Mathematics : asked on kk042563
 26.07.2020

To the nearest tenth what is the area of the triangle

. 4

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Mathematics
Step-by-step answer
P Answered by Master

A) 19.2 ft^2

B) 28.9 ft^3

Step-by-step explanation:

Thickness = 8 inches

Assuming the triangular prism is made up of an equilateral triangle hence all sides are equal

lets assume the side = 10 inches  

lets assume the thickness as the height of the prism = 8 inches

Assume length of the rectangle(l) = 5 feet

A) The surface area of the sandwich triangular prism

total surface area = bh + 2ls + lb

                             = 10*8 + 2(5*10) + ( 5 * 10 )

                             = 80 + 100 + 50 = 230 inches = 19.2 ft^2

B ) The volume of filing in cubic feet to the nearest tenth

V = \frac{1}{4} h \sqrt{-a^4 +2(ab)^2+2(ac)^2-b^4+2(bc)^2-c^4}  ------- 1

where : a = b = c = 10 inches

h = 8 inches

input the given values into the equation 1 above

V= 346.41 inches ^3  =  28.9 ft^3

 

Mathematics
Step-by-step answer
P Answered by PhD
QUESTION 1: To the nearest tenth, what is the area of a circle whose diameter is 21 inches? Use 3.14 for π. Enter your answer in the box.
 The area of a circle given its diametrom by definition is:
 A = pi * (d / 2) ^ 2
 Substituting the value of the diameter we have and applying 3.14 for the value of pi, we have:
 A = (3.14) * (21/2) ^ 2
 A = 346.185
 Round to the nearest tenth:
 A = 346.2 in ^ 2
 
 The area of a circle whose diameter is 21 inches is:
 A = 346.2 in ^ 2
 QUESTION 2: What is the circumference of a circle with a radius of 5.4 inches?
 Enter your answer as a decimal in the box. Use 3.14 for pi. Round your answer to the nearest tenth.
 By definition, the circumference of a circle is given by:
 C = 2 * pi * r
 Where,
 r : radius of the circumference
 Substituting the values we have:
 C = 2 * (3.14) * (5.4)
 C = 33,912 in
 Round to the nearest tenth:
 C = 33.9 in
 
 The circumference of a circle with a radius of 5.4 inches is:
 C = 33.9 in
 QUESTION 3: A scale model of an ancient Egyptian pyramid is 29 centimeters high, with a base length of 46 centimeters. The height of the real pyramid is 145 meters. What is the base length of the real pyramid? Enter your answer, in simplest form, in the box.
 The first thing we must do in this case is to find the scale factor.
 For this we use the relationship between the heights.
 We have then:
 145 = k * 0.29
 From here, let's clear k:
 k = (145) / (0.29)
 k = 500
 We now apply the scale factor to find the actual length of the base:
 b = k * 0.46
 b = 500 * 0.46
 b = 230 m
 
 The base length of the real pyramid is:
 b = 230 m

 QUESTION 4: Which expression is equivalent to 13 (4-5x-1)?
 For this case what you should do is rewrite the expression:
 13 ((4-1) -5x)
 13 (3-5x)
 Now we apply the commutative property:
 39-65x
  
 An expression that is equivalent to 13 (4-5x-1) is:
 39-65x
Mathematics
Step-by-step answer
P Answered by Master

A) 19.2 ft^2

B) 28.9 ft^3

Step-by-step explanation:

Thickness = 8 inches

Assuming the triangular prism is made up of an equilateral triangle hence all sides are equal

lets assume the side = 10 inches  

lets assume the thickness as the height of the prism = 8 inches

Assume length of the rectangle(l) = 5 feet

A) The surface area of the sandwich triangular prism

total surface area = bh + 2ls + lb

                             = 10*8 + 2(5*10) + ( 5 * 10 )

                             = 80 + 100 + 50 = 230 inches = 19.2 ft^2

B ) The volume of filing in cubic feet to the nearest tenth

V = \frac{1}{4} h \sqrt{-a^4 +2(ab)^2+2(ac)^2-b^4+2(bc)^2-c^4}  ------- 1

where : a = b = c = 10 inches

h = 8 inches

input the given values into the equation 1 above

V= 346.41 inches ^3  =  28.9 ft^3

 

Mathematics
Step-by-step answer
P Answered by PhD
QUESTION 1: To the nearest tenth, what is the area of a circle whose diameter is 21 inches? Use 3.14 for π. Enter your answer in the box.
 The area of a circle given its diametrom by definition is:
 A = pi * (d / 2) ^ 2
 Substituting the value of the diameter we have and applying 3.14 for the value of pi, we have:
 A = (3.14) * (21/2) ^ 2
 A = 346.185
 Round to the nearest tenth:
 A = 346.2 in ^ 2
 
 The area of a circle whose diameter is 21 inches is:
 A = 346.2 in ^ 2
 QUESTION 2: What is the circumference of a circle with a radius of 5.4 inches?
 Enter your answer as a decimal in the box. Use 3.14 for pi. Round your answer to the nearest tenth.
 By definition, the circumference of a circle is given by:
 C = 2 * pi * r
 Where,
 r : radius of the circumference
 Substituting the values we have:
 C = 2 * (3.14) * (5.4)
 C = 33,912 in
 Round to the nearest tenth:
 C = 33.9 in
 
 The circumference of a circle with a radius of 5.4 inches is:
 C = 33.9 in
 QUESTION 3: A scale model of an ancient Egyptian pyramid is 29 centimeters high, with a base length of 46 centimeters. The height of the real pyramid is 145 meters. What is the base length of the real pyramid? Enter your answer, in simplest form, in the box.
 The first thing we must do in this case is to find the scale factor.
 For this we use the relationship between the heights.
 We have then:
 145 = k * 0.29
 From here, let's clear k:
 k = (145) / (0.29)
 k = 500
 We now apply the scale factor to find the actual length of the base:
 b = k * 0.46
 b = 500 * 0.46
 b = 230 m
 
 The base length of the real pyramid is:
 b = 230 m

 QUESTION 4: Which expression is equivalent to 13 (4-5x-1)?
 For this case what you should do is rewrite the expression:
 13 ((4-1) -5x)
 13 (3-5x)
 Now we apply the commutative property:
 39-65x
  
 An expression that is equivalent to 13 (4-5x-1) is:
 39-65x
Health
Step-by-step answer
P Answered by PhD

36.5 cm²

Explanation:

The perimeter of the smaller shape = 20 cm and The area of the smaller shape = 18.6 cm²

The perimeter of the bigger shape = 28 cm

The length and breadth of the smaller shape is increased by a factor of k to produce the larger shape.

If the length of the smaller shape = l and its width = w. The perimeter of the smaller shape = 2(l + w) = 20

Since The length and breadth of the smaller shape is increased by a factor of k to produce the larger shape, the length of the larger shape = kl and its width = kw. Therefore  the perimeter of the larger shape = 2(kl + kw) = 2k (l + w) = 28 cm

To find k, divide the perimeter of the larger shape by the perimeter of the larger shape:

\frac{2k(l+w)}{2(l+w)} =\frac{28}{20} \\k=1.4

The area of the smaller shape = l * w = 18.6 cm²

The area of the larger shape = kl * kw = k² * l * w = 1.4² * 18.6 cm² = 36.5 cm²

Health
Step-by-step answer
P Answered by PhD

36.5 cm²

Explanation:

The perimeter of the smaller shape = 20 cm and The area of the smaller shape = 18.6 cm²

The perimeter of the bigger shape = 28 cm

The length and breadth of the smaller shape is increased by a factor of k to produce the larger shape.

If the length of the smaller shape = l and its width = w. The perimeter of the smaller shape = 2(l + w) = 20

Since The length and breadth of the smaller shape is increased by a factor of k to produce the larger shape, the length of the larger shape = kl and its width = kw. Therefore  the perimeter of the larger shape = 2(kl + kw) = 2k (l + w) = 28 cm

To find k, divide the perimeter of the larger shape by the perimeter of the larger shape:

\frac{2k(l+w)}{2(l+w)} =\frac{28}{20} \\k=1.4

The area of the smaller shape = l * w = 18.6 cm²

The area of the larger shape = kl * kw = k² * l * w = 1.4² * 18.6 cm² = 36.5 cm²

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