If a circle has a diameter of 24 centimeters, and the length of an arc is 36 centimeters, what is the measure of the central angle sub tended by the arc

Since triangle A'B'C' is an image of triangle ABC after a rotation and the center of rotation is D, the length of side B'C' is equal to 4 units.

In Mathematics, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Generally speaking, rotation simply refers to a type of transformation that preserves both the shape and side lengths of a geometric figure.

In this context, we can reasonably infer and logically deduce that the magnitude of side length BC before a rotation of the triangle would be equal to side length BC B'C' after rotation:

Side BC = side B'C'

4 = 4

In conclusion, the length of side B'C' is equal to 4 units.

Read more on rotation here: brainly.com/question/28854313

#SPJ1

Complete Question:

In the picture triangle A'B'C' is an image of triangle ABC after a rotation. The center of rotation is D.

What is the length of side B'C'?

Answer:

1. 6

2. 8

3. 80

4. 11

5. 60

6. 3

7. 30

8. 0.8

9. 5

10. 600

11. 150

12. 110

13. 15

14. 1.1

15. 36

Hope it helps

The 90 km distance between orlando and New York meant that the freight train was closer to the station in New York.

A linear equation is one that satisfies the algebraic formula y=mx+b. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

The New York to Boston train was traveling farther and quicker.

Even though it was delayed and moved more slowly, the train from Boston to New York is closer to New York.

1.5 hours from the New York station, the two trains crossed paths.

By this time, the passenger train from New York to Boston was 120 kilometers away from the station in New York.

The 90 km distance between orlando and New York meant that the freight train was closer to the station in New York.

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ1

Answer: -5x+6

Step-by-step explanation:

simplify by distributing the numbers on the outside, to the ones in the binomial

Answer:

-5x + 6

Step-by-step explanation:

First, rearrange the terms, you will have -2x-4(3x-10) Next, Distribute, you will have -2x-4-3x+10. Now, add the numbers without variables, you'll get -2x+6-3x. Finally, combing the like terms and you arrive with -5x+6.

The solution to the equation x² + 3x - 5 = 0 are ( -3 - √( 29 ))/2 and ( -3 +√( 29 ))/2.

The quadratic equation in its standard form is;

ax² + bx + c = 0

Where x is the unknown

To solve for x, we use the quadratic formula

x = (-b±√(b² - 4ac)) / (2a)

Given the equation in the question;

x² + 3x - 5 = 0

Hence;

a = 1

b = 3

c = -5

We substitute this values into the quadratic formula above.

x = (-b±√(b² - 4ac)) / (2a)

x = ( -3 ± √( 3² - ( 4 × 1 × -5) )) / ( 2 × 1)

x = ( -3 ± √( 9 - ( -20 ) )) / ( 2 )

x = ( -3 ± √( 9 + 20 )) / 2

x = ( -3 ± √( 29 )) / 2

x = ( -3 - √( 29 ))/2, x = ( -3 +√( 29 ))/2

Therefore, the two values of x are  ( -3 - √( 29 ))/2 and ( -3 +√( 29 ))/2.

Learn more about quadratic equations here: brainly.com/question/1863222

#SPJ1

Answer:

T=6 NUMBER OF TEN DOLLAR BILLS.

F=13 NUMBER OF FIVE DOLLAR BILLS.

Step-by-step explanation:

F+T=19 F=19-T

5F+10T=125 NOW SUBSTITUTE (19-T) FOR F IN THIS EQUATION & SOLVE FOR T

5(19-T)+10T=125

95-5T+10T=125

5T=125-95

5T=30

T=30/5

PROOF

5*13+10*6=125

65+60=125

125=125

Yes, the quadratic parent function is the parabola.

The term parent function in math is defined as the simplest function of a family of functions that preserves the definition or shape of the entire family.

Here we have to identify that whether the quadratic parent function is a parabola or not.

According to the definition of parent function, the quadratic parent function is written as,

=> f(x) = x²

And here we also know that the quadratic function is one of the form

=> f(x) = ax² + bx + c

here a, b, and c are refers the numbers with a not equal to zero.

Here we all know that the graph of a quadratic function is a curve called a parabola.

which tells, the the quadratic parent function also have the graph as parabola.

