Rationalize 5+2√3 / 7+4√3​

Given that the screw is a regular hexagon with side length 6 mm, the area of the screw is 93.5 mm^2

The area of an hexagon can be found using the following equation;

[tex]A = \mathbf{ \frac{3 \cdot \sqrt{3} }{2} \times {a}^{2}} [/tex]

Where a = The side length

However the side lengths are not equal, and the figure is a composite figure with two triangles and one rectangle;

Base length of the triangles = 12

Height of the triangles = 3

Area of each triangle = 0.5 × 12 × 3 = 18

Width of the rectangle = 12

Height of the rectangle = 6

Area of the rectangle = 12 × 6 = 72

Area of the screw = 18 + 18 + 72 = 108

However taking the screw as a regular hexagon, with side length a = 6, we have;

[tex]A = \frac{3 \cdot \sqrt{3} }{2} \times {6 \: mm}^{2} = 93.5 \: mm^2 [/tex]

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Answer:

488

Step-by-step explanation:

Calculate 20% of their take-home pay

3600 * 0.20 = 720

They already pay 122 and 110 per month

720 - (122 + 110)

720 - 232

488

So the largest monthly car payment they can afford is 488

The probability that the sample proportion will be less than 0.04 is 0.0188 or 1.88%.

The true proportion given to us (p) = 0.07.

The sample size is given to us (n) = 313.

The standard deviation can be calculated as (s) = √[{p(1 - p)}/n] = √[{0.07(1 - 0.07)}/313] = √{0.07*0.93/313} = √0.000207987 = 0.0144217.

The mean (μ) = p = 0.07.

Since np = 12.52 and n(1 - p) = 291.09 are both greater than 5, the sample is normally distributed.

We are asked the probability that the sample proportion will be less than 0.04.

Using normal distribution, this can be shown as:

P(X < 0.04),

= P(Z < {(0.04-0.07)/0.0144217}) {Using the formula Z = (x - μ)/s},

= P(Z < -2.0802)

= 0.0188 or 1.88% {From table}.

Thus, the probability that the sample proportion will be less than 0.04 is 0.0188 or 1.88%.

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The tabulated form of Two column proof attached below.

Two column proof is just tabulated form of statements and reason.

We are adding the key points to the table. As per the required questions

Thus the table formed by is attached below.

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Answer:

∠ACB = ∠DFE

Step-by-step explanation:

In SAS postulate,

S refers to Side.

A refers to Angle.

In the triangles, △ABC and △DEF,

AC = DF ( Side )

CB = FE ( Side )

The additional information required to prove is Angle.

Angle between sides AC and CB in △ABC and Angle between sides CB and FE in △DEF respectively.

Angle between sides AC and CB is ∠ACB.

Angle between sides CB and FE is ∠DFE.

So according to SAS postulate,

∠ACB = ∠DFE

Answer:

[tex]x=23, y=23\sqrt3[/tex]

Step-by-step explanation:

Since this triangle is half an equilateral triangle, x is half of 46 = 23

Use Pythagoras to solve y.

23^2 + y^2 = 46^2

[tex]y=23\sqrt3[/tex]

The two negative odd integers such that 5 times the first plus the square of the second equals -14 are: -3 and -1.

In a multiplication or division issue, an odd number of negatives will always result in a negative odd integer.

A negative odd integer carries a negative sign and is not exactly divisible by 2.

According to the question, an equation can be formed as follows:

[tex]5a+b^{2}=-14[/tex]

Here, a and b are the two negative odd integers.

Let a= -3 and b= -1,

[tex]5a+b^{2}=5(-3)+(-1)^{2}\\[/tex]

            = -15+1

            = -14

Thus, the required negative odd integers are -3 and -1.

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If Carol’s final grade is a 91, Carol's lowest test score was 82.

