A square playing field has an area of 1255 square yards. About how long is each side of the field? Please explain how to do this problem

Answer:

C. Domain: (negative infinity, infinity)   Range: (0, infinity)

Step-by-step explanation:

It's correct

The domain of the functions will be (-∞, ∞) and the range of the functions will be (0, ∞).

The domain means all the possible values of x and the range means all the possible values of y.

The functions are given below.

y = f(x)

y = g(x)

y = h(x)

y = k(x)

Then the domain of the functions will be (-∞, ∞) and the range of the functions will be (0, ∞).

Then the correct option is C.

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Answer:

a. $295

Step-by-step explanation:

Add the net pay and the interest. This is the total net income.

Then add all other amounts separately. These are the expenses.

Subtract the expenses from the total net income.

The answer is a. $295

Kendra’s net cash flow is $295 because the total net income is $2320 and total expenses are $2025 option (a) is correct.

It is defined as the money spends on the utility, the amount of money is required to buy something, in other words, it is the outflow of money from the sole earner's income or the money incurred by any organization.

It is given that:

Kendra is working on her financial plan and lists all of her income and expenses in the spreadsheet shown in the picture.

From the spreadsheet:

Add the interest to the net pay. The overall net income is shown here.

= 2300 + 200

= $2320

Next, add each additional sum separately. The costs are as follows.

= 800+120+90+45+95+80+275+520

= $2025

From the entire net income, deduct the costs.

= 2320 - 2025

= $295

Thus, Kendra’s net cash flow is $295 because the total net income is $2320 and total expenses are $2025 option (a) is correct.

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Answer:

(1,2) is the only solution to the given linear equation

Step-by-step explanation:

To see whether an ordered pair is a solution to an equation, the easiest thing to do would be to plug the pair into the equation and see if it equals the right hand side.

(1,2):

[tex]4*x+7*y=18\\4*(1)+7*(2)=18\\\therefore (1,2) \text{ is a solution}[/tex]

(8,0):

[tex]4*(8)+7*(0)=32\\\therefore (8,0) \text{ is not a solution}[/tex]

(0, -2):

[tex]4*(0)+7*(-2)=-14\\\therefore (0,-2) \text{ is not a solution}[/tex]

The pair (1,2) is a solution to the linear equation 4x+7y=18. However, the pairs (8,0) and (0,-2) are not solutions because they do not satisfy the equation.

a. To determine if the ordered pair (1, 2) is a solution to the linear equation 4x + 7y = 18, we substitute the values of x and y into the equation: 4(1) + 7(2) = 18. This simplifies to 4 + 14 = 18, which is true. Therefore, (1, 2) is a solution to the given linear equation.

b. To determine if the ordered pair (8, 0) is a solution, we substitute the values of x and y into the equation: 4(8) + 7(0) = 18. This simplifies to 32 + 0 = 18, which is false. Therefore, (8, 0) is not a solution to the given linear equation.

c. To determine if the ordered pair (0, -2) is a solution, we substitute the values of x and y into the equation: 4(0) + 7(-2) = 18. This simplifies to 0 - 14 = 18, which is false. Therefore, (0, -2) is not a solution to the given linear equation.

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The complete question is here:

Determine whether each ordered pair is a solution of the given linear equation.

4 x+7 y=18 ;(1,2),(8,0),(0,-2)

a. Is (1,2) a solution to the given linear equation?

No

Yes

b. Is $(8,0)$ a solution to the given linear equation?

Yes

No

c. Is (0,-2) a solution to the given linear equation?

