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2 years ago

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Carran is building a fence around his rectangular yard. The fence will cover the front and the 2 sides of the yard. The

1 answer:

dolphi86 [110]2 years ago

7 0

9514 1404 393

Answer:

sides: 12 feet
front: 28 feet

Step-by-step explanation:

Let x represent the length of one side of the yard. Then the width of the yard is 2x+4, and the perimeter is ...

P = 2(L +W) . . . . . . . . . . formula for perimeter of a rectangle

80 = 2(x + (2x+4)) . . . . . with values from the problem filled in

40 = 3x +4 . . . . . . . . divide by 2, collect terms

36 = 3x . . . . . . . . . subtract 4

12 = x . . . . . . . . . divide by 3. This is the length of the side fence.

2x +4 = 2(12) +4 = 28

The fence is 12 feet on the sides and 28 feet on the front. (Its total length is 52 feet.)

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The x-coordinate of the vertex of the equation y = 2x2 − 4x + 12 The x-coordinate of the vertex of the equation y = 4x2 + 8x + 3

dolphi86 [110]

So since the vertex falls onto the axis of symmetry, we can just solve for that to get the x-coordinate of both equations. The equation for the axis of symmetry is $x=\frac{-b}{2a}$ , with b = x coefficient and a = x^2 coefficient. Our equations can be solved as such:

y = 2x^2 − 4x + 12: $x=\frac{4}{2*2}=\frac{4}{4}=1$

y = 4x^2 + 8x + 3: $x=\frac{-8}{2*4}=\frac{-8}{8}=-1$

In short, the vertex x-coordinate's of y = 2x^2 − 4x + 12 is 1 while the vertex's x-coordinate of y = 4x^2 + 8x + 3 is -1.

6 0

3 years ago

Is this answer correct ?

Sever21 [200]

Yes you are correct!

6 0

3 years ago

Read 2 more answers

Question 6 of 10

Maksim231197 [3]

Answer:

(2.5 , 3.5)

Step-by-step explanation:

We can use the midpoint formula . Here the points are , (2,2) and (3,5) .

• <u>Using</u><u> </u><u>Midpo</u><u>int</u><u> Formula</u><u> </u><u>:</u><u>-</u><u> </u>

⇒ M = { (x1 + x2)/2 , (y1 + y2)/2 }

⇒ M = ( 2+3/2 , 5+2/2 )

⇒ M = ( 5/2 , 7/2 )

⇒ M = ( 2.5 , 3.5 )

<h3><u>Hence </u><u>the</u><u> </u><u>midpoint</u><u> </u><u>is</u><u> </u><u>(</u><u>2</u><u>.</u><u>5</u><u> </u><u>,</u><u> </u><u>3</u><u>.</u><u>5</u><u>)</u></h3>

6 0

2 years ago

Amy and Zach each have 24 feet of fencing for their rectangular gardens. Amy makes her fence 6 feet long . Zach makes his fence

saul85 [17]

For this case we have that by definition, the area of a rectangle is given by:

$A = w * l$

Where:

w: Is the width of the rectangle

l: is the length of the rectangle

Each of the girls has 24 feet of fencing, that is, the perimeter is $P = 2w + 2l = 24.$

Amy:

$l = 6 \ ft\\2w + 2 (l) = 24\\2w + 2 (6) = 24\\2w + 12 = 24\\2w = 24-12\\2w = 12\\w = 6$

Thus, Amy's fence area is: $A = 6 * 6 = 36 \ ft ^ 2$

Zach:

$l = 8 \ ft\\2w + 2l = 24\\2w + 2 (8) = 24\\2w + 16 = 24\\2w = 24-16\\2w = 8\\w = 4$

Thus, the area of Zach's fence is: $A = 4 * 8 = 32 \ ft ^ 2$

Answer:

Amy's garden has a greater area

$36 \ ft ^ 2-32 \ ft ^ 2 = 4ft ^ 2$ , is $4 \ ft ^ 2$ greater

5 0

3 years ago

Read 2 more answers

Jasmine buys a turkey every year . The first time she bought a turkey, in year 0, it cost $15.50. She notices the price is getti

Wittaler [7]

The price of the turkey based on the percentage given is $15.81.

<h3>How to illustrate the information?</h3>

It was stated that the cost is $15.50 but that there was a 2% increment in price.

Therefore, the new price will be:

= $15.50 + (2% × $15.50)

= $15.50 + $0.31

= $15.81

Learn more about percentages on:

brainly.com/question/24304697

#SPJ1

6 0

2 years ago