Answer:
0.305
Step-by-step explanation:
When we use the percentage (%) notation, to express for example the happening of a success is X%, we are expressing that the corresponding fact is happening X times every 100 times. Instead of X% we could use X/100.
In this example, every 100 units of his payment check, Landon takes 30,5 unites and puts them to his saving account. So, instead of 30.5% we could say 30.5/100. (30.5% = 30.5/100).
So, we have:
30.5% = 30.5/100 = 0.305
This way, 0.305 is the decimal equivalent to 30.5%.
Observation: For avoiding comas in the latter fraction we could also say: 305/1000.
If the triangles are similar then the angles in both are equal. Let's look at each set individually:
(1) Triangle 1: 25°, 35°
Triangle 2: 25°, 120°
Now it may be hard to tell if the triangles are similar at the moment so we must calculate the third angle in each triangle (The angles in a triangle add up to 180°, therefor the missing angle = 180 - (given angle 1 + given angle 2)
Triangle 1: 180 - (25 + 35) = 120°
Triangle 2: 180 - (25 + 120) = 35°
Now writing out the set of angles again we have:
Triangle 1: 25°, 35°, 120°
Triangle 2: 25°, 120°, 35°
So in fact Triangle 1 and 2 are similar.
Now we can repeat this process for (2) - (5):
(2) Triangle 1: 100°, 60°, 20°
Triangle 2: 100°, 20°, 60°
This pair is also similar
(3) Triangle 1: 90°, 45°, 45°
Triangle 2: 45°, 40°, 95°
This pair is not similar
(4) Triangle 1: 37°, 63°, 80°
Triangle 2: 63°, 107°, 10°
This pair is not similar
(5) Triangle 1: 90°, 20°, 70°
Triangle 2: 20°, 90°, 70°
This pair is similar
Therefor pairs (1), (2) and (5) are similar
Answer:
70
Step-by-step explanation:
The area of one of the four triangles is 
. So together the area of all the four traingles is 
Answer:
(-2, 3) is one of many solutions to the system
Step-by-step explanation:
Let's actually solve the system so that we can compare the result with the given pair (-2, 3):
Multiplying the second equation by -2 results in:
2x + 4y = 8
-2x - 4y = -8
We see that these equations are identical. Thus, there are infinitely many solutions.
1. is true: (-2, 3) is one of many solutions to the system
The other three possible answers are incorrect.
Answer:
For Literature = 90 pages
For Grammar = 60 pages
Step-by-step explanation:
An English book consists of two sections, literature and grammar, in a ratio of 3:2. How much of each type of content will be needed to make a book of 150 pages?
Literature : Grammar
3 : 2
Total number of Proportion = 3 + 2 = 5
For Literature
= 3/5 × 150 pages
= 90 pages
For Grammar
= 2/5 × 150 pages
= 60 pages