No

Yes

The Lagrangian is

[tex]L(x,y,z,\lambda,\mu)=x^2+y^2+z^2+\lambda(4x^2+4y^2-z^2)+\mu(2x+4z-2)[/tex]

with partial derivatives (set equal to 0)

[tex]L_x=2x+8\lambda x+2\mu=0\implies x(1+4\lambda)+\mu=0[/tex]

[tex]L_y=2y+8\lambda y=0\implies y(1+4\lambda)=0[/tex]

[tex]L_z=2z-2\lambda z+4\mu=0\implies z(1-\lambda)+2\mu=0[/tex]

[tex]L_\lambda=4x^2+4y^2-z^2=0[/tex]

[tex]L_\mu=2x+4z-2=0\implies x+2z=1[/tex]

Case 1: If [tex]y=0[/tex], then

[tex]4x^2-z^2=0\implies4x^2=z^2\implies2|x|=|z|[/tex]

Then

[tex]x+2z=1\implies x=1-2z\implies2|1-2z|=|z|\implies z=\dfrac25\text{ or }z=\dfrac23[/tex]

[tex]\implies x=\dfrac15\text{ or }x=-\dfrac13[/tex]

So we have two critical points, [tex]\left(\dfrac15,0,\dfrac25\right)[/tex] and [tex]\left(-\dfrac13,0,\dfrac23\right)[/tex]

Case 2: If [tex]\lambda=-\dfrac14[/tex], then in the first equation we get

[tex]x(1+4\lambda)+\mu=\mu=0[/tex]

and from the third equation,

[tex]z(1-\lambda)+2\mu=\dfrac54z=0\implies z=0[/tex]

Then

[tex]x+2z=1\implies x=1[/tex]

[tex]4x^2+4y^2-z^2=0\implies1+y^2=0[/tex]

but there are no real solutions for [tex]y[/tex], so this case yields no additional critical points.

So at the two critical points we've found, we get extreme values of

[tex]f\left(\dfrac15,0,\dfrac25\right)=\dfrac15[/tex] (min)

and

[tex]f\left(-\dfrac13,0,\dfrac23\right)=\dfrac59[/tex] (max)

This problem involves using Lagrangian multipliers to optimize a function with two constraints. The maximum and minimum points can be found by solving the Lagrange equations, which are derivatives of the function and constraints. These points can be confirmed by checking the positive or negative value of the second-order derivative.

To find the maximum and minimum values of the function ​f(x,y,z)=x²+y²+z² subject the cone z²=4x²+4y² and the plane 2x+4z=2, we use Lagrange multipliers. We have two constraint functions here, given by the cone and the plane equations.

The first step is to set up the Lagrange equations, with and as Lagrange multipliers. From w=gradientf=gradientg+gradienth, we have three equations: 2x=*8x+2, 2y=*8y+0, 2z=*4. The second step is to solve these three equations, together with the original constraints ​g(x,y,z)=​0 and ​h(x,y,z)=​0.

Solving these equations will give you specific values for x, y, and z that correspond to the maximum and minimum points. To determine if a point is a maximum or minimum, one can compute the second-order partial derivatives and organize them into the Hessian matrix.

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Answer:

Option B, two line perpendicular to the same line are parallel.

Step-by-step explanation:

Since DA and CB are perpendicular to AB, they are considered parallel. This is like a transversal line.

Answer:

Definition of right angles.

Step-by-step explanation:

A rectangle is a parallelogram whose opposite sides are parallel to each other. Also, these opposite sides measure the same and all four sides create right angles. In this sense the reason would complete the proof in lines 3 and 5 is the "Definition of right angles". This is because by definition the rectangle is a parallelogram with a right angle, since it is a parallelogram, its opposite is also a right angle. The other angles, which are supplementary to the previous two, add up to 180º. And since they are opposite, they are the same, therefore each of the four is a right angle.

[tex]\angle ABC = \angle BCD = \angle CDA = \angle DAB=90^{\circ}[/tex]

-5

Make the equation into slope-intercept form, which is y = mx + b, where m is the slope, and b is the y-intercept.

In the equation y = -5x - 2/3, the slope is -5 and the y-intercept is -2/3.

