Given the function: f(x) = 2| x−1 | − 3

• Fully explain the three transformations required to produce this function from the

parent function.

• Find at least 3 points on the function and show ALL of your work explaining how you

found the y-values. Use these three points to graph the function given.

Answer: 5 1/12

Step-by-step explanation:

1. Conversion a mixed number 1  3/4 to a improper fraction: 1 3/4 = 1  3/4 = 1 · 4 + 3/4 = 4 + 3/4 = 7/4

2. Conversion a mixed number 3  1/3 to a improper fraction: 3 1/3 = 3  1/3 = 3 · 3 + 1/3 = 9 + 1/3 = 10/3

3. Add: 7/4 + 10/3 = 7 · 3/4 · 3 + 10 · 4/3 · 4 = 21/12 + 40/12 = 21 + 40/12 = 61/12 

Factor of equation 4x²-x-3 is (x-1)(4x+3)

Factorization, also known as factoring, is the process of breaking down a mathematical object (such as a number, polynomial, or matrix) into simpler pieces called factors. In number theory, factorization involves expressing a positive integer as a product of smaller integers (factors). For example, the number 12 can be factored as 2 × 2 × 3, where 2 and 3 are prime factors and the quadratic expression x² + 7x + 10 can be factored as (x + 2)(x + 5), which can be verified by expanding the product.

4x²-x-3

Simplifying the terms;

4x²-4x+3x-3

Taking x-1 common from the equation

4x(x-1)+3(x-1)

(x-1)(4x+3)

Hence, factor of 4x²-x-3 is (x-1)(4x+3)

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The complete question is;

Factorise 4x²– x – 3​

The coordinates after dilation are A (-0.5 , 1) , B(1,0.5) , C(0.5,-0.5) and D(0,0).

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size.

Here , we need to find coordinates before using dilation. Then the coordinates are,

A=(-1,2) , B=(2,1) , C=(1,-1) and D=(0,0).

The scale factor = 0.5

For dilation coordinates we need to multiply coordinates by using scale factor. Then,

A = (-1,2) => (-1×0.5, 2×0.5) => (-0.5 , 1)

B = (2,1) => (2×0.5 , 1×0.5) => (1,0.5)

C = (1 , -1) => (1×0.5 , -1×0.5) => (0.5, -0.5)

D = (0 , 0) => (0×0.5 , 0×0.5) => (0,0)

Hence the coordinates after dilation are A (-0.5 , 1) , B(1,0.5) , C(0.5,-0.5) and D(0,0).

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Yes, it's possible probability for there to be girls in the group with other hair colors.

How to calculate probability?

Let's say there are n girls in the group.

The probability of a girl having red hair is 1/6, so the number of girls with red hair would be n/6.

The probability of a girl having blonde hair is 2 times more than the probability of having red hair. This means the probability of a girl having blonde hair is (2/1) times the probability of having red hair, or 2/7. So the number of girls with blonde hair would be (2/7)*n.

The probability of a girl having brown hair is three times more than the probability of having red hair. This means the probability of a girl having brown hair is (3/1) times the probability of having red hair, or 1/2. So the number of girls with brown hair would be (1/2)*n.

So far, we have accounted for:

n/6 girls with red hair

(2/7)*n girls with blonde hair

(1/2)*n girls with brown hair

If we add these up, we get:

n/6 + (2/7)*n + (1/2)*n = 7n/42 + 12n/42 + 21n/42 = 40n/42

This means that we have accounted for 40n/42 of the girls in the group. The remaining 2n/42 girls could have other hair colors, such as black or gray.

Therefore, it's possible for there to be girls in the group with other hair colors besides red, blonde, and brown.

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Answer: 17y - 12

Step-by-step explanation:

By distributing the 3 with the numbers inside the parentheses (2y - 4),

you would get: 6y - 12

You are left with: 11y + 6y - 12

Finally, by adding like terms, your answer would be 17y - 12

Therefore, Mira's yearly taxable income is Rs. 12,60,600.

Income is the amount of money an individual or organization receives over a specified period, typically measured on a monthly or annual basis. This can include wages, salaries, bonuses, commissions, rental income, investment income, and any other sources of money that come in during a specific time period. Income is often used to measure an individual's or organization's financial success or stability and can be an important factor in determining one's ability to afford certain goods and services.

by the question.

