Answer: 9 1/3
Step-by-step explanation: There are four of them and, assuming there is no space in between them, they all take up the same amount of space. So that means, if they were added up, it’d be 2 1/3 +2 1/3 + 2 1/3 +2 1/3. That can be simplified to 4 x (2 + 1/3). When multiplied, it equals 8 + 4/3=8 + 1 +1/3=9 + 1/3=9 1/3.
Answer:
8:4
Step-by-step explanation:
Given that,
The ratio of the areas of similar polygons is 64: 16, A₁:A₂=64: 16
We need to find the ratio of their sides. For similar polygons, the ratio of the area is proportional to the square of the ratio of their corresponding sides.
Let sides are x₁ and x₂. So,
So, the required ratio is 8:4.
Answer:
13/30
Step-by-step explanation:
Add: -1/
3
+ 2/
5
= -1 · 5/
3 · 5
+ 2 · 3/
5 · 3
= -5/
15
+ 6/
15
= -5 + 6/
15
= 1/
15
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(3, 5) = 15. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 5 = 15. In the next intermediate step the fraction result cannot be further simplified by canceling.
In words - minus one third plus two fifths = one fifteenth.
Subtract: 1/
2
- the result of step No. 1 = 1/
2
- 1/
15
= 1 · 15/
2 · 15
- 1 · 2/
15 · 2
= 15/
30
- 2/
30
= 15 - 2/
30
= 13/
30
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(2, 15) = 30. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 15 = 30. In the next intermediate step the fraction result cannot be further simplified by canceling.
In words - one half minus one fifteenth = thirteen thirtieths.
Let 1 angles be x, then its supplement is 180-x
x+x+12=180
2x=168
x=84
angles are 84 and 96
Answer:
Find half the area of the rectangle
Step-by-step explanation:
Given
See attachment for the Serek's steps
Required
Which can be used to determine the area of the original triangle
To do this, we simply analyze each step.
At step 2, where he joined two congruent triangles to form a parallelogram.
Half the area of the parallelogram will give the area of the original triangle (since both triangles are equal)
At step 3, where he decomposed the parallelogram to a trapezoid and a right triangle.
Half the sum of the areas of the resulting shapes (trapezoid and right triangle) will equal to the area of the original triangle but half the area of each shape will not amount to the area of the original triangle
At step 4, where the right triangle and the trapezoid are merged to form a rectangle.
The area of the rectangle will equal to the area of the parallelogram in step (2).
So, half the area of the rectangle will equal to the area of the triangle.
<em>Hence, (b) is correct</em>
