(2x-5y)+(6y+5x²)=15y​

The parent function by reversing rigid transformations are, respectively:

Case 6: f(x) = x³

Case 7: f(x) = √x

Case 8: f(x) = ㏒ x

Case 9: f(x) = |x|

Case 10: f(x) = x²

Parent functions are the most simple form of a kind of expression (i.e. power, exponential, logarithms, roots). In this problem we find five cases of images of parent functions, that is, versions modified by rigid transformations. The most common rigid transformations are, respectively:

Horizontal translation

f(x) → f(x - k)

Vertical translation

f(x) → f(x) + k

Reflection about x-axis

f(x) → - f(x)

Reflection about y-axis

f(x) → f(- x)

Vertical dilation

f(x) → k · f(x)

Horizontal dilation

f(x) → f(k · x)

Now we proceed to revert the rigid transformations used in each function:

Case 6

f(x) = 2 · (x + 6)³ + 11

Vertical translation - Horizontal translation - Vertical dilation

f(x) = x³

Case 7

f(x) = 7 + (1 / 2) · √(x - 3)

Vertical translation - Horizontal translation - Vertical dilation

f(x) = √x

Case 8

f(x) = 5 - ㏒ (x + 1)

Vertical translation - Reflection about x-axis - Horizontal translation

f(x) = ㏒ x

Case 9

f(x) = - 3 · |x + 10| + 7

Vertical translation - Reflection about x-axis - Dilation - Horizontal translation

f(x) = |x|

Case 10

f(x) = (3 / 5) · (x - 8)² - 4

Vertical translation - Dilation - Horizontal translation

f(x) = x²

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The largest prime number that divides the given expression is 229.

We can factorize the given expression as follows:

[tex]$0! \times 1 \times 1! \times 2 \times 2! \times 3 \times 3! \times \cdots \times 50! \times 50$[/tex]

Now, we can cancel out all the factorials from both sides, leaving us with:

[tex]$1 \times 1 \times 2 \times 2 \times 3 \times 3 \times \cdots \times 50 \times 50$.[/tex]

The largest prime factor of any composite number is the largest prime factor of its prime factorization. By the fundamental theorem of arithmetic, we know that the prime factorization of any composite number is unique.

The prime factorization of a number can be found by dividing the number by prime numbers and keeping dividing the quotient by prime numbers until the quotient is prime.

Now, we can start dividing the given number (the product of all numbers from 1 to 50) by the smallest prime number, 2, and keep dividing the quotient by the next prime number until the quotient is prime.

The largest prime factor of the given expression is the largest prime factor of the final quotient.

The final quotient is

[tex]2^{24} \times 3^{12} \times 5^9 \times 7^7 \times 11^5 \times 13^4 \times 17^3 \times 19^3 \times 23^2 \times 29^2 \times 31^2 \times 37^2 \times 41^2 \times 43^2 \times 47^2 \times 53^2 \times 59^2 \times 61^2 \times 67^2 \times 71^2 \times 73^2 \times 79^2 \times 83^2 \times 89^2 \times 97^2 \times 101^2 \times 103^2 \times 107^2 \times 109^2 \times 113^2 \times 127^2 \times 131^2 \times 137^2 \times 139^2 \times 149^2 \times 151^2 \times 157^2[/tex]

[tex]\times 163^2 \times 167^2 \times 173^2 \times 179^2 \times 181^2 \times 191^2 \times 193^2 \times 197^2 \times 199^2 \times 211^2 \times 223^2 \times 227^2 \times 229^2$[/tex]

The largest prime factor of the final quotient is the largest prime factor of the prime factorization, which is 229.

So the largest prime number that divides the given expression is 229.

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Answer:

x = 6

Step-by-step explanation:

[tex]\frac{8}{12}[/tex] = [tex]\frac{x}{9}[/tex] ( cross- multiply )

12x = 72 ( divide both sides by 12 )

x = 6

The coordinates of the final image are

A'' (3, 2)

B'' (0, 2)

C'' (2, 3)

The coordinates of the preimage are A(2,3), B(2,0), and C(3,2)

The transformation rule for a 90 degrees clockwise rotation is

(x, y) → (y,-x)

hence we have

A(2,3), → (3,-2)

B(2,0) → (0,-2)

C(3,2) → (2,-3)

The transformation rule for reflection in the y axis is

(x, y) → (x,-y)

hence we have

A'(3,-2) → (3, 2)

B'(0,-2) → (0, 2)

C'(2,-3) → (2, 3)

The image is plotted and attached

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According to exponent rules, when we multiply terms with the same base add the exponents. Hence, the correct answer is option D.

