Algebra 1 Quiz With Answers: Test Your Knowledge Now

The expression 4^2 represents 4 raised to the power of 2. In mathematical terms, this is referred to as "four squared." When you square a number, you multiply the number by itself.

So, 4^2 is calculated as follows:

4×4=16

Thus, 4^2 equals 16.

To solve for x, you need to isolate x on one side of the equation. Start by subtracting 3 from both sides to eliminate the constant term on the left side:

2x+3−3=11−3

This simplifies to:

2x=8

Next, divide both sides by 2 to solve for 

2x= 8/2

​Resulting in:

x=4

In algebra, a polynomial with two terms is called a binomial. Each term is referred to as a monomial, and a binomial consists of two such monomials. Common examples include expressions like x+y and 3x²−2x. The prefix "bi-" indicates two, aligning with the number of terms.

To find the value of 

𝑥 in the equation 2x−4=0, you can follow these steps:

Add 4 to both sides of the equation to isolate the term with 

x on one side:

2x−4+4=0+4

2x=4

Divide both sides by 2 to solve for 𝑥

2x / 2 = 4/2

x=2

Thus, the value of 

x is 2.

Begin by adding 6 to both sides to remove the constant term from the left side:

3y−6+6=9+6

Simplifying gives:

3y=15

y=15/3

y=5

The given expression involves adding two fractions with a common denominator of 2. When we add 4/2 and 7/2, we get a sum of 11/2. However, 11/2 can be simplified to the mixed number 5 1/2. Therefore, the correct answer is 5 1/2.

The distributive property states that multiplying a number by a sum is the same as multiplying the number by each addend separately and then adding the results. In this case, a(b+c) = ab + ac demonstrates the distributive property, where "a" is distributed to both "b" and "c." The other expressions represent different mathematical properties: B) is the commutative property of addition, C) is the associative property of multiplication, and D) is another form of the distributive property but with subtraction.

To find the value of ( y ) when ( x = -1 ) using the given formula, we can substitute ( x ) into the equation shown on the graph:



[ y = (x-1)^2 + 2 ]



Substituting ( x = -1 ):



[ y = (-1-1)^2 + 2 = (-2)^2 + 2 = 4 + 2 = 6 ]



Therefore, when ( x = -1 ), the value of ( y ) is ( 6 ).

To simplify this expression, distribute the negative sign across the terms in the second polynomial:

x²−3x+2−2x²+5x-4

Combine like terms (terms with the same variable raised to the same power):

(x²−2x²)+(−3x+5x)+(2−4)

This results in:

-x²+2x−2

To find the value of ( a ) using the Pythagorean theorem when ( b = 4 ) and ( c = 5 ), the formula used is:



[ a^2 + b^2 = c^2 ]



Given ( b = 4 ) and ( c = 5 ), substitute these values into the formula:



[ a^2 + 4^2 = 5^2 ]

[ a^2 + 16 = 25 ]



Now, solve for ( a^2 ):



[ a^2 = 25 - 16 ]

[ a^2 = 9 ]



Taking the square root of both sides gives:



[ a = √{9} ]

[ a = 3 ]



Thus, when ( b = 4 ) and ( c = 5 ), the value of ( a ) is ( 3 ).

To find the value of x in the equation, we first distribute the 2 to the terms inside the parentheses: x + 2x + 14 = 14x - 7. Then, we combine like terms: 3x + 14 = 14x - 7. Next, we isolate the variable terms on one side and the constant terms on the other side: 14 + 7 = 14x - 3x. Simplifying further, we have 21 = 11x. Finally, we divide both sides by 11 to solve for x, resulting in x = 21/11. 

Start by isolating the variable q on one side of the equation. To do this, you need to move all terms with q to one side and constants to the other side.

12q - 14q = 2 + 10

-2q = 12

Now, divide both sides by -2 to solve for q:

(-2q) / (-2) = 12 / (-2)

q = -6

So, the value of q is q = -6.