Answer:30.48
Step-by-step explanation:
The equation that solve for x is as follows;
70 + 60 + x = 180
<h3 /><h3>How to find an angle?</h3>
The equation that can be used to find the measure of angle x can be found as follows:
60 + 70 + y = 180
Therefore,
130 + y = 180
subtract 130 from both sides
130 - 130 + y = 180 - 130
y = 50°
70 + 60 + x = 180
130 + x = 180
x = 180 - 130
x = 50°
x and y are vertically opposite angles.
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Answer:
The triangle is an isosceles triangle
Answer:
3(4x - 1)(2x + 3)
Step-by-step explanation:
Rearrange the equation into standard form
Subtract 9 - 30x from both sides
24x² + 30x - 9 = 0 ← in standard form
Take out 3 as a common factor
3(8x² + 10x - 3) = 0 ← factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term
product = 8 × - 3 = - 24, sum = 10
The factors are - 2 and + 12
Use these factors to replace the x- term, that is
8x² - 2x + 12x - 3 ( factor the first/second and third/fourth terms )
2x(4x - 1) + 3(4x - 1) ← take out the common factor (4x - 1)
(4x - 1)(2x + 3)
24x² + 30x - 9 = 3(4x - 1)(2x + 3) ← in factored form
Answer:
72 sq. mi
Step-by-step explanation:
Breaking this down, we have 2 right triangles with sides of 3, 4, and 5 miles, and 3 rectangles with dimensions 3 x 5, 4 x 5, and 5 x 5 miles. Remember that the area of a triangle is 1/2 x b x h , where b and h are the triangle's base and height. The base and height of the triangles at the bases of the figure are 3 and 4, so each triangle has an area of 1/2 x 3 x 4 = 1/2 x 12 = 6 sq. mi, or 6 + 6 = 12 sq. mi together.
Onto the rectangles, we can find their area by multiplying their length by their width. Since the width of these rectangles is the same for all three - 5 mi - we can make our lives a little easier and just "glue" the lengths together, giving us a longer rectangle with a length of 3 + 4 + 5 = 12 mi. Multiplying the two, we find the area of the rectangles to be 5 x 12 = 60 sq. mi.
Adding this area to the triangle's area gives us a total area of 12 + 60 = 72 sq. mi.