Find the area of the shaded region

Answer:

A' = (-18, 54)

Step-by-step explanation:

Answer:

A.) The greatest possible distance between any of the stakes is 53 feet.

B.) A triangle with sides 15, 36, and 39 is a right triangle and has perimeter 90 feet.

Step-by-step explanation:

Given - Fiona wants to rope off a triangular region in her yard for a vegetable garden. She has 90 feet of rope to use, she wants the distance between each stake to be an integer, and the distance between two of the stakes must be 36 feet.

To find - A. What is the greatest possible distance between any of the stakes?

B. If she wants to create a right triangular region and use all of the 90 feet of rope, what would be the lengths of the sides of the region?

Solution -

A.)

Let us assume that,

Length of side 1 = x

Length of side 2 = y

Length of side 3  = z

Now,

Given that,

She has 90 feet of rope to use

⇒x + y + z = 90

And

The distance between two of the stakes must be 36 feet.

So, Let z = 36.  

∴ we get

x + y + 36 = 90

⇒x + y = 90 - 36

⇒x + y = 54

Now,

Let x be as large as possible.

i.e. To make x to be large, y has to be as small as possible.

It happens when y = 1.

( We can not take y = 0, or else a triangle won't form)

∴ we get

y = 1

⇒x + 1 = 54

⇒x = 54 - 1

⇒x = 53

∴ we get

The greatest possible distance between any of the stakes is 53 feet.

B.)

We know that,

(5,12,13) is a Pythagorean triple.

Because 5² + 12² = 13²

So,

As, we have a Pythagorean triple,

This means a triangle with sides 5, 12, 13 is a right triangle.

Now,

If a triangle has sides 5, 12, 13,

⇒ The perimeter becomes 5 + 12 + 13 = 30.

By Triple each side we get,

Length of sides 15, 36, 39.

The perimeter i= 15 + 36 + 39 =  90

Also,

We can see that,

15² + 36² = 39².

This means we have a right triangle and (15, 36, 39) is another Pythagorean triple.

Because any scaled version of a Pythagorean triple, is also a Pythagorean triple.

∴ we get

A triangle with sides 15, 36, and 39 is a right triangle and has perimeter 90 feet.

In given right triangle ACB, the ratios for sin A and cos A :

sin(A) = 48/50

cos(A) = 14/50

Consider the following diagram.

In a right triangle ACB, the angle ACB = 90 degrees.

We know that in right triangle for an angle θ, the trigonmetric ratios are:

sin(θ) = opposite side of θ/ hypotenuse

cos(θ) = adjacent side of θ / hypotenuse

Here, side AC = 14 units, side CB = 48 units and the hypotenuse AB = 50 units

We need to find the ratios for sin A and cos A

In right triangle ACB for angle A,

sin(A) = opposite side of angle A/ hypotenuse

sin(A) = CB/AB

sin(A) = 48/50

And cos(A) = adjacent side of A / hypotenuse

cos(A) = AC/AB

cos(A) = 14/50

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Answer:

3/2

Step-by-step explanation:

   Write out the following:

               5              1                      

           ----------- = --------- = 3/2

             5 1/3          2/3                      

3 1/3 = 10/3

5/1 : 10/3 = 5/1 x 3/10 => 15/10 = 3/2

Answer = 3/2

The relationship between the input  and output  is that the perimeter of a square is always equal to four times the length of one of its sides.

The perimeter of a square is the total distance around the outside of the square. It is the sum of the lengths of all four sides. To find the perimeter of a square, you simply multiply the length of one side by four, since all sides of a square are equal in length. The formula is P=4S

1.The relationship established between (side length of the square) and output (perimeter of the square) represent that A square's perimeter is always equal to 4 times one of its sides.

2.Yes, the function can be represented with an equation. The equation would be:

Perimeter = 4 × Side Length.

Side Length (input) 1  2  3  4  5

Perimeter (output)  4 8 12 16 20

This equation states that the perimeter of a square is equal to four times the length of one of its sides.

