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3 years ago

What is the image of point (4, 3) if the rotation is 90º ? Please and thank you.

Mathematics

1 answer:

Zielflug [23.3K]3 years ago

3 0

Answer: (-3, 4)

Step-by-step explanation: Given point coordinate (4,3).

We need to rotate the given point about 90º.

<em>In order to find the new coordinates of rotation 90°counterclockwise about the origin, we can apply rule (h, k) ---> (-k,h).</em>

Where (h,k) are the coordinates of original image on axes and (-k,h) are the coordinates of rotated image.

In resulting coordinates of the image first swap the x and y coordinates of the original image and then make the sign opposite of each x-coordinate.

On applying rule (h, k) ---> (-k,h), we get

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

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3 years ago

Which are the roots of the quadratic function f(b) = 62 – 75? Select two options.

elena55 [62]

Answer:

$b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}$

Step-by-step explanation:

Given

$f(b) = b^2 - 75$

Required

Determine the roots

To get the root of the function, then f(b) must be 0;

i.e. f(b) = 0

So, the expression becomes

$0 = b^2 - 75$

Add 75 to both sides

$75 + 0 = b^2 - 75 + 75$

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Take square roots of both sides

$\sqrt{75} = \sqrt{b^2}$

$\sqrt{75} = b$

Reorder

$b = \sqrt{75}$

Expand 75 as a product of 25 and 3

$b = \sqrt{25*3}$

Split the expression

$b = \sqrt{25} *\sqrt{3}$

$b = \±5 *\sqrt{3}$

$b = \±5 \sqrt{3}$

$b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}$

The options are not clear enough; however the roots of the equation are $b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}$

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3 years ago

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2 years ago

Read 2 more answers

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2 years ago

H(-4), h(0), h(4), h(8)

DIA [1.3K]

9514 1404 393

Answer:

see attached

Step-by-step explanation:

The first two x-values, -4 and 0, fall in the first part of the function definition.

There is no function definition for x = 4, as the second part only applies for x > 4.

The last x-value, 8, falls in the second part of the function definition.

The function is evaluated by putting the x-value where x is in the expression and doing the arithmetic. For example, ...

h(-4) = -(-4+1)^2 +7 = -(-3)^2 +7 = -9 +7 = -2

h(0) = 6

h(4) = undefined

h(8) = -8/3

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3 years ago