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Mathematics

1 answer:

Nimfa-mama [501]3 years ago

7 0

Answer:

All angles in a rectangle are congruent, because in a rectangle, all angles are 90 degrees.

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Find the measure of

Ann [662]

Find the measure of O?
Line UV is a supplementary line. Line UV is 180 degrees. Angle TU is 30 degrees. Angle WV is 65 degrees. Angle TW (O) is unknown. Add the given angles. 30+65=95 degrees. Subtract the sum of the two angles from 180 degrees. 180-95=85. O is 85 degrees

7 0

3 years ago

Given: KLMN is a trapezoid m∠N = m∠KML ME ⊥ KN , ME = 3√5 , KE = 8, LM:KN = 3:5 Find: KM, LM, KN, Area of KLMN

lora16 [44]

Q1)Find KM
As ME is perpendicular to KN, ∠KEM is a right angle
Therefore ΔKEM is a right angled triangle
KE is given and and ME is also given, we need to find KM
for this we can use Pythogoras' theorem where the square of hypotenuse is equal to the sum of the squares of the adjacent sides.
KM² = KE² + ME²
KM² = 8² + (3√5)²
= 64 + 9x5
KM = √109
KM = 10.44

Q2)Find LM
It is said that ratio of LM:KN is 3:5
Therefore if we take the length of one unit as x
length of LM is 3x
and the length of KN is 5x
KN is greater than LM by 2 units
If we take the figure ∠K and ∠N are equal.
Since the angles on opposite sides of the bases are equal then this is called an isosceles trapezoid. So if we draw a line from L that cuts KN perpendicularly at D, ΔKEM and ΔLDN are congruent therefore KE = DN
since KN is greater than LM due to KE and DN , the extra 2 units of KN correspond to 16 units
KN = LM + 2x
2x = KE + DN
2x = 8+8
x = 8
LM = 3x = 3*8 = 24

Q3)Find KN
Since ∠K and ∠N are equal, when we take the 2 triangles KEM and LDN, they both have;
same height ME = LD perpendicular distance between the 2 parallel sides
same right angle when the perpendicular lines cut KN
∠K = ∠N
when 2 angles and one side of one triangle is equal to two angles and one side on another triangle then the 2 triangles are congruent according to AAS theorem (AAS). Therefore KE = DN
the distance ED = LM
Therefore KN = KE + ED + DN
since ED = LM = 24
and KE + DN = 16
KN = 16 + 24 = 40
another way is since KN = 5x and x = 8
KN = 5 * 8 = 40

Q4)Find area KLMN
Area of trapezium can be calculated using the following general equation
Area = 1/2 x perpendicular height between parallel lines x (sum of the parallel sides)
where perpendicular height - ME
2 parallel sides are KN and LM
substituting values into the general equation
Area = 1/2 * ME * (KN+ LM)
= 1/2 * 3√5 * (40 + 24)
= 1/2 * 3√5 * 64
= 3 x 2.23 * 32
= 214.66 units²

8 0

2 years ago

Read 2 more answers

3.) Identify all integers.<br> a. 725<br> d. 50<br> e. 10.2<br> C. 806

NeTakaya

Answer:

A, B, C

Step-by-step explanation:

An integer is a whole number (so not a fraction)

8 0

3 years ago

Read 2 more answers

Mr. Harrow has eight boys and six girls in his Honors Pre-calculus class. If he randomly chooses two students, one at a time, wh

Sergeu [11.5K]

Answer: 15/91 which is choice B

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There are two methods to find this answer.

Method 1) We have 6 girls and 8+6 = 14 students. The probability of picking a girl is 6/14 = 3/7. After the first girl is chosen, we have 5 girls left out of 14-1 = 13 students overall. The probability of picking another girl (assuming the first selection was a girl) is 5/13. Multiply these probabilities: (3/7)*(5/13) = (3*5)/(7*13) = 15/91

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Method 2) We can use the nCr combination formula. Order does not matter.

We have nCr = 6 C 2 = 15 ways to pick 2 girls. See the attached image below for the steps (figure 1)

Out of nCr = 14 C 2 = 91 ways to pick 2 students. See the attached image below for the steps (figure 2)

So that's another way to get the answer 15/91.