Plz helppppppp me qwq
1 answer:
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Answer:
a) 1650 m
b) 1677.05 m
Step-by-step explanation:
Hi there!
<u>1) Determine what is required for the answers</u>
For part A, we're asked for solve for the horizontal distance in which the road will rise 300 m. In other words, we're solving for the distance from point A to point C, point C being the third vertex of the triangle.
For part B, we're asked to solve for the length of the road, or the length of AB.
<u>2) Prove similarity</u>
In the diagram, we can see that there are two similar triangles: Triangle AXY and ABC (please refer to the image attached).
How do we know they're similar?
- Angles AYX and ACB are corresponding and they both measure 90 degrees
- Both triangles share angle A
Therefore, the two triangles are similar because of AA~ (angle-angle similarity).
<u>3) Solve for part A</u>
Recall that we need to find the length of AC.
First, set up a proportion. XY corresponds to BC and AY corresponds to AC:
Plug in known values
Cross-multiply
Therefore, the road will rise 300 m over a horizontal distance of 1650 m.
<u>4) Solve for part B</u>
To find the length of AB, we can use the Pythagorean theorem:
where c is the hypotenuse of a right triangle and a and b are the other sides
Plug in 300 and 1650 as the legs (we are solving for the longest side)
Therefore, the length of the road is approximately 1677.05 m.
I hope this helps!
The solution to the equation x(x+4) = 6 is x = -2 + √10 or x = -2 - √10 after solving with the quadratic formula.
<h3>What is a quadratic equation?</h3>Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
We have an equation:
x(x + 4) = 6
By distributive property:
x² + 4x = 6
x² + 4x - 6 = 0
a = 1, b = 4, c = -6
Plugging all the values in the formula:
After calculating:
Thus, the solution to the equation x(x+4) = 6 is x = -2 + √10 or x = -2 - √10 after solving with the quadratic formula.
Learn more about quadratic equations here:
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