to calculate the periodicity of the function. The value of the periodicity would be the value of x (in this case t) to calculate the value of y, that is, in this case the volume.
As follows:
[tex]\begin{gathered} p=\frac{2\pi}{\frac{2\pi}{7}}=7 \\ \text{therefore x = 7, replacing} \\ V=55\cdot\: cos(\frac{2\pi}{7}\cdot7)+67 \\ V=55\cdot\: cos(2\pi)+67 \\ V=55+67 \\ V=122 \end{gathered}[/tex]Therefore the maximum volume would be 122 gallons.
Jane travels7 mph less than2 times as fast as Mike. Starting at the same point and traveling in the same direction, they are198 miles apart after6 hours. Find their speeds.
Answers
Let:
Vj = Speed of jane
Vm = Speed of mike
d = distance
t = time
Jane travels 7 mph less than 2 times as fast as Mike, therefore:
Vj = 2Vm - 7
Remeber:
distance = speed*time
Distance traveled by mike:
d=Vm*t = Vm*6
Distance traveled by jane:
d + 198 = Vj*6
where:
Vj = 2Vm - 7
d + 198 = (2Vm-7)*6
Now, let:
d=Vm*6 (1)
d + 198 = (2Vm-7)*6 (2)
Replace (1) into (2)
6Vm + 198 = 12Vm - 42
Subtract 6Vm from both sides:
6Vm + 198 - 6Vm = 12Vm - 42 - 6Vm
198 = 6Vm - 42
Add 42 to both sides:
198 + 42 = 6Vm - 42 + 42
240 = 6Vm
Divide both sides by 6:
240/6 = 6Vm/6
40 = Vm
Vm = 40mph
Replace Vm into this equation Vj = 2Vm - 7 :
Vj = 2(40) - 7 = 80 - 7 = 73mph
Perform the following transformations :First reflect the ABC across the y-axis ,then dilate by a factor of 1/2
Answers
Given the triangle ABC, you have to reflect it over the y-axis and then dilate it by scale factor k=1/2
- The reflection over the y-axis is a rigid transformation (the figure changes position but it does not change shape), which means that the resulting image will be congruent to the original.
- The dilation is a nonrigid transformation, the figure changes its shape, the resulting image after dilation is similar to the original one.
Reflection over the y-axis ΔABC to ΔA'B'C'
To reflect an image over the y-axis you have to change the sign of the x-coordinate leaving the y-coordinate of each vertex equal. The rule of the reflection can be expressed as follows:
[tex](x,y)\to(-x,y)[/tex]Preimage → Image
A(-1,-4) → A'(-(-1),-4)= A'(1,-4)
B(-3,-2) → B'(-(-3),-2)= B'(3,-2)
C(-1,2) → C'(-(-1),2)= C'(1,2)
After the reflection over the y-axis, the coordinates for the triangle are A'(1,-4), B'(3,-2), and C'(1,2).
ΔABC and ΔA'B'C' are congruent.
Dilation by scale factor k=1/2 ΔA'B'C' to ΔA''B''C''
To dilate a figure by a determined scale factor, you have to multiply the coordinates of each vertex by the said scale factor, you can write the dilation rule as follows:
Dilation factor k=1/2
[tex](x,y)\to(\frac{1}{2}x,\frac{1}{2}y)[/tex][tex]\begin{gathered} \text{Preimage \rightarrow Image} \\ A^{\prime}(1,-4)\to A^{\doubleprime}(\frac{1}{2}\cdot1,\frac{1}{2}\cdot(-4))=A^{\doubleprime}(\frac{1}{2},-2) \\ B^{\prime}(3,-2)\to B^{\doubleprime}(\frac{1}{2}\cdot3,\frac{1}{2}(-2))=B^{\doubleprime}(\frac{3}{2},-1) \\ C^{\prime}(1,2)\to C^{\doubleprime}(\frac{1}{2}\cdot1,\frac{1}{2}\cdot2)=C^{\doubleprime}(\frac{1}{2},1) \end{gathered}[/tex]After the dilation, the coordinates for the new triangle are A''(1/2,-2), B''(3/2,-1), and C''(1/2,1).
ΔABC and ΔA''B''C'' are similar.
Select the correct answer from each drop-down menu.The given equation has been solved in the table.StepStatement1= 15- - 6 =- - 6 + 6 = 15 ++4- = 21N34.2-2 - 215y = -42Use the table to complete each statement.In step 2, theIn step 4, theproperty of equality was applied.property of equality was applied.VResetNext
Answers
Solution
Step 1:
Addition Property of Equality
If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal. When you solve an equation, you find the value of the variable that makes the equation true.
Step 2
In the step 2, addition property of equality is applied.
[tex]\begin{gathered} \frac{2}{3}x\text{ - 9 =-13} \\ Apply\text{ the addition property of equality} \\ \frac{2}{3}x\text{-9 + 9=-13+9} \end{gathered}[/tex]Final answer
A) Step 2