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3 years ago

Solve The System -5x-5y=0 6x+5y=12

Mathematics

1 answer:

Naddik [55]3 years ago

5 0

9514 1404 393

Answer:

(x, y) = (12, -12)

Step-by-step explanation:

The two equations can be added to solve for x.

(-5x -5y) +(6x +5y) = (0) +(12)

x = 12 . . . . . . . . simplify

-5(12) -5(y) = 0 . . . substitute into the first equation

12 +y = 0 . . . . . . . divide by -5

y = -12 . . . . . . . . subtract 12

The solution is (x, y) = (12, -12).

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3 years ago

Use the drop-down menus to complete each equation so the statement about its solution is true.

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Answer:

Step-by-step explanation:

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3 years ago

the height h(t) of a trianle is increasing at 2.5 cm/min, while it's area A(t) is also increasing at 4.7 cm2/min. at what rate i

nekit [7.7K]

Answer:

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

Step-by-step explanation:

From Geometry we understand that area of triangle is determined by the following expression:

$A = \frac{1}{2}\cdot b\cdot h$ (Eq. 1)

Where:

$A$ - Area of the triangle, measured in square centimeters.

$b$ - Base of the triangle, measured in centimeters.

$h$ - Height of the triangle, measured in centimeters.

By Differential Calculus we deduce an expression for the rate of change of the area in time:

$\frac{dA}{dt} = \frac{1}{2}\cdot \frac{db}{dt}\cdot h + \frac{1}{2}\cdot b \cdot \frac{dh}{dt}$ (Eq. 2)

Where:

$\frac{dA}{dt}$ - Rate of change of area in time, measured in square centimeters per minute.

$\frac{db}{dt}$ - Rate of change of base in time, measured in centimeters per minute.

$\frac{dh}{dt}$ - Rate of change of height in time, measured in centimeters per minute.

Now we clear the rate of change of base in time within (Eq, 2):

$\frac{1}{2}\cdot\frac{db}{dt}\cdot h = \frac{dA}{dt}-\frac{1}{2}\cdot b\cdot \frac{dh}{dt}$

$\frac{db}{dt} = \frac{2}{h}\cdot \frac{dA}{dt} -\frac{b}{h}\cdot \frac{dh}{dt}$ (Eq. 3)

The base of the triangle can be found clearing respective variable within (Eq. 1):

$b = \frac{2\cdot A}{h}$

If we know that $A = 130\,cm^{2}$ , $h = 15\,cm$ , $\frac{dh}{dt} = 2.5\,\frac{cm}{min}$ and $\frac{dA}{dt} = 4.7\,\frac{cm^{2}}{min}$ , the rate of change of the base of the triangle in time is:

$b = \frac{2\cdot (130\,cm^{2})}{15\,cm}$

$b = 17.333\,cm$

$\frac{db}{dt} = \left(\frac{2}{15\,cm}\right)\cdot \left(4.7\,\frac{cm^{2}}{min} \right) -\left(\frac{17.333\,cm}{15\,cm} \right)\cdot \left(2.5\,\frac{cm}{min} \right)$

$\frac{db}{dt} = -2.262\,\frac{cm}{min}$

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

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3 years ago

Using a stopwatch, Tyrone determines it takes him 58. 2 minutes to travel 30 miles to work. The stopwatch measures to hundredths

nekit [7.7K]

The most accurate determination for the number of 45.36 feet per second Tyrone traveled on his way to work.

Given that,

Using a stopwatch Tyrone determines it takes him 58.2 minutes to travel 30 miles to work the stopwatch measures to hundredths of a minute going by the accuracy of the stopwatch.

We have to determine,

Which is the most accurate determination for the number of feet per second Tyrone traveled on his way to work?

According to the question,

Tyrone determines it takes him 58.2 minutes to travel 30 miles to work,

the stopwatch measures to hundredths of a minute going by the accuracy of the stopwatch are determined by,

$\rm Speed = \dfrac{Distance}{Time}$

Substitute the values in the equation,

$\rm Speed = \dfrac{Distance}{Time}\\\\Speed = \dfrac{30}{58.2}\\\\Speed = \dfrac{50}{97} \ miles \ per \ minute$

If 1 mile = 5,280 feet, then his speed is,

$\rm Speed = \dfrac{50}{97} \ miles \ per \ minute\\\\ Speed = \dfrac{50}{97} \times 5280 \\\\ Speed= \dfrac{26,400}{97}\ feet \ per \ minute\\$

And 1 minute = 60 seconds, then his speed is,

$\rm Speed= \dfrac{26,400}{97}\ feet \ per \ minute\\\\ Speed= \dfrac{26,400}{97} \times \dfrac{1}{60} \\\\ Speed = \dfrac{4400}{97} \ feet \ per \ second \\\\ Speed = 45.36 \ feet \ per \ second$

Hence, The most accurate determination for the number of 45.36 feet per second Tyrone traveled on his way to work.

For more details about Equation refer to the link given below.

brainly.com/question/971941

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3 years ago

1. y = 3(x - 4)2 - 2

oksano4ka [1.4K]

Answer:

y = 3x - 12

Step-by-step explanation:

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3 years ago