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1 year ago

If 3:y=18:24 find y.

Mathematics

1 answer:

VashaNatasha [74]1 year ago

7 0

y = 4

Explanation: $\begin{gathered} 3\text{ : y = 18 : 24} \\ 3\colon y\text{ = }\frac{3}{y} \\ 18\colon24\text{ = }\frac{18}{24} \end{gathered}$ $\begin{gathered} \frac{3}{y}\text{ = }\frac{18}{24} \\ \text{cross mult}iply\colon \\ 3(24)\text{ = y(18)} \\ \text{divide both sides by 18:} \\ \frac{3(24)}{18}\text{ = }\frac{18y}{18} \end{gathered}$ $\begin{gathered} y\text{ = }\frac{24}{6} \\ y\text{ = 4} \end{gathered}$

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Which of the following is true regarding the sequence graphed below?

Klio2033 [76]

Answer: The correct option is

(D) The sequence is not arithmetic because the terms do not have a common difference.

Step-by-step explanation: We are given to select the true statement regarding the sequence that is graphed in the figure.

From the graph, we see that some of the points are (1, 1), (2, 4), (3, 9), (4, 16), (5, 25).

That is, if we write the graphed points in terms of a sequence <a(n)>, then we get

$a(1)=1,\\\\a(2)=4,\\\\a(3)=9,\\\\a(4)=16,\\\\a(5)=25.$

The sequence <a(n)> will be arithmetic if the difference between the consecutive terms is equal. That is, the terms should have a common difference.

Now,

$a(2)-a(1)=4-1=3,\\\\a(3)-a(2)=9-4=6,\\\\a(4)-a(3)=16-9=7,\\\\a(5)-a(4)=25-16=9.$

This implies that the terms do not have a common difference and so the graphed function does not represent an arithmetic sequence.

Thus, the sequence is not arithmetic because the terms do not have a common difference.

Option (D) is CORRECT.

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3 years ago

What's the inequality for |u|-2<5

Andrew [12]

Answer:

0 ≤ u < 7 and 0 > u > - 7 and combining those two we get - 7 < u < 7.

Step-by-step explanation:

The given inequality is |u| - 2 < 5 ....... (1)

We have to solve this inequality.

Now, from the definition of f(x) = |x| we get, f(x) = x, when x ≥ 0 and

f(x) = -x when x < 0.

Hence, for u ≥ 0, the equation of inequality (1) becomes

u - 2 < 5

⇒ u < 7

Therefore, the solution is 0 ≤ u < 7 (Answer)

Again, for u < 0, the equation of inequality (1) becomes

- u - 2 < 5

⇒ u + 2 > - 5

⇒ u > - 7

Therefore, the solution becomes 0 > u > - 7 (Answer)

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