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3 years ago

Look at the system of equations below.

Mathematics

1 answer:

Paul [167]3 years ago

7 0

Answer:

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$x=2,\:y=-1$

Step-by-step explanation:

Considering the system of the equation

$\begin{bmatrix}y=-2x+3\\ 4x-3y=11\end{bmatrix}$

$\mathrm{Subsititute\:}y=-2x+3$

$\begin{bmatrix}4x-3\left(-2x+3\right)=11\end{bmatrix}$

$\mathrm{Isolate}\:x\:\mathrm{for}\:4x-3\left(-2x+3\right)=11$

$4x-3\left(-2x+3\right)=11$

$4x+6x-9=11$

$10x-9=11$

$10x-9+9=11+9$

$10x=20$

$x=2$

$\mathrm{For\:}y=-2x+3$

$\mathrm{Subsititute\:}x=2$

$y=-2\cdot \:2+3$

$y=-1$

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$x=2,\:y=-1$

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A plane flying horizontally at an altitude of "1" mi and a speed of "430" mi/h passes directly over a radar station. Find the ra

Anika [276]

Answer:

The rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station is 372 mi/h.

Step-by-step explanation:

Given information:

A plane flying horizontally at an altitude of "1" mi and a speed of "430" mi/h passes directly over a radar station.

$z=1$

$\frac{dx}{dt}=430$

We need to find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

$y=2$

According to Pythagoras

$hypotenuse^2=base^2+perpendicular^2$

$y^2=x^2+1^2$

$y^2=x^2+1$ .... (1)

Put z=1 and y=2, to find the value of x.

$2^2=x^2+1^2$

$4=x^2+1$

$4-1=x^2$

$3=x^2$

Taking square root both sides.

$\sqrt{3}=x$

Differentiate equation (1) with respect to t.

$2y\frac{dy}{dt}=2x\frac{dx}{dt}+0$

Divide both sides by 2.

$y\frac{dy}{dt}=x\frac{dx}{dt}$

Put $x=\sqrt{3}$ , y=2, $\frac{dx}{dt}=430$ in the above equation.

$2\frac{dy}{dt}=\sqrt{3}(430)$

Divide both sides by 2.

$\frac{dy}{dt}=\frac{\sqrt{3}(430)}{2}$

$\frac{dy}{dt}=372.390923627$

$\frac{dy}{dt}\approx 372$

Therefore the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station is 372 mi/h.

6 0

3 years ago

Youth tickets(y) cost $2 for a ride, while adult tickets(x) cost $3. The amount of money earned is $54. If all the seats were fi

Paha777 [63]

There are no constants here. But we have x and y here.
We will create an equation which is:
2y+3x=54.
But we will also create a second equation which states the number of seats.
x+y=24.

Now we do the two-equation solving method.
2y+3x=54
-2(x+y=24)

2y+3x=54
-2x-2y=-48

x=6

To solve for y, plug in x into one of the original equations. Which one doesn't matter.

y+6=24
y=18

7 0

3 years ago

Find the area of the square

butalik [34]

Answer:

13 units^2

Step-by-step explanation:

one side of the square =

$AD^{2} = 2^{2} +3^{2}$