Workings please......

A rectangle with vertices (3,-2),(3,-4), (7, -2), (7, -4) is reflected across the x-axis and then rotated 90° counterclockwise.

BigorU [14]

Answer: A reflection about the y-axis and a clockwise rotation of 90° around the origin.

another example is:

A counterclockwise rotation of 90° around the origin, and then a reflection about the y-axis.

Step-by-step explanation:

Let's do this for a single point because it is essentially the same.

Let's use the point (3, -2)

First, we have a reflection across the x-axis, this only changes the sign of the y-component.

Then the new point will be: (3, -(-2)) = (3, 2)

Notice that this point is on the first quadrant.

Now we do a 90° counterclockwise rotation.

Then we move to the second quadrant, and we change the order of the components in the point (and because we are in the second quadrant, the x-component is negative and the y-component is positive)

Then the new point is (-2, 3)

Now, another transformation that is equivalent to this one is to do first a reflection about the y-axis, so we only change the sign of the y-component

Then the new point is (-3, -2)

And now we are in the third quadrant.

and then we do a rotation of 90° clockwise, which moves our point to the second quadrant, changes the order of the components and leaves the y-component positive and the x-component negative, then the new point is:

(-2, 3)

Same as before.

(notice that we used the same transformations, but applied to different line and direction of rotation)

Another example is if we first start with a counterclockwise rotation of 90° around the origin, the original point (3, -2) is on the fourth quadrant, so this rotation leaves our point in the first quadrant, so we change the order of the components and both of them will have a positive sign.

The new point is: (2, 3)

Now let's do a reflection about the y-axis, which changes the sign of the x-component.

Then the final point is (-2, 3), same as before.

And there are a lot of other transformations that will be equivalent to this ones, these are just two examples.

3 0

3 years ago

Bethany wants to estimate the value of (4.296 times 10 Superscript 11) (1.8614 times 10 Superscript negative 14). Which statemen

avanturin [10]

Answer:

D. The number will be less than 1 because when adding the exponents,

11 + (-14) = -3, and a number in scientific notation with a negative exponent is less than 1.

Step-by-step explanation:

The question lacks appropriate option. Find the options below;

A. The value will be greater than 1 because 4.296 x 10^11 is a very large number and multiplication always increases the size of a number.

B. The value will be greater than 1 because 4 x 2 = 8 and 8 is larger than 1.

C. The value will be less than 1 because (4.296 x 10^11) x (1.8614 x 10^-14) will be a negative number. All negative numbers are less than one.

D. The number will be less than 1 because when adding the exponents,

11 + (-14) = 3, and a number in scientific notation with a negative exponent is less than 1.

Given the expression $(4.296*10^{11})(1.8614*10^{-14})$ , to expand the expression we will apply some of the law of indices below. If a, b and m are integers

$a^m*a^n = a^{a+m}$

$= (4.296*10^{11})(1.8614*10^{-14})\\\\= (4.296*1.8614)(10^{11}*10^{-14}) \\\\= 7.9965744 * 10^{11}*10^{-14}\\sum \ up \ the\ power\ of\ the \ exponents\\\\= 7.9965744 *10^{11-14}\\\\= 7.9965744 *10^{-3}\\$

= 0.0079965744

<em>Based on the result, it can be seen that the resulting value is less than 1 due to the negative power of its exponent (i.e -3). Any scientific notation having a negative exponent always returns a value that is less than 1.</em>

4 0

3 years ago

Read 2 more answers

Find the value of x.<br>please i need the answer today.<br>Thank you.

satela [25.4K]

Answer:

x = 61.92751306

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opposite / adjacent

tan x = 15/8

Take the inverse tan on each side