o bill starts riding his bike towards town at a constant rate of 8 mph. then, 30 minutes later, his wife starts driving on the same path at a constant average of 30 mph. how long will it take her to catch up to bill?

According to unitary method, Beau needs 60 wheels in all to build 9 puppy bots and 6 kitty bots.

The unitary method is a mathematical technique used to solve problems by finding the value of one unit and then calculating the value of the required quantity by multiplying or dividing it with the given value of units.

Given that each bot needs 4 wheels, we can find the number of wheels required to build one bot. Using the unitary method, we can say that one bot needs 4 wheels. Therefore, 9 puppy bots will need 9 times 4 wheels, which is 36 wheels.

Similarly, 6 kitty bots will need 6 times 4 wheels, which is 24 wheels. To find the total number of wheels required to build all the bots, we can add the number of wheels required for puppy bots and kitty bots

Total number of wheels required = 36 + 24 = 60

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Below is the correct matching of the questions to the right answers

The statistical measures listed in the previous question are often used to describe and analyze statistical variables.

For instance, the range of a data set is a measure of the spread of values in a variable, while the quartiles and interquartile range provide information about the distribution of the variable. Mean average deviation is a measure of the variability of the variable around its mean value.

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1. Mean average deviation - The average deviation of the data from the mean.

2. Range of a data set - The difference between the highest value and the lowest value in a numerical data set.

3. First quartile - The median in the upper half of the rank-ordered data.

4. Second quartile - The median value in the data set.

5. Third quartile - The median in the lower half of the rank-ordered data.

6. Interquartile range - he distance between the first and third quartiles of the data set.

The statistical measures are often used to describe and analyze statistical variables. For instance, the range of a data set is a measure of the spread of values in a variable, while the quartiles and interquartile range provide information about the distribution of the variable. Mean average deviation is a measure of the variability of the variable around its mean value.

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The quotient and the remainder of the rational function are x + 4 and - 4.

In this problem we find the case of a rational function of the form R(x) = P(x) / Q(x), where P(x) and Q(x) are polynomials for the numerator and the denominator, respectively. The result of the rational function is represented by the following expression:

R(x) = S(x) + D(x) / Q(x)

Where:

If we know that P(x) = 2 · x² + 16 · x + 24 and Q(x) = 2 · x + 4, then the quotient and the remainder are, respectively:

R(x) = (2 · x² + 16 · x + 24) / (2 · x + 4)

R(x) = [2 · (x² + 8 · x + 12)] / [2 · (x + 4)]

R(x) = (x² + 8 · x + 12) / (x + 4)

R(x) = [(x² + 8 · x + 16) - 4] / (x + 4)

R(x) = [(x + 4)² - 4] / (x + 4)

R(x) = (x + 4) - 4 / (x + 4)

Quotient: (x + 4)

Remainder: - 4

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The missing length is 7.5 cm.

What is a rectangular prism?

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Here, we have

Let the missing length be x cm.

The formula for the surface area of a rectangular prism is:

SA = 2lw + 2lh + 2wh

We are given that the height and width are both 9 cm, so we can substitute those values and simplify:

432 = 2(x)(9) + 2(x)(9) + 2(9)(9)

432 = 18x + 18x + 162

432 - 162 = 36x

270 = 36x

x = 270/36

x = 7.5

Hence, the missing length is 7.5 cm.

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Answer:

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The exponential function of the form y=ab^x that has the given points is y = (25/7)(7/5)^x

We can use the given points to set up a system of equations and solve for the values of a and b in the exponential function y = ab^x.

Using the point (1,5), we get:

5 = ab^1

Using the point (2,7), we get:

7 = ab^2

Now, we can solve for a and b by dividing the second equation by the first:

7/5 = (ab^2)/(ab^1

Simplifying this expression, we get:

7/5 = b

Substituting this value of b back into one of the original equations, we can solve for a:

5 = a(b^1) = a(b) = a(7/5)

Simplifying this expression, we get:

a = 25/7

So, the exponential function that passes through the points (1,5) and (2,7) is:

y = (25/7)(7/5)^x

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The number of atoms present in 8.500 mole of chlorine atoms can be calculated using Avogadro's number, which is 6.022 x [tex]10^{23}[/tex] atoms per mole. Therefore:

Number of atoms = 8.500 mole x 6.022 x [tex]10^{23}[/tex]atoms/mole

Number of atoms = 5.1177 x [tex]10^{24}[/tex] atoms

The mass of 15.50 mole of oxygen can be calculated using the molar mass of oxygen, which is 16.00 g/mol. Therefore:

Mass = 15.50 mole x 16.00 g/mole

Mass = 248 g

The number of moles of helium in 1.953 x [tex]10^{8}[/tex] g of helium can be calculated using the molar mass of helium, which is 4.00 g/mol. Therefore:

Number of moles = 1.953 x [tex]10^{8}[/tex] g / 4.00 g/mol

Number of moles = 4.883 x [tex]10^{7}[/tex] mol

The number of atoms in 147.82 g of sulfur can be calculated using the molar mass of sulfur, which is 32.06 g/mol, and Avogadro's number. Therefore:

Number of moles = 147.82 g / 32.06 g/mol

Number of moles = 4.608 mol

Number of atoms = 4.608 mol x 6.022 x [tex]10^{23}[/tex] atoms/mol

Number of atoms = 2.773 x [tex]10^{24}[/tex] atoms

The molar mass of Co (cobalt) is 58.93 g/mol.