Given;

Average in 9 tests = 90

Average when the lowest score is removed = 91

The average or Mean is calculated as thus;

Average = [tex]\dfrac{\sum x}{n}[/tex]

Where the summation of x is the sum of test scores.

n = number of tests

n = 9 - 1 = 8 and average = 91

91 =  [tex]\dfrac{\sum x}{8}[/tex]

[tex]\sum x = 91 \times 8\\\\\sum x = 728[/tex]

Thus, Carol's test score in 8 subjects is 728

Let's consider the 9th subject represent the subject Carol had the least score.

n = 9

Average = 90

Average = 728 + the 9th subject

Multiply both sides by 9

90 x 9 = 728 + the 9th subject

810 = 728 + the 9th subject

Subtract 728 from both sides

810 - 728 = 728- 728 + the 9th subject

82 = the 9th subject

Hence, Carol's lowest test score was 82.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

10.1%

Step-by-step explanation:

Interest = PRT/100

Interest = 77136.06 - 70060 = 7076.06

Interest = PRT/100

7076.06 = [(70060) × R × 1] / 100

7076.06 = 70060R/100

Cross multiply

(7076.06 × 100) = 70060R

707606 = 70060R

R = 707606/70060

R = 10.1%

Answer:

[tex]sin\ x = \frac{15}{17}[/tex]

Step-by-step explanation:

So in this case, it's similar to the previous question you asked, except this time you know cosine, and as you may know cosine is defined as: [tex]\frac{adjacent}{hypotenuse}[/tex] and sine is defined as: [tex]\frac{opposite}{hypotenuse}[/tex]. So all we need to solve for is the opposite side, but since we know two sides, we can solve for the other using the Pythagorean identity: [tex]a^2+b^2=c^2[/tex]

Plug in known values:
[tex]8^2 + b^2 = 17^2[/tex]

Simplify:

[tex]64 + b^2 = 289\\b^2 = 225\\b = 15[/tex]

So the opposite side is 15, and the hypotenuse is already given, in this case it's 17 (the denominator of cosine). So plugging this into the definition of sin gives you: [tex]\frac{15}{17}[/tex]

Answer:

[tex] \frac{15}{17} [/tex]

Step-by-step explanation:

[tex] { \sin(x) }^{2} + { \cos(x) }^{2} = 1[/tex]

[tex] \cos(x) = 8 \div 17[/tex]

[tex] \sin(x) = \sqrt{1 - { \cos(x) }^{2} } [/tex]

[tex] \sin(x) = \sqrt{1 - {(8 \div 17)}^{2} } [/tex]

[tex] \sin(x) = 15 \div 17[/tex]

All the statements are true about the triangle except

1. a diagonal line extends from angle 8 to form angle.

According to the statement

There is a triangle has angles 6, 7, 8 and there are also some statements are given that matched with the triangle.

But the statement

1. a diagonal line extends from angle 8 to form angle.

is not true because it is not possible to extend a diagonal line from angle 8.

So, All the statements are true about the triangle except

1. a diagonal line extends from angle 8 to form angle.

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Answer:

15%

Step-by-step explanation:

$2325/$15500

Answer: 15

Step-by-step explanation: It’s given that the deductions reduce the original amount of taxes owed by $2,325.00. Since the deductions reduce the original amount of taxes owed by d%, the equation 2,32515,500=d100 can be used to find this percent decrease , d . Multiplying both sides of this equation by 100 yields 232,50015,500=d, or 15 = d. Thus, the tax deductions reduce the original amount of taxes owed by 15%.

The sum of the expression is 3g^8 - 4h - 48

Given that;

(3g^8 - 4h) + ( -6 × 8)

Expand the brackets,

3g^8 - 4h - 6 × 8

Multiply the values

3g^8 - 4h - 48

Therefore, the sum of the expression is 3g^8 - 4h - 48

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Considering the definition of an inequality, the inequality she could solve to find the number of surveys, s, she needs her customers to complete this week is 18(38)- 2.50s ≥ 750

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, Patty earns $18 an hour, plus an additional $2.50 each time one of her customers completes a company survey. This week, Patty plans to work 38 hours and she wants to earn at least $750.

Being "s" number of surveys Patty needs her customers to complete this week, the inequality that expresses the previous relationship is

18× 38 hours - 2.50×s ≥ 750 or, which is the same, 18(38)- 2.50s ≥ 750

Finally, the inequality she could solve to find the number of surveys, s, she needs her customers to complete this week is 18(38)- 2.50s ≥ 750

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By solving a system of equations, we will see that now there are 3.5kg of grapes on the basket.

