Answer:
Radius of larger flower bed = 10 feet
Radius of smaller flower bed = 6 feet
Step-by-step explanation:
<u>Complete question:</u>
"You have two circular flower beds, as shown. The sum of the areas of two flower beds is 136 pi square feet. Find the radius of each bed.<em>"</em>
<em>Radius of larger flower bed = r</em>
<em>Radius of smaller flower bed = r - 4</em>
<em />
Now,
Area of circle is
Since, total area is , we can write:
Expanding and solving for r:
Radius cannot be negative, so r = 10 & r-4 = 10 -4 = 6
Radius of larger flower bed = 10 feet
Radius of smaller flower bed = 6 feet
Answers: x = 13 and y = 11
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Let's focus on the angle expressions that have x in them.
They are adjacent angles and they form a straight line. So we consider them a linear pair. All linear pair angles always add to 180
(3x+89)+(7x-39) = 180
(3x+7x) + (89-39) = 180
10x+50 = 180
10x = 180-50
10x = 130
x = 130/10
x = 13
We'll use the same idea to find y
(3y+19)+(4y+84) = 180
(3y+4y) + (19+84) = 180
7y+103 = 180
7y = 180-103
7y = 77
y = 77/7
y = 11
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Extra info (optional section)
Let's find the measures of the four angles based on the x and y values we found.
- 3x+89 = 3*13+89 = 128
- 7x-39 = 7*13-39 = 52
- 3y+19 = 3*11+19 = 52
- 4y+84 = 4*11+84 = 128
It's not a coincidence that the 3x+89 and 4y+84 angles are equal (to 128). These are vertical angles which are always congruent. The other pair of congruent vertical angles are the 3y+19 and 7x-39 angles.
Note how 128+52 = 180 to help further confirm we have the correct values.
Another thing to notice is that all four angles add up to 360 degrees.
Answer:
Angelina should buy 9 packs of pens and 8 packs of pencils.
Step-by-step explanation:
Each pack of pens = 8 pens
Each pack of pencils = 9 pencils.
Also we know that, Commutative Property of Multiplication states that
a x b = b x a for any two numbers a and b.
So, 8 x 9 = 72 = 9 x 8
Hence, she should buy 9 packs of pens, so she will have 9 x 8 = 72 pens.
And she should buy 8 packs of pencils, she will have 8 x 9 = 72 pencils.
B is true.
I think E is also true.
Hi there!
We can set up a ratio to model the problem...
540/3000 = x/100
Now, just cross multiply and solve for x.
54000 = 3000x
x = 18
Therefore, 18 percent of last semester's college costs was spent on books. Hope this helped and have a great day!