How do you find the area of the pre image and the image?
Coordinates for the pre-image are X(3,18) Y(18,18) and Z(18,9) and the image coordinates are X’(1,6) Y’(6,6) Z’ (6,3)
and what is the relationship between the two areas?
Answers
Answer: To find the area of the pre-image and the image, you can use the coordinates of the vertices of the shapes to calculate the lengths of the sides and use the formula for the area of a triangle:
Area = (base * height)/2
For the pre-image, the coordinates are X(3,18) Y(18,18) and Z(18,9). The base of the triangle is the distance between X and Z, which is 18 - 3 = 15. The height of the triangle is the distance between Y and Z, which is 18 - 9 = 9. The area of the pre-image is therefore:
Area = (15 * 9)/2 = 67.5
For the image, the coordinates are X’(1,6) Y’(6,6) Z’ (6,3). The base of the triangle is the distance between X’ and Z’, which is 6 - 1 = 5. The height of the triangle is the distance between Y’ and Z’, which is 6 - 3 = 3. The area of the image is therefore:
Area = (5 * 3)/2 = 7.5
The relationship between the two areas is that the area of the image is smaller than the area of the pre-image. This is because the image has been scaled down in size relative to the pre-image. The amount by which the image has been scaled down can be calculated by dividing the area of the image by the area of the pre-image:
Scale factor = area of image / area of pre-image = 7.5 / 67.5 = 0.11
This means that the image has been scaled down by a factor of 0.11 relative to the pre-image.
Step-by-step explanation:
Answer:
preimage area: 67.5 square unitsimage area: 7.5 square unitsimage area is 1/9 of preimage area, the square of the scale factorStep-by-step explanation:
You want to know the areas and their relationship of the preimage with coordinates X(3,18), Y(18,18), and Z(18,9), and the image with coordinates X’(1,6), Y’(6,6), Z’ (6,3).
TrianglesWhen you plot the points on a graph, you see they define right triangles. Each has sides aligned with the x- and y-axes, so it is easy to find their dimensions by counting grid squares or subtracting coordinates.
The preimage triangle is 18-3 = 15 units in the x-direction, and 18-9 = 9 units in the y-direction.
The image triangle is 6-1 = 5 units in the x-direction, and 6-3 = 3 units in the y-direction.
We notice that both the coordinates and the dimensions of the image triangle are 1/3 those of the preimage triangle.
AreasThe area of each triangle is given by the formula ...
A = 1/2bh
Using the dimensions we found above, the areas are ...
preimage area: 1/2(15)(9) = 135/2 = 67.5 . . . . square units
image area: 1/2(5)(3) = 15/2 = 7.5 . . . . square units
Relationship
We have observed that the image dimensions are 1/3 those of the preimage. The image area is 7.5/67.5 = 1/9 of that of the preimage. This value is the square of the scale factor of the dimensions,
Related Questions
28.2, 27.22, 27.62 , 27.54 , 27.5 in Greatest to Least
Answers
Answer:
28.2, 27.63, 27.54, 27.5, 27.22
Answer: 28.2, 27.62,27.5,27.22
Step-by-step explanation:
Simplify the expression. (-3+ 4n²) - (5 - 2n²)
Answers
Answer:
2(3n^2-4) and 6n^2-8
Step-by-step explanation:
There are two different answers but try at least both of them.
PLEASE HELP SOON
1. Solve the system. 3x+y = 10 y = 6x+1 Enter your answer by filling in the blanks. The solution is ( , )
2. Solve the system. 6x - y = -15 x + 2y = 17 Enter your answer as a coordinate pair in the blank.
Answers
Answer:
1. ( 1,7)
2. (17, 39)
Step-by-step explanation:
1. Replace all occurrences of y with 6x+1, and we get
9x + 1 = 10
x = 1
y = 6x + 1
y = 7
So, the answer for number 1 is (1,7)
2. 6x - y = -15x + 2y = 17
We subtract 2y and get
6x - 3y = 15x = 17
Replace all occurrences of x with 17, and we get
102 −3y = −15
x = 17
y = 39
So, the answer for number 2 is (17, 39)
i need help PLEASE DONT GIVE ME THE BITLY LINKS
Answers
Answer:
610
Step-by-step explanation:
area of triangle is A=0.5*h*b
a=0.5*20*(8+8+15)
a=310
area of square=lh
a=15*20
a=300
300+310=610
Complete the table with values for x or y that make this equation true : 3x+y=15.
