You can find the corresponding parts of two congruent triangles by aligning them perfectly on top of each other.
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be ΔABC
Let the second triangle be ΔDEF
Now , when the triangles are aligned perfectly on top of each other ,
They are corresponding and the and the measures of the angles are same
And , the measure of the legs of the triangles will also be congruent
Hence , the corresponding parts are same
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What is the area of a parallelogram whose vertices are A(−12, 2) , B(6, 2) , C(−2, −3) , and D(−20, −3) ? Enter your answer in the box.
Answer:
[tex]\boxed{90}\,\text{units$^2$}[/tex]
Step-by-step explanation:
The sides AB and CD are parallel to the x-axis and 5 units apart. The length of side AB is 6-(-12) = 18 units. The area is the product of these dimensions:
Area = (Base)(Height) = (18 units)(5 units) = 90 units²
the area of one of the smaller circles is 8 pi in2. find the area of the shaded region
the answer is D. 16 pi
Answer:
D.
Step-by-step explanation:
How many 10 are in 64785
how do you solve this 2 step equation: 9+9n=9
Tommy stands on a diving board that is 4 fee above the pools surface. He dives and touches the bottom of the pool, which is 12 feet below the pools surface. What is the total length of Tommy’s dive?
Which of the following is equivalent to 30p^4q^3r + 42p^2r - 18p^2q^2r when it is completely factored?
A. 3pr(10p^3q^3 + 12p - 9pq^2)
B. 6(5p^4q^3r + 7p^2r - 3p^2q^2r)
C. 6p^2q^2r(5p^2q + 4)
D. 6p^2r(5p^2q^3 + 7 - 3q^2)
The figure in the picture is made up of 5 congruent squares. If the perimeter of the entire figure is 21.6 cm, find its area.
Calculate the area of the irregular polygon shown below:
45 inches squared
50 inches squared
60 inches squared
85 inches squared
The equation of line p is y = 52x + 72. line q is parallel to line p. the slope of line q is?
Please be a good person and help me..I really need to get this right to boost my grade in math ((and boy do I need it!!))
Use the graph shown to fill in the blank.
When x = 1, then y = a0.
I NEED HELP I'M SOO LOST I'LL GIVE A BRAINLIEST TO THE BEST ANSWER
Contrast the tone of the following two passages. (First, determine the tone of each passage. Then determine how the tones differ. What is the tone of each? How do you know? How do the tones differ?)
Tone ONE
Envisioning paths where Russell’s discovery could lead him, Rosalind and I began grooming him for interviews with the local news and math journals. In our minds, Russell’s future was bright and without limitation, starting with a full scholarship to MIT or Northwestern.
Tone 2
I came home for brief visits, but these visits were too awkward without Rosalind. The house was profoundly still. Mommy stayed in her room. Russell didn’t talk, let alone look at me.
The first passage has a hopeful and ambitious tone, using optimistic language to express excitement for the future. The second passage has a melancholic and isolated tone, using somber phrases to convey discomfort and disconnection. These contrasting tones reflect a range of emotions in the narrative.
Explanation:To contrast the tone of two passages, we must first identify the attitude or mood present in each. In Tone ONE, the writer’s use of optimistic phrases such as "Envisioning paths," "grooming him for interviews," and "future was bright" convey a hopeful and ambitious tone. This tone suggests excitement for the future possibilities and success that lie ahead for Russell.
In contrast, Tone 2 uses phrases like "too awkward," "profoundly still," and "didn’t talk" which reveal a somber, isolated and possibly melancholic tone. It reflects the author’s feelings of discomfort, silence, and the lack of communication and connection with the family.
The two tones differ significantly, with the first being uplifted and forward-looking, while the second expresses a sense of disconnection and sadness, giving us a comprehensive view of the contrasting emotional landscapes in the same narrative context.
How long is the arc subtended by an angle of 9π/5 radians on a circle of radius 30 cm?
A) 9π
B) 27π
C) 54π
D) 108π
Answer:
54π
Step-by-step explanation:
54π is correct. (9π/5)(30)= 54π
The required length of an arc is 54π cm which is subtended by an angle.
What is an arc?The arc is a portion of the circumference of a circle.
To find the arc length, we first need to find the circumference of the circle. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.
Plugging in the values given in the problem, we find that the circumference of the circle is C = 2π(30 cm) = 60π cm.
Then, to find the arc length, we need to find the fraction of the circumference subtended by the angle of 9π/5 radians.
The circumference of the circle is 2π radians, so the fraction of the circumference subtended by the angle of 9π/5 radians is (9π/5)/(2π) = 9/10.
Multiplying the fraction of the circumference subtended by the angle by the circumference of the circle, we find that the arc length is (9/10)(60π cm) = 54π cm.
Therefore, the correct answer is (C) 54π cm.
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The perimeter of triangle ABC is 54. The triangle has side lengths AB=3x, BC=4x, and AC= 5x. Find the length of each side.