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Answer:

400 cm³

Step-by-step explanation:

The volume of the given figure can be found by using the composite figures present;

We have two simpler figures combined to form the given figure including;

a) A cube

b) A triangular prism

a) The volume of a cube, [tex]V_{cube}[/tex] = Length × Breadth × Height

∴ The volume of the cube, V₁ = 6 cm × 8 cm × 5 cm = 240 cm³

b) The volume of a triangular prism, [tex]V_{prism}[/tex] = Base length × Height × Length

The base length of the triangular prism= 8 cm

The height of the triangular prism = 4 cm

The length of the triangular prism = 5 cm

The volume of the triangular prism, V₂ = 8 cm × 4 cm × 5 cm = 160 cm³

Therefore;

The volume of the figure, V = V₁ + V₂

∴ V = 240 cm³ + 160 cm³ = 400 cm³

The volume of the figure of the finished object, V = 400 cm³.

The ordered pairs are a linear equation if the graph plotted is the straight line.

A linear equation can be represented by a graph in the Cartesian coordinate system as a straight line. If the equation is in the form of "y = mx + b" where m and b are constants, it is a linear equation. The ordered pairs of a linear equation will always satisfy this equation, and when plotted on a graph, will fall on a straight line. To check if a set of ordered pairs is a linear equation, you can plot them on a graph and see if they form a straight line or can substitute the x- and y-values of the ordered pairs into the equation "y = mx + b" and see if they make the equation true.

So, if the graph plotted is the straight line, then the ordered pairs are of a linear equation.

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Answer:

side=8 unit

Area=777 unit^2

SEE IMAGE FOR SOLUTION

Hope it helps

Have a great day

Answer:

"If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular."

Step-by-step explanation:

To find the area of a triangle, you can use the formula:

area = (base * height) / 2

In this case, the base of the triangle is 24 inches and the height is 20 inches, so plugging these values into the formula gives:

area = (24 * 20) / 2

area = 240 / 2

area = 120 square inches

So the area of the top of the cheese board is 120 square inches.

Answer: 1.06 pounds per bag of potatoes

Step-by-step explanation:

Total weight = 60.42

# of bags of potatoes = 57

60.42/57 = 1.06 pounds per bag

Answer:

h=9

r=3

and im not so sure about the other 2

Answer:

h = 81

r = N/A

a = 36\pi ^2\\

b = N/A

Step-by-step explanation:

Answer:

A( 0,2)

Step-by-step explanation:

First A has the coordinates ( 2,2) then is translate 2 units to the left and is

A(2-2, 2) so is ( 0,2)

Answer:

Describe two ways you think a sound wave could be stopped or could change change direction.

Answer:

864fans

Step-by-step explanation:

machines:days:fans

20 : 7 :560

18 : 12 : ??

we start with the days:if the days increase the number of fans being made also increase so the solving ratiowill be an increasing one:12/7 ×560=960.Then we go to the no. of machines.......if the no. of machines decrease then no. of fans being made also decrease so the solving ratio is a decreasing one:18/20 × 960=864

answer:864fans

Answer:

siesta  bien

Step-by-step explanation:

Step-by-step explanation:

-3n + 3 > -11

-3n > -14

3n < 14

n < 14/3

14/3 = 4.66666666...

the only positive integers that are smaller than 4.666666... are

4, 3, 2, 1

their sum is

4+3+2+1 = 10

Answer:

41,500 people

Step-by-step explanation:

First you find 3% of 36,000= 1,080

Then you do 1080 x 5= 4,500

Then finally do 36,000 + 4,500= 41,500

Answer:

y = 7/2x + 5

Step-by-step explanation:

The slope intercept form is: y = mx + b

Our equation is

7x -2y = -10

We subtract 7x both sides

-2y = -7x - 10

Divided by -2, both sides

y = 7/2x + 5

So, the answer is y = 7/2x + 5

Answer: No Solutions

Step-by-step explanation:

8w + 5= 4 (2 w+1)=

8w+5=(4)(2w)+(4)(1)

8w+5=8w+4

    -8w      -8w

5=4

-5  -5

0=-1

Which means there are No Solutions.

Answer:

8w+5=4(2w+1)

8w+5=8w+4

collect like terms

8w-8w = 4-5

0=-1

there is no solution

Answer:

1/9

Step-by-step explanation:

Answer:

Area = 3x^2 + 4x

Step-by-step explanation:

Givens

W = x

L = 3x + 4

Formula

Area = L * W

Solution

Area = x(3x + 4)

Area = 3x^2 + 4x

Answer:

b > 3, or D.

