Ahh yes our entire angle = 90° lets remember that. and we need to find out what x is. all we do is plug in both of our values and make it all equal 90 degrees just like an equation:) here ill show you m∠1 = (x + 33°) m∠2 = 2x° and we know that m∠1 + m∠2 = 90° so lets plug in what we have
(x + 33°) + 2x° = 90°
1st. subtract 33° from both sides <span>(x + 33°) + 2x° = 90° </span> - 33° = -33° cancels out on the left side, right side we solve it:) 90° - 33° = 57° now lets rewrite this x + 2x° = 57°
2nd. add the X's together x + 2x° = 57° becomessss 3x° = 57°
3rd. we divide both sides by 3 3x° = 57° ÷3 = ÷ 3 the left side cancels out and we solve the left side x = 19°
FINALLY! now we arent finished yet! lets plug in our x value to get our 2 angle measures we know that m∠1 = (x + 33°) so lets plug in 19° for x m∠1 = 19° + 33° SOLVE! m∠1 = 52°
wait! lets find what m∠2 equals m∠2 = 2x° so lets plug in 19° for x m∠2 = 2(19) lets solve:) 2 x 19 = 38 sooooo m∠2 = 38°
FINALLY YOUR ANSWERS AREEE <span>m∠1 = 52</span>° <span>M</span>∠2 = 38°
have a good day ma'm and dont forget 2 MARK ME BRAINLIEST! =)
First set up two equations: 4c+5p=65. C+p=14. Solve one equation and sub it in for the other: C=14-p: 4(14-p)+5p=65, 56-4p+5p=65, p=9. Sub in what you now know: c+9=14, c=5. Check both equations to make sure it's right and you get: Pepperoni=9 cheese=5 :) hope this helps!
Let x represent the amount of 80% alcohol. Then (575 -x) is the amount of 30% alcohol. The total amount of alcohol in the mix is ...
0.30(575 -x) +0.80(x) = 0.60(575)
172.5 +0.50x = 345
0.50x = 172.5 . . . . . . . . subtract 172.5
x = 345 . . . . . . . . . . . . multiply by 2; amount of 80% needed
575 -x = 230 . . . . amount of 30% needed
You should use 230 mL of 30% alcohol and 345 mL of 80% alcohol.
You can work a problem like this by writing two equations in two unknowns. The variables would be the amounts of each solution (w=weak, s=strong), and the equations would reflect the total amount and the amount of alcohol in the mix.
w+s = 575
.30w +.80s = .60(575)
You will notice that if you solve this by substitution, substituting for the "weak" variable, you get ...
w = 575 -s
0.30(575 -s) +0.80s = 0.60(575) . . . . substitute for w
which is the same equation we used above.
When you simplify this and isolate the variable, the coefficient of the variable is positive. This makes the arithmetic less prone to error. If you substitute for the "strong" variable, then the coefficients come out negative. That still works, but you need to spend extra effort to get the signs right.
Essentially, our choice of a single variable for the "strong" solution results in a single 2-step equation that is easily solved. A lot of mixture problems can be solved with this approach.