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2 years ago

Find all possible solutions for the following equation x²+7x+63=63

Mathematics

2 answers:

Ugo [173]2 years ago

8 0

Answer:

Step-by-step explanation:

X^2+7x+63=63

<=> x^2+7x=63-63=0

<=> X(x+7)=0

<=> x1=0

X2=-7

iVinArrow [24]2 years ago

4 0

Answer:

0 or -7

Step-by-step explanation:

x² + 7x + 63 = 63

⇔ x² + 7x + 63 - 63 = 0

⇔ x² + 7x = 0

⇔ x(x + 7) = 0

So either: x = 0

or x + 7 = 0 ⇔ x = -7

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It takes a train 60 seconds to completely drive through a bridge of 1260 m, and 90 seconds to completely drive through a tunnel

Olegator [25]

The length of train is 120 meters

The speed of train is 25 meter per second

Solution:

The speed is given by formula:

$speed = \frac{distance}{time}$

Given that,

It takes a train 60 seconds to completely drive through a bridge of 1260 m

And 90 seconds to completely drive through a tunnel of 2010 m

Let the length of the train be "x"

The total distance travelled by the train across the bridge is given by:

total distance = x + 1260 + x = 2x + 1260

[ here we use x + x to represent that train completely drives through bridge ]

The time taken is given as 60 seconds

Therefore, the speed is given as:

$speed = \frac{2x+ 1260}{60}$

The total distance travelled by the train through the tunnel is given by:

total distance = x + 2010 + x = 2x + 2010

The time taken is given as 90 seconds

Therefore, the speed is given as:

$speed = \frac{2x+ 2010}{90}$

The speed of the train was the same in both cases.

Equate both speeds

$\frac{2x+ 1260}{60} = \frac{2x+ 2010}{90}$

$\frac{x+630}{30} = \frac{x+1005}{45}$

$45(x+630) = 30(x+1005)\\\\45x + 28350 = 30x + 30150\\\\45x - 30x = 30150 - 28350\\\\15x = 1800\\\\x = 120$

Thus length of train is 120 meters

Find the speed of train:

$speed = \frac{2x+ 1260}{60}\\\\speed = \frac{2(120) + 1260)}{60}\\\\speed = 25$

Thus speed of train is 25 meter per second

5 0

2 years ago

Find an equation of the line passing through the pair of points. Write the equation in the form Ax +By = C.

Alexxandr [17]

9514 1404 393

Answer:

5x -y = -37

Step-by-step explanation:

One way to find the coefficients A and B is to use the differences of the x- and y-coordinates:

A = Δy = y2 -y1 = 2 -(-3) = 5

B = -Δx = -(x2 -x1) = -(-7 -(-8)) = -1

Then the constant C can be found using either point.

5x -y = 5(-7) -2 = -37

The equation of the line is ...

5x -y = -37

_____

Additional comment

This approach comes from the fact that the slope of a line is the same everywhere.

$\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{\Delta y}{\Delta x}\\\\\Delta x(y-y_1)=\Delta y(x-x_1)\qquad\text{cross multiply}\\\\\Delta y(x-x_1)-\Delta x(y-y_1)=0\qquad\text{subtract y term}\\\\\Delta y(x) -\Delta x(y) = \Delta y(x_1)-\Delta x(y_1)\qquad\text{Ax+By=C form}$