Help me!!!
Determine if the two figures are congruent and explain your answer. (10 points)
Answers
Answer:
yes they are congruent
Step-by-step explanation:
they have congruent sides to each other
The given figures are congruent.
Given are two figure ABCD and EFGH on a cartesian plane, we need to check if the figures are congruent or not,
The coordinates of the figure ABCD are:
A = (-1, 1), B = (-3, 2), C = (-4, 4) and D = (-2, 6).
The coordinates of the figure EFGH are:
E = (2, 0), F = (4, 1), G = (5, 3) and H = (3, 5).
To check if the figures ABCD and EFGH are congruent, we need to compare the corresponding sides and angles of the two figures.
Congruent figures have the same shape and size, so their corresponding sides must be equal.
Let's compare the corresponding sides of ABCD and EFGH, using the distance formula:
[tex]|D| = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
AB and EF:
[tex]|AB| = \sqrt{(-3+1)^2 + (2-1)^2}\\\\ |AB| = \sqrt{-2^2+1^2} \\\\ |AB| = \sqrt{5}[/tex]
And,
[tex]|EF| = \sqrt{(4-2)^2 + (1-0)^2}\\\\ |EF| = \sqrt{2^2+1^2} \\\\ |EF| = \sqrt{5}[/tex]
∴ AB = EF
Similarly,
[tex]BC =\sqrt{\left(-4-\left(-3\right)\right)^2+\left(4-2\right)^2}\\\\ BC = \sqrt{5}[/tex]
And,
[tex]FG =\sqrt{\left(5-4\right)^2+\left(3-1\right)^2}\\\\ FG = \sqrt{5}[/tex]
[tex]CD = \sqrt{\left(-2-\left(-4\right)\right)^2+\left(6-4\right)^2} \\\\ CD = 2\sqrt{2}[/tex]
And,
[tex]GH=\sqrt{\left(3-5\right)^2+\left(5-3\right)^2}\\\\ GH=2\sqrt{2}[/tex]
[tex]AD =\sqrt{\left(-2-\left(-1\right)\right)^2+\left(6-1\right)^2}\\\\ AD =\sqrt{26}[/tex]
And,
[tex]EH = \sqrt{\left(3-2\right)^2+\left(5-0\right)^2}\\\\EH =\sqrt{26}[/tex]
Therefore, we get,
FG = BC, GH = CD and AD = EH = √26.
Since we get all the corresponding sides are equal.
Hence the figures are congruent.
Learn more about congruency click;
https://brainly.com/question/31992651
#SPJ4
Related Questions
Solve for the value of x in the diagram: Show your work and explain the steps you used to solve.
Answers
Answer:
x = 20
Step-by-step explanation:
The triangles are similar
3 (3+5)
----- = ----------
12 (12+x)
Using cross products
3(12+x) = 12*(3+5)
3(12+x) = 12*8
3(12+x) = 96
Divide by 3
3(12+x)/3 = 96/3
12+x = 32
Subtract 12
12+x-12 =32-12
x = 32-12
x =20
SOMEONE PLEASE HELP ILL GIVE BRAINLIST
Construct 5 equivalent equations for the equation -3x + 1 = 2. Describe which value you multiplied by for each equivalent equation. Show all of your work to prove your answers are correct.
Answers
Answer:
-6x+2=4
3(-3x+1)=6
-2(3x-1)=4
-3x=1
x=-1/3
Step-by-step explanation:
Chloe wants to make a scrapbook with old family photos. An online scrapbooking company charges $45 plus $1 per page. Meanwhile, a family friend is willing to make a scrapbook for $9 plus $4 per page. For a certain number of pages, the prices would be equal. How many pages would that be? How much would Chloe be charged?
