Represent the following sentence as an algebraic expression, where "a number" is the letter x.
The quotient of a number and 9.
The quotient of a number and 9.
The quotient of a number and 9.
(x / 9) * (x / 9) * (x / 9)
Represent the following sentence as an algebraic expression, where "a number" is the letter x.
The quotient of a number and 9.
x / 9
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
2 plus the cube of a number.
2 + x^3
A triangle has side lengths of left bracket, 3, q, plus, 1, right bracket
(
3
�
+
1
)
(3q+1) centimeters, left bracket, 5, q, minus, 3, right bracket
(
5
�
−
3
)
(5q−3) centimeters, and left bracket, r, minus, 9, right bracket
(
�
−
9
)
(r−9) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answer
Multiple Choice Answers
8, q, minus, 11, plus, r
8
�
−
11
+
�
8q−11+r
minus, 8, r, plus, 2, plus, 4, q
−
8
�
+
2
+
4
�
−8r+2+4q
minus, 8, r, plus, 6, q
−
8
�
+
6
�
−8r+6q
minus, 2, plus, 8, q, minus, 8, r
−
2
+
8
�
−
8
�
−2+8q−8r
To find the perimeter, we need to add up the lengths of all three sides.
The first side is (3q+1) centimeters.
The second side is (5q-3) centimeters.
The third side is (r-9) centimeters.
Adding up the lengths of the three sides, we get:
(3q+1) + (5q-3) + (r-9)
This simplifies to:
8q - 8 + r - 11
So, the expression that represents the perimeter of the triangle is:
8q + r - 19
What is the value of the expression below when z, equals, 6
�
=
6
z=6?
8, z, plus, 9
8
�
+
9
8z+9
To find the value of the expression 8z + 9 when z = 6, we substitute z with 6:
8(6) + 9
Multiplying 8 and 6:
48 + 9
Adding 48 and 9:
57
Therefore, when z = 6, the value of the expression 8z + 9 is 57.
Drag the numbers below to put them in order from least to greatest:
minus, 1, point, 8
−
1.8
−1.8 minus, 13, point, 6
−
13.6
−13.6 minus, 7
−
7
−7 minus, 17, point, 4
−
17.4
−17.4 2, point, 7
2.7
2.7 minus, 7, point, 2
−
7.2
−7.2
From least to greatest:
-17.4, -13.6, -7.2, -7, -1.8, 2.7, 2.7, 17.4
theses numbers from least to greatest:
-16.3, -17.6, -2.1, -16.4 , 16 , -1.7
From least to greatest:
-17.6, -16.4, -16.3, -2.1, -1.7, 16
these numbers from least to greatest: 6.1, 5.92, 6.03, 6.084, 6.04, 6.007
From least to greatest:
5.92, 6.007, 6.03, 6.04, 6.084, 6.1
Point S is located at minus, 12
−
12
−12. Points T and U are each 6
6
6 units away from Point S. Where are T and U located?
Point T is located 6 units away from Point S, so it is in the positive direction from S. Its location can be found by adding 6 to the x-coordinate of Point S.
Therefore, the x-coordinate of Point T is:
-12 + 6 = -6
Point U is also located 6 units away from Point S, but in the opposite direction from T. Its location can be found by subtracting 6 from the x-coordinate of Point S.
Therefore, the x-coordinate of Point U is:
-12 - 6 = -18
So, Point T is located at (-6, y), and Point U is located at (-18, y), where y represents the y-coordinate of the points.
Evaluate the expression shown below and write your answer as a fraction in simplest form.
start fraction, 4, divided by, 17, end fraction, plus, start fraction, 10, divided by, 17, end fraction
4
17
+
10
17
17
4
+
17
10
To evaluate the expression, we need to find a common denominator for the fractions 4/17 and 10/17.
Since both fractions already have a denominator of 17, we don't need to find a common denominator. We can simply add the numerators together and keep the denominator the same.
So, the expression simplifies to:
(4 + 10) / 17
This further simplifies to:
14 / 17
Therefore, the value of the expression is 14/17.
Answer the questions below about Line 1 and Line 2 shown below.