To calculate Mira's yearly taxable income, we first need to determine her yearly basic salary, festival expenses, and provident fund deduction.

Yearly basic salary:

Mira's monthly basic salary is Rs. 55,000. So, her yearly basic salary is:

Rs. 55,000 x 12 = Rs. 6,60,000

Festival expenses:

Mira gets festival expenses equivalent to her monthly basic salary, which is Rs. 55,000. So, her yearly festival expenses are:

Rs. 55,000 x 12 = Rs. 6,60,000

Provident fund deduction:

10% of Mira's salary excluding allowance is deducted as provident fund. So, her monthly salary excluding allowance is:

Rs. 55,000 - Rs. 3,000 = Rs. 52,000

10% of Rs. 52,000 is Rs. 5,200, which is Mira's monthly provident fund deduction. So, her yearly provident fund deduction is:

Rs. 5,200 x 12 = Rs. 62,400

Now, to calculate Mira's yearly taxable income, we need to subtract her deductions from her gross income:

Yearly taxable income = Gross income - Deductions

Gross income = Yearly basic salary + Yearly festival expenses + Allowance

Gross income = Rs. 6,60,000 + Rs. 6,60,000 + Rs. 3,000 = Rs. 13,23,000

Deductions = Yearly provident fund deduction

Deductions = Rs. 62,400

Yearly taxable income = Rs. 13,23,000 - Rs. 62,400 = Rs. 12,60,600

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Answer: 4[tex]\sqrt{13}[/tex]

Step-by-step explanation:

pythagrean's therom: a^2 +b^2 = c^2

(8)^2 +(12)^2 = c^2

64 +144 = c^2

[tex]\sqrt{208}[/tex] = c

[tex]\sqrt{(4)^2 (13)}[/tex] = c

4[tex]\sqrt{13}[/tex] = c

As per the unitary method,, Shana gets back $2 as change.

First, we need to find out how much money Shana paid for the almonds. We know that she paid with two $10 bills, so the total amount of money she paid is:

2 x $10 = $20

Next, we need to find out how much money Shana should have paid if she didn't have any change. We know that the cost of the almonds is $18, so if Shana paid without any change, she would have paid:

$18

Now, we can find out how much change Shana gets back by subtracting the amount she paid from the amount she should have paid:

$20 - $18 = $2

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i think the answer is the second choice -3x +9

The 43rd term of the sequence is -4,930.

A recursive formula is one that defines each term in a sequence by reference to the one before it (s). The following parameters are defined using the recursive formulas:

The opening phrase of the series

The formula to calculate any phrase from its previous term

In the given series we have, a_1 = 1,916 and a_n = a_{n-1} - 163.

Thus,

a_1 = 1,916

a_2 = a_1 - 163 = 1,753

a_3 = a_2 - 163 = 1,590

a_4 = a_3 - 163 = 1,427

Here, each term is 163 less than the previous term.

Thus,

a_{43} = a_{42} - 163 = a_1 - 42(163) = 1,916 - 6,846 = -4,930

Hence, the 43rd term of the sequence is -4,930.

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Answer: 260:455

260 / 455 = .57

4 / 7 = .57

455 - 260 = 195

If they are equal, then the methods are consistent; if not, they yield different solutions, possibly due to varying techniques or assumptions.

Hi! Based on the information provided, it seems you are comparing two methods for finding the altitude of a triangle.

The previous activity gave an altitude of 9,000. If the new method also results in an altitude of 9,000, then both methods give the same solution.

To determine if they are the same, compare the calculated values from each method.

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The calculated length of the arc with the central angle and the radius is 2.2π inches

Given that we have the following values

Radius, r = 18 inches

Central angle, x = 22 degrees

The formula for the arc length of a circle is given as:

Arc length = (central angle / 360) x (2πr)

where r is the radius of the circle.

Substituting the given values, we get:

Arc length = (22/360) x (2π x 18)

So, we have the following

Arc length = (44/20)π

When evaluated, we have

Arc length = 2.2π or 6.91 inches

Rounding to the nearest hundredth, the arc length of the given arc is approximately 6.91 inches.