Answers
Answer:
Step-by-step explanation:
So first, with the given table you need to "plug-in" the numbers that are there for x and y.
Ok, for example 2 is listed in the "x" row. So plug it 2 for "x":
3x+y=15
3(2)+y=15
6+y=15
-6 -6
y=9
So do this for all of them...the same goes with all of the values...just plug in one, complete the steps then you'll get the answer for the other variable.
Hope this helps!
Step by step
I graphed the line and found the matching x and y points. Example, given x=2 on the table, find x =2 and find where y crosses, that’s your y value of 9. Next is a y=3, find that point on the graph, where does the line cross for x? At x=4. Continue with the remainder numbers on the table. Graph all the points.
Table as follows
2 4 6 0 3 5 2.3333
_________________________
9 3 -3 15 6 0 8
The average weekly salary of two employees is $5350. One makes $250 more than the other. Find their salaries.
One employee makes $
and the other makes $?
Answers
Answer:
g
Step-by-step explanation:
g
In altitude BH and angle bisector AL intersect at point M. Given m∠HML = 100° and m∠MLC = 110°. Find angles of △ABC
Answers
The angles of triangle ABC are 60 degrees when altitude BH and bisector AL intersect at point M.
What is equilateral triangle?
An equilateral triangle in geometry is a triangle with equal-length sides on all three sides.
Given that:
[tex]\angle HML = 100 \\\\\angle MLC = 110[/tex]
Since, BH is the altitude [tex]\angle MHC= 90[/tex].
The total angle of a quadrilateral is 360, hence:
100 + 110 + 90 + C = 360
C = 60 degrees.
Now consider triangle BHC:
The sum of angle of a triangle is 180, hence:
90 + 60 + B = 180
B = 30
Since the half angle B = 30, the entire [tex]\angle ABC = 60[/tex].
Consider triangle ABC:
Using sum of triangles, we have:
[tex]\angle A + \angle B + \angle C = 180\\\\\angle A + 60 + 60 = 180 \\\\\angle A = 60[/tex]
Hence the measure of angles of triangle ABC is 60 degrees.
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What additional information would be necessary to determine sin A?
Answers
We can determine sin an in the above triangle using the available information without applying the Pythagorean theorem since the length of BC is required because it is the side opposite A.
We are told that we must calculate sin(a) without utilizing the Pythagorean theorem.
Now, we can see from the abbreviation SOHCAHTOA that if we wish to determine Sin a, it will be; sin a = opposite/adjacent
We must now locate a side opposing the angle A or the hypotenuse.
As a result, since the triangle is ABC, the required side is BC because it is the side opposite to A.
Finally, the length of BC is required because it is the side opposite A.
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The complete question should be like:
What additional information would be necessary to determine sin(A) without using the Pythagorean theorem? Explain.
If you have 10 friends and make two equal teams, what fraction do you use?
Answers
Mai bought some party supplies from an online store. For shipping, the shop charges a flat fee of $7.95 or 6.25% of the total purchase, whichever is greater. Suppose Mai's total purchase is $128. How much shipping will she pay?
Answers
Answer:
8
Step-by-step explanation:
if we do 128+7.95 we get 135.95. but when we do 128+8(wich is 6.25% of 128) we get 136. so she will pay 8 dollars in shipping
Hope this helps.
(i) Write 3^-2 as a fraction
(ii) Find the value of 3X^0 when X=5
Answers
ans Is here i) 1/9
ii) 3
tq brainlest?
A store that specializes in shipping packages reports that the distribution of packages shipped during the winter holidays is normally distributed with a mean of 4. 5 pounds with a standard deviation of 1. 8 pounds
What is the probability that two randomly selected packages are both more than 4. 5 pounds? (assume the packages are independent of each other)
a. ) 0. 5
b. ) 1
c. ) 0
d. ) 0. 25
Answers
The correct option is option (d).
