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3 years ago

Find the indicated side of the triangle

Mathematics

1 answer:

Vadim26 [7]3 years ago

8 0

Answer:

7√2

Step-by-step explanation:

Knowing that the angle is 45° (or π/4 radians) and the opposite leg has a length of 7, you can find the length of b with:

7 / b = sin(π / 4)

7 / (sin(π / 4)) = b

b = 7 / (1 / √2)

b =7√2

A simpler way to get the answer is to note that a right triangle with one 45° angle must be an isoceles right triangle, so both legs are the same length. Using the Pythagorean Theorem:

a² + 7² = b²

Since we know a = 7,

7² + 7² = b²

b = √(2 * 49)

b = 7√2

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Step-by-step explanation:

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3 years ago

If there is 15,000 gallons of water in your basement, how long will it take the 2,500 gph

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3 years ago

Read 2 more answers

The area of a rectangle is represented by x^2- 7x + 10. What are the missing side lengths of the rectangle?

ladessa [460]

Length = x - 2
Width = x - 5

Explanation:

Area = x^2 - 7x + 10
Area = (x - 2)(x - 5)
Area = Length x Width

Length = x - 2
Width = x - 5

4 0

3 years ago

Given log4(3) =0.7925 and log4(5) =1.1610, use log properties to find log4(300).

Ede4ka [16]

Answer:

4.1145

Step-by-step explanation:

You can use the following formula to solve this kind of problems,

$log_{a}(b) + log_{a}(c) = log_{a}(bc)$

So, let's start of with log4_(300). Since the question have already gave log4_(3) =0.7925 and log4_(5) =1.1610. It means that you have to split the 300 into the simplest form where almost all of the numbers are 3 and 5.

$log_{4}(300) = log_{4}(4 \times 5 \times 3 \times 5) \\ = log_{4}(4) + log_{4}(5) + log_{4}(3) + log_{4}(5) \\ = 1 + 1.1610 + 0.7925 + 1.1610 \\ = 4.1145$

5 0

3 years ago

If x>2,then x2-x-6/x2-4=

statuscvo [17]

$\frac{x^2-x-6}{x^2-4}=(*)\\------------\\x^2-x-6=0\\a=1;\ b=-1;\ c=-6\\\Delta=b^2-4ac;\ \Delta=(-1)^2-4\cdot1\cdot(-6)=1+24=25\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\x_1=\frac{1-\sqrt{25}}{2\cdot1}=\frac{1-5}{2}=\frac{-4}{2}=-2\\\\x_2=\frac{1+\sqrt{25}}{2\cdot1}=\frac{1+5}{2}=\frac{6}{2}=3\\\\x^2-x-6=(x+2)(x-3)$
$---------------------\\x^2-4=x^2-2^2=(x-2)(x+2)\\-------------------\\\\(*)=\frac{(x+2)(x-3)}{(x-2)(x+2)}=\frac{x-3}{x-2}$

6 0

3 years ago