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3 years ago

Are two similar triangles necessarily congruent? Why?

1 answer:

5 0

if their corresponding angles are congruent and the corresponding sides are in proportion ...so it will be similar triangle

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A boy purchased a party-length sandwich 50 in. long. He wants to cut it into three pieces so that the middle piece is 6 in. long

garri49 [273]

The length of shortest piece is 12 inches and length of middle piece is 18 inches and length of longest piece is 20 inches

Solution:

Let, "x" be the shortest piece

The middle piece is 6 in. longer than the shortest piece

Middle piece = 6 + x

The shortest piece is 8 in. shorter than the longest piece

Longest piece = 8 + x

A boy purchased a party-length sandwich 50 in. long

Therefore, total length = 50

Shortest piece + Middle piece + Longest piece = 50

x + 6 + x + 8 + x = 50

14 + 3x = 50

3x = 50 - 14

3x = 36

Divide both the sides by 3

x = 12

Therefore,

shortest piece = 12

middle piece = 6 + x = 6 + 12 = 18

longest piece = 8 + x = 8 + 12 = 20

Thus, length of shortest piece is 12 inches and length of middle piece is 18 inches and length of longest piece is 20 inches

7 0

3 years ago

What is the length of the hypotenuse triangle if both sides are 36

vovikov84 [41]

Answer:

<h3> $\boxed{ \bold{ \huge{ \boxed{ \sf{36 \sqrt{2} \: \: units}}}}}$ </h3>

Step-by-step explanation:

Given,

Perpendicular ( P ) = 36

Base ( b ) = 36

Hypotenuse ( h ) = ?

Finding the hypotenuse  :

Using the Pythagoras theorem :

$\sf{ {h}^{2} = {p}^{2} + {b}^{2} }$

plug the values

⇒ $\sf{ {h}^{2} = {36}^{2} + {36}^{2} }$

Evaluate the power

⇒ $\sf{ {h}^{2} = 1296 + 1296}$

Add the numbers

⇒ $\sf{ {h}^{2} = 2592}$

Squaring on both sides

⇒ $\sf{h = 36 \sqrt{2} }$ units

Hope I helped!

Best regards!!

7 0

3 years ago

A manufacturer of tablets receives its LED screens from three different suppliers, 45% from supplier B1, 30% from supplier B2, a

Shalnov [3]

Answer:

a) 0.83 = 83% probability that a LED screen will meet specifications.

b) 0.2892 = 28.92% probability that a LED screen that meets specifications was sent by the second supplier.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

45% from supplier B1, 30% from supplier B2, and the rest from supplier B3.

So 100 - (45 + 30) = 100 - 75 = 25% from supplier B3.

a) Find the probability that a LED screen will meet specifications.

95% of 45%(supplier B1)

80% of 30%(supplier B2)

65% of 25%(supplier B3). So

$p = 0.95*0.45 + 0.8*0.3 + 0.65*0.25 = 0.83$

0.83 = 83% probability that a LED screen will meet specifications.

b) Calculate the probability that a LED screen that meets specifications was sent by the second supplier.

Conditional probability.

Event A: Meets specifications.

Event B: Sent by second supplier.

0.83 = 83% probability that a LED screen will meet specifications.

This means that $P(A) = 0.83$

Meets specifications and is sent by the second supplier.

80% of 30%, so

$P(A \cap B) = 0.8*0.3 = 0.24$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.24}{0.83} = 0.2892$

0.2892 = 28.92% probability that a LED screen that meets specifications was sent by the second supplier.

7 0

3 years ago

Yesterday, stanley's doughnut shop sold 2/3 as many chocolate doughnuts as cinnamon doughnuts. if they sold 7 1/4 trays of cinna

katovenus [111]

You figure out the amount of chocolate doughnuts sold by multiplying 2/3 by 7 1/4

first you change 7 1/4 to an improper fraction:
7 1/4= 29/4
now multiply 2/3×29/4 by multiplying the two numerators then putting that over the two denominators multiplied: (2×29)/(3×4)=58/12
now simplify:58/12=4 10/12= 4 5/6

the answer is Stanley's doughnut shop sold
4 5/6 trays of chocolate doughnuts

5 0

3 years ago

Find the surface area of each figure. Round to the nearest tenth if necessary.

Lady bird [3.3K]

Answer:

Step-by-step explanation:

Base of triangle = b = 8 cm

Height of triangle = h = 6 cm

Length of rectangle = l = 6 cm

Sides of the triangle : S1 = 6 cm ; S2 = 8 cm and S3 = 10 cm

Surface area of triangular prism= bh + l *(s1+ S2 + S3)

= 8 * 6 + 6*(6+8+10)

= 48 + 6*24

= 48 + 144

= 192 square cm

3 0

3 years ago

Are two similar triangles necessarily congruent? Why?​

Are two similar triangles necessarily congruent? Why?