One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number of sterile males that mate with fertile females but produce no offspring. let p represent the number of female insects in a population and s the number of sterile males introduced each generation. let r be the per capita rate of production of females by females, provided their chosen mate is not sterile. then the female population is related to time t by t = p + s p[(r − 1)p − s] dp. suppose an insect population with 10,000 females grows at a rate of r = 1.2 and 400 sterile males are added. evaluate the integral to give an equation relating the female population to time. (note that the resulting equation can't be solved explicitly for p. remember to use absolute values where appropriate.)

Answers

Answer 1

The relation between population and time is:
[tex]t = \int { \frac{P+S}{P[(r - 1)P - S]} } \, dP [/tex]

Since r = 1.2 and S = 400, we get:
[tex]t = \int { \frac{P+400}{P[(1.2 - 1)P - 400]} } \, dP [/tex]

= [tex] \int { \frac{P+400}{P(0.2P - 400)} } \, dP [/tex]

This is a rational function that we can write as:
[tex]\frac{P+400}{P(0.2P - 400)} = \frac{A}{P} + \frac{B}{(0.2P - 400)} [/tex]

In order to evaluate A and B, let's calculate the LCD:
[tex]\frac{P+400}{P(0.2P - 400)} = \frac{A(0.2P - 400)}{P(0.2P - 400)} + \frac{BP}{P(0.2P - 400)} [/tex]

which brings to:
P + 400 = 0.2AP - 400A + BP
= P(0.2A + B) - 400A

Since, the left side must be equal to the right side, we get the following system of equations:
[tex] \left \{ {{0.2A + B = 1} \atop {-400A = 400}} \right. [/tex]

Which gives:
[tex] \left \{ {{B=1.2} \atop {A=-1}} \right. [/tex]

Therefore, our integral can be written as:
[tex]t = \int { \frac{P+400}{P(0.2P - 400)} } \, dP = \int {( \frac{-1}{P} + \frac{1.2}{0.2P-400} )} \, dP [/tex]
= [tex]- \int { \frac{1}{P} \, dP + 1.2\int { \frac{1}{0.2P-400} } \, dP[/tex]
= [tex]- \int { \frac{1}{P} \, dP + 6\int { \frac{0.2}{0.2P-400} } \, dP[/tex]
= - ln |P| + 6 ln |0.2P - 400| + C

We now have to evaluate the constant C. In order to do so, we consider that at t = 0 P = 10000:
0 = - ln |10000| + 6 ln |0.2(10000) - 400| + C
C = ln |10000| - 6 ln |1600|
C = ln (10⁴) - 6 ln (2⁶·5²)
C = 4 ln (10) - 36 ln (2) - 12 ln (5)

Therefore, the equation relating female population with time is:
t = - ln |P| + 6 ln |0.2P - 400| + 4 ln (10) - 36 ln (2) - 12 ln (5)

Answer 2

The equation relating females population with time is [tex]\boxed{t = - \ln \left| P \right| + 6\ln \left| {0.2P - 400} \right| - 12\ln \left( 5 \right) + 4\ln \left( {10} \right) - 36\ln \left( 2 \right)}.[/tex]

Further explanation:

Explanation:

The female population is related to time and it is given as follows,

[tex]t = \int {\dfrac{{p + s}}{{p\left[ {\left( {r - 1} \right)p - s} \right]}}dp}[/tex]

The sterile males are 400 and the growth rate is 1.2.

[tex]\begin{aligned}t&= \int {\frac{{p + 400}}{{p\left[ {\left( {1.2 - 1} \right)p - 400} \right]}}dp}\\&= \int {\frac{{p + 400}}{{p\left[ {0.2p - 400} \right]}}dp}\\\end{aligned}[/tex]

The expression [tex]\dfrac{{p + 400}}{{p\left[ {0.2p - 400} \right]}}[/tex] can also be expressed as follows,

[tex]\dfrac{{p + 400}}{{p\left[ {0.2p - 400} \right]}} = \dfrac{A}{p} + \dfrac{B}{{\left( {0.2p - 400} \right)}}[/tex]

Find the least common denominator.

