Let x be the number of pounds of the $1.35 beans. The cost of those beans is $1.35 * x, or 1.35x.
<span>Let y be the number of pounds of the $1.05 beans. The cost of those beans is $1.05 * y, or 1.05y. </span>
<span>We know that 120 pounds of the mix sells for $1.15/pound, for a total of 120 * 1.15 = $138. </span>
<span>x + y = 120 </span>
<span>1.35(x) + (1.05)y = 138 </span>
<span>We can rewrite the first as </span>
<span>x = -y + 120 </span>
<span>Now we can substitute (-y + 120) in for (x) in the second equation, because we just proved they're equal. </span>
<span>1.35(x) + 1.05(y) = 138 </span>
<span>1.35(-y + 120) + 1.05y = 138 </span>
<span>-1.35y + 162 + 1.05y = 138 </span>
<span>-0.3y + 162 = 138 </span>
<span>-0.3y = -24 </span>
<span>y = 80 </span>
<span>And since x + y = 120, that means x = 40. </span>
<span>Check: </span>
<span>40 pounds of x at $1.35 costs 40 * 1.35, or $54. </span>
<span>80 pounds of y at $1.05 costs 80 * 1.05, or $84. </span>
<span>Do those add up to our target total, according to the question, of 120 * 1.15 = $138? </span>
Answer:
It is A.
Step-by-step explanation:
To solve for b, use the 45-45-90 triangle theorem, in which each of the legs is x, so the legs would be 8. The hypotenuse would therefore be 8√2.
So without further solving the answer is A, since it's the only one with 8√2.
However, I will still solve for A and C. Using the 30-60-90 theorem, we have the sides as x, x√3, and 2x. The second longest side is b. Using this, we find a = 4√6 and c to be 4√2
Answer:
B
Step-by-step explanation:
Answer:
x = 9, Angles are 54°
Step-by-step explanation:
First, we need to find x:
7x-9 = 5x+9
+9 +9
7x = 5x+18
-5x -5x
2x = 18
x = 9
Now, we plug our x value in to find our angles.
5(9) + 9 = 54
Angle B = 54°
7(9) - 9 = 54°
Angle E = 54°
(angles are the same due to AAA property)
Answer:
1. x²-2x+15
This can't be factored, I've tried multiple ways now, but it just can't be factored.
2. y²-19y+90
Let's factor y^2−19y+90
y^2−19y+90
The middle number is -19 and the last number is 90.
Factoring means we want something like
(y+_)(y+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get -19
Multiply together to get 90
Can you think of the two numbers?
Try -9 and -10:
-9+-10 = -19
-9*-10 = 90
Fill in the blanks in
(y+_)(y+_)
with -9 and -10 to get...
(y-9)(y-10)
Answer:
(y−9) (y−10)
