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zaharov [31]
3 years ago
10

Y and x have a proportional relationship, and y = 15 when x = 3. What is the value of x when y = 4?

Mathematics
1 answer:
Alex73 [517]3 years ago
4 0
X would be 20 because is like sipmle multipulcation by 5 Ex. 3x5=15 like 4x5=20
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F divides HJ in the ratio 3:1. If H = (-11,7) and J = (5,3), what are the<br> coordinates of F?
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Answer:

The coordinates of HF are (1, 4)

Step-by-step explanation:

The parameters of the line are;

The coordinate of the end points are H = (-11, 7), and J = (5, 3)

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The segments in the line are HF, and FJ

Therefore;

The fraction of the length of HJ that is represented by HF = 3/(3 + 1) × HJ = 3/4 × HJ

HF = 3/4 × HJ

Which gives the coordinates of the point F as follows;

Coordinate of F = (-11 +(5 - (-11))×3/4, 7 + (3 - 7)×3/4) =  (1, 4)

The coordinates of F are (1, 4)

We check the length of HF, from the equation for the length to of a line to get;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

l_{HF} = \sqrt{\left (4-7  \right )^{2}+\left (1-(-11)  \right )^{2}} = \sqrt{\left (-3  \right )^{2}+\left (12  \right )^{2}} = 3\cdot \sqrt{17}

Similarly, we check the length of HJ, to get;

l_{HF} = \sqrt{\left (3-7  \right )^{2}+\left (5-(-11)  \right )^{2}} = \sqrt{\left (-4  \right )^{2}+\left (16  \right )^{2}} = 4\cdot \sqrt{17}

The length of HF = 3·√(17)

The length of HJ = 4·√(17)

Therefore, from HF = 3/4× HJ, we have;

HF = 3/4 × 4·√(17) = 3·√(17)

Therefore, the coordinates of HF are (1, 4)

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