[tex]\dfrac{{p + 400}}{{p\left( {0.2p - 400} \right)}} = \dfrac{{A\left( {0.2p - 400} \right)}}{{p\left( {0.2p - 400} \right)}} + \dfrac{{Bp}}{{p\left( {0.2p - 400} \right)}}[/tex]

[tex]\begin{aligned}p + 400 &= 0.2Ap - 400A + Bp\\p + 400 &= p\left( {0.2A + B} \right) - 400A\\\end{aligned}[/tex]

Equate left and right side of the expression to obtain the value of A and B.

[tex]\begin{aligned}0.2A + B &= 1\\- 400A &= 400\\\end{aligned}[/tex]

The value of A can be obtained as follows,

[tex]\begin{aligned}A&= \dfrac{{400}}{{ - 400}}\\A& =- 1\\\end{aligned}[/tex]

The value of B is 1.2.

Integral can be expressed as follows,

[tex]\begin{aligned}t &= \int {\frac{{p + 400}}{{p\left( {0.2p - 400} \right)}}dp} \\ &= \int {\left( {\frac{{ - 1}}{p} + \frac{{1.2}}{{\left( {0.2p - 400} \right)}}} \right)dp} \\&= - \int {\frac{1}{p}dp} + 6 \times \int {\frac{{0.2}}{{0.2p - 400}}dp}\\&= - \ln \left| p \right| + 6\ln \left| {0.2p - 400} \right| + C\\\end{aligned}[/tex]

At initial time the population is 10000.

[tex]\begin{aligned}- \ln \left| {10000} \right| + 6\ln \left| {0.2 \times 10000 - 400} \right| + C &= 0\\\ln \left| {10000} \right| - 6\ln \left| {1600} \right| &= C\\4\ln 10 - 36\ln \left( 2 \right) - 12\ln \left( 5 \right) &= C\\\end{aligned}[/tex]

Substitute [tex]4\ln 10 - 36\ln \left( 2 \right) - 12\ln \left( 5 \right)[/tex] for [tex]C.[/tex]

[tex]t = - \ln \left| p \right| + 6\ln \left| {0.2p - 400} \right| + 4\ln 10 - 36\ln \left( 2 \right) - 12\ln \left( 5 \right)[/tex]

Learn more:

Learn more about inverse of the functionhttps://brainly.com/question/1632445. Learn more about equation of circle brainly.com/question/1506955. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Exponential function

Keywords: exponential growth, growth rate model, pesticides, slowing, insect population, sterile males, mate, fertile, females, explicitly, female grows, integral, female insects, male insects, capita rate, chosen mate, generation.

Related Questions

A line contains points M(1, 3) and N(5, 0). What is the slope of MN?

Answers

For this case we have the following points:
M (1,3)
N (5.0)
The slope of the line is given by:
m = (y2-y1) / (x2-x1)
Substituting values we have:
m = (0-3) / (5-1)
Rewriting we have:
m = -3 / 4
Answer:
The slope of the line is:
m = -3 / 4

The slope of the line that points M and N lies on is [tex]-\frac{3}{4}[/tex]

Given:

[tex]M(1, 3)\\N(5, 0)[/tex]

Formula for slope of a line is:

[tex]slope (m) = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Let,

[tex]M(1, 3) = (x_1, y_1)\\N(5, 0) = (x_2, y_2)[/tex]

Substitute

[tex]Slope(m) = \frac{0-3}{5-1} \\= \frac{-3}{4} \\= -\frac{3}{4}[/tex]

Therefore, the slope of the line that contains M(1, 3) and N(5, 0) is: [tex]-\frac{3}{4}[/tex]

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Z = 6.8 e j 2.57 + 5.5 e j 2.64 put z in the form z = r ∠ θ , where r > 0 , θ is in degrees, and − 180 ∘ < θ ≤ 180 ∘ .