Answers
Answer:
The prices are equal when it's 12 pages. For 12 pages, she'd be charged $57
Step-by-step explanation:
x = PER page
y = total
Online scrapbooking equation:
y = 45 + x
Family friend equation:
y = 9 + 4x
Where prices (y) would be equal:
y = 45 + x (Multiply this by -4)
y = 9 + 4x
y = 9 + 4x
-4y = -180 - 4x
-3y = -171
y = 57
y = 45 + x
-y = -9 - 4x
0 = 36 - 3x
3x = 36
x = 12
How many in five days?
Answers
Answer:
d
Step-by-step explanation:
Answer:
I think it is B
Step-by-step explanation:
(-2,0);(0,7)
A.What is the slope?
B.What is the equation in point-slope form?
Answers
Answer:
A. 7/2 B.y - 0 = 7/2(x + 2)
Step-by-step explanation:
y2 - y1 / x2 - x1
7 - 0 / 0 - (-2)
7 / 2
= 7/2
y - 0 = 7/2(x + 2)
help ASAP Please show working
Answers
(a) [tex]a+b-c\\-2+-3-4\\-5-4\\-9[/tex]
(b) [tex]b+c^3\\-3+4^3\\-3+64\\61[/tex]
(c)[tex]\frac{3b^2-c^2+a^2}{-3abc} \\\frac{3(-3)^2-(4)^2+(-2)^2}{-3(-2)(-3)(4)} \\\frac{3(9)-16+4}{6(-3)(4)} \\\frac{27-16+4}{-18(4)} \\\frac{11+4}{-72} \\\frac{15}{-72} \\-\frac{5}{24}[/tex]
Answer:
The answer to (A) is -9.
The answer to (B) is 61.
The answer to (C) is [tex]-\frac{5}{24}[/tex] in fraction form or -0.208 in decimal form.
Step-by-step explanation:
For problem (A), which is [tex]a+b-c[/tex], in order to solve for this problem, plug in the information given from the question. The problem will look like [tex](-2)+(-3)-(4)[/tex]. Solve the problem by first adding (-2) + (-3), which equals (-5), and then, solve for (-5) -(4), which equals -9. The final answer for problem (A) will be -9.
For problem (B), which is [tex]b+c^{3}[/tex], start by plugging in the information given from the question. The problem will look like [tex](-3)+(4)^{3}[/tex]. Solve the problem by cubing 4, which equals 64, and then, solve for (-3)+(64), which equals 61. The final answer for problem (B) will be 61.
For problem (C), which is [tex]\frac{3b^{2}-c^{2}+a^{2} }{-3abc}[/tex], start by plugging in the information given from the question. The problem will look like [tex]\frac{3(-3)^{2}-(4)^{2}+(-2)^{2} }{-3(-2)(-3)(4)}[/tex]. Solve the problem by first simplifying the numerator.
To simplify the numerator, raise -3 to the power of 2, which will equal 9, and multiplying 3 by 9, which will look like [tex]\frac{27-(4)^{2}+(-2)^{2} }{-3(-2)(-3)(4)}[/tex]. Next, raise 4 to the power of 2, which equals 16, and multiply -1 by 16, which will look like [tex]\frac{27-16+(-2)^{2} }{-3(-2)(-3)(4)}[/tex]. The next step is to raise -2 to the power of 2, which will look like [tex]\frac{27-16+4 }{-3(-2)(-3)(4)}[/tex]. Then, subtract 16 from 27, which equals 11, and add (11) + (4), which equals 15. The numerator equals 15.
Next, simplify the denominator. First, multiply -3 by -2, which equals 6, and the problem will look like [tex]\frac{27-16+4 }{6(-3)(4)}[/tex]. Then, multiply 6 by -3, which equals -18, and the problem will look like [tex]\frac{27-16+4 }{-18(4)}[/tex]. The next step is to multiply -18 by 4, which equals -72, and the denominator will equal -72.
Then, reduce the expression by cancelling the common factor, and the common factor is 3. The final answer will be [tex]-\frac{5}{24}[/tex] in fraction form or -0.208 in decimal form.
