Parallelogram MNPQ was dilated to create parallelogram M'N'P'Q'.
Which statements are true about the parallelograms? Check all that apply.
The length of side MN is 2 units.
The length of side M'N' is 5 units.
The image is smaller than the pre-image.
Sides MQ and M'Q' both have the same slope, 1.
The scale factor is 2/5
Answers
Answer:
Options 1,2 and 4 are correct.
Step-by-step explanation:
We have been given a parallelogram MNPQ was dilated to create parallelogram M'N'P'Q' and we asked to find out which of the given options are correct.
Let us see all the options one by one.
On using distance formula we can see that side MN is 2 units.
[tex]MN=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} }[/tex]
[tex]MN=\sqrt{(4-2)^{2} +(-2-(-2))^{2} }[/tex]
[tex]MN=\sqrt{(2)^{2} } =2[/tex]
Therefore,option 1 is correct.
We can find the side M'N' by distance formula as we solved for side MN. After solving for M'N' we will get 5 units. Therefore, option 2 is also correct.
Now let us see third option. We can see that image M'N'P'Q' is bigger than pre-image MNPQ. Therefore, option 3 is false.
Now look at our option 4.
Since we know slope is rise (difference of y coordinates) over run (difference of x coordinates) . Upon looking at our image and pre-image we can see that as we increase our x coordinate by one unit our y coordinate also increase by one.
Therefore, option 4 is correct indeed.
Upon looking at our fifth option we can see that our image is bigger than our pre-image. If our image was dilated by factor of 2/5 it would have been smaller than our pre-image. We can see the scale factor is 5/2 instead of 2/5.
Therefore, our fifth option is false.
Considering the slopes and scale factor of the diagram given, the statements that are true about the parallelogram are: A, B, and D.
How to find SlopeSlope = vertical distance / horizontal distance = change in y / change in x.
How to find Scale FactorScale factor = length of image/corresponding length of pre-image.
Find the length of MN:
MN = |4 - 2| = 2 units (Option A is true).
Find M'N':
M'N' = |10 - 5| = 5 units (Option B is true).
MNPQ is the pre-image, while M'N'P'Q' is the image, therefore, the image is bigger than the pre-image. (Option C is NOT true).
Find Slope of MQ:
Slope = 1/1 = 1
Find Slope of M'Q':
Slope = 2/2 = 1 (Option D is true).
Find the scale factor:
Scale factor = dimension of image/dimension of pre-image = M'N'/MN
Scale factor = 5/2 (Option E is NOT true).
Therefore, considering the slopes and scale factor of the diagram given, the statements that are true about the parallelogram are: A, B, and D.
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Related Questions
a spool of ribbon has 18 feet on it. pieces measuring of 8 inches will be cut from the spool of ribbon. how many 8 inch segments will be cut from the spool of ribbon
show work
Answers
By dividing the total length by the length of the pieces, we conclude that we can make 2 of these pieces.
How many 8 inch segments will be cut?To get this, we need to divide the total length by the length of the desired pieces, and then round to the next (lowest) whole number.
Then we get:
N = 18ft/8ft = 2.25
Rounding to the next whole number we get 2, so we conclude that with 18t of ribbon we can make 2 pieces of 8ft each.
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What is the value of 2 in 0.812
Answers
It is equal to two thousandths.
The first number after the decimal point is tenths.
The second number after the decimal point is hundredths
The third number after the decimal point is thousandths.
Hope This Helps You!
Good Luck :)
- Hannah ❤
The place of the digit 2 in the decimal number will be hundredths place.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.
The decimal number is given below.
⇒ 0.812
The place after the decimal starts from the tenths, hundredths, thousandths, and so on.
The place of the digit 2 in the decimal number will be hundredths place.
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The sum of two numbers is 43 . The smaller number is 19 less than the larger number. What are the numbers?
Answers
We can calculate this by using simultaneous equation, aka listing 2 equations out.
From given,
X + y = 43
Let this be equation no. 1
X + 19 = y
Let this number be equation 2.