Exponent rules are a set of rules that dictate how exponents (numbers written as a superscript) can be manipulated in mathematical operations. Some of the most commonly used exponent rules include:

        For example, [tex]x^4 * x^5 = x^{4+5} = x^9[/tex]

       For example, [tex]x^7 / x^3 = x^{7-3} = x^4[/tex]

        For example,[tex](x^3)^5 = x^{3*5} = x^{15}[/tex]

        For example,[tex](xy)^3 = x^3 * y^3[/tex]

       For example,[tex](x/y)^3 = x^3 / y^3[/tex]

According to the product of the power rule, we get that we add the exponents when we multiply terms with the same base.

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Answer:   255

Step-by-step explanation:

Try thinking backwards first; 51*(0.20)=10.2, or 10.2 is 20% of 52

To find 20% of the unknown number, just divide 51 by 0.20

51/0.20=255

Whatever the answer is, you know it has to be larger than the original number.

a. The angular velocity of the ball is 1.57rad/sec

b. The angular acceleration of the bicycle is 0.23 rad/sec²

angular is the rate of change of angular distance . it is measured in rad/sec. it is represented by w. Angular acceleration is the rate of change in angular velocity with time.

angular velocity = change in angle/ time

w = 2π/t

w = 2× 3.14/4

w = 6.28/4

w = 1.57 rad/sec

angular acceleration =( final angular velocity - initial angular velocity )/time

= (4.2 - 3.5)/3

= 0.7/3

= 0.23 rad/s²

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Plan 2 can be used to save $500 in less than 16 weeks and have $20 extra.

The number of weeks and y, which is the equation we wish to utilise, stand in for the total amount saved. Our equation will then be 15 x. Instead of the other way around, he will save 330.

Plan  Amount saved per week Total amount saved in 16 weeks

1      $31.25                                         $500

2      $35                                             $560 (with $60 extra)

3      $40                                              $640 (with $140 extra)

Plan 2 can be used to save $500 in less than 16 weeks and have $20 extra.

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Check the picture below.

Yes, each of the four sections for books is a rectangle because all four sides of the section are straight lines and the opposite sides are the same length.

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Answer:

False. This may be true with a trapezoid but not with a square or rectangle, seeing they have 2.

Step-by-step explanation:

Hope it helps! =D

The verification of the given trig identity is shown in below.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²

Now, We can simplify as;

⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²

LHS;

⇒ (1 - sin x) / (1 + sin x)

⇒ (1 - sin x) (1 - sin x) / (1 + sin x) (1 - sin x)

⇒ (1 - sin x)² / (1 - sin²x)

⇒ (1 - sin x)² / cos²x

⇒ ( (1 - sin x )/ cos x )²

RHS;

⇒ (sec x - tan x)²

⇒ ( 1/cos x - sin x / cos x)²

⇒ ( (1 - sin x) / cos x )²

Hence, We get;

⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²

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Answer: 2) x=60

Step-by-step explanation:

Applying proportion, 2520 ounces of solution Z will contain 44040 ounces of ingredient a.

To determine the number of ounces of ingredient a in 2520 ounces of solution Z, we need to first calculate the proportion of ingredient a in solutions X and Y, and then use that information to determine the proportion of ingredient a in solution Z.

Solution X contains 2 ounces of ingredient a and 3 ounces of ingredient b in one ounce of solution, so the proportion of ingredient a is 2/(2+3) = 2/5.

Solution Y contains 1 ounce of ingredient a and 2 ounces of ingredient b in one ounce of solution, so the proportion of ingredient a is 1/(1+2) = 1/3.

Solution Z is created by mixing solutions X and Y in a ratio of 3:11, so 3 ounces of solution X are mixed with 11 ounces of solution Y.

Thus, the proportion of ingredient a in solution Z = (32/5) + (111/3) = 6/5 + 11/3.

To find out the number of ounces of ingredient a in 2520 ounces of solution Z, we need to multiply the proportion of ingredient a with the number of ounces of solution Z

2520 * (6/5 + 11/3) = 2520 * (6/5 + 11/3) = 2520 * (252/15 + 11/3) = 2520 * (16+11/3) = 2520 * (16+11/3) = 2520 * (16+11/3) = 2520 * (16+37/3) = 2520 * (16+37/3) = 2520 * (53/3) = 252053/3 = 252017.66666 = 44040 ounces of ingredient a.

