Use the properties of operations to add 9(k + 1/3) + 10(1/2k - 1)
A. 14k + 13
B. 19 1/2 * k - 2/3
C. 14k - 7
D. 14k - 2/3
To add 9(k + 1/3) + 10(1/2k - 1), we can use the distributive property to simplify.
First, we distribute 9 to both terms inside the first parentheses: 9k + 9/3
Next, we distribute 10 to both terms inside the second parentheses: 10/2k - 10
Simplifying the fractions, 9/3 = 3 and 10/2 = 5.
Now we can combine like terms: 9k + 3 + 5k - 10
Combining like terms, we get: 14k - 7
Therefore, the simplified expression is 14k - 7.
The correct answer is C. 14k - 7.
Use the table to answer the question.
8 48
10 60
x 72
y 84Analyze the ratios in the table to find the missing values.(1 point)
Responses
22; 34
22; 34
432; 504
432; 504
12; 14
12; 14
18; 26
To find the missing values, let's analyze the ratios in the table.
The first ratio can be found by dividing each y-value by the corresponding x-value: 48/8 = 6 and 60/10 = 6. So, we can conclude that the ratio is 6.
The second ratio can be found by dividing each y-value by the corresponding x-value: 72/x = 6. To find the value of x, we can divide 72 by 6: x = 72/6 = 12.
The last ratio can be found by dividing each y-value by the corresponding x-value: 84/x = 6. To find the value of x, we can divide 84 by 6: x = 84/6 = 14.
Therefore, the missing values are x = 12 and y = 14.
The correct answer is 12; 14.
Use the given tables to compare the ratios 3:5
and 2:3
.
3 5
6 10
9 15
12 20
15 25
2 3
4 6
6 9
8 12
10 15
(1 point)
Responses
More rows need to be added to the tables to be able to compare the ratios.
More rows need to be added to the tables to be able to compare the ratios.
3:5 > 2:3
3:5 > 2:3
3:5 < 2:3
ratio of 3 to 5 is less than ratio of 2 to 3
3:5 = 2:3
To compare the ratios 3:5 and 2:3, we need to consider equivalent ratios.
By looking at the first table:
For the 3:5 ratio, we can see that every 3 corresponds to 5.
For the 2:3 ratio, we can see that every 2 corresponds to 3.
If we multiply the 2:3 ratio by 2, we get 4:6.
Now we can compare the ratios:
3:5 is not equal to 4:6 because 3 does not equal 4 and 5 does not equal 6.
Since we do not have any other equivalent ratios to compare, we cannot determine which ratio is greater or lesser.
Therefore, the correct response is: More rows need to be added to the tables to be able to compare the ratios.
The following tables show the amount of fat for a given number of crackers for two types of crackers. Which type of cracker has less fat per cracker?
Cracker A
Grams of Fat Number of Crackers
8 10
16 20
24 30
32 40
40 50
48 60
Cracker B
Grams of Fat Number of Crackers
6 12
12 24
18 36
24 48
30 60
36 72
(1 point)
Responses
The two types of crackers have the same amount of fat per cracker.
The two types of crackers have the same amount of fat per cracker.
Cracker A
Cracker A
More rows need to be added to the tables to be able to compare the crackers.
More rows need to be added to the tables to be able to compare the crackers.
Cracker B
Cracker B
To determine which type of cracker has less fat per cracker, we need to compare the ratios of grams of fat to the number of crackers for each type of cracker.
For Cracker A, the ratio of grams of fat to the number of crackers is:
8/10 = 0.8 grams of fat per cracker
16/20 = 0.8 grams of fat per cracker
24/30 = 0.8 grams of fat per cracker
32/40 = 0.8 grams of fat per cracker
40/50 = 0.8 grams of fat per cracker
48/60 = 0.8 grams of fat per cracker
For Cracker B, the ratio of grams of fat to the number of crackers is:
6/12 = 0.5 grams of fat per cracker
12/24 = 0.5 grams of fat per cracker
18/36 = 0.5 grams of fat per cracker
24/48 = 0.5 grams of fat per cracker
30/60 = 0.5 grams of fat per cracker
36/72 = 0.5 grams of fat per cracker
From the ratios, we can see that the amount of fat per cracker is consistently lower for Cracker B. Therefore, Cracker B has less fat per cracker compared to Cracker A.
The correct answer is: Cracker B.
3 of 53 of 5 Items
Which of the following tables could you use to compare the ratios 2:5 and 3:4?(1 point)
Responses
2 5
4 10
3 4
6 82 5 4 10 3 4 6 8
2 5
4 10
6 15
8 20
10 25
3 4
6 8
9 12
12 16
15 202 5 4 10 6 15 8 20 10 25 3 4 6 8 9 12 12 16 15 20
2 5
6 15
10 25
3 4
9 12
16 202 5 6 15 10 25 3 4 9 12 16 20
2 5
3 10
4 15
5 20
6 25
3 4
4 8
5 12
6 16
7 20
To compare the ratios 2:5 and 3:4, we need to find a table that contains equivalent ratios for both ratios.
Let's analyze the options:
Option 1:
2:5 is present, but 3:4 is not.
Option 2:
2:5 and 3:4 are both present.
Option 3:
3:4 is present, but 2:5 is not.
Option 4:
2:5 is present, but 3:4 is not.
Therefore, the correct option is option 2:
2 5
4 10
6 15
8 20
10 25
3 4
6 8
9 12
12 16
15 20
Option 2 provides an equivalent ratio for 2:5 (4:10), as well as an equivalent ratio for 3:4 (6:8). Therefore, this table can be used to compare the ratios 2:5 and 3:4.
The correct answer is option 2.
Compare the ratios 7:4 and 12:5 using the following tables. Finish the tables by filling in the missing values A and B.
7 4
14 8
21 12
28 16
A B
12 5
24 10
36 15
48 20
60 25
(1 point)
Responses
A = 35 and B = 18.
upper A equals 35 and upper B equals 18 .
A = 35 and B = 20.
upper A equals 35 and upper B equals 20 .
A = 32 and B = 20.
upper A equals 32 and upper B equals 20 .
A = 32 and B = 18.
upper A equals 32 and upper B equals 18 .