5, dot, left bracket, 4, minus, 3, right bracket
5
⋅
(
4
−
3
)
5⋅(4−3)
5, dot, 4, minus, 5, dot, 3
5
⋅
4
−
5
⋅
3
5⋅4−5⋅3
Answer
Attempt 1 out of 2
The expression was rewritten using the
.
5, dot, left bracket, 4, minus, 3, right bracket
5
⋅
(
4
−
3
)
5⋅(4−3) equals 5, dot
5
⋅
5⋅
which equals
.
5, dot, 4, minus, 5, dot, 3
5
⋅
4
−
5
⋅
3
5⋅4−5⋅3 equals
minus
−
−
which equals
The expression 5⋅(4−3) can be simplified as follows:
5⋅(4−3) = 5⋅1 = 5
The expression 5⋅4−5⋅3 can be simplified as follows:
5⋅4−5⋅3 = 20−15 = 5
Therefore, the value of both Line 1 and Line 2 is 5.
what property was used to rewrite it
The property that was used to rewrite the expression 5⋅(4−3) as 5⋅4−5⋅3 is the distributive property. The distributive property states that when multiplying a number by a sum or difference inside parentheses, you can distribute the multiplication to each term inside the parentheses.
In this case, we distributed the multiplication of 5 to both the 4 and the -3.
When solving an equation, Francesca's first step is shown below. Which property justifies Francesca's first step?
Original Equation:
Original Equation:
Original Equation:
3, left bracket, x, plus, 3, right bracket, equals, minus, 5
3
(
�
+
3
)
=
3(x+3)=
−
5
−5
First Step:
First Step:
First Step:
3, x, plus, 9, equals, minus, 5
3
�
+
9
=
3x+9=
−
5
−5
The property that justifies Francesca's first step in the equation 3(x+3) = -5 is the distributive property.
The distributive property allows us to distribute the 3 to both the x and the 3 inside the parentheses:
3(x+3) = (3 * x) + (3 * 3) = 3x + 9
This property states that when multiplying a number by a sum or difference inside parentheses, you can distribute the multiplication to each term inside the parentheses.
Which expression is equivalent to 36, plus, 18
36
+
18
36+18?
Answer
Multiple Choice Answers
3, left bracket, 12, plus, 15, right bracket
3
(
12
+
15
)
3(12+15)
3, left bracket, 12, plus, 7, right bracket
3
(
12
+
7
)
3(12+7)
6, left bracket, 6, plus, 2, right bracket
6
(
6
+
2
)
6(6+2)
3, left bracket, 12, plus, 6, right bracket
3
(
12
+
6
)
3(12+6)
The expression that is equivalent to 36 + 18 is:
36 + 18 = 3(12 + 6)
Therefore, the correct answer is 3(12+6).
Enter the missing values in the area model to find 4, left bracket, 8, w, minus, 4, right bracket
4
(
8
�
−
4
)
4(8w−4)
The area model for the expression 4(8w-4) can be filled in as follows:
- The top left box should be "4"
- The top right box should be "8w"
- The bottom left box should be "-4"
- The bottom right box should be "?"
To find the missing value in the bottom right box, we can start by multiplying 4 with -4:
4 * (-4) = -16
So, the missing value in the bottom right box is "-16".
Therefore, the completed area model is:
4 | 8w
-4 | -16
According to the model above, 4, left bracket, 8, w, minus, 4, right bracket, equals
4
(
8
�
−
4
)
=
4(8w−4)=
4(8w-4) = 32w - 16
According to the model above, 3, left bracket, 4, z, plus, 7, right bracket, equals
3
(
4
�
+
7
)
=
3(4z+7)=
3(4z+7) = 12z + 21
Enter the missing values in the area model to find 2, left bracket, 9, h, minus, 4, right bracket
2
(
9
ℎ
−
4
)
2(9h−4)
2
18h
-4
Answer
Attempt 1 out of 2
According to the model above, 2, left bracket, 9, h, minus, 4, right bracket, equals
2
(
9
ℎ
−
4
)
=
2(9h−4)
The area model for the expression 2(9h-4) can be filled in as follows:
- The top left box should be "2"
- The top right box should be "9h"
- The bottom left box should be "-4"
- The bottom right box should be "?"
