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AveGali [126]
3 years ago
10

Is (3,2) a solution of -8x-2y<6

Mathematics
2 answers:
erik [133]3 years ago
8 0
-8(3) -2(2) < 6
-24 - (-4) < 6
-28 < 6

-28 is less than 6
UkoKoshka [18]3 years ago
4 0

Answer:

yes

Step-by-step explanation:

to determine if the point is a solution substitute the x and y values into the inequality and check validity

(- 8 × 3 ) - (2 × 2) = - 24 - 4 = - 28 < - 6 ← True

hence (3, 2) is a solution of the inequality


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3 years ago
What is the length of BD?
I am Lyosha [343]

Answer:

10\sqrt{3}

Step-by-step explanation:

<u>Trigonometric Ratios </u>

This problem will be solved by the use of a trigonometric ratio called sine because it relates the opposite side of a given angle with the hypotenuse of the triangle.

Selecting the angle of 60° in triangle ABD:

<em>Sine Ratio </em>

\displaystyle \sin 60^\circ=\frac{\text{opposite leg}}{\text{hypotenuse}}

\displaystyle \sin 60^\circ=\frac{BD}{20}

Solving for BD:

\displaystyle BD=20\sin 60^\circ

Since

\sin 60^\circ=\frac{\sqrt{3}}{2}

\displaystyle BD=20\frac{\sqrt{3}}{2}

Simplifying:

\boxed{\displaystyle BD=10\sqrt{3}}

4 0
2 years ago
The identification code on a bank card consists of 1 digit followed by 2 letters. The code must meet the following conditions: T
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Answer:

For the code we have 3 selections.

The first selection is a digit that must be odd, so the options are {1, 3, 5, 7 ,9}

So we have 5 options.

The second selection is a letter from the set of all the letters (27) minus the set of the vowels (5)

So here we have 27 - 5 = 22 options

The third selection is also a letter from the previous set, but because each letter can be used only one time, and in the previous selection we already selected one of the letters, in this selection we have a letter less than in the previous selection.

Here we have 22 - 1 = 21 options.

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C = 5*22*21 = 2310.

There are 2310 different possible codes

8 0
3 years ago
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