Step-by-step explanation:

Solve for b to get the equation of the inequality.

12b - 15 > 21

Add 15 to both sides.

12b > 36

Divide both sides by 12.

b > 3

Since it is greater than and not greater than and equal to, the initial dot will not be circled, which makes it either C or D.

Since it is greater than 3, it means it will be all values to the right of 3, which makes the answer D.

The perimeter of the rectangle is 13x+7 feet

The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.

Given here: The width of a rectangle is 5x-1.5 feet and the length is 1.5x+5 feet. Therefore the perimeter of the rectangle is given by

= 2(5x-1.5+1.5x+5)

=2(6.5x+3.5)

= 13x+7

Hence, The perimeter of the rectangle is 13x+7 feet

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The number of vegetable plates can be made = 120

We know that a combination is nothing but a way of selecting items from a collection. In combination the order of selection does not matter.

We know that a formula for a combination is,

^nC_r = n! / r!(n - r)!

where,  ^nC_r = number of combinations

n = total number of items in the collection

r = number of choosing items from the collection

and n! = n × (n - 1) × (n - 2) × . . . × 1

Here, we have n = 10 and r = 3

Using combination formula,  the total number of plates made:

^10_C_3

= 10! / (3! × (10 - 3)!)

= 10! / (3! × 7!)

= (10 × 9 × 8 × 7!) /( 3! ×7!)

= (10 × 9 × 8) / (3 × 2 × 1)

= (90 × 8) / 6

= 720/6

= 120

Therefore, 120 vegetable plates maybe made

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Answer:

D, B

Step-by-step explanation:

Question 8.

The shaded area should be on or below the line [tex]y=\frac{5}{2}x-2[/tex] AND below but not on the line [tex]y=\frac{1}{2}x+2[/tex]

Question 9.

See the attached image.

Shade on or under the line [tex]y=\frac{1}{2}x-1[/tex] AND above but not on the line [tex]y=\frac{3}{2}x+1[/tex].

The number of apples that he has left will be 2 apples.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

If jimmy buys 5 apples and gets 3 apples eaten alive by him.

Then the number of apples that he has left will be given by subtracting 3 from 5. Then the expression is given as,

⇒ 5 - 3

⇒ 2

The number of apples that he has left will be 2 apples.

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The complete question is given below.

If jimmy buys 5 apples and gets 3 apples eaten alive by him. How many apples does he have left?

The midpoint formula of a quadratic equation is given by: x = -b/(2a), where a, b and c are the coefficients of the quadratic equation ax2 + bx + c = 0.

This formula is used to determine the midpoint of the roots of a quadratic equation. It works by taking the coefficients of the equation and plugging them into the formula. The result of the formula will be the x-coordinate of the midpoint of the two roots.

This formula is useful when solving quadratic equations, because it allows us to quickly find the midpoint of the two roots without having to solve for both roots first. It is also useful for graphing the quadratic equation, as it reveals the location of the vertex of the parabola. Knowing the midpoint of the two roots also makes it easier to determine the nature of the roots, whether they are real or imaginary.

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The annual income of a certain household that has a z-score of 1.5, is 80,000.

The relationship between a value and a group of values' mean is described statistically by the Z-score. Standard deviations from the mean serve as the unit of measurement for Z-score. The score for a data point is equal to the mean score if the Z-score is 0. A value that deviates by one standard deviation from the mean is indicated by a Z-score of 1.0.

Z-scores can either be positive or negative, with a positive value indicating that the score is above the mean and a negative value indicating that the score is below the mean. Z-scores are measurements of an instrument's variability used in investing and trading that traders can use to estimate volatility.

Let the annual income be x.

x has μ = 50000, σ = 20000

We know that for given x, z = (x−μ)/σ

Given that z - score = 1.5

Substituting the values we get

⇒ 1.5 = (x−50000)/20000

​⇒ 1.5 × 20000 = x−50000

​⇒ 30000 = x − 50000

⇒ x = 30000 + 50000

⇒ x = 80,000

Thus, The annual income of a certain household that has a z-score of 1.5, is 80,000.

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