Let's define the variables:

We know that:

x = 2y

When we add 2kg to the basket, it has 0.5k more than the box, then:

y + 2 = x + 0.5

Then we have a system of equations:

x = 2y

y + 2 = x + 0.5

We want to solve this for y, then we can replace the first equation into the second one:

y + 2 = (x = 2y) + 0.5

y + 2 = 2y + 0.5

2 - 0.5 = 2y - y

1.5 = y

This means that, originally, there are 1.5 kg of grapes on the basket. And then we added 2kg, so now there are:

1.5kg + 2kg = 3.5kg

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Answer:

There are now 3.5kg of grapes.

Part 1

By the inscribed angle theorem, arc GFJ measures 55 degrees.

Part 2

By the inscribed angle theorem, arc FH measures 72 degrees.

Answer:

$7.76

Step-by-step explanation:

So you can express the price in the slope-intercept form: y=mx+b where m is the slope, but in this context it's the price per km,  and b is the y-intercept, but in this context it's the base price (how much it costs even if the length is 0 km)

So it gives you the slope of $0.22 per km. so you now have the equation

y = 0.22x + b

To find the base amount or y-intercept, you can take some of the given points, the price will be y, and the length will be x.

I'll use the point (6, 4.68)

Plugging these values into the equation you get:

4.68 = 0.22(6) + b

multiply

[tex]4.68 = 1.32 + b[/tex]

subtract 1.32 from both sides

[tex]3.36 = b[/tex]

So now we have the full equation:

y = 0.22x + 3.36

Now to find the price if the length is 20km, simply plug in 20 as x

y = 0.22(20) + 3.36

Multiply

y = 4.4 + 3.36

Add

y=7.76

40(1.25-t) is missing from the table

Time, speed, and distance are the three factors must be taken into account.

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed X Time

We provide both time and speed.

It is necessary to compute the distance.

55 miles per hour is the commuter speed

Worktime equals 1.25-T

Home-bound speed is 40 miles per hour.

1.25 seconds to get home

Time in Total = T + t = 1.25

Travel distance to home

Distance/Time x Speed

40 = Total Distance/t

Distance overall = 40 (1.25-t)

As a result, 40(1.25-t) is the right response.

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Answer:

A

Step-by-step explanation:

75% of the air pressure at sea level is simply

0.75 × Po

this is what we need to set as the expected result of the function, and it becomes the left side of the equation.

we don't change anything on the right side for this, as the full, unchanged function has to be used to find the h for the desired result.

The length of A"B" is 20 units

From the figure, we have:

A = (1, 4)

B = (4, 8)

The distance AB is:

[tex]AB = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]AB = \sqrt{(1 -4)^2 + (4-8)^2[/tex]

Evaluate

[tex]AB = \sqrt{25[/tex]

This gives

AB = 5

The scale factor of dilation is 4.

So, we have:

A'B' = 5 * 4

Evaluate

A'B' = 20

Hence, the length of A"B" is 20 units

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Answer:

For plan B to save money cell phone user need to send 6000 texts per month as [tex]$\frac{x}{y}$[/tex] expresses the average texts sent per month by cell phone user and its obtained value is 6000.

Step-by-step explanation:

In the question it is given that a cell phone company offers two plans for minutes.

Plan A: $15 per month and $2 for every 300 texts.

Plan B: $25 per month and $0.50 for every 100 texts.

It is required to find that how many texts would be needed to send per month for plan B to save money. be needed to send per month for plan B to save money.

Step 1 of 6

In Plan A $15 per month and $2 for every 300 texts are costed so the cost of Plan [tex]$\mathrm{A}$[/tex] is given by following equation,

[tex]$A=15 y+\frac{2 x}{300}$[/tex]

In Plan B [tex]$\$ 25$[/tex] per month and [tex]$\$ 0 \cdot 50$[/tex]for every 100 texts are costed so the cost of Plan B is given by following equation,

[tex]$B=25 y+\frac{0 \cdot 50 x}{100}$[/tex]

Step 2 of 6

Now comparing the obtained equations [tex]$A=15 y+\frac{2 x}{300}$[/tex]

and [tex]$B=25 y+\frac{0 \cdot 50 x}{100}$[/tex]

[tex]$15 y+\frac{2 x}{300}=25 y+\frac{0 \cdot 50 x}{100}$[/tex]

Step 3 of 6

Subtract $15 y$ from both the sides of the obtained equation [tex]$15 y+\frac{2 x}{300}=25 y+\frac{0 \cdot 50 x}{100}$[/tex] and simplify using subtraction properties.

