Answer:
see below
Step-by-step explanation:
f(x) = 4x^2 + 8x − 5
To find the x intercepts set y = 0
0 =4x^2 + 8x − 5
Factor
0=(2x-1)(2x+5)
Using the zero product property
2x-1 =0 2x+5 =0
2x=1 2x = -5
x = 1/2 x = -5/2
The x intercepts are ( 1/2 ,0) and ( -5/2,0)
Rewriting in vertex form by completing the square
4 ( x^2 + 2x) -5
4 ( x^2+2x +1) -4*1 -5
4 ( x+1) ^2 -9
Vertex form is
a( x-h) ^2 +k where ( h,k) is the vertex
The vertex is ( -1,-9)
We know it opens upwards since a > 0
Plot the vertex and the x intercepts
The graph is symmetric on based on the vertex
Answer: If he has 3 mystery books, and those are 1/8 of his whole collection, he has 24 books.
Step-by-step explanation:
3 = 1/8 × x
multiply both sides by the reciprocal of 1/8 which is 8/1 ("flipped fraction")
8 × 3 = 8/1(1/8) x <em>When you multiply a fraction by its reciprocal, it produces 1, so it "cancels" in the multiplication</em>
<em>24 = x </em>
<em>This may seem complicated, but understanding the process will help you solve more complicated questions like this in the future, I hope.</em>
<em />
To find the area of a quarter circle, you simply take a quarter of a full circle. As all quarters are equal, this means that the formula would be <span><span>π<span><span>r2</span>4</span></span><span>π<span><span>r2</span>4</span></span></span><span>. But wait, there's more. If you notice, </span><span><span>π<span><span>r2</span>4</span>=π<span><span>r2</span>2</span></span><span>π<span><span>r2</span>4</span>=π<span><span>r2</span>2</span></span></span><span>. This coincides with the circle formula, just with half the radius. Notice anything? A quarter of a circle can be calculated in the same way a circle a quarter the size can. This means that a quarter circle is equal to a circle a quarter size. In this same way, a ninth of a circle is equal to a circle of one ninth the size.</span>
So, you would 13 + 9 = which is 22 feet and since the angle is 50 degrees, you would multiply 22 x tan(50) to find the height of the streetlamp:22 x tan(50) = 26.21. So, the streetlamp is about 26 feet tall!Hope this helps!
Answer: I used the Pythagorean theorem and got 6.24, but if I was supposed to use another method, just let me know.
The formula is a^2+b^2=c^2
a=5
c=8
b=?
5^2+b^2=8^2
25+b^2=64
b^2=39
b=6.24,
(If it doesn't work, put x=6.24, x=-6.24. It can be both technically, but most teachers ask only for the first one. )
