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Sergeu [11.5K]
2 years ago
9

A sign is in the shape of a rhombus with a 60° angle and sides of 12 cm long. Find its area to the nearest tenth. Select one: a.

62.4 cm2 b. 5.2 cm2 c. 124.7 cm2 d. 10.4 cm2
Mathematics
1 answer:
murzikaleks [220]2 years ago
3 0
The area of a rhombus can be computed from its side (s) and angle (θ) by
.. A = s^2*sin(θ)
For your numbers, this is
.. A = (12 cm)^2*sin(60°) ≈ 124.7 cm^2
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Find the exact values of cos 3 pi/4 radians sin 3 pi/4 radians.
Liula [17]
If you consult the unit circle, you will see that:

cos(\frac{3\pi}{4}) = -\frac{\sqrt{2}}{2}\\\\sin(\frac{3\pi}{4}) = \frac{\sqrt{2}}{2}

3pi/4 in degrees is 3pi/4 * 180/pi = 3/4 * 180 = 135 degrees. And please refer to the attachment to how you can obtain the values above.

Now, lets multiply it together.

-\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} =\\\\-\frac{2}{4} =\\\\ \boxed{\bf{-\frac{1}{2}}}

So, <span>cos(3pi/4)sin(3pi/4) = -1/2</span>

7 0
3 years ago
Two angles are supplementary if their sum is​ 180°. the larger angle measures five degrees more than four times the measure of a
wlad13 [49]
Let x represent the smaller angle.
Let y represent the larger angle.

The problem states that the larger angle measures five degrees more than four times the measure of the smaller angle.
With this given information, we can create the following equation.

y=4x+5

Also, they a supplementary, meaning that they add up to 180. We can create another equation.

x+y=180

Since we have two linear equations and we want to find the solution, we have a system of linear equations. Let's solve this system by using the substitution method.

Substitute y=4x+5 into x+y=180

x+y=180

After substituting, you get

x+4x+5=180

Now, combine the x's

5x+5=180

Subtract both sides by 5

5x=175

Divide both sides by 5.

x=35

Now, we can solve for y using the equation x+y=180 since we know the value of x.

35+y=180

Subtract both sides by 35.

y=145

The smaller angle has a measure of 35 degrees and the larger one has a measure of 145 degrees. Have an awesome day! :)
5 0
3 years ago
A garden table and a bench cost 607 combined. The garden table costs 43 less than the bench. What is the cost of the bench?
Paha777 [63]

Answer is 564

607-40=567

567-3=564


5 0
3 years ago
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What is the percent of change from 25 to 18?<br> Can you explain the steps for me pls and thanks!
levacccp [35]

Answer:

18 is 72% of 25 which is also known as 28% less of 25

Step-by-step explanation:

18/25=.72

1-.72=.28

.28=28%

8 0
2 years ago
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Which ordered pair makes both inequalities true? y &lt; –x + 1 y &gt; x On a coordinate plane, 2 straight lines are shown. The f
goldenfox [79]

Answer:

Option B.

Step-by-step explanation:

The given inequalities are

y

y>x

We need to find the ordered pair which makes both inequalities true.

Check the above inequalities for each given ordered pair.

For (-3,5),

(5) (False)

For (-2,2),

(2) (True)

y>x\Rightarrow 2>-2 (True)

So, both inequalities are true for (-2,2). Option B is correct.

For (-1,-3),

y>x\Rightarrow -3>-1 (False)

For (0,-1),

y>x\Rightarrow -1>0 (False)

Both inequalities are not true for (-3,5), (-1,-3) and (0,-1).

Therefore, the correct option is B.

3 0
2 years ago
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