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1 year ago

For what value of x is line m parallel to line n?

Mathematics

1 answer:

kogti [31]1 year ago

3 0

Answer:

$x=10$

Step-by-step explanation:

Here, we can use an angle rule.

We see that angles $(8x+50)$ ° and 130° are under a sort of F shape, where lines m and n are the horizontal parts of the letter and where the diagonal line is the vertical part of the letter.

This means we can use the rule:

Corresponding angles are equal.

This means that:

$8x + 50 = 130$

We can now use this equation we have formed to solve for $x$ :

$8x + 50 = 130\\8x = 80\\x = 10$

Therefore, our final answer is $x=10$ .

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1 year ago

Choose the option that best answers the question.The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle. If Angl

Sunny_sXe [5.5K]

Answer:

The correct option is 1.

Step-by-step explanation:

Given information: The coordinates of a right angled triangle ABC are A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6). Angle ABC = 90°.

It means AB and BC are legs of the right angled triangle ABC.

Side AB lies on the y-axis because the x-coordinate of both A and B is 0.

Two legs are perpendicular to each other. So, BC must be parallel to x-axis and the y-coordinate of both B and C is must be same.

$4a-5=2a+6$

$4a-2a=5+6$

$2a=11$

Divide both sides by 2.

$a=\frac{11}{2}$

The value of a is 2. So the coordinates of triangle ABC are

$B(0,4a-5)=B(0,4(\frac{11}{2})-5)\Rightarrow B(0,17)$

$C(2a+1,2a+6)=C(2(\frac{11}{2})+1,2(\frac{11}{2})+6)\Rightarrow C(12,17)$

The area of a triangle is

$Area=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

The area of triangle ABC is

$Area=\frac{1}{2}|0(17-17)+0(17-0)+12(0-17)|$

$Area=\frac{1}{2}|12(-17)|$

$Area=\frac{1}{2}|-204|$

$Area=\frac{1}{2}(204)$

$Area=102$

The area of triangle ABC is 102. Therefore the correct option is 1.

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3 years ago

What is the minimum number of bits required to store each binary string of length 50? (b) what is the minimum number of bits req

antiseptic1488 [7]

In order to answer the above question, you should know the general rule to solve these questions.
The general rule states that there are 2ⁿ subsets of a set with n number of elements and we can use the logarithmic function to get the required number of bits.
That is:
log₂(2ⁿ) = n number of bits

a). What is the minimum number of bits required to store each binary string of length 50?

Answer: In this situation, we have n = 50. Therefore, 2⁵⁰ binary strings of length 50 are there and so it would require:

log₂(2⁵⁰) = 50 bits.

b). what is the minimum number of bits required to store each number with 9 base of ten digits?

Answer: In this situation, we have n = 50. Therefore, 10⁹ numbers with 9 base ten digits are there and so it would require:

log2(109)= 29.89
 = 30 bits. (rounded to the nearest whole #)

c). what is the minimum number of bits required to store each length 10 fixed-density binary string with 4 ones?

Answer: There is (10,4) length 10 fixed density binary strings with 4 ones and
so it would require:
log₂(10,4)=log₂(210) = 7.7
= 8 bits. (rounded to the nearest whole #)

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2 years ago