The triangles XYZ and ABC are congruent by SAS postulate.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
Given two triangles XYZ and ABC.
If the two triangles are congruent, their corresponding sides and angles must be equal.
Given,
∠Y = ∠B
XY ≅ AB
YZ ≅ BC
SAS congruence theorem states that if two sides and an included angle of a triangle is equal to corresponding two sides and an included angle of the other triangle, then they are congruent.
So, ΔXYZ ≅ ΔABC by SAS postulate.
Hence the two triangles are congruent by SAS postulate.
Learn more about Congruence of Triangles here :
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A rectangular prism has a length of 9 in., a width of 4 in., and a height of 112 in.
The prism is filled with cubes that have edge lengths of 12 in.
How many cubes are needed to fill the rectangular prism?
Answer:
432
Step-by-step explanation:
Answer: 4032
Step-by-step explanation: 9x4x112 is 4032
i took the test and pls give brainiest
Help please ASAP I have to have this done In the hour
Answer:
A. 1,2,3,4
B. 1,2,3
C. 5 and up
D. $30
Step-by-step explanation:
Use trigonometric identities to simplify the expression.
cot(β+π)sin(β
Answer:
cosβ
Step-by-step explanation:
cot(β+π)sinβ
cot(x)=cos(x)/sin(x), so we can rewrite our expression as:
(cos(β+π)/sin(β+π)) * sinβ
sin(a+b)=sin(a)cos(b)+cos(a)sin(b), so we can rewrite our expression as:
(cos(β+π)/(sinβcosπ+cosβsinπ)) * sin(β)
cos(a+b)=cos(a)cos(b)-sin(a)sin(b), so we can rewrite our expression as:
(cosβcosπ-sinβsinπ)/(sinβcosπ+cosβsinπ)) * sin(β)
cosπ=-1 and sinπ=0, so we can rewrite our expression as:
(-cosβ)/(-sinβ) * sin(β)
(-cosβ)/(-sinβ) * sin(β)
=(cosβ/sinβ)(sinβ)
=cosβ
A line has a slope of -5 and includes the points (-1,r) and (-2,-2). What is the value of r?
Answer:
-7
Step-by-step explanation:
express(16^5)^1/4 in simplest radical form.
Answer:
32
Step-by-step explanation:
Hello, in (16^5)^1/4, you would multiply the exponents together like this:
16^5 x 1/4= 16^5/4
The exponents multiplied make 5/4. Now you need to multiply 16 with 5/4 like this:
16 x 5/4= 80/4
80 divided by 4 is 32 so therefore, the answer is 32.
Please help me! I really don't understand this.
Answer:
B
Step-by-step explanation:
x is less than -1 and the point is on -1.
I NEED HELP CLICK HERE PLEASE
Answer:
A- II
B- I
C- III
D- IV
Step-by-step explanation:
Someone please help me and explain it in simple words please and thank you.
Answer:
if you have a calculator above ti 84 you can enter integrals by pressing alpha window and selecting the integral option other than that it is not simple on paper you should look up a vid but it will take at least 15 mins to learn
alt optio. is to use wolfram alpha it works great you just input your problem
PLEASE HELP ANSWER THIS QUESTION!!!
Answer:
about 64.03
Step-by-step explanation:
A soft drink costs $1.65 and each refill for the drink costs $0.95. If you have $4.50, how many refills can you purchase?
Answer: 3 refills
Step-by-step explanation:
$1.65 + 0.95 + 0.95 + 0.95 = $4.50
please help! what is the measure of each central angle?
Answer:
9.3
Step-by-step explanation:
Among all rectangles that have a perimeter of 202, find the dimensions of the one whose area is largest. Write your answers as fractions
reduced to lowest terms.
Answer:
How to write by fraction? 50 1/2 by 50 1/2
Step-by-step explanation:
the maximum area for a rectangle is a square.
To find a square with p = 202, divide it by 4,
202 / 4 = 50.5
Pls only give direct answers
Answer:
B
Step-by-step explanation:
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answer:
maybe the second?
Step-by-step explanation:
Help .....................
Answer:
1. 8 is bigger
2. -9 is bigger
3. 12 is bigger
Step-by-step explanation:
72,-36,18,-9 find the common ratio
What value is missing from the table
Answer:
C. $15.75
Step-by-step explanation:
If one costs $1.05, 15 would be:
15 (1.05) = 15.75
Answer:
15.75
Step-by-step explanation:
1.05 a gallon times 15 gallons is 15.75
An initial amount of money is placed in an account at an interest rate of 3% per year, compounded continuously. After six years, there is $1819.77 in the account. Find the initial amount placed in the account. Round your answer to the nearest cent.
