Create a relation with 5 coordinates that is a function. Create the mapping for your relation

Answer:

Step-by-step explanation:

$3120 and $3888

width of the road=2m

outer Rectangle, I = 40m, b = 16m

Inner Rectangle, I = 36m, b = 12m

Area of Outer rectangle = 40x16= 640m2

Area of inner Rectangle = 36x12= 432m2

Area of the road=640-432 =208m2

cost of paving bricks  $15

=208x15 = $3120. Ans

Area of inner Rectangle 432m2

cost of covering with grass  $9

= 432x9= $3888.

Answer: brick cost= 3120 grass cost =3888

Step-by-step explanation:

Calculate area of the road by subtracting the area of the inner plot (36x12) from the area of the whole plot (40x16). Multiply the individual costs by the area of their respective places.

(40x16) - (36x12) = 208

208x16 = 3120

36x12 = 432

432x9 = 3888

Yes, if a figure can be rotated 360° to be mapped onto itself, it is considered to have rotational symmetry.

This is because a 360° rotation means that the figure will return to its original position, making it symmetrical. Rotational symmetry is a type of symmetry where a figure can be rotated about a central point and still look the same. The degree of rotational symmetry depends on the number of times a figure can be rotated to match its original appearance. Therefore, if a figure can be rotated 360° and maintain its original appearance, it is said to have rotational symmetry of degree 1. This is true regardless of the size, orientation, or position of the figure. Yes, a figure that can be rotated 360° to be mapped onto itself is considered to have rotational symmetry. Rotational symmetry occurs when an object can be rotated around a central point and still appear the same as its original position. In the case of a 360° rotation, the figure returns to its initial configuration, confirming its rotational symmetry.

To know more about symmetry visit:

https://brainly.com/question/29044130

#SPJ11

The square root of the number 84 is 2√21.

To find the square root of 84, follow these steps:

Thus, the square root of 84 is equal to 2√21, which is in simplest radical form.

Learn more about square root:

brainly.com/question/3617398

#SPJ11

Answer:

y = 1

d = 4

Step-by-step explanation:

8y - 2d = 0 ---------------(I)

5y + 4d = 26 1/4

5y + 4d =  105/4  ------------------(II)

(I)*2      16y  - 4d = 0

(II)          5y + 4d = 105/4      {add (I) &(II)}

             21y        = 105/4

\(y = \frac{105}{5*21}\\\\y=\frac{105}{105}\\\\y = 1\)

Substitute y =1 in equation (I)

8*1 - 2d = 0

8 - 2d = 0

   -2d = -8

      d = -8/-2

d = 4

Answer:

  (y, d) = (1.25, 5)

Step-by-step explanation:

We can add twice the first equation to the second.

  2(8y -2d) +(5y +4d) = 2(0) +26 1/4

  21y = 26 1/4

  y = (105/4)/21 = 105/84 = 5/4

  8(5/4) -2d = 0

  5 = d . . . . . . . . . . add 2d, divide by 2

The solution to this system of equations is ...

  y = 5/4, d = 5

\(\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =312 \end{cases}\implies s=\cfrac{(312)\pi (4)}{180}\implies s=\cfrac{104\pi }{15}\implies s\approx 21.8\)

Answer:

4 2/3

Step-by-step explanation:

7/9 multiplied by 6/1 = 42/9

Simplify: 14/3

Turn that into a mixed number: 4 2/3

In the given options, only option C has the form of a second-degree function, y = x², where a=1, b=0, and c=0.

Therefore, the correct answer is C.

What is the polynomial equation?

A polynomial equation is an equation in which the variable is raised to a power, and the coefficients are constants. A polynomial equation can have one or more terms, and the degree of the polynomial is determined by the highest power of the variable in the equation.

The function y = x² is a second-degree function because it contains a variable, x, raised to the second power.

Option A, y = x, is a first-degree function because it contains a variable, x, raised to the first power.

Option B, y = 3x - 7, is a first-degree function because it contains a variable, x, raised to the first power.

Option D, y = 3, is a constant function because it does not contain any variable raised to any power.

Therefore, the answer is option C, y = x² has the form of a second-degree function.

To learn more about the polynomial equation visit:

brainly.com/question/1496352

#SPJ1

Answer:

8(7+6)

Step-by-step explanation:

Answer:

10 30 15 16 48 24 25 75 37.5

Answer:

it will tale 11weeks to pay back his friends and he will have $112left after.

Step-by-step explanation:

88÷8=11.

