choose the option that has the following numbers in order from least to greatest
-3, 6, -2/3, -7, | -5 | (the 5 is abulsote value)
-7, -3, -2/3, | -5 |, 6
Which expression is equivalent to -9x + 24.6?
-3(2x + 2.8)
-3(3x - 8.2)
-3(3x + 24.6)
-3(3x-24.6)
-3(3x - 8.2)
Sorry here’s the choices again
-3(2x + 8.2)
-3(3x - 8.2)
-3(3x + 24.6)
-3(3x-24.6)
-3(3x - 8.2)
John's family has a US flag with the dimensions of 4 feet x 7 feet. Which of the following could be scaled versions of this flag? Select all that apply! (Hint, you will have TWO correct answers)
2 feet by 3.5 feet
1 foot x 2 feet
2 feet x 4 feet
20 feet by 35 feet
12 feet by 24 feet
"2 feet x 3.5 feet" and "12 feet by 24 feet" are the correct scaled versions of the flag.
What’s the reasoning
The reasoning behind the correct choices is that the scaled versions of the flag should maintain the same aspect ratio as the original flag. The aspect ratio is the ratio of the width to the height.
In the original flag, the aspect ratio is 4:7 (width:height).
By comparing the aspect ratios of the options, we can determine which ones are scaled versions of the original flag:
- "2 feet x 3.5 feet" has an aspect ratio of 2:3.5, which is equivalent to 4:7 when simplified. So this is a scaled version.
- "1 foot x 2 feet" has an aspect ratio of 1:2, which is not equivalent to 4:7. So this is not a scaled version.
- "2 feet x 4 feet" has an aspect ratio of 2:4, which is equivalent to 1:2 when simplified. This is not the same as the aspect ratio of the original flag, so this is not a scaled version.
- "20 feet by 35 feet" has an aspect ratio of 20:35, which can be simplified to 4:7. So this is a scaled version.
- "12 feet by 24 feet" has an aspect ratio of 12:24, which can be simplified to 1:2. This is not the same as the aspect ratio of the original flag, so this is not a scaled version.
Based on the aspect ratios, "2 feet x 3.5 feet" and "20 feet by 35 feet" are the correct scaled versions of the flag.
Azeriah is making punch with orange juice and pomegranate juice. She mixes the two juices according to the amounts indicated in the table below. How many cups of pomegranate juice should she add to 25 cups of orange juice?
Number of cups of orange juice
5
20
25
Number of cups of pomegranate
3
12
?
The table shows the temperatures of four cities at 11 a.m. and the changes in these temperatures in the next three hours. Which city is the coldest at 2 p.m.?
City f - 11 am > -7, 2 pm 9 degrees warmer
City g - 11 am > 6, 2 pm 8 degrees colder
City h - 11 am > -4, 2 m 4 degrees warmer
City I - 11 am > 3, 2 pm 3 degrees colder