Due to length restrictions, we kindly invite to see the explanation below to know the answer with respect to each component of the question concerning linear equations.
<h3>How to determine a linear equation describing the daily distance of a runner</h3>
In this question we need to derive an expression of the <em>daily</em> distance as a function of time. Now we proceed to complete the components:
- <em>Linear</em> equations have an <em>independent</em> variable (t - time) and a dependent variable (x - daily distance).
- We notice that the daily distance increases linearly in time, then then we have the following pattern:
t 1 2 3 4 5 6
x 2 2.5 3 3.5 4 4.5 - The equation that represents the n-th term of the sequence is x(n) = 2 + 0.5 · (n - 1).
- The week when Susie will run 10 miles per day is:
10 = 2 + 0.5 · (n - 1)
8 = 0.5 · (n - 1)
n - 1 = 16
n = 17
Susie will run 10 miles per day in the 17th week. - It is not reasonable to think that pattern will continue indefinitely as it is witnessed in the difficulties experimented by <em>fastest</em> runners in the world to increase their <em>peak</em> speeds.
- A marathon has a distance of 26 miles, then we must solve the following equation:
26 = 2 + 0.5 · (n - 1)
24 = 0.5 · (n - 1)
48 = n - 1
n = 49
Susie should start her training 49 weeks before the marathon.
To learn more on linear equation: brainly.com/question/11897796
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Answer:
40
Step-by-step explanation:
Answer:
Step-by-step explanation:
Mark the two points (-1,7) and (1,-1) on the graph. Then draw a straight line between them. To determine the equation that goes through these two points, we can use the two given points to find the slope of the line. The standard form of a straight line equation is
y = mx + b,
where m is the slope and y is the y-intercept (the value of y when x = 0).
Slope is also known as the "Rise"/"Run" - the change in y divided by the change in x. We can use the two points to calculate this:
Rise (-1-(7) = -8 Run = (1 - (-1) = 2
The slope is therefore (-8/2) or -4.
y = -4x + b
We can find b by entering either of the two points in y = -4x + b and solve for b. I'll use (1,-1) since I have my 1's multiplication table memorized
y = -4x + b
-1 = -4(1) + b
b = 3
The straight line equation that connects the two points is
y = -4x + 3
You can graph this equation (e.g., on DESMOS) to see how it intersects the points. <u>[Attached]</u>
The coordinates of the y intercept are (0,3).
<span>Discriminant is 28 (c)
First get the equation into the form: Ax^2 + Bx + C = 0 (the quadratic equation)..
By subtracting 10x both sides (to get it on the other side)..
9x^2 + 2 = 10x
9x^2 - 10x + 2 = 10x - 10x
9x^2 - 10x + 2 = 0
Now the discriminant is: b^2 - 4ac
The quadratic equation is Ax^2 + Bx + C = 0
Here, A = 9, B = -10 and C = 2
(-10)^2 - 4 (9)(2)
= 100 - 4 (18)
= 100 - 72
= 28</span>
<span>The meeting point of the 3 </span>perpendicular bisectors<span> of a triangle's sides is called </span><span>the circumcenter.
</span><span><span>The circumcenter of an </span>acute triangle<span> is always </span>inside<span> the triangle.
so the answer is "a"
Source:
http://www.1728.org/trictr.htm
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