a rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). what dimensions should be used so that the enclosed area will be a maximum?

36×(35)-1000=1260-1000=260

Answer:

550.4 square units.

Step-by-step explanation:

This problem is easier than it seems.

To find the area of the parallelogram, multiply 11 and 32 to get 352 sq. units

The two semicircles must be equal because the sides of a parallelogram must be equal.

So if you add the semicircles together, you get a circle.

So we're really finding parallelogram+circle.

The area of a circle is [tex]\pi[/tex]x[tex]r^{2}[/tex], and the circle's radius is 8 because the radius is half of the diameter.

[tex]\pi[/tex]≈3.1 because you're rounding to the nearest tenth.

3.1x64=198.4 sq. units

198.4+352=550.4 square units.

In order to get the same outcomes as a form mirrored across the y-axis and turned counterclockwise, a shape can be reflected across the x-axis and then rotated 90 degrees in a clockwise manner around the origin. This suggests a similarity between these two transformative sequences.

What does mathematics mean by reflection?

A flip is the term used in geometry to describe a reflection. The mirror image of the form is a reflection. An image can reflect through a line known as the line of reflection. When all of the points in a figure are evenly spaced away from one another, the two figures are said to reflect each other.

(X, Y) > when a form is rotated 90 degrees counterclockwise (y, -x).

When the picture is reflected across the y-axis, (x, y) > (-x, y).

When those two transformations are used, it is the same as reflecting a shape across the line y = -x, where (x, y) > (-y, -x).

For instance: After being rotated 90 degrees clockwise and reflecting across the y-axis,

(2, 1) > (1, -2) > (-1, -2); and

(2, 1) > (-1, -2)

after being reflected across the y = -x line

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The graph has no vertex

The transformations from the parent function are

The graph represents the given parameter

As a general rule, the maximum or the minimum of a graph is the vertex

However, the graph has no maximum or minimum

This means that there is absence of a vertex in the graph

Here, we have:

This transformation can be represented as (x - 4, y - 2)

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The choice which describes a sequence of transformations in which the blue figure is the image of the red figure is: 4. Rotate the triangle 90º clockwise about the origin and then translate it 1 unit left and 7 units down.

In Mathematics, the rotation of a geometric figure 90° about the origin in a clockwise or counterclockwise direction would produce a geometric figure that has these coordinates (y, -x).

From the information provided in the graph about the transformation applied to the red triangle to create the blue triangle, we have the following ordered pairs that represents a rotation of 90º clockwise:

(x, y)                                    →              (y, -x)

Ordered pair A = (-5, 2)            Ordered pair A' = (2, 5)

Ordered pair B = (-5, 6)             Ordered pair B' = (6, 5)

Ordered pair C = (-1, 2)             Ordered pair C' = (2, 1)

After a translation of 1 unit left and 7 units down, we have:

Ordered pair A' = (2, 5)       →     Ordered pair A' = (2 - 1, 5 - 7) = (-1, -2)

Ordered pair B' = (6, 5)       →     Ordered pair B' = (6 - 1, 5 - 7) = (.5, -2)

Ordered pair C' = (2, 1)        →     Ordered pair C' = (2 - 1, 1 - 7) = (-1, -6)

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Answer:

Option D: 160 square feet

Step-by-step explanation:

Area of the lawn

= (7 feet × 8 feet) + (13 feet × 8 feet)

= 56 square feet + 104 square feet

= 160 square feet

The corresponding measure of each angle is 80, 80, 80, 100 and 100 degrees

Given: m<7=100 degrees

To find <6, <8, <2, <5 and <11

In the <7 is vertically opposite <5. Since vertically opposite angles are equal.

Thus, <5 =  <7 =   100 degrees

Also,  <5 and <6 are angles on a straight, and the sum of angles on a straight line is 180 degrees. Thus:

<5 + <6 = 180

100 + <6 = 180

<6 = 180 -100 = 80 degrees

Also, <6  and <8 are vertically opposite.

Thus, <8 = <6 = 80 degrees

<2 and <6 are corresponding angles, and corresponding angles are equal. Thus, <2 = <6 = 80 degrees

Likewise, <11 and <7 are corresponding angles

Thus, <11 = <7 = 100 degrees

Therefore, the measure of angle <6, <8, <2, <5 and <11 are 80, 80, 80, 100 and 100 degrees respectively

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Answer:

y = m x + b       equation for a straight line

when x = 4     y = 5

5 = m * 4 + b

m = (5 - b) / 4      solving for m

when x = -3      y = -1

-1 = (5 - b) / 4 * -3 + b = -3 * (5 - b) / 4 + 4 b / 4

-1 = (-15 + 3 b + 4 b) / 4

11 = 7 b      b = 11 / 7

Since m = (5 - b) / 4

m = (5 - 11/7) / 4  = 6/7

We then have y = 6 x / 7 + 11 / 7

Or 7 y = 6 x + 11

Check:

when (4 , 5)     35 = 24 + 11 = 35

Answer: The general form for an equation that models a wave is this: (+/-) a (sin/cos) (2π(x-p)/T), where a is your amplitude, p is your phase shift, and T is your period. The (+/-) becomes + if the graph is to start in the positive direction, and - if it is to start in the negative direction. The (sin/cos) becomes sine if the graph is to start at 0 before being shifted, while it becomes cosine if the graph is to start at the amplitude.

