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3 years ago

The three steps are shown below were used to find an expression equivalent to 2/5( 15x- 30y)+10x

Mathematics

1 answer:

Tresset [83]3 years ago

8 0

step 1 is to distribute the bracket by $\frac{2}{5}$

= $\frac{2}{5}$ × 15x - $\frac{2}{5}$ × 30y + 10x

= 6x - 12y + 10x ← step 1

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Suppose that poaching reduces the population of an endangered animal by

Sedbober [7]

Answer:

38.26 years.

Step-by-step explanation:

We have been given that the population of an endangered animal by reduces 8% per year. the current population of the animal is 1700. When the population of this animal falls below 70, its extinction is inevitable.

Let us write the model for population of this animal (y) after x years.

Since we know that an exponential decay function is in form: $y=a*(1-r)^x$ , where,

a= Initial value.

r = Rate in decimal form.

Let us convert our given rate in decimal form.

$8\%=\frac{8}{100}=0.08$

Upon substituting a= 1700 and r = 0.08 in exponential function, we will get the model of animal population as:

$y=1700*(1-0.08)^x$

$y=1700*(0.92)^x$

Let us find, when the animal population will face extinction by substituting y=70 in our function.

$70=1700*(0.92)^x$

$\frac{70}{1700}=\frac{1700*(0.92)^x}{1700}$

$0.0411764705882353=0.92^x$

Let us take natural log of both sides of our equation.

$ln(0.0411764705882353)=ln(0.92^x)$

$ln(0.0411764705882353)=x*ln(0.92)$

$-3.1898882879949483163=x*-0.0833816089390511$

$x=\frac{-3.1898882879949483163}{-0.0833816089390511}$

$x=38.2564971890460849445284\approx 38.26$

Therefore, the population of the animal will face extinction after 38.26 years.

5 0

4 years ago

If the perimeter of the rectangle to the right is 96 inches, find the value of x

abruzzese [7]

You must have an illustration to give an idea what x represents. If not, then we can never find a way to answer this for you. However, for educational purposes, let me just suppose a figure for us to solve. The diagram is shown in the attached picture.

The rectangle has dimensions of 6 + x by x units, where x is the width and (6+x) is the length. If you are given the perimeter of the rectangle, then the working equation to be used is shown below.

Perimeter = 2L + 2W

Generally, perimeter is the sum of all sides of the figure. Since rectangle is defined to be made up of two sets of equal parallel sides called length and width, the perimeter is simplified to be that way. Substituting the values,

96 inches = 2(6+x) + 2x
96 = 12 + 2x + 2x
96 = 12 + 4x
4x = 96 - 12
4x = 84
x = 84/4
x = 21 inches

6 0

4 years ago

Lorraine checking account has a balance of less than -$200. Which statement is true about how much lorraine owes the bank?

bulgar [2K]

Do you have answer choices, or is this an open-ended one?

3 0

3 years ago

Read 2 more answers

Two Submarines starting from the same point cruise for two hours, one

Aleksandr [31]

Answer:

2 hour

Step-by-step explanation:

5 0

4 years ago

X =<br><br> a) 43<br> b) 58<br> c) 71

Eduardwww [97]

$28 \textdegree = \frac{1}{2} ( 114 \textdegree - \angle x)$

$28 \textdegree = 57 \textdegree - \frac{1}{2} \angle x$

$\frac{1}{2} \angle x = 57 \textdegree - 28 \textdegree$

$\frac{1}{2} \angle x = 29 \textdegree$

$\angle x = 29 \textdegree \times 2$

$\angle x = 58 \textdegree$

6 0

4 years ago