Question

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.

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.

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.

QUESTION 4: Which expression is equivalent to 13(4−5x−1) ?

Answer 1

346.185 inches square

65.94 inches

230 mts

39-65x

Explanation:

Question 1:

diameter = 21 inches, Hence Radius = 10.5 inches

Area of circle = π r²

= 3.14*10.5*10.5

= 346.185 inches Square

Q2:

Circumference = 2πr

= 2*3.14*10.5

= 65.94 Inches

Question 3:

The scaled pyramid and the original pyramid will be similar to each other and hence the ratio of sides of them will be equal

Hence

`(29)/(46)=(145)/(base)`

`base=(145*46)/(29)`

Base = 230 meters

Question 4 :

13(4-5x-1)

Bringing like terms together in bracket

13(4-1-5x)

13(3-5x)

Applying distributive law

39-65x

Answer

Answer 2

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
Answer:
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
Answer:
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
Answer:
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
Answer:
An expression that is equivalent to 13 (4-5x-1) is:
39-65x