Nicole is a wedding organizer. The guest will sit at a circular tables with a diameter of 180 cm. Each quest needs 70 cm around the circumference of the table. How many guest can be seating each table

When we multiply the given inequality that is [tex](\frac{x^{2} - 25}{2x^{2} +10x +12})(\frac{x+6-x^{2} }{x^{2} +2x-15})[/tex], then we get the required equation as [tex](\frac{-x+5}{2x+6}) ; x[/tex] ≠ [tex]-3,3,-2,-5[/tex]

If you multiply one side of an inequality by a number, you can multiply the other side of the inequality by the same number .

The denominator should not be 0  that is the value of x .

Given: [tex](\frac{x^{2} - 25}{2x^{2} +10x +12})(\frac{x+6-x^{2} }{x^{2} +2x-15})[/tex]

On solving ,we get

[tex]=(\frac{(x+5)(x-5)}{2(x+2)(x+3)}) (\frac{(-1)(x-3)(x+2)}{(x-3)(x+5)})[/tex]

Since denominator cannot be equal to zero.

Therefore x ≠ -2, x ≠ -3

and x ≠ 3, x ≠ -5

So ,x ≠ -2,-3,3,-5

It is the condition for x .

On cancelling common terms ,we get

[tex]=(\frac{(-1)(x-5)}{(2)(x+3)})[/tex]

[tex]=(\frac{-x+5}{2x+6})[/tex]

This is the required equation obtained .

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Answer:

F is the correct answer

Step-by-step explanation:

5x-15-3x+10

2x-5

Square is the geometrical figure with certain properties which distinguishes from other geometrical figures.

In geometry, a square is a two-dimensional plane shape with four equal sides and four equal angles that add up to 90 degrees. The characteristics of a rectangle and a square are somewhat similar, although a rectangle only has its opposite sides equal. As a result, a rectangle is only referred to as a square if its four sides are of the same length.

Square

Below is a list of a square's key characteristics:

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Answer:

     6\sqrt3

Step-by-step explanation:

Since 30-60-90 tri, small side is 6.

This means x=[tex]6\sqrt3[/tex]

Answer:

[tex]x = 6\sqrt{3}[/tex]

Step-by-step explanation:

Utilize the trigonometric ratio cosine.

[tex]\cos(30\textdegree ) = \dfrac{x}{12}[/tex]

Solve for x by multiplying both sides by 12.

[tex]12\cos(30\textdegree ) = x[/tex]

[tex]12\left(\dfrac{\sqrt{3}}{2} \right) = x[/tex]

[tex]x = 6\sqrt{3}[/tex]

We can find the mean absolute deviation by the dot plot of the number line.

The mean absolute deviation is the average of all the variations in a dataset. It can be defined as a measure of finding out spread out the values of a dataset are from the mean. The mean is calculated by adding the absolute deviations and dividing the sum by the number of values in the data set.

Absolute mean deviations can be represented graphically on a number line from a dot plot. These dot plots can be used to find out the mean absolute deviation on a number line.

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The side and angle is in the right angle triangle respectively x = 3,  68°.

What is a right angle triangle?

A right triangle, also known as a right-angled triangle, is a triangle with one angle that is a right angle (i.e., a 90-degree angle) and two perpendicular sides.

We have,

            [tex]1) Opposite = x, \ Adjustment = 12, \ \theta = 18.\\\\2) Opposite = 25, \ Adjustment = 10, \ \theta = ?.[/tex]

How to determine the angle in a right angled triangle,

                                        [tex]Tan (\theta ) = \frac{opposite}{adjacent}[/tex]

                                        [tex]cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]1) \ Opposite = x, Adjustment = 12, \ \theta = 18.[/tex]

                   [tex]cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

                  [tex]Hypotenuse = \frac{Adjacent}{cos(\theta)}[/tex]

                 [tex]Hypotenuse = \frac{Adjacent}{cos(18)}[/tex]

                                 [tex]= 12.61755[/tex]

           [tex]Opposite = \sqrt{Hypotenuse^{2} - Adjacent^{2} }[/tex]

                          [tex]= \sqrt{12.6175466908592 - 122}[/tex]

                         [tex]= \sqrt{15.202484496012}[/tex]

         ∴  [tex]Opposite(x) = 3.89904[/tex]  

[tex]2) \ Opposite = 25, \ Adjustment = 10, \ \theta = ?.[/tex]

                  [tex]Hypotenuse = \sqrt{{Opposite^{2} - Adjacent^{2} }[/tex]

                               [tex]= \sqrt{25^{2} + 10^{2} }[/tex]

                               [tex]= \sqrt{725} \\\\= \ 26.92582 \ = \ 5\sqrt{29}[/tex]

                    [tex]\theta =\ sin^{-1} {\frac{Opposite }{Hypotenuse} }[/tex]

                    [tex]\theta = \ sin^{-1} (\frac{25}{26.92} )[/tex]

                    [tex]\theta = \ sin^{-1} (\frac{25}{26.92} )[/tex]

                     [tex]= sin^{-1} (0.92847669088526)[/tex]

                    [tex]\theta = \ 68[/tex]°

Hence, The side and angle is in the right angle triangle respectively x = 3,  68°.

