Answer:
Triangles would be congruent through ASA if Angle A is equal to Angle T.
Triangles would be congruent via AAS if Angle B matches Angle P.
Step-by-step explanation:
It is established that sides AC and TQ are congruent, along with angles BCA and PQT. If angles A and T are equal, we apply the ASA theorem. Similarly, if angle B equals angle P, we reference the AAS theorem.
Since only two options need to be selected, you can conclude your options there.
<span>5.7 liters of a 5% solution combined with 4.3 liters of a 40% solution.
To begin, define the problem with formulas.
x Represents the liters of the 5% solution utilized.
10-x Represents the liters of the 40% solution used.
This forms an equation: 5% of x plus 40% of (10-x) equals 20% of 10.
0.05x + 0.40(10-x) = 0.20 * 10
Now, distribute the 0.40 coefficient.
0.05x + 4.0 - 0.40x = 0.20 * 10
Next, combine the terms.
4.0 - 0.35x = 2.0
Add 0.35x to each side.
4.0 = 2.0 + 0.35x
Subtract 2 from both sides.
2.0 = 0.35x
Lastly, divide both sides by 0.35.
5.7 = x
Thus, 5.7 liters of a 5% solution is required. To determine the volume of the 40% solution, subtract from 10.
10.0 - 5.7 = 4.3</span>
9514 1404 393
Answer:
96 cubic feet
Step-by-step explanation:
The volume calculation for the dimensions of 16 ft by 18 ft by 1/3 ft is as follows:
V = LWH
V = (16 ft)(18 ft)(1/3 ft) = 96 ft³
Thus, 96 cubic feet of concrete will be required.
Part a) When a page is scaled down to 80%, how much enlargement is necessary to bring it back to its original size?
Let
x---------> the percent enlargement
Given the original size is 100%
This means:
x*80%=100%
x=(100%/80%)
x=1.25--------> 1.25=(125/100)=125%
Thus,
The answer to Part a) is
The percent enlargement required is 125%
Part b) Estimate how many successive copies of a page are needed to make the final copy less than 15% of its original size.
Since the photocopy machine reduces sizes to 80% of the original
Therefore:
Copy N 1
0.80*100%=80%
Copy N 2
0.80*80%=64%
Copy N 3
0.80*64%=51.2%
Copy N 4
0.80*51.2%=40.96%
Copy N 5
0.80*40.96%=32.77%
Copy N 6
0.80*32.77%=26.21%
Copy N 7
0.80*26.21%=20.97%
Copy N 8
0.80*20.97%=16.78%
Copy N 9
0.80*16.78%=13.42%-------------> 13.42% < 15%
Therefore,
The answer to Part b) is
The necessary number of copies to achieve this is 9
