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Sholpan [36]
3 years ago
9

What is the area of the rectangle?

Mathematics
2 answers:
VLD [36.1K]3 years ago
4 0
The area of the rectangle is A. 6000
Olin [163]3 years ago
3 0
A. 6,000 units^2

The area of a rectangle equals its length times its width. 60 • 100 = 6,000
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For positive acute angles A and B, it is known that tan A = 35/12 and sin B = 20/29. Find the value of sin(A - B ) in the simple
almond37 [142]

Answer:

\displaystyle \sin(A-B)=\frac{495}{1073}

Step-by-step explanation:

We are given that:

\displaystyle \tan(A)=\frac{35}{12}\text{ and } \sin(B)=\frac{20}{29}

Where both A and B are positive acute angles.

And we want to find he value of sin(A-B).

Using the first ratio, we can conclude that the opposite side is 35 and the adjacent side is 12.

Then by the Pythagorean Theorem, the hypotenuse is:

h = \sqrt{35^2 + 12^2} =37

Using the second ratio, we can likewise conclude that the opposite side is 20 and the hypotenuse is 29.

Then by the Pythagorean Theorem, the adjacent is:

a=\sqrt{29^2-20^2}=21

Therefore, we can conclude that:

So, for A, the adjacent is 12, opposite is 35, and the hypotenuse is 37.

For B, the adjacent is 21, opposite is 20, and the hypotenuse is 29.

We can rewrite sin(A-B) as:

\sin(A-B)=\sin(A)\cos(B)-\cos(A)\sin(B)

Using the above conclusions, this yields: (Note that since A and B are positive acute angles, all resulting ratios will be positive.)

\displaystyle \sin(A-B)=\Big(\frac{35}{37}\Big)\Big(\frac{21}{29}\Big)-\Big(\frac{12}{37}\Big)\Big(\frac{20}{29}\Big)

Evaluate:

\displaystyle \sin(A-B)=\frac{735-240}{1073}=\frac{495}{1073}

6 0
3 years ago
What is the diameter, circumference, and area of a circle that has the radius of 7?
user100 [1]

Answer:

the diameter is: 14

the circumference is: C≈43.98

the area is: A≈153.94

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
At a school fair, students were challenged to hit one of the small congruent circles on the large rectangular board with a ball.
shtirl [24]

Answer:

~4.7%

Step-by-step explanation:

Area of the rectangle: 35*52=1820

Area of 1 small circle: A=πr2=π·32≈28.27433

28.27433*3=84.82299

84.82299/1820=0.04660603846

Therefore, about 4.7%

6 0
2 years ago
What is the first step when rewriting y = 3x2 9x – 18 in the form y = a(x – h)2 k?
stiks02 [169]
A quadratic equation has the general form of: <span>

y=ax² + bx + c

It can be converted to the vertex form in order to determine the vertex of the parabola. It has the standard form of:

y = a(x+h)² - k

This can be done by completing a square. The steps are as follows:

</span><span>y = 3x2 + 9x – 18
</span>y = 3(x2 <span>+ 3x) – 18
</span>y + 27/4= 3(x2 <span>+ 3x+ 9/4) – 18 
</span>y = 3(x2 + 3/2)^2 – 99<span>/4
</span>
Therefore, the first step is to group terms with the variable x and factoring out the coefficient of x^2.
3 0
3 years ago
Read 2 more answers
Given y=(2x+3)2, choose the standard form of the given quadratic equation
Naddika [18.5K]

Rewrite using the formula for the standard form

The answer is y-4x^2 + 12x + 9

6 0
3 years ago
Read 2 more answers
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