The number of men and women participating in the Winter Olympic Games has been steadily increasing in recent years. In the 19th Winter Olympics, 1389 men and 787 women participated. 1660 men and 1121 women participated in the 22nd Winter Olympics.



Part A

Which system describes the number of men and women participating if x represents the number of winter games after the 22nd Winter Olympics?



Multiple choice question.

A)
y=1389x+1660y=787x+1121


B)
y=2713x+1121y=3343x+1660


C)
y=2713x+1389y=3343x+787


D)
y=2713x+1660y=3343x+1121

Answer:

A. 3.    B. 20

Step-by-step explanation:

2 divided by 2/3 is 2/ 2/3 or  6/2   which is 3.

3 divided by 1/10 is  3/ 1/10 or 30.

Answer:

Step-by-step explanation:

Let the width of the rectangle = x

As length is 5 inches longer than width, we have to add 5 to width

Length = x + 5

Perimeter of ractangle = 56 in

2* (length + width) = 56

2*( x + 5 + x) = 56

2* (2x + 5)    = 56

Use distributive property: a*(b +c) =(a*b) + (a * c)

2*2x + 2*5   = 56

4x  + 10 = 56

Subtract 10 from both sides

4x = 56- 10

4x = 46

Divide both sides by 4

x = 46/4

x = 11.5

Width = 11.5 in

length = 11.5 + 5

            = 16.5 in

Answer: 15

Step-by-step explanation:

Check the picture below.

so the surface area of the pyramid will be the sum of the areas of the base and the four triangular faces.

[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{4 triangular faces}}{4\left[ \cfrac{1}{2}(7.5)(16) \right]}~~ + ~~\stackrel{\textit{rectangular base}}{(7.5)(7.5)}}\implies 240~~ + ~~56.25\implies 296.25~ft^2[/tex]

the lcm would be 79380

Step-by-step explanation:

5×7×7

2×2

×3×3×3×3

muliply all the 3 numbers and then you get 79380

Answer:

x=17.771mm

Step-by-step explanation:

given a right triangle

to find vslue of x

solution (perpendicular) ² + (base) ² =(hypotenus) ²

using pythagorus theorem

(16.5)²+(6.6)²=(x)²

272.25+43.56=(x)²

315.81=(x)²

√315.81=x

x=17.771mm

Answer:

By Pythagoras theorem

H^2=P^2+B^2

x^2=(6.6)^2+(16.5)^2

x^2=43.56+272.25

x^2=315.81

x=√315.81

x=17.771mm

The measure of the angle that would maximize the area of this isosceles trapezoid is equal to 0.4395 rad.

Given the following data:

Mathematically, the area of a trapezium is given by this formula:

A = ½ × (a + b) × h

A = ½ × (12 + 2l) × h

A = h(6 + l)

Next, we would derive a mathematical expression for A in terms of h as follows;

A = (6 + 4sin(θ)) × 4cosθ

In order to determine the value of θ for which the area of this isosceles trapezoid is maximized, we would differentiate the area (A) with respect to angle (θ):

Note: sin²θ + cos²θ = 1   ⇒ cos²θ = 1 - sin²θ.

[tex]\frac{dA}{d\theta} =16 cos^{2} \theta - 4sin \theta(6+4sin \theta)\\\\\frac{dA}{d\theta} = 16 cos^{2} \theta - 16 sin^{2} \theta - 24sin\theta\\\\\frac{dA}{d\theta} =16(1-sin^{2} \theta)- 16 sin^{2} \theta - 24sin\theta\\\\\frac{dA}{d\theta} = - 32 sin^{2} \theta - 24sin\theta+16\\\\32 sin^{2} \theta + 24sin\theta-16=0[/tex]

Next, we would use the quadratic formula to solve for the value of sinθ.

Mathematically, the quadratic formula is given by this equation:

[tex]sin\theta = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Where:

Substituting the parameters into the formula, we have;

[tex]sin\theta = \frac{-24\; \pm\; \sqrt{24^2 - 4(32)(-16)}}{2(32)}\\\\sin\theta = \frac{-24\; \pm\; \sqrt{2624}}{64}\\\\sin\theta = \frac{-24\; \pm\; 51.23}{64}\\\\sin\theta = \frac{-24\;+\; 51.23}{64}\\\\sin\theta = \frac{27.23}{64}\\\\sin\theta = 0.4255\\\\\theta = sin^{-1}(0.4255)[/tex]

θ = 0.4395 rad.

Note: We would only consider the positive value of the quadratic root.