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The vertices of the original triangle are:

(-3,-2) , (0,6) and (1,3)

Given,you rotate a triangle 270° counterclockwise about the origin.

Then you translate its image 2 units right and 1 unit down.

The vertices of the final image are (0, 2), (8,-1), and (5,-2).

we are asked to find  the vertices of the original triangle =?

Before translating the image of final image 2 units right and 1 unit down.

the vertices of the triangle is:

(0-2,2+1) → (-2,3)

(8-2,-1+1) → (6,0)

(5-2 , -2+1) → (3,-1)

{translate the final image 2 units left, 1 unit up again}

then before rotate 270° counterclockwise.

the vertices of the triangle is:

(-2,3) → (-3,-2)

(6,0) → (0,6)

(3,-1) → (1,3)

{rotate 270° clockwise again }

Hence the vertices of the original triangle is:

(-3,-2) (0,6) and (1,3)

Hence we get the required vertices of the triangle.

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Given that a photocopier takes 8s to make 20 copies and we need to find out how long would it take to make 45 copies .

This can be solved using Unitary Method as ,

To make 20 copies it takes 8 s.

To make 1 copy it would take 8/20 s

Hence to make 45 copies it would take 8/20*45 = 18s

And we are done!

Answer:

45 copies = 18 seconds

Step-by-step explanation:

Time taken to make 1 copy,

→ Total time ÷ Total copies

→ 8 ÷ 20

→ 8/20 seconds

Then the time taken for 45 copies,

→ 45 × (8/20)

→ (45 × 8)/20

→ 360/20

→ 18 seconds

Hence, time taken is 18 seconds.

The number of blue tiles is 68.

Given:

Red tiles = 1/5 of the total

Total tiles = 85

Red tiles = 1/5*85

= 17.

Number of blue tiles = total tiles - red tiles

= 85 - 17

= 68.

Therefore the number of blue tiles is 68.

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The first 100 natural numbers are 1,2,3,...,100 is 50.5.

An average is a single number chosen to represent a group of numbers; it is typically the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.

We know that the sum of the first n natural numbers is = 2n(n+1)

​Therefore, the sum of the first 100 natural numbers is = 2×100(101)

                                                                             =200(101)=20200

Hence, the sum of the first 100 natural numbers is = 20200  = 101

                                                                                         200

Hence, the average of the first 100 natural numbers is = 101  = 50.5

                                                                                               2

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Based on the charged amount, Lupita drove 8.76 miles.

Let us assume the number of miles rode bh Lupita be x. Forming the equation now -

Total charge = flat rate + cost per mile × number of miles

Keep the values in above mentioned equation to find the value of x

40.03 = 6.75 + 3.20×x

Rewriting the equation with respect to x

3.20x = 40.03 - 6.75

3.20x = 33.28

Shifting 3.20 to Right Hand Side of the equation

x = 33.28 ÷ 3.20

Performing division on Right Hand Side of the equation

x = 8.76 miles

Thus, Lupita drove 8.76 miles.

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Answer:

Step-by-step explanation:

(x 2 y) 4 = x2*4 y 1*4  = x 8 y4

An exponent raised to another exponent means to multiply the exponents. If a number does not have a visible exponent, then it is an implied 1.

The required simplified form of the expression is 1 / (x² · y⁴) which is the correct answer would be an option (D).

When multiplying similar bases, keep the base and add the exponents the same. When comparing one power to another, keep the base constant and multiply the exponents. Keep the base constant when dividing like bases and subtract the denominator exponent from the numerator exponent.

Simplify x raised to the negative second power over y raised to the fourth power.

The expression is given in the question below as:

x⁻² / y⁴

The expression can be simplified as follows:

⇒ x⁻² / y⁴

⇒ (1 / x²) / (y⁴)

⇒ 1 / (x²) · y⁴)

⇒ 1 / (x² · y⁴)

Therefore, the simplified form of the expression is 1 / (x² · y⁴).

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In 2001, 150 000 students were expected to enroll at the institution.

