100 points!!!!!!!!


Martina is playing a carnival game. She is blindfolded while she throws a dart at a board of 12 balloons, as shown below. Each balloon is labeled "S" for small,
"M" for medium, "L" for large, or "XL" for extra-large. The board has 5 small balloons, 1 medium balloon, 4 large balloons, and 2 extra-large balloons. She hits one of the balloons at random and wins a stuffed animal of that size.

(a)Find the odds in favor of Martina winning a medium stuffed animal.

(b) Find the odds against Martina winning a medium stuffed animal.

Answers

Answer 1

Answer:

(a) The odds in favor of Martina winning a medium stuffed animal is 1/12, as there is only 1 medium balloon on the board out of the total of 12 balloons.

(b) The odds against Martina winning a medium stuffed animal is 11/12, as there are 11 balloons on the board that are not medium out of the total of 12 balloons.

Answer 2

Answer:

(a) The odds in favor of Martina winning a medium stuffed animal is 1/12, as there is only 1 medium balloon on the board out of the total of 12 balloons.

(b) The odds against Martina winning a medium stuffed animal is 11/12, as there are 11 balloons on the board that are not medium out of the total of 12 balloons.


Related Questions

9,100 dollars is placed in a savings account with an annual interest rate of 5%. If no money is added or removed from the account, which equation represents how much will be in the account after 6 years?

1.) M=9,100(1 + 0.05)^6
2.)M=9,100(1 - 0.05)^6
3.)M=9,100(1 + 0.05)(1 + 0.05)(1 + 0.05)
4.)M=9,100(0.95)^6

Answers

Answer:

1.) M=9,100(1 + 0.05)^6

Step-by-step explanation:

Compound Interest Rate Formula:


[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

In this formula the "P" represents the principle amount, or the original amount. The "r" represents the interest rate in decimal form, while the "n" represents the number of compounds in the time unit (usually years), and the "t" represents the amount of time that has passed (usually years)

In this case it says annual interest rate of 5% and nothing of compound monthly, etc... so n=1, and r=0.05. We're also given the principle amount of 9,100 and the time passed is just 6 years, so t=6. Plugging all this information into the equation we get:

[tex]A=9,100(1+0.05)^6[/tex]

which makes the first option correct.

Support for character vector or string inputs will be removed in a future release. Instead, use syms to declare variables and replace inputs such as dsolve('Dy = -3*y') with syms y(t); dsolve(diff(y,t) == -3*y).

Answers

The support vector of the input dsolve('Dy = -3*y') is "dsolve(diff(y,t) == -3*y)".

A symbol is a mathematical object that represents a mathematical entity, such as a number, a variable, or a function. In mathematical software, symbols are used to represent variables, which can be used in mathematical expressions to perform computations.

In the past, character vectors or strings were used to represent symbols in certain mathematical software programs.

In the future release of this software, support for character vectors or strings will be removed. Instead, the program will require users to use the "syms" function to declare variables as symbols.

As an example of how this might be used in practice, consider the differential equation

=> "dy/dt = -3y".

In the past, this equation might have been entered into a mathematical software program using a character vector or string to represent the variable "y".

However, in the future release of this software, the user will need to use the "syms" function to declare "y" as a symbol. The equation would then be entered using the "diff" function, like this:

=> "dsolve(diff(y,t) == -3*y)".

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Find the equation of the line containing the points (-3, 11)
and (-4,1).
Write the equation in slope-intercept form.

Answers

The equation in slope-intercept form is y = 10x + 41.

What is the point-slope form?

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

m represents the slope.x and y are the points.

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (-3, -4).

Points on y-axis = (11, 1).

At point (-3, 11), a linear equation of this line can be calculated in slope-intercept form as follows:

y - 11 = (1 - 11)/(-4 + 3)(x + 3)

Y - 11 = 10(x + 3)

y = 10x + 30 + 11

y = 10x + 41.

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Mrs. Imperiale's credit card has an APR of 13.2%. She does not ever pay her balance off in full, so she always pays a finance charge. Her next billing cycle starts today. The billing period is 31 days long. She is planning to purchase $7,400 worth of new kitchen cabinets this billing cycle. She will use her tax refund to pay off her entire bill next month. If she purchases the kitchen cabinets on the last day of the billing cycle instead of the first day, how much would she save in finance charges? Round to the nearest ten dollars.

