Simplify the expression.
(h+12)+(p+24)
(1 point)
Responses
hp+36
h p plus 36
h+p+36
h plus p plus 36
hp+288
h p plus 288
12h+24p
12 h plus 24 p
h+p+36
h plus p plus 36
Simplify the expression.
94x+4+2x
(1 point)
Responses
15x+12
15 x plus 12
5x+4
5 x plus 4
x+4
x plus 4
113x+4
11 thirds x plus 4
wrong
I apologize for the mistake. The correct answer is:
96x+4
96 x plus 4
Simplify the expression.
9/4x+4+2x
(1 point)
Responses
15x+12
15 x plus 12
5x+4
5 x plus 4
x+4
x plus 4
11/3x+4
11/3x+4
Simplify the expression.
(5y−1)+(−2y+4)
(1 point)
Responses
3y−5
3 y minus 5
7y+3
7 y plus 3
3y+3
3 y plus 3
7y−5
3y+3
3 y plus 3
Simplify the expression. (3/4 x - 1) + (3/4 x - 2)
A. 1
B. 3/4 x + 1
C. -3
D. 3/2x-3
B. 3/4 x + 1
Simplify the expression. 7x + 3 (x - 2) - 4x + 8
A. 6x + 14
B. 6x + 2
C. 14x + 2
D. 14x + 14
To simplify the expression 7x + 3 (x - 2) - 4x + 8, we first distribute the 3 to the terms inside the parentheses:
7x + 3x - 6 - 4x + 8
Next, we combine like terms:
(7x + 3x - 4x) + (-6 + 8) = 6x + 2
Therefore, the simplified expression is B. 6x + 2.
Simplify the expression. (3x - 8) + (2x + 5) - 4x - 8)
A. 9x - 11
B. x + 5
C. 9x + 5
D. x - 11
To simplify the expression (3x - 8) + (2x + 5) - (4x - 8), we first remove the parentheses:
3x - 8 + 2x + 5 - 4x + 8
Next, we combine like terms:
(3x + 2x - 4x) + (-8 + 5 + 8) = x + 5
Therefore, the simplified expression is B. x + 5.
Which expression is equivalent to 2.2 - 0.5 (0.06x - 1.8)?
A. 1.3 - 0.3x
B. 0.3x + 1.3
C. 0.3x + 3.1
D. 3.1 - 0.3x
To distribute the -0.5 to the terms inside the parentheses, we have:
2.2 - 0.5(0.06x - 1.8) = 2.2 - (-0.5)(0.06x) - (-0.5)(-1.8)
= 2.2 + 0.03x - 0.9
Next, we combine like terms:
2.2 + 0.03x - 0.9 = 1.3 + 0.03x
Therefore, the expression is equivalent to A. 1.3 - 0.3x.
Simplify. -6 (1/4x - 2/3x + 5/6x)
A. -x
B. -2 1/2x
C. 3/4x
D. 2x
To simplify the expression -6 (1/4x - 2/3x + 5/6x), we first distribute the -6 to the terms inside the parentheses:
-6 * 1/4x - 6 * -2/3x + -6 * 5/6x
Next, we simplify each term:
-6 * 1/4x = -6/4x = -3/2x
-6 * -2/3x = 12/3x = 4x
-6 * 5/6x = -30/6x = -5x
Now, we combine the simplified terms:
-3/2x + 4x - 5x = -3/2x - x
Therefore, the simplified expression is B. -2 1/2x.
Simplify. - 1/2 (-6x + 3)
A. -3x -3
B. -3x + 3/2
C. 3x + 3
D. 3x - 3/2
To simplify the expression - 1/2 (-6x + 3), we first distribute the -1/2 to the terms inside the parentheses:
- 1/2 * -6x + -1/2 * 3
Next, we simplify each term:
1/2 * -6x = -6/2x = -3x
1/2 * 3 = 3/2
Now, we combine the simplified terms:
-3x + 3/2
Therefore, the simplified expression is B. -3x + 3/2.
Simplify. 11−9(−2x−3) (1 point) Responses −4x−6 negative 4 x minus 6 18x−38 18 x minus 38 −4x+6 negative 4 x plus 6 18x+38
To simplify the expression 11−9(−2x−3), we need to perform the distributive property:
11 - 9(-2x - 3) = 11 + 18x + 27
Simplifying the expression further, we have:
11 + 18x + 27 = 18x + 38
Therefore, the simplified expression is 18x + 38.
