Factor the expression completely.
100x+1000
To factor the expression completely, we look for the greatest common factor (GCF) of the terms 100x and 1000. The GCF of 100 and 1000 is 100.
So, we can rewrite the expression as:
100(x + 10)
Simplify.
3−(4x−5)+6
To simplify the expression, we can start by distributing the negative sign to the terms inside the parentheses:
3 - 4x + 5 + 6
Next, we can combine like terms:
(3 + 5 + 6) - 4x
= 14 - 4x
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?
Another expression to calculate the total amount spent can be:
5(20) + 3(20)
Which number sentence shows how the distributive property can be used to represent the area of the entire rectangle (both rectangles together)?
To represent the area of the entire rectangle using the distributive property, we can use the following number sentence:
(A + B) ⋅ W
Where A represents the area of the first rectangle, B represents the area of the second rectangle, and W represents the width of both rectangles.
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)
Responses
The expression that can be used to represent the combined earnings of Charity and Sabria for the week would be:
(75 * C + 65) + (70 * S + 95)
Where 75 * C represents the earnings of Charity for the number of sets of nails completed (C), 65 represents Charity's tips, 70 * S represents the earnings of Sabria for the number of sets of nails completed (S), and 95 represents Sabria's tips.
To factor the expression 100x + 1000 completely, we need to find the greatest common factor (GCF) of the terms.
Step 1: Find the GCF of the numbers 100 and 1000.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
The factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.
The common factors shared by both 100 and 1000 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. The greatest common factor is 100.
Step 2: Factor out the GCF from each term.
We can rewrite the expression as: 100(x + 10).
Therefore, the expression 100x + 1000 can be factored completely as 100(x + 10).