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.

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 ).

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 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.