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3 years ago

What is the value of n

Mathematics

2 answers:

Vladimir79 [104]3 years ago

8 0

<h2>Answer:</h2>

<u>The correct option is</u><u> (D) 69</u>

<h2>Step-by-step explanation:</h2>

n = (interior angle of 131° + interior angle of 160°)

From the figure we can see that

The interior angle of angle 131° = 180 - 131 = 49° because the sun of the two angles must be 180 for a straight line

Similarly

The interior angle of angle 160° = 180 - 160 = 20° because the sun of the two angles must be 180 for a straight line

Now the sum of interior angles of a triangles is 180 so n = 49° + 20° = 69°

Crank3 years ago

7 0

Answer:

The correct answer is option D. 69°

Step-by-step explanation:

Points to remember

1). The sum of angles in a linear pair is 180°

2). In a triangle sum of two angles are equal to the exterior angle of third angle

From the figure we can see a triangle in which two exterior angles area given.

<u>To find the value of n</u>

from figure we get,

n = (interior angle of 131° + interior angle of 160°)

interior angle of 131° = 180 - 131 = 49°

interior angle of 160° = 180 - 160 = 20°

n = 49° + 20° = 69°

Therefore the correct answer is option D. 69°

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Aleksandr [31]

Answer:

a) SPAZ is equilateral.

b) Diagonals SA and PZ are perpendicular to each other.

c) Diagonals SA and PZ bisect each other.

Step-by-step explanation:

At first we form the triangle with the help of a graphing tool and whose result is attached below. It seems to be a paralellogram.

a) If figure is equilateral, then SP = PA = AZ = ZS:

$SP = \sqrt{[4-(-4)]^{2}+[(-2)-(-4)]^{2}}$

$SP \approx 8.246$

$PA = \sqrt{(6-4)^{2}+[6-(-2)]^{2}}$

$PA \approx 8.246$

$AZ =\sqrt{(-2-6)^{2}+(4-6)^{2}}$

$AZ \approx 8.246$

$ZS = \sqrt{[-4-(-2)]^{2}+(-4-4)^{2}}$

$ZS \approx 8.246$

Therefore, SPAZ is equilateral.

b) We use the slope formula to determine the inclination of diagonals SA and PZ:

$m_{SA} = \frac{6-(-4)}{6-(-4)}$

$m_{SA} = 1$

$m_{PZ} = \frac{4-(-2)}{-2-4}$

$m_{PZ} = -1$

Since $m_{SA}\cdot m_{PZ} = -1$ , diagonals SA and PZ are perpendicular to each other.

c) The diagonals bisect each other if and only if both have the same midpoint. Now we proceed to determine the midpoints of each diagonal:

$M_{SA} = \frac{1}{2}\cdot S(x,y) + \frac{1}{2}\cdot A(x,y)$

$M_{SA} = \frac{1}{2}\cdot (-4,-4)+\frac{1}{2}\cdot (6,6)$

$M_{SA} = (-2,-2)+(3,3)$

$M_{SA} = (1,1)$

$M_{PZ} = \frac{1}{2}\cdot P(x,y) + \frac{1}{2}\cdot Z(x,y)$

$M_{PZ} = \frac{1}{2}\cdot (4,-2)+\frac{1}{2}\cdot (-2,4)$

$M_{PZ} = (2,-1)+(-1,2)$

$M_{PZ} = (1,1)$

Then, the diagonals SA and PZ bisect each other.

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2 years ago

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Eva8 [605]

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6 0

3 years ago

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Andreas93 [3]

Answer: 12.5 cm

Step-by-step explanation:

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Firlakuza [10]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Find the least common multiple of 8y^2 and 7m

Flura [38]

Answer: $56y^2m$

which is the same as writing 56y^2m

====================================================

Explanation:

Let's focus on the coefficients 8 and 7 for now.

To find the LCM of those values, list out the multiples. Circle the smallest number that can be found in both sets at the same time.

multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, ...
multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, ....

We see that 56 is the LCM of 7 and 8.

Or you could use this shortcut

LCM = (x*y)/GCF

where x and y are the two numbers. The mention of "GCF" refers to the GCF of x and y. In this case, the GCF is 1 so,

LCM = (x*y)/GCF = (8*7)/1 = 8*7 = 56.

----------------------

Once we determine that, we look at the variable terms now.

The y^2 and m will be tacked onto the 56 to arrive at the final answer 56y^2m

This is because y and m are the unique variables, and we go for the highest exponent of each. It's similar to the LCM formula used earlier.

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2 years ago