Question
A triangle is drawn and squares are created from the lengths of each side.
Square A has an area of 25 units² and Square C has an area of 70 units².
What must be the area of the 3rd square for triangle to have a right angle? Click Here for Help Video.
(1 point)
The area of square B is
units².
To find the area of square B, we need to find the length of the side of square B.
We know that the area of square A is 25 units², so the side length of square A would be the square root of 25, which is 5 units.
Similarly, we know that the area of square C is 70 units², so the side length of square C would be the square root of 70.
Now, let's consider the triangle. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (Pythagorean theorem).
So, the square of the side length of square A plus the square of the side length of square B should be equal to the square of the side length of square C.
(5²) + (side length of square B)² = (sqrt(70))²
25 + (side length of square B)² = 70
(side length of square B)² = 70 - 25
(side length of square B)² = 45
Side length of square B = sqrt(45)
Therefore, the area of square B would be (sqrt(45))², which is 45 units².
Determine the missing values that would make this equation have infinite amount of solutions. Click Here for Help Video.
2(6x+7)=3x+▢x+△
(1 point)
▢=
△ =
To have an infinite amount of solutions, the missing values must make the equation equivalent to an identity, where the left side is equal to the right side for all values of x.
First, let's simplify the equation:
2(6x + 7) = 3x + ▢x + △
Distribute 2:
12x + 14 = 3x + ▢x + △
Combine like terms:
12x + 14 = (3 + ▢)x + △
Now, to make the equation an identity, the coefficients of x on both sides of the equation must be equal. This means that 12 must be equal to 3 + ▢.
12 = 3 + ▢
Solving for ▢:
▢ = 12 - 3 = 9
Now that we have determined the value of ▢, we need to find the value of △ that would make the equation an identity. To do this, we compare the constant terms on both sides of the equation:
14 = △
Therefore,
▢ = 9
△ = 14
Question
Determine the missing value that would make this equation have zero solutions. Click Here for Help Video.
2(6x+7)=3x+▢x+14
(1 point)
▢ =
To have zero solutions, the missing value must make the equation inconsistent, where the left side is never equal to the right side for any value of x.
First, let's simplify the equation:
2(6x + 7) = 3x + ▢x + 14
Distribute 2:
12x + 14 = 3x + ▢x + 14
Combine like terms:
12x + 14 = (3 + ▢)x + 14
Now, to make the equation inconsistent, the coefficients of x on both sides of the equation must be different. This means that 12 must not be equal to 3 + ▢.
12 ≠ 3 + ▢
To find the value of ▢ that would make the equation inconsistent, we need to solve for ▢:
▢ = 12 - 3 = 9
Therefore,
▢ = 9