Answer:
i think it is Answer D i am not sure
Step-by-step explanation:
The transformation of a function may involve any change. The function f(x) is vertically stretched and shifted 5 units upwards to form h(x).
<h3>How does the transformation of a function happen?</h3>
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
- Left shift by c units, y=f(x+c) (same output, but c units earlier)
- Right shift by c units, y=f(x-c)(same output, but c units late)
Vertical shift
- Up by d units: y = f(x) + d
- Down by d units: y = f(x) - d
Stretching:
- Vertical stretch by a factor k: y = k \times f(x)
- Horizontal stretch by a factor k: y = f(\dfrac{x}{k})
The function f(x)=x^(1/3) is transformed to form the function of h(x)=(2x)^(1/3)+5. Therefore, the transformation made to the function is,
Vertically stretched by a factor of 2^(1/3) ⇒ 2^(1/3) × x^(1/3) = (2x)^(1/3)
Up by 5 units ⇒ (2x)^(1/3) + 5
Hence, the function f(x) is vertically stretched and shifted 5 units upwards to form h(x).
Learn more about Transforming functions:
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Answer: The angles inside a triangle are called interior angles. ... The three interior angles in a triangle will always add up to 180°. At each corner the exterior and interior angles are on a straight line, so at each corner these two angles add up to 180°.
Step-by-step explanation:
Sal proves that the angles of an equilateral triangle are all congruent (and therefore they all measure 60°), and conversely, that triangles with all congruent angles are equilateral.
Answer:
<em>97.5 sq. ft.</em>
Step-by-step explanation:
Im presuming the question asks to find area of the shaded region.
First of all, the total figure is a rectangle. We can write an expression(in words) for the shaded area.
<em>Shaded Area = Area of Rectangle - Area of Small Triangle(White) - Area of Large Triangle(White)</em>
Now, we find respective areas.
Area of rectangle:
length * width = (5+10) * (12) = 15 * 12 = 180
Area of Small Triangle (white):
A = (1/2) * base * height = (1/2) * 5 * (12-3) = (1/2) * 5 * 9 = 22.5
Area of Large Triangle (white):
A = (1/2) * base * height = (1/2) * 10 * (12) = 60
Now, we find area of shaded region:
<em>Shaded Area = Area of Rectangle - Area of Small Triangle(White) - Area of Large Triangle(White)</em>
<em>Shaded Area = 180 - 22.5 - 60 = 97.5 sq. ft.</em>
No solutions =the linear functions are parallel to eachother
one solution = the linear functions are intersecting lines.
infinite solutions = the linear functions are the same line/function
