Class 9 Math Trivia
1.
A is 40% of B. What percentage is B of A?
Answer:
250%
Explanation:
If A is 40% of B, this means A = 0.4B. To find what percentage B is of A, you rearrange this equation to solve for B in terms of A:B = A / 0.4This can be rewritten as:B = 2.5ATo convert the factor 2.5 into a percentage, you multiply it by 100:2.5 x 100 = 250%Thus, B is 250% of A, indicating that B is more than twice the size of A.
2.
If x + 5 = 10, then what is the value of x?
Answer:
5
Explanation:
To solve for x in the equation x + 5 = 10, you need to isolate x. You do this by subtracting 5 from both sides of the equation.Here’s the step-by-step solution:x + 5 - 5 = 10 - 5,which simplifies to:x = 5.Thus, x equals 5. This solution can be verified by substituting 5 back into the original equation: 5 + 5 = 10, which is true. Therefore, the correct value of x is 5.
3.
Given the equation x2+4x+3=0, what are the values of x?
Answer:
-1 or -3
Explanation:
To solve the quadratic equation x^2 + 4x + 3 = 0, you can factorize it:
(x + 3)(x + 1) = 0
Setting each factor equal to zero gives:
x + 3 = 0
Solving for x, x = -3
x + 1 = 0
Solving for x, x = -1
Thus, the solutions for x are -1 and -3. These are the values that make the original equation true when substituted back into it.
(x + 3)(x + 1) = 0
Setting each factor equal to zero gives:
x + 3 = 0
Solving for x, x = -3
x + 1 = 0
Solving for x, x = -1
Thus, the solutions for x are -1 and -3. These are the values that make the original equation true when substituted back into it.
4.
What is the next number in the sequence: 3, 7, 15, 31, ?
Answer:
63
Explanation:
The given sequence is increasing, and each number is obtained by doubling the previous number and then adding 1.
Starting with 3:
3 * 2 + 1 = 7
7 * 2 + 1 = 15
15 * 2 + 1 = 31
To find the next number, we apply the same pattern:
31 * 2 + 1 = 63
So, the next number in the sequence is 63.
Starting with 3:
3 * 2 + 1 = 7
7 * 2 + 1 = 15
15 * 2 + 1 = 31
To find the next number, we apply the same pattern:
31 * 2 + 1 = 63
So, the next number in the sequence is 63.
5.
Given the equation y2+ 4=20, what are the values of y?
Answer:
4 or -4
Explanation:
To solve the equation y^2 + 4 = 20, first subtract 4 from both sides:
y^2 + 4 - 4 = 20 - 4
This simplifies to:
y^2 = 16
Next, find y by taking the square root of both sides. Remember, squaring a number results in a positive value, and the square root of a positive number has both a positive and negative solution:
y = sqrt(16)
This gives:
y = 4 and y = -4
Therefore, y equals both 4 and -4.
y^2 + 4 - 4 = 20 - 4
This simplifies to:
y^2 = 16
Next, find y by taking the square root of both sides. Remember, squaring a number results in a positive value, and the square root of a positive number has both a positive and negative solution:
y = sqrt(16)
This gives:
y = 4 and y = -4
Therefore, y equals both 4 and -4.
6.
The price of an item increases by 20% and then decreases by 20%. What is the net effect on the price?
Answer:
Decreased by 4%
Explanation:
The given sequence is increasing, and each number is obtained by doubling the previous number and then adding 1.
Starting with 3:
3 * 2 + 1 = 7
7 * 2 + 1 = 15
15 * 2 + 1 = 31
To find the next number, we apply the same pattern:
31 * 2 + 1 = 63
So, the next number in the sequence is 63.
Starting with 3:
3 * 2 + 1 = 7
7 * 2 + 1 = 15
15 * 2 + 1 = 31
To find the next number, we apply the same pattern:
31 * 2 + 1 = 63
So, the next number in the sequence is 63.
7.
The ratio of girls to boys in a school is 5:7. If there are 525 girls, how many boys are there?
Answer:
735
Explanation:
The ratio of girls to boys in the school is 5:7. This means for every 5 girls, there are 7 boys. Given there are 525 girls, we first determine how many times the part of the ratio (5) fits into the actual number of girls (525).
Calculate the multiplier for the ratio:
525 (number of girls) / 5 (girl ratio part) = 105
Now, use this multiplier to find the number of boys:
Multiply the boy ratio part by the multiplier:
7 (boy ratio part) x 105 (multiplier) = 735
Therefore, there are 735 boys in the school.
