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Anuta_ua [19.1K]
3 years ago
6

Which expression represents the algebraic phrase “nine times a number plus thirteen”? A. 9 - y + 13

Mathematics
2 answers:
kirza4 [7]3 years ago
5 0
C. 9y + 13
9y is the same as 9 times y (a variable representing a number), + 13
lesantik [10]3 years ago
4 0

Answer:  The correct option is (C) 9y + 13.

Step-by-step explanation:  We are given to select the expression that represents the following statement :

“nine times a number plus thirteen”

Let the number be represented by y.

Then, nine times the number is written as follows :

9\times y=9y.

Since we are to add 13, so the final expression is given by

E=9y+13.

Thus, the required expression is 9y+13.

Option (C) is CORRECT.

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Naddik [55]

I assume you know about the dot product, and that for two vectors \mathbf a and \mathbf b, the angle between them \theta satisfies

\mathbf a\cdot\mathbf b=\|\mathbf a\|\|\mathbf b\|\cos\theta\iff\cos\theta=\dfrac{\mathbf a\cdot\mathbf b}{\|\mathbf a\|\|\mathbf b\|}

Then the vectors are parallel if the angle between them is 0 or 180 degrees (0 or pi radians), which would make \cos\theta=1 or \cos\theta=-1, respectively.

Part A)

\vec v_1=\langle\sqrt3,1\rangle\implies\|\vec v_1\|=\sqrt{(\sqrt3)^2+1^2}=\sqrt4=2

\vec v_2=\langle-\sqrt3,-1\rangle=-\vec v_1\implies\|\vec v_2\|=\|\vec v_1\|=2

\vec v_1\cdot\vec v_2=(\sqrt3)(-\sqrt3)+(1)(-1)=-4

Then the angle between \vec v_1,\vec v_2 is such that

\cos\theta=\dfrac{-4}{(2)(2)}=-1\implies\theta=\pi\,\mathrm{rad}

so these vectors are parallel ("antiparallel", more specifically, which means they are parallel but point in opposite directions).

Part B) involves the same computations:

\vec u_1=\langle2,3\rangle\implies\|\vec u_1\|=\sqrt{2^2+3^2}=\sqrt{13}

\vec u_2 has the same components but differing by sign and order, as \vec u_1; its magnitude remains the same, though:

\vec u_2=\langle-3,-2\rangle\implies\|\vec u_2\|=\sqrt{(-3)^2+(-2)^2}=\sqrt{13}

\vec u_1\cdot\vec u_2=(2)(-3)+(3)(-2)=-12

\implies\cos\theta=\dfrac{-12}{(\sqrt{13})(\sqrt{13})}=-\dfrac{12}{13}\implies\theta=\cos^{-1}\left(-\dfrac{12}{13}\right)

which is neither 0 nor pi, which means these vectors are not parallel.

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4 years ago
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Answer:

1.  5/6 ≥ 2/3

2. 1/5 ≤ 2/8

3. 9/10 ≥ 6/8

4. I can't see it's out of the pic

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6. 2/5 ≥ 2/6

7. 1/3 ≤ 3/8

8. I can't see it's out of the pic.

9. 8/10 ≥ 3/4

10. 3/8 ≤ 11/12

11. 2/3 ≤ 10/12

12. Can't see :(

13. 3/8 ≤ 7/8

14. 2/4 = 4/8

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16. Can't see

Step-by-step explanation: All you have to do is divide the numerator by the denominator to make it into a decimal. For instance....

5/6 = approximately 0.83

I hope this helps you! It took forever....



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Answer:

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Step-by-step explanation:

480 divided by 15 equals 32.

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