What are the zeros of the function y = x2 + 10x – 171, and why?
2 answers:
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Answer:
Step-by-step explanation:
Slope-intercept form of a <u>linear equation</u>:
where:
- m is the slope.
- b is the y-intercept (where the line crosses the y-axis).
<u>Slope formula</u>
<u>Equation 1</u>
<u />
Define two points on the line:
<u>Substitute</u> the defined points into the slope formula:
From inspection of the graph, the line crosses the y-axis at y = 1 and so the y-intercept is 1.
Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:
<u>Equation 2</u>
<u />
Define two points on the line:
<u>Substitute</u> the defined points into the slope formula:
From inspection of the graph, the line crosses the y-axis at y = -4 and so the y-intercept is -4.
Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:
<u>Conclusion</u>
Therefore, the system of linear equations shown by the graph is:
Learn more about systems of linear equations here:
Answer:
c = 5√5
Step-by-step explanation:
When we have a right triangle, there is a property about its measurements that is <em>always</em> true, and its called the "Pythagorean Theorem"
First, let's understand the basic terms we use to describe the sides of a triangle:
we can call one leg "a", the other leg "b" and the slanted side "c"
("c" is also called the hypotenuse--and it's always opposite the 90-degree angle)
the pythagorean theorem:
a² + b² = c²
here, our "a" is 5, our "b" is 10 {and we don't know what c is}
let's try plugging these values into our formula:
a² + b² = c²
5² + 10² = c²
25 + 100 = c²
125 = c²
now, we know what c² is--but we want to know c,
so we must take the square root of both sides
√125 = √c²
√125 = c
now, while √125 <em>is </em>our answer, we can simplify further!
this is because 125 can be made up of 5 · 25
so,
and
we can take out the square root of 25 (5):
we write this as such:
so, in simplest radical form, c = 5√5
(√125)
hope this helps!! have a lovely day :)