Consecutive integers are 1 apart
they are
x,x+1,x+2
the sum of their squares is 194
x²+(x+1)²+(x+2)²=194
expand
x²+x²+2x+1+x²+4x+4=194
x²+x²+x²+2x+4x+1+4=194
3x²+6x+5=194
minus 5 from both sides
3x²+6x=189
3(x²+2x)=189
divide both sides by 3
x²+2x=63
minus 63 from bot sides
x²+2x-63=0
what 2 numbers multiply to get -63 and add to get 2
-7 and 9
(x-7)(x+9)=0
set each to zero
x-7=0
x=7
x+9=0
x=-9
for x=7
x+1=8
x+2=9
for x=-9
x+1=-8
x+2=-7
the integers are 7,8,9 or -9,-8,-7
(y+5)(y+5)
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(y-8)(y+5)
y+5 cancels out so the answer is y+5
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y-8
Given:
Each smoothie requires 20 ounces of cranberry juice and 10 ounces of passion fruit.
There are 1260 ounces of cranberry juice.
There are 650 ounces of passion fruit juice.
For the maximum servings of the smoothie, let
x = the number of 20-ounce cranberry juice used,
y = the number of 10-ounce passion fruit juice used.
The cranberry juice runs out when
20x = 1260
x = 63 servings
The passion fruit juice runs out when
10y = 650
y = 65 servings
Because x reaches, the cranberry juice runs out first after 63 servings of the smoothie.
There will be two 10-ounces = 20 ounces of the passion fruit left.
Answer:
(a) The cranberry juice runs our first.
(b) There will be 20 ounces of the passion fruit left over.
Answer:
<u><em>The error Vikam made:</em></u><u><em> He actually used the wrong expression to represent the area of the base of the given pyramid. </em></u>
Step-by-step explanation:
The surface area of the pyramid that is given = 4 * (0.5 * 34.2 * 28.4) + 34.2 * 34.2
Now, the Total area of it is = (2 * 0.5 * 36.5 * 25.6) + (2 * 0.5 * 37.8 * 16.2) + (25.6 * 16.2)
= (36.5 * 25.6) + (37.8 * 16.2) + (25.6 * 16.2)