For this case we have that the equation of the line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have the following equation:

[tex]y = - \frac {2} {3} -5x[/tex]

Reordering:

[tex]y = -5x- \frac {2} {3}[/tex]

So, we have to:

[tex]m = -5\\b = - \frac {2} {3}[/tex]

Answer:

The slope is -5

Answer:

1. [tex]f(x)=-10^{x-1}-10[/tex] - [tex]-\frac{101}{10}[/tex]

2. [tex]f(x)=-3^{x+5}-9[/tex] - [tex]-252[/tex]

3. [tex]f(x)=-3^{x-2}-1[/tex] - [tex]-\frac{10}{9}[/tex]

4.  [tex]f(x)=-17^{x-1}+2[/tex] - [tex]\frac{33}{17}

Step-by-step explanation:

We are given the exponential functions and we are to match them with their y-intercepts.

1. [tex]f(x)=-10^{x-1}-10[/tex]:

Substituting x = 0 to find the y-intercept:

[tex]f(x)=-10^{0-1}-10 = -\frac{101}{10}[/tex]

y-intercept ---> [tex]-\frac{101}{10}[/tex]

2. [tex]f(x)=-3^{x+5}-9[/tex]:

Substituting x = 0 to find the y-intercept:

[tex]f(x)=-3^{x+5}-9=-252[/tex]

y-intercept ---> [tex]-252[/tex]

3. [tex]f(x)=-3^{x-2}-1[/tex]:

Substituting x = 0 to find the y-intercept:

[tex]f(x)=-3^{x-2}-1=-\frac{10}{9}[/tex]

y-intercept ---> [tex]-\frac{10}{9}[/tex]

4. [tex]f(x)=-17^{x-1}+2[/tex]:

Substituting x = 0 to find the y-intercept:

[tex]f(x)=-17^{x-1}+2=\frac{33}{17}[/tex]

y-intercept ---> [tex]\frac{33}{17}

Answer:

  D.  p + q = 7

Step-by-step explanation:

The slope of AB is ...

  slope AB = (1 -4)/(6 -p) = 3/(p -6)

The slope of BC is ...

  slope BC = (q -1)/(9 -6) = (q -1)/3

The product of these is -1, so we have ...

  (slope AB)·(slope BC) = -1 = (3/(p -6))·((q -1)/3)

Multiplying by q -1 gives ...

  -(q -1) = p -6 . . . . . . the factors of 3 in numerator and denominator cancel

  1 = p + q -6 . . . . . . add q

  7 = p + q . . . . . . . . add 6 . . . . matches choice D

Answer:

D. p + q = 7

Step-by-step explanation:

Just did this quiz on edmentum :P

The vertex form of the equation of a parabola is

                     f(x) = a( x − h)^2 + k

where (h,k) is the vertex of the parabola. In this case, we are given that      (h,k) = (5,0). Hence,

                     f(x) = a( x − 5)^2 + 0

                           =a( x − 5)^2

Since we also know the parabola passes through the point (7,−2), we can solve for a because we know that f(7) = −2.

                        a( 7 − 5)^2 = -2

                           a(2)^2 = -2

                              4a = -2

                               a = -1/2

Thus, the given parabola has equation

                      f(x) = -1/2(x − 5)^2

Answer:

i couldnt answer please be more specific

Step-by-step explanation:

Answer: [tex]cos(\pi-x)=-cos(x)[/tex]

Step-by-step explanation:

We need to apply the following identity:

[tex]cos(A - B) = cos A*cos B + sinA*sin B[/tex]

Then, applying this, you know that for [tex]cos(\pi-x)[/tex]:

[tex]cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)[/tex]

We need to remember that:

[tex]cos(\pi)=-1[/tex] and [tex]sin(\pi)=0[/tex]

Therefore, we need to substitute these values into [tex]cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)[/tex].

