Answer:
(- 5, 0), (3, 4)
Step-by-step explanation:
Given the 2 equations
2y - x = 5 → (1)
x² + y² - 25 = 0 → (2)
Rearrange (1) expressing x in terms of y
x = 2y - 5 → (3)
Substitute x = 2y - 5 into (2)
(2y - 5)² + y² - 25 = 0 ← expand parenthesis and simplify
4y² - 20y + 25 + y² - 25 = 0
5y² - 20y = 0 ← factor out 5y from each term
5y(y - 4) = 0
Equate each factor to zero and solve for y
5y = 0 ⇒ y = 0
y - 4 = 0 ⇒ y = 4
Substitute these values into (3) for corresponding values of x
y = 0 : x = 0 - 5 = - 5 ⇒ (- 5, 0)
y = 4 : x = 8 - 5 = 3 ⇒ (3, 4)
Answer:
A
Step-by-step explanation: add 15+12+7
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Answer:
JLP = 16 degrees.
Step-by-step explanation:
KNP = 90 degrees. KNP is the supplement of NPL which is a right angle
KPN + PNK + PKN = 180 degrees. All triangles have 180 degrees.
- KPN = 44 Given
- PNK = 90 1st step here
- PKN = ?
Find JKN
- 44 + 90 + PKN = 180
- 134 + PKN = 180
- PKN = 180 - 134
- PKN = 46
- JKN = 2*PKN The angle is bisected. PKN = 1/2 JKN
- JKN = 2*46 = 92
J + JKL + L = 180
56 + 92 + L = 180
148 + L = 180
L = 32
1/2 L = JLP
JLP = 16 degrees
Answer:
(x + 3)² + (y - 4)² = 32
Step-by-step explanation:
Since we are given the coordinates of the centre and a point on the circle, we can use distance formula to find the radius.
r = √((1 - (-3))² + (8 - 4)²)
r = √(16 + 16)
r = √32
Now, formula for equation of a circle with centre (h, k) is;
(x - h)² + (y - k)² = r²
Our centre is (-3, 4) with r = √32
Thus;
(x - (-3))² + (y - 4)² = (√32)²
(x + 3)² + (y - 4)² = 32
Obtuse angle= (>90 degrees) Opened wider than a perfect 'L' angle
Right angle= Perfect 'L' angle (90 degrees)
Acute angle= (<90 degrees) Smaller than a perfect 'L' angle
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