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d1i1m1o1n [39]
4 years ago
8

Look at the figures. How can you prove the triangles are congruent?

Mathematics
1 answer:
butalik [34]4 years ago
6 0

Answer: 1. Congruence among line segments: Two line segments are congruent if they have the same length. Thus, line segment PQ ≅ line segment RS as PQ = RS = 6 cm. 2. Congruence of Angles: Two angles are congruent if they have the same measure. Thus, ∠AO’B ≅ ∠QOP, as m ∠AO’B = m ∠QOP = 40

Step-by-step explanation:

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-7b-(4b-12) is reduced how?
Alex_Xolod [135]
Combine the -7b and 4b with Like terms to simplify
5 0
3 years ago
The length of the room is 3 times the width and the total area of the room is 27 square meters. What is the length of the living
Vika [28.1K]
l=3w\\
lw=27\\\\
3w\cdot w=27\\
3w^2=27\\
w^2=9\\
w=3 \vee w=-3\\
-3\not\in\mathbb{N}\\\\
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7 0
3 years ago
Find the degree of the polynomial <br> 5mn^4+7mn^2p^5+15np
user100 [1]

Answer:

The degree of this polynomial is "8"

Step-by-step explanation:

Recall that the degree of a polynomial is given by the degree of its leading term. Recall as well that the degree of a term is the maximum number of variables that appear in it.

So, let's examine each of the terms in the given polynomial, and count the number of variables they contain to find their individual degrees. then pick the one with maximum degree, and that its degree would give the actual degree of the entire polynomial.

1) term  5\,m\,n^4  contains one variable "m" and four variables "n", so a total of five. Then its degree is: 5

2) term  7\,m\,n^2\,p^5  contains one variable "m", two variables "n", and five variables "p". that is a total of eight variables. Then its degree is: 8

3) term 15\, n\, p  contains one variable n and one variable p. That is a total of 2. Then its degree is 2.

Based on the analysis above, and the fact that the term with highest degree is that of degree 8, the polynomial has degree 8.

6 0
3 years ago
Read 2 more answers
Simplify the fractions 81/126=
trapecia [35]

Answer:

9/14

Step-by-step explanation:

81/126=9x9/9x14=9/14

5 0
3 years ago
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What are the magnitude and direction of w = ❬–10, –12❭? Round your answer to the thousandths place.
san4es73 [151]

The direction of a vector is the orientation of the vector, that is, the angle it makes with the x-axis.

The magnitude of a vector is its length.

The formulas to find the magnitude and direction of a vector are:

\begin{gathered} u=❬x,y❭\Rightarrow\text{ Vector} \\ \mleft\Vert u|\mright|=\sqrt[]{x^2+y^2}\Rightarrow\text{ Magnitude} \\ \theta=\tan ^{-1}(\frac{y}{x})\Rightarrow\text{ Direction} \end{gathered}

In this case, we have:

• Magnitude

\begin{gathered} w=❬-10,-12❭ \\ \Vert w||=\sqrt[]{(-10)^2+(-12)^2} \\ \Vert w||=\sqrt[]{100+144} \\ \Vert w||=\sqrt[]{244} \\ \Vert w||\approx15.620\Rightarrow\text{ The symbol }\approx\text{ is read 'approximately'} \end{gathered}

• Direction

\begin{gathered} w=❬-10,-12❭ \\ \theta=\tan ^{-1}(\frac{-12}{-10}) \\ \theta=\tan ^{-1}(\frac{12}{10}) \\ \theta\approx50.194\text{\degree} \\ \text{ Add 180\degree} \\ \theta\approx50.194\text{\degree}+180\text{\degree} \\ \theta\approx230.194\text{\degree} \end{gathered}

Therefore, the magnitude and direction of the vector are:

\begin{gathered} \Vert w||\approx15.620 \\ \theta\approx230.194\text{\degree} \end{gathered}

3 0
2 years ago
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