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kkurt [141]
1 year ago
6

The sides of a parallelogram are 14ft and 16ft. One angle is 41° while another angle is 139°. Find the lengths of the diagonals

of the parallelogram (to the nearest tenth of a foot).
Mathematics
1 answer:
Semenov [28]1 year ago
7 0

We will have the following:

First, we have that the problem can be seeing as follows:

Now, knowing this and the the properties of the diagonals we will have that [We use the law of cosines}:

First diagonal [AC} is given by:

\begin{gathered} AC=\sqrt{16^2+14^2-2cos(41)}\Rightarrow AC=10.67193085... \\  \\ \Rightarrow AC\approx10.7 \end{gathered}

So, one of the diagonals has an approximate length of 10.7 ft.

Second diagonal [BD] is given by:

\begin{gathered} BD=\sqrt{16^2+14^2-2(16)(14)cos(139)}\Rightarrow BD=28.10889347... \\  \\ \Rightarrow BD\approx28.1 \end{gathered}

So, the second diagonal has a length of approximately 28.1 ft.

<em>**Diagonals**</em>

\begin{gathered} AC\approx10.7ft \\  \\ BD\approx28.1ft \end{gathered}

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3 years ago
A principal is ordering pizzas for a school pizza party. He knows that 9 pizzas will
My name is Ann [436]

Answer:

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3 years ago
Multiply each equation by a constant that would help to eliminate the y terms.
Zinaida [17]

Answer:

Therefore the required resulting equation is

6x-15y=-63\\-15x+15y=90

6 x minus 15 y = negative 63.

Negative 15 x + 15 y = 90

Step-by-step explanation:

Given:

2x-5y=-21         ......................Equation ( 1 )

3x-3y=-18         ......................Equation ( 2 )

To Find:

Expression after multiplying to eliminate y term,

Solution:

So to eliminate 'y' term we need to multiply equation 1 by a constant 3 and equation 2 by a constant -5,  such that equations  becomes

3(2x-5y)=3\times -21\\\\6x-15y=-63 .....( 1 )

-5(3x-3y)=-5\times -18\\\\-15x+15y=90  .....( 2 )

so now by adding new equation one and two we can eliminate y term that means -15y and +15y will get cancel,

Therefore the required resulting equation is

6x-15y=-63\\-15x+15y=90

6 x minus 15 y = negative 63.

Negative 15 x + 15 y = 90

3 0
3 years ago
Read 2 more answers
Simplify the expression cos x cot x+ sin x please select the best answer from the choices provided a.0, b.csc x, c. Tan x, d sec
expeople1 [14]

Answer:

cot x = \frac{cos x}{sin x}

cos x \frac{cos x}{sin x} + sin x

\frac{cos^2 x}{sin x} +sin x

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Solving for cos^2 x we got cos^2 x =1 -sin^2 x and replacing this we got:

\frac{1-sin^2 x}{sin x} +sin x

\frac{1}{sin x} -\frac{sin^2 x}{sin x} +sin x

csc x -sin x + sin x = csc x

And then the best option for this case would be:

b.csc x

Step-by-step explanation:

For this case we have the following expression given:

cos x cot x + sin x

We know from math properties that the definition for cot is cot x = \frac{cos x}{sin x}

If we use this definition we got:

cos x \frac{cos x}{sin x} + sin x

\frac{cos^2 x}{sin x} +sin x

Now we can use the following identity:

sin^2 x + cos^2 x =1

Solving for cos^2 x we got cos^2 x =1 -sin^2 x and replacing this we got:

\frac{1-sin^2 x}{sin x} +sin x

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And then the best option for this case would be:

b.csc x

4 0
4 years ago
#9. Solve: 8x + 5 = 3x + 15<br><br> X = 4<br> x = 2<br> x = 20/11<br> x = 20
Jobisdone [24]

Answer:

x = 2

Step-by-step explanation:

8x + 5 = 3x + 15

8x - 3x + 5 = 3x - 3x + 15

5x + 5 = 15

5x + 5 - 5 = 15 - 5

5x = 10

5x / 5 = 10 / 5

x = 2

6 0
3 years ago
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