9th Grade Math Quiz With Answers

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.

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.

To find the average speed, divide the total distance by the total time:Distance/time =  Speed
300 km / 5 hours = 60 km/h

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.

To find the LCM of 12, 18, and 24, list the prime factorizations of each number:
12 = 22×3
18 = 2×32
24 = 23×3
Take the highest power of each prime factor:
For 2, the highest power is 23.
For 3, the highest power is 32.
Therefore, the LCM is 23×32=8×9=72.

To find the sale price after a 20% discount, calculate 20% of $50:
0.20 × 50 = 10
Subtract this from the original price:
50 - 10 = 40

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.

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.

To solve the equation 4x - 7 = 3(x + 2), first distribute the 3 on the right side, giving 4x - 7 = 3x + 6. Next, subtract 3x from both sides to get x - 7 = 6. Finally, add 7 to both sides to isolate x, resulting in x = 13. Therefore, the value of x that satisfies the equation is 13.

1. Calculate the perimeter:
The perimeter of a rectangle is the total length of all its sides added together.
Formula: Perimeter = 2 * (length + width)
In this case: Perimeter = 2 * (100m + 70m) = 2 * 170m = 340m
2. Determine the number of posts:
A post is needed every 5 meters along the perimeter.
Divide the total perimeter by the distance between each post: 340m / 5m = 68 posts

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

The original area of the garden is 12×8=96 square meters. With the path added, the new area is 96+80=176 square meters.
Let x be the width of the path. The new dimensions of the garden with the path are (12+2x) by (8+2x).
Setting up the equation:
(12+2x)(8+2x)=176
Expanding and solving this equation gives x=1.5 meters.

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.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Among the given options, only y = 3x - 2 is in this form. The other equations are either in standard form (like 2x + 3y = 6 and 4x - 2y = 8) or represent a different type of equation (like x^2 + y^2 = 25, which is a circle equation).