To solve this problem, we need to find the probability that two randomly selected packages are both more than 4.5 pounds. Since the distribution is normal, we can use the standard normal distribution table to find the probability.
The first step is to standardize the weight of the packages by subtracting the mean from the weight and dividing it by the standard deviation. The weight of 4.5 pounds is the mean, so the standardized weight is (4.5 - 4.5) / 1.8 = 0.
The probability that a package weighs more than 4.5 pounds is the same as the probability that a standardized package weighs more than 0. This probability is equal to 1 - P(Z < 0) , where Z is the standardized weight.
Using a standard normal distribution table, we find that P(Z < 0) = 0.5. Therefore, the probability that a package weighs more than 4.5 pounds is 1 - 0.5 = 0.5.
Since the two packages are independent, we can find the probability that both packages are more than 4.5 pounds by multiplying the probability of one package being more than 4.5 pounds by itself. So, the probability that two randomly selected packages are both more than 4.5 pounds is 0.5 * 0.5 = 0.25.
In conclusion, the probability that two randomly selected packages are both more than 4.5 pounds is 0.25
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8⁶ ÷ 8?
can yall help me my brains gone dead
Answers
Answer:
32768
Step-by-step explanation:
8^6 is 262144, divide by 8. Your answer is 32768
Answer:
32768
Step-by-step explanation:
8 to the power of 6 is 262144
262144 divided by 8=32768
also invite me to ur brains funeral
10) En un triángulo rectángulo ABC, B es un ángulo
recto y m < A = 23° (medida del ángulo A). Si el
lado opuesto al ángulo A mide 17cm ¿Cuánto
mide la hipotenusa?
Answers
Answer:
140
Step-by-step explanation:
Primera tienes que sumar 23 y 17 despues tienes que buscar la differencia de 180 y 40.
Pls solve this 15 points
Answers
Answer:
128
Step-by-step explanation:
1/3base area×height
Find the greatest common factor of $144$ and $405$.
Answers
Answer:The answer to your question is 9
6^7/6^5 in index form
Answers
Answer:
[tex]6^{2}[/tex]
Step-by-step explanation:
When dividing numbers with same bases with indices this is the rule:
[tex]\frac{x^{y}}{x^{z} } =x^{y-z}[/tex]
So the answer is:
[tex]6^{7-5} = 6^{2}[/tex]
A vegetable store sold 3 fewer tons of vegetables on the first day than on the second, and on the third day it sold 5 9 of the amount sold in the first two days. How many tons of vegetables did the store sell on each of the days if it sold a total of 98 tons of vegetables on those three days
Answers
On solving the provided question, we can say that by equation
30 tons of veggies were sold on the first day, 33 tons on the second day, and 35 tons on the third day.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
x = amount (ton) of vegetables sold on day one; y = amount (ton) of vegetables sold on day two. Z = the amount of vegetables sold on the third day (in tons).
[tex]x=y-3\\z=(5/9)*(x+y)\\x+y+z=98\\x+y+[(5/9)*(x+y)]=98\\ 9x+9y+5x+5y=882\\14x+14y=882\\x=y-3\\14x+14y=882[/tex]
solution
[tex]x=30\\y=33\\x+y+z=98---- > z=98-(x+y)---- > z=98-63--- > 35[/tex]
30 tons of veggies were sold on the first day, 33 tons on the second day, and 35 tons on the third day.
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Evaluate the expression: 15(6 – 4)
WILL MARK BRAINLIEST
Answers
Answer:
30
Step-by-step explanation:
15(6 – 4)
=15(2)
=30
Answer:
larespuesta a conseguir sería 86
PLEASE ASAP ILL GIVE BRAINLIEST.
Answers
Answer:
The first law of motion
Step-by-step explanation:
Willow has a board that is 10 feet long. She needs to cut the board into equal pieces that are 1/3 feet long.
How many pieces can she cut?
Answers
Answer:
12
Step-by-step explanation:
y 65° 25
can someone solve this ?
Answers
Explanation: I am assuming you are looking for “a” so if you heard the method of 45, 45, 90 it helps you solve it. So by the 45 being across from 25 makes the 45 across a 25 as well, hope this was what you were looking for…
Write a recursive formula for an,the nth term of the sequence 125, -25, 5, ...