200- 88 =112

Answer:

4.5

Step-by-step explanation:

Domain means that value of x and range means the value of f(x) so

\(f(x)=2x+1 \\f(1.75)=2(1.75)+1\\f(1.75)=4.5\)

so the range value is 4.5

A 120° angle and the side lengths can form more than one unique triangles

Malik's claim about the triangle is true

From the question, we have Malik's claim to be:

A 120° angle and side lengths of 3 cm and 4 cm can form more than one unique triangle

The above claim is true;

This is so because, the 120 degrees angle can be between the side lengths of 3 cm and 4 cm and the angle can be located not between the side lengths

This means that there are at least two unique triangles that can be formed using the given parameters

Hence, Malik's claim about the triangle is true

Read more about unique triangles at:

https://brainly.com/question/17972372

Answer:

2.048, 2.48, 2.4812, 2.5

From lowest to highest

Step-by-step explanation:

Answer

2.048 ,2.48, 2.4812, 2.5

Step-by-step explanation:

A point that would satisfy both inequalities include the following: B. (10, 9).

In order to graph the solution for the given system of linear inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of linear inequalities and then check the point of intersection;

y > -1/4(x) - 5          .....equation 1.

y > x - 2       .....equation 2.

Based on the graph, we can logically deduce that the solution to the given system of linear inequalities is the shaded region after the point of intersection of the dashed lines on the graph representing each, which may be denoted by the ordered pairs (10, 9).

Read more on inequalities here: brainly.com/question/17064077

#SPJ1

There are no dimensions that minimize the cost of the box while maintaining a volume of 20.

To find the dimensions that minimize cost, we need to consider the relationship between the volume of the box and the cost of the materials used.

Let's start by determining the dimensions of the box. We know that the box has a volume of 20. Since the box is constructed out of two different types of metal, we can divide the box into two parts: the top and bottom, which are both squares, and the sides.

Let's assume the length of each side of the top and bottom squares is x. Therefore, the area of each square is x * x = x^2.

The height of the box can be represented by h.

Since the box has a volume of 20, we can set up an equation:
x^2 * h = 20

Now, let's determine the cost of the materials used.

The metal for the top and bottom squares costs 1/ft^2, so the cost for each square is x^2 * (1/ft^2) = x^2/ft^2.
The metal for the sides costs 2/ft^2, so the cost for the sides is 4 * (x * h) * (2/ft^2) = 8xh/ft^2.
The total cost of the materials is the sum of the cost for the top and bottom squares and the cost for the sides:
Cost = (x^2/ft^2) + (8xh/ft^2)

To minimize the cost, we can differentiate the cost function with respect to x and h, and then set the derivatives equal to zero:
dCost/dx = 2x/ft^2 + 8h/ft^2 = 0  (equation 1)
dCost/dh = 8x/ft^2 = 0  (equation 2)

From equation 2, we can see that x = 0 is not a valid solution since it represents a box with zero dimensions. Therefore, x ≠ 0.

From equation 1, we can solve for h:
2x/ft^2 + 8h/ft^2 = 0
8h/ft^2 = -2x/ft^2
h = -2x/8

Since h represents the height of the box, it cannot be negative. Therefore, h ≠ -2x/8.
To find the valid values of x and h, we can substitute the value of h into the equation for the volume:
x^2 * (-2x/8) = 20

Simplifying this equation gives:
-2x^3/8 = 20
-2x^3 = 160
x^3 = -80

Since we're looking for dimensions, x cannot be negative. Therefore, there are no valid values of x and h that satisfy the equation for the volume.

In conclusion, there are no dimensions that minimize the cost of the box while maintaining a volume of 20.

To know more about volume refer here:

https://brainly.com/question/32714484

#SPJ11

Answer:

y+t+x+1

Step-by-step explanation:

y+t+x+1 since all the variables are unlike terms

Answer:

A no. is correct one

Step-by-step explanation:

Hope it will help you. and please mark me brilliant

Answer:

A

Step-by-step explanation:

12x+6x=90deg

90deg+90deg=180deg

Answer:

Answer:

1.) \(\frac{1}{2}\) ÷ 4 = \(\frac{1}{8}\)

2.) \(\frac{1}{3}\) ÷ 4 = \(\frac{1}{12}\)

3.) \(\frac{1}{4}\) ÷ 5 = \(\frac{1}{20}\)

4.) \(\frac{1}{4}\) ÷ 4 = \(\frac{1}{16}\)

5.) 3 ÷ \(\frac{1}{4}\) = 12

6.) 4 ÷ \(\frac{1}{2}\) = 8

7.) 5 ÷ \(\frac{1}{4}\) = 20

8.) 4 ÷ \(\frac{1}{4}\) = 16

Hope this helps!

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{540 \: m}}}}}\)

Step-by-step explanation:

Let the length and breadth be 5x and 4x respectively.