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To compare the two accounts, we need to calculate the final amount in each account after the given period.

For the simple interest account:

I = P * r * t

I = 250 * 0.03 * 3 = $22.50

Final amount = P + I = $272.50

For the compound interest account:

Final amount = P * (1 + r/n)^(nt)

Final amount = 250 * (1 + 0.04/2)^(22) = $276.16

Therefore, the compound interest account earns more by $3.66 ($276.16 - $272.50).

Answer:4% over 2 years

Step-by-step explanation:

Step-by-step explanation:

1) v=πr^2×h

v= π 1.5^2×3

v=21.205750411731

to 2dp v= 21.21

2) v=πr^2×h

v=π×1.5^2×3.5

v=24.740042147019

to 2 dp v= 24.74

Answer:

1.  6.75π or 21.2 cubic inches (nearest tenth)

2. 7.875π or 24.7 cubic inches (nearest tenth)

Step-by-step explanation:

The formula to find the volume of a cylinder is:

[tex]\boxed{V=\pi r^2 h}[/tex]

where:

[tex]\hrulefill[/tex]

Given values:

Substitute the given values into the formula and solve for V:

[tex]\begin{aligned}\implies V&=\pi r^2 h\\&=\pi \cdot 1.5^2 \cdot 3\\&= \pi \cdot 2.25 \cdot 3\\&=6.75 \pi \\&=21.2\; \sf in^3\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the volume of the cylinder is 6.75π or 21.2 cubic inches.

Given values:

Substitute the given values into the formula and solve for V:

[tex]\begin{aligned}\implies V&=\pi r^2 h\\&=\pi \cdot 1.5^2 \cdot 3.5\\&= \pi \cdot 2.25 \cdot 3.5\\&=7.875\pi \\&=24.7\; \sf in^3\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the volume of the cylinder is 7.875π or 24.7 cubic inches.

As per the proportion, we need to replace 3.6 liters of the mixture with pure wine to get a concoction containing wine and spirit in equal proportion.

Let's start by understanding the given information. We have a concoction of 12 liters that contains wine and spirit in the ratio of 2:3. This means that out of every 5 liters of the concoction, 2 liters are wine and 3 liters are spirit.

We are asked to find 'x', the quantity of the mixture that needs to be replaced, such that the resultant mixture has wine and spirit in equal proportion. In other words, we need to find 'x' such that:

(2x + 2)/(12 + 'x') = 3(12 - 'x')/5(12 + 'x')

Let's simplify this equation using cross-multiplication:

5(2x + 2)(12 - 'x') = 3(12 + 'x')(12 - 'x')

Simplifying further:

10x² - 36x + 36 = 0

Dividing both sides by 2:

5x² - 18x + 18 = 0

We can solve this quadratic equation using the quadratic formula:

x = [18 ± √(18² - 4(5)(18))]/(2(5))

Simplifying:

x = [18 ± 6]/10

x = 1.8 or 3.6

Since we cannot replace a fraction of a liter, the only possible value of 'x' is 3.6 liters.

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Of the company's customers, the number that would be expected to experience pain relief from the shoes is 2832.

An experiment is a process done by scientific and mathematical methods.

Analysis:

The number of people in each group is:

in the first group "60x70% = 672

in the second group 960X 60% =576

in the third group 960x 450 x 8432

in the fourth group 960 x 55% =528

in the fifth group 960x65% =62e

The total number of five experimental groups of customers is

2832.

Therefore, the total number of five experimental groups of customers is

2832.

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The solutions for the equation [tex]y=-4(x-2)^2+6[/tex] are as follows [tex]x = 2 + \sqrt{(6 - Y) / 4}[/tex] or [tex]x = 2 - \sqrt{(6 - Y) / 4}[/tex].

The given equation is in standard form for a quadratic equation, where the coefficient of [tex]x^2[/tex] is negative. This means the graph of the equation is a downward-opening parabola, and the vertex of the parabola is (2, 6).

