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2 years ago

Solve for 'x' in the following equation, explaining each step. 3^ (-3x+7) = 3^ (7x-13)

Mathematics

1 answer:

Yanka [14]2 years ago

5 0

Answer:

x = 2

Step-by-step explanation:

In order to have the two sides of the equation be equal, the exponents must equal.

-3x + 7 = 7x - 13

Add 3x to both sides.

7 = 10x - 13

Add 13 to both sides.

20 = 10x

Divide by 10.

2 = x

Check:

3^(-3•2+7)=3^(7•2-13)

3^1 = 3^1

3 = 3

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A train is traveling at a speed of 80 km/h when the conductor applies the brakes. The train slows with a constant acceleration o

hodyreva [135]

Answer:

The train will travel 493.817 meters until it stops completely.

Step-by-step explanation:

In this case, we know that train applies the brakes and decelerates at constant rate until rest is reached after travelling an unknown distance. Travelled distance ( $\Delta s$ ), measured in meters, can be found by using this kinematic formula:

$v^{2} = v_{o}^{2}+2\cdot a \cdot \Delta s$ (Eq. 1)

Where:

$v_{o}$ - Initial speed, measured in meters per second.

$v$ - Final speed, measured in meters per second.

$a$ - Acceleration, measured in meters per square second.

Now travelled distance is cleared within the formula:

$\Delta s = \frac{v^{2}-v_{o}^{2}}{2\cdot a}$

If we know that $v_{o} = 22.222\,\frac{m}{s}$ , $v = 0\,\frac{m}{s}$ and $a = -0.5\,\frac{m}{s^{2}}$ , then the distance travelled by the train is:

$\Delta s = \frac{\left(0\,\frac{m}{s} \right)^{2}-\left(22.222\,\frac{m}{s} \right)^{2}}{2\cdot \left(-0.5\,\frac{m}{s^{2}}\right) }$

$\Delta s = 493.817\,m$

The train will travel 493.817 meters until it stops completely.

3 0

4 years ago

−2x−8y=10

Vilka [71]

Answer:

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4 0

3 years ago

Terra wants wall-to-wall carpeting in her bedroom, which measures 10’ x 12’6”. Carpeting is on sale for $24.99 per sq. yd. What

dlinn [17]

Answer:

$347.08

Step-by-step explanation:

10' x 12'6" = 125 ft^2

one yd^2 = 9 ft^2

125/9 = 13.89 yd^2

13.89 x $24.99 = $347.08

6 0

3 years ago

JUL DEJU ILI<br> Determine the value of y, if x is – 7.<br> y = x2 + 1<br> I need help

Arada [10]

Answer:

y=-13

Step-by-step explanation:

Plugging in -7:

y= (-7)2 + 1

-7 * 2 = -14

So:

y= -14 + 1

-14+1=-13

5 0

3 years ago

A bag contains 4 white, 3 blue, and 3 red marbles. Find the probability of choosing a red marble, then a white marble if the mar

scZoUnD [109]

Answer: 2 / 15

Step-by-step explanation:

3 red / 10 total

4 white / 9 total

3/10 * 4/9 = 12/90 = 2/15

5 0

3 years ago