Then, you get:

[tex]cos(\pi-x)=(-1)*cos(x)+0*sin(x)[/tex]

[tex]cos(\pi-x)=-1cos(x)+0[/tex]

[tex]cos(\pi-x)=-cos(x)[/tex]

We can use the concept of derivative to find this result, but since the problem states we must use algebraic procedures, then we solve this as follows:

[tex]h(t)=-16t^2+25t+5[/tex]

[tex]h(t)=-16(t^2-\frac{25}{16}t-\frac{5}{16})[/tex]

X-term: [tex]-\frac{25}{16}[/tex]

Half of the x term: [tex]-\frac{25}{32}[/tex]

After squaring: [tex](-\frac{25}{32})^2=\frac{625}{1024}[/tex]

[tex]h(t)=-16(t^2-\frac{25}{16}t-\frac{5}{16}+\frac{625}{1024}-\frac{625}{1024}) \\ \\ h(t)=-16(t^2-\frac{25}{16}t+\frac{625}{1024}-\frac{5}{16}-\frac{625}{1024}) \\ \\ h(t)=-16(t^2-\frac{25}{16}t+\frac{625}{1024}-\frac{945}{1024}) \\ \\[/tex]

[tex]h(t)=-16[(t-\frac{25}{32})^2-\frac{945}{1024}] \\ \\ \boxed{h(t)=-16(t-\frac{25}{32})^2-\frac{945}{64}}[/tex]

Finally, the vertex of this function is:

[tex](\frac{25}{32},\frac{945}{64})[/tex]

So in this vertex we can find the answer to this problem:

The ball will reach its maximum height at [tex]t=\frac{25}{32}s=0.78s[/tex]

The ball maximum height is [tex]H=\frac{945}{64}=14.76ft[/tex]

Also we will use completing squares. We can use the concept of derivative to find this result, but since the problem states we must use algebraic procedures, then we solve this as follows:

[tex]R(p)=-5p^2+1230p[/tex]

[tex]R(p)=-5(p^2-246p)[/tex]

X-term: [tex]-246[/tex]

Half of the x term: [tex]-123[/tex]

After squaring: [tex](-123)^2=15129[/tex]

[tex]R(p)=-5(p^2-246p+15129-15129)[/tex]

[tex]R(p)=-5[(x-123p)^2-15129] \\ \\ R(p)=-5(x-123p)^2+75645[/tex]

Finally, the vertex of this function is:

[tex](123,75645)[/tex]

So in this vertex we can find the answer to this problem:

The price will maximize the revenue is [tex]p=123 \ dollars[/tex]

The maximum revenue is [tex]R=75645[/tex]

Answer:

13

Step-by-step explanation:

The longest side must be less than the sum of the shorter sides:

c < a + b

c < 6 + 8

c < 14

So the largest whole number length is 13.

Answer:

Answer: Nolan took 97.75 Seconds

Step-by-step explanation:

85 x .15 = 12.75  

85 + 12.75 = 97.75

Finding x.

Suzette ran = x

Suzette biked = 4x

7 = x + 4x --) 7 = 5x --)  1.4 = x

Suzette ran for 1.4 hours

Finding y.

Quickest way is to use Suzette biked = 4x and substitute the x for 1.4 to find how much she biked.

4 x 1.4 = 5.6

1.4 + 5.6 = 7 hours the total time exercising

And the mileage adds up to.

5(1.4) + 20(5.6) = 119

Answer:

Its value in 2006 would be $99, 183, 639, 920

Step-by-step explanation:

Use the compounding interest formula for this one, which looks like this in its standard form:

[tex]A(t)=P(1+r)^t[/tex]

Our P is the initial amount of $24, the r in decimal form is .06, and the time between 2006 and 1626 in years is 380.  Fitting this into our formula we get:

[tex]A(t)=24(1+.06)^{380}[/tex] or

[tex]A(t)=24(1.06)^{380}[/tex]

First raise the 1.06 to the power of 380 on your calculator and then multiply in 24.

