If each painting takes 3 hours, and he has to do 8 then he would spend 24 hours doing all 8 portraits
Qt = 16.
Because since rs Is equal to qr since r is the midpoint of qs. So qr is 8 and because s is the midpoint of the whole line. I multiply it by 2. Giving me 16 for the whole line
Here is the problem.....√(15x + 10) = 2x+3
to remove the square root, we do the opposite which is to square everything.
(√(15x + 10))² = (2x + 3)² (the square negates the square root)
15x + 10 = (2x +3)(2x + 3) (use the distributive property to continue)
15x + 10 = 4x² + 6x + 6x + 9 (combine like terms)
15x + 10 = 4x² + 12x + 9 (subtract 15x and 10 from each side)
-15x - 10 -15x - 10
0 = 4x² - 3x - 1 (factor completely)
(x - 1) (4x + 1) (set each to equal 0)
x - 1 = 0 4x + 1 = 0
x = 1 4x = -1
x = -1/4
place both into the equation to check for reasonableness...we see the negative number is not reasonable, but the x value of 1 is a solution.
answer is 1
Answer:
A number less than 4 was rolled 18 times.
The number cube was rolled 50 times. The relative frequency of rolling a number less than 4 is 36%.
18 kg of 15% copper and 72 kg of 60% copper should be combined by the metalworker to create 90 kg of 51% copper alloy.
<u>Step-by-step explanation:</u>
Let x = kg of 15% copper alloy
Let y = kg of 60% copper alloy
Since we need to create 90 kg of alloy we know:
x + y = 90
51% of 90 kg = 45.9 kg of copper
So we're interested in creating 45.9 kg of copper
We need some amount of 15% copper and some amount of 60% copper to create 45.9 kg of copper:
0.15x + 0.60y = 45.9
but
x + y = 90
x= 90 - y
substituting that value in for x
0.15(90 - y) + 0.60y = 45.9
13.5 - 0.15y + 0.60y = 45.9
0.45y = 32.4
y = 72
Substituting this y value to solve for x gives:
x + y = 90
x= 90-72
x=18
Therefore, in order to create 90kg of 51% alloy, we'd need 18 kg of 15% copper and 72 kg of 60% copper.
