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2 years ago

Which is an equation of a direct proportion? CLEAR CHECK y=8x y=12x+4 y=12x y=4x−4

Mathematics

1 answer:

elena-s [515]2 years ago

8 0

Answer:

$y=8x, \\y=12x$

Step-by-step explanation:

Proportional functions can be written as $y=kx$ , where $k$ is some constant of proportional. Since directly proportional functions always pass through the origin, the y-intercept must be 0 (no additional number before or after $x$ term). The only answers that fit this format are:

$\rightarrow \boxed{y=8x}\\\rightarrow \boxed{y=12x}$

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2 years ago

Factor the GCF:

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The greatest common factor (GCF) is the product of the greatest common factors of the numerical coefficients and the variables involving x and y.

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3 years ago

A post is supported by two wires (one on each side going in oppositedirections) creating an angle of 80° between the wires. The

Vladimir [108]

Using the Sine rule,

$\frac{\sin A}{A}=\frac{\sin B}{B}=\frac{\sin C}{C}$ $\begin{gathered} \text{Let A = 14m,} \\ Substituting the variables into the formula,Where the length of the wires are, AP = xm and BP = ym[tex]\begin{gathered} \frac{\sin80^0}{14}=\frac{\sin40^0}{x} \\ \text{Crossmultiply,} \\ x\times\sin 80^0=14\times\sin 40^0 \\ Divide\text{ both sides by }\sin 80^0 \\ x=\frac{14\sin40^0}{\sin80^0} \\ x=9.14m \end{gathered}$

Hence, the length of wire AP (x) is 9.14m.

For wire BP (y)m,

Sum of angles in a triangle is 180 degrees,

$A^0+P^0+B^0=180^0$ $\begin{gathered} \text{Where A}^0=\text{ unknown,} \\ P^0=80^0\text{ and,} \\ B^0=40^0 \\ A^0+80^0+40^0=180^0 \\ A^0+120^0=180^0 \\ A^0=180^0-120^0 \\ A^0=60^0 \end{gathered}$

Using the side rule to find the length of wire BP,

$\begin{gathered} \frac{\sin 60^0}{y}=\frac{\sin 80^0}{14} \\ \text{Crossmultiply,} \\ y\times\sin 80^0=14\times\sin 60^0 \\ \text{Didive both sides by }\sin 80^0 \\ y=\frac{14\times\sin 60^0}{\sin 80^0} \\ y=12.31m \end{gathered}$

Hence, the length of wire BP (y) is 12.31m

Therefore, the length of the wires are (9.14m and 12.31m).

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Kisachek [45]

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Step-by-step explanation:

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3 years ago

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