In this case, our graph starts out negative, and at the amplitude with no phase shift, so the (+/-) becomes -, (sin/cos) becomes cos, and p is zero. Substituting in the values given in the problem, a = 9 and T = 7, we find this equation: d = -9cos(2πt/7).

Step-by-step explanation:

Answer: he will be left with 31.74 dollars

Step-by-step explanation:

i first put 55.00 - 4.50 = 50.5

then you subtract 50.5 with 6.25  3 times so the and is 31.74

hope this helped !!

Step-by-step explanation:

70.31

hope it's helpful

Answer:

Step-by-step explanation:

no

The probability of drawing two yellow marbles if the first one is placed back in the bag before the second draw is 0.022

Since the formula we refer to in calculating probability is

P = no of possible outcomes/ total number of outcomes

Since we were provided with 10 marbles out of which 2 are yellow, 3  are pink and  5 are blue

So the total outcomes are = 1,The total number of yellow marble is  2

The probability that  the first ball drawn is yellow :

P₊= 2/10= 1/5

the probability of drawing the second ball to be yellow is:

P₂= 1/9

the total probability of  drawing two yellow marbles if the first one is placed back in the bag before the second draw is :

P= 1/5 *  1/9

= 1/45

= 0.022

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What is the probability of drawing two yellow marbles if the first one is NOT placed back into the bag before the second draw? There are 10 marbles total, 2 yellow, 3 pink, and 5 blue

The amount of energy that the ball will have at 10 m/s is; 600 J

From the given table, we see that when the velocity is 2 m/s, then the energy is 20 J.

If we take the square of the velocity, we get 2² = 4.

Thus, we need to multiply 4 by 6 to get the energy that is equal to 24 as 4 * 6 = 24.

Similarly;

For velocity equal to 3 m/s, the energy is given as:

E = 6 * 3²

E = 54 J

Thus, the general formula to find the energy is given as:

E = 6 * v²

where;

E is the energy

v is the velocity

Now, for velocity equal to 10 m/s, energy is given as;

E = 6 * 10

E = 60 J

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The equation of linear equation is y = -5x +3.

What is equation of linear equation?

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.

The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable. The standard form of linear equations in two variables is expressed as, Ax + By = C; where A, B and C are any real numbers, and x and y are the variables.

The slope intercept form of linear equation is

y = mx + b

where m is the slope.

Given,

The slope = -5

and the points are (4, -17)

y = -17, x = 4, m = -5

-17 = -5(4) + b

-17 = -20 + b

-17 + 20 = b

b =3

The equation of linear equation is y = -5x + b

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By using the concept of supplementary angle, it can be calculated that

The two angles are 47° and 133°

What are supplementary angles?

At first it is important to know about angle.

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

Two angles are said to be supplementary if the sum of the angles is 180°

Let one angle be x

Other angle = 180 - x

The supplement of an angle is 8 less than three times the measure of the angle

By the problem

180 - x = 3x - 8

3x + x = 180 + 8

4x = 188

x = [tex]\frac{188}{4}[/tex]

x = 47°

Other angle = 180 - 47 = 133°

The two angles are 47° and 133°

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The 4.89 hours after midnight did the temperature first hit 63 degrees.

A sinusoidal function can be used to mimic the daily variation in outdoor temperature. Assume you are aware that the daily average temperature starts at 9 am and swings between 60 and 70 degrees throughout the day.

We have to find to two decimal places, how many hours after midnight did the temperature first hit 63 degrees.

Max T=70 and Min T=60

D = (Max + Min)/2

   = 70+60/2

   = 65

A = Max- D

   = 70 - 65

   = 5

Since,

Period is 24 hours,

So,

W = 2π/24

   = π/12

The function will be:

T(t) = 5 Sin (π/12(t-C)) + 65

Given average temperature occurs at 8 am so,

T(9)=65

Solving this we get

C=9

Hence,

T(t)= 5Sin(π/12( t-9))+65

Now,

We need to find t such that T(t)=63

63=5Sin(π/12( t-9))+65

t = 4.89 hours.

Therefore, The 4.89 hours after midnight did the temperature first hit 63 degrees.