Calculate the multiplier for the ratio:
525 (number of girls) / 5 (girl ratio part) = 105
Now, use this multiplier to find the number of boys:
Multiply the boy ratio part by the multiplier:
7 (boy ratio part) x 105 (multiplier) = 735
Therefore, there are 735 boys in the school.
8.
David and John share $455 in the ratio of 2:3, respectively. How much money does John get?
Answer:
$273
Explanation:
David and John share $455 in the ratio of 2:3. This means for every 2 units that David receives, John receives 3 units. To find out how much money each person gets, you first need to determine the total number of parts into which the money is divided:
Total parts = 2 (David) + 3 (John) = 5 parts
Now, calculate the value of one part:
Value of one part = Total money / Total parts = $455 / 5 = $91
Finally, calculate how much John receives by multiplying the value of one part by the number of parts John receives:
Money John receives = 3 parts x $91/part = $273
Therefore, John receives $273.
Total parts = 2 (David) + 3 (John) = 5 parts
Now, calculate the value of one part:
Value of one part = Total money / Total parts = $455 / 5 = $91
Finally, calculate how much John receives by multiplying the value of one part by the number of parts John receives:
Money John receives = 3 parts x $91/part = $273
Therefore, John receives $273.
9.
If x-12y = 0, what is y/x?
Answer:
1/12
Explanation:
To find the ratio of y/x from the equation x-12y = 0, first rearrange the equation to solve for y in terms of x. By moving all terms involving y to one side and all other terms to the opposite side, we get x = 12y. Now, divide both sides of this equation by x to isolate y/x on one side. This gives us y/x = 1/12. Hence, the value of y/x equals 1/12. This is calculated by dividing the coefficient of y by the coefficient of x in the rearranged equation.
10.
What is 3/20 as a decimal?
Answer:
0.15
Explanation:
To convert the fraction 3/20 into a decimal, divide the numerator by the denominator. The calculation is performed by dividing 3 by 20. When you divide 3 by 20, you get 0.15. Therefore, the decimal equivalent of the fraction 3/20 is 0.15. This decimal value directly results from the division process, representing the proportion of 3 parts out of a total of 20 parts.
11.
What is 68/0.00001 as an ordinary number?
Answer:
6800000
Explanation:
To express the fraction 68/0.00001 as an ordinary number, you can perform the division:
68 ÷ 0.00001
Converting the decimal value into fraction, we get:
68 ÷ 1/100000 = 68 * 100000 = 6800000
So, 68/0.00001 is equal to 6,800,000 as an ordinary number.
68 ÷ 0.00001
Converting the decimal value into fraction, we get:
68 ÷ 1/100000 = 68 * 100000 = 6800000
So, 68/0.00001 is equal to 6,800,000 as an ordinary number.
12.
What is the value of 4*4-2*(-3)+6= ?
Answer:
28
Explanation:
To solve the expression 4 * 4 - 2 * (-3) + 6 using the BODMAS (Brackets, Order, Division and Multiplication, Addition and Subtraction) rule:
First, evaluate the multiplication and division from left to right:
4 * 4 = 16
-2 * (-3) = 6 (The double negative becomes a positive)
Now, rewrite the expression with the results: 16 + 6 + 6
Finally, perform the addition from left to right: 16 + 6 = 22
22 + 6 = 28
So, 4 * 4 - 2 * (-3) + 6 = 28.
First, evaluate the multiplication and division from left to right:
4 * 4 = 16
-2 * (-3) = 6 (The double negative becomes a positive)
Now, rewrite the expression with the results: 16 + 6 + 6
Finally, perform the addition from left to right: 16 + 6 = 22
22 + 6 = 28
So, 4 * 4 - 2 * (-3) + 6 = 28.
13.
What is the result when you reduce $80 by 11%?
Answer:
$71.20
Explanation:
To find the amount remaining after reducing $80 by 11%, first calculate 11% of $80. Multiply 80 by 0.11 to get the reduction amount. This calculation gives 80 * 0.11 = $8.80. Now, subtract this amount from the original $80 to find the reduced total. The calculation is 80 - 8.80 = $71.20. Therefore, when you reduce $80 by 11%, you will get $71.20. This result is achieved by applying the percentage reduction to the original amount and subtracting the calculated value from the original total.
14.
What is 0.67543 rounded to 2 significant figures?
