Answer:
let n be the number then the sum of this number and 7 is n +7 and 3 times this sum is 3(n +7) 5 times the number less thirteen is 5n − 13
Step-by-step explanation:
Answer:
y = 0.5x
Step-by-step explanation:
Given that x and y vary directly then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition x = 1, y = 0.5, then
k =
=
= 0.5, hence
y = 0.5x ← equation of variation
Answer:
Dimensions = 7 cm by 20 cm.
Step-by-step explanation:
Let the length and width of the rectangle be L & W respectively.
Given the following data;
Area of rectangle = 140 cm²
L = W - 13
To find the dimensions of the rectangle;
The area of rectangle = L * W
Substituting into the above formula, we have;
140 = L * W
140 = (W - 13) * W
140 = W² - 13W
W² - 13W - 140 = 0
Solving the quadratic equation using factorization method;
Factors are -20 and 7
W² - 20W + 7W - 140 = 0
W(W - 20) + 7(W - 20) = 0
(W - 20)(W + 7) = 0
W - 20 = 0
W = 20
W + 7 = 0
W = -7
Thus, W = 20 or -7
But the width has to be positive, W = 20 centimeters.
Next, to find the length of rectangle
L = W - 13
L = 20 - 13
L = 7 centimeters.
Answer:
As the points are collinear, the slope of the line joining
any two points, should be same as the slope of the line joining two other
points.
Slope of the line passing through points (x
1
,y
1
) and (x
2
,y
2
) =
x
2
−x
1
y
2
−y
1
So, slope of the line joining (p,0),(0,q)= Slope of the line joining
(0,q) and (1,1)
0−p
q−0
=
1−0
1−q
−
p
q
=1−q
Dividing both sides by q,
−
p
1
=
q
1
−1
=>
p
1
+
q
1
=1
Answer:213.7
Step-by-step explanation: