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Ivahew [28]
3 years ago
8

Solve -3+12-5(2y-7) The solution y is:

Mathematics
1 answer:
jolli1 [7]3 years ago
8 0

Answer:

+12

Step-by-step explanation:

1. distribute the negative 5 to 2y and negative 7

2. combine like term's -3+12-10y+35

3.Get the Y value by itself -44 from both sides -44-2y=

                                                                             -44         -44

4. divide negative 2 from both sides<u> 2y</u>=<u>-44</u>

                                                            -2= -2

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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
12 divided by the sum of h and 2
irinina [24]
Putting this into expression form, it would be: 
12 ÷ (h + 2) 
Hope this helps!
6 0
3 years ago
For which pair of triangles would you use AAS to prove the congruence of the 2 triangles
DerKrebs [107]

Answer:

The correct option is B.

Step-by-step explanation:

According to AAS congruence rule, two triangles are congruent if two angles and a non included side are congruent to corresponding angles and side of another triangle.

We need two angles and a non included side, to use AAS postulate.

In option A, two sides and their inclined angle are congruent, therefore these triangles are congruent by SAS postulate and option A is incorrect.

In option B, two angles and a non included side are congruent, therefore these triangles are congruent by AAS postulate and option B is correct.

In option C, two angles and their included side are congruent, therefore these triangles are congruent by ASA postulate and option C is incorrect.

In option D, all sides are congruent, therefore these triangles are congruent by SSS postulate and option D is incorrect.

8 0
3 years ago
Read 2 more answers
I need help on this math problem ​
Mila [183]

Answer:

x = 2

y = —3

Step-by-step explanation:

3x — 9 = —2x + 1

x = 2

y = —3

8 0
2 years ago
The mass of an adult North Pacific right whale is about 70,000 kg, or 7 x 104
olasank [31]

Answer:

Answer B: 1*10^2 times

Step-by-step explanation:

To find how many times more massive is the whale relative o the polar bear, we just need to find the quotient of one over the other:

\frac{7*10^4}{7*10^2} = \frac{7*10^2*10^2}{7*10^2}=1*10^2 times

Therefore our answer agrees with the one shown as answer B.

6 0
3 years ago
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