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Answer: 16

Step-by-step explanation:

You need to divide 12 by 3/4

To do this you turn 12 into a fraction by making it 12/1

Then you do Keep Change Flip

Keep 12/1

Change the division into multiplication

Flip 3/4 into 4/3

Then you do 12/1 × 4/3 which is 48/3

Finally you simplify 48/3 into 16

A whopping 95% of people fall within the IQ ranges of 70 and 130. 99.7% of people in the world have IQs between 55 and 145. Only about 0.3% of people have IQ scores that fall outside of this range (less than 55 or higher than 145).

According to the one-standard-deviation rule, 32 percent of the population has an IQ score that is at least 15 points off from 100: 16 percent have IQs over 115, and 16 percent have IQs below 85.

The equation IQ=mc100, where m is the mental age and c is the chromological age, determines a person's IQ. Find the range of their mental ages if a group of 12-year-old youngsters has an IQ between 80 and 140.

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If the  height of the football could be described by the model: f(x) = -16x² + 64x , then the time at which the ball at its highest point after being kicked is t = 2 seconds .

In order to find time at which ball is at its highest point,

we have to find the time at which the derivative of height function is = 0.

the height function is ⇒ f(x) = -16x² + 64x ;

So , the derivative of the height function will be :

⇒  f'(x) = -32x + 64 ;

equating the derivative of height function to 0 , and solving for x ,

we get ;

⇒ -32x + 64 = 0

⇒ -32x = -64

⇒ x = 2

Therefore , the time at which the ball is at its highest point is 2 seconds .

The given question is incomplete , the complete question is

Justin punts a football. The height of the football could be described by the model: f(x) = -16x² + 64x. h describes the height of the ball in feet and the time in seconds after the ball was kicked.

At what time in seconds is the ball at its highest point after being kicked ?

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Answer:

1: 0.15x = 0.15x * x = discount (percentage) * original price = discount

2: x - 0.15x = x (1 - 0.15) = original price - discount

3: 0.15 x 15.99 = 2.39

15.99 - 2.39= 13.59

x= $13.59

Tubby is not correct. 1.15x is not an expression that represents the new price for the ornament. It represents the original price plus a 15% increase, not a discount. To find the new price after a discount, you need to multiply the original price by (1- the percentage discount) or subtract the percentage discount from the original price.

Step-by-step explanation:

Hand-grip strength is a sign of general toughness and a good indicator of significant consequences.

For grip strength measurements, current, population-specific reference values are required to interpret the results appropriately.

Objectives

To offer grip-strength reference values and formulae based on population for US citizens ages 18 to 85.

Methods

In this cross-sectional study, hand-grip data from 1232 participants, aged 18 to 85, were taken from the database of the 2011 normative phase of the US National Institutes of Health Toolbox project. Equations and descriptive reference values were derived from the data.

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The question is incomplete
the standard deviation for hand grip strength. what Objectives and Methods of the distribution

The y-intercept for function f(x) has the same value as the x-intercept of f-inverse.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

As

we can see from figure that y-intercept for f(x)=3

and x-intercept for f inverse = 3

Hence,

         The y-intercept for function f(x) has the same value as the x-intercept of f-inverse

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Answer:

x-intercept

domain of f

Step-by-step explanation:

i just did it

The factors of the expression mn-4m-5n+20 are (m-5)(n-4)

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression mn-4m-5n+20, we need to factorize it,

On factorizing the expression, mn-4m-5n+20, we get,

= mn-4m-5n+20

= m·n-4·m-5·n+5·4

= m(n-4)-5(n-4)

= (m-5)(n-4)

Hence, the factors of the expression mn-4m-5n+20 are (m-5)(n-4)

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Due to the lack of a common ratio, the above sequence is not geometric.

A series of integers with a common ratio is referred to as a geometric sequence. A geometric sequence has a next number that is a multiple of the one before it.

if the sequence is geometric.the common ratio of the number's

-1, 1, 4, 8, are

-1/1 = -1 ratios of the numbers in the sequence

4/1 = 4

8/4 = 2

There isn't a ratio that unites the numbers.

The lack of a common ratio leads us to the conclusion that the presented sequence is not geometric.

