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pashok25 [27]
3 years ago
13

How do you solve this problem??​

Mathematics
1 answer:
Ad libitum [116K]3 years ago
5 0

Answer: x = 64

<u>Step-by-step explanation:</u>

First, order each of the three right triangles by the lengths of the sides.  Each triangle has a small (s) leg, a medium (m) leg, and a hypotenuse (h). You can determine their order visually.

Left Δ:    s = 36                  m = unknown            h = 60

Right Δ:  s = unknown       m = x                          h = unknown

Big Δ:     s = 60                  m = unknown            h = 36 + x

Next, notice that you can set up a proportion with the Left and Big triangles using the s and h. <em>We can't use m because it has two unknowns</em>.

\dfrac{s}{h}:\quad \dfrac{36}{60}=\dfrac{60}{36+x}

Cross multiply and solve for x:

36(36 + x) = 60(60)

1296 + 36x = 3600

           36x = 2304

               x = 64

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DanielleElmas [232]

Answer:

1

Step-by-step explanation:

First, convert all the secants and cosecants to cosine and sine, respectively. Recall that csc(x)=1/sin(x) and sec(x)=1/cos(x).

Thus:

\frac{sec(x)}{cos(x)} -\frac{sin(x)}{csc(x)cos^2(x)}

=\frac{\frac{1}{cos(x)} }{cos(x)} -\frac{sin(x)}{\frac{1}{sin(x)}cos^2(x) }

Let's do the first part first: (Recall how to divide fractions)

\frac{\frac{1}{cos(x)} }{cos(x)}=\frac{1}{cos(x)} \cdot \frac{1}{cos(x)}=\frac{1}{cos^2(x)}

For the second term:

\frac{sin(x)}{\frac{cos^2(x)}{sin(x)} } =\frac{sin(x)}{1} \cdot\frac{sin(x)}{cos^2(x)}=\frac{sin^2(x)}{cos^2(x)}

So, all together: (same denominator; combine terms)

\frac{1}{cos^2(x)}-\frac{sin^2(x)}{cos^2(x)}=\frac{1-sin^2(x)}{cos^2(x)}

Note the numerator; it can be derived from the Pythagorean Identity:

sin^2(x)+cos^2(x)=1; cos^2(x)=1-sin^2(x)

Thus, we can substitute the numerator:

\frac{1-sin^2(x)}{cos^2(x)}=\frac{cos^2(x)}{cos^2(x)}=1

Everything simplifies to 1.

7 0
2 years ago
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Answer:

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Step-by-step explanation:

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Answer: The slope is 15/4.

Step-by-step explanation:

M = (y2 - y1)/(x2 - x1)

M = (5 - (-10))/(-1 - (-5))

M = (5 + 10)/(-1 + 5)

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6 0
3 years ago
What are the factors of X squared -100?
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Answer:

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Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
The perimeter of a rectangle is 62 m. The length is four more than two times the width. What is the length?
Travka [436]
--------------------------------------------------
Define length and width
--------------------------------------------------
Let x be the width
width = x
Length = 2x + 4

--------------------------------------------------
Formula
--------------------------------------------------
Perimeter = 2(length + width)

--------------------------------------------------
Find Length and width
--------------------------------------------------
62 = 2(2x + 4 + x)
62 = 2(3x + 4)            <em> ← combine like terms  </em> 
62 = 6x + 8                 <em>← remove bracket </em>  
62 - 8 = 6x                  <em>← minus 8 on both sides </em>
6x = 54                      <em> ← swap sides  </em>
x = 54 ÷ 6                   <em>← divide by 6 on both sides</em>
<em>x = 9 m</em>

--------------------------------------------------
Find Length and Width
--------------------------------------------------
Width = x = 9 m
Length = 2x + 4 = 2(9) + 4 = 22 m

--------------------------------------------------
Answer: Length = 22m
--------------------------------------------------
3 0
3 years ago
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