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AnnZ [28]
3 years ago
10

Find the value of x if A, B, and C are collinear points and B is between A and C.

Mathematics
1 answer:
Andrew [12]3 years ago
7 0

Answer:

x = 6

Option A.

Step-by-step explanation:

We know that

If A, B and C are collineal points, they all pass through a common line.

<--------------14-------------->

A-----------B----------------C

<-----x-----><------x+2---->

Based on the problem and the diagram above,

(x) + (x+2) = 14

(2x+2) = 14

(2x) = 12

(x) = 6

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Answer:

16) y=\frac{1}{4}x +5

17) y = -x - 4

18) y = -2x - 1

19) y = -2x

20)y=\frac{-5}{3} -3

Step-by-step explanation:

With the two points you find the slope using \frac{y_{2}-y_{1}  }{x_{2}-x_{1} }

Then using that slope, plug the slope in with one of the points values of x and y into the point slope formula, and smiplify that into the y-intercept formula.

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3 years ago
Ms. Grant’s car gets between 20 and 22 miles per gallon, inclusive. The gasoline she uses costs between $4.20 and $4.50 per gall
maria [59]

Answer:

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Step-by-step explanation:

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3 years ago
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.

3 0
3 years ago
Hey can someone pls help me asap
vfiekz [6]

Answer:

non-Proportional

Step-by-step explanation:

It doesn't go through the origin (0,0)

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2 years ago
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