The formula mass of Ca3(PO4)2 can be calculated by adding the atomic masses of each element in the compound. The atomic masses are:

Ca = 40.08 g/mol

P = 30.97 g/mol

O = 16.00 g/mol

Formula mass = (3 x Ca) + (2 x P) + (8 x O)

Formula mass = (3 x 40.08 g/mol) + (2 x 30.97 g/mol) + (8 x 16.00 g/mol)

Formula mass = 310.18 g/mol

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Answer:

x=25.1

Step-by-step explanation:

by using Pythagorean theorem, [tex]a^{2} +b^{2}=c^{2}[/tex] where c is the hypotenuse

[tex]18.15^{2}[/tex]= 329.4225

[tex]17.39^{2}[/tex]= 302.4121

since those two side lengths are the legs, the sum of the numbers is the length of the hypotenuse squared

therefore, 631.8356 (the sum) = [tex]c^{2}[/tex]

by taking the square root of 631.8356, you will get approx 25.1 for the hypotenuse (aka x)

The value of angle G for both kites are respectively:

∠G = 110°

∠G = 80°

In a kite, the angles between the two non- congruent sides usually have the same angle size. Thus:

∠E ≅ ∠G

In a quadrilateral, the sum of the inner angles is 360 degrees. Thus:

100 + 40 + ∠E + ∠G = 360

140 + 2(∠G) = 360

2(∠G) = 360 - 140

(∠G) = 220/2

∠G = 110°

Similarly, for the second kite:

∠G = 360 - (110 + 60 + 110)

∠G = 80°

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Therefore , the solution of the given problem of probability comes out to be the experimental likelihood that a reggae CD will be the next one lent out is roughly 0.4615, or 46.15%.

Any considerations technique's main objective is to determine the likelihood event that a claim is true or that a particular incident will happen. Any number from 0 to 1, where 0 traditionally represents a percentage and 1 typically denotes the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.

Here,

Given: 86 Latin CDs were lent out, 16 were rock CDs, 45 were hip-hop CDs, and 126 were reggae CDs.

=> CDs loaned out in total: 86 + 16 + 45 + 126 = 273

=> 126 reggae CDs were lent out.

Number of reggae CDs loaned out relative to the total number of CDs loaned out, experimental likelihood of lending a reggae CD

=> A reggae CD's experimental chance of being lent out  = 126/273.

We may calculate the experimental probability's approximation using a calculator as follows:

=> A reggae CD will be lent out with an experimental probability of 0.4615.

Therefore, the experimental likelihood that a reggae CD will be the next one lent out is roughly 0.4615, or 46.15%.

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Answer:

126/273

Step-by-step explanation:

Answer:

-17 - 3y = 8x

Step-by-step explanation:

The total cost of mower is $10,228.48. The correct option from the following option given is D.

A down payment on a cottage is the money paid in advance by the buyer in a real estate transaction or other large purchase. Down payments are typically a portion of the sales price and can range from 3% to 20% for a primary residence.

The total cost of the mower will be the sum of the down payment and the total amount paid through the loan:

Down payment = $1,000

Total amount paid through the loan = (monthly payment) x (number of months) = $192.26 x 48 = $9,228.48

The total cost of the mower is:

Total cost = Down payment + Total amount paid through the loan

Total cost = $1,000 + $9,228.48

Total cost = $10,228.48

Therefore, the total cost of the mower is $10,228.48.

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The decimal which is less than 0. 8 and greater than 0. 02 is 0. 46 (option B).

To answer this question, we need to understand how decimals work. A decimal is a number that represents a value less than one, and it is denoted by a dot or a period. The digits that come after the dot represent the number of tenths, hundredths, thousandths, etc., depending on the place value of the digit.

Now, let's consider the given options: 0.81, 0.46, 0.86, and 0.6. We need to find the decimal that lies between 0.8 and 0.02.

We can eliminate option D, 0.6, as it is less than 0.8. Similarly, we can eliminate option A, 0.81, as it is greater than 0.8.

To choose between options B, 0.46, and C, 0.86, we need to compare them with the given values, 0.8 and 0.02. We can see that 0.46 is less than 0.8 but greater than 0.02.

Therefore, the answer is option B, 0.46.

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Rounding the result off to the nearest 10th, the lateral surface area of the cylinder is 822 inches².

Surface area is the total area of the exposed surfaces of a three-dimensional object. It is measured in square units such as square centimeters (cm2) or square meters (m2). Surface area is an important concept in mathematics, science, and engineering, as it is the total area that determines properties such as friction, heat transfer, and fluid dynamics. For example, a larger surface area can increase the rate of heat transfer and allow for more efficient cooling. Similarly, a larger surface area can increase the friction between two objects, allowing them to grip better. Surface area is also important in chemistry, as it affects the amount of gas or liquid that can be absorbed or released by a given object.

