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3 years ago

Find the missing measurements of the right triangle.

Mathematics

1 answer:

svlad2 [7]3 years ago

3 0

Step-by-step explanation:

as always, the sum of all angles in a triangle is always 180°.

therefore, the angle at B is

B = 180 - 27 - 90 = 63°.

for the missing sides we use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

where the sides are always opposite of the related angles.

so,

AB/sin(90) = 12/sin(27)

since sin(90) = 1, we have

AB = 12/sin(27) = 26.43227118... ≈ 26.4

AC/sin(63) = 12/sin(27)

AC = 12×sin(63)/sin(27) = 23.55132607... ≈ 23.6

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Figure 2 was constructed using figure 1. For the transformation to be defined as a rotation, which statements must be true? Sele

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Answer:

The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2).

The transformation is rigid.

Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.

If figure 1 is located 360° about point C, it will be mapped onto itself.

Step-by-step explanation:

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2 years ago

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of t

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3 years ago

The Lopez family and the Russell family each used their sprinklers last summer. The water output rate for the Lopez family's spr

grin007 [14]

L = hours used by the Lopez's sprinkler

R = hours used by the Russell's sprinkler

so, we know the Lopez's sprinkler uses 15 Liters per hour, so say after 1 hour it has used 15(1), after 2 hours it has used 15(2), after 3 hours it has used 15(3) liters and after L hours it has used then 15(L) or 15L.

likewise, the Russell's sprinkler, after R hours it has used 40R, since it uses 40 Liters per hour.

we know that both sprinklers combined went on and on for 45 hours, therefore whatever L and R are, L + R = 45.

we also know that the output on those 45 hours was 1050 Liters, therefore, we know that 15L + 40R = 1050.

$\bf \begin{cases}
L+R=45\implies \boxed{L}=45-R\\
15L+40R=1050\\
----------\\
15\left(\boxed{45-R} \right)+40R=1050
\end{cases}
\\\\\\
675-15R+40R=1050\implies 25R=375\implies R=\cfrac{375}{25}\\\\\\ R=15$

how long was the Lopez's on for? well, L = 45 - R.

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3 years ago

Simplify the given polynomial expressions as much as possible

bazaltina [42]

Answer:

34a^2 + 21a - 20

Step-by-step explanation:

(12a^2 + 6a -8) - (-22a + 12 - 15a)

12a^2 + 6a - 8 + 22a + 12 - 15a

34^2 + 6a - 8 - 12 + 15a

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2 years ago

2h divided by 15 equals 20

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3 years ago