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3 years ago

Parallelogram Problem

Mathematics

1 answer:

NemiM [27]3 years ago

8 0

Answer:

x=6, AB=13, y=10, AD=13, P=46

Step-by-step explanation:

3x-5=x+7

2x=12

x=6

AB: 3(6)-5= 13

2y-7=y+3

y=10

AD: 10+3=13

Perimeter= 13+13+10+10=46

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Lin runs 12 laps around a track in 15 minutes.

nalin [4]

Answer:

1.25

Step-by-step explanation:

15/12

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3 years ago

imagine you live only one mile from work and you decide to walk. If you walk four miles per hour how long will it take you to wa

GenaCL600 [577]

It takes 15 minutes to walk one mile

3 0

3 years ago

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Six hundred paving stones were examined for cracks, and 15 were found to be cracked. The same 600 stones were then examined for

9966 [12]

Answer: 0.01

Step-by-step explanation:

Let the events are :

C = paving stones found to be cracked.

D = paving stones found to be discolored.

Given : Total stones : T = 600 (i)

C = 15

D= 27

C'∩D'= 564 (ii)

Since C'∩D' = (C∪D)' = T- C∪D (iii)

From (i) , (ii)and (ii) , we have

564 = 600- C∪D

⇒ C∪D=600- 564= 36

Formula : C∩D= C+D- C∪D

Put values , we get

C∩D= 15+27-36=6

Now ,

$P(C\cap D)=\dfrac{C\cap D}{T}=\dfrac{6}{600}=0.01$

The probability that it is both cracked and distorted is 0.01.

4 0

3 years ago

If m∠4 = 35, find m∠2. Explain.

Bad White [126]

Answer:

Option (1)

Step-by-step explanation:

From the picture attached,

Triangle CAB is a right triangle.

Therefore, m∠1 = 90°

Similarly, m∠ACD = 90°

m∠ACD = m∠ACB + m∠BCD = 90°

= m∠3 + m∠4 = 90°

Since m∠4 = 35°,

m∠3 + 35° = 90°

m∠3 = 90° - 35°

= 55°

In the triangle ABC,

m∠ACB + m∠CBA + m∠BAC = 180° [Property of a triangle]

m∠3 + m∠2 + m∠1 = 180°

55° + m∠2 + 90° = 180°

m∠2 + 145° = 180°

m∠2 = 180° - 145°

= 35°

Since, AB║CD and BC is a transverse,

Therefore, m∠2 = m∠4 = 35° [Alternate interior angles]

Option (1) is the correct option.

4 0

3 years ago

A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid.

Tanzania [10]

The total area of pyramid is 113.569 square units

The equation to find the total area of the pyramid is Total area = base area + lateral area.

Solution:

Given, A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6.

The total area of pyramid is given by:

$A=A_{b}+A_{l}$ ---- eqn 1

Where,

$A_{b} \text { is the base area and } A_{l} \text { is the lateral area }$

The area of base is given as:

$A_{b}=\frac{3 \sqrt{3}}{2} l^{2}$

Where "l" is the side of hexagon.

Substituting we get,

$\begin{array}{l}{A_{b}=\frac{3 \sqrt{3}}{2}(4)^{2}} \\\\ {=\frac{3 \sqrt{3}}{2} \times 16=3 \sqrt{3} \times 8} \\\\ {A_{b}=24 \sqrt{3}}\end{array}$

The lateral area is given as:

$A_{l}=3 b h$

Where,

b: base of the triangle

h: height of the triangle

Substituting we get,

$\begin{array}{l}{A_{l}=3 \times(4) \times(6)} \\\\ {A_{l}=72}\end{array}$

Plugging in the values we found in eqn 1 we get,

$A=24 \sqrt{3}+72$

A = 113.569 square units

Summarizing the results:

The total area of pyramid is 113.569 square units approximately

The equation used to find total area of pyramid is Total area = base area + lateral area.

8 0

2 years ago