Answer:
x=3
x=−3
Step-by-step explanation:
2x^2 - 5 = 13
Subtract 13 from both sides.
2x^2 - 5 - 13 = 0
Subtract 13 from −5 to get −18.
2x^2 - 18 = 0
Divide both sides by 2.
x^2 - 9 = 0
Consider x^2−9. Rewrite x^2−9 as x^2−3^2. The difference of squares can be factored using the rule: a^2−b^2=(a−b)(a+b).
(x−3)(x+3)=0
To find equation solutions, solve x−3=0 and x+3=0.
x=3
x=−3
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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Using <u>distance between two points</u>, it is found that the total distance covered on the tour is of 3400 miles.
Given two points
and
, their distance is given by:

In this problem, the formula is used to find the distance covered on each tour, hence:




Then, the total <em>distance </em>is given by the sum of each separate distance, hence:

The total distance covered on the tour is of 3400 miles.
You can learn more about <u>distance between two points</u> at brainly.com/question/25929988