Area of rectangular field = 18000 m²

Finding the value of x

Area of rectangle = \( \sf{l \times b}\)

Plug the values

⇒\( \sf{18000 = 5x \times 4x}\)

Calculate the product

⇒\( \sf{18000 = 20 {x}^{2} }\)

Swap the sides of the equation

⇒\( \sf{20 {x}^{2} = 18000}\)

Divide both sides of the equation by 20

⇒\( \sf{ \frac{20 {x}^{2} }{20} = \frac{18000}{20} }\)

Calculate

⇒\( \sf{ {x}^{2} = 900}\)

Squaring on both sides

⇒\( \sf{x = 30}\)

Replacing the value of x in order to find the value of length and breadth

Length = \( \sf{5x = 5 \times 30 = 150 \: m}\)

Breadth = \( \sf{4x = 4 \times 30 = 120 \: m}\)

Finding the perimeter of the rectangular field

Perimeter of rectangle = \( \sf{2(l + b)}\)

plug the values

⇒\( \sf{2(150 + 120)}\)

Distribute 2 through the parentheses

⇒\( \sf{300 + 240}\)

Add the numbers

⇒\( \sf{540 \: m}\)

Hope I helped !

Best regards!!

If they sold 100 lunches, they would make a profit of $180.

a) Write the corresponding equation for cost, revenue, and profit. Cost equationC(x) = 3x + 120 where x is the number of lunchesRevenue equationR(x) = 6xProfit equationP(x) = R(x) − C(x)Therefore,P(x) = 6x − (3x + 120)P(x) = 3x − 120

b) How many rations of lunch must the graduating class sell to break even?The equation for the profit function is:P(x) = 3x − 120Let P(x) = 0, since we want to find out when the profit equals zero0 = 3x − 120120 = 3x40 = xTherefore, the number of lunch the graduating class must sell to break even is 40.

c) What profit or loss would result if they sold 100 lunches?

Given: number of lunches sold, x

= 100 Substitute x

= 100 into the profit equation to find the profit or loss P(x)

= 3x − 120P(100)

= 3(100) − 120P(100)

= 300 − 120P(100)

= $180

To know more about lunches visit:

brainly.com/question/11128867

#SPJ11

The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.

Triangles are polygons with three sides and three perpendicular bisectors, whose equations need the informations of slopes and midpoints of each side. Bisectors are lines that partitions line segments in two parts of equal length.

First, determine the midpoints of each side:

Side AB

M₁(x, y) = 0.5 · (- 3, 0) + 0.5 · (0, 6)

M₁(x, y) = (- 1.5, 0) + (0, 3)

M₁(x, y) = (- 1.5, 3)

Side BC

M₂(x, y) = 0.5 · (0, 6) + 0.5 · (4, 6)

M₂(x, y) = (0, 3) + (2, 3)

M₂(x, y) = (2, 6)

Side AC

M₃(x, y) = 0.5 · (- 3, 0) + 0.5 · (4, 6)

M₃(x, y) = (- 1.5, 0) + (2, 3)

M₃(x, y) = (0.5, 3)

Second, determine the slope of the perpendicular bisectors:

Side AB

m = (6 - 0) / [0 - (- 3)]

m = 2

m' = - 1 / m

m' = - 1 / 2

Side BC

m = (6 - 6) / (4 - 0)

m = 0

m' = - 1 / m

m' = NaN  (Vertical line)

Side AC

m = [4 - (-3)] / (6 - 0)

m = 7 / 6

m' = - 1 / (7 / 6)

m' = - 6 / 7

Third, derive the equations of the bisectors:

Side AB

b = 3 - (- 1 / 2) · (- 1.5)

b = 9 / 4

y = - (1 / 2) · x + 9 / 4

Side BC

x = 2

Side AC

b = 3 - (- 6 / 7) · (0.5)

b = 24 / 7

y = - (6 / 7) · x + 24 / 7

The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.

To learn more on bisectors: https://brainly.com/question/13880193

#SPJ1

As we have proved that if p is an odd prime, then the product 1² · 3² · ... · (p-2)² is congruent to -1 modulo p.

To prove the statement, let's consider the product P = 1² · 3² · ... · (p-2)². Our goal is to show that P ≡ -1 (mod p), which means P leaves a remainder of -1 when divided by p.

First, we note that p is an odd prime. This means that p can be expressed as p = 2k + 1, where k is an integer. We can rewrite P using this representation:

P = (1 · 1) · (3 · 3) · ... · ((2k - 1) · (2k - 1)).

Now, let's examine P more closely. We can write each factor in P as:

(2i - 1) · (2k - (2i - 1)).

Expanding this expression, we get:

(2i - 1) · (2k - 2i + 1) = 4ik - 2i + 2ki - k - 2i + 1 = 4ik - 4i + 2ki - k + 1.

