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
Musya8 [376]
2 years ago
13

Owen’s rectangular garden has a length of (x+3) feet and a width of (x−4) feet. If the area of the garden is 18 square feet, wha

t are the dimensions of the garden?
Mathematics
2 answers:
taurus [48]2 years ago
7 0

Answer:

length: 9 units width: 2 units

Step-by-step explanation:

The formula to find the area of a rectangle is length*width (LW)

x+3 is the length and x-4 is the width; together they multiply up to 18

(x+3)(x-4) = 18

x^2 - 4x + 3x - 12 = 18 (multiply it out using FOIL)

x^2 - x - 12 = 18 (combine like terms on the left side)

x^2 - x -30 = 0 (subtract 18 from both sides so that the right side is 0)

<em>Think what two numbers multiply up -30 and add up to -1 (5 and -6)</em>

(x+5)(x-6) = 0 (factor it)

x+5 = 0 and x-6 = 0 (solve using zero-product property)

x = -5 and x = 6 (solve)

x = 6 (only this one works since you cannot have a negative side length)

(6+3)(6-4) = 18 ? (plug in to find side lengths and check)

9 * 2 = 18 (Correct!)

Alexxandr [17]2 years ago
6 0

Answer:

  length: 9 ft

  width: 2 ft

Step-by-step explanation:

This can be worked using a quadratic equation, or it can be worked by considering factors of the area value.

__

<h3>difference in dimensions</h3>

The difference in length between the long side (x+3) and the short side (x-4) is ...

  (x +3) -(x -4) = 3+4 = 7 . . . . feet

<h3>area factors</h3>

The area formula is ...

  A = LW

The given area is 18 square feet, so we want to find numbers that multiply to give 18 and that differ by 7 in their values. Here are the integer factors of 18:

  18 = 1×18 = 2×9 = 3×6

Of these factor pairs, the values 2 and 9 differ by 7.

The garden is 9 feet long and 2 feet wide.

_____

<em>Additional comment</em>

We can check to see if these numbers are consistent with the given expressions:

  x+3 = 9  ⇒  x = 6

  x -4 = 6 -4 = 2 . . . . the other dimension we found

__

If you solve this using a quadratic equation, you will find that dimensions -2 ft and -9 ft also pop out. That is x +3 = -2, or x = -5 is also a solution to the quadratic. Of course, that is an extraneous solution, which we avoid by considering only positive factors of 18.

The quadratic equation we're referring to is A=18 ⇒ (x+3)(x-4) = 18.

You might be interested in
What is the standard deviation of the following data? If necessary, round your answer to two decimal places.
katrin2010 [14]
 we are given with the set of data containing the elements listed above and is asked to find out the standard deviation of the data. SD is used to determine the distance between the points to the best fit line gained from the data. The formula to be followed is the square root of the summation of (x-mean) over n-1. sd is equal to <span>5.13.</span>
7 0
2 years ago
84 students are in the school choir. The ratio of girls to boys is 3:4. How many members are girls?
Paul [167]
3 + 4 = 7
84 ÷ 7 = 12 = 1 (in terms of the ratio)
12 × 3 = 36, which is the answer
Hope this helps :)
7 0
2 years ago
Read 2 more answers
Circle.center:(2,-5).radius:9
Kaylis [27]

Answer:

Step-by-step explanation:

eq. of circle with center (h,k) and radius=r is

(x-h)²+(y-k)²=r²

reqd. eq. is

(x-2)²+(y+5)²=9²

8 0
3 years ago
Solve the equation y = ax - b for the variable a.
lorasvet [3.4K]

Answer:

y-b/x = a

Step-by-step explanation:

y-b/x = a

7 0
3 years ago
BRAINLIEST AND MAX PTS<br><br> CONVERT y = 40x + 600 to point-slope form
IRISSAK [1]

Answer:

The answer to your question is y - 0 = 40(x - 15)

Step-by-step explanation:

                                  y = 40x + 600

Convert to                 y - y₁ = m(x - x₁)          

Process

1.- Factor 40 in the right side of the equation

                                 y = 40(x - 15)

2.- Give the form of the point slope form

                                 y - 0 = 40(x - 15)

where

y₁ = 0

m = 40

x₁ = 15

3 0
3 years ago
Read 2 more answers
Other questions:
  • HELPPPPPPPPP 55 POINTS Isabel graphed the following system of equations.
    7·1 answer
  • Oak grove and salem are 87 mi from each other. How far apart would the cities be on a map that has a scale of 5in: 29mi
    7·1 answer
  • Sarah drives 55 mi/h for h hours. which expression shows the number of miles that sarah drove?
    5·2 answers
  • Help me. I don't understand it.
    6·1 answer
  • 2+2+3+4+4+5+5+8+9+5800= ??????????????? divided by 6 times 34 bb
    15·1 answer
  • Find the volume of the solid bounded by z = 2 - x2 - y2 and z = 1. Express your answer as a decimal rounded to the hundredths pl
    11·1 answer
  • A group of 5 teachers bought 3 pens and 1 eraser each. Their total cost for all the materials was $12.89. If the eraser was $0.9
    12·1 answer
  • Find the measure of the missing angle.<br> a<br> 77°
    12·1 answer
  • Ivan biked 4 2 3 hours on Monday, 1 1 3 hour on Tuesday, and 2 2 3 hours on Wednesday. What is the total number of hours Ivan sp
    11·1 answer
  • Wich function describes the graph shown below?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!