Answers

A suitable calculator* handles this easily. The one shown is a TI-83/84 work-alike. The first calculation is done in Radians mode. Since you want the answer in degrees, the second calculation is done in Degrees mode.

z = 12.29255119 ∠ 149.0434722°

_____
* You already need a calculator for the trig functions. You may as well use the other capabilities it offers.

What is the total surface area of the cone? 90π cm2 65π cm2 120π cm2 115π cm2

Answers

Final answer:

The total surface area of a cone can be found using the formula A = πr(r + l), where A is the total surface area, r is the radius of the base, and l is the slant height. In this case, the correct answer is 115π cm².

Explanation:

The total surface area of a cone can be found using the formula A = πr(r + l), where A is the total surface area, r is the radius of the base, and l is the slant height.

In this case, the correct answer is 115π cm². Let's calculate it:

Let's assume the radius of the cone is r.And let's assume the slant height of the cone is s.The total surface area of the cone is A = πr(r + s).We can substitute the given values into the formula: A = π(4)(4 + 7) = 115π cm².

Therefore, the correct answer is 115π cm².

Type the correct answer in each blank. Use numerals instead of words. If necessary, use / for the fraction bar(s). John hosts an art workshop on the weekends. He has an average of 14 students in each session and charges a fee of $12 per session. He estimates that for every $2 increases in the fee, the average number of students reduces by 1. Complete the equation that models this scenario, where c(x) is the revenue generated and x is the number of $2 fee increases.
c(x) =_x^2 +_x+_

Answers

We know that John is hosting an art workshop on the weekends. He has an average of 14 students in each session and charges a fee of $12 per session. . He estimates that for every $2 increases in the fee, the average number of students reduces by 1.

Therefore, we can conclude that his revenue is [tex]14 * 12[/tex] or [tex]168[/tex] bucks.

The session price goes up in a pattern of 2.

For example, from 12 the session price goes to 14, 16, 18 and so on.

As each jumps goes by 2, the amount of students drop by 1.

(i.e from 14 students the number decreases to 13, to 12 and so on.)

As we can see the revenue begins at 168 and continues upward until it reaches 200 dollars and then starts to descend.

This indicates that the U-turn or vertex of the revenue function is approximately 4200, where h represents 4, and k is 200.

To solve we can use Parabola.

⇒ Parabola: any point is at an equivalent separation from:

a settled point (the concentration ), and

a settled straight line (the directrix )

____________________________________________________

[tex]f (x) = a(x - h)^2 + k[/tex], where (h, k) is the vertex of the parabola.

⇒ [tex] \left \{ {{y=192} \atop {x=2}} \right. [/tex]

⇒ [tex]192 = a(2-4)^2+200[/tex]

⇒ [tex]-8=a(-2)^2[/tex]

⇒ [tex]-8=a*2^2[/tex]

⇒ [tex]-8=a*4[/tex]

⇒ [tex]-8=4a[/tex]

⇒ [tex] -\frac{8}{4} = \alpha [/tex]

⇒ [tex] \alpha = -2 [/tex]

Now lets do the final step: Simplifying

[tex]y-2(x-4)^2+200[/tex]

[tex]y=-2(x^2-8x+16)+200[/tex]

[tex]y=-2x^2+16x-32+200[/tex]

[tex]c(x) = -2x^2+16x+168[/tex]

Answer:

c(x) = -2x^2+16x+168

Step-by-step explanation:

just did it on edmentum

If 555 is divided by 2, what is the remainder? A) 1 B) 2 C) 3 D) 5

Answers

Hello!!

If 555 is divided by 2 then the quotient is 277 and the remainder is 1.

2 goes into 15 at most 7 times (Last step of long division).

Good luck :)

Step-by-step explanation:

If 555 is divided by 2 then the quotient is 277 and remainder is 1.

What is 7/10 expressed as a decimal? Enter your answer in the box.

Answers

Dividing a number by 10 moves the decimal over one place to the left. Knowing this:

7 ÷ 10 = 0.7

6 + 12 ÷ 3 – 2 × 2 =

Answers

photomath will give you full work and answer

6 use PEMDAS to figure out

the length of johns patio is 5 feet less than 3 times the length of howards patio .johns patio has a length of 40 feet . what is the length of howards patio

Answers

Hi there! The answer is 15 feet.

The easiest way of solving this problem is by setting up and solving an equation.

Let the length of Howard's patio be represented by X. Now we can get the following expressions

3 times the length of Howard's patio would be 3X (multiply by three).
5 feet less than 3 times the length of Howard's patio would be 3X - 5 (just subtract five).

Now we've found an expression that represents the length of John's patio. Knowing this we can set up and solve an equation.

[tex]3x - 5 = 40[/tex]
First add 5 to both sides of the equation.

[tex]3x = 40 + 5[/tex]
[tex]3x = 45[/tex]
Finally divide both sides by 3.

[tex]x = \frac{45}{3} = 15[/tex]
Therefore, the length of Howard's patio is 15 feet. The answer is 15 feet.

~ Hope this helps you!

ralph is a electrician he charges an initial fee of 24$ , plus 24 per hour. If ralph earned 144$ on the job , how long did the job take.

Answers

it took him 5 hours

he worked five hours

Haseem was given the following enlargement. What is the perimeter, in centimeters, of the enlarged triangle?

Answers

To find the lengths of the enlarged triangle, we would find the scale factor from the given length
22.5/5 = 4.5
So to find the other sides you would multiply 3 and 6 by 4.5
3 * 4.5 = 13.5
6 * 4.5 = 27
So all 3 lengths of the triangle are 22.5, 13.5, and 27
To find the perimeter you add all
22.5 + 13.5 + 27 = 63
Your answer is 63

Solve the equation by factoring. z2 − 6z − 27 = 0

Answers

The answer is x= 9 and -3

You must fine 2 number that multiply to equal -27 and add to equal -6

(x-9) (x+3)
Then equal the parts of the binomial to zero

x - 9 = 0
x + 3 = 0

You must get x by its self.
When you do so, you'll have the answer as -3 and 9

To solve the quadratic equation z² -6z - 27 = 0, factor it to get (z - 9)(z + 3) = 0. Using the Zero Product Property, we find that the solutions are z = 9 and z = -3.

Solving Quadratic Equations by Factoring

To solve the quadratic equation z ²
- 6z - 27 = 0 by factoring, we must find two numbers that add up to -6 and
multiply to -27. After identifying these numbers, we can factor the quadratic expression
into a product of two binomials and then apply the Zero Product Property to find the
values of z.

The two numbers that meet these criteria are -9 and 3, as (-9)*(3) = -27 and (-9)+(3) =
-6. Therefore, we can express the quadratic equation as:

(z - 9)(z + 3) = 0

By the Zero Product Property, we find the solutions to the equation by setting each
binomial equal to zero:

z - 9 = 0
z = 9

z + 3 = 0
z = -3

Thus, the solutions to the quadratic equation are z = 9 and z = -3. These are the z-values that satisfy the original equation.

10,456 to the nearest tenth

Answers

10,456 ≈ 10,5

Answer: 10,5

10,456 to the nearest tenth = 10,456.0

Answer = 10,456.0

Hope this helped☺☺

5:36, 2:9, 3:18 , 1:3 which ratio is the largest?

Answers

Hello there, and thank you for posting your question here on brainly.

Short answer: 1:3

Why?