HOLY CHICKIE NUGGIES WHAT IS THIS?!?!? I AM CONFUSION??
PLEASE HELP ASAP THIS IS A TIMED QUESTION!!!!
Answers
Answer:
Ok!
Step-by-step explanation:
Answer:
Step-by-step explanation:
I honeslty don't know any of this but it is probably comparing parrallel lines.
Plsss help I will give brainliest
Answers
In the table, it shows that for both grades 7 and 8 there are 10 students in band so it’s equal
What is the value of p in the equation 8p + 2 = 4p − 10?
ayudame Help pls
Answers
Answer:
p = -3
Step-by-step explanation:
8p + 2 = 4p - 10
combine like terms:
8p + 2 = 4p - 10
-2 -2
(+2 - 2 = 0 ~ this cancels out)
8p = 4p - 12
-4p -4p
(+4p - 4p = 0 ~ this cancels out)
4p = -12
isolate the variable through division
4p/4 = -12/4
p = -3
Find the product.
(5)(1)
(67)
5/13
5/6
5/42
42/5
Answers
Answer:
1: 5
2: 67
3: 65
4: 30
5: 210
6: 210
Step-by-step explanation:
simplify the following expression 4^-11/3÷4^-2/3
A.1/12
B.1/64
C.12
D.64
Answers
Question:
Simplify the following expression:
[tex]4^{-\frac{11}{3}[/tex]÷[tex]4^{-\frac{2}{3} }[/tex]
A.1/12
B. 1/64
C.12
D.64
Answer:
B. 1/64
1. Tyler's hourly salary is $14. If Tyler works
hours a day, then how much will be earned in a
day?
Answers
Answer:
????
Step-by-step explanation:
The number of hours he works is missing???
Coraline was training for cross country season an app to track 24 laps around the track that measures 110 m what was the total distance Coraline ran in kilometers
Answers
Answer:
2.64 km
Step-by-step explanation:
The first step is to calculate the distance in meters
= 24×110
= 2640 meters
1km= 1000 meter
2640 meters to kilometer
= 2640/1000
= 2.64 kilometers
Hence the distance is 2.64 km
What is the value of x?
sin 49° = COS X
Enter your answer in the box.
X =
Answers
Answer:
x = 41°
Step-by-step explanation:
Using the cofunction identity
sinx = cos(90 - x) , then
sin49° = cos(90 - 49)° = cos49°
with x = 41°
Chasidy and Shelby went to the candy store. Chasidy bought 5 pieces of fudge and 3 pieces
bubble gum for a total of $5.25. Shelby bought 2 pieces of fudge and 3 pieces of bubble gu
for a total of $3.00. What was the cost of the fudge and the gum?
please answer ASAP
Answers
Answer:
75cents for the fudge while the bubble gum are .50 cents
Step-by-step explanation:
because we got that 75 cents is for the fudge so they we multiple 75cents w 2 and when you sum it up if it makes the amount they spent then its right
straight line graphs
Answers
Answer:
I don't get it what is the question ❓
How do I solve this?
Answers
Answer:
3p³ + 2p² – 3p – 11
Step-by-step explanation:
From the question given above, the following data were obtained:
Side 1 (S₁) = –1(p + 5)
Side 2 (S₂) = 2(p² – 3)
Side 3 (S₃) = 3p³ – 2p
Perimeter (P) =?
The perimeter of the triangle can be obtained as follow
P = S₁ + S₂ + S₃
P = –1(p + 5) + 2(p² – 3) + 3p³ – 2p
Clear bracket
P = –p – 5 + 2p² – 6 + 3p³ – 2p
Rearrange
P = 3p³ + 2p² – 2p – p – 6 – 5
P = 3p³ + 2p² – 3p – 11
Therefore, the perimeter of the triangle is 3p³ + 2p² – 3p – 11
b) Find x and y.
x = 10-6
Answers
Answer:
to find y you have to do trigonometry
Si Marcia dispone de $ 75.000 y gasta los "dos tercios" de dicha cantidad, ¿con cuánto dinero queda Marcia.?
