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3 years ago

The farmer brought 80 acorn squash to the market.

1 answer:

4 0

The total number of acorn squash that the farmer brought to the market = 80
Percentage of acorn squash was less when the day ended = 35%
Then
The amount by which the
number of acorn squash decreased at the end of the day = (35/100) * 80
   = 280/10
   = 28
Then
The number of acorn squash left with the farmer = 80 - 28
   = 52
So from the above deduction, we can easily conclude that the farmer was left with 52 acorn squash at the end of the day.

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Given ΔABC, m∠A = 120°, b = 13 cm, and c= 15 cm. Find the triangle's area. Round to the nearest tenth.

zzz [600]

Refer to the diagram shown below.

m∠A = 120°
b = 13 cm
c = 15 cm

From the Law of Sines, the area of the triangle is
Area = (1/2)*b*c*sin(A)
= 0.5*13*15*sin(120°)
= 84.4375 cm²

Answer: 84.4 cm² (nearest tenth)

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3 years ago

Given a map scale of 1 inch = 10 km, what is the distance between two mountains that measure 1.25 in. apart on the map?

balu736 [363]

The easiest way to solve this problem is to just move the decimal point to the right one place.

1.25 → 12.5

Your answer should be 12.5

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3 years ago

Read 2 more answers

let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)

statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

$\sin (\theta)=\frac{3}{5}$

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

$x^2+3^2=5^2$

Solving for x, we have

$\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}$

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

$\tan (y)=\frac{12}{5}$

Describes the following triangle

Using the Pythagorean Theorem again, we have

$5^2+12^2=h^2$

Solving for h, we have

$\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}$

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

$\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}$

To calculate the sine and cosine of the sum

$\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}$

We can use the following identities

$\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}$

Using those identities in our problem, we're going to have

$\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}$

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1 year ago