We can simplify this further as:

(4ik - 4i + 2ki - k + 1) = (4ik - 4i) + (2ki - k + 1) = 4i(k - 1) + k(2i - 1) + 1.

Now, let's consider the expression (2i - 1) modulo p. Since p = 2k + 1, we can rewrite (2i - 1) as:

(2i - 1) ≡ 2i - 1 (mod p).

Substituting this back into our expression for P, we have:

P ≡ (4i(k - 1) + k(2i - 1) + 1) (mod p).

Now, let's consider the sum (4i(k - 1) + k(2i - 1)) modulo p. We can write this as:

(4i(k - 1) + k(2i - 1)) ≡ 4ik - 4i + 2ki - k ≡ -3i + k(i - 1) (mod p).

Since p = 2k + 1, we have -3i + k(i - 1) ≡ -3i + (p - 1)(i - 1) (mod p).

Expanding (p - 1)(i - 1), we get:

-3i + (p - 1)(i - 1) = -3i + pi - p - i + 1 = -4i - p + pi + 1.

Now, let's consider the expression (-4i - p + pi + 1) modulo p. We can rewrite this as:

(-4i - p + pi + 1) ≡ -4i - p (mod p).

Since -p ≡ 0 (mod p), we have -4i - p ≡ -4i (mod p).

Therefore, we have shown that:

P ≡ -4i (mod p).

Now, let's consider the range of i. We know that i takes on values from 1 to (p - 2)/2, inclusive. Since p is an odd prime, (p - 2)/2 is an integer. Therefore, we can rewrite P as:

P ≡ -4(1 + 2 + 3 + ... + [(p - 2)/2]) (mod p).

The sum 1 + 2 + 3 + ... + n can be expressed as n(n + 1)/2. Substituting this into our expression for P, we get:

P ≡ -2[(p - 2)/2] [(p - 2)/2 + 1] (mod p).

Simplifying further, we have:

P ≡ -[(p - 2)/2] [(p - 2)/2 + 1] (mod p).

Since p is an odd prime, we can rewrite p - 2 as 2k - 1. Substituting this into our expression, we get:

P ≡ -[k] [k + 1] (mod p).

Now, let's expand the product [k] [k + 1]:

[k] [k + 1] = k² + k.

Substituting this back into our expression for P, we have:

P ≡ -(k² + k) (mod p).

Now, recall that p = 2k + 1. Substituting this into our expression, we get:

P ≡ -(k² + k) ≡ -(k² + k + 1) + 1 ≡ -(k² + 2k + 1) + 1 ≡ -[(k + 1)²] + 1 (mod p).

Since p = 2k + 1, we have (k + 1)² ≡ -1 (mod p). Substituting this back into our expression, we finally have:

P ≡ -[(k + 1)²] + 1 ≡ -1 + 1 ≡ 0 ≡ -1 (mod p).

To know more about prime here

https://brainly.com/question/30646191

#SPJ4

Answer:

The total length of the string is 7.85 feet and  the center should be 2.236 feet far the string be nailed into the base

Step-by-step explanation:

Circumference of ellipse = \(\pi(a+b)\)

Circumference of semi-ellipse = \(\frac{\pi(a+b)}{2}\)

we are given that The opening is to have a height of 2 feet at the center and a width of 6 feet along the base.

So, \(a = \frac{6}{2}=3 , b = 2\)

Circumference of semi-ellipse =\(\frac{3.14(3+2)}{2}=7.85 feet\)

Distance from center =\(\sqrt{a^2-b^2}=\sqrt{3^2-2^2}=2.236 feet\)

Hence the total length of the string is 7.85 feet and  the center should be 2.236 feet far the string be nailed into the base

Answer: Right

Step-by-step explanation: You have 3 angles, two are less than 90 degrees while the other is exactly 90, that would make this a right triangle.

Answer:

sat: 28:63

sun:32:72

Step-by-step explanation:

thats is.

If p(a) = 0.3, p(b) = 0.2, and p(a and b) = 0.0, then we can say that events a and b are mutually exclusive.

When two events are said to be mutually exclusive or disjoint, it means that they cannot occur simultaneously. This can be demonstrated mathematically using the formula:

P(A and B) = 0If two events, A and B, are mutually exclusive, the probability of their joint occurrence is zero.

As a result, when p(a) = 0.3, p(b) = 0.2, and p(a and b) = 0.0, it implies that events a and b are mutually exclusive.

This means that when event A occurs, event B will not occur, and vice versa. In other words, the occurrence of event A excludes the occurrence of event B and the occurrence of event B excludes the occurrence of event A.

Learn more about the probability at:

https://brainly.com/question/14051468

#SPJ11