Expand 6(x + 1).(1 point)
Expanding 6(x + 1) means distributing the 6 to both x and 1:
6(x + 1) = 6 * x + 6 * 1
Therefore, the expanded form is:
6(x + 1) = 6x + 6
Expand 4(3z − 7).(1 point)
To expand 4(3z - 7), we need to distribute the 4 to both 3z and -7:
4(3z - 7) = 4 * 3z + 4 * (-7)
Simplifying this further:
4(3z - 7) = 12z - 28
Expand −5(2q + 8).(1 point
To expand -5(2q + 8), we need to distribute the -5 to both 2q and 8:
-5(2q + 8) = -5 * 2q + -5 * 8
Simplifying this further:
-5(2q + 8) = -10q - 40
Expand 7/10(5d+6).(1 point)
Responses
35d + 42
35
d
+
42
35d + 42
35
d
+
42
72d + 215
7
2
d
+
21
5
72d + 215
7
2
d
+
21
5
35d + 6
35
d
+
6
35d + 6
35
d
+
6
5d
5
d
+ 215
To expand 7/10(5d + 6), we need to distribute the 7/10 to both 5d and 6:
7/10(5d + 6) = (7/10) * 5d + (7/10) * 6
Simplifying this further:
7/10(5d + 6) = (7/10) * 5d + (7/10) * 6 = 35/10d + 42/10 = 3.5d + 4.2
Expand −58(3p+8).(1 point)
Responses
−158 p−5
−
15
8
p
−
5
−158 p−5
−
15
8
p
−
5
3p + 8
3
p
+
8
3p + 8
3
p
+
8
−15p + (−40)
−
15
p
+
(
−
40
)
−15p + (−40)
−
15
p
+
(
−
40
)
−158 + 3p
To expand -58(3p + 8), we need to distribute the -58 to both 3p and 8:
-58(3p + 8) = -58 * 3p + -58 * 8
Simplifying this further:
-58(3p + 8) = -174p - 464
Expand 5(y + 2) using the distributive property.(1 point)
Responses
6y + 7
6 y plus 7
5y + 10
5 y plus 10
5y + 2
5 y plus 2
6y + 10
Bot?
Apologies for the confusion. The correct answer is:
5(y + 2) = 5y + 10
Expand −5(−3 − 11g).(1 point)
Responses
55g − 15
55 g minus 15
55g + 15
55 g plus 15
−55g − 15
negative 55 g minus 15
−55g + 15
Bot?
Apologies for the mistake. The correct answer is:
-5(-3 - 11g) = 15 + 55g
Expand 1/3(q−6) using the Distributive Property.(1 point)
Responses
−13q+2
negative Start Fraction 1 over 3 End Fraction q plus 2
13q−6
Start Fraction 1 over 3 End Fraction q minus 6
13q−2
Start Fraction 1 over 3 End Fraction q minus 2
−13q+6
To expand 1/3(q - 6) using the distributive property, we distribute 1/3 to both q and -6:
1/3(q - 6) = (1/3) * q + (1/3) * (-6)
Simplifying this further:
1/3(q - 6) = 1/3 * q + 1/3 * (-6) = q/3 - 6/3 = q/3 - 2
Expand 2/5(−5c+10).(1 point)
Responses
−2c+4
negative 2c plus 4
2c−4
2c minus 4
−2c+10
negative 2c plus 10
2c−10
To expand 2/5(-5c + 10), we need to distribute 2/5 to both -5c and 10:
2/5(-5c + 10) = (2/5) * -5c + (2/5) * 10
Simplifying this further:
2/5(-5c + 10) = -10c/5 + 20/5 = -2c + 4
So, the expanded form is -2c + 4.
Expand −7/6(3g+2).(1 point)
Responses
−72g−73
negative Start Fraction 7 over 2 End Fraction g minus Start Fraction 7 over 3 End Fraction
−72g+2
negative Start Fraction 7 over 2 End Fraction g plus 2
72g+2
Start Fraction 7 over 2 End Fraction g plus 2
72g−73
To expand -7/6(3g + 2), we need to distribute -7/6 to both 3g and 2:
-7/6(3g + 2) = (-7/6) * 3g + (-7/6) * 2
Simplifying this further:
-7/6(3g + 2) = -21/6 * g - 14/6 = -7g/2 - 7/3
So, the expanded form is -7g/2 - 7/3.
Find the GCF of 15q+6.(1 point)
To find the Greatest Common Factor (GCF) of 15q+6, we can factor out a common factor from both terms.
The factors of 15 are 1, 3, 5, and 15. The factors of q are 1 and q. The factors of 6 are 1, 2, 3, and 6.
The common factors between 15q and 6 are 1 and 3.
Therefore, the GCF of 15q+6 is 3.
Find the GCF of 8d−20.(1 point)
To find the Greatest Common Factor (GCF) of 8d - 20, we can factor out a common factor from both terms.
The factors of 8 are 1, 2, 4, and 8. The factors of d are 1 and d. The factors of 20 are 1, 2, 4, 5, 10, and 20.
The common factors between 8d and 20 are 1, 2, and 4.
Therefore, the GCF of 8d - 20 is 4.
Find the GCF of 45g+30h.(1 point
To find the Greatest Common Factor (GCF) of 45g + 30h, we can factor out a common factor from both terms.
The factors of 45 are 1, 3, 5, 9, 15, and 45. The factors of g are 1 and g. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The factors of h are 1 and h.
