justification three common tangents

The area of ​​the inner square to the area of ​​the outer square ratio is:  [tex]\frac{(a-b)^2+b^2}{a^2}[/tex]

Given a figure in which an inner square is inscribed inside the outer square.

The area of ​​a square is the product of the two sides of the square. Also known as side square.

Firstly, we will find the side of the inner square by finding the distance between the points (0,b) and (a-b,0)

S₁=√(a-b-0)²+(b-0)²

S₁=√(a-b)²+b²

Now, we will find the area of the inner square, we get

The area of the inner square=(side)²

A₁=(S₁)²

A₁=(√(a-b)²+b²)²

A₁=(a-b)²+b²square cm.

Further, we will find the side of the outer square by finding the distance between the points (0,0) and (a,0).

S₂=√(a-0)²+0²

S₂=√a²

S₂=a

Furthermore, we will find the area of the outer square, we get

The area of the outer square=(side)²

A₂=(S₂)²

A₂=a² square cm.

Hence, the area of the inner square to the area of the outer square ratio is [tex]\frac{(a-b)^2+b^2}{a^2}[/tex].

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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:

Step-by-step explanation:

What is 3*(4x-2x)*5+3*2 simplified?

3*(4x-2x)*5+3*2=

3*2x*5+6 =

6x*5+6=

30x+6

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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Hello,

Answer:

12⁰ = 1

Step-by-step explanation:

We have any number with exponent 0 = 1  

(a⁰) = 1

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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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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Answer:

1. y + 12 = x^2 + x

2. y - 17 = x^2 -9x

3. y + 5 = x^2 - 3x

4. y - 15 = -x^2 + 4x

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%

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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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.

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]

The value of U and V will be (x – 3) and 8y, respectively. Then the correct option is A.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The expression is given below.

⇒ (U + V)(U – V)

Where U and V are either constant or single variable expression.

Then the expression will be

⇒ U² – V²

Then the value of U and V will be (x – 3) and 8y, respectively.

Then the correct option is A.

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Answer:

88.08 m tall

Step-by-step explanation:

Pole:

tall/long
3/1.72

Building:

tall/long

x/50.5

Solve for x:

3/1.72 = x/50.5

1.72x = 151.5

x ≈ 88.08

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:

(-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

Answer:

128 3 digit number which are divisible by 7

Answer:

128

Step-by-step explanation:

I just looked it up because the only way I know would take a lot of time.

Know the times table?

You can make a chart that starts from 100 to 999 and circle every single number you know can be divided by 7. That's 128 numbers.

I hope the answer helps, but I hope someone can actually find a formula or something for you to use. Best of luck.

The value of x and y in the rhombus are 5 and 25 respectively.

The sum of angles of a rhombus is 360 degrees. The opposite angles of a rhombus is equal.

Therefore,

11x = 55

x = 55 / 11

x = 5

Therefore,

5y + 5y + 55 + 55 = 360

10y + 110 = 360

10y = 360 - 110

10y = 250

y = 250 / 10

y = 25

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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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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:

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.

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 distance can be expressed in equation d=5.3*[tex]10^{-4}m[/tex].

Given voltage of 96.6 V and electric field strength of 1.8 KV/cm.

We know that d=V/E

We have to find the distance in equation form.

We know that  electric field strength between the plates of a parallel plate capacitor is

E=V/d

Distance is the measurement between two sides or points.

where E=electric field strength

V=potential difference

d=distance between the plates

In equation form distance looks like:

d=V/E

from the question we are that V=96.6 V

E=1.8KV/cm.

Converting to V/m

E=180000V/m

d=96.6/180000

=0.00053

d=5.3*[tex]10^{-4}m[/tex].

Hence the distance can be expressed as d=[tex]5.3*10^{-4} m[/tex].

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Answer:

Step-by-step explanation:

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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Answer:

x=70, y=40, z=70

Step-by-step explanation:

So whenever you have a straight line, the angle is going to be 180 degrees, and whenever you have multiple angles that make up one angle, the sum of the multiples angles is going to be the angle of the one angle.

So let's look at x. The 180 degree angle consists of 110 degrees and x, the sum of these two should add up to 180 degrees, you can set up an algebraic equation to solve for x, but you can also do some simple mental math to see that x=70, so that 110+70=180. You do the same thing for the other angles

For y, you simply need to know 140+y = 180 so y=40

For z there is two methods, you can use the fact that opposite angles are congruent, or you can use the fact that the sum of the interior angles of a triangle is 180 degrees. This means that x+y+z=180 and since we know that x=70 and y=40 then 70+40=z so 110+z=180 so z=70, which is also the same as the opposite angle, you could use either method although knowing that opposite angles are congruent is much more easier. It's called the vertical angles theorem.

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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Answer:

1) x=1; x= 0 is an extraneous solution

Step-by-step explanation:

5 = 4x + 1

5 = 4 x 1 + 1

5 = 5

x = 1

______________________

x x^2

0 x 0^2

0 x 0 = 0

x = 0

:)