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3 years ago

The difference of three times a number and six is nine.

Mathematics

2 answers:

Dafna11 [192]3 years ago

7 0

Answer:

The number is 3

Step-by-step explanation:

3 times 3 is 9

6 times 3 is 18

the difference between 9 and 18 is 9 therefore the number is 3

jolli1 [7]3 years ago

3 0

Answer = 3..........

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5. An object is accelerating at 10 m/s2. If the mass is doubled, what

drek231 [11]

Answer:

If the net force on an object is doubled, its acceleration will double If the mass of an object is doubled, the acceleration will be halved.

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3 years ago

Kelly earns $23.00 for 4 hours of work. At that rate, how long would she have to work to earn $57.50?

ankoles [38]

Answer:

10 hours

Step-by-step explanation:

5.75x 10= 57.50

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2 years ago

Average of 2721 2557 2999 2278 4339

victus00 [196]

Answer:

Step-by-step explanation:

So we know that the average of numbers is all of the numbers added up and divided by the total amount of numbers.

2721

+ 2557

-------------------

5278

.... AND SO ON.........

=14,894 is all of the number added together!!!

Then we count up the numbers= 5

14,894/5

=2978.8

I hope this helps!!!

7 0

3 years ago

On a hiking trip LaShana notes that she hiked about 12 kilometers every 4 hours. If she continues at this rate' how many kilomet

scoray [572]

Answer:

18 Kilometers

Step-by-step explanation:

If you divide 12 by 4 you get 3, so she is going about 3 kilometers an hour. Add 3 for each hour, and you get 18 kilometers in 6 hours.

8 0

3 years ago

Find x?<br> In 3x - In(x - 4) = ln(2x - 1) +ln3

earnstyle [38]

Answer:

$x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

Step-by-step explanation:

Because $3\, x$ is found in the input to a logarithm function in the original equation, it must be true that $3\, x > 0$ . Therefore, $x > 0$ .

Similarly, because $(x - 4)$ and $(2\, x - 1)$ are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, $x > 4$ .

Let $a$ and $b$ represent two positive numbers (that is: $a > 0$ and $b > 0$ .) The following are two properties of logarithm:

$\displaystyle \ln (a) + \ln(b) = \ln\left(a \cdot b\right)$ .

$\displaystyle \ln (a) - \ln(b) = \ln\left(\frac{a}{b}\right)$ .

Apply these two properties to rewrite the original equation.

Left-hand side of this equation:

$\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}$

Right-hand side of this equation:

$\ln(2\, x- 1) + \ln(3) = \ln\left(3 \left(2\, x - 1\right)\right)$ .

Equate these two expressions:

$\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ .

The natural logarithm function $\ln$ is one-to-one for all positive inputs. Therefore, for the equality $\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ to hold, the two inputs to the logarithm function have to be equal and positive. That is:

$\displaystyle \frac{3\ x}{x - 4} = 3\, (2\, x - 1)$ .

Simplify and solve this equation for $x$ :

$x^2 - 5\, x + 2 = 0$ .

There are two real (but not rational) solutions to this quadratic equation: $\displaystyle \frac{5 + \sqrt{17}}{2}$ and $\displaystyle \frac{5 - \sqrt{17}}{2}$ .

However, the second solution, $\displaystyle \frac{5 - \sqrt{17}}{2}$ , is not suitable. The reason is that if $x = \displaystyle \frac{5 - \sqrt{17}}{2}$ , then $(x - 4)$ , one of the inputs to the logarithm function in the original equation, would be smaller than zero. That is not acceptable because the inputs to logarithm functions should be greater than zero.

The only solution that satisfies the requirements would be $\displaystyle \frac{5 + \sqrt{17}}{2}$ .

Therefore, $x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

7 0

3 years ago