Answers

If Mrs. Imperiale's credit card has an APR of 13.2%. The amount she would  save in finance charges Round to the nearest ten dollars is $80.

What is the amount saved?

Finance charge if bought on the first day

Finance charge = (31 × 7400 ÷ 31) × (0.132 ÷ 12)

Finance charge = 7400  ×  0.011

Finance charge= $81.40

Finance charge if bought on the last day

Finance charge = (1 × 7400 ÷ 31) × (0.132 ÷ 12)

Finance charge = 238.709677 ×  0.011

Finance charge= $2.625

Finance charge = $2.63

Savings = $81.40 - $2.63

Savings = $78.77

Savings = $80 ( Approximately)

Therefore the savings is $80.

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What is the area of rhombus ABCD?
24.57 cm^2
39.00 cm^2
98.28 cm^2
78.00 cm^2

Answers

The area of rhombus ABCD is 98.28 cm². Therefore, option C is the correct answer.

What is area?

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

Given that, in rhombus ABCD, AD=10 cm and OC=7.8 cm.

Here, BC²=OC²+OB²

10²=7.8²+OB²

OB²=100-60.84

OB²=39.16

OB=√39.16

OB=6.3 cm

AC=2×7.8

AC=15.6 cm

BD=2×6.3 =12.6 cm

We know that, area of rhombus is 1/2 ×(Product of diagonals)

Now, area= 1/2 ×15.6×12.6

= 98.28 cm²

Therefore, option C is the correct answer.

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Find the volume of the solid obtained by rotating about the x-axis the region enclosed by the curves y = 16 /(x^2 + 16) , y = 0, x = 0, and x = 4.
The answer is supposed to come out to pi + (pi^2)/2.

Answers

The volume of the solid obtained by rotating about the x-axis the region enclosed by the curves is 32π/5 cubic units.

In this problem, we are asked to find the volume of a solid obtained by rotating a region enclosed by curves about the x-axis. We will use integration to calculate the volume.

First, let's sketch the region and the solid we need to find the volume of.

The region is enclosed by the curves

=> y = 16 /(x² + 16), y = 0, x = 0, and x = 4.

When we rotate this region about the x-axis, we get a solid with a hole in the center, shaped like a donut.

To find the volume of this solid, we can use the method of cylindrical shells.

We start by taking a thin strip of the region, parallel to the y-axis, and of width dy. This strip has height y, and we rotate it about the x-axis to get a cylindrical shell of thickness dy and radius x.

The volume of this cylindrical shell is given by the formula V = 2πxy dy, where x is the distance from the y-axis to the edge of the shell.

To express x in terms of y, we can solve for x in the equation

y = 16 /(x² + 16).

y(x² + 16) = 16

x² = 16/y - 16

x = √(16/y - 16)

Now we can substitute x into the formula for V to get:

V = 2πx(16/(x² + 16)) dy

[tex]= 2\pi(16/y - 16)^{1/2}(16/y) dy \\\\= 32\pi(y - y^{3/2}) dy[/tex]

To find the total volume, we integrate this expression from y = 0 to y = 1 (since the maximum value of y is 16/16 = 1):

[tex]\int_0^1 32\pi(y - y{(3/2)}) dy = 32\pi/5[/tex]

Therefore, the volume of the solid obtained by rotating the region about the x-axis is 32π/5 cubic units.

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9.5 less than a number n equals 27

Answers

Answer:

N-27 = 9n + 5

Step-by-step explanation:

write equation to the word sentence 9.5 less than a number n equals 27 the answer n-27 = 9n + 5 that is posted to this question on your website is wrong according to my homework check.

For example:

The value of n for the given condition "9.5 less than a number n equals 27" is, 36.5

Given that,

A statement,

"9.5 less than a number n equals 27"

To solve for the value of "n",

we can start by subtracting 9.5 from both sides of the equation,

9.5 less than a number n = 27

So, it can be written as,

n - 9.5 = 27

n = 36.5

Therefore, 9.5 less than a number n equals 27 the answer n-27 = 9n + 5

Can anyone help me solve this? Thank you!

Your friend sings every Saturday night at your favorite bar in San Diego. During his show, people show up at the rate of 1 person every minute.

a) What is the probability that on a random minute, at least 3 people show up?

b) What is the probability that he will have to wait at least 3 minutes for the next person to show up?

c) If he has already waited for 1 minute for the next person to show up, what is the probability that he will have to wait at least 3 more minutes for the next person to show up?