For the 2018 academic year, 468000 students are anticipated to enroll at the

The size of a population refers to its total number of members. The average person count per unit of area or volume is referred to as population density.

a. The formula to solve the question is as follows:

y = 123.1(1.069)x.

Hence x is the amount of time that was passed.

2001 - 1998 = 3y = 123.1 (1.069)³y

= 123.1 x  1.2216115y = 150.4

In 2001, the school is expected to have 150000 students enrolled.

b. 2018

The distinction x, or the variation between the years we are to calculate, must be considered:

x = 2018 - 1998

= 20.y = 123.1 x  (1.069)²⁰y

= 123.1 x  3.798y

= 467.5468

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Answer:

I agree due to everything stated there everything is perpendicular and is equal to the each other.

PLEASE GIVE BRAINLIEST THANK YOU!!!

1. When a function passes the horizontal line test, we can infer that its inverse is both known and exists.

You can use the vertical line test to determine whether an expression is actually a function; if it succeeds, it is. If the graph does, in fact, pass the vertical line test before passing the horizontal line test, it is a function. If it also passes the horizontal line test, it is a one-to-one function, which means there is a unique x-coordinate value for every unique y-coordinate value. Only one-to-one functions have an inverse expression that is also a function.

Graph:

A graph is a logical visual representation of any data in mathematics. The correlation between the variable values is depicted on the graph. A graph is used in graph theory to depict a group of items that are interconnected in some way. In essence, the vertices or nodes of the objects are mathematical notions, and the edges are representations of the connections between the nodes. In mathematics and statistics, many graph types are used to visually display data. The study of points and lines is the focus of the field of graph theory. It is a branch of mathematics with a focus on graph analysis. The mathematical truth is clearly illustrated in this artwork. Relationships are studied using the graph theory.

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The number of green fish are in the aquarium is 6.

Given that,

The aquarium has 3 more yellow fish than green fish.

60 percent of the fish are yellow.

Let us assume the green fishes be x and the yellow fishes are y.

Total no of fished = x + y.

And, y = x + 3

Based on the above information, the calculation is as follows:

Now, put y = x + 3

So,  

60%(y+x)=y

[tex]\frac{60}{100}(x+3+x)=x+3[/tex]

60(2x+3)=100(x+3)

120x + 180 = 100x + 300

20x = 120

x = 6

Hence the number of green fishes are x=6  

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Answer: 4.1 hours (4 hours and 6 minutes)

Equation: 250=50x+45

Step-by-step explanation:

The equation would be: 250=50x+45

x represents the number of hours worked

Next, solve your own equation: 250=50x+45

205=50x

4.1=x

Answer:

704 people out of 800

Step-by-step explanation:

88% of 800= 704

Answer:

A. <

Step-by-step explanation:

Hope this helps! ^^

Answer:

>

Step-by-step explanation:

2/5 is greater than 7/10. Therefore, the best symbol to compare the two would be the greater than symbol, >.

Hence, the two triangles have the same side length so they are congurent triangles.

What is the congurency?

The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.

Here given triangles are

In Δ[tex]FGH[/tex] and Δ[tex]JKL[/tex] are congruent. If they are, give the reason, if they aren't choose "not congruent".

[tex]F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)[/tex]

We know the distance formula

ie., [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Length in between [tex]FG[/tex] is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(-2-(-5))^2+(2-10)^2}\\\\d=\sqrt{(-2+5)^2+(2-10)^2}\\\\d=\sqrt{(3)^2+(-8)^2}\\\\d=\sqrt{9+64}\\\\d=\sqrt{73}[/tex]

Length in between [tex]GH[/tex] is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(-9-(-2))^2+(-7-2)^2}\\\\d=\sqrt{(-9+2)^2+(-7-2)^2}\\\\d=\sqrt{(-7)^2+(-9)^2}\\\\d=\sqrt{49+81}\\\\d=\sqrt{130}[/tex]

Length in between [tex]HF[/tex] is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(-5-(-9))^2+(10-(-7))^2}\\\\d=\sqrt{(-5+9)^2+(10+7)^2}\\\\d=\sqrt{(4)^2+(17)^2}\\\\d=\sqrt{16+289}\\\\d=\sqrt{305}[/tex]

Length in between [tex]JK[/tex] is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(9-0)^2+(2-(-5))^2}\\\\d=\sqrt{(9)^2+(2+5)^2}\\\\d=\sqrt{(9)^2+(7)^2}\\\\d=\sqrt{81+49}\\\\d=\sqrt{130}[/tex]

