1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
AlekseyPX
3 years ago
11

Suppose that a family wants to increase the size of the garden which is currently 16 feet long and 8 feet wide without changing

the basic shape of the garden. That is, the family wants to ensure that the length of the garden remains twice the width (see figure).
1. Write an equation for the area of the new garden.
2. Write an equation that calculates how much more area the new garden will have as compared to the current garden. Simplify the equation into a quadratic equation in standard form.
3. Using the equation from Exercise 2, determine what effect increasing the width of the garden by two feet will have on the length of the garden and the total area of the garden.
4. Using the equation from Exercise 2 and factoring, determine how much the width of the garden will need to be increased in order for the garden area to be 160 square feet larger than its original area.
5. Using the equation from Exercise 2 and factoring, determine how much the width of the garden will need to be increased in order for the garden area to be four times its original area.

Mathematics
1 answer:
Cloud [144]3 years ago
3 0

Answer:

See below

Step-by-step explanation:

<u>Sides of the garden</u>

  • 16 feet and 8 feet

<u>New dimensions of the garden</u>

  • 16 + 2x and 8 + x

<u>1. The area of the new garden</u>

  • (16 + 2x)(8 + x) =
  • 2x^2 + 32x + 128

<u>2. The difference in area </u>

  • 2x^2 + 32x + 128 - 16*8 =
  • 2x^2 + 32x

<u>3. x= 2 effect on the area</u>

  • 2*2^2 + 32*2 =
  • 8 + 64 =
  • 72 ft²

<u>4. Area difference = 160</u>

  • 2x^2 + 32x = 160
  • x^2 + 16x - 80 = 0
  • Solving we get positive root of 4 ft

<u>5. Area difference = 4 times</u>

  • 2x^2 + 32x = 128*3
  • 2x^2 + 32x - 384 = 0
  • x^2 + 16x - 192= 0
  • Solving we get positive root of 8 ft

You might be interested in
Rachel is keeping track of how much water she drinks. On Friday, she drank two bottles of water with snacks and 5 cups of water
xeze [42]

Answer:

2 CUPS

Step-by-step explanation:

Write two equations, where "b" = bottles, and "c" = cups

2b +5c = b +7c -->

b = 2c

THERE ARE 2 CUPS IN A BOTTLE

6 0
3 years ago
Read 2 more answers
Which BEST explains the expression x( y z + 1 2 )? A) x depends on ( y z + 1 2 ). B) ( y z + 1 2 ) depends on x. C) x and ( y z
Alekssandra [29.7K]

9514 1404 393

Answer:

  D)  x and ( y z + 1 2 ) are independent of each other

Step-by-step explanation:

Assuming this is not intended to be describing a function named x with an argument of yz+12, the variables in any expression are assumed to be independent of each other, unless additional information is provided showing their dependencies.

Here, there is no such additional information, so we must assume ...

  x and (yz +12) are independent of each other

_____

<em>Additional comment</em>

The assumption stated in the answer is intended to ensure we're not concerned with something of the form ...

  g(x)

which is an expression saying 'g' is dependent on 'x'. If we know 'g' is a function name, then g(yz+12) will make 'g' be dependent on (yz+12).

Similarly, if x(a) is intended to mean that x is a function of 'a', then the corresponding x(yz+12) will mean that x is dependent on (yz+12). This would be quite unusual, since letters toward the end of the alphabet are usually used for variable names, while letters in the middle of the alphabet are used for function names.

8 0
2 years ago
A package weighs 80 ounces. What is the weight of the package in pounds?
Degger [83]

Answer:

5

Step-by-step explanation:

1 ounce = 0.0625

0.0625 x 80 = 5

3 0
2 years ago
Lily is a botanist who works for a garden that many tourists visit. The function f(s) = 2s + 30 represents the number of flowers
Vesnalui [34]

Answer:

  A. b(w) = 80w +30

  B. input: weeks; output: flowers that bloomed

  C. 2830

Step-by-step explanation:

<h3>Part A:</h3>

For f(s) = 2s +30, and s(w) = 40w, the composite function f(s(w)) is ...

  b(w) = f(s(w)) = 2(40w) +30

  b(w) = 80w +30 . . . . . . blooms over w weeks

__

<h3>Part B:</h3>

The input units of f(s) are <em>seeds</em>. The output units are <em>flowers</em>.

The input units of s(w) are <em>weeks</em>. The output units are <em>seeds</em>.

Then the function b(w) above has input units of <em>weeks</em>, and output units of <em>flowers</em> (blooms).

__

<h3>Part C:</h3>

For 35 weeks, the number of flowers that bloomed is ...

  b(35) = 80(35) +30 = 2830 . . . . flowers bloomed over 35 weeks

7 0
2 years ago
-4r &lt; 22<br><br> Can someone help with this inequality?
svp [43]
Lol u thought I was writing an answer hahahaha
8 0
3 years ago
Other questions:
  • One million four hundred ninety-six thousand seven hundred seventy -two in standard form
    7·2 answers
  • Select each correct answer.
    12·1 answer
  • Which of the triangle(s) shown is similar to triangle c? b d e f g h
    7·2 answers
  • Can Someone Help Me Simplify These Expressions
    12·1 answer
  • What is the answer to 3•8-6/2
    7·1 answer
  • A person drives north 6 blocks, then drives west 6 blocks. the displacement is a straight line from the starting point to the fi
    15·1 answer
  • A) Complete the table of values for y = 6 - 2x<br><br> 0<br> 1<br> 2<br> 3<br> 4<br> 5<br> -4
    12·1 answer
  • A rectangular shaped pond is 16 meters long and 14 meters wide. The dimensions of a rectangular shaped lake nearby is 350%
    7·1 answer
  • 34. The number of songs that an MP3 player can
    12·1 answer
  • 38 divided by 817,152​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!