To know more about function here.

https://brainly.com/question/28193995

#SPJ4

The slope of the line (-3, 4) and (0, 2) is -2/3.

In the given question, we have to find the slope of the line (-3, 4) and (0, 2).

A line's slope is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

The given points are (-3, 4) and (0, 2).

We can find the slope from the given point using the formula

m = [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]

From the given points;

x(1) = -3, y(1) = 4, x(2) = 0, y(2) = 2

Now putting the values in the formula;

m = (2 - 4)/(0 - (-3))

m = (-2)/(0 + 3)

m = -2/3

Hence, the slope of the line (-3, 4) and (0, 2) is -2/3.

To learn more about slope of the line link is here

brainly.com/question/14511992

#SPJ4

Answer:

The first step in solving this system of equations by elimination method is to eliminate one of the variables by adding or subtracting the two equations.

-9x - 4y = 1

3x + 3y = 3

If we multiply the first equation by 3 and the second equation by -9, we get:

-27x - 12y = 3

-27x - 27y = -27

Now we can add these two equations:

-12y = -24

y = 2

Now we can substitute this value of y back into one of the original equations to find the value of x.

-9x - 4(2) = 1

-9x - 8 = 1

-9x = 9

x = -1

So the solution of this system of equations is (x,y) = (-1,2)

Answer:

You just have to plug in one equation into the other, though you might already know this but the answer would be,

(-1,2)

The smallest integer greater than 38 which cannot be the length of the hypotenuse of a right triangle is 39.

Since 39 is divisible by 3, it cannot be the hypotenuse in any Pythagorean triples. Because for primitive Pythagorean triples, the hypotenuse is never divisible by 3.

A primitive Pythagorean triple is one where a, b and c are coprime (which is, they have no common divisor larger than 1). For example, (3, 4, 5) is a primitive Pythagorean triple while (6, 8, 10) is not. For any primitive Pythagorean triple the integer c or the hypotenuse cannot be divisible by 3. Divisibility by 3 is only reserved for spots a and b.

There are an infinite number of Pythagorean triples. If 2n+1 is a square, it forms a Pythagorean triple. But 2n+1 comprises all the odd numbers; each of other square numbers is odd; there are an infinite number of odd squares; thus, there are an infinite number of Pythagorean triples.

Learn more about Pythagorean triple at: https://brainly.com/question/15190643

#SPJ4

Answer: -2 !

Step-by-step explanation: All you have to do is simplify the equation !

Answer:

Step-by-step explanation:

The rule in adding unlike integers(integers with different signs) is to subtract the two integers and copy the sign of the bigger number. So     6 + (-8) = -2

Answer:

Step-by-step explanation:

3x+6y = 18

y=4

2x+5y= 24

y=9.5

A perpendicular bisector is a line segment or a ray or a line that intersects a given line segment at a 90-degree, and also it passes through the midpoint of the line segment

At its midway, a segment bisector crosses another segment. A Perpendicular Bisector is a segment, ray, line, or plane that is perpendicular to another segment at its halfway.

A perpendicular bisector is a line that precisely splits a given line segment into two halves, generating a 90-degree angle at the junction point. A perpendicular bisector is a line segment that crosses through the midway. It can be built with a ruler and a compass.

When two lines cross at 90 degrees or at right angles, they are said to be perpendicular to each other. A bisector, on the other hand, is a line that divides a line into two equal halves.

For more questions on Perpendicular bisector

https://brainly.com/question/11006922

#SPJ4

The value of variable x in the coordinate plane is 3.

A coordinate plane is a two-dimensional plane that is created when two number lines cross. The x-axis, one of these number lines, is a horizontal number line, and the y-axis, another number line, is vertical. The coordinate plane is formed by the perpendicular intersection of these two number lines.

The reason the plane is referred to as two-dimensional is because any point on it to which you can put your finger will require two measurements to determine its location: its distance from the x-axis and its distance from the y-axis.

For negative integers, the left and bottom portions of the plane have negative x- and y-axes. The origin is the place where the number lines come together.