To find the missing value in the bottom right box, we can start by multiplying 2 with -4:
2 * (-4) = -8
So, the missing value in the bottom right box is "-8".
Therefore, the completed area model is:
2 | 9h
-4 | -8
Use the distributive property to write an equivalent expression.
9, left bracket, 7, r, minus, 3, s, plus, 10, right bracket
9
(
7
�
−
3
�
+
10
)
9(7r−3s+10)
To write an equivalent expression using the distributive property, we need to distribute the 9 to each term inside the parentheses:
9 * 7r = 63r
9 * (-3s) = -27s
9 * 10 = 90
So, using the distributive property, the equivalent expression is:
63r - 27s + 90
Write an equivalent expression by distributing the "minus
−
−" sign outside the parentheses:
minus, left bracket, 4, k, minus, 1, point, 9, right bracket
−
(
4
�
−
1.9
)
−(4k−1.9)
When we distribute the minus sign outside the parentheses, the signs of each term inside the parentheses will change.
The expression -(4k - 1.9) can be rewritten as:
-4k + 1.9
Therefore, the equivalent expression, after distributing the minus sign outside the parentheses, is -4k + 1.9.
Between which two consecutive whole numbers does square root of, 13, end square root
13
13
lie? Fill out the sentence below to justify your answer and use your mouse to drag square root of, 13, end square root
13
13
to an approximately correct location on the number line.
The square root of 13 lies between the whole numbers 3 and 4.
To justify this answer, we can square both 3 and 4 to determine their squares. The square of 3 is 9 (3 * 3 = 9) and the square of 4 is 16 (4 * 4 = 16).
Since 13 falls between the squares of 3 and 4 (9 and 16), it follows that the square root of 13 falls between the whole numbers 3 and 4.
Therefore, the square root of 13 is approximately between 3 and 4 on the number line.
Since square root of, empty space, end square root
2
2
equals
=
=
and square root of, empty space, end square root
2
2
equals
=
=
it is known that square root of, 13, end square root
13
13
is between
The square root of 13 is known to be between the square root of 9 (which equals 3) and the square root of 16 (which equals 4). So, the square root of 13 is between 3 and 4.
Enter the missing values in the area model to find 4, left bracket, 8, t, plus, 2, right bracket
4
(
8
�
+
2
)
4(8t+2)
4
8t
+2
The area model for the expression 4(8t+2) can be filled in as follows:
- The top left box should be "4"
- The top right box should be "8t"
- The bottom left box should be "2"
- The bottom right box should be "?"
To find the missing value in the bottom right box, we can start by multiplying 4 with 2:
4 * 2 = 8
So, the missing value in the bottom right box is "8".
Therefore, the completed area model is:
4 | 8t
2 | 8
Question
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Enter the missing values in the area model to find 7, left bracket, 5, t, plus, 1, right bracket
7
(
5
�
+
1
)
7(5t+1)
7
5t
+7
Answer
Attempt 1 out of 2
According to the model above, 7, left bracket, 5, t, plus, 1, right bracket, equals
7
(
5
�
+
1
)
=
7(5t+1)=
The area model for the expression 7(5t+1) can be filled in as follows:
- The top left box should be "7"
- The top right box should be "5t"
- The bottom left box should be "1"
- The bottom right box should be "?"
To find the missing value in the bottom right box, we can start by multiplying 7 with 1:
7 * 1 = 7
So, the missing value in the bottom right box is "7".
Therefore, the completed area model is:
7 | 5t
1 | 7
Question
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Between which two consecutive whole numbers does square root of, 73, end square root
73
73
lie? Fill out the sentence below to justify your answer and use your mouse to drag square root of, 73, end square root
73
73
to an approximately correct location on the number line.
Real
√73
__
_
Answer
Attempt 1 out of 2
Since square root of, empty space, end square root
2
2
equals
=
=
and square root of, empty space, end square root
2
2
equals
=
=
it is known that square root of, 73, end square root
73
73
is between
and
.