Step-by-step explanation:
2x+3=x+x+3
add the X's on the right side together.
2x+3=2x+3
subtract 2x from both sides
3=3
subtract 3 from both sides
0=0
the statement is true for any value of x
Answer:
yes it is correct
Step-by-step explanation:
Answer:
#1 is 30 degrees
#2 is obtuse
#3 is "No rhombuses are rectangles"
#4 is D
#5 is A
Step-by-step explanation:
For #1, we have an angle vertical to 120 degrees which includes a right angle, so we make an equation:
90+x=120
x=30
So angle x is 30 degrees aka. Option A
For #2, obtuse angles have the sum of the square of the side lengths that are less than the square of the hypotenuse. In this case, 6^2+4^2<9^2 or 50<81
For #3, rhombuses have two pairs of congruent sides but no right angles while rectangles have two pairs of congruent sides but they also have right angles.
For #4, they are similar because one of the triangles is dialated by a scale factor of 1.5.
For #5, just think of turning the triangle on its other side, aka. option A
Answer:
y = -4
Step-by-step explanation:
3y - 2(5y - 7) = -9y + 6 (Given)
3y - 10y + 14 = -9y + 6 (Distribute)
-7y + 14 = -9y + 6 (Add like terms)
2y + 14 = 6 (Add 9y on both sides)
2y = -8 (Subtract 14 on both sides)
y = -4 (Divide 2 on both sides)
You can check by substituting the solution for y:
3(-4) - 2(5(-4) - 7) = -9(-4) + 6
-12 - 2(-20 - 7) = 36 + 6
-12 - 2(-27) = 42
-12 + 54 = 42
42 = 42
Answer:
Step-by-step explanation:
"Find the values of x that satisfy 3x - 2x^2 = 7." Please do not use " × " to represent a variable; " × " is an operator, the "multiply" operator.
Rearrange these three terms in descending order by powers of x:
-2x^2 + 3x - 7 = 0. Here the coefficients are a = -2, b = 3 and c = -7, and so the discriminant of this quadratic is b^2-4ac, or 9 - 4(-2)(-7), or 9 - 56, or -47.
Because the discriminant is negative, we'll have two different complex roots here. The quadratic formula becomes
-3 ± i√47 -3 ± i√47
x = ----------------- = -------------------
2(-2) -4
