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3 years ago

4x-5y=5 -0.08+0.10y=0.10 How many solution or there to the system of equations?

Mathematics

2 answers:

iVinArrow [24]3 years ago

7 0

An infinate amount of solutions

Inessa [10]3 years ago

6 0

Answer:

A) no solution

Step-by-step explanation:

The given system of equations are:

4x - 5y = 5

-0.08x + 0.10y = 0.10

Let's find the slope of the each equation.

4x - 5y = 5

Write the equation in slope-intercept form y = mx + b.

-5y = -4x + 5

Dividing both sides by -5, we get

y = -4/-5 x +5/-5

y = 0.8x - 1

Here slope = 0.8 and y-intercept (b) = -1

-0.08x + 0.10y = 0.10

0.10y = 0.08x + 0.10

Divide both side by 0.10, we get

y = 0.8x + 1

Here the slope = 0.8 and y-intercept (b) = 1

From the both the equations, the slopes are the same and y-intercepts are different.

Therefore, the given system of equations are parallel.

If the system of equations are parallel, then there is no solution.

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Answer:

The parabolic shape of the door is represented by $y - 32 = -\frac{2}{49}\cdot x^{2}$ . (See attachment included below). Head must 15.652 inches away from the edge of the door.

Step-by-step explanation:

A parabola is represented by the following mathematical expression:

$y - k = C \cdot (x-h)^{2}$

Where:

$h$ - Horizontal component of the vertix, measured in inches.

$k$ - Vertical component of the vertix, measured in inches.

$C$ - Parabola constant, dimensionless. (Where vertix is an absolute maximum when $C < 0$ or an absolute minimum when $C > 0$ )

For the design of the door, the parabola must have an absolute maximum and x-intercepts must exist. The following information is required after considering symmetry:

$V (x,y) = (0, 32)$ (Vertix)

$A (x, y) = (-28, 0)$ (x-Intercept)

$B (x,y) = (28. 0)$ (x-Intercept)

The following equation are constructed from the definition of a parabola:

$0-32 = C \cdot (28 - 0)^{2}$

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The parabolic shape of the door is represented by $y - 32 = -\frac{2}{49}\cdot x^{2}$ . Now, the representation of the equation is included below as attachment.

At x = 0 inches and y = 22 inches, the distance from the edge of the door that head must observed to avoid being hit is:

$y -32 = -\frac{2}{49} \cdot x^{2}$