What is the image of (-2, 3) after a rotation of 90 degrees counterclockwise?

Consider the diagram below. which of the following represents the values x,y and z?

Gemiola [76]

Answer:

$x=4\sqrt{6}\ units$

$y=4\sqrt{2}\ units$

$z=4\sqrt{3}\ units$

Step-by-step explanation:

The picture of the question in the attached figure

step 1

In the right triangle ABD

Applying the Pythagorean Theorem

$x^2=y^2+(12-4)^2$

$x^2=y^2+64$

$y^2=x^2-64$ ----> equation A

step 2

In the right triangle BDC

Applying the Pythagorean Theorem

$z^2=y^2+4^2$

$z^2=y^2+16$

$y^2=z^2-16$ ----> equation B

step 3

In the right triangle ABC

Applying the Pythagorean Theorem

$12^2=x^2+z^2$

$144=x^2+z^2$ ----> equation C

step 4

Equate equation A and equation B

$x^2-64=z^2-16$

$x^2=z^2+48$ -----> equation D

step 5

substitute equation D in equation C

$144=z^2+48+z^2$

solve for z

$2z^2=144-48$

$2z^2=96$

$z^2=48$

$z=\sqrt{48}\ units$

simplify

$z=4\sqrt{3}\ units$

Find the value of x

$x^2=z^2+48$

$x^2=48+48=96$

$x=\sqrt{96}\ units$

$x=4\sqrt{6}\ units$

Find the value of y

$y^2=z^2-16$

$y^2=48-16$

$y^2=32$

$y=\sqrt{32}\ units$

$y=4\sqrt{2}\ units$

3 0

3 years ago

The difference between 4/9 of a number and 7 is 5

vodomira [7]

first what quantities do we need to talk about?

the problem speaks of “a number”, let’s call that number x.

now write the equation that relates x to the other numbers we know.

the first clue is the word “difference”.

this means “subtraction”, but we need to subtract something from something else.

what are the two somethings? ”a number times 7” and “4”.

so, since we have a name for “a number”, let’s translate this as x*7 - 4 what else do we know?

it says the difference is 9. So complete the equation x*7 - 4 = 9 if we rewrite this cosmetically, 7x - 4 = 9

i assume that you know how to solve this for x.

so then wehn solving 7x - 4 =9 we take -4 change it to +4 so then +9 we go and get 13

7x = 13

7/7 = 13/7

x= 13/7

8 0

3 years ago

How to write a whole number as a improper fraction

Dimas [21]

Follow these 3 steps to convert a mixed number to an improper fraction:<span>Multiply the whole number by the denominator.Add the answer from Step 1 to the numerator.<span>Write answer from Step 2 over the denominator.</span></span>

4 0

3 years ago

Which equation could be used to solve for the measure of angle P?

lutik1710 [3]

Answer:

$y+w=180$

Step-by-step explanation:

As we know that the sum of opposite angles of a cyclic quadrilateral is 180.

The equation which is used to solve for the measure of angle P is y+w= 180.

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8 0

3 years ago

Read 2 more answers

The explicit rule for a sequence is given.

never [62]

Answer:

$a_{1} =\frac{2}{5}$ ,Recursive formula is :

$a_{n} =a_{n-1} .5$

Step-by-step explanation:

To find a1 we put n=1 in the given Geometric sequence :

$a_{1} =\frac{2}{5}5^{1-1}$

$a_{1} =\frac{2}{5}$

$a_{2} =\frac{2}{5}5^{2-1} = 2$

Common difference = 2÷ $\frac{2}{5}$ = 5.

r=5.

Recursive formula for a geometric sequence is

$a_{n} =a_{n-1} .r$

Recursive formula is :

$a_{n} =a_{n-1} .5$

7 0

3 years ago

Read 2 more answers

What is the image of (-2, 3) after a rotation of 90 degrees counterclockwise? ​

What is the image of (-2, 3) after a rotation of 90 degrees counterclockwise?