We can do simultaneous equations either by substitute method or elimination. In this case I'm using substitute.
We can already obtain the value of y (in terms of x) in euqation no. 2, so all we gonna do is to put y into equation 1.
X + x + 19 = 43
Solve this by algebra.
2x = 43 - 19
X = 12
Now we know the exact value of x
Now substitute x = 12 into equation no. 2
12 + 19 = y
Y = 31
So the answer is 12 and 31
By setting up a system of equations, we find that the larger and smaller numbers in question are 31 and 12, respectively. We solve for the larger number first and then use it to find the smaller number.
Explanation:To solve this problem, we can use variables to represent the two unknown numbers. Let's call the larger number x and the smaller number y. We have two pieces of information that can be turned into mathematical equations:
Now we can substitute the second equation into the first one to solve for x:
x + (x - 19) = 43
Simplifying the equation, we get:
2x - 19 = 43
Adding 19 to both sides gives us:
2x = 62
Dividing both sides by 2 gives us:
x = 31
Now that we have the value of x, we can find y:
y = 31 - 19
This gives us:
y = 12
Therefore, the larger number is 31 and the smaller number is 12.
What would you do isolate the variable in the equation below,using only one step?
X-3=7
Select the correct answer below.
A.add 7 to both sides
B. Subtract 3 from both sides of the equation
C.add 3 to the left, 7 to the right.
D.add 3 to both sides
Answers
How can i use decimal models to add decimals?
Answers
what is 4.333333333 as a fraction.
I need this answer right now!!
Answers
Which expression represents the distance between −14.6 and −5.2 on the number line?
Answers
Answer:
9.4
Step-by-step explanation:
We are given that two integers -14.6 and -5.2
We have to find distance between -14.6 and -5.2.
Difference between =-5.2-(14.6)
Difference=-5.2+14.6=9.4
Distance is the absolute value of 9.4
Therefore,
[tex]\mid 9.4\mid =9.4[/tex]
Distance between -14.6 and -5.2 is 9.4
Which of the binomials below is a factor of this trinomial? x^2-7x-44
Answers
because
(x-11)(x+4)
when you multiply that you get x^2 - 7x -44
Answer:
C. (x -11)
Step-by-step explanation:
The given trinomial is [tex]x^2 - 7x - 44[/tex]
Let's factor it. To find factor, we need to find the factors of -44 such that when you add them, we have to get -7
-44 = -11*4
- 7 = -11 + 4
so the correct factors are -11 and 4
Now we can write the middle term - 7x = -11x + 4x
[tex]x^2 - 7x - 44 = x^2 - 11x + 4x - 44[/tex]
Now let's group the first two terms and second two terms and factor it.
= x(x - 11) + 4(x - 11)
Here (x-11) is common factor, so we can take outside and rewrite.
= (x - 11)(x + 4)
So the factors are (x - 11) and (x + 4)
Answer is C. (x -11)
All but two of the here amid’s built by the ancient Egyptians have faces inclined at 52° angles. Suppose an archaeologist discovers the ruins of a pyramid. Most of the pyramid has eroded, but the length of a side of the square base is 82 m. How tall was the pyramid, assuming it’s faces were inclined at 52°? Round your answer to the nearest meter.
A) 25m
B) 32m
C)52m
D) 105m
Answers
One of its sides is the height of the pyramid, with length H. The other side is half of the square base, so its length is 81 m. The hypotenuse of this triangle is the height of one of the faces.
By right triangle trigonometry,
[tex]\displaystyle{ \tan52^o= \frac{H}{41 \ m } [/tex],
thus,
[tex]H=\tan52^o\cdot41 \ m=1.28 \cdot41 \ m=52 \ m[/tex].
Answer: C) 52 m
if 152 divided by x equals 36 what would x be?
Answers
x[(152/x)] = 36x
152 = 36x
152/36 = x
38/9 = x
heather has 500 dollars in her savings account she withdraws 20 dollars per week for gas write an eqaution heather can use to see how many week it will take her to have a balance of 220 dollars
Answers
I think this is right
Cookies are sold singly or in packages of 10
or 30
.
