Factor this expression completely.
100x + 1000
To factor the expression 100x + 1000, we can start by factoring out the greatest common factor (GCF). The GCF of 100x and 1000 is 100.
Factoring out 100:
100(x + 10)
So, the expression is completely factored as 100(x + 10).
Which expression is equivalent?
11 − 9(−2x − 3)
Responses
A 18x + 3818x + 38
B −4x + 6−4x + 6
C 18x − 3818x − 38
D −4x − 6
To simplify the expression 11 − 9(−2x − 3), we can distribute the -9 to the terms inside the parentheses:
11 − 9(−2x − 3) = 11 + 18x + 27
Combining like terms, we get:
11 + 18x + 27 = 18x + 38
So the equivalent expression is A) 18x + 38.
Terry and Susan both detail cars. Terry chargers $75 for each car and Susan charges $70 for each car. This week Terry made an additional $65 in tips and Susan made an additional $95 in tips. Given that T and S represent the number of cars detailed by Terry (T) and Susan (S), which expression can be used to represent their combined earnings for the week?
Responses
To represent Terry's earnings, we can use 75T + 65 (since Terry charges $75 for each car and made an additional $65 in tips).
To represent Susan's earnings, we can use 70S + 95 (since Susan charges $70 for each car and made an additional $95 in tips).
To represent their combined earnings, we can sum up their individual earnings:
(75T + 65) + (70S + 95)
Simplifying this expression, we get:
75T + 70S + 160
So, the expression that can be used to represent Terry and Susan's combined earnings for the week is 75T + 70S + 160.
At West High School, 2/5
of the students play a sport. Of the students who play a sport, 1/4
play football. What fraction of the students at West High School play football?
To find the fraction of students at West High School who play football, we need to multiply the fractions representing the proportion of students who play a sport (2/5) and the proportion of students who play football among those who play a sport (1/4).
The resulting fraction will be (2/5) × (1/4).
Now let's multiply the numerators and denominators separately:
Numerator: 2 × 1 = 2
Denominator: 5 × 4 = 20
Therefore, the fraction of students at West High School who play football is 2/20, which can be simplified to 1/10.
0.625 + 3/4
To add 0.625 and 3/4, we first need to convert 0.625 to a fraction with a denominator of 4.
0.625 can be written as 625/1000.
Next, we need to find a common denominator for the two fractions, which in this case is 4.
Converting 625/1000 to have a denominator of 4, we get (625/1000) * (1/4) = 625/4000.
Now we add the two fractions together:
625/4000 + 3/4.
Since the denominators are already the same, we can simply add the numerators:
625 + 3 = 628.
Therefore, the sum of 0.625 and 3/4 is 628/4000. However, this fraction can be simplified by dividing both the numerator and denominator by their greatest common factor (which is 4 in this case).
Dividing 628 and 4000 by 4, we get 157/1000.
So, 0.625 + 3/4 = 157/1000.
Simplify.
0.625 + 3/4
A. 10/9
B. 11/8
C. 3/2
D. 8/11