Solve the two equations
simultaneously
2x - 3y = 7
4x + 3y = 5
6x = 12, x = 2
Substitute in 2x - 3y = 7
4 - 3y = 7; -3y = 3
y =-1
Distance of point (2,-1) from (4,3)
Distance = $\sqrt{(4 - 2)^2 + (3--1)^2}$
= $\sqrt{4 + 16}$ = $\sqrt20$
= $\sqrt{4\times 5}$ = 2$\sqrt5$
johnmulu answered the question on March 6, 2017 at 09:50
- Evaluate.
$\frac{12.4\times \sqrt2}{(5^2 + 6 )\sqrt{0.125}}$(Solved)
Without using tables evaluate.
$\frac{12.4\times \sqrt2}{(5^2 + 6 )\sqrt{0.125}}$
Date posted: March 6, 2017. Answers (1)
- In a regular polygon with n sides, the interior angle is 150o. How many triangles can the polygon be divided into(Solved)
In a regular polygon with n sides, the interior angle is 150o. How many triangles can the polygon be divided into
Date posted: March 6, 2017. Answers (1)
- Evaluate
$\frac{28 -(-18)}{2}$ - $\frac{15 -(-2)6}{3}$(Solved)
Evaluate
$\frac{28 -(-18)}{2}$ - $\frac{15 -(-2)6}{3}$
Date posted: March 6, 2017. Answers (1)
- A factory assembles computers and normally produces 600 in x days.
i) Write down an expression involving x for the number produced per day(Solved)
A factory assembles computers and normally produces 600 in x days.
i) Write down an expression involving x for the number produced per day
ii) The rate of production is increased so that 600 are now produced in one day less (x -1). Write down an expression involving x for the number produced
iii) If the difference between these daily rates of production is 50, form an equation in x and show that it reduces to x2 - x - 12 = 0
iv) Hence find the number produced per day
Date posted: March 6, 2017. Answers (1)
- A hot water tap can fill a bath in 5 minutes while a cold water tap can fill the same bath in 3 minutes. The drain pipe can empty the full bath in $\frac{4}{15}$.(Solved)
A hot water tap can fill a bath in 5 minutes while a cold water tap can fill the same bath in 3 minutes. The drain pipe can empty the full bath in $\frac{4}{15}$. The two taps and the drain pipe are fully open for 1$\frac{1}{2}$ minutes after which the drain pipe is closed. How long will it take to fill the bath?
Date posted: March 6, 2017. Answers (1)
- A shopkeeper bought 400 spades which he marked a selling price of sh 35 each. He sold 250 spades at this(Solved)
A shopkeeper bought 400 spades which he marked a selling price of sh 35 each. He sold 250 spades at this price, but on the remainder he allowed a discount of 10% off. The ratio of the marked price to the price that the shopkeeper paid for each spade was 5:4, calculate
a) The profit on a spade sold at a discount as percentage of the cost price
b) the total profit on the whole transaction
Date posted: March 6, 2017. Answers (1)
- A map is drawn to a scale of 1: 50 000 on the map, the area of a town is 4 cm2. Calculate the actual area of the town in hectares. (Solved)
A map is drawn to a scale of 1: 50 000 on the map, the area of a town is 4 cm2. Calculate the actual area of the town in hectares.
Date posted: March 6, 2017. Answers (1)
- Simplify the algebraic expression given by -2[-x - 2a - (a - x)](Solved)
Simplify the algebraic expression given by
-2[-x - 2a - (a - x)]
Date posted: March 6, 2017. Answers (1)
- Simplify $\frac{2x^2 – 3xy – 2y^2}{4x^2 – y^2}$(Solved)
Simplify $\frac{2x^2 – 3xy – 2y^2}{4x^2 – y^2}$
Date posted: March 6, 2017. Answers (1)
- Solve the following equation for x
($\frac{5}{6}$)x + 1 = ($\frac{216}{125}$)2x + 3(Solved)
Solve the following equation for x without using tables or calculators
($\frac{5}{6}$)x + 1 = ($\frac{216}{125}$)2x + 3
Date posted: March 6, 2017. Answers (1)
- The largest angle of a triangle exceeds ten times the smallest angle by 10o. The third angle is equal by 60o. Find the size of the largest angle.(Solved)
The largest angle of a triangle exceeds ten times the smallest angle by 10o. The third angle is equal by 60o. Find the size of the largest angle.
