MATHEMATICS MIDDLE SCHOOL

How many fifths are in 6 4\5? Use your answer to rewrite 6 4\5 in the form \5?

Answers

Answer 1

Answer:

The number of fifths in 6 4/5 is; 34 fifths.

Place value

A fifth can be represented mathematically as; 1/5

On this note the number of fifths in 6 4/5( otherwise represented as 34/5) is;

34/5 ÷ 1/5

34/5 × 5

The number of fifths is therefore = 34 fifths.

To rewrite 6 4\5 in the form \5 is therefore; 34/5.

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A window is 4 feet wide and 8 feet tall. A rectangle is shown. The length of the rectangle is labeled 4 feet. The width of the rectangle is labeled 8 feet.

A manufacturer wants to use a scale factor of 1.5 to enlarge a window. What will the area of the window be after it is enlarged?

Answers

The relationship between linear scale factor and area scale factor can be

used to find the area of the window after it is enlarged.

The area of the window after it is enlarged is 72 square feet

Reasons:

The length of the window = 4 feet

The width of the window = 8 feet

The scale factor the manufacturer wants to use, LSF = 1.5

Required:

The area of the window after it is enlarged

Solution:

The scale factor of area, Area SF = The square of the length scale factor, LSF²

Therefore;

Area SF = 1.5² = 2.25

Area of the window after it is enlarged = Original area × 2.25

The original area = 8 ft. × 4 ft. = 32 ft.²

Therefore;

Area of the window after it is enlarged = 32 ft.² × 2.25 = 72 ft.²

Learn more about scale factors here:

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I've attached the answer below.

I need o fine the length and the width of the rectangle that haves the area 9in and the perimeter

Answers

The perimeter = (2 lengths) + (2 widths) = 12

(1 length) + (1 width) = 6

Area = (length) x (width)

So you need two numbers that add to 6 and multiply to 9 .

How about 3 and 3 ?

Area = 3 x 3 = 9
Perimeter = 3 + 3 + 3 + 3 = 12

It works, and your rectangle is actually a square !

The composite figures below are made of right prisms.Note: figures not drawn to scale.

Place the figures in order from least surface area to greatest surface area.

Answers

Answer:

Figure 1's surface area: 550 $feet^2$

Figure 2's surface area: 530 $feet^2$

Figure 3's surface area: 790 $feet^2$

So, the order of the figures' surface areas is: Figure 2 < Figure 1 < Figure 3.

Step-by-step explanation:

Bearing in mind that the surface area of a 3D object is the total area of its surface (that is the sum of the areas of its faces), we can count the number of distinct shapes in each figure, calculate their areas and add them up. Be careful not to add the faces that are "inside".

Figure 1

Its surface area consists of 13 squares of 5x5 $feet^2$ and 3 rectangles of 15x5 $feet^2$ . So, its surface area is (13x25 + 3x75) $feet^2 = 550feet^2$

Figure 2

Its surface area consists of 6 squares of 5x5 $feet^2$ , 3 rectangles of 17x5 $feet^2$ , 1 rectangle of 13x5 $feet^2$ and 2 triangles of base 12 feet and height 5 feet. So, its surface area is (17x5x3+6x5x5+13x5+12x5x2:2) $feet^2 = 530feet^2$

Figure 3

Its surface area consists of 2 rectangles of 12.5x5 $feet^2$ , 1 rectangle of 11x5 $feet^2$ , 2 triangles of base 12 feet and height 5 feet, 1 rectangle of 11x13 $feet^2$ , 2 rectangles of 12.5x11 $feet^2$ and 1 rectangle of 12x11 $feet^2$ .

So, its surface area is (2x12.5x5+11x5+2x12x5:2+11x13+2x12.5x11+12x11) $feet^2 = 790feet^2$

Answer:

Least surface area to greatest surface area:

Blue - Red - Green

Step-by-step explanation:

All the surfaces of the shapes are rectangles, then their surface is computed as:

Surface = Length*Width

Blue figure

Area of the top:

5*5 + 5*5 + 5*5 + 5*5 + 5*5 = 125 ft^2

Area of the sides:

2*(5*10) = 100 ft^2

Area of the bottom:

10*5 = 50 ft^2

Area of the front and the back

2*(5*5 + 15*5) = 200 ft^2

Total: 125 + 100 + 50 + 200 = 475 ft^2

Red figure

Area of the top:

5*5 + 13*5 = 90 ft^2

Area of the left side:

5*10 = 50 ft^2

Area of the right side:

5*5 = 25 ft^2

Area of the bottom:

17*5 = 85 ft^2

Area of the front and the back:

2*(17*5 + 12*5/2 + 5*5) = 280 ft^2

Total: 90 + 50 + 25 + 85 + 280 = 530 ft^2

Green figure

Area of the top:

12.5*11 + 13*11 = 280.5 ft^2

Area of the left side:

11*5 = 55 ft^2

Area of the bottom:

(12.5+12)*11 = 269.5 ft^2

Area of the front and the back:

2*(12.5*5 + 12*5/2) = 185 ft^2

Total: 280.5 + 55 + 269.5 + 185 = 790 ft^2

At a rate of 4.25% over 24 months. If he pays $51.00 in interest, what was the original amount of his loan?

Answers

I = PRT.....rearrange.....P = I / RT

P = 51 / (0.0425* 2).....I used 2 because 24 months = 2 yrs
P = 51 / 0.085
P = 600 <===

Which special version of the Pythagorean Theorem can you use to find the length of any square's diagonal, d, using only the length of its side, s?

Answers

Using the Pythagorean Theorem, the length of a square diagonal, in function of it's sides s, is given by:

$d = s√(2)$

The Pythagorean Theorem relates the length of the legs $l_1$ and $l_2$ of a right triangle with the length of the hypotenuse h, according to the following equation:

$h^2 = l_1^2 + l_2^2$

In a square, as given in the figure below, the legs are the sides s, of equal measure, while the hypotenuse is the diagonal d, thus:

$d^2 = s^2 + s^2$

$d^2 = 2s^2$

$d = √(2s^2)$

$d = s√(2)$

A similar problem is given at brainly.com/question/21691542

the square's diagonal is the triangle's hypotenuse.

the original Pythagorean theorem is $a^(2) + b^(2) = c^(2)$ where a and b are the two sides and c is the hypotenuse.

that means the Pythagorean theorem for this question is:

$s^(2) + s^(2) = d^(2)$ or $2( s^(2) )= d^(2)$

0.45833333333 as a fraction

Answers

That decimal is equivalent to

45,833,333,333 / 100,000,000,000 .

If the numerator and denominator have any common factor,
then the fraction can be simplified. But I doubt it.

Final answer:

The decimal number 0.45833333333 is equivalent to the fraction 11/27. We arrived at this answer by setting up an equation with the decimal as an unknown, then manipulating and solving the equation to find its equivalent fraction form.

Explanation:

The decimal number 0.45833333333 represents a recurring decimal where '58333' repeats itself infinitely. To convert recurring decimals into fractions, we can use a method involving algebra.

Let's represent 0.45833333333 as 'x'. We can express 'x' in the form of 0.45833... = x. Then, multiply both sides of the equation by 10 to the power of a number of repeating digits (which is 5 in this case): 10^5*x = 45833.33333...

Now, subtract the original equation from the one after multiplication, we get 99999x = 45833. Then, solve for 'x', x = 45833/99999. Simplifying this fraction gives us x = 11/27.

Therefore, 0.45833333333 as a fraction is 11/27.

Learn more about Converting decimals to fractions here:

brainly.com/question/35123994

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