Hi
Let's call X the amount in the beginning.
we have X*1.03^6 = 1819.77
X = 1819.77 / 1.03^6
X ≈ 1524.03
Which value of x will make these ratios equivalent
24/42=4/x
A.19
B.15
C.7
D.5
Kinetic energy is expressed using the unit
A. Meters
b.Meters per second square
C. Joule per second
d Joule
Answer:
C or d
Step-by-step explanation:
kinetic energy is the energy a body possesses due to its motion because it is energy, kinetic energy it expresses the unit of joules. Velocity is very similar to speed. The difference is that Velocity is the speed in the given direction
Given X=[b a 4 a], Y=[c d a b], and Z=[a c 16 b]. What is Y if x-2y=z?
Answer:
A
[2, -4, -6, -2]
Step-by-step explanation:
help please will give brainest.
Hi, you didn't add any picture or attached the info
Two numbers total 51 and have a difference of 23. Find the two numbers?
Answer:
14 and 37
I just kept checking all the pairs I could think of until I got to this answer.
a shipping company charges a cost per pound plus a fixed fee to ship a package. The total cost, f(x), in dollars, of shipping x pounds is modeled by the function shown. f (x) = 4.99x + 5.75 which part of the function represents the fixed fee
Answer:
5.75
Step-by-step explanation:
Think about it like this, which number is changing with "X" ? Obviously the total f(x) and the number being multiplied by x (the slope) 4.99 so the fixed number is 5.75
PLEASE HELP WILL GIVE BRAINLIEST
Answer:
12.5%
Step-by-step explanation:
r = (1/4)((1500/1000) - 1) = 0.125
r = 0.125 = 12.5%
What is the probability of choosing a clubs or a numbered card from a deck of cards? Type your answer as a fraction.
Answer:
13/52
Step-by-step explanation:
Rotate the vector (3,-2) 90°
counter-clockwise about the
origin.
If the coordinate is (3, -2) then after the 90° counter-clockwise about the origin. Then new coordinate will be (2, 3).
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Convert the cartesian coordinate to the polar coordinate. Then we have
[tex]r = \sqrt{3^2 + (-2)^2}\\\\r = \sqrt{9 + 4 }\\\\r = 3.61\\\\\theta = \tan ^{-1}\dfrac{-2}{3}\\\\\theta = -33.69^o\\\\\theta = 326.31^o[/tex]
Then 90° counter-clockwise about the origin, then the angle will be
θ = 326.31 + 90 = 431.31
But θ is from 0 to 360. Then
θ = 431.31 - 360 = 56.31
Then convert the polar coordinate to the cartesian coordinate. Then we have
x = r cosθ
x = 3.61 × cos 56.31
x = 2
and
y = r sinθ
y = 3.61 × sin 56.31
y = 3
More about the coordinate geometry link is given below.
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Answer:
-2,-3
Step-by-step explanation:
2x^2=4+6x
Show your work please
Answer: x = 3 - sqrt 17 / 2 , x = 3 + sqrt 17 / 2
Step-by-step explanation:
2x^2 = 4 + 6x
divide both sides by 2
x^2 = 2 + 3x
move expression to the left
x^2 - 2 - 3x = 0
reorder the terms
x^2 - 3x - 2 = 0
use the quadratic formula
x = - (-3) +- sqrt (-3)^2 - 4 x (-2) / 2 x 1
calculate
x = 3 +- sqrt 17 / 2
answer
x = 3 - sqrt 17 / 2 , x = 3 + sqrt 17 / 2
Given: cos θ = -4/5 , sin x = -12/13, θ is in the third quadrant, and x is in the fourth quadrant; evaluate tan x.
-12/5
-13/5
-5/12
Answer:
Step-by-step explanation:
Given: cos θ = -4/5 , sin x = -12/13, θ is in the third quadrant, and x is in the fourth quadrant; evaluate tan x.
-12/5
-13/5
-5/12
Figure A is enlarged to create figure B. The ratio of the areas of A and B is 16:49.
One side of B is 5ft long. How long would the corresponding side on figure B be. Leave your answer as a fraction. (No image was provided, only the question itself.)
Answer: [tex]\dfrac{20}{7}[/tex]
Step-by-step explanation:
Given
The ratio of the area of the similar triangles is equal to the square of the side of the corresponding sides
Suppose the corresponding side on figure A is [tex]x[/tex]
On solving
[tex]\Rightarrow \dfrac{16}{49}=[\dfrac{x}{5}]^2\\\\\Rightarrow \dfrac{x}{5}=\sqrt{\dfrac{16}{49}}\\\\\Rightarrow \dfrac{x}{5}=\dfrac{4}{7}\\\\\Rightarrow x=\dfrac{20}{7}[/tex]