Answer: the number of students that were surveyed is 40
Step-by-step explanation:
Let x = total number of students that were surveyed about their favorite colors
1/4 of the students preferred red.
This means that the number of students that preferred red is 1/4 × x = x/4
1/8 of the students preferred blue.
This means that the number of students that preferred blue is 1/8 × x = x/8
The remaining number of students will be the total number of students - the sum of the number of students that preferred red and the number of students that preferred blue. It becomes
x - (x/4 + x/8) = x - 3x/8 = 5x/8
3/5 of the remaining students were for green. This means that the number of students that preferred green is 3/5 × 5x/8 = 3x/8
if 15 students prefer green, then
3x/8 = 15
3x = 120
x = 120/3 = 40 students
Answer:
- sum: 3x² -4x -4
- product: (x -2)(3x +2)
Step-by-step explanation:
The areas of four regions are given. We can simply add them to find the sum. To express them as a product, we need to look at common factors.
<h3>Sum</h3>
The total of the given area expressions is ...
3x² +2x -6x -4 = 3x² -4x -4 . . . . sum
<h3>Product</h3>
Extending the table to show common factors of each row and column, we have ...
Since each cell of the table is the product of the corresponding common factors, we can write the area as the product ...
(x -2)(3x +2) . . . . product
Taxi A
1mile £3.50+£1.75=£5.25
Taxi B
1mile £1.25+£2.00=£3.25
Taxi A
2miles £3.50+£3.50=£7.00
Taxi B
2miles £1.25+£4.00=£5.25
Taxi A
3miles £3.50+£5.25=£8.75
Taxi B
3miles £1.25+£6.00=£7.25
Taxi A
4miles £3.50+£7.00=£10.50
Taxi B
4miles £1.25+£8.00=£9.25
Taxi A
5miles £3.50+£8.75=£12.25
Taxi B
5miles £1.25+£10.00=£11.25
Taxi A
6miles £3.50+£10.50=£14.00
Taxi B
6miles £1.25+£12.00=£13.25
Taxi A
7miles £3.50+£12.25=£15.75
Taxi B
7miles £1.25+£14.00=£15.25
Taxi A
8miles £3.50+£14.00=£17.50
Taxi B
8miles £1.25+£16.00=£17.25
Taxi A
9miles £3.50+£15.75=£19.25 (the same)
Taxi B
9miles £1.25+£18.00=£19.25 (the same)
^^^
They would have to drive 9 miles for the taxi to cost the same.
Hope this helped, this is the longest way to work it out but also the simplest.
The area of the rect. is 100 ft times 64 ft, or 6400 ft^2.
Let's list factors of 6400: 64,100
64= 2^6
100= 2^2*5^2
Here we see that 2 appears 8 times as a factor, and 5 appears 2 times:
6400 = 2^6 * 10^2 = 2^8*5^2