For the obtuse interior angles of the trapezoid, we have [tex](\frac{\pi}{2} +0.4395)[/tex]

Similarly, the measure of the acute interior angles of the trapezoid is [tex](\frac{\pi}{2} -0.4395)[/tex]

Read more on isosceles trapezoid here: https://brainly.com/question/4758162

Answer:

x = 9,-21

Step-by-step explanation:

Given:

[tex]\displaystyle \large{|x+6|-7=8}[/tex]

Transport -7 to add 8:

[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]

Cancel absolute sign and add plus-minus to 15:

[tex]\displaystyle \large{x+6=\pm 15}[/tex]

Transport 6 to subtract ±15:

[tex]\displaystyle \large{x=\pm 15-6}[/tex]

Consider:

[tex]\displaystyle \large{x= 15-6}[/tex] or [tex]\displaystyle \large{x = -15-6}[/tex]

[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]

Solution:

[tex]\displaystyle \large{x = 9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]

__________________________________________________________

Second Method

Given:

[tex]\displaystyle \large{|x+6|-7=8}[/tex]

Transport -7 to add 8:

[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]

Absolute Function Property:

[tex]\displaystyle \large{|x-a| = \begin{cases} x-a \ \ (x \geq a) \\ -x+a \ \ (x < a) \end{cases}}[/tex]

Consider both intervals:

When x ≥ a then:

[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{x+6=15}[/tex]

Transport 6 to subtract 15:

[tex]\displaystyle \large{x=15-6}\\\displaystyle \large{x=9}[/tex]

When x < a then:

[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{-(x+6)=15}\\\displaystyle \large{-x-6=15}[/tex]

Transport -6 to add 15:

[tex]\displaystyle \large{-x=15+6}\\\displaystyle \large{-x=21}[/tex]

Transport negative sign to 21:

[tex]\displaystyle \large{x=-21}[/tex]

Solution:

[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]

__________________________________________________________

Let me know if you have any questions regarding this question, my answer or explanation. Hope this answer and explanation helps you and good luck with your assignment!

so we know that 40% for the rent payment is for food, and we also know that those 40% are really 200 bucks, so what would it be for the 100%?

[tex]\begin{array}{ccll} \%&amount\\ \cline{1-2} 40 & 200\\ 100& x \end{array} \implies \cfrac{40}{100}=\cfrac{200}{x}\implies \cfrac{2}{5}=\cfrac{200}{x} \\\\\\ 2x=1000\implies x=\cfrac{1000}{2}\implies x=500[/tex]

Answer:

$149 - skateboard price

$52 - carly's money

$20 × 5 cars = $100

$100 + $52 = $152

$152 - $149 = $3 left

Answer:

Step-by-step explanation:

Scale:- 1box=1units

So

Take one side of each

Scale factor(A to B)

[tex]\\ \rm\rightarrowtail \dfrac{6}{10}=\dfrac{3}{5}[/tex]

#6

Scale factor (A to B)

[tex]\\ \rm\rightarrowtail \dfrac{12}{6}=2[/tex]

Scale factor (B to A)

[tex]\\ \rm\rightarrowtail \dfrac{6}{12}=0.5[/tex]

Answer:

is this from flvs?

Step-by-step explanation:

Answer:

half a circle

Answer:

(2a-b)(2a+b-1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

B) 9 and 36

================================================

9 is a common factor of

9 and 36.

Here's why:

6 is not evenly divisible by 9

16 is not divisible evenly by 9 (it is divisible by 8)

All the other numbers are divisible by 9.

=============================================

Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer. :)

Answer:

54

Step-by-step explanation:

9x6=54

Answer:

h=9

g=61

Step-by-step explanation:

16-h=7

g+4=65

&

Opposite angles and sides are equal in a paralleogram

Amd

Answer:

[tex] \orange{ \boxed{ \sf{ ( \: {x}^{2} + 11x + 18 \: ) \: sq. \: units}}}[/tex]

Solution :

Lenght = x + 9

Width = x + 2

[tex] \sf \green{area \: = \: (x + 9)(x + 2)} \\ \sf \green{ = \: { {x}^{2} + 11x + 18}} [/tex]

Answer:

[tex]x^2+11x+18\: \sf(square\:units)[/tex]

Step-by-step explanation:

To use the area model of solving multiplication and division problems, calculate the area of each of the colored rectangles and add them together.

Area of a rectangle = Length × Width

Area of blue rectangle:  [tex]x \times x = x^2[/tex]

Area of pink rectangle:  [tex]x \times 9 = 9x[/tex]

Area of green rectangle:  [tex]2 \times x=2x[/tex]

Area of orange rectangle:  [tex]2 \times 9=18[/tex]

Area of entire rectangle = blue + pink + green + orange

                                        = [tex]x^2+9x+2x+18[/tex]

                                        = [tex]x^2+11x+18\: \sf(square\:units)[/tex]

Answer:

D should be the answer because the rate of Mason and Evan is 3 pages per a minute because three goes into both like so 30÷10=3 and 12÷4=3. Which is why D is your answer.

