Answer:
No, these triangles cannot lie on the same line.
Step-by-step explanation:
For two triangles to lie on the same line they must have the same slope.
The slope of the bigger triangle is
and the slope of the smaller triangle is
slopes are negative because the triangles are leaning to the left.
We see that the slopes of the two triangles are not the same; therefore, they cannot lie on the same line.
Correct answer is: F(x)=-x^2-3
Step-by-step explanation:
We are given a function:
The graph of is also shown in the given question figure.
It is a parabola with vertex at (0,0).
Sign of is positive, that is why the parabola opens up.
General equation of parabola is given as:
Here, in G(x), a = 1
Vertex (h,k) is (0,0).
As seen from the question figure,
The graph of F(x) opens down that is why it will have:
Sign of as negative. i.e.
And vertex is at (0,-3)
Putting the values of a and vertex coordinates,
Hence, the equation of parabola will become:
Answer:
<u>108</u>
Step-by-step explanation:
Volume of a Square Pyramid :
- V = 1/3 x Base Area x Height
Solving :
- V = 1/3 x (6)² x 9
- V = 36 x 3
- V = <u>108</u> cubic centimeters
Answer: You will pay $13.52 for this shirt.
Step-by-step explanation: 0.9435
Since the tax is 7.5%, you have to multiply 12.58 by 7.5% to find the amount of money paid as tax.
7.5% = 0.075
12.58 x 0.075 = 0.9435
Since we are dealing with money we have to round to the nearest hundredth -- 0.9435 = 0.94
Then to find the final cost of the shirt, we have to add 12.58 and 0.94 to get $13.52.
Using the dot product:
For any vector x, we have
||x|| = √(x • x)
This means that
||w|| = √(w • w)
… = √((u + z) • (u + z))
… = √((u • u) + (u • z) + (z • u) + (z • z))
… = √(||u||² + 2 (u • z) + ||z||²)
We have
u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37
z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74
u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46
and so
||w|| = √((2√37)² + 2•46 + (√74)²)
… = √(4•37 + 2•46 + 74)
… = √314 ≈ 17.720
Alternatively, without mentioning the dot product,
w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩
and so
||w|| = √((-5)² + 17²) = √314 ≈ 17.720