Answer:
0.68
Explanation:
To round the number 0.67543 to 2 significant figures:Identify the first two significant figures, which are 6 and 7.Look at the third digit, which is 5. Since 5 is greater than or equal to 5, you round up the second significant figure (7) to 8.Therefore, 0.67543 rounded to 2 significant figures is 0.68. This process ensures the number is represented accurately while maintaining the specified precision.
15.
What is the simplified form of 5ab - 7ba + 4ab=?
Answer:
2ab
Explanation:
First, recognize that ab and ba are equivalent (since multiplication is commutative). Therefore, we can combine the terms:
5ab−7ab+4ab
Now, combine like terms:
(5−7+4)ab
2ab
Thus, the simplified form of 5ab−7ba+4ab is 2ab.
5ab−7ab+4ab
Now, combine like terms:
(5−7+4)ab
2ab
Thus, the simplified form of 5ab−7ba+4ab is 2ab.
16.
What is the value of x in the equation 4(x+2)=24?
Answer:
X=4
Explanation:
To solve the equation 4(x+2)=24
Distribute the 4:
4x+8=24
Subtract 8 from both sides to isolate the term with x:
4x=16
Divide both sides by 4 to solve for x:
x=16/4
Therefore, the value of x is 4.
Distribute the 4:
4x+8=24
Subtract 8 from both sides to isolate the term with x:
4x=16
Divide both sides by 4 to solve for x:
x=16/4
Therefore, the value of x is 4.
17.
The sum of three consecutive even numbers is 222. What are the numbers?
Answer:
72,74,76
Explanation:
Let the three consecutive even numbers be
𝑥, x+2, and x+4.
Their sum is given by:
x+(x+2)+(x+4)=222
Combine like terms:
3x+6=222
Subtract 6 from both sides:
3x=216
Divide both sides by 3:
x=72
Therefore, the three consecutive even numbers are:
x=72
x+2=74
x+4=76
So, the numbers are 72, 74, and 76.
𝑥, x+2, and x+4.
Their sum is given by:
x+(x+2)+(x+4)=222
Combine like terms:
3x+6=222
Subtract 6 from both sides:
3x=216
Divide both sides by 3:
x=72
Therefore, the three consecutive even numbers are:
x=72
x+2=74
x+4=76
So, the numbers are 72, 74, and 76.
18.
What is the gradient of the line x+3y=9?
Answer:
-1/3
Explanation:
To find the gradient (or slope) of the line given by the equation x+3y=9, we need to rewrite the equation in the slope-intercept form, y=mx+b, where mmm is the gradient.
Starting with: x+3y=9
Isolate y by first subtracting xxx from both sides: 3y=−x+9
Then, divide every term by 3: y=−1/3x+3
In the equation y=−1/3x+3, the gradient m is −1/3
Therefore, the gradient of the line x+3y=9 is −1/3
Starting with: x+3y=9
Isolate y by first subtracting xxx from both sides: 3y=−x+9
Then, divide every term by 3: y=−1/3x+3
In the equation y=−1/3x+3, the gradient m is −1/3
Therefore, the gradient of the line x+3y=9 is −1/3
19.
If 2x-3y +4x-7y=0, then what is the value of y/x?
Answer:
3/5
Explanation:
2x - 3y + 4x - 7y = 0
Combining like terms:
(2x + 4x) - (3y + 7y) = 0
6x - 10y = 0
Now, let's solve for y in terms of x:
10y = 6x
y = (6/10)x
Simplify the fraction:
y = (3/5)x
So, the value of y/x is 3/5.
Combining like terms:
(2x + 4x) - (3y + 7y) = 0
6x - 10y = 0
Now, let's solve for y in terms of x:
10y = 6x
y = (6/10)x
Simplify the fraction:
y = (3/5)x
So, the value of y/x is 3/5.
20.
If 2x+5y=18 and x=2, what is the value of 4x+5y?
Answer:
22
Explanation:
First, substitute x=2 into the equation 2x+5y=18:
2(2)+5y=18
4+5y=18
Next, solve for 𝑦 by isolating y:
5y=18−4
5y=14
y=2.8
Now, substitute x=2 and y=2.8 into the expression 4x+5y:
4(2)+5(2.8)
8+14
22
Therefore, the value of 4x+5y is 22.
2(2)+5y=18
4+5y=18
Next, solve for 𝑦 by isolating y:
5y=18−4
5y=14
y=2.8
Now, substitute x=2 and y=2.8 into the expression 4x+5y:
4(2)+5(2.8)
8+14
22
Therefore, the value of 4x+5y is 22.
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