Answers

Answer:

Step-by-step explanation:

a) The number of people showing up at the bar during any given minute is a Poisson process with an average rate of 1 person per minute. Let X be the number of people who show up during a random minute. Then X follows a Poisson distribution with parameter λ = 1. The probability of at least 3 people showing up in a random minute is:

P(X >= 3) = 1 - P(X < 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))

We can use the Poisson probability mass function to find P(X = k) for k = 0, 1, 2:

P(X = k) = (e^-λ) * (λ^k) / k!

Plugging in λ = 1, we get:

P(X = 0) = e^-1 / 0! = 1/e

P(X = 1) = e^-1 * 1^1 / 1! = 1/e

P(X = 2) = e^-1 * 1^2 / 2! = 1/2e

So, the probability of at least 3 people showing up in a random minute is:

P(X >= 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2)) = 1 - (1/e + 1/e + 1/2e) = 1 - (2/e + 1/2e) = 1 - (5/2e)

b) The probability of having to wait at least 3 minutes for the next person to show up is equal to the probability of having 0, 1, or 2 people show up during the first three minutes. Using the same calculation as above, we find:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = (1/e) + (1/e) + (1/2e) = (2/e + 1/2e) = (5/2e)

So, the probability of having to wait at least 3 minutes for the next person to show up is 1 - (5/2e) = 1 - P(X <= 2).

c) If he has already waited for 1 minute, the probability of having to wait at least 3 more minutes for the next person to show up is equal to the probability of having 0 or 1 people show up during the next 2 minutes. Using the same calculation as above, we find:

P(X <= 1) = P(X = 0) + P(X = 1) = (1/e) + (1/e) = 2/e

So, the probability of having to wait at least 3 more minutes for the next person to show up is 1 - (2/e) = 1 - P(X <= 1).

If my answer met your requirements, please rate it BRAINLY AWESOME.

RECAP NEED HELP STILL

Answers

Using trigonometric functions and Pythagoras' theorem, the x value of different right-angled triangles is found.

What is a right-angled triangle?

A right triangle, also known as a right-angled triangle, is a triangle with one right angle, or two perpendicular sides. The sum of the other two angles is 90 degrees.

In all of these figures, one of the angles is 90°. So we can use Pythagoras' theorem and trigonometric relations, to solve the questions.

1) Opposite side = 5

sin 27° = Opposite side/ hypotenuse

0.45 = 5/x

x = 11.11

2) Hypotenuse = 16

   cos 63 = adjacent side/hypotensue

    0.45 = x / 16

    x = 7.2

3) Hypotenuse = 29

    sin 67 = opposite side/hypotensue

    0.92 = x/29

      x =  26.68

4) Opposite side = 27

  tan 39° = opposite side/ adjacent side = 27/x

0.81 = 27/x

x = 33.33

 

5) sin Q = opposite side / hypotensue = 14/50 = 7/25

   sin R = opposite side / hypotensue = [tex]\sqrt{50^2 - 14^2}[/tex]/50 = 48/50 = 24/25

  cos Q = PQ/ 50 = 48/50 = 24/25

   cos R = PR/50 = 14/50 = 7/25

tan Q = sin Q/cos Q = 7/24

tan R = sin R/cos R = 24/7

Therefore using trigonometric functions and Pythagoras' theorem, the x value of different right-angled triangles is found.

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In Year 1, Kim Company sold land for $80,000 cash. The land had originally cost $60,000. Also, Kim sold inventory that had cost $110,000 for $198,000 cash. Operating expenses amounted to $36,000. Find Sales revenue: Cost of goods sold: Gross margin; Expenses; Operating expenses; Operating income; Non-Operating Items; Gain on sale of land; Net income?

Answers

As per the question Sales revenue is $198,000 (from the sale of inventory)

What is Sales revenue?

Sales revenue, which is sometimes referred to as revenue from sales or just sales, is the entire sum of money that a business makes from the selling of goods or services to clients. It is one of the main revenue streams for the majority of businesses and is frequently used as a key performance indicator (KPI) to gauge a business's success.

Calculating sales income involves multiplying the quantity sold by the cost per unit. As an illustration, if a business sells 1,000 pieces of a product at $100 each, its sales revenue would be $100,000 ($100 x 1,000).

Sales revenue is a crucial indicator for businesses to monitor since it indicates how much demand there is for a company's goods or services.

