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erma4kov [3.2K]
2 years ago
6

Which statement correctly describes the relationship between the graph of f(x)g(x) and g(x)=f(x−7)?

Mathematics
2 answers:
Talja [164]2 years ago
8 0

Answer:

The graph of g(x) is the graph of ​f(x)​ translated 7 units right.

Step-by-step explanation:

Given : Two graph f(x) and g(x)=f(x-7)

To find : The relationship between f(x) and g(x)

Solution : In the graph g(x) the function f(x) changes with 7 unit

As we know, if the value b is subtract from x then there is a right shift in the graph

f(x)→f(x-a)⇒ there is a right shift with b unit.

⇒ In graph g(x), b=7

So there is right shift in graph with 7 unit.

Therefore,The graph of g(x) is the graph of ​f(x)​ translated 7 units right.

Lelu [443]2 years ago
4 0
G(x) would have to be -->7 units.
The relationship between f(x) and s(x) where s(x)=af(x-b)+z is that g(x) is f(x) stretched by the reciprocal of a, b is the liar (all x values go up if b goes down and visa versa), and it moves up z units. 
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Find the point (x,y) of x2+14xy+49y2=100 that is closest to the origin and lies in the first quadrant.
Gala2k [10]

Notice that

x^2+14xy+49y^2=(x+7y)^2

so the constraint is a set of two lines,

(x+7y)^2=100\implies\begin{cases}x+7y=10\\x+7y=10\end{cases}

and only the first line passes through the first quadrant.

The distance between any point (x,y) in the plane is \sqrt{x^2+y^2}, but we know that \sqrt{f(x,y)} and f(x,y) share the same critical points, so we need only worry about minimizing x^2+y^2. The Lagrangian for this problem is then

L(x,y,\lambda)=x^2+y^2+\lambda(x+7y-10)

with partial derivatives (set equal to 0)

L_x=2x+\lambda=0

L_y=2y+7\lambda=0

L_\lambda=x+7y-10=0

We have

L_y-7L_x=2y-14x=0\implies y=7x

which tells us that

x+7y-10=0\iff x+49x=10\implies x=\dfrac15\implies y=\dfrac75

so that \left(\dfrac15,\dfrac75\right) is a critical point. The Hessian for the target function x^2+y^2 is

H(x,y)=\begin{bmatrix}2&0\\0&2\end{bmatrix}

which is positive definite for all x,y, so the critical point is the site of a minimum. The minimum distance itself (which we don't seem to care about for this problem, but we might as well state it) is \sqrt{\left(\dfrac15\right)^2+\left(\dfrac75\right)^2}=2.

3 0
2 years ago
Which test point holds true for y − 2x ≤ 1?
CaHeK987 [17]
So in order to find the correct answer, we can just easily plug in the values to check which ordered pair matches the given inequality above. So based on my solutions, the correct answer would be the last pair. 
<span> y − 2x ≤ 1
0 - 2(5)</span> ≤ 1
0-10  ≤ 1
-10  ≤ 1
Hope this answer helps.
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2 years ago
The function f(x) = –(x – 20)(x – 100) represents a company’s monthly profit as a function of x, the number of purchase orders r
ad-work [718]
The correct answer is choice A. 20
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2 years ago
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The perimeter of triangle ABC is 82 inches. The triangle is rotated about a line that passes through points B and D.
Musya8 [376]

Answer:

A cone with base radius of 17 in

Step-by-step explanation:

Given

Triangle ABC

Where

AB = BC = 24in

D = Midpoint of AC

Required

Which best describes the resulting three-dimensional figure?

First, the length of the third side of the triangle has to be calculated

The sides of triangle ABC are AB, AC and BC

Given that the perimeter = 82 in

AB + AC + BC = 82

Recall that AB = BC = 24in; The equation becomes

24 + AC + 24 = 82

Collect like terms

AC = 82 - 24 - 24\\AC = 34

Given that, the triangle is rotated at D, the midpoint of AC

The length of the midpoint has to be calculated

D = \frac{1}{2}AC

D = \frac{1}{2} * 34

D = \frac{34}{2}

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At this point, we can dismiss options C and D.

This is because; a triangular pyramid is formed by more than 1 triangles (at least 3 triangle) and in this case, we're dealing with only 1 triangle.

So, we have option A and B to select from.

When the triangle is rotated at point D, it generates a cone such that the radius of the cone is the distance at point D.

This implies that, a cone with base radius D is generated.

Recall that D = 17.

Hence, <em>A cone with base radius of 17 in</em>

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Assemble the proof by dragging tiles to the statements and reasons columns
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Answer:

Here, I did the assignment. I wish you good luck!

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