Answer:

Line 2

Step-by-step explanation:

When factoring the second bracket, 1 x -8 is -8.

Answer:

4

Step-by-step explanation:

Answer: ur dad

Step-by-step explanation:

lol

There are 7 positive integers in between 28/3 and 83/5.

What is an integer?

An integer is a whole number (not a fractional number) that can be positive, negative or zero.

Given that;

Two fractions are;

28/3 and 83/5.

Now, Write fraction into decimal form as;

28/3 = 9.33

83/5 = 16.6

So, All Integers in between 9.33 and 16.6 are;

⇒ 10, 11, 12, 13, 14, 15, 16

Thus, There are 7 positive integers in between 28/3 and 83/5.

Learn more about the integers visit:

https://brainly.com/question/24653557

#SPJ2

Answer:

50°

Step-by-step explanation:

In a parallelogram opposite angles have the same measure. Angle ABC has then the same measure of angle ADC, which is 38°+12°=50°

Answer:

She was finished with dinner at 6:50

Step-by-step explanation:

3:45 + 2 = 5:45

5:45 + 30 = 6:05

6:05 + 45 = 6:50

Answer:

an = a1 + d (n - 1)

aⁿ = a₁ˣ⁻1

Using a system of equations, it is found that the equation that could be used to find the value of b is given by:

3×4−8=b

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

Fatima has 3 packs of batteries. Each pack contains 4 batteries, hence:

b = 3 x 4

She gives her brother 8 batteries to put in his toy robot, hence:

b = 3 x 4 - 8

Which means that the first expression is correct.

More can be learned about a system of equations at https://brainly.com/question/24342899

Answer:

[tex]\displaystyle \textcolor{black}{4.}\:[-3, -5][/tex]

[tex]\displaystyle \textcolor{black}{3.}\:[8, -1][/tex]

[tex]\displaystyle \textcolor{black}{2.}\:[4, -7][/tex]

[tex]\displaystyle \textcolor{black}{1.}\:[3, -2][/tex]

Step-by-step explanation:

When using the Elimination method, you eradicate one pair of variables so they are set to zero. It does not matter which pair is selected:

[tex]\displaystyle \left \{ {{2x - 3y = 9} \atop {-5x - 3y = 30}} \right.[/tex]

{2x - 3y = 9

{⅖[−5x - 3y = 30]

[tex]\displaystyle \left \{ {{2x - 3y = 9} \atop {-2x - 1\frac{1}{5}y = 12}} \right. \\ \\ \frac{-4\frac{1}{5}y}{-4\frac{1}{5}} = \frac{21}{-4\frac{1}{5}} \\ \\ \boxed{y = -5, x = -3}[/tex]

------------------------------------------------------------------------------------------

[tex]\displaystyle \left \{ {{x - 2y = 10} \atop {x + 3y = 5}} \right.[/tex]

{x - 2y = 10

{⅔[x + 3y = 5]

[tex]\displaystyle \left \{ {{x - 2y = 10} \atop {\frac{2}{3}x + 2y = 3\frac{1}{3}}} \right. \\ \\ \frac{1\frac{2}{3}x}{1\frac{2}{3}} = \frac{13\frac{1}{3}}{1\frac{2}{3}} \\ \\ \boxed{x = 8, y = -1}[/tex]

_______________________________________________

[tex]\displaystyle \left \{ {{y = -3x + 5} \atop {y = -8x + 25}} \right.[/tex]

{y = −3x + 5

{−⅜[y = −8x + 25]

[tex]\displaystyle \left \{ {{y = -3x + 5} \atop {-\frac{3}{8}y = 3x - 9\frac{3}{8}}} \right. \\ \\ \frac{\frac{5}{8}y}{\frac{5}{8}} = \frac{-4\frac{3}{8}}{\frac{5}{8}} \\ \\ \boxed{y = -7, x = 4}[/tex]

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[tex]\displaystyle \left \{ {{y = -x + 1} \atop {y = 4x - 14}} \right.[/tex]

{y = −x + 1

{¼[y = 4x - 14]

[tex]\displaystyle \left \{ {{y = -x + 1} \atop {\frac{1}{4}y = x - 3\frac{1}{2}}} \right. \\ \\ \frac{1\frac{1}{4}y}{1\frac{1}{4}} = \frac{-2\frac{1}{2}}{1\frac{1}{4}} \\ \\ \boxed{y = -2, x = 3}[/tex]

_______________________________________________

I am joyous to assist you at any time.