According to question:

Cost of goods sold = $110,000 (the cost of the inventory that was sold)

Gross margin = Sales revenue - Cost of goods sold = $198,000 - $110,000 = $88,000

Expenses = Cost of goods sold + Operating expenses = $110,000 + $36,000 = $146,000

Operating income = Gross margin - Operating expenses = $88,000 - $36,000 = $52,000

Non-Operating Items = Gain on sale of land = $80,000 (the difference between the selling price and the original cost of the land)

Net income = Operating income + Non-Operating Items = $52,000 + $80,000 = $132,000

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Find the volume of the irregular figure. 1 cm 5 cm 1 cm 6 cm 4 cm 10 cm 12 cm [?] cm ³ Enter​

Answers

The volume of the irregular figure is solved to be

78 cubic centimeters

How to find the volume of the irregular figure

The volume of the irregular figure is solved by the formula

= area of the figure * thickness

The area of the figure is solved by dividing the firue into regular shapes and this will result to two rectangles

Area of the first rectangle

= length x width

= 4 * (12 - 5)

= 4 * 7

= 28 square centimeters

Area of the second rectangle

= 10 * 5

= 50 square centimeters

Total area = 50 + 28 = 78

volume = 78 * 1 = 78 cubic centimeters

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please help with explanation

Answers

The answer to the question on the value of x in a triangle is x = 60 degrees.

What is the value of x ?

The fact that all the angles are labeled as x means that this is an equilateral triangle which is a triangle where all the angles are equal.

Should this be the case, the value of x would be:

= Sum of interior angles of triangles / Number of sides in triangle

Sum of interior angles of triangles = 180 degrees

Number of sides = 3 sides

The value of x is:

= 180 / 3

= 60 degrees

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A line with a slope of 7 passes through the points (-7, 5) and (g, -2). What is the value of g?
g=

Answers

[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{g}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{g}-\underset{x_1}{(-7)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 7 }\implies \cfrac{-7}{g+7}=7\implies -7=7(g+7) \\\\\\ \cfrac{-7}{7}=g+7\implies -1=g+7\implies \boxed{-8=g}[/tex]

Find the surface area of the prism.
S.A.
?
cm²
5cm
4cm
7cm
Please hurryyyy

Answers

The Total Surface Area for given prism will be 166 [tex]cm^2[/tex].

How to calculate the total surface area of Rectangular Prism?

The entire surface area of a rectangular prism may be computed by adding the areas of its six sides. A rectangular prism's surface area may be determined using the following formula:

[tex]Surface Area = 2(l*w) + 2(l*h) + 2(w*h)[/tex]

where:

l = length of the rectangular prism

w = width of the rectangular prism

h = height of the rectangular prism

Using this formula for given problem,

Given,

l=5cm

w=4cm

h=7cm

[tex]\text{Total Surface area}=2.(5.7)+2.(4.5)+2.(4.7)\\\\=70+40+56\\\\=166\;cm^2[/tex]

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What is the surface area of the cylinder with height 8 in and radius 8 in? Round your
answer to the nearest thousandth.

Answers

Answer:

The surface area of a cylinder can be calculated using the formula:

Surface area = 2πr^2 + 2πrh

Where r is the radius and h is the height of the cylinder.

Plugging in the values we have:

Surface area = 2π(8^2) + 2π(8)(8) = 2π(64) + 2π(64) = 128π

Rounding to the nearest thousandth, we have:

Surface area = 128π = 403.23 in^2 (rounded to the nearest thousandth)

So the surface area of the cylinder with height 8 in and radius 8 in is 403.23 in^2.

Step-by-step explanation:

3. If 17 and 36 are the lengths of two sides of a triangle, what is the range of possible values for the length of the third side?

Answers

Answer:

19 < x < 53

Step-by-step explanation:

given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides , that is

36 - 17 < x < 36 + 17

19 < x < 53

could you please help me find out how to add m+x

Answers

Answer:

i got u i have your email

Step-by-step explanation:

What is the range of this equation

This is college algebra

Answers

The range is the set of y-coordinates of the function.

As per graph we can see:

All positive values included as well as zero;There is one negative value, at y = - 2.