Length in between [tex]KL[/tex] is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(-8-9)^2+(-2-2)^2}\\\\d=\sqrt{(-8-9)^2+(-2-2)^2}\\\\d=\sqrt{(-17)^2+(-4)^2}\\\\d=\sqrt{289+16}\\\\d=\sqrt{305}[/tex]

Length in between [tex]LJ[/tex] is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(0-(-8))^2+(-5-(-2))^2}\\\\d=\sqrt{(0+8)^2+(-5+2)^2}\\\\d=\sqrt{(8)^2+(-3)^2}\\\\d=\sqrt{64+9}\\\\d=\sqrt{73}[/tex]

Therefore, [tex]FG[/tex]≅[tex]LJ-GH[/tex]≅[tex]JK-HF[/tex]≅[tex]KL[/tex]

Hence, the two triangles have the same side length so they are congurent triangles.

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The other midpoint is 3+9i in the given complex plane.

Given that,

We know that the middle point is: (-1+i)

And the end point  is: (-5-7i)

We know that the formula to find the middle point is:

(x1+ x2 /2, z1+z2/2)

We wish to find the point x1,z1

So we can write the following equation

x1 + (-5)/2 = -1  --------> 1

and

z1 + (-7i)/2 = i ----------->2

Now we clear x1 from equation (i) and clear z1 from equation (ii)

For equation (i) we have:

-2 = x1 -5

x1 =3

For equation (ii) we have:

2i = z1 - 7i

z1 = 9i

Then the initial point is: 3+9i

So, The other endpoint is 3+9i

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The area of the given quadrilateral trapezoid ABCD with vertices A (-3,2) B (1,5) C (7,-3) D (0,-2) will be 37.5 square units.

A quadrilateral is a geometrical 2d shape with four sides, each side being connected and making a close polygon.

In other words, a quadrilateral is a polygon in which four sides, such as a trapezoid, square, and parallelogram, are quadrilateral.

As per the given quadrilateral as trapezoid,

The area of the trapezoid = 1/2 x (sum of parallel length) x perpendicular

The given trapezoid has been drawn below,

The length associated to two points (x₁, y₁) and (x₂, y₂)  is given by the formula;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

The smaller parallel line = 5 unit

Bigger parallel line = 10 unit

Perpendicular distance = 5 unit

Area = 1/2 x (5 + 10) x 5 = 37.5 unit square.

Hence "The area of the given quadrilateral trapezoid ABCD with vertices A (-3,2) B (1,5) C (7,-3) D (0,-2) will be 37.5 square units".

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The total height gained from start to finish is 58m and the average gradient from start to finish is 29/210

What is an average gradient?

The gradient of a straight line drawn between two points is the average gradient between the two points.

Here, we have

A road has a gradient of 1/5 for 90 m.

Horizontal section 130 m long

The final section has a gradient of 1/5 for 200 m.

First, we will find the total height gained from start to finish

Total height from start to finish = 90 ×1/5 +200 × 1/5

= 18 + 40  

Total height from start to finish =58 m

The average gradient from start to finish = 58/(90 + 130 +200)

= 58/420

= 29/210

Hence the total height gained from start to finish is 58m and the average gradient from start to finish is 29/210

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Answer:

Sam has 6 marbles

Step-by-step explanation:

42 ÷ 7 = 6

7 times means that whatever Joey has it is sams × 7. so to find answer we the do reserve.

Answer:

x < 5

Step-by-step explanation:

The variable that can be used to represent the number of points scored before is x and the algebraic expression is (3x - 2).

Algebra refers to the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

let

3 times the number of points scored before

= 3 × x

= 3x

two points fewer than 3 times the number of points scored before

= 3x - 2

Other examples of algebraic expression are:

2t - 5 + 3t

65x + y - 8y + 5x

In conclusion, the expression can be written in algebra form as 3x - 2

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One solution:  3x- 5y = 8; 5x - 3y = 2

3x + 2y = 8; 4x +3y = 1

acc to our question-

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Valentina should use a gear on the back wheel that has larger diameter to be more efficient

The problem deals with circumference of the wheel.

Circumference is a function of diameter such that: A larger wheel will have a larger circumference and a smaller wheel will have a smaller circumference

The wheel is assumed to be a circle and equation of circumference of a circle is pi * diameter

Gear has the function of rotating the wheel when a gear makes a initiates one revolution of the wheel

say wheel x, diameter = 5 and wheel y, diameter = 10

distance covered by one revolution = circumference

circumference of x = pi * 5 = 5pi

circumference of y = pi * 10 = 10pi

comparing both shows that wheel y will cover double the distance of x hence more efficient.

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