Given that ΑF =  FE

So if triangle DFE Transforms with F as centre and rotate E to become A

Then we will have an rectangle ACDF and E became A

In rectangle ACDF,

AC = FD

AC = 5x + 9

FD = 2(2x +6)

5x + 9 = 4x + 12

5x - 4x = 12 - 9

x = 3

Thus, the value of variable x in the coordinate plane is 3.

Learn more about coordinate plane

https://brainly.com/question/13611766

#SPJ1

Answer: Numeric is anything of, relating to, or containing numbers. The numbering system consists of ten different digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If a value is an alphanumeric, it contains letters and numbers.

Step-by-step explanation:

The fucntion f (x) = - 1 is an even fucntion.

Write the given function as

[ f(x) = - 1 ]

To determine if the function is even or odd, the following steps apply:

If [ f( -x) = f (x) ] then the given function is even.

On the other hand if [ f(-x) = - f (x) ]

Now find f (-x),

[ f(- x) = - 1 ] which is equal to f(x).

Since [ f( -x) = f (x) ], therefore the given function is an even function as it meets the criteria to be an even function.

You can learn more about even function at

https://brainly.com/question/23934926

#SPJ4

Interior angle of a polygon = (n-2) * 180 / n

Exterior angle of a polygon = 360 / n

To translate coordinates in a two-dimensional plane, you need to know the translation vector. A translation vector is a pair of numbers (a, b) that indicates the amount of movement in the x-direction and y-direction.

To translate a point (x, y) by the translation vector (a, b), you can use the following formulas:

x' = x + a

y' = y + b

Where x' and y' are the new coordinates of the point after the translation.

A translation is a transformation that moves a figure a certain distance in a certain direction without rotating or reflecting it. In this case, we are asked to translate the triangle EFG 2 units down. This means that we need to move the triangle down 2 units on the y-axis.

To translate a point (x, y) down 2 units, we can add -2 to the y-coordinate. The new coordinates of the point will be (x, y - 2).

The coordinates of E are (-4, 1), so the coordinates of E' after the translation are (-4, 1-2) = (-4,-1)

The coordinates of F are (-3,-2), so the coordinates of F' after the translation are (-3,-2-2) = (-3,-4)

The coordinates of G are (2, 1), so the coordinates of G' after the translation are (2,1-2) = (2,-1)

So the new coordinates for the triangle EFG' after the translation are:

E'(-4,-1)

F'(-3,-4)

G'(2,-1)

It's important to notice that the x-coordinates didn't change because we are only translating the triangle down, on the y-axis.

To learn more about translate coordinates visit:

brainly.com/question/30095010

#SPJ1

Is the relation shown below is not a function.

To learn more about function refer to:

https://brainly.com/question/12604756

#SPJ1

Answer: 570

Step-by-step explanation: In survey the total customers were 150 so our sample size is 150.

Total number of First time customer = 95

Probability of being a first time customer = 95/150 = 0.63

So on first day using same probability the first time customers will be 900 × 0.63 = 570

Answer:  542+(87+41) = 670

Step-by-step explanation:

The length of PQ + the length of QR Equals the length of PR according to the segment addition rule because Q is the line segment so PR = 14

A line is an endlessly long object without breadth, depth, or curvature in geometry. Consequently, a line is a one-dimensional entity, while it may also exist in two-, three-, and more-dimensional regions. In common use, a line segment with two points serving as its ends is referred to as a line. A line is a single-dimensional, straight form with no thickness that can go on forever in both directions. To indicate that a line has no "wobble" anywhere along its length, it is frequently referred to as a straight line or an ancient accurate line (Casey 1893)

 Point Q is on line segment PR

PQ = 2 and QR = 14

The length of PQ + the length of QR Equals the length of PR according to the segment addition rule because Q is the line segment PR, so:

PQ + QR = PR ; 3 + 11 = P so PR = 14

To know more about line visit:

https://brainly.com/question/2696693

#SPJ1

The value of 'n' in this right-angled triangle is n = 8.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sum of all the interior angles in a triangle is 180°.

Therefore, From the given information 3.4n + 9.2n - 10.8 = 90.

12.6n = 100.8

n = 100.8/12.6.

n = 8.