Due to the lack of a common ratio, the above sequence is not geometric.

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The required values are A) 5/3, B) 15, C) 20, D) 86°, E) 15°.

Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal. Consequently, if A = X and AB/XY = AC/XZ, then ABC XYZ.

Because of similarity, Corresponding angles are equal and corresponding sides are Proportional.

So,

In ΔABC

∠A = 180 - 60 - 36

∠A = 180 - 96 = 86°

Which is equal to ∠F

So,D) angle ∠F = 86°

A) Scale factor = AB/EF

= 5/3

So Scale factor is 5/3.

We can say length of side ΔABC = 5/3 Side of ΔDEF.

So, For x

25 = 5x/3

x = 15

For y

y = 5(12)/3

y = 20

And value of z,

4z = 60 degree

z = 15 degree.

Thus, required values are A) 5/3, B) 15, C) 20, D) 86°, E) 15°

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Using the triangle inequality theorem, the length of the third side is: D. 4 < c < 42.

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

In this case, we know that side A measures 23 inches and side B measures 19 inches. To find possible values for side C, we can use the triangle inequality theorem by adding the lengths of sides A and B and comparing the sum to all possible values of side C.

A + B > C

23 + 19 > C

42 > C

So, the length of side C must be less than 42 inches.

Also

C > A - B

C > 23 - 19

C > 4

So, the length of side C must be greater than 4 inches.

Therefore, the possible side lengths of the third side, C, must be between 4 inches and 42 inches (not including 4 inches and 42 inches).

The answer is: D. 4 < c < 42

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The slope is -Ea/R and the intercept is equal to ln(A)

The Arrhenius equation is a mathematical equation that describes the relationship between the rate constant of a chemical reaction and temperature:

k = Ae^(-Ea/RT)

where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

The slope and intercept of the linear plot of the Arrhenius equation using a semilogarithmic (semilog) plot can be determined by transforming the equation into a linear form. The semilog plot is created by taking the logarithm of the rate constant (k) on the y-axis and the reciprocal of the temperature (1/T) on the x-axis:

ln(k) = ln(A) - Ea / RT

The slope of the plot is equal to -Ea/R and the intercept is equal to ln(A). By fitting a straight line to the semilog plot, the values of Ea and A can be determined.

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The total distance of the trip Ella's family took is 700 miles.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Ella slept through the last 14% of the trip.

So, Before Ella fell to asleep they covered (100 - 14)% = 86% of the trip.

Let The total distance be 'x'.

Therefore, 602 miles is 86% of 'x' which can be numerically expressed as,

(86/100)×x = 602.

0.86x = 602.

x = 602/0.86.

x = 700 miles.

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All the solution of the blank words are given below.

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.

Given:

Figure ABCD is the pre-image.

And A'B'C'D' is the image.

The line of the reflection is y = 0.

The coordinates of the output:

A'(3, -6), B;(1, -1), C'(11, - 1) and D'(6, -6)

Therefore, all the blank words are given above.

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The solution for the given equations is x = 26, y = 15.

What is the linear equation in two variables?

A linear equation in two variables is an equation that can be written in the form of "ax + by = c", where a, b, and c are constants, and x and y are the variables.

To solve the equation y = x-11 for x, we can add 11 to both sides of the equation, resulting in y+11 = x.

To solve the equation y=15 for x, we can substitute 15 in the place of y in the first equation

15 = x - 11

So, x = 26

Hence, the solution for the given equations is x = 26, y = 15.

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The length of the segment PS is 100 units.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

From the given image we can see that the segments PT, PQ, and TQ form a right- angled triangle PQT.

Applying Pythagorean theorem to this triangle we have:

PQ^2 + TQ^2 = PT^2

(45)^2 + (TQ)^2 = (53)^2

2025 +  (TQ)^2 = 2809

(TQ)^2 = 2809 - 2025

(TQ)^2 = 784

TQ = 28

Similarly, segments PR, PS, and SR form a right-angled triangle PRS, where TQ = SR = 28 and PR = 96.

Applying Pythagorean theorem to this triangle we have:

PR^2 + SR^2 = PS^2

(96)^2 + (28)^2 = (PS)^2

(PS)^2 = 9216 + 784

(PS)^2 = 10000

PS = 100

Hence, the length of the segment PS is 100 units.

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Answer:

¿Qué quieres comer?

Step-by-step explanation: