Asked by Sakza
17 trillion in scientific notation
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Sakza
X³=125
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Sakza
(5×)°
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Sakza
Mr t. can travel a certain distance in 3hours 30 minutes at an avarage speed of 90km At what avarage speed he travel to complete the trip in 3hours
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Sakza
Calculate the simple interest on R4 400 at 4% per annum for 7 years
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Sakza
A father is three times as old as his son. Six years ago he was five years old as his son. How old they now
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Sakza
X(-1;4), Y(0;5), Z(1;6) are points on a straight line XYZ Determine the equation of the line
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Bot
1.7 x 10^13
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The cube root of 125 is 5. Hence, x = 5.
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Bot
It's not possible to give an exact answer to "(5×)°" because there is no value or variable to which the exponent would be applied.
In general, an expression with the degree notation (°) means that the entire expression should be raised to the exponent given.
For example, if we had (5x)³°, this would mean to raise the entire expression of 5x to the 3rd power, which would be (5x)³ = 125x³.
However, in the case of just (5×)°, we can't determine what it means without additional information.
In general, an expression with the degree notation (°) means that the entire expression should be raised to the exponent given.
For example, if we had (5x)³°, this would mean to raise the entire expression of 5x to the 3rd power, which would be (5x)³ = 125x³.
However, in the case of just (5×)°, we can't determine what it means without additional information.
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Bot
Let's say the distance he needs to travel is "d" km.
From the given information, we know that he can travel "d" km in 3 hours and 30 minutes (or 3.5 hours) at an average speed of 90 km/h. We can use the formula:
Speed = Distance ÷ Time
To find the distance, we can rearrange the formula:
Distance = Speed × Time
So the distance "d" that Mr. T can travel in 3.5 hours at 90 km/h is:
d = 90 km/h × 3.5 h
d = 315 km
Now we need to find at what average speed Mr. T needs to travel to complete the trip in 3 hours. We know the distance is "d" km and the time is 3 hours, so we can use the formula again to solve for the speed:
Speed = Distance ÷ Time
Speed = d ÷ 3
Speed = 315 km ÷ 3 hours
Speed = 105 km/h
Therefore, to complete the trip in 3 hours, Mr. T needs to travel at an average speed of 105 km/h.
From the given information, we know that he can travel "d" km in 3 hours and 30 minutes (or 3.5 hours) at an average speed of 90 km/h. We can use the formula:
Speed = Distance ÷ Time
To find the distance, we can rearrange the formula:
Distance = Speed × Time
So the distance "d" that Mr. T can travel in 3.5 hours at 90 km/h is:
d = 90 km/h × 3.5 h
d = 315 km
Now we need to find at what average speed Mr. T needs to travel to complete the trip in 3 hours. We know the distance is "d" km and the time is 3 hours, so we can use the formula again to solve for the speed:
Speed = Distance ÷ Time
Speed = d ÷ 3
Speed = 315 km ÷ 3 hours
Speed = 105 km/h
Therefore, to complete the trip in 3 hours, Mr. T needs to travel at an average speed of 105 km/h.
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Bot
The formula to calculate the simple interest is:
Simple Interest = (Principal × Rate × Time) ÷ 100
where:
- Principal is the initial amount invested or borrowed.
- Rate is the annual interest rate, as a percentage.
- Time is the number of years for which the interest is calculated.
In this case, the principal is R4 400, the rate is 4%, and the time is 7 years. We can plug in these values in the formula and calculate the simple interest:
Simple Interest = (4400 × 4 × 7) ÷ 100
Simple Interest = (123200) ÷ 100
Simple Interest = 1232
Therefore, the simple interest on R4 400 at 4% per annum for 7 years is R1 232.
Simple Interest = (Principal × Rate × Time) ÷ 100
where:
- Principal is the initial amount invested or borrowed.
- Rate is the annual interest rate, as a percentage.
- Time is the number of years for which the interest is calculated.
In this case, the principal is R4 400, the rate is 4%, and the time is 7 years. We can plug in these values in the formula and calculate the simple interest:
Simple Interest = (4400 × 4 × 7) ÷ 100
Simple Interest = (123200) ÷ 100
Simple Interest = 1232
Therefore, the simple interest on R4 400 at 4% per annum for 7 years is R1 232.
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Bot
Let the father's age be F and the son's age be S.
From the first sentence, we know that:
F = 3S ...(1)
From the second sentence, we know that six years ago:
(F - 6) = 5(S - 6) ...(2)
Now we can use equation (1) to substitute for F in equation (2):
(3S - 6) - 6 = 5S - 30
Simplifying the left side:
3S - 12 = 5S - 30
Subtracting 3S from both sides:
-12 = 2S - 30
Adding 30 to both sides:
18 = 2S
Dividing by 2 on both sides:
S = 9
So the son is 9 years old. We can use equation (1) to find the father's age:
F = 3S = 3(9) = 27
Therefore, the father is 27 years old and the son is 9 years old.
From the first sentence, we know that:
F = 3S ...(1)
From the second sentence, we know that six years ago:
(F - 6) = 5(S - 6) ...(2)
Now we can use equation (1) to substitute for F in equation (2):
(3S - 6) - 6 = 5S - 30
Simplifying the left side:
3S - 12 = 5S - 30
Subtracting 3S from both sides:
-12 = 2S - 30
Adding 30 to both sides:
18 = 2S
Dividing by 2 on both sides:
S = 9
So the son is 9 years old. We can use equation (1) to find the father's age:
F = 3S = 3(9) = 27
Therefore, the father is 27 years old and the son is 9 years old.
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To find the equation of the straight line that passes through points X(-1,4), Y(0,5), and Z(1,6), we can use the point-slope form of the equation, which is:
y - y1 = m(x - x1)
where:
- m is the slope of the line, and
- (x1, y1) is any point on the line.
We can use any two of the given points to calculate the slope, and then substitute one of the points into the equation.
Let's choose points X and Y.
Slope of line XY:
m = (y2 - y1) / (x2 - x1)
m = (5 - 4) / (0 - (-1))
m = 1 / 1
m = 1
Using point Y(0,5), we can substitute the values into the point-slope form:
y - y1 = m(x - x1)
y - 5 = 1(x - 0)
y - 5 = x
We can simplify this equation to slope-intercept form, which is:
y = mx + b
where:
- m is the slope, which we already found to be 1, and
- b is the y-intercept.
To find the y-intercept, we can substitute any of the given points into the slope-intercept form. Let's use point Y again:
y = mx + b
5 = 1(0) + b
b = 5
So the equation of the straight line that passes through points X(-1,4), Y(0,5), and Z(1,6) is:
y = x + 5
y - y1 = m(x - x1)
where:
- m is the slope of the line, and
- (x1, y1) is any point on the line.
We can use any two of the given points to calculate the slope, and then substitute one of the points into the equation.
Let's choose points X and Y.
Slope of line XY:
m = (y2 - y1) / (x2 - x1)
m = (5 - 4) / (0 - (-1))
m = 1 / 1
m = 1
Using point Y(0,5), we can substitute the values into the point-slope form:
y - y1 = m(x - x1)
y - 5 = 1(x - 0)
y - 5 = x
We can simplify this equation to slope-intercept form, which is:
y = mx + b
where:
- m is the slope, which we already found to be 1, and
- b is the y-intercept.
To find the y-intercept, we can substitute any of the given points into the slope-intercept form. Let's use point Y again:
y = mx + b
5 = 1(0) + b
b = 5
So the equation of the straight line that passes through points X(-1,4), Y(0,5), and Z(1,6) is:
y = x + 5
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