As for the second part of the question, I'm not quite sure how it's supposed to be answered. But maybe you can figure that out according to what the unit normally asks you to do.

Answer:

11.4 million

Step-by-step explanation:

Let's define the variables i and i' to represent the number of infected bacteria initially and after 1 hour, and the variables n and n' to represent the number of non-infected bacteria initially and after 1 hour. The biologist's theory predicts ...

0.50i +0.20n = i'

0.50i +0.80n = n'

In matrix form, the equation looks like ...

[tex]\left[\begin{array}{cc}0.5&0.2\\0.5&0.8\end{array}\right] \left[\begin{array}{c}i&n\end{array}\right]=\left[\begin{array}{c}i'&n'\end{array}\right][/tex]

If i''' and n''' indicate the numbers after 3 hours, then (in millions), the numbers are ...

[tex]\left[\begin{array}{cc}0.5&0.2\\0.5&0.8\end{array}\right]^3 \left[\begin{array}{c}11&5.2\end{array}\right]=\left[\begin{array}{c}i'''&n'''\end{array}\right][/tex]

Carrying out the math, we find i''' = 4.8006 (million) and n''' = 11.3994 (million).

The population of non-infected bacteria is expected to be about 11.4 million after 3 hours.

For this case we must indicate the percentage that represents the following expression:

[tex]\frac {1} {20}[/tex]

By a rule of three we can solve them:

20 ----------> 100%

1 ------------> x

Where the variable x represents the percentage of 1 with a base of 20.

[tex]x = \frac {1 * 100} {20}\\x = 5[/tex]

So, we have that [tex]\frac {1} {20}[/tex] represents 5%

Answer:

Option A

The required  1/20 is equal to 5% when expressed as a percentage. Option A is correct.

To find the percent equivalent to 1/20, we need to express it as a fraction of 100.

First, we can convert 1/20 into a decimal by dividing 1 by 20, which gives us 0.05.

Next, we multiply the decimal by 100 to express it as a percentage: 0.05 * 100 = 5%.

Therefore, 1/20 is equivalent to 5%.

In conclusion, 1/20 is equal to 5% when expressed as a percentage.

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Answer:

342.24 units²

Step-by-step explanation:

The area of one of the 8 triangular sections of the octagon is ...

A = (1/2)r²·sin(θ) . . . . . where θ is the central angle of the section

The area of the octagon is 8 times that, so is ...

A = 8·(1/2)·11²·sin(360°/8) = 242√2

A ≈ 342.24 units²

The area of the octagon should be 342.24 units²

Since the area of 1 of the 8 triangular sections of the octagon should be.

[tex]A = (1\div 2)r^2.sin(\theta)[/tex]

Here θ represent the central angle of the section

Since

The area of the octagon is 8 times

So,

[tex]A = 8.(1/2).11^2.sin(360\div 8) \\\\= 242\sqrt2[/tex]

A ≈ 342.24 units²

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Answer:

AE = 3

Step-by-step explanation:

Answer:

option b 5√2  

option a 20

option c 4

option d 3/4

option b 3

Step-by-step explanation:

To solve all these questions we will use trigonometry identity which says that

sinΔ = opposite / hypotenuse

1)

sin45 = 5 / KL

Kl = [tex]\frac{5}{\frac{\sqrt{2}}{2} }[/tex]

KL = 5√2  

2)

TanФ = opp / adj

Ф = Tan^-1(5/14)

Ф = 19.65

   ≈ 20

3)

sin(30) = rq / 8

rq = sin(30)(8)

rq = 4

4)

tan(Ф) = 6/8

5)

angle 3

Answer:

Step-by-step explanation:

1. The function is good for years 1880 to 2009, 0 to 129 years after 1880. Values of x can be anything in the domain [0, 129].