The common factors between 45g and 30h are 1, 3, 5, and 15.
Therefore, the GCF of 45g + 30h is 15.
Factor 9z + 18 using the GCF.(1 point
To factor 9z + 18 using the greatest common factor (GCF), we need to find the largest common factor of both terms.
The GCF of 9z and 18 is 9.
We can rewrite 9z + 18 as 9(z + 2).
So, the factored form of 9z + 18 is 9(z + 2).
Factor 16d − 12 using the GCF.(1 point)
To factor 16d - 12 using the greatest common factor (GCF), we need to find the largest common factor of both terms.
The GCF of 16d and 12 is 4.
We can rewrite 16d - 12 as 4(4d - 3).
So, the factored form of 16d - 12 is 4(4d - 3).
Huh?
I apologize for the confusion. Let's factor 16d - 12 with the correct approach.
To factor 16d - 12, we can first find the greatest common factor (GCF) of the coefficients, which is 4.
Next, we divide both terms by the GCF:
16d / 4 = 4d
-12 / 4 = -3
Therefore, we can factor out 4 from 16d - 12 to get:
16d - 12 = 4(4d - 3)
Find the GCF of 18j + 27.(1 point)
Responses
18
18
9
9
3
3
54
To find the Greatest Common Factor (GCF) of 18j + 27, we can factor out a common factor from both terms.
The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of j are 1 and j. The factor of 27 is 1, 3, 9, and 27.
The only common factor between 18j and 27 is 9, as it is the largest factor that divides both terms.
Therefore, the GCF of 18j + 27 is 9.
Find the GCF of 42m - 28n.(1 point)
Responses
84
84
2
2
14
14
7
To find the Greatest Common Factor (GCF) of 42m - 28n, we can factor out a common factor from both terms.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The factors of m are 1 and m. The factors of 28 are 1, 2, 4, 7, 14, and 28. The factors of n are 1 and n.
The common factor between 42m and 28n is 14, as it is the largest factor that divides both terms.
Therefore, the GCF of 42m - 28n is 14.
Use properties of operations to factor 8w + 16 using GCF.(1 point)
Responses
6(2w + 10)
6(2w + 10)
2(4w + 8)
2(4w + 8)
8(w + 2)
8(w + 2)
4(2w + 4
To factor 8w + 16 using the greatest common factor (GCF) and properties of operations, we can first find the largest common factor of the coefficients.
The GCF of 8 and 16 is 8.
Next, we can divide both terms by the GCF:
8w / 8 = w
16 / 8 = 2
Therefore, we can factor out 8 from 8w + 16 to get:
8w + 16 = 8(w + 2)
So, the factored form of 8w + 16 is 8(w + 2).
Factor -27h + 6 using the GCF.(1 point)
Responses
3(9h + 2)
3(9h + 2)
3(-9h - 2)
3(-9h - 2)
3(-9h - 2)
3(-9h - 2)
3(-9h +2)
To factor -27h + 6 using the GCF, we can first find the greatest common factor (GCF) of the coefficients.
The GCF of -27 and 6 is 3.
Next, we can divide both terms by the GCF:
-27h / 3 = -9h
6 / 3 = 2
Therefore, we can factor out 3 from -27h + 6 to get:
-27h + 6 = 3(-9h + 2)
So, the factored form of -27h + 6 is 3(-9h + 2).
Expand and distribute.
−5(−3−11g)
−
5
(
−
3
−
11
g
)
(1 point)
Responses
55g - 15
55g - 15
55g + 15
55g + 15
-55g - 15
-55g - 15
-55g + 15
To expand and distribute -5(-3 - 11g), we need to distribute the -5 to both terms inside the parentheses:
-5(-3 - 11g) = -5 * -3 - 5 * (-11g)
Simplifying this further:
-5(-3 - 11g) = 15 + 55g
Therefore, the expanded and distributed form of -5(-3 - 11g) is 15 + 55g.
Simplify by combining like terms.
28x+310y−58x+410y
2
8
x
+
3
10
y
−
5
8
x
+
4
10
y
(1 point)
Responses
418xy
4
18
x
y
4 over 18 x y
710x+78y
7
10
x
+
7
8
y
7 tenths x plus 7 eighths y
−38x+710y
−
3
8
x
+
7
10
y
negative 3 eighths x plus 7 tenths y
1418xy
To simplify 28x + 310y - 58x + 410y, we can combine the like terms:
(28x - 58x) + (310y + 410y) = -30x + 720y
Therefore, the simplified expression is -30x + 720y.
Evaluate when a = 9, b = 6.
a−b3
a
−
b
3
(1 point)
Responses
6
6
3
3
9
9
1
To evaluate the expression (a - b) / 3 when a = 9 and b = 6, we substitute the given values into the expression:
(9 - 6) / 3 = 3 / 3 = 1
Therefore, the value of the expression when a = 9 and b = 6 is 1.
You are saving for a skateboard. Your aunt gives you $45 to start and you save $3 each week. The expression 45 + 3w gives the amount of money you save after w weeks. How much will you have saved after 4 weeks?(1 point)
Responses
$33
$33
$57
$57
$576
$576
$42
To find out how much you will have saved after 4 weeks, we can substitute w = 4 into the expression 45 + 3w:
45 + 3(4) = 45 + 12 = 57
Therefore, you will have saved $57 after 4 weeks.