Step-by-step explanation:
let's look at the full numbers under the square roots when bringing the external factors back in :
sqrt(9×9×2) - sqrt(3×3×7) + sqrt(8) - sqrt(28)
and let's present these numbers as the product of their basic prime factors
sqrt(3×3×3×3×2) - sqrt(3×3×7) + sqrt(2×2×2) - sqrt(2×2×7)
now we see that we have 2 pairs of square roots : 1 pair ends with a factor of 2, and one pair with a factor of 7.
let's combine these
sqrt (3×3×3×3×2) + sqrt(2×2×2) - sqrt(3×3×7) - sqrt (2×2×7)
and now we move the factors of 2 and 7 back out in front (of course, we need to apply the square root on these factors) :
9×sqrt(2) + 2×sqrt(2) - 3×sqrt(7) - 2×sqrt(7) =
= (9+2)×sqrt(2) - (3+2)×sqrt(7) = 11×sqrt(2) - 5×sqrt(7)
and that is the first answer option.
Answer:
Number of ml of 40% sugar = x = 1000mL
Number of ml of 85% sugar used = y = 800mL
Step-by-step explanation:
Let the
Number of ml of 40% sugar = x
Number of ml of 85% sugar used = y
From the above question, our system of equations is given as:
x + y = 1800mL ....... Equation 1
x = 1800 - y
40% × x + 85% × y = 60% × 1800mL
0.4x + 0.85y = 1080.... Equation 2
We substitute 1800 - y for x in Equation 2
0.4(1800 - y) + 0.85y = 1080
720 - 0.4y + 0.85y = 1080
- 0.4y + 0.85y = 1080 - 720
0.45y = 360
y = 360/0.45
y = 800mL
Solving for x
x = 1800 - y
x = 1800 - 800
x = 1000mL
Therefore,
Number of ml of 40% sugar = x = 1000mL
Number of ml of 85% sugar used = y = 800mL
0, No solution.
-4x-11=2 (x-3x)+13
-4x-11=2 (-2x)+13
-4x-11=-4x+13
-11 is not equal to 13 so there is no solution
Answer:
3×(3×7)
Step-by-step explanation:
Just move the perenthasies to the right
A(h)=4h+70, A(h)=dollars to rent for h hours, h=hours rented.
B(h)=5h+60, same variable explanations...
....
To compare the two values at 6 hours you have:
A(6)=4(6)+70=24+70=$94
B(6)=5(6)+60=30+60=$90
So at 6 hours Company B would charge $4 less than Company A
...
Savings at 7 hours of rental by using B instead of A is:
S(h)=A(h)-B(h)
S(h)=4h+70-5h-60
S(h)=-h+10
S(7)=-7+10=$3
So at 7 hours, Company B saves you $3.
