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Talja [164]
2 years ago
8

Amanda needs to make a garden plot which has an area less than 18 sq. feet. The length should be 3 feet longer than the width. W

hat are the possible dimensions of the garden plot?
Mathematics
1 answer:
SCORPION-xisa [38]2 years ago
6 0

Answer:

<em>Any width less than 3 feet</em>

Step-by-step explanation:

<u>Inequalities</u>

The garden plot will have an area of less than 18 square feet. If L is the length of the garden plot and W is the width, the area is calculated by:

A = L.W

The first condition can be written as follows:

LW < 18

The length should be 3 feet longer than the width, thus:

L = W + 3

Substituting in the inequality:

(W + 3)W < 18

Operating and rearranging:

W^2 + 3W - 18 < 0

Factoring:

(W-3)(W+6)<0

Since W must be positive, the only restriction comes from:

W - 3 < 0

Or, equivalently:

W < 3

Since:

L = W + 3

W = L - 3

This means:

L - 3 < 3

L < 6

The width should be less than 3 feet and therefore the length will be less than 6 feet.

If the measures are whole numbers, the possible dimensions of the garden plot are:

W = 1 ft, L = 4 ft

W = 2 ft, L = 5 ft

Another solution would be (for non-integer numbers):

W = 2.5 ft, L = 5.5 ft

There are infinitely many possible combinations for W and L as real numbers.

You might be interested in
Can two fractions with the same numerator and different denominators be equal?
Ede4ka [16]

Answer:

No

Step-by-step explanation:

You can only have the same denominator

Example:

2                3           5

-       +        -    =      -

9               9            9

8 0
3 years ago
Please explain how to do this, I'm using all my points<br><br>A. 40 L<br>B. 80 L<br>C. 4 L <br>D. 8L
exis [7]

Answer: choice A. 40 liters

====================================

Explanation:

x = number of liters of the 50% alcohol solution

If we have x liters of 50% alcohol, then we have 0.50*x liters of pure alcohol. This is added to 0.90*40 = 36 liters of pure alcohol (from the 90% solution).

So far we have 0.50*x + 36. This expression represents the total amount of pure alcohol. We want a 70% solution, so we want 70% of the total 40+x meaning 0.50*x + 36 is to be set equal to 0.70*(40+x) and we solve for x as shown below

0.50*x + 36 = 0.70*(40+x)

0.50*x + 36 = 0.70*(40)+0.70*(x)

0.50*x + 36 = 28+0.70*x

36 - 28 = 0.70*x - 0.50x

8 = 0.20x

0.20x = 8

x = 8/0.20

x = 40

So that is why the answer is choice A. 40 liters

6 0
2 years ago
Charlotte’s weekly paycheck is based on the number of hours worked during the week and on the weekend. If she works 13 hours dur
Gelneren [198K]
I am setting the week hourly rate to x, and the weekend to y.  Here is how the equation is set up:

13x + 14y = $250.90
15x + 8y = $204.70

This is a system of equations, and we can solve it by multiplying the top equation by 4, and the bottom equation by -7.  Now it equals:

52x + 56y = $1003.60
-105x - 56y = -$1432.90

Now we add these two equations together to get:

-53x = -$429.30 --> 53x = $429.30 --> (divide both sides by 53) x = 8.10.  This is how much she makes per hour on a week day.

Now we can plug in our answer for x to find y.  I am going to use the first equation, but you could use either.

$105.30 + 14y = $250.90.  Subtract $105.30 from both sides --> 14y = $145.60 divide by 14 --> y = $10.40

Now we know that she makes $8.10 per hour on the week days, and $10.40 per hour on the weekends.  Subtracting 8.1 from 10.4, we figure out that she makes $2.30 more per hour on the weekends than week days.
7 0
3 years ago
Read 2 more answers
What is 245 divided by 2?
olga nikolaevna [1]

Answer:

122.5

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
HELP ME PLZ WILL MARK BR ASAP
Murljashka [212]

Answer:

the answer is A. 47

Step-by-step explanation:

tanθ = 15/14

the answer for 15/14 comes out to be about 1.0714 and so you put that value into your calculator using the sin^-1 button. it should look something like this sin^-1(1.0714) and press enter and you'll get 46.974 and round will result in 47

3 0
3 years ago
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