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3 years ago

Noah is solving an equation, and one of his moves is unacceptable. Here are the moves he made.

Mathematics

1 answer:

faust18 [17]3 years ago

3 0

Answer:

b. When you divide both sides by 2x = 6x it could lead us to think that there is no solution while, in fact, the solution is x = 0.

Step-by-step explanation:

The solution is correct up to the step 2x = 6x

2x = 6x

Subtract 2x from both sides.

0 = 4x

Divide both sides by 4.

x = 0

You cannot divide both sides by x since x could be zero, and in fact, it is.

Answer: b. When you divide both sides by 2x = 6x it could lead us to think that there is no solution while, in fact, the solution is x = 0.

You might be interested in

If the ratio of radius of two spheres is 4:7, the ratio of their volume is?

Kazeer [188]

Answer:

64 : 343

Step-by-step explanation:

First use the radii to find the volume

1) Radius of first sphere is 4 (taken from 4:7 ratio)

Insert it into the equation for volume of a sphere: V=4 /3πr^3

V = (4/3)(π)(4^3)

V = (4/3)(π)(64)

V = 256/3 π

Volume of the first sphere = 256/3 π

2) Radius of the second sphere is 7 (also taken from 4:7 ratio)

Insert it into the equation for volume of a sphere: V=4 /3πr^3

V = (4/3)(π)(7^3)

V = (4/3)(π)(343)

V = 1372/3 π

Volume of the second sphere = 1372/3 π

Next, calculate the ratio by dividing the two numbers

256/3 π ÷ 1372/3 π

Answer should be 64 : 343

The simple way to do this problem is to just cube the numbers:

4:7 becomes 4^3 : 7^3 = 64 : 343

Either way works.

6 0

3 years ago

Which of the following is not a function?

Annette [7]

Answer:

The first option.... The one with the blue dot I guess you have chosen that

8 0

3 years ago

The school band will sell pizzas to raise money for new uniforms. The supplier charges $143 plus $5 per

aev [14]

Answer:

7 x > 4 x + 100

7 x - 4 x > 100

3 x > 100

x > 100 : 3

x > 33.33

Answer: they have to sell 34 pizzas to make a profit.

Step-by-step explanation:

6 0

3 years ago

Calculate the pH of a buffer solution made by mixing 300 mL of 0.2 M acetic acid, CH3COOH, and 200 mL of 0.3 M of its salt sodiu

Lesechka [4]

Answer:

Approximately $4.75$ .

Step-by-step explanation:

Remark: this approach make use of the fact that in the original solution, the concentration of $\rm CH_3COOH$ and $\rm CH_3COO^{-}$ are equal.

${\rm CH_3COOH} \rightleftharpoons {\rm CH_3COO^{-}} + {\rm H^{+}}$

Since $\rm CH_3COONa$ is a salt soluble in water. Once in water, it would readily ionize to give $\rm CH_3COO^{-}$ and $\rm Na^{+}$ ions.

Assume that the $\rm CH_3COOH$ and $\rm CH_3COO^{-}$ ions in this solution did not disintegrate at all. The solution would contain:

$0.3\; \rm L \times 0.2\; \rm mol \cdot L^{-1} = 0.06\; \rm mol$ of $\rm CH_3COOH$ , and

$0.06\; \rm mol$ of $\rm CH_3COO^{-}$ from $0.2\; \rm L \times 0.3\; \rm mol \cdot L^{-1} = 0.06\; \rm mol$ of $\rm CH_3COONa$ .

Accordingly, the concentration of $\rm CH_3COOH$ and $\rm CH_3COO^{-}$ would be:

$\begin{aligned} & c({\rm CH_3COOH}) \\ &= \frac{n({\rm CH_3COOH})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}$ .

$\begin{aligned} & c({\rm CH_3COO^{-}}) \\ &= \frac{n({\rm CH_3COO^{-}})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}$ .

In other words, in this buffer solution, the initial concentration of the weak acid $\rm CH_3COOH$ is the same as that of its conjugate base, $\rm CH_3COO^{-}$ .

Hence, once in equilibrium, the $\rm pH$ of this buffer solution would be the same as the ${\rm pK}_{a}$ of $\rm CH_3COOH$ .

Calculate the ${\rm pK}_{a}$ of $\rm CH_3COOH$ from its ${\rm K}_{a}$ :

$\begin{aligned} & {\rm pH}(\text{solution}) \\ &= {\rm pK}_{a} \\ &= -\log_{10}({\rm K}_{a}) \\ &= -\log_{10} (1.76 \times 10^{-5}) \\ &\approx 4.75\end{aligned}$ .

7 0

3 years ago

How to solve 7(1+4n)+4

mylen [45]

7 + 28n + 4
28n + (7 + 4)
28n + 11

6 0

3 years ago