If f(x) is the total number of bacteria present in a sample after x hours, which of the following statements best describes the meaning of f(2) = 12? (1 point)
Solve for y 3y-9=6 show work
What is the coefficient in the expression 3x/13+4 ?
Enter your answer in the box.
A supplier offers a discount on a product bought in bulk. If you buy 240 parts, you get a $5 discount on each part, which reduces the cost to the same as buying 200 parts at full price. How much is each part?
What issues does a person "charged" with a crime typically have to deal with?
Which expression is equivalent to 32⋅32⋅32⋅32 ?
32⋅4
(32)4
342
324
Answer: [tex]32^4[/tex].
Step-by-step explanation:
The given expression : [tex]32\cdot 32\cdot 32\cdot32[/tex]
Using the law of exponent :-
[tex]a\times\atimes....\times a (\text{ n times})=a^n[/tex]
Now, the given expression ,becomes
[tex]32\cdot 32\cdot 32\cdot32\text { (4 times)}=32^4[/tex]
Hence, the expression is equivalent to the given expression [tex]32\cdot 32\cdot 32\cdot32[/tex] is [tex]32^4[/tex].
A clipboard costs 2.23. it costs 0.53 more than a notebook. lisa buys two clipboards and one notebook, and paid with a ten dollar bill. use a tape diagram with calculations to show her change
Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?
howdy!!
yr answer is
A. {–7, 1} !!!
If three times the supp. of an angle is subtracted from seven times the comp. of the angle, the answer is the same a that obtained by trisecting a right angle. Find the supplement.
A piece of land is to be fenced and subdivided as shown so that each rectangle has the same dimensions. Express the total amount of fencing needed as an algebraic expression in x.
If two or more rectangles have the same dimensions is because they are congruent. In this way, they share two corresponding sides. Our first rectangle has the following sides:
L1 = x
L2 = 3x + 4
Therefore the second and third rectangles need to have the same sides. Therefore, we will have that the sides of the second one is also:
L1 = x
L2 = 3x + 4
and the sides of the third one is also:
L1 = x
L2 = 3x + 4
Therefore, the total amount of fencing needed is:
T = 3(3x + 4) + 4(x)
T = 9x + 12 + 4x
T = 13x + 12
Moreover, we can compute the area of the fence as follows:
A = [(3x + 4) + (3x + 4) + (3x + 4)]x = (3x + 3x + 3x + 4 + 4 + 4)x
A = (9x + 12)x
A = 9x² + 12x
The algebraic expression that expresses the total amount of fencing needed is 11X + 20.
CalculusGiven that a piece of land is to be fenced and subdivided as shown so that each rectangle has the same dimensions, to express the total amount of fencing needed as an algebraic expression in X, the following calculation must be performed:
3X + 4 = 6 wooden fence blocksEach rectangle has 3 blocks on each side and 6 blocks in front.Number of fronts = 3Number of sides = 4(3X + 4) x 3 + ((3X + 4) x 4) / 2 = Algebraic expression9X + 12 + (4X + 16) / 2 = Algebraic expression9X + 12 + 2X + 8 = Algebraic expression11X + 20 = Algebraic expressionTherefore, the algebraic expression that expresses the total amount of fencing needed is 11X + 20.
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If a bag contains 16 red,6 yellow, 24 blue, and 8 white ballons, what is the part-to-whole ratio of yellow ballons to all ballons
9 more than the quotient of negative 36 and negative 4
A wooden board is leaning against a house. the base of the board is 10 ft from the base of the house and the base of the board forms a 35 degree angle with the ground
so what is the length of the wooden board?
Lannie order 12 copies of the same book for his book club members to build cost $19 each and the order has a $15 shipping charge what is the total cost of lannie's order
Ow is the constant max_length declared inside a method with the value of 99.98?
Triangle DEF is formed by the three squares P, Q, and R:
A right triangle DEF is shown. On the side DE of this triangle is a square. Inside the square is written Square P, and below it and inside the square is written Area equal to 64 square units. On the side EF of this triangle is another square. Inside the square is written Square Q, and below it and inside the square is written Area equal to 225 square units. On the side DF of this triangle is another square. Inside the square is written Square R, and below it and inside the square is written Area equal to 289 square units.
Which statement best explains the relationship between the sides of triangle DEF?
DE + EF = DF, because 64 + 225 = 289
(DE)2 + (EF)2 = (DF)2, because 172 + 82 = 152
(DE)2 + (EF)2 = (DF)2, because 64 + 225 = 289
DE + EF = DF because, 172 + 82 = 152
using the Pythagorean Theorem
a^2 + b^2 = C^2
so correct answer is:
(DE)2 + (EF)2 = (DF)2, because 64 + 225 = 289
Answer:
(DE)2 + (EF)2 = (DF)2, because 64 + 225 = 289
Step-by-step explanation:
How many 3-digit numbers can you write using only the digits 1 and 2?