Answers
Recursive formula for a(n) , the nth term of the sequence is
⇒ a(n) = 125 × (5)ⁿ⁻¹
What is Geometric sequence?An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
We have to given that;
The sequence is,
⇒ 125, - 25, 5 , ....
Clearly, The sequence is a geometry sequence with common ratio - 5 and first term 125.
We know that;
The nth term of geometry sequence is,
⇒ a(n) = a rⁿ⁻¹
Where, 'r' is common ratio and 'a' is first term of the sequence.
Substitute all the values, we get;
The nth term of the given sequence is,
⇒ a(n) = a rⁿ⁻¹
⇒ a(n) = 125 × (5)ⁿ⁻¹
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What is 200/51 equal to
Answers
Answer:
Approx 3.92
Step-by-step explanation:
To indirectly measure the distance across a river, Houa stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Houa draws the diagram below to show the lengths and angles that she measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.
Answers
According to the Houa's drawing the distance across the river PR is
198.95 feetHow to measure the distance PRThe length of line PR is calculated using the knowledge of similar triangles
While similar triangles is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent.
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shown, the pair of equivalent sides are
PO and OC, PR and RE,
The solution is worked out using sides PO and OC, PR and RE,
PO / OC = PR / RE
let PR be equal to y such that PO = 140 + y
(140 + y) / 230 = y / 135
cross multiplying
135(140 + y) = 230y
Expanding
18900 + 135y = 230y
collecting like terms
18900 = 230y - 135y
95y = 18900
y = 198.95 feet
Hence PR = 198.95 feet
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what is the correct value of 3x + 2 for x = 5?
Answers
Answer:
17
Step-by-step explanation:
3x + 2
x = 5
3x + 2
3(5) + 2
15 + 2
17
[tex]\boxed{The\:value\:of\:3x\:+\:2\:for\:"x\:=\:5"\:is\:17.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]3x + 2 \\ = 3(5) + 2 \\ = 3 \times 5 + 2 \\ = 15 + 2 \\ = 17[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
I need help for number 2
Answers
The measure of the exterior angle for Object 1 - a decagon is 36°, while th measure of the exterior angle for Object 2 - a dodecagon is 30°.
What is a Decagon and a Dodecagon?n object with 12 sides is called a dodecagon while an object with 10 sides is called a decagon.
Note that the exterior angles of all shapes, regular or irregular is 360°. In this case, the shapes are regular, which means that the sides are equal, hence their angles will be equal.
To derive the exterior angle of a regular geometric shape, the formula is given as:
Exterior angle measure = 360 / number of sides
Hence for A (the decagon), we have:
EAM = 360/10
= 36°
For B (the dodecagon) we have:
EAM = 360/12
= 30°
Thus the exterior angle for both shapes are 36° and 30° respectively.
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Quadrilateral ABCD is similar to quadrilateral A'B'C'D'. Write 2 equations that could be used to solve for missing lengths?
Answers
2 equations that could be used to solve for missing lengths are:
[tex]\frac{AD}{A'D'} = \frac{BC}{B'C'}[/tex]
Now, According to the question:
Two quadrilaterals are similar if their corresponding angles are equal and also their corresponding sides must be proportional.
Quadrilateral ABCD is similar to quadrilateral A'B'C'D'.
ABCD ~ A'B'C'D'
So,
[tex]\frac{AB}{A'B'} = \frac{BC}{B'C'}\\ \\ \frac{CD}{C'D'} = \frac{AD}{A'D'}[/tex]
Hence, 2 equations that could be used to solve for missing lengths are:
[tex]\frac{AD}{A'D'} = \frac{BC}{B'C'}[/tex]
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Simplify the polynomial.
3x2 – 2x + 4x2 – X+X
Answers
Answer:
[tex]7x^{2} - 2x[/tex]
Step-by-step explanation:
combine like terms. not trying to be mean, but that all you have to do.
Answer:
14-2x
Step-by-step explanation:
collect like terms
3×2+4×2-2x-x-x
6+8-2x
=14-2x
Solve the proportion.
8 / 3 = g / 3
a. 1 / 8
b. 9 / 8
c. 8
d. 8 / 9