Please Answer!

In the picture :) Basically a world problem that used algebra. Thank you!

Allushta [10]

<h3>Answer: Equation is 4x^2+44x = 240</h3>

This is the same as 4x^2+44x-240 = 0

You can divide everything by 4 to get x^2+11x-60 = 0

There are a number of ways to represent the equation

There's only one final answer for x however and it is x = 4

<h3>The width of the path is 4 feet</h3>

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Explanation:

The garden is 10 ft by 12 ft, so its area is 10*12 = 120 square feet. This is ignoring the boundary surrounding the garden. It's simply the garden area itself.

Adding on the border will have the 10 ft jump to 10+x+x = 2x+10 ft. Similarly, the 12 turns to 2x+12. The larger rectangle is (2x+10) ft by (2x+12) ft giving an area of...

(2x+10)*(2x+12) = 2x*2x + 2x*12 + 10*2x + 10*12

(2x+10)*(2x+12) = 4x^2 + 24x + 20x + 120

(2x+10)*(2x+12) = 4x^2 + 44x + 120

You can use the FOIL rule, distributive property, or the box method to expand out what is shown above.

4x^2 + 44x + 120 represents the area of the garden plus the border, aka the area of the larger rectangle. Subtract off the area of the smaller rectangle (120) and we get...

border area only = (larger rectangle area) - (smaller rectangle area)

border area only = (4x^2 + 44x + 120) - (120)

border area only = 4x^2 + 44x

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We're told the concrete path or border is 240 square feet, so,

4x^2 + 44x = 240 ... is one way to write the equation

4x^2 + 44x - 240 = 0 ... is another way

4(x^2 + 11x - 60) = 0

x^2 + 11x - 60 = 0 ... yet another way

(x + 15)(x - 4) = 0 ... factoring

x+15 = 0 or x-4 = 0 ... zero product property

x = -15 or x = 4

The x value is a width. A negative width makes no sense. We will ignore x = -15 and only focus on x = 4.

The concrete path has a width of 4 feet. Therefore, the initial 10 ft dimension jumps to 2x+10 = 2*4+10 = 18 ft and the 12 ft jumps to 2x+12 = 2*4+12 = 20 ft

Basically, the 10 by 12 smaller rectangle jumps to a 18 by 20 ft rectangle

The larger rectangle has area 18*20 = 360, then we subtract off the garden area (120) getting 360-120 = 240 which is the proper path area we were initially told. This confirms we have the right answer.

5 0

3 years ago

Read 2 more answers

What’s the value of x?<br> G<br><br> 53°<br> 45<br> H<br> x°

Kazeer [188]

Answer:

x = 98°

Step-by-step explanation:

95 + 53 + (180 - x) = 180

148 + 180 - x = 180

328 - x = 180

328 - x + x = 180 + x

x + 180 = 328

x + 180 - 180 = 328 - 180

x = 98°

7 0

3 years ago

Cedar Point has 17 roller coasters. If you want to ride at least 15 of them, how many different combinations of roller coasters

stellarik [79]

<h3>Answer: 154</h3>

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Explanation:

I'll be using the formula

$_n C _r = \frac{n!}{r!*(n-r)!}$

which is the nCr combination formula. We use nCr instead of nPr because the order of coasters doesn't matter. The whole time, the value of n stays fixed at n = 17 which is the total number of coasters to pick from.

While n is constant, the value of r will vary. It ranges from r = 15 to r = 17 inclusive of both endpoints. In other words, r will take on values from the set {15,16,17}. So we have three cases to consider. The r value is how many coasters we select. This is due to the "at least 15" which means "15 or more".

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If you ride r = 15 coasters, then we have the following number of combinations

$_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{17} C _{15} = \frac{17!}{15!*(17-15)!}\\\\_{17} C _{15} = \frac{17!}{15!*2!}\\\\_{17} C _{15} = \frac{17*16*15!}{15!*2!}\\\\_{17} C _{15} = \frac{17*16}{2!}\\\\_{17} C _{15} = \frac{17*16}{2*1}\\\\_{17} C _{15} = \frac{272}{2}\\\\_{17} C _{15} = 136\\\\$

There are 136 ways to ride exactly 15 coasters (when selecting from a pool of 17 total). The order doesn't matter.

We'll use this result later, so let x = 136.

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If r = 16, then we follow the same steps as above. You should get 17C16 = 17

There are 17 ways to ride 16 coasters where order doesn't matter. Effectively this is the same as saying "there are 17 ways of picking a coaster that you won't ride"

Let y = 17 so we can use it later

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Lastly, if r = 17, then nCr = 17C17 = 1 represents one way to ride all 17 coasters where order doesn't matter.

Let z = 1

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Add up the values of x, y, and z to get the final answer

x+y+z = 136+17+1 = 154

4 0

3 years ago

Barbara signed up for dance lessons at Dance Unlimited. She was charged $55 per month for lessons and a one-time recital fee of

Lubov Fominskaja [6]

Answer:

G. 6 months

Step-by-step explanation:

1. 495-165 to remove the one-time payment = 330

2. 330/55 to find the number of months = 6

4 0

4 years ago

Write the slope-intercept form of the equation that passes through the point (4,-6) and is parallel to the line y = -3/4x - 5

Karolina [17]

The equation that runs through the location (4,-6) has the slope-intercept form, $y=-\frac{3}{4}x-3$ .

<h2>Formation of the equation</h2>

A line's equation written in the slope-intercept form:

y=mx+b

where m= slope & b= y-intercept

The slope of two parallel lines is equal.

Currently, we know the line's equation:

$y=-\frac{3}{4} x-5$

here, slope, m= $-\frac{3}{4}$

A line equation is created by adding the slope's value and the point's coordinates (4, -6):

$-6=-\frac{3}{4}(4)+b$

⇒ -6=-3 +b [adding 3 to both sides]

⇒-3=b

⇒b= -3

Hence the solution is $y=-\frac{3}{4}x-3$ .

Learn more about slope-intercept form here:

brainly.com/question/9682526

#SPJ4

5 0

2 years ago