T (6,2) T’ (9,3 find the scale factor was used in the dilation shown

The angle of CAE is 22

A line known as a perpendicular bisector cuts a specified line segment precisely in half, creating a 90° angle at the junction. The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler. On both sides of the line segment being divided, it forms a 90° angle.

Perpendicular bisector of ABC's side AB crosses BC at point E and side AB at point D. Additionally, m CAB = 82 and m C = 68.

Adopt A E.

In ABC, the triangle's angle sum property is A+B+C=180°.

82°+∠B+68°=180°

∠B= 180°-150°

∠B=30°

AD=B DDE is a perpendicular bisector in A DE and B DE.

If ADE=BDE=90°

DE is common.

Δ A DE ≅ Δ E DB→→[S AS]

∠DEB=∠D A E→→[CPCT]----(1)

In Δ DBE

∠EDB + ∠DBE+∠BED=180°→→Angle sum property of Triangle.

90° +30°+∠BED=180°

∠BED=180°-120°

∠BED=60°

So, ∠BAE=∠BED=60°------[using (1)]

∠CAE=∠CAB - ∠BAE

= 82°-60°

= 22°

Therefore the angle CAE is 22

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The half-life of radon-222 is 3 days, it will take an additional 3 days for the remaining 42% of the sample to decay, for a total of 6 days for the sample to decay completely.

The half-life of a radioactive is time for 50% of its particles to decay or disintegrate into a new element. The pace at which a radioactive material will decay is predicted using this indicator of an isotope's stability. An element's half-life, which differs substantially across various elements, is based on the unique characteristics of its nucleus.

For instance, the half-life of uranium-238 is 4.5 billion years whereas that of carbon-14 is 5,730 years. This indicates that half of the carbon-14 atoms in a sample will have decayed after 5,730 years, and half of the uranium-238 atoms will have decayed after 4.5 billion years.

How to solve?

(a) After 3 days, the sample has decayed to 58% of its original amount, which means that half of the original amount has already decayed. Therefore, the half-life of radon-222 is 3 days.

(b) Since the half-life of radon-222 is 3 days, it will take an additional 3 days for the remaining 42% of the sample to decay, for a total of 6 days for the sample to decay completely.

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The inverse of the function f(x) = 4(x - 3) is f⁻¹(x)=(x+12)/4.

A function that "undoes" another function is known as an inverse in mathematics. In other words, if f(x) generates y, then y entered into f's inverse creates x. x . Invertible refers to a function that has an inverse, which is represented by the symbol f1.

Inverse functions are functions that "reverse" one another in the broadest sense. If f, for instance, goes from a to b, then its inverse, f 1 f -1 f 1f, start superscript, minus 1, end superscript, must go from b to a.

Make f a function. Any horizontal line that crosses the f graph more than once indicates that f lacks an inverse. F has an inverse if there are no horizontal lines that cross the graph of f more than once.

Let f(x)=y

f(x)=4(x-3)

f(x)=y

y=4(x-3)

x=4(y-3)

x=4y-12

4y=x+12

y=(x+12)/4

Therefore, f⁻¹(x)=(x+12)/4

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Answer:

-133.16472

Step-by-step explanation:

N/A

Answer:

-133.16472

Step-by-step explanation:

The factorization given is not a prime factorization.

Given that,
A factorization of a number is given we have to discuss whether the factors are prime factors or not.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

here,
Given factorization = 2² + 3 + 5⁴ + 8 + 11².
Since the above 8 cannot be taken in prime factor,
So the given factorization is not the prime factorization of the number.

Thus, the factorization given is not a prime factorization.

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Given that x is in quadrant 3, its value for tan x=1/2 will be 206.565°, and its value for cos(206.565°) will be -0.894.

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry. The sine, cosine, and tangent are the three fundamental trigonometric operations. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical concepts are built.

Here,

Tan x=1/2

π<x<3π/2

x=tan⁻¹/²(1/2)

x=26.565°

As the x is in quadrant 3,

=180+26.565°

=206.565°

cos(206.565°)=-0.894

The value of x for tan x=1/2 will be 206.565° as x is in quadrant 3 and for the same value of x, cos(206.565°) will be -0.894.

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Answer:

-sqrt 5 - 2 sqrt 5/10

Step-by-step explanation:

Edge 2023

The value of k will be equal to 4/3 and there will be two real and different roots.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given that the equation is k + 4/x +3/x² =0. The value of k will be calculated as,

k + 4/x +3/x² =0.

kx² + 4x + 3 = 0

b² - 4ac =0

4² = 4 x k x 3

16 = 12k

k = 4/3

Therefore, the value of k will be equal to 4/3 and there will be two real and different roots.

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Answer:

[tex](4 , -5)[/tex]

Step-by-step explanation:

Note that when you move left or right any amount of units, you will be making the changes to the x-variable. If you move up or down any amount of units, you will be making the changes to the y-variable.

In this case, it is given that:

(x , y) = (-3 , -5)

You will want to move right 7 units, as you are trying to find your starting position. Add 7 from the x variable:

[tex](x , y) = (-3 , -5) = (-3 (+7) , -5)\\\\= (-3 (+7) , -5)\\= ((-3 +7) , -5)\\= (4 , -5)[/tex]

[tex](4 , -5)[/tex] is your starting position.

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Answer:

60%

Step-by-step explanation:

Shaun won 60% percent of the games.

Answer:

Shaun won 60% out of the 10 video games he played.

Step-by-step explanation:

If Shaun played 10 video games and only won six out of all of them, he won 60% since we can count 10 as 100% and 6 as 60%.

Answer:56.6%

Step-by-step explanation:

30 - 13 = 17

17 /30 x 100 = 56.6 %

The expected value of these outcomes are  $262.5, $496 and $648 respectively

You should know that the expected value are the proportion of the values when valued with the percentages

The given values are $210, $320 and $540

The given percentages are 25%, 55% and 20%

The expected values are

0.25*210 = $52.5+210=$262.5

0.55*320=176+320=$496

0.20*540=108+540=$648

Therefore the projected values of the project are  $262.5, $496 and $648 respectively

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The cost of each DVD as per the given data will be 20.08  without tax.  and 21.35 with sales tax.

Cost of DVD,

with sales tax

(40.15 + 2.55) / 2

= 42.70/2

= 21.35 per DVD

without sales tax

40.15 / 2

= 20.08 per DVD

Sales taxes are a type of tax that is paid to a governing body when goods and services are sold. Sales tax is an indirect tax that is often assessed at the time that certain taxable products are purchased or exchanged. It is assessed as a percentage of the item's retail price.

The government in power and the specific rules it enforces determine the sales tax, which is typically easy to calculate and collect. The sales tax can be thought of simply as an additional sum of money paid while buying products or services.

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Cutting perfect slices of pie can be tricky. Crusts can crumble, bottoms can buckle and fillings can spill over, but there are a lot of tricks for a good slice.

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Answer:

EP = GP

GP = HP

angle EFH = 45

Think these 3 are the right answers, hope it helps.

The bus is covering a distance of 42 miles in 1 hour 30 minutes then the speed of the bus will be 28 mph.

The overall distance the object covers in a given amount of time is its average speed. The scalar quantity represents the average speed. It does not have direction; it is represented by magnitude.

As per the given data provided in the question,

Total distance traveled by bus = 42 miles

Total time is taken by the bus = 1 hour 30 minutes = 1.5 hours.

Then the average speed of the bus will be,

[tex]Average\ Speed(S) = Total\ Distance/Total\ Time[/tex]

S = 42/1.5

S = 28 mph.

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Answer:

53 degrees

Step-by-step explanation:

This is a transversal question (look at attached). Because the lines are parallel, g will equal to 180(a straight line is 180 degrees) - a. Then, because g + f + e = 180 (since it is a straight line), substitute the values that we know and solve. (61) + f +(66) = 180. f = 53

Answer:

Step-by-step explanation:

$38, 20% off = $30.40

$30.40, 10% off = $27.36

$27.36 is the final price of the shirt

Answer:

Below

Step-by-step explanation:

Sum of interior angles for the uppr right triangle = 180

52 + 90 + '2' = 180

'2' =38°

American adults believes in alien for the  given 95% confidence interval and sample surveyed is in the interval range of ( 0.66 , 0.78 ).

As given in the question,

Sample of American adults surveyed 'n' = 200

Percent of people believes in aliens are success  'p'= 72%

                                                                                      = 0.72

Percent of people who don't believes (failure) in aliens ' 1 - p'  = 1 - 0.72

                                                                                          = 0.28                                                                                    

95% Confidence interval that represents Americans adults who believes in aliens

value of z - score for 95% confidence interval = ± 1.96

Margin of error 'MOE'= (z-score)√p ( 1- p) /n

                                   = ( 1.96)√(0.72 × ( 1 - 0.72 )/ 200

                                   = 1.96 ( √0.2016 / 200)

                                   = 1.96 ×√0.001008

                                   = 0.063

Lower limit = p - MOE

                 = 0.72 - 0.063

                 = 0.66

Upper limit =  p + Margin of error

                 = 0.72 + 0.063

                 = 0.78

Therefore, 95% confidence interval with sample size of the Americans adults who believes in alien are in the interval of ( 0.66 , 0.78 ).

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The equation of line s is y + 7 = -7/6(x - 7).

What is slope of a line?

A line's steepness and direction are measured by the line's slope. A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates,  Δy, Δx respectively. Consequently, it is possible to write the change in y coordinate with respect to the change in x coordinate as m = Δy/Δx

Given equation of line r is y = 6/7x+1.

