A plan for a park has a rectangular plot of wild flowers that needs to be enclosed by 54 feet of fencing. Only three sides need to be enclosed because one side is bordered by the parking lot. use Desmos to get your answers. 1. What is the largest area possible for the garden? DO NOT ROUND YOUR ANSWER. ____ squared feet2. What width will produce the maximum area? ____ feet3. What is the length of the garden that will produce the maximum area?

opposite to angle 65 = BC

adjacent to angle 65 = 7

Explanation

Step 1

First, graph the inequality 1

the related equation is

now, get 2 coordinates of the line

a) when x=1

b)when x=0

now, draw a line that pases trought the coordinates we found.

Since the inequality is ≤ , not a strict one, the border line is solid

Step 2

Now, do the same for inequality 2

so

the related equation is

find 2 coordinates of the line

a)when x=0

b) when x=-2

now, draw the line 2, this lines passes trougth the coordiantes 3 and 4

Since the inequality is >, a strict one, the border line is dotted

Step 3

Graph:

in inequality (1) we need the values smaller r than -2x-3, it measn all values under the line,

and in Inequality 2 we need the values greater than 4x+7, it means all values over the line

so, the solution is the dark purple zone

I hope this helps you

Answer:

(x+4)(x-5)

Step-by-step explanation:

Second order polynomial in the following format:

ax² + bx + c = 0

Has roots x¹ and x².

Can be factored as:

(x - x¹)(x - x²)

So, we have to find the roots.

Finding the roots:

Bhaskara formula, which is:

In the polynomial given in this question:

a = 1, b = -1, c = -20

So

The roots are:

The factored form is:

(x - x¹)(x - x²) = (x - (-4))(x - 5) = (x+4)(x-5)

Use cosine law to find b:

To find the angles 1 and 2:

In the above triangle, the angles opposite to the equal sides are equal.

Let us take,

So, using the angle sum property of a triangle

Hence, the angles are

ANSWER

EXPLANATION

Given;

Recall, the general formula for slope - intercept form is;

comparing the given equation with the standard slope intercept form formula;

Hence, the graph of the given equation is;

One way to find the least common multiple of two numbers is to first list the prime factors of each number.

Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor by the greatest number of times it occurs.

Given:

⇒There are 61 students in total.

⇒12 of them got an A while 32 of them got a B.

⇒In total, 44 students did not get a C.

⇒So, 44 out of 61 students did not get a C.

Convert 44/61 into decimal form.

Answer:

The probability that a randomly chosen student did not get a C is 0.721 approximately.

The given numbers are -7,-5,-3.

The common differen

Answer:

D. 8pi yd^2

Explanation:

Area of a sector is expressed as;

r is the radius of the circle

theta is the angle substended at the centre

Given the following

r = 9yd

theta = 360-200

theta = 160degrees

Substitute

A = 160/360 * pi(9)^2

A = 4/9*18pi

A = 72pi/9

A = 8pi yd2

Hence the area of the shaded sector is 8pi yd2

We are asked to determine the total amount paid for 6 batteries and 4 folders. To do that we need to determine the unit price of each item. We do that by dividing the amount spent by the number of items that were bought. That is:

Now we multiply the desired number of items by each of the corresponding unit prices:

Solving the operations:

Therefore, the total amount paid is $11.

In order to calculate the product of a pair of conjugate terms, we can use the pattern below:

So we have:

1) Let's calculate that. Start by multiplying the factors 7, and 5.

After that, we use the property of the exponents when multiplying. Repeat the base and then add the exponents -8 + (-5) = -8 -5 = -13.

Using the distributive property, the maximum number of players that can be in the NBA is; 450 players

The distributive property is a property of algebra that states that you can distribute the contents of one parentheses into another to find an answer. For example;

a(b + c) = ab + ac

Now, we are told that there are 30 teams in the national basketball association and that each team has 12 healthy players plus three on injured reserve. Thus;

Number of players on each team = (12 + 3)

Now, for the 30 teams;

Total number of players for the teams = 30(12 + 3)

Applying distributive property, we have;

(30*12 + 30*3) = 450

Read more about distributive property at; https://brainly.com/question/2807928

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Answer:

which question you want to be answered

Answer:

[tex]\textsf{13.\;a)}\quad d=\dfrac{P}{0.5 \pi +1}[/tex]

[tex]\textsf{13.\;b)}\quad d=14\; \sf inches[/tex]

Step-by-step explanation:

The perimeter, P inches, of a semicircle of diameter, d inches, is represented by the equation:

[tex]\boxed{P=0.5 \pi d+d}[/tex]

Part (a)

To express d in terms of P, rearrange the equation to isolate d.

