A plan of a house is drawn to a scale of 2:1000. A room in the house is 6m long. The length of the room on…

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A plan of a house is drawn to a scale of 2:1000. A room in the house is 6m long. The length of the room on the map is: The y-intercept of a line is −5 and the gradient is −3. The equation of the line

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23. A plan of a house is drawn to a scale of 2:1000. A room in the house is 6m long. The length of the room on the map is:

Convert the real length of the room from meters to centimeters.
$6 \text{ m} = 6 \times 100 \text{ cm} = 600 \text{ cm}$
Apply the given scale of 2:1000.
This means 2 units on the map represent 1000 units in real life.
$\frac{\text{Length on map}}{\text{Actual length}} = \frac{2}{1000}$
Substitute the actual length and solve for the length on the map.
$\frac{\text{Length on map}}{600 \text{ cm}} = \frac{2}{1000}$ $\text{Length on map} = \frac{2}{1000} \times 600 \text{ cm}$ $\text{Length on map} = \frac{1200}{1000} \text{ cm}$ $\text{Length on map} = 1.2 \text{ cm}$
The length of the room on the map is 1.2 cm.
The correct option is [B] 1.2cm.

24. The y-intercept of a line is -5 and the gradient is -3. The equation of the line is:
Recall the general equation of a straight line, which is $y = mx + c$ , where $m$ is the gradient and $c$ is the y-intercept.
Substitute the given values for the gradient ( $m = -3$ ) and the y-intercept ( $c = -5$ ) into the equation.
$y = (-3)x + (-5)$ $y = -3x - 5$
The equation of the line is y = -3x - 5.
The correct option is [D] y = -3x - 5.

25. The coordinates of the midpoint of the straight line joining the points $M(4, y)$ and $N(-6, 4)$ is $P(-1, 2)$ . The value of $y$ is:
Recall the midpoint formula for two points $(x_1, y_1)$ and $(x_2, y_2)$ , which is $P\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ .
We are given the points $M(4, y)$ and $N(-6, 4)$ , and the midpoint $P(-1, 2)$ .
We need to find the value of $y$ . We will use the y-coordinate part of the midpoint formula.
$y_P = \frac{y_M + y_N}{2}$
Substitute the given y-coordinates into the formula.
$2 = \frac{y + 4}{2}$
Solve for $y$ .
$2 \times 2 = y + 4$ $4 = y + 4$ $y = 4 - 4$ $y = 0$
The value of $y$ is 0.
The correct option is [D] 0.

26. Given that $\frac{m-n}{x} = y$ , then expressing $n$ in terms of $m, y$ and $x$ gives?
Start with the given equation.
$\frac{m-n}{x} = y$
Multiply both sides by $x$ to eliminate the denominator.
$m-n = xy$
Subtract $m$ from both sides to isolate the term with $n$ .
$-n = xy - m$
Multiply both sides by $-1$ to solve for $n$ .
$n = -(xy - m)$ $n = -xy + m$ $n = m - xy$
Expressing $n$ in terms of $m, y$ and $x$ gives n = m - xy.
The correct option is [C] m - xy.

27. Given that $x + 2y = 5$ and $x - 2y = 8$ . Then the value of $4x$ is:
Write down the given system of equations.
1. $x + 2y = 5$
2. $x - 2y = 8$
Add equation (1) and equation (2) to eliminate $y$ .
$(x + 2y) + (x - 2y) = 5 + 8$ $x + 2y + x - 2y = 13$ $2x = 13$
Solve for $x$ .
$x = \frac{13}{2}$
Calculate the value of $4x$.
$4x = 4 \times \frac{13}{2}$ $4x = 2 \times 13$ $4x = 26$
The value of $4x$ is $\boxed{\text{26}}$ .

Point	x	y
x-intercept	−1.67	0
y-intercept	0	−5

A plan of a house is drawn to a scale of 2:1000. A room in the house is 6m long. The length of the room on the map is: The y-intercept of a line is -5 and the gradient is -3. The equation of the line

Step-by-step solution

Convert the real length of the room from meters to centimeters.

Apply the given scale of 2:1000.

Substitute the actual length and solve for the length on the map.

Recall the general equation of a straight line, which is $y = mx + c$ , where $m$ is the gradient and $c$ is the y-intercept.

Substitute the given values for the gradient ( $m = -3$ ) and the y-intercept ( $c = -5$ ) into the equation.

Recall the midpoint formula for two points $(x_1, y_1)$ and $(x_2, y_2)$ , which is $P\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ .

We are given the points $M(4, y)$ and $N(-6, 4)$ , and the midpoint $P(-1, 2)$ .

Substitute the given y-coordinates into the formula.

Solve for $y$ .

Start with the given equation.

Multiply both sides by $x$ to eliminate the denominator.

Subtract $m$ from both sides to isolate the term with $n$ .

Multiply both sides by $-1$ to solve for $n$ .

Write down the given system of equations.

Add equation (1) and equation (2) to eliminate $y$ .

Solve for $x$ .

Calculate the value of $4x$.

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More Mathematics Questions

A plan of a house is drawn to a scale of 2:1000. A room in the house is 6m long. The length of the room on the map is: The y-intercept of a line is -5 and the gradient is -3. The equation of the line

Step-by-step solution

Convert the real length of the room from meters to centimeters.

Apply the given scale of 2:1000.

Substitute the actual length and solve for the length on the map.

Recall the general equation of a straight line, which is y=mx+cy = mx + cy=mx+c, where mmm is the gradient and ccc is the y-intercept.

Substitute the given values for the gradient (m=−3m = -3m=−3) and the y-intercept (c=−5c = -5c=−5) into the equation.

Recall the midpoint formula for two points (x1,y1)(x_1, y_1)(x1​,y1​) and (x2,y2)(x_2, y_2)(x2​,y2​), which is P(x1+x22,y1+y22)P\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)P(2x1​+x2​​,2y1​+y2​​).

We are given the points M(4,y)M(4, y)M(4,y) and N(−6,4)N(-6, 4)N(−6,4), and the midpoint P(−1,2)P(-1, 2)P(−1,2).