Date posted: March 6, 2017. Answers (1)
- Two farm workers Mutua and Musyoka can cultivate a field in 6 days. Mutua alone can complete the cultivation in 15 days. After Mutua and Musyoka had worked for 4 days, Mutua fell sick(Solved)
Two farm workers Mutua and Musyoka can cultivate a field in 6 days. Mutua alone can complete the cultivation in 15 days. After Mutua and Musyoka had worked for 4 days, Mutua fell sick. Find the time taken by Musyoka to complete the cultivation.
Date posted: March 6, 2017. Answers (1)
- Evaluate$\frac{14\div \frac{1}{3} of\; 5\frac{1}{4} - \;\frac{3}{4}\times\;1 \frac{1}{3}}{\frac{3}{5}\times 6\frac{1}{4} + 1\frac{1}{2}}$(Solved)
Without using a calculator evaluate
$\frac{14\div \frac{1}{3} of\; 5\frac{1}{4} - \;\frac{3}{4}\times\; 1\frac{1}{3}}{\frac{3}{5}\times 6\frac{1}{4} + 1\frac{1}{2}}$
Date posted: March 6, 2017. Answers (1)
- A garage owner bought a certain number of litres of petrol for sh 760. If the petrol cost sh x per litre........(Solved)
A garage owner bought a certain number of litres of petrol for sh 760. If the petrol cost sh x per litre
a) write down an expression for the number of litres of petrol he obtained
b) When the price per litre was up by 25 cents he found that he obtained 5 litres fewer for the same sum of money
i) Form an equation in x and show that it reduces to 4x2 + x – 95 = 0
ii) Solve the equation and calculate the price of petrol after the rise
Date posted: March 6, 2017. Answers (1)
- In harambee organized in aid of a school development project, it was decided that each , man present would pay sh 200 and each woman sh 150. There were altogether 400 men and women present. If the harambee raised sh 69 200 in this way(Solved)
In harambee organized in aid of a school development project, it was decided that each , man present would pay sh 200 and each woman sh 150. There were altogether 400 men and women present. If the harambee raised sh 69 200 in this way, Find the number of men present
Date posted: March 6, 2017. Answers (1)
- Two grades of coffee A and grade B costing sh 30 per kg and sh 24 to produce a mixture costing sh 26.40 per kg. Determine the ratio in which grade A and B were mixed (Solved)
Two grades of coffee A and grade B costing sh 30 per kg and sh 24 to produce a mixture costing sh 26.40 per kg. Determine the ratio in which grade A and B were mixed
Date posted: March 6, 2017. Answers (1)
- Use tables of square roots and squares to evaluate to 4 significant figures 4.3462 + $\sqrt{47.32}$(Solved)
Use tables of square roots and squares to evaluate to 4 significant figures
4.3462 + $\sqrt{47.32}$
Date posted: March 6, 2017. Answers (1)
- The lines 3x + 2y – 7 = 0 and ax + 3y + 2 = 0
Are perpendicular(Solved)
The lines 3x + 2y – 7 = 0 and ax + 3y + 2 = 0
Are perpendicular
Date posted: March 6, 2017. Answers (1)
- Simplify the expression:
4x - $\frac{3x + y}{8}$ - $\frac{x – 3y}{4}$
(Solved)
Simplify the expression:
4x - $\frac{3x + y}{8}$ - $\frac{x – 3y}{4}$
Date posted: March 6, 2017. Answers (1)
- The numerator of a fraction is three less than the denominator. When both the numerator and the denominator are increased by 5, the fraction becomes $\frac{5}{6}$. Find the original fraction(Solved)
The numerator of a fraction is three less than the denominator. When both the numerator and the denominator are increased by 5, the fraction becomes $\frac{5}{6}$. Find the original fraction
Date posted: March 6, 2017. Answers (1)