You have 200 feet of fencing to enclose a rectangular plot that borders on a river (a long side borders the river). If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?

Looking at the diagram, PQ = 18 and PR = 31

We can see that

PQ + QR = PR

Therefore,

18 + QR = 31

QR = 31 - 18

QR = 13

The number of mosquitoes on the colony after 4 days is 2800.

The number of days that there are 70,000 mosquitoes will be 114 dad.

The population of a colony of mosquitoes obeys the law of uninhibited growth and there are 1000 mosquitoes initially and there are 1600 after 1 day. The common difference will be:

= 1600 - 1000

= 600

The formula for the arithmetic sequence will be:

= a + (n - 1)d

a = 1000

d = 600

n = 4

The colony after 4 days will be:

= a + (n - 1)d

= 1000 + (4 - 1)600

= 1000 + 1800

= 2800

The number of days that there are 70,000 mosquitoes will be:

a + (n - 1)d = 70000

1000 + 600(n - 1) = 70000

1000 + 600n - 600 = 70000

Collect like terms

600n = 70000 - 1000 + 600

600n = 68400

n = 68400/600

n = 114 days

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Answer: - 37

Step-by-step explanation:

so (2-5)(3+7) - (4+3) start off by the right side really doesn't matter what side you start on, but I added 4+3=7

x= (2-5)(10) - (7) Then add 3+7=10

x= (-3)(10) - (7) 3rd subtract 2-5=-3

x= -30 - 7 Next multiply -3*10=-30 because two numbers together with parenthesis means multiplication.

x= -37  Lastly subtract -30 - 7 and I got -37

The selling price of the adventurers swing set given the wholesale price and the mark-up price is $3,674.84.

The selling price of the adventurers swing set is the sum of the wholesale price and the percentage mark-up. Mark-up is the rate at which the selling price of an item is increased.

Percentage is the rate of an amount expressed as a number out of hundred. The sign that is used to represent percentages is %.

Selling price = wholesale price x (1 + mark-up price)

3,056 x (1 + 0.2025)

3056 x 1.2025 = $3,674.84

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The circumference of a circle whose area is 9π cm² in terms of pi is 6π centimeters.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

The circumference of a circle is expressed mathematically as;

C = 2πr

Given that the area of the circle is 9πcm², we determine the radius of the circle.

A = πr²

9πcm² = π × r²

r² = 9πcm² / π

r² = 9cm²

r = √9cm²

r = 3cm

Now, we determine the circumference of the circle.

C = 2πr

C = 2 × π × 3cm

C = 6cm × π

C = 6π cm

Therefore, the circumference of the circle is 6π centimeters.

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Answer:

18$ with a 1/3 discount applied

Step-by-step explanation:

27 divided by 3=9

27-9=18

Answer:

$18

Step-by-step explanation:

1/3 = ~33.33% off

33.33% of 27 = 9

27-9 = 18

Hope that helps

By focusing on x- axis we can get value of f(3).

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

We have a function f(x).

Now, we have to find the value of f(3) from the graph

So, If we had the graph of f(x) and wanted to find f(3), we would look for the location on the graph where x = 3, then determine its y-value.

The response to f(3) is that y-value.

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Answer:

Step-by-step explanation:

STEP

1

:

           9

Simplify   —

           4

Equation at the end of step

1

:

                       9

 ((x2) -  5x) -  (0 -  —)  = 0

                       4

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  4  as the denominator :

               x2 - 5x     (x2 - 5x) • 4

    x2 - 5x =  ———————  =  —————————————

                  1              4      

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  x2 - 5x  =   x • (x - 5)

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • (x-5) • 4 - (-9)     4x2 - 20x + 9

————————————————————  =  —————————————

         4                     4      

Trying to factor by splitting the middle term

3.3     Factoring  4x2 - 20x + 9

The first term is,  4x2  its coefficient is  4 .

The middle term is,  -20x  its coefficient is  -20 .

The last term, "the constant", is  +9

Step-1 : Multiply the coefficient of the first term by the constant   4 • 9 = 36

Step-2 : Find two factors of  36  whose sum equals the coefficient of the middle term, which is   -20 .

     -36    +    -1    =    -37

     -18    +    -2    =    -20    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -18  and  -2

                    4x2 - 18x - 2x - 9

Step-4 : Add up the first 2 terms, pulling out like factors :

                   2x • (2x-9)

             Add up the last 2 terms, pulling out common factors :

                    1 • (2x-9)

Step-5 : Add up the four terms of step 4 :

                   (2x-1)  •  (2x-9)

            Which is the desired factorization

Equation at the end of step

3

:

 (2x - 9) • (2x - 1)

 ———————————————————  = 0

          4        

STEP

4

:

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 (2x-9)•(2x-1)

 ————————————— • 4 = 0 • 4

       4      

Now, on the left hand side, the  4  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  (2x-9)  •  (2x-1)  = 0

Theory - Roots of a product :

