What is the area of the parallelogram with vertices at (0,1), (-1,2), (5,4) and (6,3)?
12 square units
10 square units
8 square units
16 square units

Answer:

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

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.

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

Learn more about area of a rectangle here:

https://brainly.com/question/20693059

#SPJ1

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

Learn more about the ratio here:

https://brainly.com/question/29774220

#SPJ4

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.

To know more about the Perimeter of square, check out:

https://brainly.com/question/25092270

#SPJ1

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].

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.

x=7, y=-2, and z=-2

just trust me on it

Annabelle collected data from a sample of people that were convenient for her to access, such as her immediate neighbors, and used this to draw her conclusion.

Annabelle performed a convenience sample investigation, which is a type of statistical investigation. This involves collecting data from a sample of people that are convenient for the researcher to access. In this case, Annabelle asked a couple of her immediate neighbors to find out how many people in her neighborhood were going to the rock concert..

Convenience sampling is useful when time or resources are limited, however the results may not be representative of the larger population. Therefore, it is important to consider the limitations of the sample when drawing conclusions. For example, Annabelle may not have considered that the neighbors she asked may not be representative of the whole neighborhood.

Learn more about sample here

https://brainly.com/question/25894237

#SPJ4

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 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.

Learn more about Quadratic Equation here:

https://brainly.com/question/28038123

#SPJ4

Answer:

A' = (-18, 54)

Step-by-step explanation:

The distance in miles represented by a length on the map of 7 inches is 0.28

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

Given;

The scale of a map says that 2 inches represents 50 miles.

2 inches = 50 miles

1 Mile = 2/50 inches

Hence, 7 Mile = 7 * 2/50 inches

7 Mile = 14/50 inches

7 Mile = 0.28 inches

Therefore, the scale factor of 7miles in the map will be 0.28inches

To learn more about scale factor;

brainly.com/question/24771289

#SPJ1

something noteworthy is that the x-coordinate is the same for each point, so Check the picture below.

Answer:

side=8 unit

Area=777 unit^2

SEE IMAGE FOR SOLUTION

Hope it helps

Have a great day

Answer:

siesta  bien

Step-by-step explanation:

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:

the length of arc=

[tex]2\pi \times 6 \times \frac{60}{360} \\ 2\pi[/tex]km

We spent a total of 40.2 + 24.5+ 37.8 = $102.50

A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator.

Fractions are used to represent the parts of an entity or collection of entities. The components of a fraction are two. The figure at the top of the line is the numerator. It provides information on how many equal sections from the total or collection were taken. The number that appears below the line is the denominator.

We multiply the initial price by the fractions' decimal conversions to determine how much we spent. The quantities are then combined.

You purchased sneakers for $60 and paid 2/3 of that amount, or $0.6666, for a total of $40.20, saving $19.80.

Sweater costs $35 and you paid $7.50 for it, saving you $10.50. 35(0.7)=$24.50.

You paid $45 for a jacket, and since 5/6=0.8333, 45(0.84)=$37.80, you made a $7.20 profit.

We spent a total of 40.2 + 24.5+ 37.8 = $102.50

To learn more about fractions refer to:

https://brainly.com/question/78672

#SPJ4

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.

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.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

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?

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

Therefore ,the answer to the above trigonometry issue is therefore that the river is 70 feet wide.

The study of the connections between the angles and sides of triangles is known as trigonometry. Due to the fact that each straight-sided figure may be reduced to a collection of triangles, trigonometry is commonly utilized in geometry. There are a mind-boggling number of connections between trigonometry and other branches of mathematics, especially algebra, real or complex, integrals, logarithms, and infinite series.

Here,

Figure depicts a right triangle which, in relation to angle, its next side has length d or its wrong side is equal to the river's width, y. As a result,

tanθ= d/ y

=> y=dtanθ

=> y = (100m)tan(35.00)=70ft

The river measures 70 feet in width.

As a result, the trigonometry problem's answer indicates that the river's width is 70 feet.

To know more about trigonometry , visit

brainly.com/question/12068045

#SPJ1

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:

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