Answer:
Step-by-step explanation:
If a point (x, y) is translated by 4 units horizontally right and 1 unit upwards, coordinates of the image point will be,
(x, y) → (x + 4. y + 1)
Therefore, vertices of the image triangle ABC will be,
A(2, 2) → A'(2+4, 2+1)
→ A'(6, 3)
B(5, -1) → B'(5+4, -1+1)
→ B'(9, 0)
C(1, -2) → C'(1+4, -2+1)
→ C'(5, -1)
Then reflected across y-axis.
Rule for the reflection across y-axis will be,
(x, y) → (-x, y)
A'(6, 3) → A"(-6, 3)
B'(9, 0) → B"(-9, 0)
C'(5, -1) → C"(-5, -1)
Answer:
(Opt.B) 18
Step-by-step explanation:
4x = 2y - x (vertically opposite angles are equal)
4x + x = 2y
5x = 2y ----- (1)
4x + 2y + x = 180 (Linear pair angles)
5x + 2y = 180
From (1) we can understand that, the value of 5x and 2y is the same. So,
5x + 5x = 180
10x = 180
x = 180/10
x = 18
Just completing,
Putting the value of x in (1)
5*18 = 2y
90 = 2y
90/2 = y
45 = y
Hope you understand
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Answer:
see the explanation
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
m∠PQS+m∠SQR=m∠PQR ----> equation A (by Addition Angle Postulate)
we have that
m∠PQR=90° ----> equation B given problem (because is a right angle)
substitute equation B in equation A
m∠PQS+m∠SQR=90°
Remember that
Two angles re complementary is their sum is equal to 90 degrees (Definition of complementary angles)
therefore
m∠PQS and m∠SQR are complementary angles
Answer:
50 tickets with a meal and 20 tickets without a meal
Step-by-step explanation:
Create two equations. Group the information based on labels. All the amounts that have $ in it go with one equation and the number of tickets will be in the second equation.
I will let x represent with a meal and y will represent without a meal
35x + 25y = 2250
x + y = 70
I will solve using substitution, so I will solve for y in the second equation. To do this, I will subtract x from both sides.
x - x + y = 70 - x
y = 70 - x
Now I will substitute in for y in the first equation and solve for x.
35x + 25(70 - x) = 2250
35x + 1750 - 25x = 2250
10x + 1750 = 2250
10x + 1750 - 1750 = 2250 - 1750
10x = 500
10x/10 = 500/10
x = 50
Now I will solve for y. I will use the original second equation and substitute 50 in for x.
x + y = 70
50 + y = 70
50 - 50 + y = 70 -50
y = 20
50 tickets with a meal and 20 tickets without a meal
Answer:
Step-by-step explanation:
Use identity : (a + b)² =a² + 2ab + b²
49m⁴ + 140m² + 100 = 7²(m²)² + 2 * 7m² * 10 + 10²
= (7m²)² + 2 *7m²*10 + 10²
= (7m² + 10)²
= (7m² + 10)(7m² + 10)