So, The value of n is 8.

learn more about triangles here :

https://brainly.com/question/2773823

#SPJ1

The given expression is equivalent  to 125.

What is algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants .

The given expression is

(5^-2) (5 ^ -1 )

The expression is about two powers with the same base, so we can use the power property of multiplication, which states that we must proceed we writing only one base and sum exponents

(5^-2) (5 ^ -1 )  = 5 ^ (-2-1)

= 5 ^ -3

= 1/(5*5*5)

Then, we use the negative exponent property

= 1/125

Finally, we solve the power

1/5*5*5 = 1/125

Therefore, the given expression is equivalent to 125.

To learn more about Algebraic expression from the given link.

https://brainly.com/question/953809

#SPJ1

Answer:

Factored equation: (x-4)² = 55

Solution set
x = 11.416 and x = -3.416

Step-by-step explanation:

Given equation is
x² - 8x = 39

We have to somehow get this equation in the form (x + a)² = b

(x + a)² = x² +2ax + a²

Comparing we get
2ax = -8x

==> a = -4

Add a² = (-4)² = 16 to both sides of x² - 8x = 39

==>  x²  - 8x +16 = 39 + 16

==> x²  - 8x +16 = 55

x²  - 8x + 16 = (x - 4)²

==> (x-4)² = 55

I think this is what they were asking, not exactly the solution to the original equation.

Nevertheless,

(x-4)² = 55

==> x - 4 = ±√55

==> x = 4 ± √55

==> x = 4 + √55 and x = 4 - √55 are the two roots

This works out to

x = 11.416 and x = -3.416

The fraction of people were born in France is 7/24 .

What is a Pie Chart?

A pie chart is a graphical representation used to describe the composition of a data using degrees or percentages.

Given,

The pie chart represents the results when 120 people in a shopping centre were asked which country they were born in.

So, from the given pie chart

105° is given as the number of people that were born in the France

That's about: 105/360 × 120 = 35 people.

35 out of 120 people would give us a fraction of: 35/120 = 7/24 .

Hence, The fraction of people were born in France is 7/24 .

To Learn more about pie chart from the given link.

brainly.com/question/26851221

#SPJ1

The area of yellow rectangles KH'C'J and LJE'A' is greater than the area of blue rectangle DFCE. .

Rectangle is a flat, four-sided shape with four right angles and a pair of parallel lines. It is one of the most basic and commonly used shapes in geometry. It is also the most common shape used in architecture and construction. Rectangles have area, perimeter, and diagonal measurements, which makes them a useful tool for measuring and calculating. They are also used in a variety of other applications, such as designing window frames, creating art, and laying out floor plans.

To determine the area of DFCE, multiply the length of the base (DF) by the height (CE). The area of the two yellow rectangles, KH'C'J and LJE'A', can be determined by adding the area of each rectangle. The area of rectangle KH'C'J is equal to the product of the length of its base (KH') and the height (C'J). The area of rectangle LJE'A' is equal to the product of the length of its base (LJ) and the height (E'A'). Adding the areas of both yellow rectangles gives us the total area of both, which is greater than the area of blue rectangle DFCE.

To know more about rectangle click-
https://brainly.com/question/25292087
#SPJ1

he length of the longest pencil that can fit inside the tin is 17.6 cm.

Now, According to the question:

The tin is a rectangular prism with a length of 14 centimeters,

A width of 10 centimeters,

and a height of 4 centimeters.

To find the length of the longest pencil that can fit inside the tin.

Length of diagonal

[tex](10^2+14^2)^0^.^5=17.204[/tex]

Height of the box is 4

[tex]17.204^2+4^2=316^0^.^5=17.6 cm[/tex]

Hence, The length of the longest pencil that can fit inside the tin is 17.6 cm.

Learn more about Rectangular prism at:

https://brainly.com/question/21308574

#SPJ4

Answer:

[tex]\frac{2}{3}[/tex]

Hope this helps!

Step-by-step explanation:

Slope = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

b = ( -2, 0 )

a = ( -5, -2 )

[tex]slope = \frac{0 - (-2) }{-2 - ( -5)}[/tex]

slope = [tex]\frac{2}{3}[/tex]