A two digit number is 18 more than the number formed by reversing the digits. If the sum of the digits is 10. Find the number
For the original number,
let the unit digit be x, and the tens digit by y
x+y = 10
the original number has value 10y + x
the reversed number has value 10x + y
10y + x - (10x + y) = 18
9y - 9x = 18
y - x = 2
add this last equation to x+y = 10 to get y, then you can find x
and everything else.
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Solve
A private developer bought this piece of land at a
Price of ksm 400,000 per hectare and later sold the all land at 2.25 million shillings.Determine the price at which he bought the whole piece of land?
We know that the private developer bought the land at a price of 400,000 per hectare. Let's assume that the whole piece of land was x hectares.
So, the price at which he bought the whole piece of land will be:
Total price = Price per hectare x Total hectares
Total price = 400,000 * x
Later, the private developer sold the whole land for 2.25 million shillings.
1 million = 1,000,000
2.25 million = 2.25 x 1,000,000 = 2,250,000
We can set up an equation based on the information given:
Selling price = Total price + Profit
2,250,000 = 400,000 * x + Profit
We can solve for Profit by subtracting the Total price from the Selling price:
Profit = 2,250,000 - 400,000 * x
We can then substitute this expression for Profit into the previous equation:
2,250,000 = 400,000 * x + (2,250,000 - 400,000 * x)
Simplifying the equation:
2,250,000 = 2,250,000
This is a true statement, which means that our assumption that the whole piece of land was x hectares is correct.
So, the private developer bought the whole piece of land at a price of:
Total price = 400,000 * x
Total price = 400,000 * (area of land in hectares)
Total price = 400,000 * (2.25 million / 400,000)
Total price = 2.25 million shillings
Therefore, the private developer bought the whole piece of land at a price of 2.25 million shillings.
A) To find the coordinates of point r where the line l intersects the x-axis, we set y = 0 in the equation:
3y - 2x = -2
3(0) - 2x = -2
-2x = -2
x = 1
So, the point r has coordinates (1,0) since it lies on the x-axis.
B) The given equation is:
3y - 2x = -2
To find the equation of the line l that is perpendicular to l at r, we first need to find the slope of the line l. We can rearrange the given equation to obtain y in terms of x:
3y - 2x = -2
3y = 2x - 2
y = (2/3)x - 2/3
So, the slope of the line l is 2/3.
We know that the line l is perpendicular to the line l at point r. Since the product of slopes of perpendicular lines is -1, the slope of the line l passing through point r is:
m = -1 / (2/3)
m = -3/2
We can use the point-slope form of a linear equation to find the equation of this line:
y - y1 = m(x - x1)
where (x1, y1) is the point (1,0) and m is the slope we just calculated.
y - 0 = (-3/2)(x - 1)
y = (-3/2)x + 3/2
So, the equation of the line l that is perpendicular to l at r is y = (-3/2)x + 3/2.
A) Since line l3 is parallel to l2, it has the same slope as l2. The slope of l2 was found to be (2/3), so the slope of l3 is also (2/3). We can use the point-slope form of a linear equation to find the equation of l3:
y - y1 = m(x - x1)
where (x1, y1) is the point (-4, 1) and m is the slope (2/3).
y - 1 = (2/3)(x + 4)
y = (2/3)x + 19/3
So, the equation of l3 is y = (2/3)x + 19/3.
B) To find the coordinates of point S, at which l1 and l3 intersect, we need to solve the system of equations:
3y - 2x = -2 (equation of l1)
y = (2/3)x + 19/3 (equation of l3)
We can substitute the expression for y from the second equation into the first equation and solve for x:
3(2/3)x + 19/3 - 2x = -2
2x/3 - 6x/3 = -21/3
-4x/3 = -7
x = 21/4
Then we can substitute this value of x into either equation to find y:
y = (2/3)(21/4) + 19/3
y = 37/6
So, the coordinates of point S are (21/4, 37/6).
64
64 is a perfect square and its square root is 8.
A straight line l, whose equation is 3y-2x=-2 meets the x axis at r.Determine the coordinates of r
B) A second line l is perpendicular to l at r.Find the equation of l in the form y = mx+c where m and c are constants.