Answer:
10m x 15m
Step-by-step explanation:
You are given some information.
1. The area of the garden: A₁ = 150m²
2. The area of the path: A₂ = 186m²
3. The width of the path: 3m
If the garden has width w and length l, the area of the garden is:
(1) A₁ = l * w
The area of the path is given by:
(2) A₂ = 3l + 3l + 3w + 3w + 4*3*3 = 6l + 6w + 36
Multiplying (2) with l gives:
(3) A₂l = 6l² + 6lw + 36l
Replacing l*w in (3) with A₁ from (1):
(4) A₂l = 6l² + 6A₁ + 36l
Combining:
(5) 6l² + (36 - A₂)l +6A₁ = 0
Simplifying:
(6) l² - 25l + 150 = 0
This equation can be factored:
(7) (l - 10)*(l - 15) = 0
Solving for l we get 2 solutions:
l₁ = 10, l₂ = 15
Using (1) to find w:
w₁ = 15, w₂ = 10
The two solutions are equivalent. The garden has dimensions 10m and 15m.
Answer:
14 1/4
Step-by-step explanation:
Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.
Adding all of these should equal to 180 from the way the angle is set up.
So the equation should be:
(3x + 2) + (2x + 5) + (2x - 9) = 180
You can remove parentheses as it doesn’t affect the equation since it is all addition.
Let’s first add the common variables together.
3x + 2x + 2x = 7x
2 + 5 + (-9) = -2
So now we should have:
7x - 2 = 180
Now add 2 to both sides.
7x = 182
Divide both sides by 7 to isolate x.
x = 26
So x is 26.
The answers are 3/8 and 1/6.
There are 8 possible outcomes in the sample space for flipping 3 coins. Of those, 3 include two heads and 1 tail. This makes the probability 3/8.
Choosing a quarter for the first coin is 3/10, since there are 3 quarters out of 10 coins. After this, choosing a dime is given by 5/9, since there are 5 dimes out of 9 coins left:
3/10(5/9) = 15/90 = 1/6
Answer:
49π in²
Step-by-step explanation:
Step 1: Find the radius.
- To find radius given diameter, just divide the diameter by 2:
- 14/2 = 7, so the radius is 7.
Step 2: Apply area of circle formula.
- The formula to find the area of a circle is πr², where r = radius.
- Now, plug in the value of r: π(11)².
Step 3: Simplify.
Since we're finding the area in terms of pi, we don't have to multiply 121 by pi, so the answer is 49π in².
