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2 years ago

5

Find the value of x. Write your answer in simplest form.

1 answer:

slega [8]2 years ago

7 0

Answer:

x = (9/2)√2

Step-by-step explanation:

The ratio of leg x to the hypotenuse 9 is equal to the cosine of 45 degrees:

cos 45 degrees = x/9

To find the value of x, multiply both sides of this equation by 9, obtaining 9*cos 45 degrees, which comes out to x =9(1/√2). Rationalizing the denominator, we get x = (9/2)√2

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Lionfish are considered an invasive species, with an annual growth rate of 67%. A scientist estimates there are 8,000 lionfish i

natita [175]

<em>Answer:</em>

<em>There would be 173,535 lionfish after 6 years.</em>

<em>Step-by-step explanation:</em>

<em>Since lionfish are considered an invasive species, with an annual growth rate of 67%, ya scientist estimates there are 8,000 lionfish in a certain bay after the first year, A) to write the explicit equation for f (n) that represents the number of lionfish in the bay after n years; B) determine how many lionfish will be in the bay after 6 years; and C) if scientists remove 1,200 fish per year from the bay after the first year, determine what is the recursive equation for f (n); the following calculations must be performed:</em>

<em></em>

<em>A)</em>

<em>8000 x 1.67 ^ n = f </em>

<em>B)</em>

<em>8000 x 1.67 ^ 6 = X</em>

<em>8000 x 21.691961596369 = X</em>

<em>173,535.692770952 = X </em>

<em>C)</em>

<em>(8000 - 1200 x 1 ^ n) x 1.67 ^ n = f</em>

<em>Therefore, there would be 173,535 lionfish after 6 years.</em>

5 0

2 years ago

What is the perimeter of the figure

anastassius [24]

Answer:

Option A.

$P=73.4\ units$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

In this problem we have a triangle with a circle inscribed in it

so

$A.F=A.B\\C.B=C.D\\E.F=E.D$

step 1

Find the length side B.C

$C.B=A.C-A.B$

substitute the given values

$C.B=23-14=9\ units$

step 2

Find the length side C.D

Remember that

$C.D=C.B$

therefore

$C.D=9\ units$

step 3

Find the length side E.D

we know that

$E.D=E.C-C.D$

substitute the given values

$E.D=22.7-9=13.7\ units$

step 4

Find the length side E.F

Remember that

$E.F=E.D$

therefore

$E.F=13.7\ units$

step 5

Find the length side A.F

Remember that

$A.F=A.B$

therefore

$A.F=14\ units$

step 6

Find the perimeter

$P=23+22.7+13.7+14$

$P=73.4\ units$

6 0

3 years ago

you want to purchase a new pair of jeans that cost $48 but on sale for 15% off. what's the sale price?

jekas [21]

40.8 because u take 15 percent of 48 and subtract it from 48

7.2 - 48 = 40.8

3 0

3 years ago

12 A pilot needs to know the maximum height an aircraft can fly at. The cabin has been tested and is safe to a height of 15679 m

abruzzese [7]

15.6 kilometers rounded down because it is not safe to go above what has been approved

7 0

2 years ago

3 friends share the cost of a gift. The gift costs $70, but the store manager takes $10 off the market price. What amount should

My name is Ann [436]

Answer:

Amount each friend pays for the gift = $20

Step-by-step explanation:

Market price of a gift = $70

The store manager takes $10 off the market price.

Marked down amount = $10

New cost price = Marked price - Marked down amount $=\$70-\$10=\$60$

The cost of the gift is divided among three friends.

This means that the cost of gift which is $60 is divided by three to get each one's contribution in the gift.

∴ Amount each friend pays for the gift $=\frac{60}{3}=\$20$

4 0

3 years ago