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erastovalidia [21]
2 years ago
14

POSSIBLE POINTS: 5

Mathematics
1 answer:
alexgriva [62]2 years ago
6 0

Answer:

15

Step-by-step explanation:

becayse if you ultipy 5 and three you get 15.

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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
What’s the slope and y - intercept of this equation ?
zavuch27 [327]

Answer:

Slope = -\frac{7}{3}

Y-intercept = 4

Step-by-step explanation:

-> See attached

-> This equation is in slope-intercept form.

         [] When we use y = mx + b, the m is the slope and the b is our y-intercept.

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

5 0
2 years ago
Read 2 more answers
A stockbroker has money in three accounts. The interest rates on the three accounts are 10 % 10%, 11 % 11%, and 12 % 12%. If she
leva [86]

Answer: he invested $200 at 10%, $400 at 11% and $600 at 12%

Step-by-step explanation:

Let x represent the amount invested in the account earning 10% interest.

Let y represent the amount invested in the account earning 11% interest.

Let z represent the amount invested in the account earning 12% interest.

If she has twice as much money invested at 11 % as she does in 10 %, it means that

y = 2x

If she has three times as much at

12 % as she has at 10 %, it means that

z = 3x

The interest from the first account is

x × 0.1 × 1 = 0.1x

The interest from the second account is

y × 0.11 × 1 = 0.11y

The interest from the third account is

z × 0.12 × 1 = 0.12z

If the total interest for the year is $136, it means that

0.1x + 0.11y + 0.12z = 136 - - - - - - - - 1

Substituting y = 2x and z = 3x into equation 1, it becomes

0.1x + 0.11(2x) + 0.12(3x) = 136

0.1x + 0.22x + 0.36x = 136

0.68x = 136

x = 136/0.68 = 200

y = 2x = 2 × 200

y = $400

z = 3x = 3 × 200

z = $600

4 0
3 years ago
The Tigers, a football team, must gain 10 yards in the next four plays to keep possession of the ball . The Tigers lose 12 yards
mestny [16]

No because They lose 12 sand that puts them at -12. Then they gain 5 which puts them at -7 and then they lose 8 which puts them at -15. Please mark as brainliest

5 0
3 years ago
Rationalize the expression. Write it in simplest form.<br><br> 9x/√-2x-11
GenaCL600 [577]
This appears to be just an expression we are simplifying, not an equation we are solving.  I THINK you are saying that the expression looks like this:
\frac{9x}{ \sqrt{-2x-11} }
If you rationalize the denominator, you would get this expression:
\frac{9x}{ \sqrt{-2x-11} } * \frac{ \sqrt{-2x-11} }{ \sqrt{-2x-11} }
which, after simplifying, looks like this:
\frac{9x \sqrt{-2x-11} }{-2x-11}
and that's as simple as I can see that one getting.  You can't factor anything out of the denominator to cancel with the numerator, so I think you're as simple as you can get there!
3 0
3 years ago
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