Dina started swimming at 3:42 P.M. She swam until 4:27 P.M. How long did Dina swim?

45 mins

Step-by-step explanation:

The correct answers are:

#1) B - 2x+9

#2) B - 16

#3) D - x+10y

#4) C - 8(3p+8)

#5) No equation, cannot be done

#6) B - w = -4

#7) A - q = 4

#8) D - q = 144

#9) A - b = 8

#10) A - y = -125

#11) D - a = 6

#12) B - x = 3

#13) C - x = 24

#14) D - -4

#15) D - Z>13

#16) same as 15

#17) Not listed; Q < -22

#18) C - y < -3

#19) A - K>-20

#20) D - g< 7

#21) A - V > 8

Explanation:

#1) "Nine more than" means something plus 9. "Two times a number" means 2x. Together, this gives us 2x+9.

#2) For 3m-5 if m=7, substitute 7 for m. 3(7)-5 = 21-5 = 16.

#3) To simplify 4x+8y-3x+2y, combine like terms. We can use the commutative property to rewrite the like terms together: 4x-3x+8y+2y. Combining like terms, we have x+10y.

#4) To factor, we pull out the GCF. To find the GCF, we find the prime factorization of 24 and 64:

24 = 2(12) = 2(4)(3) = 2(2)(2)(3)

64 = 2(32) = 2(4)(8) = 2(2)(2)(2)(4) = 2(2)(2)(2)(2)(2)

They have 3 2's in common, so the GCF is 2(2)(2) = 8. Pulling this out of our expression, we have:

24p+64 = 8(3p+8)

#5) We have no equation to solve.

#6) We add 8 to each side:

w-8+8 = -12+8; w = -4

#7) We divide both sides by 3:

3q/3 = 12/3; q = 4

#8) We multiply both sides by 6:

(q/6)(6) = 24(6); q = 144

#9) 3b-9 = 15

First, add 9 to each side:

3b-9+9 = 15+9; 3b = 24

Now divide both sides by 3:

3b/3 = 24/3; b = 8

#10) y/5 + 10 = -15

First subtract 10 from both sides:

y/5+10-10 = -15-10; y/5 = -25

Now multiply both sides by 5:

(y/5)(5) = -25(5); y = -125

#11) -3(4-a) = 6

First use the distributive property:

-3(4) - -3(a) = 6; -12+3a = 6

Add 12 to each side:

-12+3a+12 = 6+12; 3a = 18

Divide both sides by 3:

3a/3 = 18/3; a = 6

#12) 5(x+6) = 45

Use the distributive property:

5(x)+5(6) = 45; 5x+30=45

Subtract 30 from each side:

5x+30-30 = 45-30; 5x=15

Divide both sides by 5:

5x/5 = 15/5; x = 3

#13) 4x+8=104

Subtract 8 from each side:

4x+8-8 = 104-8; 4x=96

Divide both sides by 4:

4x/4 = 96/4; x = 24

#14) We want a number larger than -6. For negative numbers, this means a number closer to 0; the number closest to 0 is -4.

#15) Add 4 to each side: z-4+4 > 9+4; z > 13

#16) Same as 15

#17) Subtract 7 from each side: q+7-7<-15-7; q<-22

#18) Divide both sides by -3 (remember, when you multiply or divide an inequality by a negative number, you must flip the inequality symbol): -3y/-3>9/-3; y<-3

#19) Multiply both sides by 5: (k/5)(5)>-4(5); k>-20

#20) 4g-8<20

First add 8 to each side: 4g-8+8<20+8; 4g<28

Divide both sides by 4: 4g/4<28/4; g<7

#21) v/-2 +12 < 8

First subtract 12 from each side: (v/-2)+12-12<8-12; (v/-2)<-4

Multiply both sides by -2 (remember to flip the inequality symbol): (v/-2)(-2)<-4(-2); v>8