__

2. 1950 -1880 = 70. The year 1950 corresponds to x=70, so the function tells us the water level rose ...

  f(70) = 1.6·70 = 112 . . . . . mm

__

3. We want to find x when f(x) = 100. That will be the solution to ...

  100 = 1.6x

  100/1.6 = x = 62.5

Then 62.5 years after 1880 is year 1942.5. The water level was 100 mm higher than in 1880 in the year 1942.

Let Hannah = X and Heather = Y.

The sum of their ages is 30, so you would have x + y = 30

Then Hannah's age is 4 less than 2 times Heather's age so X = 2y-4

The equations are :

X + Y = 30 and X = 2y - 4

The answer is C.

Answer:

0.74 m

Step-by-step explanation:

The distance around a circle on the other hand is called the circumference (c).

A line that is drawn straight through the midpoint of a circle and that has its end points on the circle border is called the diameter (d) .

Half of the diameter, or the distance from the midpoint to the circle border, is called the radius of the circle (r).

The circumference of a circle is found using this formula:

C=π⋅d

or

C=2π⋅r

Given r = 119.3 mm

So, C = 2 * 3.14 * 119.3 = 749.2 mm = 0.74 m

Answer:

c ≈ 4.105

Step-by-step explanation:

You want to find c in ...

cos(13°) = 4/c

Multiply the equation by c/cos(13°) and evaluate.

c = 4/cos(13°) ≈ 4.105

Answer:

Solve the equation where the sine of 30 degrees is equal to YZ/50.

Solve 180 – (30 + 90) = 60 to find the measure of angle Z. Then use the cosine of Z to write and solve an equation.

Use the 30°-60°-90° triangle theorem to find that YZ = 50/2.

Step-by-step explanation:

These are the sample answers, use how you would like :)

2, -2, 2, -2, ...

This is a geometric progression.

First term = 2

The rate of geometric progression = -1

a1 = 2

a2 = a1 × (-1) = -2

a3 = a2 × (-1) = 2

And so on

⇒ This is a infinite geometric sequence

Answer:

Infinite geometric sequence

Step-by-step explanation:

2, -2, 2, -2, ...

Lets find the difference of the terms

-2 -2=0

2-(-2)=0

LEts check with common ratio

-2/2= -1

2/-2=-1

so common ratio r=0, so its geometric

The sequence is repeating because of common ratio -1

So it goes on infinitely

Hence it is Infinite geometric sequence

The slope is 3

I am not that shure on the y intercept

Answer:

  8 ft

Step-by-step explanation:

The height of the cross section through the apex will be the same as the height of the apex: 8 ft.

Start by describing the data given about the flower Heliconia's varieties. Then, conduct a significance test, possibly using ANOVA, to compare their mean lengths. However, the computation for the p-value and F-statistical is not specified in the question. You can just round your numbers according to the instructions.

The first step in a complete analysis is the description of the data. From the question, we have three types of tropical flower Heliconia, namely H. bihai, H. caribaea red, and H. caribaea yellow. We have the respective data points for each class, n, the sample mean, x-bar, standard deviation, s, and the standard error, s_(x-bar).

The next step is to carry out a significance test. This can be done using ANOVA (Analysis of variance), which compares the means of three or more samples. The test statistic in ANOVA is the F statistic, and the null hypothesis is that the population means are equal.

Given numbers, you can compute the F-statistic, but from the question, it's unclear how the actual computation was done. The p-value can also be calculated from the F statistic; it's the probability of getting an extreme or more extreme result in your observed data, assuming the null hypothesis is true.

The instruction is explicit regarding how to round your numbers: sample mean to four decimal places, standard deviation to three decimal places, and your test statistic (F-statistic) to two decimal places. The p-value should also be rounded to three decimal places.

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Answer:

  y = 90°

Step-by-step explanation:

The angle y subtends an arc of 180°, so its measure is 180°/2 = 90°. (We know the arc is 180° because the end points of it are on a diameter, so it is half a circle.)