Add all together to get the range:

y = - 2 and y ≥ 0

As interval the range is:

y ∈ {-2} ∪ [0, + ∞)

composite functions homework

Answers

The composite function has its value to be g o h(x) = -20x^2 - 30x

How to determine the composite function

from the question, we have the following parameters that can be used in our computation:

h(x) = 4x + 6

g(x) = -5x

Using the above as a guide, we have the following:

g o h(x) = g(x) * h(x)

substitute the known values in the above equation, so, we have the following representation

g o h(x) = (4x + 6) * -5x

Evaluate

g o h(x) = -20x^2 - 30x

Hence, the value is g o h(x) = -20x^2 - 30x

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Task
You put two targets in the field. The coordinates for target 1 (6 Points)
The coordinates for target 2 (4 points). See the figure below.
Informe the coach
You asked the players to shoot the ball on the targets 4 times. You added that if
they hit one of the targets, they get the target points.
Test 1:
Messi shot the ball. His ball followed the path of the equation where x is the target
points:
3(3x-4)= 24
6.8 (2.3x + 5.7) = 132.6
Test 2:
Ronaldo shot the ball. His ball followed the path of the equation where y is the
target points.

2/3 (6y - 18) = -16.4. : 2 times


8.2 (x/2 - 5) = - 16.4. : 2 times

Answers

Answer:

Step-by-step explanation:

3/2*2/3(6y)=30*3/2

6y=45

6y/y=45/y

y=7.5

Drag the numbers to complete the column two-way relative frequency table. Numbers may be used once, more than once, or not at all.

2829383949100
7th 8th Total
0–300 61%
% 50%
300+
% 62% 50%
Total
%
% 100%

Answers

Answer:

YOU L HAHA

Step-by-step explanation:

LOS ER

Need help quick pls and thanks

Answers

a) The average rate of change is -0.6333.

b) For $500 after the inflation rate from 1917 to 1920 the worth will be 242.20631771406.

What is Rate of Change?

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.

Given:

a) The average rate of change

= (15.9- 17.8)/ (1920 - 1917)

= -1.9 / 3

= -0.6333

So, the equation can be

y = -0.6333x + b

and, 17.8 = -0.63333(1917)+ b

b= 1231.79

So, y= -0.6333x + 1231.79

b) For $500 after the inflation rate from 1917 to 1920 the worth will be 242.20631771406.

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x = [ √(a+2) + √(a-2) ]/[ √(a+2) - √(a-2) ], then a =? the correct answer is a = x+(1/x). explain
how.

Answers

The inverse of the radical equation x = [√(a + 2) + √(a - 2)] / [√(a + 2) - √(a - 2)] is the equation a = x + 1 / x. (Correct choice: A)

How to clear a variable in a radical equation

In this problem we find the case of a radical equation in explicit form, that is, a variable x only in terms of a variable a, and we need to obtain the inverse of the function, that is, an expression in terms of a variable x. This problem can be solved by algebra properties.

First, write the original equation:

x = [√(a + 2) + √(a - 2)] / [√(a + 2) - √(a - 2)]

Second, rationalize the expression:

x = [[√(a + 2) + √(a - 2)] · [√(a + 2) + √(a - 2)]] / [[√(a + 2) - √(a - 2)] · [√(a + 2) + √(a - 2)]]

x = [√(a + 2) + √(a - 2)]² / [(a + 2) - (a - 2)]

x = [a + 2 - 2 ·√(a² - 4) + a - 2] / 4

x = [a - √(a² - 4)] / 2

2 · x = a - √(a² - 4)

Third, eliminate the square root operator by algebra properties:

√(a² - 4) = a - 2 · x

a² - 4 = (a - 2 · x)²

Fourth, find the solution to the expression:

a² - 4 = a² - 4 · x · a + 4 · x²

- 4 = - 4 · x · a + 4 · x²

1 = x · a - x²

1 + x² = x · a

a = (1 + x²) / x

a = 1 / x + x

a = x + 1 / x

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help with this problem, I don't get it, I will give brainliest

Answers

The equation cos (π/6 + β) is solved to get

√3 / 2

How to solve for the cosine

From the question it was given that sine β = -0.8

solving for β

sine β = -0.8

β = arc sine ( -0.8 )

β = -0.9273

β ≈ -π/3

substituting the value into cos (π/6 + β)

cos (π/6 + β)

cos (π/6 - π/3)

cos (π/6 - π/3)

= √3 / 2

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How do you do part ii

Answers

The value of k is,

The probability distribution as a table:

r   1     2          3

P(X)   0    1/15  2/15

What is probability?

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

To find the value of k, we can use the fact that the sum of the probabilities for all possible values of X must equal 1.

