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3 years ago

For each pair of similar triangles find the ratio of two side lengths. How do the ratios compare

Mathematics

1 answer:

UkoKoshka [18]3 years ago

5 0

Answer:

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.Step-by-step explanation: ratios

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Find the coordinates of point P that lies along the directed line segment AB in a 2:3 ratio given A (-2, 1), B (3, 4).

saul85 [17]

Answer:

$P(x,y) = (0,\frac{11}{5})$

Step-by-step explanation:

Given

$A = (-2,1)$

$B = (3,4)$

$m:n = 2:3$

Required

Determine the coordinates of P

The coordinate of a point when divided into ratio is:

$P(x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})$

Where

$(x_1,y_1) = (-2,1)$

$(x_2,y_2) = (3,4)$

$m:n = 2:3$

This gives:

$P(x,y) = (\frac{2 * 3 + 3 * -2}{2 + 3},\frac{2 * 4 + 3 * 1}{2 + 3})$

$P(x,y) = (\frac{6 - 6}{5},\frac{8 + 3}{5})$

$P(x,y) = (\frac{0}{5},\frac{11}{5})$

$P(x,y) = (0,\frac{11}{5})$

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3 years ago

Let m = 6x +5.<br> Which equation is equivalent to (6x + 5)^2 – 10 = -18x – 15 in terms of m?

aev [14]

Answer: m² + 3m - 10 = 0

Step-by-step explanation:

From the expression, considering

6x + 5 = m

The original expression

( 6x + 5 )² - 10 = -18 - 15

Factorize the right hand expression,

-18 - 15 = -3( 6x - 15 )

Since m = 6x + 5 , we now substitute for m in that expression

m² - 10 = -3m

Now re arrange the equation in the form,

ax² - bx + c = 0

Now back to the equation,

m² + 3m - 10 = 0,

So the equivalent equation will be

m² + 3m - 10 = 0

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4 years ago

Given f(x) = 3 and g(x) = cos(x). What is lim [F(x) - g(x)]?

Flura [38]

Answer:

Step-by-step explanation:

$\lim_{n \to \ -\pi } (f(x) - g(x))\\\\ = \lim_{n \to \ -\pi } (3 - cos x)\\\\ = 3 - cos( - \pi) = 3 - cos(\pi)\\\\ = 3 - (-1) = 3 + 1 = 4$

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3 years ago

For the situation, write and solve an equation. Then, explain what your solution means. If you get stuck, try drawing a diagram

Bess [88]

Answer:

5r + (5 x 6) = 84

looking for rice per pound.

Step-by-step explanation:

5r + (5 x 6) = 84

This shows an equation where we need to make r the subject to establish how many pounds a bag of rice weighs.

5r + (5 x 6) = 84

5r + (30) = 84

5r = 84-30

5r = 54/5

r = 10 4/5

r = 10.8 pounds

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