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Snowcat [4.5K]
2 years ago
13

Simplest form of 45/120

Mathematics
2 answers:
Sergeu [11.5K]2 years ago
8 0

Answer:

3/8

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 45 and 120 is 15

Divide both the numerator and denominator by the GCD

45 ÷ 15

120 ÷ 15

Reduced fraction:

3

8

Therefore, 45/120 simplified to lowest terms is 3/8.

Vesna [10]2 years ago
4 0

Answer:

3/8

Step-by-step explanation:

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3. The backyard of a home is a rectangle 25m by 30m. A garden of uniform width is to be
KiRa [710]

Answer:

Part A

The width of the garden is approximately 3.987 meters

Part B

Please find attached the drawing of the solution

Step-by-step explanation:

Part A

The given parameters are;

The dimensions of the backyard of the home = 25 m by 30 m

The width of the garden to be built in the yard = Uniform width

The shape of the grass left inside = Rectangular

The area of the grass at the center = The area of the garden

Let 'x' represent the width of the garden, we have;

The length of the rectangular grass area at the center, l = 30 - 2·x

The width of the rectangular area of grass at the center, w = 25 - 2·x

The area of the rectangular backyard, A = 30 m × 25 m = 750 m²

The area of the rectangular backyard, A = (The area of the garden) + (The area of the rectangle of grass inside)

The area of the rectangle of grass, GA = (30 - 2·x)·(25 - 2·x) = The area of the garden

The area of the rectangular backyard, A = 750 = (30 - 2·x)·(25 - 2·x) + (30 - 2·x)·(25 - 2·x)  = 2 × (30 - 2·x)·(25 - 2·x) = 8·x² - 220·x + 1,500

∴ 750 = 8·x² - 220·x + 1,500

8·x² - 220·x + 1,500 - 750 = 0

8·x² - 220·x + 750 = 0

x = (220 ± √(220² - 4 × 8 × 750))/(2 × 8)

x ≈ 23.513, or x = 3.987

When x = 25.513, the width of the rectangle of grass inside, w = 25 - 2 × 23.513 = -22.026, which is not a natural (physically possible)

Therefore, the possible width of the garden, x ≈ 3.987

Part B

The drawing of the solution created with MS Visio is attached

6 0
2 years ago
The graph shows that is translated horizontally and vertically to create the function .
yarga [219]

According to the function transformations, the value of h is -2

<h3>How to determine the value of h?</h3>

The complete question is in the attachment

The functions are given as:

f(x) = (2.5)^x

g(x) = (2.5)^{x-h

From the question, we understand that the function f(x) is translated to the left to get g(x)

From the attached graph, we can see that the function h(x) is 2 units to the left of f(x).

This transformation is represented by:

(x, y) => (x + 2, y)

So, we have:

x - h = x + 2

Evaluate the like terms

h = -2

Hence, the value of h is -2

Read more about function transformations at:

brainly.com/question/3381225

#SPJ1

3 0
2 years ago
Last season two running back’s on the Steelers football team rushed or a combined total of 1550 yards one rushed four times as m
ruslelena [56]

Answer:

One ran 1240 yards the other ran 310 yards.

Step-by-step explanation:

1550/5=310

310 times 4 is 1240

5 0
3 years ago
Read 2 more answers
Hello everyone I need help with this worksheet it's ten problems answer the ones you know for me please it's homework.
Fed [463]

Answer:

1. Slope = -4/5

2. Slope = 2/3

3. Slope = 0

4. Slope = 3/-4

5. Slope = 7/-12

6. Slope = 1/2

7. Slope = -2/0 --> Undefined

8. Slope = 3/-2

9. Slope = 5/-4

10. Slope = 4/3

Step-by-step explanation:

Ok so I'm assuming that you want the slope for all the two points. Basically, the formula for slope is rise/run, or y2-y1/x2-x1. Solve using that. For example, for number 1, it would be:

10-2/1-11 = 8/-10 = -4/5

5 0
2 years ago
Please helppp ASAP Content attribution
Aliun [14]

Answer:

The LCD of the two given fraction is (x + 4)(x + 5)(x + 7)

Step-by-step explanation:

<em>In the algebraic fractions, the LCD is the least common denominator to find it do that:</em>

  • Factorize each denominator
  • Take all the factors without repeating factors

<em>Let us do that with our question</em>

∵ The denominator of the first fraction is m² + 9m + 20

→ Factorize it into two factors

∵ 20 = 4 × 5 ⇒ the last term

∵ 4 + 5 = 9 ⇒ the coefficient of the middle term

∴ m² + 9m + 20 = (x + 4)(x = 5)

∴ The factors of m² + 9m + 20 are (x + 4) and (x + 5)

<em>Do the same with the 2nd denominator</em>

∵ The denominator of the second fraction is m² + 11m + 28

→ Factorize it into two factors

∵ 28 = 4 × 7 ⇒ the last term

∵ 4 + 7 = 11 ⇒ the coefficient of the middle term

∴ m² + 11m + 28 = (x + 4)(x + 7)

∴ The factors of m² + 11m + 28 are (x + 4) and (x + 7)

∵ The factors of the two denominators are (x + 4), (x + 5), (x + 4), (x + 7)

→ LCD will be all factors without repeating which means we will

   take the factor (x + 4) just one time, we will not repeat it.

∴ LCD = (x + 4)(x + 5)(x + 7)

∴ The LCD of the two given fraction is (x + 4)(x + 5)(x + 7)

5 0
3 years ago
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