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Answer :
Sure, I'll be happy to provide a detailed, step-by-step solution!
1. Solve the equation [tex]$x - 5 = 7$[/tex]:
To solve for [tex]\( x \)[/tex]:
[tex]\[
x - 5 = 7
\][/tex]
Add 5 to both sides:
[tex]\[
x = 7 + 5
\][/tex]
[tex]\[
x = 12
\][/tex]
Therefore, the answer is c) [tex]\( x = 12 \)[/tex].
2. Convert 800 grams to kilograms:
We know that 1 kilogram = 1000 grams. To convert grams to kilograms, we divide by 1000:
[tex]\[
800 \text{ grams} = \frac{800}{1000} \text{ kilograms} = 0.8 \text{ kilograms}
\][/tex]
Therefore, the answer is d) 0.8 kg.
3. Calculate 2% of 400 students:
[tex]\[
\text{Number of students absent} = \frac{2}{100} \times 400 = 8
\][/tex]
Therefore, the answer is b) 8.
4. Simplify the expression [tex]\(\frac{x^2}{xy}\)[/tex]:
[tex]\[
\frac{x^2}{xy} = \frac{x \cdot x}{x \cdot y} = \frac{x}{y}
\][/tex]
Therefore, the answer is b) [tex]\( \frac{x}{y} \)[/tex].
5. Find the area of a square with side length 100 meters:
The area [tex]\( A \)[/tex] of a square is given by:
[tex]\[
A = \text{side length}^2
\][/tex]
[tex]\[
A = 100^2 = 10000 \text{ square meters}
\][/tex]
Therefore, the answer is c) [tex]\( 10,000 \, m^2 \)[/tex].
6. Sum of [tex]\(\frac{2}{5} + \frac{1}{4}\)[/tex]:
Find a common denominator, which is 20:
[tex]\[
\frac{2}{5} = \frac{8}{20}, \quad \frac{1}{4} = \frac{5}{20}
\][/tex]
[tex]\[
\frac{8}{20} + \frac{5}{20} = \frac{13}{20}
\][/tex]
Therefore, the answer is c) [tex]\( \frac{13}{20} \)[/tex].
7. Number of prime numbers between 10 and 20:
The prime numbers between 10 and 20 are 11, 13, 17, and 19.
[tex]\[
\text{There are 4 prime numbers.}
\][/tex]
Therefore, the answer is a) 4.
8. Simplify the expression [tex]\( x + 2y + 3x - y \)[/tex]:
Combine like terms:
[tex]\[
x + 3x + 2y - y = 4x + y
\][/tex]
Therefore, the answer is d) [tex]\( 4x + y \)[/tex].
9. Calculate the new intake with a 20% increase from 120 students:
A 20% increase means the intake increases by:
[tex]\[
\text{Increase} = \frac{20}{100} \times 120 = 24
\][/tex]
[tex]\[
\text{New intake} = 120 + 24 = 144
\][/tex]
Therefore, the answer is c) 144.
10. Find the value of [tex]\(\cos 60^\circ\)[/tex]:
The cosine of 60 degrees is a known trigonometric value:
[tex]\[
\cos 60^\circ = \frac{1}{2}
\][/tex]
Therefore, the answer is a) [tex]\( \frac{1}{2} \)[/tex].
I hope this helps. If you have any more questions, feel free to ask!
1. Solve the equation [tex]$x - 5 = 7$[/tex]:
To solve for [tex]\( x \)[/tex]:
[tex]\[
x - 5 = 7
\][/tex]
Add 5 to both sides:
[tex]\[
x = 7 + 5
\][/tex]
[tex]\[
x = 12
\][/tex]
Therefore, the answer is c) [tex]\( x = 12 \)[/tex].
2. Convert 800 grams to kilograms:
We know that 1 kilogram = 1000 grams. To convert grams to kilograms, we divide by 1000:
[tex]\[
800 \text{ grams} = \frac{800}{1000} \text{ kilograms} = 0.8 \text{ kilograms}
\][/tex]
Therefore, the answer is d) 0.8 kg.
3. Calculate 2% of 400 students:
[tex]\[
\text{Number of students absent} = \frac{2}{100} \times 400 = 8
\][/tex]
Therefore, the answer is b) 8.
4. Simplify the expression [tex]\(\frac{x^2}{xy}\)[/tex]:
[tex]\[
\frac{x^2}{xy} = \frac{x \cdot x}{x \cdot y} = \frac{x}{y}
\][/tex]
Therefore, the answer is b) [tex]\( \frac{x}{y} \)[/tex].
5. Find the area of a square with side length 100 meters:
The area [tex]\( A \)[/tex] of a square is given by:
[tex]\[
A = \text{side length}^2
\][/tex]
[tex]\[
A = 100^2 = 10000 \text{ square meters}
\][/tex]
Therefore, the answer is c) [tex]\( 10,000 \, m^2 \)[/tex].
6. Sum of [tex]\(\frac{2}{5} + \frac{1}{4}\)[/tex]:
Find a common denominator, which is 20:
[tex]\[
\frac{2}{5} = \frac{8}{20}, \quad \frac{1}{4} = \frac{5}{20}
\][/tex]
[tex]\[
\frac{8}{20} + \frac{5}{20} = \frac{13}{20}
\][/tex]
Therefore, the answer is c) [tex]\( \frac{13}{20} \)[/tex].
7. Number of prime numbers between 10 and 20:
The prime numbers between 10 and 20 are 11, 13, 17, and 19.
[tex]\[
\text{There are 4 prime numbers.}
\][/tex]
Therefore, the answer is a) 4.
8. Simplify the expression [tex]\( x + 2y + 3x - y \)[/tex]:
Combine like terms:
[tex]\[
x + 3x + 2y - y = 4x + y
\][/tex]
Therefore, the answer is d) [tex]\( 4x + y \)[/tex].
9. Calculate the new intake with a 20% increase from 120 students:
A 20% increase means the intake increases by:
[tex]\[
\text{Increase} = \frac{20}{100} \times 120 = 24
\][/tex]
[tex]\[
\text{New intake} = 120 + 24 = 144
\][/tex]
Therefore, the answer is c) 144.
10. Find the value of [tex]\(\cos 60^\circ\)[/tex]:
The cosine of 60 degrees is a known trigonometric value:
[tex]\[
\cos 60^\circ = \frac{1}{2}
\][/tex]
Therefore, the answer is a) [tex]\( \frac{1}{2} \)[/tex].
I hope this helps. If you have any more questions, feel free to ask!
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