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2 years ago

What is the image of the point (-5, 6) after a rotation of 90°

Mathematics

1 answer:

ycow [4]2 years ago

3 0

Answer:

(-6, -5)

Step-by-step explanation:

rule for 90° counterclockwise about the origin:

(x, y) => (-y, x)

so:

(-5, 6) => (-6, -5)

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Make an inference about which fish increased its predicted average population from Year 1 to Year 2.

galben [10]

Make an inference about which fish increased its predicted average population from Year 1 to Year 2.
All three types of fish increased their predicted average population.
Trout increased its predicted average population.
Bass increased its predicted average population.
None of the fish increased their predicted average population.

4 0

3 years ago

Read 2 more answers

Hi! I was wondering if you could help with this question please :)

Makovka662 [10]

Answer:

$R=\frac{QJ}{I^2t}$

Step-by-step explanation:

So we have the equation:

$Q=\frac{I^2Rt}{J}$

And we want to solve for R.

First, let's multiply both sides by J to remove the fraction on the right. So:

$(J)Q=(J)\frac{I^2Rt}{J}$

Simplify the right:

$JQ=I^2Rt$

We can rewrite our equation as:

$JQ=R(I^2t)$

So, to isolate the R variable, divide both sides by I²t:

$\frac{JQ}{I^2t}=\frac{R(I^2t)}{I^2t}$

The right side cancels, so:

$R=\frac{QJ}{I^2t}$

And we are done!

7 0

3 years ago

Find the value of 9!

katrin2010 [14]

Answer: 362880

The exclamation mark means factorial notation. The rule is we start with the given number, then count down til we get to 1, multiplying all along the way. In this case, we start with 9, then multiply with 8, 7, 6, etc til we get to 1, like so...

9! = 9*8*7*6*5*4*3*2*1 = 362880

Some calculators have a factorial button built in. The button should be labeled with an exclamation mark.

5 0

3 years ago

Read 2 more answers

A dressmaker needs to cut 18-inch pieces of ribbon from rolls of ribbon that are 6 feet

SashulF [63]

You have 10 rolls and each is 6 feet so therefore you have 60 feet of ribbon. Convert that to inches you need to multiply by 12 so 60 x 12 = 720 inches of ribbon.
If the dress maker needs 18 inch pieces you divide to 720 by 18.
720 divided by 18 will give you 40 pieces.

Final answer:

The dressmaker will get 40, 18-inch pieces of ribbon from 10, 6 foot rolls.

4 0

3 years ago

Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Spr

NeX [460]

Answer:

20.2057 Units.

Step-by-step explanation:

First, we determine the length of the cable.

Distance between Centerville (8,0) and point (x,0) is given as:

$\sqrt{(8-x)}^2=8-x$

Distance between point (x,0) and Springfield(0,7) is:

$\sqrt{(7-0)^2+(0-x)^{2}}=\sqrt{(7)^2+(x)^{2}}$

Distance between point (x,0) and Shelvyfield(0,-7) is:

$\sqrt{(-7-0)^2+(0-x)^{2}}=\sqrt{(7)^2+(x)^{2}}$

Therefore the Length of the Cable L(x)

$L(x)=(8-x)+2\sqrt{(7)^2+(x)^{2}}$

To find the critical point, we set the derivative of L(x)=0

$L^{'}(x)=-1+\frac{2x}{\sqrt{\left( 49 - x^{2}\right) }}$

$\frac{-\sqrt{\left( 49 - x^{2}\right)}+2x}{\sqrt{\left( 49 - x^{2}\right)}}=0\\-\sqrt{\left( 49 - x^{2}\right)}+2x=0\\\sqrt{\left( 49 - x^{2}\right)}=2x\\(\sqrt{\left( 49 - x^{2}\right)})^2=(2x)^2\\49 - x^{2}=4x^2\\49=5x^2\\x^2=\frac{49}{5}\\x= 3.1305$

To verify that L(x) has a minimum at this critical number we compute the second derivative L″(x) and find its value at the critical number.

$L^{''}(x)=\frac{\left( 98\right) \,\sqrt{\left( 49 - x^{2}\right) }}{{\left( 7 - x\right) }^{2}\,{\left( 7+x\right) }^{2}}\\At \:x=3.1305, L^{''}=0.3993$

Since $L^{''}(x)$ is positive, the minimum point of L(x) exists.

Next, we find the minimum length by substituting z=3.1305 into L(x)

$L(3.1305)=(8-3.1305)+2\sqrt{(7)^2+(3.1305)^{2}}$

Minimum Length, L=20.2057

The minimum length of the cable is 20.2057 Units.

6 0

2 years ago