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Answer:

your answer is 16

Step-by-step explanation:

So, to solve (1 + 3)²

first add 1 and 3

then you will get 4

and your equation would be (4)²

then you just square 4.

(4)² > 4x4 = 16

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The predicted fuel efficiency for a speed of 30 mph will be 26.50 mpg when the least-squares regression line is given.

If the data demonstrates a stronger link between two variables, the line that best matches this linear relationship is known as a least-squares regression line, and it minimizes the vertical distance between the data points and the regression line. A regression line is a straight line that illustrates how a response variable y varies when an explanatory variable x changes. The line is a mathematical model that predicts the value of y given a value of x. A regression line predicts the value of y for a given value of x. A regression line is discovered through regression analysis. When the explanatory variable changes, the regression line shows how much and in which direction the response variable changes.

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The equation, in vertex form, of the graph in the diagram is determined as: y = 1|x - 3| + 5.

The formula that represents the equation in vertex form of an absolute value function is y = a|x - h| + k, where:

Vertex = (h, k).

Therefore, we will need to determine what the values of a, h, and k is using the information derived from the graph.

Thus:

(h, k) = (3, 5)

a = 1 (this is because the graph opens upward)

To write the equation of the graph, substitute a = 1, h = 3, and k = 5 into:

y = 1|x - 3| + 5

The equation is, y = 1|x - 3| + 5.

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The area of the figure is 21. 25 m². Option D

It is important to note that the figure is a kite.

The formula for calculating the area of a kite is expressed as;

A= pq/2

Where;

Using tangent identity

tan 45 = x/ 2. 5

1(2. 5) = x

x = 2. 5

p = 2. 5 + 2. 5 = 5

q = 2. 5 + 6 = 8. 5

Now, substitute the values into the formula

Area = 5(8. 5)/ 2

Area = 42. 5/ 2

divide the values

Area = 21. 25 m²

Hence, the value is 21. 25m²

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The measure of angle EAC IS 50°

The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts. For example, an angle bisector of a 60-degree angle will divide it into two angles of 30 degrees each. In other words, it divides an angle into two smaller congruent angles. Given below is an image of an angle bisector of ∠AOB.

∠BAE = x + 30, ∠EAC = 3x - 10

If AE is a line that bisects BAC,

then ∠BAE = ∠EAC

which becomes,

x + 30 = 3x - 10

collecting like terms,

x - 3x = -10 - 30

-2x = -40

x = -40/-2

x = 20°

But m ∠EAC = 3x - 10

substituting x = 20°

we have ∠EAC = 3(20) - 10

                          = 60 - 10

    ∠EAC       = 50°

In conclusion, the value of  ∠EAC  = 50°

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The cost of s and 20 songs are $1.25s and $25 respectively.

Multiplication is mathematical arithmetic operation. It is also a process of adding same types of expression to some number of times.

Example - 2 × 3 means 2 is added three times or 3 is added 2 times.

Given that music services cost $6 per month to Nachelle.

And to download songs for offline listening, the service charges $1.25 per song.

If she wants to download s songs,

The cost of s songs = the cost of one song multiplied by s

The cost of s songs =$1.25 multiplied by s

The cost of s songs = $1.25s

Here s = 20 then

cost of 20 songs = $1.25 x 20

                           = $25

Therefore the cost of s and 20 songs are $1.25s and $25 respectively.

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Answer:

156°

Step-by-step explanation:

m5 = m7 (vertical angles)
m4 + m5 = 180 (supplementary)
m5 = 180 - 124 = 156

So measure of both angle 5 and 7 is 156

As RS=TU and ST=UR by distance formula, The given quadrilateral RSTU is rectangle and The diagonals RT=US so they are equal and bisect each other at right angle.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel. An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.

Here,

Calculate the length of sides by distance formula.

RS=√(y2-y1)²+(x2-x1)²

=√(2-4)²+(-2-2)²

=√4+8

=√(12

=2√3 units

ST=√(y2-y1)²+(x2-x1)²

=√(0-2)²+(-1-(-2))²

=√(4+1)

=√5 units

TU=√(y2-y1)²+(x2-x1)²

=√(2-0)²+(3-(-1))²

=√(4+8)

=√12

=2√3 units

UR=√(y2-y1)²+(x2-x1)²

=√(4-2)²+(3-2)²

=√(4+1)

=√5 units

RT=√(y2-y1)²+(x2-x1)²

=√(0-4)²+(-1-2)²

=√(16+9)

=√25

=5 units

US=√(y2-y1)²+(x2-x1)²

=√(2-2)²+(-2-3)²

=√(0+25)

=√25

=5 units

Because the given quadrilaterals, RS=TU and ST=UR, are rectangles and the diagonals, RT=US, are equal and at right angles to one another, according to the distance formula.

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