Therefore, we have:

P(X = 1) + P(X = 2) + P(X = 3) = k(4(1)(1²) + 4(2)(2²) + 4(3)(3²))

                                              = 24k

Since we also know that P(X = 1) = 0, we have:

P(X = 1) + P(X = 2) + P(X = 3) = P(X = 2) + P(X = 3) = 0.8

Substituting this into the equation above, we get:

0.8 = 24k

k = 0.8/24 = 1/30

Therefore, the probability distribution can be written as:

r 1 2 3

P(X) 0 1/15 2/15

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A line passes through the origin and (4, 6). What are two other points on this line?

Answers

Two other points on this line are (1, 1.5) and (2, 3)

How to determine the two other points on this line?

From the question, we have the following parameters that can be used in our computation:

A line passes through the originAnd it passes through (4, 6).

This means that the slope (m) of the line is

m = 6/4

Evaluate

m = 1.5

For the other points, we have

f(2) = 2 * 1.5 = 3

f(1) = 1 * 1.5 = 1.5

So, we have (1, 1.5) and (2, 3)

Hence, the points are (1, 1.5) and (2, 3)

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An auto maker is interested in information about how long transmissions last. A sample of transmissions are run constantly and the number of miles before the transmission fails is recorded. The auto maker claims that the transmissions can run constantly for over 150,000 miles before failure. The results of the sample are given below.

Answers

1) From Given output confidence level, is 95% level of significance = 1-0.95

10.05

How to calculate the value

2) null hypothesis : M = 150000

=

3) Alternative hypothesis Ha: [M> 150000]

4) since P value = 0.033 is less than d=0.05 Reject null hypothesis.

5) There is sufficient evidence to conclude that the mean life of transmissions is over 1500 comity

6) 95% CI = â ± E

-1519±1.129

=(151.2-1.129, 151.2+1.129)

=(150.071, 152.329)

7) Since M=150 fall out side of the C. We Shoul retect null hypothesis.

8) The null hypothesis value fall outside of the Confidence Interval.

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picture in the box findiing the average

-

Answers

[tex]\cfrac{6}{4+\sqrt{2}}\implies \cfrac{6}{4+\sqrt{2}}\cdot \cfrac{4-\sqrt{2}}{4-\sqrt{2}}\implies \cfrac{6(4-\sqrt{2})}{\underset{\textit{difference of squares}}{(4+\sqrt{2})(4-\sqrt{2})}} \implies \cfrac{6(4-\sqrt{2})}{(4)^2 - (\sqrt{2})^2} \\\\\\ \cfrac{6(4-\sqrt{2})}{16 - 2}\implies \cfrac{6(4-\sqrt{2})}{14}\implies \cfrac{3(4-\sqrt{2})}{7}\implies \cfrac{12-3\sqrt{2}}{7}[/tex]

helpppp geometry 8th grade

Answers

The length of the segment QV is  9.2 units

What is a square?

Regular quadrilaterals, such as a square, have four equal sides and four equal angles (right angles, 90-degree angles, or angles of /2 radian). It is also known as a rectangle with two neighbouring sides of identical length. It is the only regular polygon whose internal angle, central angle, external angle, and diagonal length are all equal (90°).

diagonal length, d=a√2 , where,  d--> diagonal length ,  a= side length

So, d= 13* 1.4142 = 18.3847 units

Diagonals bisect each other

QV = d/2 = 18.3847/2  = 9.1923

Rounding to 1 decimal place

QV = 9.2 units

The length of the segment QV is  9.2 units

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Set up two equations and solve.
9. The perimeter of a rectangle is 400 meters. The length is 20 meters longer than the
width. Find the length and width of the rectangle.

Answers

The width of rectangle  = 90 m

And, The length of rectangle = 110 m

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The perimeter of a rectangle is 400 meters.

And, The length is 20 meters longer than the width.

Now, Let the width of rectangle = x

Then, The length of rectangle = x + 20

We know that;

Perimeter of rectangle = 2 ( Length + width )

Substitute values ,

⇒ 400 = 2 (x + x + 20)

⇒ 400 = 2 (2x + 20)

⇒ 200 = 2x + 20

⇒ 2x = 200 - 20

⇒ 2x = 180

⇒ x = 90

Thus, The width of rectangle = x = 90 m

And, The length of rectangle = x + 20 = 90 + 20 = 110 m

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