4.2    A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

4.3      Solve  :    2x-9 = 0

Add  9  to both sides of the equation :

                     2x = 9

Divide both sides of the equation by 2:

                    x = 9/2 = 4.500

Solving a Single Variable Equation:

4.4      Solve  :    2x-1 = 0

Add  1  to both sides of the equation :

                     2x = 1

Divide both sides of the equation by 2:

                    x = 1/2 = 0.500

Supplement : Solving Quadratic Equation Directly

Solving    4x2-20x+9  = 0   directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

5.1      Find the Vertex of   y = 4x2-20x+9

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 4 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   2.5000  

Plugging into the parabola formula   2.5000  for  x  we can calculate the  y -coordinate :

 y = 4.0 * 2.50 * 2.50 - 20.0 * 2.50 + 9.0

or   y = -16.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 4x2-20x+9

Axis of Symmetry (dashed)  {x}={ 2.50}

Vertex at  {x,y} = { 2.50,-16.00}

x -Intercepts (Roots) :

Root 1 at  {x,y} = { 0.50, 0.00}

Root 2 at  {x,y} = { 4.50, 0.00}

Answer:

3 feet

Step-by-step explanation:

s= sandra

L= Lamp

if you know that the lamp is four feet away, and the bird is five feet away. go vertically up from the lamp until the distance from the lamp vertically equals five feet back to sandra.

The graph of h against m is plotted in form of a curve.

Given:

A tree branch is observed to bend as the fruit growing on it increases in size.

The height h in metres of the branch end above the ground is closely approximated by the function [tex]h=2-0.2*1.60^{0.2m}[/tex] where m is the estimated mass, in kilograms, of fruit on the branch.

We have to sketch the graph of h against m.​

The x-axis represents the mass in kg while the y-axis represents the height of the branch above the ground in metres.

Hence a curved graph is obtained by plotting the function.

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Using a system of equations, it is found that the amounts of money that each of Gabriel, Daniel and Edgar have are given as follows:

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the problem.

In the context of this problem, the variables are given as follows:

Gabriel has double the amount of Daniel, hence:

x = 2y.

Gabriel has five times the amount of Edgar, hence:

x = 5z.

If Gabriel loans Q14 to Daniel and Q33 to Edgar, they will have the same amount, hence:

x - 47 = y + 14 = z + 33.

Since x = 2y, we can replace into the first two sides of the equality above and solve for y as follows:

2y - 47 = y + 14

y = 61. (Daniel's amount).

The solution for x is given as follows:

x = 2y = 2(161) = 122 (Gabriel's amount).

The solution for z is given as follows:

x - 47 = z + 33

122 - 47 = z + 33

75 = z + 33

z = 75 - 33

z = 42 (Edgar's amount).

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Answer: the slope of this equation is 8

Step-by-step explanation: y = 8x - 15, the 8x represents the slope of this equation

Answer:

y - 4 = 3(x - 3) or y - 7 = 3(x - 4)

Step-by-step explanation:

y1 = mx1 + b

y2 = mx2 + b

(3, 4) = (x1, y1)

(4, 7) = (x2, y2)

4 = 3m + b

7 = 4m + b

-3 = -m

m = 3

y - y1 = m(x - x1)

y - 4 = 3(x - 3)

Answer:

Answer down below!

Step-by-step explanation:

If we draw this out, we already know that m<7 = 96

Using what we already know, we can figure out the rest

m<6 also equals 96 because m<7 and m<6 are verticle angles

m<3 also equals 96 because m<6 and m<3 are opposite interior angles

m<2 also equals 96 because m<3 and m<2 are verticle angles

Now, to find m<4, simply subtract 96 from 180. That should give you 84

Thus, m<2 = 96 and m<4 = 84

Answer:

The set of all the first element of the ordered pairs of R is called domain and the set of all the second element of the ordered pairs of R is called range .

The perimeter of the triangle is 29.31 units and the area of the triangle is 38.87 units^2

To find the perimeter and area of the triangle, we have to use the formula of distance between two points.

Distance between AB

[tex]d_a_b = \sqrt{(a_1+a_2)^2 + (b_1 + b_2)^2} \\d_a_b = \sqrt{(3+1)^2 + (-3-3)^2}\\ d_a_b = \sqrt{4^2 + 9^2} \\d_a_b = 9.85 units[/tex]

Distance between BC

[tex]d_b_c = \sqrt{(b_1+b_2)^2 + (c_1+c_2)^2}\\d_b_c = \sqrt{(-9)^2 + (7)^2}\\d_b_c = \sqrt{130} \\d_b_c = 11.40 units[/tex]

Distance between AC

[tex]d_a_c = \sqrt{(a+1_a_2)^2 + (c_1+c_2)^2} \\d_a_c = 8.06 units[/tex]

The perimeter of the triangle is equal to

[tex]p = 9.85 + 11.40 + 8.06 = 29.31 units[/tex]

The area of the  triangle is 38.87 units^2

Kindly find the attached graph below;

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The number of time Easton's song was played on commercials is 10 times.

