Answer:
C.7, -2
Step-by-step explanation:
A quadratic equation is a polynomial of degree two. A quadratic equation is in the form:
ax² + bx + c = 0; where a, b, c are constants.
Quadratic equation can be solved using different methods, such as completing the square method, quadratic formula.
Solving the equation 2x² - 10x - 20 = 8 using completing the square:
2x² - 10x - 20 = 8
2x² - 10x = 28
Divide through by 2, to make the coefficient of x² to be 1:
x² - 5x = 14
Add to both sides, the square of half of the coefficient of x [i.e. (-5/2)² = 6.25]
x² - 5x + 6.25 = 14 + 6.25
(x - 2.5)² = 20.25
taking square root of both sides:
x - 2.5 = √20.25
x - 2.5 = ±4.5
x = 2.5 ± 4.5
x = 2.5 + 4.5; or x = 2.5 - 4.5
x = 7 or x = -2
Answer:
rigid motion preserves the original shape and size of the figure—so the new figure after the rigid motion and the old figure before it would be congruent.
Answer:
9-x
Step-by-step explanation:
The difference between x and 3 is x-3.
Now 6 minus x-3:
6-(x-3)=
= 6-x+3
= 9-x
Answer:
x = 4
y = 9
Step-by-step explanation:
It is given that figure (NPQR) is a square. One property of a square is that all sides of a square are congruent. This property also applies to the given square, thus one can make the following statement;
PQ = NR
Substitute,
10y - 29 = 5y + 16
Inverse operations,
10y - 29 = 5y + 16
-5y -5y
5y - 29 = 16
+29 +29
5y = 45
/5 /5
y = 9
Another property of a square is that all of the interior angles of a square have a measure of (90) degrees. Moreover, the diagonals (segment connect non-adjacent vertices) bisect these angles. Thus, twice the measure of an angle formed between a side and a diagonal forms a (90) degree angle. Therefore, one can draw the following conclusion;
2(m<QPR) = 90
Substitute,
2(6x + 21) = 90
Simplify,
12x + 42 = 90
Inverse operations,
12x + 42 = 90
-42 -42
12x = 48
/12 /12
x = 4
Answer:
Step-by-step explanation:
Here are your answers in order.
4
3
1
2
