Answer:
Step-by-step explanation:
This is written in the standard form of a quadratic function:
where:
- ax² → quadratic term
- bx → linear term
- c → constant
You need to convert this to vertex form:
where:
To find the vertex form, you need to find the vertex. For this, use the equation for axis of symmetry, since this line passes through the vertex:
Using your original equation, identify the a, b, and c terms:
Insert the known values into the equation:
Simplify. Two negatives make a positive:
X is equal to 3 (3,y). Insert the value of x into the standard form equation and solve for y:
Simplify using PEMDAS:
The value of y is -6 (3,-6). Insert these values into the vertex form:
Insert the value of a and simplify:
:Done
Answer: original angle = 75°
Its supplement 105°
Its complement = 15°
Step-by-step explanation:
We know that,
- Sum of supplementary angles is 180 degrees.
- Sum of complementary angles is 90 degrees.
Let x be the original angle , then its supplement = 180° - x
its complement = 90° - x
As per given,
180° - x = 7(90° - x)
⇒ 180° - x = 630° - 7x
⇒ 7x- x = 630° -180°
⇒ 6 x = 450°
⇒ x = 75° [divide both sides by 6]
So, original angle = 75°
Its supplement = 180° - 75° = 105°
Its complement = 90° -75° = 15°
Hence, original angle = 75°
Its supplement 105°
Its complement = 15°
An isosceles triangle is a triangle that has one pair of equal sides. The Formula in finding the perimeter of a triangle is PΔ=S₁+S₂+S₃. Since two legs are missing, and the given are the base and perimeter, we will use the formula : S₁+S₂ = PΔ-S₃, where: S₁+S₂ are the legs and <span>S₃ is the base.
Substitute values:
</span><span>S₁+S₂ = 43cm - 7 cm
</span> = 36 cm
since S₁ and S₂ are equal, divide 36cm by 2. Therefore S₁ and <span>S₂ measures 18cm.
Check: </span><span>PΔ=S₁+S₂+S₃
</span><span> = 18cm + 18 cm + 7cm
= 43cm
</span>
Step-by-step explanation:
x -2 -1 2 7
y -6 -6 -2 3
All y are in under root
Answer:19.2
Step-by-step explanation:
