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3 years ago

Write 16 1/2 as an improper fraction

2 answers:

6 0

To write 16 1/2 as an improper fraction, multiply the whole number by the denominator and then add the product to the numerator.

Then place the final answer the denominator.

16 1/2 becomes 33/2.

goldfiish [28.3K]3 years ago

4 0

The improper fraction of 16 1/2 would be 33/2

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Mimi has 16 more bouncy balls than Leah

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Let X: Leah
Answer: X+16

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3 years ago

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Find x? 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

Please help I’ll mark brainliest if correct please explain also

adell [148]

Answer:

2/5

Step-by-step explanation:

5x+6y=11

as we have to find x coordinate

while y coordinate 3/2 is already given in question

so only put value of y coordinate in given equation to get x coordinate value

5x+6y=11

5x+6*(3/2)=11

5x+3*3=11

5x+9=11

5x=11-9

5x=2

x=2/5

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3 years ago

I really need help quick!!:) please!! I will give brainliest to first right answer!!!

kykrilka [37]

Answer:

SA = 41.

Step-by-step explanation:

Add up everything and you get 41 as the SA.

8 0

2 years ago

Can someone help please?

SSSSS [86.1K]

Answer:

B is the correct answer.

Step-by-step explanation:

Pi=3.14

So, 7+3.14=10.14

So yes, B is your correct answer.

Mark brainliest please!

8 0

3 years ago

Read 2 more answers