Answer:
x = 3
y = 2
Step-by-step explanation:
3x + 2y = 12
-2x + 3y = 5 to find the solution we will use elimination method and for that, multiply second equation with 3 and the first equation with 2
<em>2 * 3x + 2y = 12</em>
<em>6x + 4y = 24</em>
<u>3 * -2x + 3y = 5</u>
<u>-6x + 9y = 15</u> now find the sum of both equation:
<em>6x + 4y </em><u>-6x + 9y</u> = 24 + 15 add like terms
13y = 39 divide both sides by 13
y = 3 now that we found the value of y we can use this to calculate the value of x
3x + 2y = 12 replace y with 3
3x + 2*2 = 12
3x + 4 = 12 subtract 4 from both sides
3x = 9 divide both sides by 3
x = 3
Given:
h = high quality bean ; costs 6 per pound
c = cheaper bean ; costs 3.25 per pound
160 pounds of blended coffee beans at 4.97 per pound
h + c = 160
6h + 3.25c = 160(4.97)
6h + 3.25c = 795.20
h = 160 - c
6(160-c) + 3.25c = 795.20
960 - 6c + 3.25c = 795.20
- 2.75c = 795.20 - 960
- 2.75c = -164.80
c = - 164.80 / -2.75
c = 59.92 or 60 pounds
h = 160 - c
h = 160 - 60
h = 100 pounds
Sarah must blend 100 pounds of high quality bean and 60 pounds of cheaper bean.
4x^2 - 64
= 4(x + 4) (x - 4)
The triangle has sides a,b,c such that
a = 2*sqrt(5), b = sqrt(5), and c = 2*sqrt(10)
Square each value
a = 2*sqrt(5)
a^2 = (2*sqrt(5))^2
a^2 = 2^2(sqrt(5))^2
a^2 = 4*5
a^2 = 20
b^2 = 20 for similar reasons as side 'a'
c = 2*sqrt(10)
c^2 = (2*sqrt(10))^2
c^2 = 2^2*(sqrt(10))^2
c^2 = 4*10
c^2 = 40
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Using the pythagorean theorem, we see that
a^2 + b^2 = c^2
20 + 20 = 40
40 = 40
So the initial equation a^2 + b^2 = c^2 is true making the triangle with sides a,b,c defined above to be a right triangle
Answer:
thirty-six, thirty six, 36%, thirty-six percent, thirty six percent, or 36 percent