A fraction is at it's largest when it's closest to zero. The option 1:3 is the closest to zero, all the others are equal to 2:9

Hope this helped you! ♥

1:3 because it's a third, I think cause it's kinda like fractions well named

Use the normal distribution of fish lengths for which the mean is 1111 inches and the standard deviation is 44 inches. assume the variable x is normally distributed. left parenthesis a right parenthesis(a) what percent of the fish are longer than 1212 inches? left parenthesis b right parenthesis(b) if 300300 fish are randomly selected, about how many would you expect to be shorter than 77 inches?

Answers

(a) P(x > 12) ≈ 0.4013
About 40% of the fish are longer than 12 inches.

(b) 300*P(x < 7) ≈ 48
about 48 of 300 fish could be expected to be shorter than 7 inches.

PLEASE HELP ME ILL GIVE U A BRAINLIST a man who is 6 feet tall cats a shadow that is 15 feet long.A tree casts a similar shadow is 22 FT how tall is the tree?

Answers

Hello There

Answer: 13

Here are the steps:
First we subtract 15 from 22 and then got 7

15 - 22 = 7

Finally we Add 7 + 6 = 13

Which is our final answer

I hope I helped
-Chris.

Can someone help me with this question, please?

Answers

f(x) is a vertical stretch of g(x) by a factor of 3. The origin will remain at the origin, immediately eliminating choices (C) and (D).

The vertical stretch will make f look narrower than g, so the appropriate choice is ...
(B)

Which expression is equivalent to 10x^6y^12/-5x^-2y^-6 ? Assume . –50x8y18 –2x8y18 –2x12y72 5x8y18

Answers

The Answer Is: B)-2x^8y^18

Answer:

Option B is correct, i.e. -2 x^8 y^18.

Step-by-step explanation:

To find the equivalent expression to (10)(x^6)(y^12) / (-5)(x^-2)(y^-6)

Step 1: simplify numerical terms

(10) / (-5) = -2

Step 2: simplify exponents of x-terms

(x^6) / (x^-2) = (x^6) * (x^2) = x^(6+2) = x^8

Step 3: simplify exponents of y-terms

(y^12) / (y^-6) = (y^12) * (y^6) = y^(12+6) = y^18

It means (10)(x^6)(y^12) / (-5)(x^-2)(y^-6) = -2 x^8 y^18

Hence, option B is correct, i.e. -2 x^8 y^18.

20 points Easy question
what is 5/20 simplify

Answers

1/4 or.25 or 0.25 is the answer

Hi there!

To simplify this question, we can just divide both sides of the fraction by 5.

5 / 5 = 1
20 / 5 = 4

So, the fully simplified fraction would be 1/4.

Hope this helps!

The circumference of a circle is 28 pi inches. What is the length of the radius of this circle?

Answers

Answer:

The length of the radius of this circle is 14 inches.

Step-by-step explanation:

Circumference of the circle = [tex]28\pi[/tex]

Let's take the length of the radius of the circle as [tex]a[/tex]

Circumference of a circle = [tex]2\pi r[/tex]

Where,

r is the radius of the circle.

Therefore,

[tex]2\pi a=28\pi[/tex]

[tex]2a=28[/tex]

[tex]a=14[/tex]

Therefore, the length of the radius of this circle is 14 inches.

A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 199 milligrams with s = 16.5 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

Answers

Final answer:

To construct a 95% confidence interval, use the formula: Confidence Interval = sample mean ± (critical value * (sample standard deviation / sqrt(sample size))). The confidence interval for the true mean cholesterol content is approximately 190.37 to 207.63 milligrams.

Explanation:

To construct a 95% confidence interval for the true mean cholesterol content of all chicken eggs, we can use the formula:

Confidence Interval = sample mean ± (critical value * (sample standard deviation / sqrt(sample size)))

Given that the sample mean is 199 milligrams, the sample standard deviation is 16.5 milligrams, and the sample size is 12, we need to determine the critical value for a 95% confidence level. Since we have a small sample size, we need to use the t-distribution.

