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3 years ago

Is -5 a solution to the equation for 6x + 5 = 5x + 8 + 2x? Explain?

Mathematics

1 answer:

grigory [225]3 years ago

8 0

For this case we have the following equation:

$6x + 5 = 5x + 8 + 2x$

We must find the solution.

We add similar terms from the right side of the equation:

$6x + 5 = 7x + 8$

We subtract 5 from both sides of the equation:

$6x = 7x + 8-5\\6x = 7x + 3$

We subtract 7x on both sides of the equation:

$6x-7x = 3$

Different signs are subtracted and the sign of the major is placed:

$-x = 3$

We multiply by -1 on both sides of the equation: $x = -3$

Thus, the solution of the equation is $x = -3$ . -5 is not a solution to the equation.

Answer:

$x = -3$ . -5 is not a solution to the equation

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3 years ago

3. Are these ratios equivalent? 35:28 and 10:8 *

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Reduce each ratio to its minimum expression to find if they are equal.

35:28

$\begin{gathered} \frac{35}{28}=\frac{7\cdot5}{7\cdot4} \\ =\frac{5}{4} \end{gathered}$

10:8

$\begin{gathered} \frac{10}{8}=\frac{2\cdot5}{2\cdot4} \\ =\frac{5}{4} \end{gathered}$

Since both ratios reduce to 5:4, they are equivalent.

Another way to check a:b is equivalent to c:d, is that a*d = b*c

In this case, this will be true if 35 times 8 is equal to 10 times 28:

$\begin{gathered} 35\cdot8=280 \\ 10\cdot28=280 \end{gathered}$

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8 months ago

The standard IQ test has a mean of 97 and a standard deviation of 17. We want to be

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Variances add, so the standard deviations add in quadrature, like the Pythagorean Theorem in n dimensions. This means the standard deviation of the average x is

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We want to be 95% certain

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By the 68-95-99.7 rule, 95% certain means within two standard deviations. That means we're 95% sure that

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Comparing to what we want, that's means we have to solve

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√n = 2 (17/5)

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We better round up.

Answer: We need a sample size of 47 to be 95% certain of being within 5 points of the mean

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