To solve the equation, we can first isolate the variable Y on one side:

[tex]Y - 6 = -4(x - 2)^2[/tex]

Then we can divide both sides by -4:

[tex](Y - 6) / -4 = (x - 2)^2[/tex]

Next, we can take the square root of both sides:

[tex]\sqrt{[(Y - 6) / -4] }= x - 2[/tex]

[tex]\pm \sqrt{(Y - 6) / -4}= x - 2[/tex]

So the solutions are:

[tex]x = 2 + \sqrt{(6 - Y) / 4}[/tex] or [tex]x = 2 - \sqrt{(6 - Y) / 4}[/tex]

These equations give the x-coordinates of the points on the graph of the equation for a given value of Y.

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Answer:

b = 6(x - 3)

Step-by-step explanation:

Answer:

P-8+5

Step-by-step explanation:

When people get off, you lose them (duh), which means there will be negative people on the bus, so -8. Then +5

Answer:

The first one : p - 8 + 5

Hope this helps!

Step-by-step explanation:

8 people get off = - 8

5 more people get on = + 5

(a) The area of the top of the circular table is  1632.66 square inches.

(b) The area of the top of the square table is  1296 square inches.

(c) The circular tables is the most appropriate as it allow for better communication and interaction among all members, as everyone is facing towards the center of the table.

Assuming a family size of 6 persons, the minimum diameter of a circular table to seat all members can be calculated as follows:

Minimum circumference = (number of persons × 24 inches)

Minimum diameter = Minimum circumference / π

Minimum diameter = (6 × 24) / π

Minimum diameter ≈ 45.63 inches

The minimum length of the side of a square table can be calculated as follows:

Minimum perimeter = (number of persons × 24 inches)

Minimum length of side = Minimum perimeter / 4

Minimum length of side = (6 × 24) / 4

Minimum length of side = 36 inches

The area of the top of the circular table can be calculated as follows:

Area = π × (diameter/2)²

Area = π × (45.63/2)²

Area ≈ 1632.66 square inches

The area of the top of the square table can be calculated as follows:

Area = (length of side)²

Area = 36²

Area = 1296 square inches

Based on the calculations, the circular table has a larger surface area than the square table, and hence it would be more appropriate for the family size of 6. Additionally, circular tables allow for better communication and interaction among all members, as everyone is facing towards the center of the table.

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The equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

What is the rate?

A rate is a measure of the amount of change of one quantity with respect to another quantity. It is expressed as a ratio of two different units, and it indicates how fast or slow one quantity is changing in relation to another quantity.

If we assume that a person's height decreases by 0.06 cm per year starting at age 30,

we can use the following equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

where h(30) represents the person's height at age 30.

This equation assumes that the rate of height decrease is constant and linear over time.

Hence, the equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

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[tex]\cfrac{1}{2}(1-x)-\cfrac{1}{3}(2+x)+\cfrac{1}{4}(3-x)=1 \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{1}{2}(1-x)-\cfrac{1}{3}(2+x)+\cfrac{1}{4}(3-x) \right)~~ = ~~12(1)} \\\\\\ 6(1-x)-4(2+x)+3(3-x)=12\implies 6-6x-8-4x+9-3x=12 \\\\\\ 7-13x=12\implies 7=13x+12\implies -5=13x\implies \cfrac{-5}{13}=x[/tex]

A quadratic functiοn f whose zeroes are 2 and 5 is f(x) = x² - 7x + 10.

A quadratic functiοn is a secοnd-degree pοlynοmial functiοn οf the fοrm:

f(x) = ax² + bx + c

where a, b, and c are cοnstants, and a is nοt equal tο 0. The graph οf a quadratic functiοn is a parabοla, which can οpen upwards οr dοwnwards depending οn the sign οf the leading cοefficient a.

The term ax² is the quadratic term, bx is the linear term, and c is the cοnstant term. The cοefficient a determines the shape οf the parabοla, while the cοnstants b and c determine its pοsitiοn and οrientatiοn.

Quadratic functiοns can have οne, twο, οr zerο real rοοts (alsο knοwn as sοlutiοns οr zerοs), which cοrrespοnd tο the x-intercepts οf the parabοla. The number and nature οf the rοοts depend οn the value οf the discriminant, which is given by b² - 4ac.