The number of time Easton's song was played during a movie is 4 times.

The first step is to form a system of equations:

40c + 110m = 840 equation 1

c - m = 6

c = 6 + m equation 2

Where:

The system of equations would be solved using the substitution method.

Substitute for c in equation 1 using equation 2

40(6 +  m) + 110m = 840

240 + 40m + 110m = 840

40m + 110m = 840 - 240

150m = 600

m = 600 / 150

m = 4

Substitute for m in equation 2.

c = 6 + 4

c = 10

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Explanation

Given the trigonometric expression

We can find the solutions below;

From trigonometry identities;

Therefore; we will have;

Therefore, the general solutions for the above is given as;

Answer:

Answer:

r = 3t/t-1

Step-by-step explanation:

t = r/r-3

1. times both sides by r-3

t(r-3) = r

= tr - 3t = r

2. add 3t to both sides

tr = 3t + r

3. minus r

tr - r = 3t

4. factorise out r

r(t-1)=3t

5. divide by t-1

r = 3t/t-1

Answer:

94 ft

Step-by-step explanation:

The z-scores for a 67-inch- man and a 62-inch woman are -0.9667 and -0.5526, respectively.

The z-score is a numerical measurement used in statistics to determine the sample data value's relationship to the mean of a group of values, measured in terms of standard deviation from the mean. It is measured as the difference of the sample data value and the sample mean over the standard deviation, such that

z-score = (x – μ) / σ

where x = sample data value

μ = mean

σ = standard deviation

For a 67-inch- man, use the formula to solve for the z-score.

x = 67

μ = 69.9

σ = 3.0

z-score = (x – μ) / σ

z-score = (67 - 69.9) / 3.0

z-score = -0.9667

Do the same for a 62-inch- man, use the formula to solve for the z-score.

x = 62

μ = 64.1

σ = 3.8

z-score = (x – μ) / σ

z-score = (62 - 64.1) / 3.8

z-score = -0.5526

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The height of the yellow mark above the water is 1 foot.

This is further explained below.

Generally, The radius of a waterwheel is 4 feet, and its center is 1 foot below the waterline.

Estimation of feet:

cos π/3 = OB/OA

1/2 = OB/4

OB = 2

t

In conclusion,A yellow mark should be placed above the water

= OB - OD

= 2 - 1

= 1 foot

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Answer:

the other answer is correct is A. 1 foot

Step-by-step explanation:

Got it right on edge

Answer:

y = -x + 6

Step-by-step explanation:

Slope-intercept is the y = mx + b form, in which m is the slope, and b is the y-intercept.

From the graph provided, we can see that the line intercepts the y axis when the y-coordinate is 6, so we can use 6 as "b" in the equation.y₂

The slope can be found by picking two points on the graph, calling the first point (x₁, y₁) and the second point (x₂, y₂), and applying the formula slope = (y₂ - y₁) ÷ (x₂ - x₁).

Now, we pick two points - I'm choosing (1, 5) and (2, 4) - and apply the formula.

(4 - 5)  ÷ (2 - 1) = -1/1 = -1

Therefore, we know our slope is -1

Putting this all together, we get y = -1x + 6, which we can simplify to y = -x + 6 (since -1 * x is the same as -x)

The pipe leaking in gallons per day is [tex]\frac{69}{16}[/tex] gallons/day.

The Janitor find the leakage in the pipe at a rate of [tex]23[/tex] fl oz per hour.

We have to find how fast was the pipe leaking in gallons per day​.

To find the leaking in gallons per day​ we have to convert [tex]23[/tex] fl oz per hour into gallons per day.

As we know that

[tex]1[/tex] gallon[tex]=128[/tex] fl oz

So [tex]1[/tex] fl oz[tex]=\frac{1}{128}[/tex] gallons

There are [tex]24[/tex] hours in a day so we multiply with [tex]24[/tex] to convert in day.

So the expression should be

[tex]=23[/tex] fl oz/hours[tex]\times\frac{1}{128}[/tex] gallons/fl oz[tex]\times24[/tex] hours/day

[tex]=\frac{23\times24}{128}[/tex] gallons/day

[tex]=\frac{23\times3}{16}\\[/tex] gallons/day

[tex]=\frac{69}{16}[/tex] gallons/day

Hence, the pipe leaking in gallons per day is [tex]\frac{69}{16}[/tex] gallons/day.

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Answer: 10%

Step-by-step explanation:

     First, we will find the amount that was saved from the markdown.

$50 - $45 = $5

     Next, we will find what percent this is of $50.

$5 / $50 = 0.1 ➜ 10%

     The discount, as a percentage, is 10%.

Answer:

C

Step-by-step explanation:

I'm to lazy to type it out so...I took a photo

I hope this helps :D

and I need brainiliest so bad...