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Salsk061 [2.6K]

3 years ago

6

The weight of a box varies directly as the volume of the box . If a 138 - pound box has a volume of 23 gallons , what is the wei

ght of a box that has a volume of 25 gallons ?

1 answer:

Marizza181 [45]3 years ago

3 0

Answer:

150 lb

Step-by-step explanation:

138lb/23 gal = x/25 gal

cross multiply and solve for x

23x = 138·25

x = 3450/23

x = 150 lb

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The total length of pencils A, B and C is 29 cm. Pencil a is 11 cm shorter then pencil B, and pencil B is twice as long a pencil

satela [25.4K]

The length of pencil A is 5 cm

<em><u>Solution:</u></em>

Let the length of pencil A be "x"

Let the length of pencil B be "y"

Let the length of pencil C be "z"

<em><u>The total length of pencils A, B and C is 29 cm</u></em>

Therefore,

length of pencil A + length of pencil B + length of pencil C = 29

x + y + z = 29 ------------ eqn 1

<em><u>Pencil A is 11 cm shorter then pencil B</u></em>

x = y - 11 ------- eqn 2

<em><u>Pencil B is twice as long a pencil C</u></em>

y = 2z

$z = \frac{y}{2}$ ------ eqn 3

<em><u>Substitute eqn 2 and eqn 3 in eqn 1</u></em>

$y - 11 + y + \frac{y}{2} = 29\\\\2y + \frac{y}{2} = 29 + 11\\\\\frac{4y+y}{2} = 40\\\\5y = 80\\\\y = 16$

<em><u>Substitute y = 16 in eqn 2</u></em>

x = 16 - 11

x = 5

Thus length of pencil A is 5 cm

5 0

3 years ago

A carpenter cut out a small trapezoid as a wooden support for the front step. it has an altitude of 4 inches. One base of the tr

docker41 [41]

Area of wooden support is 36 square inches

<em><u>Solution:</u></em>

Given that, carpenter cut out a small trapezoid as a wooden support for the front step

<em><u>The area of trapezoid is given as:</u></em>

$area = \frac{a+b}{2} \times h$

Where, "h" is the height

"a" and 'b" are the length of base

Here given that,

Height = h = 4 inches

a = 6 inches

b = 12 inches

Substituting the values we get,

$area = \frac{6+12}{2} \times 4\\\\area = 18 \times 2\\\\area = 36$

Thus area of wooden support is 36 square inches

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3 years ago

Find the area of the semicircle. diameter = 12

dimaraw [331]

Answer:

$\huge\boxed{\sf Area\ of \ Semicircle = 56.55 \ units^2}$

Step-by-step explanation:

Diameter = 12

Radius = 12/2 = 6

$\sf Area\ of \ Semicircle =\frac{\pi r^2}{2} \\Area\ of \ Semicircle =\frac{\pi (6)^2}{2} \\Area \ of \ Semicircle = \frac{\pi (36)}{2}\\ Area \ of \ Semicircle = 18 \ pi$

$\sf Area\ of \ Semicircle = 56.55 \ units^2$

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3 years ago

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A circle has a square etched inside of it, with the endpoints of the square touching the circle. if the circle has a radius of 1

ch4aika [34]

First, illustrate the problem by drawing a square inside a circle as shown in the first picture. Connect each corner of the square to the center of the circle. Since the square is inscribed in the circle, they have the same center points. Each segment drawn to the corners is a radius of the circle measuring 1 unit. Also, a square has equal sides. So, the angle made between those segments are equal. You can determine each angle by dividing the whole revolution into 4. Thus, each point is 360°/4 = 90°.

Next, cut a portion of one triangle from the circle as shown in the second picture. Since one of the angles is 90°, this is a right triangle with s as the hypotenuse. Applying the pythagorean theorem,

s = √(1²+1²) = √2

So each side of the square is √2 units. The area of the square is, therefore,

A = s² = (√2)² = 2

The area of the square is 2 square units.

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3 years ago

An employee earns $195 for 15 hours of work. Assuming he is paid by the hour, how much will the employee earn in 8 hours?

vampirchik [111]

Answer:

$104

Step-by-step explanation:

First, find the employee’s hourly rate. You can do this by dividing the total amount earned by the total hours worked. $\frac{195}{15}=13$
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3 years ago