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2 years ago

Which off the following is a true statement about the rhombus shown?

Mathematics

1 answer:

timama [110]2 years ago

6 0

Answer:

The statement is false

Step-by-step explanation:

It is because the lines are not the same

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James has a piece of constrution paper with area of 65 1/4 inches . It is 9 2/3 inches long. What is the width of the piece of c

MrMuchimi

Answer:

The width of the piece of construction paper is 6.75 inches.

Step-by-step explanation:

The area of the paper = $65\frac{1}{4} = 65.25$ sq inches

The length of the paper = $9\frac{2}{3} = 9.66$ in

Let the width of the paper = w inches

Now, AREA OF THE PAPER = LENGTH x WIDTH

or, 65.25 sq. inches = 9. 66 in x w in

⇒ 65.25 = 9.66 x w

or, $w = \frac{65.25}{9.66} \implies w = 6.75$

or, w = 6. 75 inches

Hence, the width of the piece of construction paper is 6.75 inches.

6 0

3 years ago

In a certain neighborhood, there's a sagging power line between two utility poles. The utility poles are 50 feet tall and 120 fe

e-lub [12.9K]

<h3>Answer: 33.75 feet</h3>

In fraction form, this value is equal to 135/4

33.75 ft is equivalent to 33 ft, 9 inches.

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

Explanation:

Refer to the diagram below.

The key point to start with is point H, which is the vertex of the parabola.

Recall that vertex form is

y = a(x-h)^2 + k

What we'll do is plug in the vertex (h,k) = (60,30) which is the location of point H. We'll also plug in (0,45) which is the y intercept, aka the location of point C.

So,

y = a(x-h)^2 + k

y = a(x-60)^2 + 30 .... plug in vertex

45 = a(0-60)^2 + 30 .... plug in y intercept coordinates

45 = a(-60)^2 + 30

45 = a(3600) + 30

45 = 3600a + 30

45-30 = 3600a

3600a = 15

a = 15/3600

a = 1/240

This then means:

y = a(x-h)^2 + k

y = (1/240)(x-60)^2 + 30

This is the equation of our parabola. Plug in x = 30 to determine the height of point K

y = (1/240)(x-60)^2 + 30

y = (1/240)(30-60)^2 + 30

y = (1/240)(-30)^2 + 30

y = (1/240)(900) + 30

y = 15/4 + 30

y = 15/4 + 120/4

y = 135/4

y = 33.75

Therefore, the height of the power line, when it is 30 feet away from one of the poles, is 33.75 feet. This is the y coordinate of point K.

Side note: 33.75 ft = 33 ft + 0.75 ft = 33 ft + 12*0.75 in = 33 ft + 9 inches

8 0

2 years ago

A pigpen is to be enclosed using 640 m of fencing along three of its sides, the fourth side being a barn. Determine the dimensio

Basile [38]

Answer:

$W_{max}=480m\\ L_{max}=160m$

Step-by-step explanation:

Since we know we only have 640 feet of fence available, we know that L + W + L = 640, $\implies$ 2L + W = 640. This allows us to represent the width, W, in terms of L: W = 640 – 2L

Remember, the area of a rectangle is equal to the product of its width and length, therefore,

$A_{\rm pigpen}=L(640-2L)\implies 640L-2L^2$

Notice that, quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.

recall,