[tex]$$\begin{aligned}&15 y+\frac{2 x}{300}-15 y=25 y-15 y+\frac{0.50 x}{100} \\&\frac{2 x}{300}=10 y+\frac{1 x}{200}\end{aligned}$$[/tex]

Step 4 of 6

Subtract [tex]$\frac{x}{200}$[/tex] from both the sides of the obtained equation [tex]$\frac{2 x}{300}=10 y+\frac{1 x}{200}$[/tex] and simplify using subtraction properties.

[tex]$$\begin{aligned}&\frac{2 x}{300}-\frac{x}{200}=10 y+\frac{1 x}{200}-\frac{x}{200} \\&\frac{x}{600}=10 y\end{aligned}$$[/tex]

Step 5 of 6

Multiply both the sides of the obtained equation [tex]$\frac{x}{600}=10 y$[/tex] by 600 and simplify using multiplication properties.

[tex]$$\begin{aligned}&\frac{x}{600} .600=10 y .600 \\&x=6000 y\end{aligned}$$[/tex]

Step 6 of 6

Divide both the sides of the obtained equation x=6000 by y and simplify using division properties. As [tex]\frac{x}{y}[/tex] expresses the average texts sent per month by cell phone user. So, for plan B to save money cell phone user need to send 6000 texts per month.

[tex]$$\begin{aligned}&\frac{x}{y}=\frac{6000 y}{y} \\&\frac{x}{y}=6000\end{aligned}$$[/tex]

The rigid transformations that maps ΔABC onto ΔFED by reflection then translation.

The correct option is (B).

Reflection is a from of transformation whereby a figure is flipped over a line of reflection, making both figures exactly the same shape and size after the transformation.

given:

ΔABC ≅ ΔFED are congruent by the SSS Congruence Theorem.

Hence, the rigid transformations that maps ΔABC onto ΔFED by reflection then translation.

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Answer:

B

Step-by-step explanation:

Trust me bro

Answer:

Step-by-step explanation:

[tex]6(y -9) = 3y-36...the \: given \: expression \\ 6y - 54 = 3y - 36...apply \: the \: distributive \: law \: a(b - c) = ab - ac \\ 6y - 54 + 54 = 3y - 36 + 54...add \: both \: sides \: 54 \\ 6y = 3y + 18 \\6y - 3y = 3y + 18 - 3y...subtract \: 3y \: from \: both \: sides \\ 3y = 18 \\ \frac{3y}{3} = \frac{18}{3} ...divide \: both \: sides \: by \: 3 \\ y = 6...simplified[/tex]

Answer:

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

Step-by-step explanation:

Given Equation of line: y=mx+c,

where m = slope of line.

So, we will have to make y the subject to find the slope.

[tex]2x-3y=19\\2x-3y-2x=19-2x\\-3y=-2x+19\\y=\frac{-2x+19}{-3} \\y=\frac{2}{3} x-\frac{19}{3}[/tex]

From here, we can see the slope of the line is [tex]\frac{2}{3}[/tex].

Answer: 2/3

Step-by-step explanation:

2x-3y=19

minus 2x from both sides

-3y=-2x+19

divide both sides by -3

y=2/3x-19/3

slope is 2/3

Answer:

There are 3 red marbles.

Step-by-step explanation:

The ratio of red marbles to blue marbles is 3:2, so for every two blue marbles there are three red marbles. This means that there are three red marbles for every four marbles in the bag. Therefore, if there are five marbles in the bag, there must be three red marbles and two blue marbles.

The horizontally compress the exponential function f(x)=2^x by a factor of 3 is f(3x)=2^3x

When we compress a function y=f(x) by a scale factor of 'k', where k >1, then the function after compression will become :

y=f(x), where k>1

We have given the Exponential function.

The scale factor is a measure for similar figures, that look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.

The scale factor of the compression (k): 5

Then after horizontal compression, the exponential function will become

f(3x)=2^3x

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Answer:

(-2,-8)

(-1,-1)

(0,0)

(1,1)

(2,8)

Step-by-step explanation:

y = x^3

y = -2^3

= -8

y = -1^3

= -1

y = 0^3

= 0

y = 1^3

= 1

y = 2^3

=  8