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serious [3.7K]
2 years ago
13

Which expression is equivalent to the expression below? (m+3/m^2-16)/(m^2-9/m+4)

Mathematics
2 answers:
maria [59]2 years ago
8 0

Answer:

\frac{1}{(m-3)(m-4)}

Step-by-step explanation:

(m+3/m^2-16)/(m^2-9/m+4)

Lets factor the numerator and denominator

use identity a^2 - b^2 = (a+b)(a-b)

m^2 - 16= m^2 - 4^2 = (m+4)(m-4)

m^2 - 9= m^2 - 3^2 = (m+3)(m-3)

we have divisiion sign in  between, change the division symbol in to multiplication symbol by flipping the fraction in the denominator

(m+3/m^2-16)*(m+4/m^2-9)

\frac{m+3}{(m+4)(m-4)} * \frac{m+4}{(m+3)(m-3)}

Cancel put m+3  and m+4  at the top and botom

\frac{1}{(m-3)(m-4)}

Lemur [1.5K]2 years ago
4 0

Answer:

B. 1/(m-4)(m-3)



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Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P'Q'R' has
Whitepunk [10]

Answer:

Please find attached the required plot accomplished with an online tool

Part A:

1/4

Part B:

P''(-1, 0),  Q''(0, -1), and R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent

Step-by-step explanation:

Part A:

Triangle ΔPQR has vertices P(4, 0), Q(0, -4), R(-8, -4)

Triangle ΔP'Q'R' has vertices P'(1, 0), Q'(0, -1), R'(-2, -1)

The dimensions of the sides of the triangle are given by the relation;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates on the ends of the segment

For segment PQ, we place (x₁, y₁) = (4, 0) and (x₂, y₂) = (0, -4);

By substitution into the length equation, we get;

The length of segment PQ = 4·√2

The length of segment PR = 4·√10

The length of segment RQ = 8  

The length of segment P'Q' = √2

The length of segment P'R' = √10

The length of segment R'Q' = 2

Therefore, the scale factor of the dilation of ΔPQR to ΔP'Q'R' is 1/4

Part B:

Reflection of (x, y) across the y-axis gives;

(x, y) image after reflection across the y-axis = (-x, y)

The coordinates after reflection of P'(1, 0), Q'(0, -1), R'(-2, -1) across the y-axis is given as follows;

P'(1, 0) image after reflection across the y-axis = P''(-1, 0)

Q'(0, -1) image after reflection across the y-axis = Q''(0, -1)

R'(-2, -1) image after reflection across the y-axis = R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent as the dimensions of the sides of triangle PQR and P''Q''R'' are not the same.

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kykrilka [37]
#21: Even
#23: Neither
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Hope this helps!! :)

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You would shade in 135 of the squares in the grid(s)
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