An equilateral triangle has an altitude length of 27 feet. Determine the length of a side of the triangle

Mathematics

1 answer:

lesya692 [45]3 years ago

7 0

See image attached.

Getting this answer involved finding and using 30-60-90 triangles within the equilateral triangle. We find that a side of the triangle = 18√3 feet

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State the equation of the line described.

nikdorinn [45]

Answer:

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes. This means that when you multiply the slopes of the perpendicular lines, its product = -1.

Given the linear equation, y = -9x - 1, and the point, (-3, 7):

Since the slope of the given linear equation is: m1 = -9, then it means that the slope of the other line (m2) = 1/9:

m1 × m2 = -1

-9 × 1/9 = -1

Next, we need to find the y-intercept of the other line. The y-intercept is the point on the line where it crosses the y-axis, and has coordinates (0, b). It is also the value of the y-coordinate when its corresponding x-coordinate = 0.

Using the given point, (-3, 7), and the slope of the other line, m2 = 1/9:

We need to substitute these values into the slope-intercept form, y = mx + b, to solve for the y-intercept, (b):

y = mx + b

7 = 1/9(-3) + b

7 = -1/3 + b

Add 1/3 to both sides of the equation to solve for b:

7 + 1/3 = 1/3 -1/3 + b

22/3 = b

Therefore, the y-intercept (b) = 22/3.

The linear equation of the other line is: y = 1/9x + 22/3

4 0

2 years ago

The coordinate plane below represents a town. Points A through F are farms in the town.

Elena-2011 [213]

To solve this, use the point - slope form formula
Point D (-4, 2) and Point E (-1, 5)
y - y1 = [(y2 - y1)/(x2 - x1)](x - x1)
y - 2 = [(5 - 2/-1 -(-4))](x + 4)
y - 2 = x + 4
y = x + 6

To answer this, input the values of points D or E into the equation and make sure that they answer the equation in part A.
y = x + 6
2 = -4 + 6 = -2 so it satisfies the solution

8 0

3 years ago

||x-4|-2|<3 Solve for X

miv72 [106K]

Answer:

x<11

Step-by-step explanation:

x−4(|−2|)<3

Simplifies to:

x−8<3

Let's solve your inequality step-by-step.

x−8<3