9th Grade Math Test With Answers

Explanation
The sequence is decreasing by 3 each time. So, the next three numbers would be obtained by subtracting 3 from the previous number. Therefore, the next three numbers in the sequence are 0, -3, -6.

Explanation
If the dimensions of a rectangle are doubled, the area will increase by a factor of 4.
The original area of the rectangular yard is calculated by multiplying its length and width:
Area = Length × Width = 8m × 6m = 48 square meters.
When both dimensions are doubled (8m × 2 = 16m and 6m × 2 = 12m), the new area will be:
New Area = New Length × New Width = 16m × 12m = 192 square meters.
Comparing the new area to the original area:
192 square meters (new area) / 48 square meters (original area) = 4.
So, when each dimension is doubled, the area becomes 4 times the original area.

Explanation
Let's solve each of these step-by-step:

a). (2/5 + [- (3/7)])

This is equivalent to (2/5 - 3/7).

To add or subtract fractions, you need a common denominator. In this case, it is 35.

(2/5) can be represented as (14/35) and (3/7) can be represented as (15/35).

(14/35 - 15/35 = -1/35)

So, a). (2/5 + [- (3/7)] = -1/35)

b). (- (2/9) + 1/6)

To add or subtract these fractions, you need a common denominator. The least common multiple of 9 and 6 is 18.

(- (2/9)) can be represented as (-4/18) and (1/6) can be represented as (3/18).

(-4/18 + 3/18 = -1/18)

So, b). (- (2/9) + 1/6 = -1/18)

c). (- (2/3) x 1/4)

To multiply these fractions, multiply the numerators together and then multiply the denominators together.

(-2 x 1 = -2)

(3 x 4 = 12)

So, c). (- (2/3) x 1/4 = -2/12)

But, (-2/12) can be simplified to (-1/6).

d). (7/12 ÷ [- (1 3/4)])

First, convert (- (1 3/4)) to an improper fraction:

(- (1 3/4) = - (4 + 3)/4 = -7/4)

Now, to divide by a fraction, you multiply by its reciprocal:

(7/12 ÷ [- (1 3/4)] = 7/12 x -4/7)

(7 x -4 = -28)

(12 x 7 = 84)

So, d). (7/12 ÷ [- (1 3/4)] = -28/84)

But, (-28/84) can be simplified to (-1/3).

In summary:
a) -1/35
b) -1/18
c) -1/6
d) -1/3

Explanation
The value of Pi is commonly represented as 3.14, which is an approximation of the mathematical constant π. It is often used in mathematical calculations involving circles and is widely recognized as the standard value for Pi.

Explanation
The gallon is larger in quantity compared to the liter and ounce. A gallon is a unit of measurement for liquid volume in the imperial system, and it is equivalent to approximately 3.785 liters. On the other hand, an ounce is a smaller unit of measurement, with 1 gallon being equal to 128 ounces. Therefore, the gallon is the largest quantity out of the options given.

Explanation
First, let's find out how many man-days it takes to make one car:
5 men × 5 days = 25 man-days (to make 1 car)
Now, if 10 men are working, they can complete those 25 man-days of work in:
25 man-days ÷ 10 men = 2.5 days (to make 1 car)
For 2 cars, it will take:
2 cars × 2.5 days/car = 5 days
So, 10 men will take 5 days to make 2 cars.

Explanation
The pattern in the given sequence is that each term is double the previous term. Starting with 7, the next term is obtained by multiplying 7 by 2, resulting in 14. Continuing this pattern, the next term is 28. To find the next three terms, we continue doubling the previous term: 28 * 2 = 56, 56 * 2 = 112, and 112 * 2 = 224. Therefore, the next three terms in the sequence are 56, 112, and 224.

Explanation
To calculate the number of posts needed, first find the perimeter of the field:
Perimeter = 2 × (length + width) Perimeter = 2 × (100m + 70m) Perimeter = 2 × 170m Perimeter = 340m
Now, calculate the number of posts needed. Since a post is placed every 5m along the perimeter:
Number of posts = (Perimeter / 5) + 4 (for the corners) Number of posts = (340m / 5) + 4 Number of posts = 68 + 4 Number of posts = 72
So, a total of 72 posts are needed to enclose the field.

Explanation
In this scenario, you have a total of 2+5=7 beads, and you want to arrange them in a circular order (since it's a bracelet). So, the number of different bracelets can be calculated as P(7,7):
P(7,7)=7!/(7−7)!​=7!/0!​=7!
7!=7×6×5×4×3×2×1=5040
Therefore, there are 5040 different bracelets that can be made using 2 red and 5 blue beads.

Explanation
The sum of all angles in a triangle is always 180 degrees. This is a fundamental property of triangles in Euclidean geometry. Regardless of the size or shape of the triangle, the sum of its angles will always be equal to 180 degrees. Therefore, the correct answer is 180 degrees.