Answer:
5√2
Step-by-step explanation:
With reference angle 45°
perpendicular (p) = 5
hypotenuse (h) = x
sin 45 ° = p / h
1/√2 = 5 / x
x = 5√2
Answer:
Step-by-step explanation:
A) Use the distributive property to eliminate parentheses. Then combine like terms. (The only "like terms" are the constants.)
... = 12 +3·2y +3·(-3) . . . use the distributive property to multiply each term in parentheses by the factor 3 outside those parentheses
... = 12 +6y -9 . . . . . . . . simplify
... = 6y + (12 -9) . . . . . . group like terms together
... = 6y + 3 . . . . . . . . . . simplify
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B) Look for factors of each term that are also found in the other term.
... 18b has factors 3×6×b
... 12 has factors 2×6
The only common factor is 6, so we factor that out using the distributive property.
... 18b -12 = 6(3b -2)
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<em>Comment on factoring</em>
For factoring problems, it helps immensely if you know your times tables and some of the rules for divisibility. (Even numbers are divisible by 2, numbers ending in 0 or 5 are divisible by 5, numbers whose sum of digits is divisible by 3 are divisible by 3, for example.)
Answer: 3/4
Step-by-step explanation:
By finding the roots of the polynomial, we conclude that the correct graph is the second one.
<h3>
Which is the graph of the polynomial?</h3>
Here we have the polynomial:
![f(x) = x^3 + x^2 - 2x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E3%20%2B%20x%5E2%20-%202x)
To identify it, we need to find the roots, we can rewrite the equation as:
![f(x) = x*(x^2 + x - 2)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%2A%28x%5E2%20%2B%20x%20-%202%29)
And we can rewrite the last part by using the Bhaskara's formula:
![x = \frac{-1 \pm \sqrt{1^2 + 4*2} }{2} \\\\x = (-1 \pm 3)/2](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-1%20%5Cpm%20%5Csqrt%7B1%5E2%20%2B%204%2A2%7D%20%7D%7B2%7D%20%5C%5C%5C%5Cx%20%3D%20%28-1%20%5Cpm%203%29%2F2)
Then the roots are:
x = -2
x = 1
Then we rewrite:
![f(x) = x*(x + 2)*(x - 1)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%2A%28x%20%2B%202%29%2A%28x%20-%201%29)
So the roots are at x = 0, x = -2, and x = 1.
The graph with these roots is the second graph (top right).
If you want to learn more about polynomials:
brainly.com/question/4142886
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