Answer:
y + 2x = 10 (third option)
Step-by-step explanation:
We can see that every time x increases by one, y increases by -2, meaning that the slope is -2.
We also know that the y-intercept is 10 because that is the value of y when x is equal to 0.
Now, we can create the equation using the slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept).
y = -2x + 10
If you look at the third option, that equation is just a rearranged form of our equation (y + 2x = 10).
This means that the third option is correct.
Solve for <em>x</em> when √(<em>x</em> ² - 4) = 1 :
√(<em>x</em> ² - 4) = 1
<em>x</em> ² - 4 = 1
<em>x</em> ² = 5
<em>x</em> = ±√5
We're looking at <em>x </em>≤ 0, so we take the negative square root, <em>x</em> = -√5.
This means <em>f</em> (-√5) = 1, or in terms of the inverse of <em>f</em>, we have <em>f</em> ⁻¹(1) = -√5.
Now apply the inverse function theorem:
If <em>f(a)</em> = <em>b</em>, then (<em>f</em> ⁻¹)'(<em>b</em>) = 1 / <em>f '(a)</em>.
We have
<em>f(x)</em> = √(<em>x</em> ² - 4) → <em>f '(x)</em> = <em>x</em> / √(<em>x</em> ² - 4)
So if <em>a</em> = -√5 and <em>b</em> = 1, we get
(<em>f</em> ⁻¹)'(1) = 1 / <em>f '</em> (-√5)
(<em>f</em> ⁻¹)'(1) = √((-√5)² - 4) / (-√5) = -1/√5
The sign must be negative; see the attached plot, and take note of the negatively-sloped tangent line to the inverse of <em>f</em> at <em>x</em> = 1.
Hi there!
So to get this we just need to multiply 300 by 5 because it is 1/5 of the hour work. 300 x 5 = 1500 light bulbs. Hope this helps!
This kind of triangle is acute triangle because on the given three angles, none of them does not exceed more than 90°.