Factor this expression completely. 35x−40 (1 point) Responses 7(5x+8) 7 times open paren 5 x plus 8 close paren 7(5x−8) 7 times open paren 5 x minus 8 close paren 5(7x+8) 5 times open paren 7 x plus 8 close paren 5(7x−8)
To factor the expression 35x - 40 completely, we can first factor out the greatest common factor, which is 5:
35x - 40 = 5(7x - 8)
Therefore, the fully factored form of the expression is 5(7x - 8).
Factor the expression completely. 45x−18y+36 (1 point) Responses 5(9x−2y+4) 5 times open paren 9 x minus 2 y plus 4 close paren −9(5x+2y+4) negative 9 times open paren 5 x plus 2 y plus 4 close paren 9(5x−2y+4) 9 times open paren 5 x minus 2 y plus 4 close paren 9y(5x−2y+4)
To factor the expression 45x - 18y + 36 completely, we can first factor out the greatest common factor, which is 9:
45x - 18y + 36 = 9(5x - 2y + 4)
Therefore, the fully factored form of the expression is 9(5x - 2y + 4).
Factor this expression completely. −21x+28 (1 point) Responses −7(3x−4) negative 7 times open paren 3 x minus 4 close paren −7(3x+4) negative 7 times open paren 3 x plus 4 close paren 7(3x−4) 7 times open paren 3 x minus 4 close paren −(21x−4) negative open paren 21 x minus 4 close paren
To factor the expression −21x + 28 completely, we can first factor out the greatest common factor, which is -7:
−21x + 28 = -7(3x - 4)
Therefore, the fully factored form of the expression is -7(3x - 4).
Which factorization is equivalent to this expression? −42k−54 (1 point) Responses −6(7k−9) negative 6 times open paren 7 k minus 9 close paren 6(−7k+9) 6 times open paren negative 7 k plus 9 close paren −6(7k+9) negative 6 times open paren 7 k plus 9 close paren 6(7k+9) 6 times open paren 7 k plus 9 close paren
To factor the expression −42k−54 completely, we can first find the greatest common factor, which is -6:
−42k−54 = -6(7k + 9)
Therefore, the equivalent factorization is −6(7k + 9).
Factor the expression completely. 100x+1000 (1 point) Responses 10(10x+100) 10 times open paren 10 x plus 100 close paren 100(x+10) 100 times open paren x plus 10 close paren 100(x+100) 100 times open paren x plus 100 close paren 1000(10x+1)
To factor the expression 100x + 1000 completely, we can first find the greatest common factor, which is 100:
100x + 1000 = 100(x + 10)
Therefore, the fully factored form of the expression is 100(x + 10).
Simplify. 3−(4x−5)+6 (1 point) Responses −4x+14 negative 4 x plus 14 4x+4 4 x plus 4 12x+21 12 x plus 21 −4x+4
To simplify the expression 3 − (4x − 5) + 6, we need to start by resolving the parentheses:
3 - (4x - 5) + 6 = 3 - 4x + 5 + 6
Next, we combine like terms:
3 - 4x + 5 + 6 = 14 - 4x
Therefore, the simplified expression is 14 - 4x.
Simplify.
3−(4x−5)+6
Responses
−4x+14 negative 4 x plus
14 4x+4 4 x plus 4
12x+21
12 x plus 21 −4x+4
To simplify the expression 3 − (4x − 5) + 6, we need to start by resolving the parentheses:
3 - (4x - 5) + 6 = 3 - 4x + 5 + 6
Next, we combine like terms:
3 - 4x + 5 + 6 = 14 - 4x
Therefore, the simplified expression is 14 - 4x.
Simplify. 3- (4x - 5) + 6
A. -4x + 14
B. 4x + 4
C. 12x +21
D. -4x + 4
To simplify the expression 3 - (4x - 5) + 6, we need to start by resolving the parentheses:
3 - (4x - 5) + 6 = 3 - 4x + 5 + 6
Next, we combine like terms:
3 - 4x + 5 + 6 = -4x + 14
Therefore, the simplified expression is A. -4x + 14.
