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y=a(x-h)2+k is the equation of a parabola where (h,k) is the vertex y=-2(x+2)2+2 vertex=(-2,2) let x=0 y=-2(0+2)2+2 y=-2(2)2+2 y=-2(4)+2 y=-8+2 y=-6 for the y-intercept

s+35=x s+7=d s+d+x=255 s+s+7+s+35=255 3s+42=255 3s=255-42 3s=213 s=213/3 s=71 x=71+35=106 d=71+7=78 78+106+71=255

1) is there a typo ? no power can turn a positive number (1/3) into a negative number (-5)     no solution in the set of real numbers   2)  p=kd      630=k*90      630/90=k      k=7     ...

11-3=8 she answered 8 correctly out of 11 8/11= ?           0.  7  2  7  2  7  2  7  2  7  2....=72.72727272...%   (the 7 and the 2 continuously repeat)        ...

the sphere and the cylinder have the same height because of this the height of the cylinder is equal to the diameter of the sphere the diameter of the sphere is 2*7=14 cm, so the height of the cylinder is also 14 cm the radius of the cylinder is 7 cm V=∏*r^2*h V=3.14159*7^2*14 V=3...

use the formula n!/r!(n-r)! where n=total number and r=how many you are choosing from that total choose 2 women from 6 women 6!/2!(6-2)! 6!/2!4! 6*5/2=30/2=15 ways to choose 2 women choose 2 men from 6 men 6!/2!(6-2)! 6!/2!4! 6*5/2=30/2=15 ways to choose...

let x=the amount of money each had (x-58)/(x-37)=1/4 cross multiply 4(x-58)=1(x-37) 4x-232=x-37 4x-x=232-37 3x=195 x=195/3 x=\$65 is the amount they started with 65-58=7 65-37=28 7/28=1/4

-8(x-3)=-32   -8x+24=-32    distributive property -8x+24+(-24)=-32+(-24)    addition property of equality -8x+0=-56    property of opposites, or, additive inverses (a number plus its opposite equals zero); also,...

let x and y be the numbers x+y=91 x/y=6/7 cross multiply 7x=6y x=(6/7)y substitute in the equation x+y=91 (6/7)y+y=91 (1 6/7)y=91 (13/7)y=91 multiply both sides by 7/13 (7/13)(13/7)y=(7/13)(91) y=7*7 because when you simplify 13 goes into...

(7cscx+7)(7cscx-7) FOIL 49csc2x-49 49(csc2x-1) csc2x=1+cot2x substitute 49(1+cot2x-1) 49cot2x seems to be the simplest form although cot=1/tan and cot=cos/sin or, csc2x-1=cot2x and then substitute to get 49cot2x

17=17 (prime) 51=3*17 (51 is divisible by 3 because 5+1=6 and 6 is divisible by 3) GCF=17

sin2x+2sinx-2=0 let n=sinx n2+2n-2=0 use the quadratic equation a=1, b=2, c=-2 [-2±√(4+8)]/2 [-2±√12]/2 [-2±2√3]/2 -1±√3 n=-1+√3=-1+1.73205=0.73205 n=-1-√3=-1-1.73205=-2.73205 n=sinx sinx=0.73205 using arcsin calculator...

you can set up a proportion (1 1/3)/24 = n/27 cross multiply 24n=(1 1/3)(27) 24n=(4/3)(27) 24n=36 n=36/24 n=1 1/2 cups of flour or,... 4/3 cups for 24 cookies (4/3)/24=(4/3)(1/24)=4/72=1/18 cup per cookie (1/18)(27)=27/18=3/2=1 1/2 cups again

distance=rate*time d=r*t 100=(r+c)(2) 100=(r-c)(2 2/3) 50=(r+c)  first equation simplified 100=(r-c)(8/3) 300=8(r-c)   300/8=r-c 37.5=r-c  second equation simplified 50=r+c add the equations 87.5=2r r=87.5/2 r=43...

d=rt 12=(r+c)t 12=(15+c)t 12=(15-c)(5/3-t)  where 1 hour 40 minutes=1 2/3 hours=5/3 hours 12/(15+c)=t substitute 12=(15-c)(5/3-[12/(15+c)]) simplify(5/3-[12/(15+c)]) {5(15+c)-3(12)}/3(15+c) (75+5c-36)/3(15+c) (39+5c)/3(15+c) 12=(15-c)(39+5c)/3(15+c) 12(3)(15+c)=(15-c)(39+5c) 36(15+c)=(15-c)(39+5c) 540+36c=585-39c+75c-5c2 540+36c=585+36c-5c2 5c2-36c-585+540+36c=0 5c2-45=0 5c2=45 c2=9 c=±3 c=3...

x=# of correct answers y=# of wrong answers 13x-7y=60 x+y=40 x=40-y substitute 13(40-y)-7y=60 520-13y-7y=60 520-20y=60 -20y=60-520 -20y=-460 20y=460 2y=46 y=46/2 y=23 wrong answers x+23=40 x=40-23 x=17 correct answers...

32 correct out of a total of 40 (32+8=40) 32/40=(32/8)/(40/8)=4/5=0.8=80%, or... 4/5=(4*20)/(5*20)=80/100=80%

695.35=6%x+9.5%(9885-x) 695.35=0.06x+0.095(9885-x) 695.35=0.06x+939.075-0.095x 695.35=939.075-0.035x 695.35-939.075=-0.035x -243.725=-0.035x 243.725=0.035x 243,725=35x x=243,725/35 x=\$6963.57 at 6% \$9885-\$6963.57=\$2921.43 at 9.5%

x=# of 5-cent pencils y=# of 10-cent pens x+y=25 5x+10y=200 (in terms of pennies) divide both sides by 5 in equation two x+2y=40 x+y=25 subtract these equations y=15 pens x+15=25 x=25-15 x=10 pencils   x+y=25 5x+10y=200 x+y=25...