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3 years ago

A ladder that is 32 ft long leans against a building. The angle of Elevation of the Ladder is 70 degrees

Mathematics

1 answer:

netineya [11]3 years ago

3 0

Answer:

B. 30 ft

Step-by-step explanation:

The ladder is 32 ft long

The angle of elevation of the ladder is 70°

The height (h) of the top of the ladder to the ground is what we are to find.

$\frac{h}{32}$ = sin 70°

h = 32 × sin 70° = 30.07016387 or 30 ft (rounded off to nearest feet)

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A coach purchases 47 hats for his players and their families at a total cost of $302. The cost of a small hat is $5.50. A medium

frosja888 [35]

Answer:

The answer is below

Step-by-step explanation:

Let x represent the number of small hat purchased, y represent the number of medium hat purchased and z represent the number of large hat purchased.

Since a total of 47 hats where purchased, hence:

x + y + z = 47 (1)

Also, he spent a total of $302, hence:

5.5x + 6y + 7z = 302 (2)

He purchases three times as many medium hats as small hats, hence:

y = 3x

-x + 3y = 0 (3)

Represent equations 1, 2 and 3 in matrix form gives:

$\left[\begin{array}{ccc}1&1&1\\5.5&6&7\\-3&1&0\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}47\\302\\0\end{array}\right] \\\\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1&1&1\\5.5&6&7\\-3&1&0\end{array}\right] ^{-1} \left[\begin{array}{c}47\\302\\0\end{array}\right] \\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}6\\18\\23\end{array}\right]$

Therefore he purchases 6 small hats, 18 medium hats and 23 large hats

5 0

3 years ago

Need helpppppp!!!!!!

uysha [10]

These are 45-45-90 triangles, whose hypotenuses are $\sqrt{2}$ times their legs. Given a side of length 1, for example, the diagonal length is $\sqrt{2}\approx 1.4142.$ The first few ordered pairs $(x,y)$ in the table would be $(1,1.41),(2,2.83),(3,4.24),(4,5.66),...$

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3 years ago

Nick cut a circular cookie into 5 equal slices. what is the angle measure of each slice?

NemiM [27]

Answer:

72°

Step-by-step explanation:

The cookie has a shape of a circle. A circle is the locus of a point such that its distance from a point (center) is always the same. The sum of angles around the circle center is 360°.

Let x be the measure of the angle in each slice. Therefore the sum of the total 5 slice is:

x + x + x + x + x = 360

5x = 360

Dividing through by 5:

5x / 5 = 360 / 5

x = 72°

Each slice has an angle measure of 72°

5 0

3 years ago

Combine like terms and simplify the expression: -2+6x+4+4x

serg [7]

-2+6x+4+4x
=2+10x
hope it helps