Answer:
#5: 180 paperclips in total.
#6: 126 stamps in total.
#7: Elena should give Lucy 15 colored pencils.
Step-by-step explanation:
This explanation solves each question by setting a single unknown, 
.
<h3>#5</h3>
Let the initial number of paperclips of Antonio. That should also be the number of Abby's paperclips.
Initially:
- Antonio: paperclips;
- Abby: paperclips.
Antonio gives 
paperclips to Abby. After that,
- Antonio:
paperclips; - Abby:
paperclips.
Abby now possess twice as many paperclips as Antonio does. In other words,
.
By the distributive property:
.
Substract 
from both sides
.
Both Antonio and Abby initially possess 90 paperclips. That's 180 in total.
<h3>#6</h3>
Similarly, let be the number of Emily's stamps. That should be the same as the number of Jasmine's stamps.
Initially:
- Emily: stamps;
- Jasmine: stamps.
After Emily gives 
stamps to Jasmine:
- Emily:
stamps; - Jasmine:
stamps.
Jasmine now possesses twice as many stamps as Emily does. In other words,
.
.
Jasmine used to possess 126 stamps. Now she possesses 
stamps after receiving stamps from Emily.
<h3>#7</h3>
Let the number of pencils that Elena needs to give to Lucy be .
Initially:
- Elena: 60 pencils;
- Lucy: 26 pencils.
After Elena gives pencils to Lucy:
- Elena:
pencils; - Lucy:
pencils.
Elena should now possess four more pencils than Lucy does. In other words,
.
.
.
The numbers in this problem are ordered pairs, which are points on a graph.
These are (10, 20), (-10, 20), (-10, -10), and (10, -10).
To find the area and perimeter of this shape, you must first find the distance between each point.
Distance between (10, 20) and (-10, 20):
Since the y-value remains the same here, we just have to find the difference in x-values.
This means 10 - (-10)
A negative being subtracted is the same as a positive being added.
That means 10 - (-10) is the same as 10 + 10.
10 + 10 = 20, so the distance between (10, 20) and (-10, 20) is 20 units.
Distance between (-10, 20) and (-10, -10):
The x-values are the same here so just find the difference between the y-values.
20 - (-10) = 20 + 10 = 30
The distance between the (-10, 20) and (-10, -10) is 30 units.
Distance between (-10, -10) and (10, -10):
The y-values are the same so just find the difference between the x-values.
10 - (-10) = 10 + 10 = 20
The distance between (-10, -10) and (10, -10) is 20 units.
Distance between (10, -10) and (10, 20):
The x-values are the same so find the difference between the y-values.
20 - (-10) = 20 + 10 = 30
The distance between (10, -10) and (10, 20) is 30 units.
So now we know the side lengths of the room are 20 units, 30 units, 20 units, and 30 units.
To find the perimeter, add all the side lengths together.
20 + 30 + 20 + 30 = 100
The perimeter of the room is 100 units.
To find the area, multiply the length by the width.
The length is 20 units and the width is 30 units.
20 • 30 = 600
The area of the room is 600 units.
Final answers:
Perimeter = 100
Area = 600
Hope this helps!
Exponentiate the log or In because Exponentials are inverses of Logs and lns.
Answer:
10 cm.
Step-by-step explanation:
We'll begin by calculating the area of the small bubble. This can be obtained as follow:
Radius (r) = 5 cm
Area (A) =?
Since the bubble is circular in nature, we shall use the formula for area of circle to determine the area of the bubble. This is illustrated below:
A = πr²
A = π × 5²
A = 25π cm²
Next, we shall determine the total area of the small bubbles. This can be obtained as follow:
Area of 1 bubble = 25π cm²
Therefore,
Area of 4 bubbles = 4 × 25π cm²
Area of 4 bubbles = 100π cm²
Finally, we shall determine the radius of the large bubble. This can be obtained as follow:
Area of large bubble = total area of small bubbles = 100π cm²
Radius (r) =?
A = πr²
100π = πr²
100 = r²
Take the square root of both side
r = √100
r = 10 cm
Thus, the radius of the large bubble is 10 cm
The answer is 0, hope it helps lol