With this packaging, how many ways can you buy 60
cookies?
Answers
30+30
10+10+10+10+10+10
Naomi has 50 red beads and white beads. The number of red beads is 1 more than 6 times the number of white beads. How many red beads does Noami have?
Answers
Let the number of white beads be w.
r + w = 50
r = 6w + 1
Substitute 6w + 1 in for r in the first equation.
6w + 1 + w = 50
7w + 1 = 50
7w = 49
w = 7
She has 7 white beads.
Now we use the first equation to find the number of red beads.
r + w = 50
r + 7 = 50
r = 43
She has 43 red beads.
Simone is in a bike a thon for a fundraiser. she recives 15 dollars. for each mile she bikes if she wants to raise 510 dollars how many miles does she need to bring ke
Answers
5 (9/12 - 1/4) + 0.5
Answers
5 (9/12 - 3/12) + 0.5
5 (6/12) + 0.5
5(2.5) + 0.5
12.5 + 0.5
13
next we want to subtract 3/4 - 1/4 and we get 2/4
next we want to multiply 5 * 2/4 and we get 10/4
and lastly we want to add 5/2 + 0.5 to get our answer
Answer: 3
To make lemonade, you used one gallon of water, four quarts of lemon juice, and 32 ounces of honey. How many quarts of lemonade did you make?
Answers
We already know there are 4 quarts of lemon juice.
And there are 32 ounces in a quart, so that would equal 1 quart of honey.
So all you need to do now is add 4 quarts, 4 quarts, and 1 quart to get 9 quarts. You would get 9 quarts of lemonade.
I hope this helped you! :)
To make lemonade, using one gallon of water, four quarts of lemon juice, and 32 ounces of honey, you would make 34 quarts of lemonade.
Explanation:First, notice that gallons are larger than quarts. You are moving from a larger unit of measure to a smaller unit of measure. This means you will need to multiply. There are 4 quarts in a gallon, so your conversion factor is 4. Now, multiply. Take the given number of gallons and multiply by 4.
8(1/2) x 4 = (17/2) x (4/1) = 68/2 = 34
The answer is 8(1/2) gallons - 34 quarts.
Joy organized a wedding.
Guests had to choose their meal from beef, chicken or vegetarian.
1/3 of the guests chose beef
5/12 of the guests chose chicken
23 of the guests chose vegetarian
How many guests were at the wedding?
Answers
so 23 times 4 is 92
We draw a random sample of size 36 from a population with the standard deviation 3.5. if the sample mean is 27, what is a 95% confidence interval for the population mean?
Answers
[tex]SE = \frac{s}{\sqrt{n}} = \frac{3.5}{\sqrt{36}} = \frac{3.5}{6} = 0.583[/tex]
Confidence interval is:
[tex][27 -2(.583), 27+2(.583)][/tex]
What does X equal?
15= x/6 - 1
Answers
first add the one to the 15 then multiply it by 6 and you get 96
First, add 1 to both sides, get 16=x/6.
Then, multiply both sides by 6.
Get your answer of x=96
Hope this helps
When solving for a system of equations, if you get an answer of 6=0, what does this solution mean regarding the solution to the system ?
Answers
how do you read this number. 7,654,321?
Answers
convert 220 from degrees to radians
Answers
to convert degrees to radians, multiply by π180°, since a full circle is 360° or 2π radians.220°⋅π180° radians Cancel the common factor of 20 111⋅π9 radians Multiply 111and π9 to get 11π911π9 radians
I hope this helps.
The conversion of the given degrees 220° is equal to 11π/9 radians approximately.
To convert degrees to radians, use the following formula:
radians = degrees × (π / 180)
Let's apply this formula to convert 220 degrees to radians:
radians = 220 × (π / 180)
radians = 220π / 180
Now, to simplify the fraction, you can divide both the numerator and denominator by their greatest common divisor, which is 20:
radians = (220/20)π / (180/20)
radians = 11π / 9
Therefore, 220 degrees is equal to approximately 11π/9 radians.
