Is 13,82,90 a right triangle

Dimensions of the Rectangle are : 16 feet by 13 feet .

A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal . A rectangle has two dimensions. we can measure its length and, perpendicular to that, its width.

Rectangle is 3 feet longer than it is wide and its area is 208 sq-feet .

Area of Rectangle = l×b  ( Where l = length , b = breadth )

Therefore , Let X be the the width of rectangle . then from given it's length is (X+3).

∴ X × (X+3) = 208

∴ [tex]x^{2}[/tex]+3X-208 = 0

(X+16)(X-13) = 0

X = -16 & X = 13

Distance can't be negative so Width = X = 13 feet.

∴ Length = X+3 = 16 feet.

Thus the Dimensions are 16 feet by 13 feet .

To learn more about Rectangle visit  :  brainly.com/question/8663941

#SPJ4

For the given triangle the coordinate of circumcenter is obtained as (1/3, 7/3).

The circumcenter for a triangle is defined as the center of the circle that touches all the vertices of the triangle. It is also found as the point of intersection of all of the perpendicular bisectors of the sides of triangle. All the vertices of the triangle are equidistant from the circumcenter.

Suppose the coordinate of the circumcenter be (x, y).

Now, all the vertices of the triangle should be equidistant from the circumcenter.

The equation can be written using distance formula as follows,

(x - 0)² + (y - 0)² = (x - 2)² + (y - 4)²

⇒ 4x + 8y = 20

⇒ x + 2y = 5                  (1)

And, (x - 0)² + (y - 0)² = (x - 5)² + (y - 1)²

⇒ 10x + 2y = 26

⇒ 5x + y = 13                  (2)

Multiply equation (2) by 2 nd then subtract equation (1) to get,

2(5x + y) -  (x + 2y) = 13 × 2 - 5

⇒ 9y = 21

⇒ y = 7/3

Substitute y = 7/3 in equation (1) to get,

x + 2 × 7/3 = 5

⇒ x = 5 - 14/3

⇒ x = 1/3

Hence, the coordinate of the circumcenter is given as (1/3, 7/3).

To know more about circumcenter click on,

https://brainly.com/question/16276899

#SPJ1

Answer:

The mistake was made when we rewrote the equation wrong after dividing 2 to both sides

Step-by-step explanation:

After we divide two on both sides the equation should have been rewriting as   [tex]2x-20=-6[/tex]     not       [tex]6x-20=-12[/tex]

The sum of the two complex numbers will give:

(-4 + i) + (10 - 5i) = 6 - 4i

So the correct option is the third one.

Let's assume we have two complex numbers which are:

A = a + bi

B = c + di

The sum between these two complex numbers is:

A + B = (a + bi) + (c + di)

Taking i as a common factor we can rewrite:

(a + bi) + (c + di) = a + c + (b + d)i

And that is the general sum.

Here we want to solve:

(-4 + i) + (10 - 5i)

Again, if we take i as a common factor we can rewrite:

-4 + 10 + (1 - 5)*i

6 - 4i

So the correct option is the third one.

Learn more about complex numbers by reading:

https://brainly.com/question/10662770

#SPJ1

Answer:

management accountant prepared a decision model which solve sell at split off or process

further decision problem. Which function did he provided?

A. Scorekeeping function C) Problem solving function

B. Attention directing function. D) Record keeping function E) None

Answer:

Step-by-step explanation:

Let's call the four integers x, y, z, and w. We know that the mean of these four integers is 8, so:

x + y + z + w = 8 * 4 = 32

We also know that the median of these four integers is 6, which means that two of the integers are less than 6 and two are greater than 6. The mode of 6 means that one of the integers is 6.

Let's assume that x and y are the two integers that are less than 6. This means that z and w are the two integers that are greater than 6. We can then set up the following system of equations to represent this information:

x + y + z + w = 32

x + y < 12

z + w > 12

We also know that the range of these four integers is 14, which is the difference between the largest and smallest integers. Since z and w are the two largest integers, the range is equal to w - x. We can set up another equation to represent this information:

w - x = 14

We can solve this system of equations using substitution. First, we can solve the second equation for x:

x = 12 - y

We can then substitute this expression for x in the third equation to get:

w - (12 - y) = 14

w = 14 + y

Finally, we can substitute this expression for w in the first equation to get:

x + y + z + (14 + y) = 32

x + 2y + z = 18

We can then substitute the expression for x in the third equation to get:

(12 - y) + 2y + z = 18

-y + 2y + z = 18

z = 18 - y

We can then substitute this expression for z in the third equation to get:

w = 14 + y = 14 + (18 - z) = 14 + 18 - y = 32 - y

Substituting this expression for w in the first equation gives us:

x + y + z + (32 - y) = 32

x + 2y + z = 32

We can then substitute the expressions for x and z in the third equation to get:

(12 - y) + 2y + (18 - y) = 32

-y + 2y + 18 - y = 32

18 = 32

This equation is clearly not true, so the original assumptions we made about which integers were less than 6 and which were greater than 6 must be incorrect.

However, we can use a similar process to solve for the other possibility: that x and z are the two integers that are less than 6, and y and w are the two integers that are greater than 6.

In this case, we can set up the following system of equations:

x + y + z + w = 32

x + z < 12

y + w > 12

w - x = 14

Solving this system of equations using substitution gives us the solution x = 4, y = 10, z = 6, and w = 8.

Therefore, the four integers are 4, 6, 8, and 10.

After solving the equation the length of AB is [tex]2\sqrt{3}[/tex]

What do you mean by trigonometry?

Trigonometry  “triangle” and  “measure”) is a branch of mathematics that studies the relationship between the side lengths and angles of triangles.

A trigonometric ratio is the ratio between the edges of a right triangle.

The sine function (sin) defined as the ratio of the opposite side of the angle to the hypotenuse.

In the given triangle ABC , use sin ratio to find AB.

tan θ = P/B

tan 30 = AB/6

[tex]\frac{1}{\sqrt{3} } =AB/6[/tex]

AB = [tex]\frac{6}{\sqrt{3} }[/tex] = [tex]\frac{6}{\sqrt{3} }\times \frac{\sqrt{3}}{\sqrt{3}}= \frac{6\sqrt{3}}{3}=2\sqrt{3}[/tex]

Therefore, length of AB is [tex]2\sqrt{3}[/tex]

To learn more about trigonometry from the given link.

https://brainly.com/question/24349828

#SPJ1

Answer: <D, < E, <C

Step-by-step explanation:

Answer:

D.  b + c = 68

    0.08b + 0.15c = 6.00

Step-by-step explanation:

The total cost is $6.00

The total amount of copies is 68

To find the total cost, we multiply the amount of copies by the individual price. So we get

0.08b + 0.15c = 6.00

We add the amount of copies bought to get a total of 68, so we get this equation:

b + 6 = 68

Answer:

there will be only 1 more slice to eat

To prove that the two circles are similar, the answer which would be the correct second step in his proof is:

A - C = 2-pi-r/C = 2-pi-r and C/C = r/r by the division property of equality

What is a Circle?

This refers to a round plane who has a centre as a fixed point that has equal distance from each ot

With this in mind, we can see that Circle O and Circle X are shown and they are said to be similar, hence, the second step to prove that they are similar is A - C = 2-pi-r/C = 2-pi-r and C/C

To learn more about Circle visit :

https://brainly.com/question/11833983

#SPJ1

The total area of the two lawns is 200 ft²

Area is the region occupied by an object.

Since Anton mows two lawns. The first lawn is 8 feet long and 5 feet wide. The second lawn has the same length, and width that is 4 times the first one, since the lawns are rectangles, their area is the area of a rectangle.

The area of a rectangle is given by

A = LW where

Given that for the first lawn it is 8 feet long and 5 feet wide, we have that

So, its area A = LW

= 8 ft × 5 ft

= 40 ft²

Also, for the second lawn, the same length, and width that is 4 times the first one. So, we have that

So, its area A' = L'W'

= 8 ft × 20 ft

= 160 ft²

So, the total area of the two lawns is A" = A + A'

=  40 ft² +  160 ft²

=  200 ft²

So, the total area is  200 ft²

Learn more about  total area of lawn here:

https://brainly.com/question/29324938

#SPJ1

Answer:

x ≥ 72/5

8.6 ≤ x -5 4/5= 8.6 ≤ x -29/5

8.6 ≤ x -29/5= x ≥ 72/5

Answer:

D

Step-by-step explanation:

base= y2-y1

height = x3-x1

so (1/2)×(y2-y1)×(x3-x1)

By evaluating a revenue equation, we will see that she earned $139 last week.

We know that Isha is a pet sitter, and she earns $5 for each cat and $12 for each dog.

So, if she pet sats for x cats and y dogs, the revenue will be:

R(x, y) = $5*x + $12*y

In this case we know that she pet sat for 11 cats and 7 dogs, then we have:

x = 11

y = 7

So we need to evaluate the above revenue function, we will get:

R(11, 7) = $5*11 + $12*7

R(11, 7) = $55 + $84

R(11, 7) = $139

Isha earned $139 last week.

Learn more about revenue at:

https://brainly.com/question/16232387

#SPJ1

Answer:

3(4) - 2 is 10 the value is 10

5(2) + 6 is 16 the value is 16

I hope this helps have a good day or night!

The value of the x would be 9.

Option (A) is correct.

What is a complementary angle?

A complementary angle is an angle that, when added to another angle, forms a right angle (90 degrees). Complementary angles are pairs of angles that add up to 90 degrees.

Angle JKM and angle MKN are complementary angles

so

   (3x + 2) + (6x + 7) = 90

  9x + 9 = 90

  9(x + 1) = 90

     x + 1 = 10

    x = 9

Hence, the value of the x would be 9.

To learn more about the complementary angles, visit:

https://brainly.com/question/98924

#SPJ1

After solving the equation the value of the x would be 9. Therefore, the correct option is A.

What is a complementary angle?

A complementary angle is a pair of angles that add up to 90 degrees. Complementary angles can be adjacent angles, or angles that share a common vertex and side, or they can be nonadjacent angles that have no common points or sides. Complementary angles are usually referred to by their sum, such as "90-degree angles" or "angles that add up to 90 degrees." Complementary angles can also be called supplementary angles when they add up to 180 degrees.

Angle JKM and angle MKN are complementary angles

so   (3x + 2) + (6x + 7) = 90

 9x + 9 = 90

 9(x + 1) = 90

    x + 1 = 10

   x = 9

Hence, the value of the x would be 9.

To learn more about the complementary angles, visit:

brainly.com/question/98924

#SPJ1

Answer:

x + x - x = x

explanation:

give us the actual formula lol

Answer: $71.53

Step-by-step explanation:

77.76 = 100%

Step-by-step explanation:

d is the answer as far as I can tell from a little experience

Answer:

The possible coordinates of point A are (-3, 8) and (-3, -4).

Step-by-step explanation:

We can find the possible coordinates of point A by using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of (x2-x1)^2 + (y2-y1)^2. We know that the x-coordinate of point A is -3 and the distance between point A and point B is 10 units. We can use this information to solve for the y-coordinate of point A:

Copy code

d = sqrt((x2-x1)^2 + (y2-y1)^2)

d = sqrt((5-(-3))^2 + (2-y1)^2)

d = sqrt(8^2 + (2-y1)^2)

d = sqrt(64 + (2-y1)^2)

d = sqrt(64 + (y1-2)^2)

d = 10

sqrt(64 + (y1-2)^2) = 10

64 + (y1-2)^2 = 100

(y1-2)^2 = 36

y1-2 = +/- 6

y1 = 8 or -4

Therefore, the possible coordinates of point A are (-3, 8) and (-3, -4).

Interior angle-

All interior angles of a regular polygon are equal. The formula for calculating the magnitude of the interior angle is:

Interior angle of polygon = sum of interior angles ÷ number of sides. The sum of the exterior angles of a polygon is 360°.

Exterior angle-

An exterior angle is an angle that is parallel to, but outside, the interior angle of a polygon. The exterior angle measurement is equal to the sum of the two opposite interior angles.

according to the question,

given data

interior angle=8 exterior angle

we know that,

interior angle+ exterior angle=180

let us consider ,

exterior angle=x

so we can say that,

8 exterior angle + exterior angle =180

8x+x=180

9x=180

x=20

we know that ,

the number of sides=360/x

=360/20

=36/2

=18

the number of sides of the polygon is 18

To know more about angle visit

https://brainly.com/question/17581088

#SPJ4

The number of volunteers recruited for the first 5 weeks is; 486 people

A geometric sequence is defined as a sequence in which the result of the division of consecutive terms is always the same, called common ratio r.

The nth term of a geometric sequence is given by:

aₙ = a₁rⁿ⁻¹

where;

a₁ is the first term

r is the common ratio

In this question, on the first week there are 6 people, and since each new people involve three more, the common ratio is 3, hence the parameters for the geometric sequence are:

a₁ = 6

r = 3

Hence the number of people after n weeks is:

aₙ = 6(3)ⁿ⁻¹

Thus, the number of volunteers recruited for the first 5 weeks is;

a₅ = 6(3)⁵⁻¹

a₅ = 6 * 3⁴

a₅ = 486

Read more about geometric Sequence at; https://brainly.com/question/24643676

#SPJ1

the area of the generic rectangle will be x²-2x-15.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and width of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

Area of rectangle is A = a*b

(x + 3)(x - 5) in a generic rectangle

The product will give the area

x²-2x-15

hence the area of the generic rectangle will be x²-2x-15.

Learn more about rectangular by following the link below.

brainly.com/question/25292087

#SPJ1

Answer: He bought three adult tickets and two child tickets

Step-by-step explanation:

The answer is 28$

2+2= 4

8+8= 16

16 + 4= 20

20 + 8 =28

He bought two child tickets and three adult tickets

Answer:

-2

Step-by-step explanation:

Given,

g(x) = f(4)

or, 2 - 4x = 3*4 - 2

or, 2 - 4x = 10

or, 2 - 10 = 4x

or, -8 = 4x

or, x = -2

Answer: Therefore, the correct formula is {a}_{21}  = 2000 * 0.5^{20}.

Step-by-step explanation:

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant factor called the common ratio. In this case, the common ratio is 0.5, since each term is found by dividing the previous term by 2.

To find the nth term in a geometric sequence, we can use the formula:

a_n = a_1 * r^(n-1)

where a_1 is the first term in the sequence, a_n is the nth term, and r is the common ratio. In our case, the first term is 2000, the nth term is the 21st term, and the common ratio is 0.5. Therefore, the formula we need to use is:

a_21 = 2000 * 0.5^(21-1)

    = 2000 * 0.5^20

Therefore, the correct formula is {a}_{21}  = 2000 * 0.5^{20}.

Answer:

 (a) A  and B are similar but not congruent

Step-by-step explanation:

All of the rectangles have sides in the ratio of 2:1, so are all similar. Only the rectangles that are the same size are congruent: A and C.