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Katarina [22]
3 years ago
11

The graph of g(x) is the graph of f(x)=x+9 reflected across the y-axis.

Mathematics
2 answers:
ICE Princess25 [194]3 years ago
8 0

Answer:

g(x) = -x +9

Step-by-step explanation:

Reflecting across the y-axis involves changing the sign of x, so the reflection of f(x) is ...

... g(x) = f(-x) = (-x) +9

The appropriate choice is ...

... g(x) = -x+9

777dan777 [17]3 years ago
4 0
<h2>Answer:</h2>

The equation which describes the function g is:

               g(x)=-x+9

<h2>Step-by-step explanation:</h2>

The graph of the function f(x) is given by:

                 f(x)=x+9

Now, we know that the transformation of the function f(x) when the graph is shifted across the y-axis then it is given by:

                 f(x) → f(-x)

This means that:

 g(x)=f(-x)

i.e.

g(x)= -x+9

Hence, the equation which will represent the graph of the function g(x) is given by:

                    g(x)=-x+9

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USPshnik [31]

Answer:

sin w = 15/17

Step-by-step explanation:

sin w = opp/hyp

opp of W is VX = 15

hyp is the longest = 17

sin w = 15/17

7 0
3 years ago
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The ratio of the area of the shaded part to the unshaded part is______.
elena-14-01-66 [18.8K]

Answer: 1 : 3

Shaded area:

\Longrightarrow \sf  Length \ \times \  Breadth = \dfrac{x}{4}  \ \times \ x  \ = \ \dfrac{1}{4}x^2

Unshaded area:

\Longrightarrow \sf  Length \ \times \  Breadth = (x  - \dfrac{x}{4}) \ \times \ x  \ = \ \dfrac{3}{4}x^2

Ratio of shaded to unshaded:

\Longrightarrow \sf \dfrac{1}{4} x^2 \ : \ \dfrac{3}{4} x^2  =  1 : 3 \quad (simplified)

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2 years ago
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dem82 [27]

Answer:

6

Step-by-step explanation:

This can be solved by the use of proportions

2/5÷3=x÷7.2

Cross multiply to solve

2/5*7.2=18

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We now have 3x=18

Divide by 3 and get 6

Hope this helps!

8 0
3 years ago
15. The equation below defines z as a differentiable function of x and y. Find the value of dz/dy at the point (1, 1, 1).
MariettaO [177]

Isolate the term with z^2.

x^2 - 5y^2 + xyz^2 = y - 4 \implies xyz^2 = -x^2 + 5y^2 + y - 4

Differentiate both sides with respect to y.

\dfrac{\partial(xyz^2)}{\partial y} = \dfrac{\partial(-x^2 + 5y^2 + y - 4)}{\partial y}

By the product and chain rules,

xz^2 + 2xyz \dfrac{\partial z}{\partial y} = 10y + 1

Solve for the partial derivative, then evaluate at (x,y,z) = (1,1,1).

\dfrac{\partial z}{\partial y} = \dfrac{10y + 1 - xz^2}{2xyz}

\dfrac{\partial z}{\partial y} \bigg|_{x=1,y=1,z=1} = \dfrac{10 + 1 - 1}{2} = \boxed{5}

4 0
2 years ago
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
o-na [289]

Answer:

y = 2(x - 1/4)

Step-by-step explanation:

To find an equation of the tangent to a given curve, we need two vital information; one is the slope of the tangent (SOP) and the other is the point of tangency (POT).

to find the slope of tangent i will use the implicit differentiation to find the slope then apply the point given

so, first, the slope using implicit differentiation;

f(x) = x^{2} +y^{2} =(3x^{2}+4y^{2} -x) ^{2}

f'(x) = {tex}2x + 2y dy/dx = 2(3x^{2} + 4y^{2} - x)(6x + 8y dy/dx - 1){/tex}

applying the co-ordinates given; x = 0 and y = 1/4

SOP  2(0) + 2(1/4) dy/dx = 2[3(0)^2 + 4(1/4)^2 - 0][6(0) + 8(1/4) dy/dx - 1)

1/2 dy/dx = 2[4(1/16)][(8/4) dy/dx - 1]

1/2 dy/dx = 2[1/2][2 dy/dx - 1]

1/2 dy/dx = 2 dy/dx - 1

putting the dy/dx together

1 = 2 dy/dx - 1/2 dy/dx

1 = dy/dx (2 - 1/2)

make dy/dx subject

1 / 1/2 = dy/dx

therefore SOP = 2

POT

f(x) = (0)^2 + (1/4)^2 = [3(0)^2 + 4(1/4)^2 - 0]^2

1/16 = [4(1/16)]^2

1/16 = (1/4)^2

1/16 = 1/16

y = 0

using the slope formula

m = y - y2/ x - x2

2 = y - 0/ x - 1/4

y = 2(x - 1/4)

7 0
3 years ago
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