Ella Grace bought 5 plants for her backyard for $20 each and 3 chairs for her firepit for $20 each. She used this expression to calculate the total amount she spent.
(5⋅20)+(3⋅20)
What is another expression to calculate the total amount spent?
A. 5 . (20 +3)
B. (5 + 3) . 20
C. (5 +20) . (3 +20)
D. 5 . 20 . 3
To calculate the total amount spent, we can multiply the number of plants by the cost per plant and add it to the product of the number of chairs and the cost per chair.
Another expression to calculate the total amount spent is (5 + 3) * 20.
Therefore, the answer is B. (5 + 3) * 20.
Which number sentence shows how the distributive property can be used to represent the area of the entire rectangle (both rectangles together)? (1 point) Responses (9+6)⋅(9+11) open paren 9 plus 6 close paren times open paren 9 plus 11 close paren 9⋅6⋅11 9 times 6 times 11 11(6+9) 11 times open paren 6 plus 9 close paren (9⋅6)+(9⋅11)
To represent the area of the entire rectangle (both rectangles together) using the distributive property, we can use the number sentence (9+6)⋅(9+11).
Therefore, the answer is (9+6)⋅(9+11).
Charity and Sabria both are nail artists. Charity charges $75 for a set of nails with designs and Sabria charges $70 for the same type set of nails. This week Charity made an additional $65 in tips and Sabria made an additional $95 in tips. Given that C and S represent the number of sets of nails completed by Charity (C) and Sabria (S), which expression can be used to represent their combined earnings for the week.(1 point)
A. 145CS + 160
B. 145 (C + 2) + 160
C. 75C +70S + 160
D. 65C +70S + 160
To represent the combined earnings of Charity and Sabria for the week, we can use the expression 75C + 70S + 65 + 95, where C represents the number of sets of nails completed by Charity and S represents the number of sets of nails completed by Sabria.
Therefore, the correct answer is D. 65C + 70S + 160.
Christine(C) and Ty(T) save quarters in a jar together. The jar had $28 in it, then Christine put in C quarters and Ty put in T quarters. Which expression can be used to represent the amount of money in the bank now?(1 point) Responses
A. CT + 28
B. 0.50 (C + T) + 28
C. 0.25C +0.25T + 28
D. 0.25FJ + 28
To represent the amount of money in the bank after Christine and Ty put in their quarters, we can use the expression 0.25C + 0.25T + 28.
Therefore, the correct answer is C. 0.25C + 0.25T + 28.
A ribbon 6 1/8 feet in length is shortened by having 2 1/12 feet cut off one end. What is the length of the shortened ribbon?(1 point)
A. 4 1/24 feet
B. 4 5/24 feet
C. 3 5/24
D. 4 9/24
To find the length of the shortened ribbon, we subtract the length that was cut off from the original length of the ribbon.
Original length of the ribbon: 6 1/8 feet
Length cut off: 2 1/12 feet
To subtract these lengths, we need to find a common denominator. The common denominator for 8 and 12 is 24.
Converting the fractions:
6 1/8 feet = 49/8 feet
2 1/12 feet = 25/12 feet
Now we can subtract the lengths:
49/8 feet - 25/12 feet = (49*3 - 25*2) / (8*3) = 147/24 feet
Therefore, the length of the shortened ribbon is 6 7/24 feet.
The correct answer is not given among the options provided.
A ribbon 6 1/8 feet in length is shortened by having 2 1/12 feet cut off one end. What is the length of the shortened ribbon?(1 point)
A. 4 1/24 feet
B. 4 5/24 feet
C. 3 5/24
D. 4 9/24
(best guess)
To find the length of the shortened ribbon, we subtract the length that was cut off from the original length of the ribbon.
Original length of the ribbon: 6 1/8 feet
Length cut off: 2 1/12 feet
To subtract these lengths, we need to find a common denominator. The common denominator for 8 and 12 is 24.
Converting the fractions:
6 1/8 feet = 49/8 feet
2 1/12 feet = 25/12 feet
Now we can subtract the lengths:
49/8 feet - 25
0.625 + 3/4
0.625 + 3/4
A. 11/8
B. 3/2
C. 11/9
D. 8/11
96x+4
96 x plus 4