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2 years ago

What are the coordinates of the image of vertex R -3,4 after a reflection across the y-axis? (–4, 3) (4, –3) (–3, –4) (3, 4)

2 answers:

7 0

The coordinate of the image after being reflected is R(3,4).

When dealing with reflection of a line or shape or a figure in the coordinate plane, especially if it is reflected across the y- axis, you just have to give the opposite of the given (original) x- coordinate in order to give a symmetric figure.

Yanka [14]2 years ago

7 0

A reflection on the vertical axis is given by the following transformation:

(x, y) -----------------> (-x, y) ----------------> (x ', Y')

Applying the transformation for the point (-3, 4) we have:

(-3, 4) -----------------> (- (- 3), 4) ----------------> (3, 4)

Therefore, the new ordered pair after the reflection on the vertical axis is given by:

(3, 4)

Answer:

the coordinates of the image of vertex R -3.4 after a reflection across the y-axis are:

(3, 4)

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7 girls audition for 12 roles in a school play. What is the probability that at least 2 of the girls audition for the same part?

Sophie [7]

Answer:

Step-by-step explanation:

This is one minus the probability that all the girls audition for different roles. The total number of ways of assigning roles to the girls is 12^7, because to each of the 7 girls, you have a choice of 12 roles.

Then if each girl is to receive a different role, then there are 12!/5! possibilities for that. If you start assigning roles to the girls, then for the first girl, there are 12 choices, but for the next you have to choose one of the 11 different ones, so 11 for the next, and then one of the 10 remaining for the next etc. etc., and this is 12*11*10*...*6 = 12!/(12-7)! =12!/5!

The probability that a random assignment of one of the 12^7 roles would happen to be one of the 12!/5! roles where each girl has a different role, is

(12!/5!)/12^7 = 12!/(12^7 5!)

Then the probability that two or more girls addition for the same part is the probability that not all the girls are assigned different roles, this is thus:

1 - 12!/(12^7 5!)

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2 years ago

A plate moves south at a rate of 2 cm/year. How many meters south from its original location will the plate be in 4,000 years?

Neporo4naja [7]

Answer:

I hope I can help

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2 years ago

Read 2 more answers

Stacey has a square piece of cloth. She cuts 3 inches off of the length of the square and 3 inches off of the width. The area of

ratelena [41]

Answer:

The side length of the original square was 6 inches

Step-by-step explanation:

we know that

The area of a square is

$A=b^2$

where

b is the length side of the square

Let

x ---> the length of the original square

The area of the original square is

$A=x^{2}\ in^2$

The length of the smaller square is

$b=(x-3)\ in$

The area of the smaller square is

$A=(x-3)^2\ in^2$

The area of the smaller square is 1/4 the area of the original square

$(x-3)^2=\frac{1}{4} x^{2}$

solve for x

$x^2-6x+9=\frac{1}{4} x^{2}$

Multiply by 4 both sides

$4x^2-24x+36=x^{2}$

$4x^2-x^2-24x+36=0\\3x^2-24x+36=0$

Solve the quadratic equation by graphing

using a graphing tool

x=2, x=6

see the attached figure

The solution is x=6 in

Remember that the solution must be greater than 3 inches (because Stacey cuts 3 inches off of the length of the square and 3 inches off of the width)

therefore

The side length of the original square was 6 inches

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2 years ago

Aro diagrams his river rafting trip, estimating the time it will take him to paddle upstream against the current, and then back

eduard

Answer:

Upstream

5.2=(x-y)5

Downstream

5.2=(x+y)2.5

Step-by-step explanation:

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2 years ago

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Set up a double integral for calculating the flux of the vector field F⃗ (x,y,z)=xi⃗ +yj⃗ through the open-ended circular cylind

katrin [286]

Parameterize the cylinder (call it $S$ ) by

$\vec s(\theta,z)=\sqrt8\cos\theta\,\vec\imath+\sqrt8\sin\theta\,\vec\jmath+z\,\vec k$

with $0\le\theta\le2\pi$ and $0\le z\le9$ . Then

$\vec F(x(\theta,z),y(\theta,z),z(\theta,z))=\sqrt8\cos\theta\,\vec\imath+\sqrt8\sin\theta\,\vec\jmath$

Take the normal vector to $S$ to be

$\vec s_\theta\times\vec s_z=\sqrt8\cos\theta\,\vec\imath+\sqrt8\sin\theta\,\vec\jmath$

Then the flux of $\vec F$ across $S$ is

$\displaystyle\iint_S\vec F(x,y,z)\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9\vec F(x(\theta,z),y(\theta,z),z(\theta,z))\cdot(\vec s_\theta\times\vec s_z)\,\mathrm dz\,\mathrm d\theta$

$=\displaystyle\int_0^{2\pi}\int_0^98(\cos^2\theta+\sin^2\theta)\,\mathrm dz\,\mathrm d\theta=\boxed{144\pi}$

7 0

2 years ago