Factor out the common term d from the right side of the equation:

[tex]\implies P=d(0.5 \pi +1)[/tex]

Divide both sides by (0.5π + 1):

[tex]\implies \dfrac{P}{0.5 \pi +1}=\dfrac{d(0.5 \pi +1)}{0.5 \pi +1}[/tex]

[tex]\implies \dfrac{P}{0.5 \pi +1}=d[/tex]

[tex]\implies d=\dfrac{P}{0.5 \pi +1}[/tex]

Part (b)

Given:

Substitute the given values into the equation derived in part (a) and solve for d:

[tex]\implies d=\dfrac{36}{0.5 \left(\frac{22}{7}\right) +1}[/tex]

[tex]\implies d=\dfrac{36}{\frac{11}{7} +1}[/tex]

[tex]\implies d=\dfrac{36}{\frac{11}{7} +\frac{7}{7}}[/tex]

[tex]\implies d=\dfrac{36}{\frac{18}{7}}[/tex]

[tex]\implies d=36 \times \dfrac{7}{18}[/tex]

[tex]\implies d=\dfrac{252}{18}[/tex]

[tex]\implies d=14[/tex]

Therefore, the diameter is 14 inches.

we have that

interval (-infinite,0) ------> f(x)=5x+4

interval [0, infinite) ------> f(x)=x+7

Part B

f(0)

For x=0 ------> belong to the interval [0, infinite)

so

f(x)=x+7

substitute

f(0)=0+7

Part C

f(3)

For x=3 ---> belong to the interval [0, infinite)

so

f(x)=x+7

substitute

f(3)=3+7

Answer:

To graph a line you have to find two points on the line, one way of doing this is first setting x=0 and solving for y, as follows:

With the above calculations, we got that the point (0,-1) is on the line.

Now, to find another point on the line we set y=0 and solve for x:

With the above calculations, we got that the point (-4/3,0) is on the line.

Once we have those points we draw the line that passes through those points.

The graph of the given equation is:

The daily rate can be found by dividing the total number of books over the number of calendar days.

15,260 / 28 = 545

545 books per day

a For any relation to be a function, an independent variable x cannot produce different dependent varible y

From the table,

when x = 5, y = 2

Also, when x = 5, y = 5

and when x = 5, y = 7

We can see that x= 5 produces 3 different values of y ( that is 2, 5, and 7). This has disobeyed the rule of a function

Hence, the table is not a function

The answer is False

OPTION C

A quartic function is a fourth-degree polynomial: a function that has, as its highest order term, a variable raised to the fourth power.

From our question, it was easy to

Let:

A = Getting a 7

a = Number of sides with 7

N = Number of sides

so:

Given: (x² + 5x - 2)-(3x²-x+4)

Remove the parentheses:

Add like terms:

Answer:

An obtuse angle is an angle that measures more than 90° but not eauql or greater than 180°.

COA is the sum of COB and BOA, which is 90°, so COA is not obtuse.

BOA is 60°, so it is not obtuse.

DOA is a straight line, so it is 180°, so not obtuse.

DOB is COD plus COB. Since COA is 90°, DOC is also 90°, so DOC ples COB is 120°, which is between 90° and 180°, so DOB is obtuse and the correct alternative is C.

To calculate the maximum distance that the ball takes, we can use the first and second derivatives of y to find out this. We have:

Using the second derivative criterion, we have that y'' < 0, therefore, we have a maximum in the root of the first derivative. For that, we get the following:

Therefore, at x=28 is where the maximum distance is. Now we only substitute x=28 in y to find out:

Finally, we have that the ball will go 59 feet from the child

Solution:

An amount compounded is given as;

Given that;

Thus, we have;

Thus, the interest accrued in the first 4 years is;

FINAL ANSWER: $26,164.20

The correct option is:

Because we need to remember that the equation for a circumference centered in (h,k) and with radius r is:

x is an unknown number

twice a number means: 2x

and twice a number minus 19 means: 2x - 19

Answer:

Explanation:

Given:

$5.28 for 6 candy bars

$12.75 for 15 candy bars

To determine the better buy, we simplify each option first:

For $5.28 for 6 candy bars:

5.28/6 = $0.88 per candy bar

For $12.75 for 15 candy bars:

12.75/15 = $0.85 per candy bar

Therefore,

The square root of 2 is irrational

Here, we want to check if the square root of 2 is rational or not

When we talk of rational numbers, we mean numbers that can be expressed as the ratio of two integers

Roots of non-perfect squares such as two are not rational. They are referred to as irrational numbers. The special name they are called is surd

For the square, we have that each side's length is 2p, since the perimeter is the sum of the length of all sides of a geometric figure, this means that we have to add all the lengths of the square like this:

And we can do the same with the 3 sides of the triangle: