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3 years ago

15

Find the measure of the indicated side or angle.

1 answer:

lozanna [386]3 years ago

7 0

Answer:

60°

Step-by-step explanation:

We'll begin by calculating EC. This can be obtained as follow:

Angle EAC = 39°

Hypothenus = EA = 3.7 m

Opposite = EC =?

Sine EAC = Opposite /Hypothenus

Sine 39 = EC / 3.7

Cross multiply

EC = 3.7 × Sine 39

EC = 2.3 m

Finally, we shall determine angle BEC. This can be obtained as follow:

Adjacent = EC = 2.3 m

Hypothenus = BC = 4.6 m

Angle BEC =?

Cos BEC = Adjacent / Hypothenus

Cos BEC = 2.3 / 4.6

Cos BEC = 0.5

Take the inverse of Cos

BEC = Cos¯¹ 0.5

BEC = 60°

Thus, angle BEC is 60°

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A can in your pantry has a 1.4 inch radius and is 5 inches tall. What is the surface area of the can to the nearest tenth?

WITCHER [35]

Well, let's do the math. The formula of a cylinder is 2 (pi, which will be estimated to 3.14) r h + 2 pi (radius times radius).
First of all, do 2 x pi, which is 6.28. Multiply 6.28 x 1.4 is 8.792. 8.792 x 5 = 43.96.
Now for 2 times 3.14 again, which is 6.28. But this time, we do 1.4 x 1.4, which is 1.96. With our new number, we do 6.28 x 1.96, which is 12.3088.
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4 years ago

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3 years ago

At a store, markers are sold in packages of 12 and pens are sold in packages of 8. What is the least amount of markers and pens

liubo4ka [24]

Given:

Markers are sold in packages of 12 and pens are sold in packages of 8.

To find:

Least amount of markers and pens Rick needs to buy to have an equal number of markers and pens

Solution:

To find the least amount of markers and pens, we need to find the LCM of 12 and 8.

Prime factors of 8 and 12 are

$8=2\times 2\times 2$

$12=2\times 2\times 3$

To find the LCM, multiply all factors but the common factors are included only once.

$LCM(8,12)=2\times 2\times 2\times 3$

$LCM(8,12)=24$

Therefore, the least amount of markers and pens Rick needs to buy to have an equal number of markers and pens is 24.

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4 years ago

The middle school is 2.72 Kilometers from Kim's house and 1.54 kilometers from Terri's house. How much farther in meter does Kim

TiliK225 [7]

Answer: 1,180 meters.

Step-by-step explanation:

Hi, to answer this question we have to subtract Terri's distance from the school (1.54) to Kim's distance from the school (2.72)

Mathematically speaking:

2.72 km - 1.54km = 1.18 km

Since the answer must be expressed in meters.

1000 meters = 1 kilometer

1.18 km x 1000 m/km = 1,180 meters.

Feel free to ask for more if needed or if you did not understand something.

4 0

3 years ago

What is the area of a triangle whose vertices are X(1, 1), Y(3, -1), and Z(4,4)?

shepuryov [24]

Answer:

Step-by-step explanation:

Note that in this diagram, point A represents point X, point B represents point Y, and point C represents point Z.

From the diagram, it appears as if $\overline{XZ} \perp \overline{XY}$ . To determine if this is the case, we can find the slopes of both segments.

$m_{\overline{XZ}}=\frac{4-1}{4-1}=1\\m_{\overline{XY}}=\frac{-1-1}{3-1}=-1$

Since these slopes are negative reciprocals, we know that they are perpendicular.

This means we can use the formula $A=\frac{1}{2}bh$ , where b is the base (XY) and h is the height (XZ).

Note these are interchangeable.

Using the distance formula,

$XY=\sqrt{(3-1)^{2}+(-1-1)^{2}}=2\sqrt{2}\\XZ=\sqrt{(4-1)^{2}+(4-1)^{2}}=3\sqrt{2}$

This means the area is $\frac{1}{2}(2\sqrt{2})(3\sqrt{2})=\boxed{6}$

7 0

2 years ago