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Naddik [55]
3 years ago
7

If a car factory checks 320 cars and 12 of them have defects, how many out of 560 will have defects? Use proportions

Mathematics
1 answer:
Viefleur [7K]3 years ago
4 0

Answer:

Total number number of cars which do not have defects = 539

and 21 are defected out of 560 i.e. 560 - 539 = 21

Step-by-step explanation:

Total cars checked by Car factory = 320

Number of defected cars = 12

The number of cars which do not have defects = 320 - 12 = 308

Total Number of cars = 560

So the equation becomes

\left[560\:\times \:308\right]\:\div \:320

⇒  \frac{560\times \:308}{320}

\mathrm{Multiply\:the\:numbers:}\:560\times \:308=172480

⇒  \frac{172480}{320}

\mathrm{Divide\:the\:numbers:}\:\frac{172480}{320}=539

⇒  539

Therefore, total number number of cars which do not have defects = 539

and 21 are defected out of 560 i.e. 560 - 539 = 21

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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
Is 1/2(2p+9)=-p+5 a one solution or infinite solution or no solution​
vitfil [10]

Your inequality has one solution which is p = 1/4

4 0
2 years ago
When y=7.5 x=2 what is the value of y when x is 2 1/4
swat32
<h2>Answer:</h2>

The value of y is 8.4375

<h2>Step-by-step explanation:</h2><h3>Known :</h3>
  • y = 7.5
  • x = 2

<h3>Asked :</h3>
  • The value of y when x is 2.25

<h3>Solution :</h3>

2/7.5 = 2.25/y

Do a cross multiplication,

2/7.5 = 2.25/y

=> 20/75 = 2.25/y

=> 75 . 2.25 = 20y

=> 168.75 = 20y

Reverse the equation,

168.75 = 20y

=> 20y = 168.75

Find the value of y,

20y = 168.75

=> y = 8.4375

<h3>Conclusion :</h3>

y = 8.4375

7 0
2 years ago
If the smallest angle of a triangle is 20° and it is included between sides of 4 and 7, then (to the nearest tenth) the smallest
lawyer [7]

Answer:

3.5

Step-by-step explanation:

The smallest side of a triangle is formed by the smallest angle in the triangle.

To find the side opposite (formed by) the 20 degree angle, we can use the Law of Cosines. The Law of Cosines states that for any triangle, c^2=a^2+b^2-ab\cos \gamma, where a, b, and c are the three sides of the triangle and \gamma is the angle opposite to c.

Let c be the side opposite to the 20 degree angle.

Assign variables:

  • a\implies 4
  • b\implies 7
  • \gamma \implies 20^{\circ}

Substituting these variables, we get:

c^2=4^2+7^2-2(4)(7)\cos 20^{\circ},\\c^2=16+49-56\cos 20^{\circ},\\c^2=12.377213236,\\c=\sqrt{12.377213236}=3.51812638147\approx \boxed{3.5}

Therefore, the shortest side of this triangle is 3.5.

5 0
3 years ago
A regular pentagon has side lengths of 10 cm and an
Fittoniya [83]

Answer: 172 square centimeters.

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Area of a pentagon (A) = 1/2× 5s × a

Where:

s : side of the pentagon

a: apothem

Replacing with the values given and solving for A (area):

A =1/2 x (5 x10) x 6.88

A = 172 square centimeters.

Feel free to ask for more if needed or if you did not understand something.

7 0
2 years ago
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