Using a t-table or a statistical calculator, we find that the critical value for a 95% confidence level with a sample size of 12 is approximately 2.179.

Substituting the values into the formula, we get:

Confidence Interval = 199 ± (2.179 * (16.5 / sqrt(12)))

Simplifying and calculating, the confidence interval is approximately 190.37 to 207.63 milligrams.

Final answer:

To construct a 95% confidence interval for the mean cholesterol content of chicken eggs, we use the sample data provided, along with the t-distribution for a sample size less than 30, and apply the standard formula for confidence intervals.

Explanation:

The question asks to construct a 95% confidence interval for the true mean cholesterol content of chicken eggs based on the given sample data. To calculate this, we first need to use the sample mean (μ), which is 199 milligrams, and the standard deviation (s), which is 16.5 milligrams. Since the sample size is less than 30, we will use the t-distribution to find the critical value. With n=12, the degrees of freedom (df) are 11.

First, look up the critical t-value for df=11 at a 95% confidence level. Let's assume it is approximately 2.201. Next, calculate the standard error (SE) of the mean by dividing the sample standard deviation by the square root of the sample size. That's SE = 16.5 / sqrt(12).

Now, we can construct the confidence interval using the formula: mean ± (t-value * SE). Plugging in the numbers, we get 199 ± (2.201 * SE).

d. A 95 percent confidence interval means that if we took many samples and built a confidence interval from each of them, we'd expect about 95 percent of those intervals to contain the true mean cholesterol level of all such eggs. Because of sample variability, the interval provides a range of values within which we are 95% confident the true mean lies.

Hey can you please help me posted picture of question

Answers

Vertical stretching a function means multiplying it by a constant.

So, vertical stretching of F(x) by a factor of 7 will be equal to 7 F(x).

Thus,

G(x) = 7 F(x)

G(x) = 7x²

So, option C gives the correct answer

The mean output of a certain type of amplifier is 117 watts with a variance of 100. if 42 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 3.3 watts? round your answer to four decimal places.

Answers

The probability that mean sample will differ from population mean by 3.3 watts will be given as follows:
P(113.7<x<120.3)
z-score is given by:
z=(x-μ)/σ

but
n=42
hence:
σ/√n
100/√42=15.43
thus
when x=113.7
z=(-3)/15.43
z=-0.1944
P(z<-0.1944)=0.4247

when x=120.3
z=3.3/15.43
z=0.214
P(z<0.214)=0.5832
hence:
P(113.7<x<120.3)=0.5832-0.4247=0.1585

The interior angles formed by the sides of a hexagon have measures that sum to 720 degrees. What is the measure of angle F?

Answers

sum of interior angles of polygon = (n - 2) x 180
in this case n = 6
so (6 - 2 ) x 180 = 4 x 180 = 720

x - 60 + x - 40 + 130 + 120 + 110 + x - 20 = 720
3x + 240 = 720
3x = 480
x = 160

m<F = x - 20 = 160 - 20 = 140

answer
<F = 140°

-2(bx - 5) = 16

What’s does b and x equal?

Answers

To solve this problem you must apply the proccedure shown below:
You have the following equation given in the problem above:
-2(bx - 5) = 16
When you solve for bx, you have:
-2(bx - 5) = 16
-2bx-10=16
-2bx=26
bx=26/-2
bx=-13

When you solve for b, you obtain:
-2(bx - 5) = 16
-2bx=26
b=-(26/2x)

When yoo solve for x:
2bx=26
x=-(26/2b)

Easy 20 points!

Which expression finds the length of side y in this right triangle?

Answers

The Last one is your answer

Answer:

The last one i did this before

Step-by-step explanation:

The Science Club went on a two-day field trip. The first day the members paid $30 for transportation plus $18 per ticket to the planetarium. The second day they paid $85 for transportation plus $15 per ticket to the geology museum. Write an expression to represent the total cost in dollars for two days for the n members of the club.