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one integer is 30 more than another integer if the difference between the larger and twice the smaller is 8 find the integers
Answers
x = larger int
y = smaller int
---
x - y = 30
x - 2y = 8
---
put the system of linear equations into standard form
---
x - y = 30
x - 2y = 8
---
solution:
x = larger int = 52
y = smaller int = 22
---
Joe tapped his maple tree to get syrup. The tree filled 3/4 of a cup in 1/2 hour.At what rate does syrup flow from the tree?
Answers
The rate of flow of syrup from the tree will be in mixed fraction form, equal to 1 1/2.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the data mentioned in the question,
The amount of syrup obtained from the tree = 3/4 cup
The time is taken to fill 3/4 cup = 1/2 hour
Then, the rate of flow of syrup will be,
(3/4) ÷ (1/2)
3/4 × 2/1
= 6/4 = 3/2
It can also be written in mixed fraction form,
= 1 1/2
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You measure the width of a doorway and find that it is 0.93 m wide. Find the greatest possible error of your measurement
Answers
Answer:
0.5 m
Step-by-step explanation:
The greatest possible error is 1/2 of the unit you are measuring in.
We are measuring in meters; this means the greatest possible error is 0.5 m.
Answer:
The right answer is 0.005m
Step-by-step explanation:
The greatest possible error in a measurement is the half of the measuring unit, it is one hald of the precision unit.
To solve it first you should recognize the measurement unit, in this case meters.
Then, because it is 0.93, you should notice that the last decimal occupies the place of the hundredth, so the GPE might be: 0.01/2 equal to 0.005, your answer.
Find all the real cube roots of 1000/27
10/3
10/9
-10/9
-10/3
Answers
1000
100 * 10
10 * 10 * 10
27
9 * 3
3 * 3 * 3
cube root (1000/27) = 10/3
Answer:
10/3
Step-by-step explanation:
Price Tax Rate Tax
$199 5%
$4,750 6%
$99.50 4.7%
$19.88 6.9%
$8.95 7.2%
$14.27 6.8%
$544.38 4.2%
$7.49 8.1%
$28.56 7.5%
$14.98 4.9%
Answers
199 *0.05 = 9.95
4750 * 0.06 = 285
99.50 * 0.047 = 4.68
19.88 * 0.069 = 1.37
8.95 * 0.072 = 0.64
14.27 * 0.068 = 0.97
544.38 * 0.042 = 22.86
7.49 * 0.081 = 0.61
28.56 * 0.075 = 2.14
14.98 * 0.049 = 0.73
The only way to sober up after drinking is
Answers
The body metabolizes and eliminates alcohol at a fixed rate, which can only be sped up with time. Hydrating and eating food may make you feel better, but they do not speed up the process of becoming sober.
Explanation:The only way to sober up after drinking is to allow time for your body to metabolize and eliminate the alcohol. No amount of coffee, water, or food can speed up this process. The liver processes alcohol at a fixed rate, and it takes about one hour to metabolize one standard drink. Other factors such as sex, weight, and age can affect this rate, but ultimately, getting sober just takes time. While waiting to sober up, hydrating and eating food can make you feel better, but doesn't actually speed up the sobriety process.
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What is difference between 164 and 220
Answers
The difference between 164 and 220 is 56.
The difference between 164 and 220 is 56. In mathematical terms, you calculate the difference by subtracting the smaller number from the larger one:
220 - 164 = 56.
If f(x) = 2x2 + 1 and g(x) = x2 – 7, find (f + g)(x).
A. 3x2 + 8
B. 3x2 – 6
C. x2 – 6
D. x2 + 8
Answers
Therefore:
(f+g)(x) = f(x) + g(x) Substitute the functions for f(x) and g(x)
(f+g)(x) = (2x² + 1 )+ (x² - 7)
Notice that we first want to write the functions in as parenthesis before we add them. This helps us keep from getting confused on what signs to give each term.
(f+ g)(x) = 2x² + x² + 1 - 7 Collect like terms
(f + g) (x) = 3x² - 6
Answer is B