If the zeroes are x = 2 and x  = 5 then the solutions must be:

(x - 2)(x - 5)

Multiply them and make a quadratic function

⇒ (x - 2)(x - 5)

⇒ (x²  - 5x)- (2x - 5)

⇒ x² -5x - 2x + 5

⇒ x² -5x - 2x + 5

⇒ x² - 7x + 5

Comparing this to the form of the quadratic function f(x) = ax² + bx + c, we see that a = 1, b = -7, and c = 10. Therefore, the quadratic function with zeros at 2 and 5 is:

f(x) = x²- 7x + 10

So, the correct option is f(x) = x² - 7x + 10.

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The coordinates of B, considering the proportions in the context of the problem, are given as follows:

(4.33, 8).

The coordinates of B are obtained applying the proportions in the context of the problem.

BC is 50% longer than AB, hence point B is at one-third of the way from A to C, and thus the equation is given as follows:

B - A = 1/3(C - A).

The x-coordinate of B is then given as follows:

x - 1 = 1/3(11 - 1)

x - 1 = 3.33

x = 4.33.

The y-coordinate of B is then given as follows:

y - 3 = 1/3(18 - 3)

x - 3 = 5

y = 8.

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Caleb's yearly expense for his internet service and Netflix subscription is $695.76.

To write an equation for Caleb's yearly expenses, we need to first determine his total monthly expense and then multiply it by 12 to get the yearly expense.

Caleb's monthly expense can be calculated as the sum of the internet and Netflix costs, which is:

$14.99 + $14.99 = $29.98

To include the initial setup fee of $28, we can add it to the monthly expense to get

$29.98 + $28 = $57.98

This is Caleb's total monthly expense, and to find his yearly expense, we can multiply it by 12

$57.98 x 12 = $695.76

Therefore, the equation for Caleb's yearly expense is

Yearly expense = 12 x (monthly internet cost + monthly Netflix cost + initial setup fee)

Yearly expense = 12 x ($14.99 + $14.99 + $28)

Yearly expense = $695.76

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The given question is incomplete, the complete question is:

Caleb got internet service at home from a company called "Inter-What??". The company charged him $28 to hook it up. Then joined Netflix. He pays $14. 99 a month to keep the internet connected and he also pays the same amount for Netflix. Write an equation and find the yearly expense

The solutions to the equatiοn [tex]2x^2 + 2x - 12 = 0[/tex] are x = 2 and x = -3.

It is a secοnd-degree quadratic equatiοn, an algebraic equatiοn in x. The quadratic equatiοn in its standard fοrm is written as Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term. An equatiοn must have a zerο-terminal term (a 0) fοr the x²  cοefficent in οrder tο qualify as a quadratic equatiοn.

When cοnstructing a quadratic equatiοn in standard fοrm, the x²  term is written first, fοllοwed by the x term, and finally the cοnstant term. The numerical values οf letters a, b, and c are typically expressed as integral values rather than fractiοns οr decimals.

[tex]x = (-b \± \sqrt{ (b^2 - 4ac)}) / 2a[/tex]

where a = 2, b = 2, and c = -12. Substituting these values, we get:

[tex]x = (-2 \± \sqrt{(2^2 - 4(2)(-12))) / 2(2)[/tex]

[tex]x = (-2 \± \sqrt{(100)}) / 4[/tex]

[tex]x = (-2 \± 10) / 4[/tex]

Sο the sοlutiοns are:

x = (-2 + 10) / 4 = 8/4 = 2

x = (-2 - 10) / 4 = -12/4 = -3

Therefore, the solutions to [tex]2x^2 + 2x - 12 = 0[/tex] are x = 2 and x = -3.

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The area of the rectangle can be represented by the expression a = 160l - l² if the field of length l and width w has a perimeter of 320 yards.

It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that:

A field of length l and width w has a perimeter of 320 yards.

As we know, the perimeter of the rectangle = 2(l + w)

2(l + w) = 320

l + w = 320/2

l + w = 160

The area of the rectangle = lxw

Let a is the area of the rectangle.

a = lw

Plug w = 160 - l in the above equation:

a = l(160 - l)

a = 160l - l²

The above expression represents the area of the rectangle in terms of l.

Thus, the area of the rectangle can be represented by the expression a = 160l - l² if the field of length l and width w has a perimeter of 320 yards.

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