Answer:
5. TS ≅ ML
6. ∠N≅∠U
9. m∠P = 80°
10. QR = 3
Step-by-step explanation:
The congruent symbol ≅ indicates that the two shapes have the same angle and side lengths.
5. TS are the third and second letter in RSTUV. The third and second letters in KLMNO are ML. TS ≅ ML
6. N is the fourth letter in KLMNO. The fourth letter is RSTUV is U. ∠N≅∠U
9. ∠P is congruent to ∠W. Notice they are both on the longer side and the wider angle. Since m∠P ≅ m∠W, and m∠W = 80°, then m∠P = 80°
10. QR is congruent to XY. They are both the shortest sides of the shape. QR ≅ XY and XY = 3, then QR = 3
Flip over x-axis
down 8 units
Answer:
m∠R is 72°
Step-by-step explanation:
In the given figure
∵ ΔPQR ≅ ΔUVW
→ From congruency
∵ m∠P = m∠U
∵ m∠Q = m∠V
∴ m∠R = m∠W
∵ m∠R = (10x - 18)°
∵ m∠W = 8x°
∵ m∠R = m∠W
→ Equate their measures
∴ 10x - 18 = 8x
→ Add 18 to both sides
∵ 10x - 18 + 18 = 8x + 18
∴ 10x = 8x + 18
→ Subtract 8x from both sides
∴ 10x - 8x = 8x - 8x + 18
∴ 2x = 18
→ Divide both sides by 2 to find x
∴ x = 9
→ Substitute the value of x in the m∠R
∵ m∠R = 10(9) - 18
∴ m∠R = 90 - 18
∴ m∠R = 72°
∴ m∠R is 72°
If it has no real solutions, that means the graph does not intersect the x axis
since we have ax^2+bx+c=0, the parabola opens either up or down
since the vertex is in the second quadrant (x is negative and y is positive in this reigon) and the graph does not cross the x axis, the parabola must open up
if the value of 'a' is positive, then the parabola opens up
so 'a' must be positive
if it is translated to the 4th quadrant, then the vertex is now below the x axis
it will now have 2 x intercepts because the vertex is in the 4th quadrant and look at a graph of a parabola opening up with vertex in 4th quadrant and seehow many time it crosses the x axis
Answer:
2 exponents (2) times 5 exponents (3)
Step-by-step explanation:
To find the prime factors you start by dividing the number by the first prime number which is 2 if there is not a remainder meaning you can divide evenly anymore write down how many 2's you were able to divide by evenly now try dividing by the the next prime factor which is 3 the goal is to get to a quotient of 1