1. 50.000
2. 15.000
3. 20.000
4. 25.000
5. 30.000
Answers
Answer:
25.000
Step-by-step explanation:
75.000(2/3) = 50.000
75.000-50.000= 25.000
what is the percent increase between 8,863,052 and 9,149,840?
Answers
Answer:
[tex]increase = 9149840 - 8863052 \\ = 286788 \\ \% \: increase = \frac{286788}{8863052} \times 100\% \\ = 3.24\%[/tex]
Answer:
=3.23577% increase
Step-by-step explanation:
1) subtract final value minus starting value
2) divide that amount by the absolute value of the starting value
3) multiply by 100 to get the percent increase
4) if the percentage bis negative, it means there was a decrease and not an increase
What is the slope that passes through the points (-8, -7) and (-5, 2)?
Answers
Answer:
3
Step-by-step explanation:
The equation for finding a slope is (y2-y1)/(x2-x1), where (x1, y1) is a set and (x2,
y2) is another set. (2-(-7))/(-5-(-8) = (2+7)/(-5+8) = 9/3 = 3. Hope this makes sense and helps!
Answer:
3
Step-by-step explanation:
To find the slope given two points, we use the slope formula
m = ( y2-y1)/(x2-x1)
m = ( 2 - -7)/(-5 - -8)
= (2+7)/( -5+8)
9/3
3
Please help will give brainliest
Answers
Answer:
-2
Step-by-step explanation:
(fxg)(0)
= f(0) x g(0)
since f(0) = -1 and g(0) = 2so (fxg)(0) = -2
Which graph represents the function f(x) = (x - 5) + 3?
Answers
Answer:
It's exponential function, the base is 5.
Horizontal asymptote is y = 0
At x = 0, y = 3
x = 1, y = 15
Step-by-step explanation:
The nth term of the sequence is given by 2n² + 1. Write down the next four terms of the sequence.
1.3, 9, 19, 33
2.4, 10, 20, 34
3.5, 11, 21, 35
4.6, 12, 22, 36
if your answer is write so i will mark as brainliest
Answers
Answer:
1. 3, 9, 19, 33
Step-by-step explanation:
2(4)²+1 = 2(16)+1 = 32+1 = 33
Nolan plots the y-intercept of a line at (0, 3) on the y-axis. He uses a slope of 2 to graph another point. He draws a line through the two points. Which equation represents Nolan’s line?
y = 2x + 1
y = 2x + 3
y = 3x + 2
y = 3x + 5
Answers
Answer:
B
Step-by-step explanation:
The equation of Nolan's line is
The slope-intercept form of a line is given by:
Here
m is the slope of the line
and b is the y-intercept.
Given
y-intercept = b = 3
slope = m = 2
The values of m and b can be put into the equation to find the line's equation
So,
Putting the value
Hence,
The equation of Nolan's line is
What is the value of x?
Answers
Answer:
The value of x is 88° enjoy
Can someone help?
A family has a monthly budget of $2,400. How much money is spent on each category?
a 44% is spent on housing
b 23% is spent on food.
c 6% is spent on clothing
d 17% is spent on transportation
e the rest is put into savings
Answers
a 1,056$ on housing
b 552$ on food
c 144$ on clothing
d 408$ on transportation
e 240$ on savings
Mark's average after 9 exams was 60. After 10 exams it had decreased to 50. How many marks did he score in his 10th exam?
Answers
Answer:
hey how much mark he scored in 9th exam give proper data or how many subject there
Help plssss I need help
Answers
Answer: 7 cm sorry if im wrong
Step-by-step explanation:
1*8*5 = 40 cm
the grid below is made up of squares with sides of 1cm draw a rectangle with an area of 12 cm squared
Answers
Answer:
6 is length and 2 is width.