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2 years ago

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John painted his most famous work,in his country,in 1930 on composition board with perimeter 103.48 in. If the rectangular paint

ing is 5.83 in. Taller it is wide,find the dimensions of the painting. what is the width? what is the length?

1 answer:

Alexxandr [17]2 years ago

5 0

Answer:

Width $=22.955$ in

length $=28.785$ in

Step-by-step explanation:

let width $=x$

painting is $5.83$ in taller than it is wide

length $=x+5.83$

Perimeter of rectangle $=2$ (length+width)

Perimeter of painting $=103.48$

$2(x+x+5.83)=103.48\\2x+5.83=51.74\\2x+51.74-5.83\\2x=45.91\\x=\frac{45}{2} \\x=22.955$

width $=x=22.955$ in

length $=x+5.83=22.955+5.83=28.785$ n

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Answer:

Step-by-step explanation:

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m∠2 = 50°

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m∠1 = 130°

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m∠5 = 180° - m∠3

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Barbara drives between Miami, Florida, and West Palm Beach, Florida. She drives 50 mi in clear weather and then encounters a thu

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Distance traveled in clear weather = 50 miles

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Let speed in clear weather = x

⇒ Speed in thunderstorm = x-20

Total time taken for trip = 1.5 hours

We need to determine average speed in clear weather (i.e. x) and average speed in the thunderstorm (i.e. x-20 ).

Total time taken for trip = Time taken in clear weather + Time taken in thunderstorm

⇒ Total time taken for trip = $\frac{Distance covered in clear weather}{Speed in clear weather}$ + $\frac{Distance covered in thunderstorm}{Speed in thunderstorm}$

⇒ 1.5 = $\frac{50}{x}$ + $\frac{15}{x-20}$

⇒ 1.5 = $\frac{50(x-20)+15(x)}{(x)(x-20)}$

⇒ 15*x*(x-20) = 10*[50*(x-20)+15*x]

⇒ 15x² - 300x = 500x - 10,000 + 150x

⇒ 15x² - 300x = 650x - 10,000

⇒ 15x² - 950x + 10,000 = 0

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The above equation is in the format of ax² + bx + c = 0

To determine the roots of the equation, we will first determine 'D'

D = b² - 4ac

⇒ D = (-190)² - 4*3*2,000

⇒ D = 36,100 - 24,000

⇒ D = 12,100

Now using the D to determine the two roots of the equation

Roots are: x₁ = $\frac{-b+\sqrt{D}}{2a}$ ; x₂ = $\frac{-b-\sqrt{D}}{2a}$

⇒ x₁ = $\frac{-(-190)+\sqrt{12,100}}{2*3}$ and x₂ = $\frac{-(-190)-\sqrt{12,100}}{2*3}$

⇒ x₁ = $\frac{190+110}{6}$ and x₂ = $\frac{190-110}{6}$

⇒ x₁ = $\frac{300}{6}$ and x₂ = $\frac{80}{6}$

⇒ x₁ = 50 and x₂ = 13.33

So speed in clear weather can be 50 mph or 13.33 mph. However, we know that in thunderstorm was 20 mph less than speed in clear weather.

If speed in clear weather is 13.33 mph then speed in thunderstorm would be negative, which is not possible since speed can't be negative.

Hence, the speed in clear weather would be 50 mph, and in thunderstorm would be 20 mph less, i.e. 30 mph.

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The distributive property can be applied to which expression to factor 12x3 – 9x2 4x – 3?

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Let s represent number of shirts and h represent number of hats.

We have been given that the organizers of a talent show have budgeted $1800 to buy souvenir clothing to sell at the event. They can buy shirts for $10 each and hats for $8 each.

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We are also told that organizers plan to buy at least 5 times as many shirts as hats. This means that number of shirts should be greater than or equal to 5 times hats. We can represent this information in an inequality as:

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Step-by-step explanation:

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