Answers

c = n(30 +18 +85 +15)
This simplifies to
c = 148n

Answer:

n(30 +18 +85 +15) , and if you slove the expression it'll be $148 dollars .

Step-by-step explanation:

The front wall of your shed is in the shape of a trapezoid. The bottom measures 22 feet, the top measures 20 feet, and the height is 10 feet. Calculate the area of the front wall of your shed.

Answers

The area of a trapezoid is given by the formula:
A = (1/2)×(b₁ +b₂)×h
Substitute the given information and evaluate.
A = (1/2)×(22 ft +20 ft)×(10 ft)
A = (1/2)×(42 ft)×(10 ft)
A = (21 ft)×(10 ft)
A = 210 ft²

The area of the front wall of your shed is 210 ft².

Answer:

the answer on edge is D. 66^2

Step-by-step explanation:

Eight students were absent the following number of days in a year: 4,8,0,1,7,2,6,and 3. Decide if the range or interquartile range better describes the data set, and explain your reasoning.

Answers

For this example the range is 8 - 0 = 8. The interquartile range is 6.5 - 1.5 = 5.

The range is the better measure of variability because the data is arranged so that the spread of data is about the same from the beginning to the end.

There are not more numbers that fall in the middle half of the data when compared to the entire data set.

corey has 42 feet of fencing around his garden. The garden is rectangular in shape, and its length is equal to twice the width minus 3 feet. Define the variables, and write a system of equations to find the length and width of the garden

Answers

w= width
l= length

2w+2l=42
l=2w-3

w= 8
l= 13

The variables as length are L and width is W and the system of equations is L = 2W - 3 and 42 = 2(L + W) and the length and width are 13 feet and 8 feet respectively.

What is a rectangle?

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

As per the given total fencing = 42 feet

Let's say the length is L and the width is W.

As per the given,

L = 2W - 3

Perimeter = 2(length + width)

42 = 2(L + W)

21 = 2W - 3 + W

21 + 3 = 3W

W = 8 feet

And, L = 2(8) - 3 = 13 feet

Hence "The variables as lengths are L and width is W and the system of equations is L = 2W - 3 and 42 = 2(L + W) and the length and width are 13 feet and 8 feet respectively".

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HELP ASAP How do I find the answer to this

Answers

Since triangle ABD and triangle BCD are similar traingles, we can establish a proportion between the lengths of corresponding sides:
[tex] \frac{CD}{BD} = \frac{BD}{AD} [/tex]

Notice that we know for our problem that [tex]BD=h[/tex]. Also, we can find the length of AD by subtracting CD from AC:
[tex]AD=AC-CD[/tex]
[tex]AD=25-16[/tex]
[tex]AD=9[/tex]

Now we can replace the values in our proportion:
[tex] \frac{CD}{BD} = \frac{BD}{AD} [/tex]
[tex] \frac{16}{h} = \frac{h}{9} [/tex]
Solving for [tex]h[/tex]:
[tex]h^2=(16)(9)[/tex]
[tex]h^2=144[/tex]
[tex]h= \sqrt{144} [/tex]
[tex]h=12[/tex]

We can conclude that the correct answer is: B. 12

AC=25

Triangle BCD:
BD=h
CD=16

Triangle ABD:
BD=h
AD=AC-CD=25-16→AD=9

Suppose <CBD is x and the <ABD is y
x+y=90°

The <BCD must be equal to y; and the <BAD must be equal to x, then the triangles ABD and BCD are similars, because they have two congruent angles (x and y), so theirs sides must be proportionals:

Opposite to angle x / opposite to angle y

Triangle ABD Triangle BCD
BD / AD = CD / BD

Replacing values:
h/9=16/h

Solving for h. Cross multiplication:
(h)(h)=(9)(16)
h^(1+1)=144
h^2=144
sqrt(h^2)=sqrt(144)
h=12

Answer: The value of h in the figure is 12

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