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uranmaximum [27]

3 years ago

12

Avril invested 60,000 in a partnership with Lane, Jules, Ray, Ravi, and Petra. The total investment of all partners was $320,000

. What percent of the business does avril own?

1 answer:

8090 [49]3 years ago

8 0

Answer:

$Percentage\ of\ Avril=18.75\%$

Step-by-step explanation:

Concept Used: Percentage: $x\ amount\ of\ y.\ Percentage=\frac{x}{y}\times 100$

$Total\ investment=\$320000\\\\Avril's\ Investment=\$60000\\\\Percentage\ of\ Avril=\frac{Avril's\ investment}{Total\ investment}\times 100\\\\Percentage\ of\ Avril=\frac{60000}{320000}\times 100\\\\Percentage\ of\ Avril=\frac{60000}{3200}\\\\Percentage\ of\ Avril=18.75\%$

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Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha

Nookie1986 [14]

Answer:

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ . The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

If we know that $(3, -30)$ , $(-2, 0)$ and $(18, 0)$ are part of the parabola, the following linear system of equations is formed:

$9\cdot a +3\cdot b + c = -30$

$4\cdot a -2\cdot b +c = 0$

$324\cdot a +18\cdot b + c = 0$

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

$a = \frac{2}{5}$ , $b = -\frac{32}{5}$ , $c = -\frac{72}{5}$ .

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ .

Now, we calculate the average rate of change ( $r$ ), dimensionless, between $x = -2$ and $x = 8$ by using the formula of secant line slope:

$r = \frac{y(8)-y(-2)}{8-(-2)}$

$r = \frac{y(8)-y(-2)}{10}$

$x = -2$

$y = \frac{2}{5}\cdot (-2)^{2}-\frac{32}{5}\cdot (-2)-\frac{72}{5}$

$y(-2) = 0$

$x = 8$

$y = \frac{2}{5}\cdot (8)^{2}-\frac{32}{5}\cdot (8)-\frac{72}{5}$

$y(8) = -40$

$r = \frac{-40-0}{10}$

$r = -4$

The average rate of change of the parabola is -4.

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3 years ago

Dan says that all quadrilaterals are parallelograms. Tom says that it is not true. Explain who is correct??

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Tom is correct, and Dan is wrong. A quadrilateral is a closed figure with four sides, for example, like a kite. A parallelogram is a four sided rectangular figure with opposite sides that are parallel.

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2 years ago

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What is this answer?

zhuklara [117]

Answer:

B is the correct answer

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3 years ago

If the ratio of the length of segment AC to the length of segment CB is 3:1, what is the y-coordinate of point C?

Yuki888 [10]

Answer:

The coordinates of point C are (8,8.5)

Step-by-step explanation:

The picture of the question in the attached figure

Let

$(C_x,C_y)$ ----> coordinates of point C

we have that

The horizontal distance AB is equal to

$AB_x=10-2=8\ units$

The vertical distance AB is equal to

$AB_y=10-4=6\ units$

Find the horizontal coordinate of point C

we know that

$\frac{AC}{CB}=\frac{3}{1}$

so

$\frac{AC_x}{CB_x}=\frac{3}{1}$

$AC_x=3CB_x$ ----> equation A

$AC_x+CB_x=8$ ----> equation B

substitute equation A in equation B

$3CB_x+CB_x=8$

$4CB_x=8\\CB_x=2$

$AC_x=3(2)=6$

so

The x-coordinate of point C is equal to the x-coordinate of point A plus the horizontal distance between the point A and point C

$C_x=A_x+AC_x=2+6=8$

Find the vertical coordinate of point C

we know that

$\frac{AC}{CB}=\frac{3}{1}$

so

$\frac{AC_y}{CB_y}=\frac{3}{1}$

$AC_y=3CB_y$ ----> equation A

$AC_y+CB_y=6$ ----> equation B

substitute equation A in equation B

$3CB_y+CB_y=6$

$4CB_y=6\\CB_y=1.5$

$AC_y=3(1.5)=4.5$

so

The y-coordinate of point C is equal to the y-coordinate of point A plus the vertical distance between the point A and point C

$C_y=A_y+AC_y=4+4.5=8.5$

therefore

The coordinates of point C are (8,8.5)

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3 years ago