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Tanya [424]
1 year ago
5

Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not simila

r, explain why.

Mathematics
1 answer:
Ierofanga [76]1 year ago
3 0

Answer: \triangle XYZ \sim \triangle GFH by AA.

Step-by-step explanation:

Finding the third angle in triangle XYZ,

m\angle YXZ=180^{\circ}-77^{\circ}-48^{\circ}=55^{\circ},

Thus, \triangle XYZ \sim \triangle GFH by AA.

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What is the difference between exponent form and expanded form (repeated multiplication)?
Inga [223]
Expanded FormExpanded form refers to a base and an exponent written as repeated multiplication. ExponentExponents are used to describe the number of times that a term is multiplied by itself. ExpressionAn expression is a mathematical phrase containing variables, operations and/or numbers.
5 0
3 years ago
The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Th
Fantom [35]

Answer:

∫6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C

Step-by-step explanation:

To find:

∫6x^5(x^6-2)\,dx

Solution:

Method of substitution:

Let x^6-2=t

Differentiate both sides with respect to t

6x^5\,dx=dt

[use (x^n)'=nx^{n-1}]

So,

∫6x^5(x^6-2)\,dx = ∫ t\,dt = \frac{t^2}{2}+C_1 where C_1 is a variable.

(Use ∫t^n\,dt=\frac{t^{n+1} }{n+1} )

Put t=x^6-2

∫6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C_1

Use (a-b)^2=a^2+b^2-2ab

So,

∫6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C

where C=2+C_1

Without using substitution:

∫6x^5(x^6-2)\,dx = ∫6x^{11}-12x^5\,dx = \frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C

So, same answer is obtained in both the cases.

7 0
2 years ago
LM=9, NR=16, SR=8. Find the perimeter of △SMP.
Amanda [17]

Answer:

<h2>perimeter of △SMP = 25</h2>

Step-by-step explanation:

The perimeter of the triangle △SMP is the sum of al the sides of the triangle.

Perimeter of △SMP = ||MS|| + ||MP|| + ||SP||

Note that the triangle △LRN, △LSM, △MPN and △SRP are all scalene triangles showing that their sides are different.

Given LM=9, NR=16 and SR=8

NR = NP+PR

Since NP = PR

NR = NP+NP

NR =2NP

NP = NR/2 = 16/2

NP = 8

From △LSM,  NP = PR = <u>MS</u><u> = 8</u>

Also since LM = MN, MN = 9

From △SRP, SR = RP = <u>PS =  9</u>

Also SR =<u> MP = 8</u>

From the equation above, perimeter of △SMP = ||MS|| + ||MP|| + ||SP||

perimeter of △SMP = 8+8+9

perimeter of △SMP = 25

5 0
3 years ago
Which of the following statements best describes the relationship between a line and a point in a plane? exactly one plane conta
Alexandra [31]

Answer: (b) exactly one plane contains a given line and a point not on the line.


Step-by-step explanation: The basic postulates of geometry are very-well known to all of us. For example-

(i) The intersection of two lines determines a point,

(ii) Two parallel lines give result to a plane,

(iii) A line and a point not on the line determines a plane, etc...

Thus, with the help of the third point, we can easily arrive at the conclusion that a given line and a point not lying on the line is contained in a plane. For example- see the attached figure, AB is a line and P is any point not on the line. They both contained in the plane ABC.

Hence, the correct option is (b).


8 0
3 years ago
Read 2 more answers
Maria solved the equation below and got x = –4. Which of the following choices verifies that her solution is correct? 5x + 22 =
VladimirAG [237]
5(-4)+22 = (-4)+6
-20+22 = -4+6
2 = 2
Maria is correct, since both sides equally match.
3 0
3 years ago
Read 2 more answers
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