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nlexa [21]
3 years ago
15

Hi! If you can, please help me with this question. And show the steps on how you got your answer. Thank you!

Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
6 0
<h3>Answer: 35.5</h3>

===============================

Explanation:

The triangles are identical. So this means that the triangle on the left has the horizontal portion of 50 ft, and the other sides are x ft (where x is a placeholder for a number).

Add up the sides for the either triangle. We have x+x+50 = 2x+50. This expression is the perimeter of one triangle. The perimeter of both triangles is simply us doubling that expression

combined perimeter of 2 triangles = 2*(perimeter of one triangle)

combined perimeter of 2 triangles = 2*(2x+50)

combined perimeter of 2 triangles = 2*(2x)+2*(50) ... distribute

combined perimeter of 2 triangles = 4x+100

We're told that the combined perimeters total 242 ft, so this means 4x+100 must equal 242

Solve for x

4x+100 = 242

4x+100-100 = 242-100 ... subtract 100 from both sides

4x = 142

4x/4 = 142/4 ... divide both sides by 4

x = 35.5

note: 35.5 feet = 35 feet, 6 inches because 1/2 ft = 0.5 ft = (0.5*12) inches = 6 inches

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On a coordinate plane, parallelogram R S T U has points (negative 4, 4), (2, 6), (6, 2), and (0, 0). What is the area of paralle
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Answer:

The area of the parallelogram is;

32 square units

Step-by-step explanation:

The given parameters are;

The coordinates of the parallelogram RSTU = R(-4, 4), S(2, 6), T(6, 2), and U(0, 0)

We note that the area of a parallelogram = Base length × Height

From the drawing of the parallelogram RSTU, we have;

The base length = The length of \overline {TU} = The length of \overline {SR} = √((2 - (-4))² + (6 - 4)²) = 2·√10

The height of a parallelogram is perpendicular to its base length = The line \overline {VT}

∴ Where, the slope of the base length = m, the slope of the height = -1/m

The slope, 'm' of \overline {SR} = (6 - 4)/(2 - (-4)) = 1/3

Therefore, the slope of the height = -1/(1/3) = -3

We note that a point on the height is the point 'T', therefore, the equation of the line in point and slope form is therefore;

y - 0 = -3·(x - 0)

∴ y = -3·x

Therefore, the coordinates of the point 'V' is given by the simultaneous solution of the equations of \overline {SR} and \overline {VT}

The equation of the line \overline {SR} in point and slope form from the point 'R' and the slope 'm = 1/3' is given as follows;

y - 4 = (1/3) × (x - (-4)) = (1/3) × (x + 4)

y = x/3 + 4/3 + 4 = x/3 + 16/3

y = x/3 + 16/3

We then have the coordinate at the point 'V' (x, y) is given as follows;

-3·x = x/3 + 16/3

-9·x = x + 16

-10·x = 16

x = -16/10 = -1.6

x = -1.6

∴ y = -3·x = -3 × -1.6 = -4.8

y = 4.8

The coordinate at the point, V = (-1.6, 4.8)

The length of the line \overline {VT} = The height of the parallelogram = √((-1.6 - 0)² + (4.8 - 0)²) = 8/5·√10

The height of the parallelogram = 8/5·√10

The area of the parallelogram, A = Base length × Height

∴ A = 2·√(10) × 8/5·√(10) = (16/5) × 10 = 32

The area of the parallelogram, A =  32 square units.

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Answer:

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Total sugar required = 0.4 x 4

= 1.6 cups of sugar

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