The slope of line r is m = 6/7

The slope of the line that is perpendicular to line r is -1/m = - 7/6.

The equation of line that passes through the point (x₁, y₁) with slope m is y - y₁ = m(x - x₁).

Putting m = - 7/6, x₁ = 7 and y₁ = -7 in y - y₁ = m(x - x₁):

y - (-7) = - 7/6(x - 7)

y + 7 = - 7/6(x - 7)

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If the pond now contains 320 gallons of water, number of weeks it has been since the pond was at full capacity is 5 week.

Given that, a full pond containing 625 gallons of water begins losing its water at a rate of 20% per week.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here, number of gallons water being used for x weeks is

625-320=305 gallons

Now, number of gallons of water used in a week= 20% of 305

= 20/100 ×305

= 0.2 ×305

= 61 gallons

So, number of weeks = x=305/61

= 5

Therefore, if the pond now contains 320 gallons of water, number of weeks it has been since the pond was at full capacity is 5 week.

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Answer:

5

Step-by-step explanation:

Look that guys answer is better

The fraction is 7/9 according to given information.

What is fraction?

A fraction, which derives from the Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal parts. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when spoken of in everyday English. A common, vulgar, as well as simple fraction is one that has a non-zero denominator displayed below (or after) the line that separates the numerator from the denominator. Compound fractions, complex fractions, as well as mixed numeral fractions are examples of uncommon fractions that use numerators and denominators.

Main Body:
Let the fraction be a/b
In First condition
b = a + 2(1)
In Second condition
a + 1/b + 1 = 4/5
5(a + 1) = 4(b + 1)
5a + 5 = 4b + 4
5a - 4b = 4 - 5
5a - 4b = -1
Using 1
5a - 4(a + 2) = -1
5a - 4a - 8 = -1
a = 8 - 1
a = 7
Now,
Using 1
b = a + 2
b = 7 + 2
b = 9
Fraction = a/b = 7/9
hence , the fraction is 7/9.

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Answer:

a and f are 14°

Angles b, c, d, and e are all 166°

Step-by-step explanation:

Alternate interior angles are congruent

x + 9 = 4x - 6  Subtract x from both sides

9 = 3x - 6    Add 6 to both sides

15 = 3x  Divide both sides by 3

5 = x

Plug this back into the equation for find the angles measurements

x + 9

5 + 9

14

or

4x _ 6

4(5) -6

20 - 6

14

angles a and f are vertical angles so they are congruent and equal to 14

B ,c , d and e are all supplements to the found angles

180-14 = 166

An equation of line having slope 1/6 and passes through the point (0,-3) is y = 1/6x - 3

We know that the slope-point form of line is:

(y - y1) = m(x - x1)

Here, we need to find an equation of line having slope 1/6 and passes pae through the point (0,-3)

let (x1, y1) = (0, -3)

and m = 1/6

substitute values in above formula,

(y - (-3)) = 1/6 (x - 0)

y + 3 = 1/6 (x)

y = 1/6x - 3

which is slope-intercept form of line (y = mx + b)

Therefore, equation of line is y = 1/6x - 3

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Answer:

4

Step-by-step explanation:

First we need to get some definitions out of the way

Definition of a turning point

Definition of degree of polynomial

Answer:

14

Step-by-step explanation:

To find g(f(3)), you will need to first find f(3) and then substitute that value into the function g(x).

To find f(3), substitute 3 for x in the equation for f(x):

f(3) = 3(3) - 2 = 9 - 2 = 7

Now substitute the value of f(3) into the equation for g(x):

g(f(3)) = g(7) = 2(7) = 14

Therefore, g(f(3)) = 14

Answer:

f(3)=7  g(3)=6

Step-by-step explanation:

f(x)=3x-2

f(3)=3(3)-2

f(3)=9-2

f(3)=7

g(x)=2x

g(3)=2(3)

g(3)=6

Answer:

4.

y = -1/6 * x - 7/3

Step-by-step explanation:

We can just check:

1.

y =  -1/6 * x

this doesn't work for x = -2 and y = -2 (first point) because we get

-2 = -1/6 * -2 = 1/3

this is nonsense

2.

y = -6x - 3/7

this doesn't work for x = -2 and y = -2 (first point) because we get

-2 = -6 * -2 - 3/7 = 12 - 3/7 = 11 + 4/7

this is nonsense

3.

y = -6x

this doesn't work for x = -2 and y = -2 (first point) because we get

-2 = -6 * -2 = 12

this is nonsense

4.

y = -1/6 * x - 7/3

this works for x = -2 and y = -2 because

-2 = -1/6 * -2 - 7/3 = 2/6 - 7/3 = 1/3 - 7/3 = -6/3 = -2

it also works for x = 4 and y = -3 because

-3 = -1/6 * 4 - 7/3 = -4/6 - 7/3 = -2/3 - 7/3 = -9/3 = -3