The cylinder has a radius of 11 inches and a height of 12.5 inches. To find the lateral surface area of a cylinder, the formula used is A = 2πrℎ, where r is the radius and h is the height of the cylinder. After plugging in the values, the lateral surface area of the cylinder is 821.75 inches². Rounding the result off to the nearest 10th, the lateral surface area of the cylinder is 822 inches².

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The total surface area of the triangular prism is calculated to be equal to 608 square centimeters.

The triangular prism can be observed to be a large rectangle and two identical triangles, so we shall calculate for the total surface area as follows:

area of one triangle = 1/2 × 8 cm × 12 cm

area of one triangle = 48 cm²

area of the two triangle faces = 2(48) = 96 cm²

area of the large rectangle face = (10 + 12 + 12) cm × 16 cm = 512 cm²

Total surface area of prism = 96 cm² + 512 cm² = 608 cm²

Therefore, the total surface area of the triangular prism is calculated to be equal to 608 square centimeters.

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Using the trigonometric ratios Cos and Tan we can find Cos A = 0.8 and Tan C = 0.75 from the given diagram.

Trigonometric ratios are mathematical functions used to relate the angles and sides of a right-angled triangle. The three primary trigonometric ratios are:

Sine : It is the ratio between the opposite side of the right triangle and the hypotenuse of the right triangle.

Cosine : It is the ratio between the adjacent side of the right triangle and the hypotenuse of the right triangle.

Tangent : It is the ratio between the opposite side of the right triangle and the adjacent side of the right triangle.

We know that Cos A = adjacent side of the right triangle/ hypotenuse of the right triangle

That is Cos A = AB/AC = 32/40 = 0.8

Similarly Tan C = opposite side of the right triangle/ adjacent side of the right triangle

That is Tan C = BC/AB = 24/32 = 0.75

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The surface area of the conical grain storage tank is 1,671 m².

The surface area of a cone is the total area that is covered by the surface of the cone.

Surface area =πr(r+√h²+r²)

the given parameters that will assist us do the question are

π = 3.14

h = height

r = radius = diameter / 2 = 20 / 2 = 10 m

3.14 x 10(10 + √100 + 1764 =  1,671 m²

Therefore, the surface area of the pyramid 1671 m ²

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The unit for the coefficient k would be dollars per unit of length squared.

To find the units for the coefficient k in the formula C = klw, we need to analyze the units of each variable.

C represents the cost of the home, which is measured in dollars.

l represents the length of the home, which is measured in some units of length, such as feet or meters.

w represents the width of the home, which is also measured in some units of length, such as feet or meters.

Therefore, we can determine the units for k by analyzing how the units for C, l, and w combine in the formula C = klw.

Starting with the left-hand side of the equation, we know that C represents dollars.

On the right-hand side of the equation, we have k times l times w. To determine the units of k, we need to figure out what units would make the entire right-hand side of the equation equal to dollars.

Since we are multiplying three quantities (k, l, and w), the units of k must cancel out the units of length in l and w in order to leave us with units of dollars.

This means that the units of k must be dollars per unit of length squared. We can write this as:

k = $/length^2

So, the units for the coefficient k in the formula C = klw are dollars per unit of length squared.

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The hexadecimal system numbering system is base 16; in other words, 16 numerals are used to express any given number.

In this system, 16 numerals are used to represent any given number. The numerals used in this system are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F, where A represents 10, B represents 11, and so on, up to F, which represents 15.

This system is commonly used in computer science, as it is more compact than the decimal system, and allows for easier conversion between binary and decimal systems. In the hexadecimal system, each digit represents a power of 16, just as each digit in the decimal system represents a power of 10.

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As a result, the cruise ship has travelled roughly 443.92 miles of distance from its starting point.

This merely indicates that the cruise ship moved 325 miles east since it cruises 325 miles directly east. We can more clearly grasp what is happening if we draw a vertical line where he stops. I created the diagram I believe best illustrates this.

According to the diagram, we now need to determine h because it is the distance between our starting point and destination.

The supplement is 150 degrees because the outside angle is 30 degrees.

As a result, we can now use the cosine rule to find h.

x²  = 325² + 150² - 2(325)(150)cos(180 - 30)

x²  = 105625 + 22500 - 97500 cos(150)

x²  = 128125 - 97500 *(-0.707)

x²  = 128125 +68942.91

x²  = 197068

x = 443.92 miles.

As a result, the cruise ship has travelled roughly 443.92 miles from its starting point.

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The inequality expression representing the area of the shaded region, indicating both the shaded area and the broken line is; y > 0

An inequality is a mathematical statement consisting two expressions joined with inequality symbols, which includes; '<', '>', '≠', '≤', and '≥'.

The area of the shaded region is the part of the coordinate plane above the x-axis.

The region shaded can therefore be indicated by the area y > 0

The x-axis on the coordinate plane representing the boundary of the shaded region consists of broken line, which indicates that the line is not included in the shaded region.

The inequality representing the area of the shaded region is therefore;

y > 0

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Step-by-step explanation:

There are multiple ways to do this,

  Here is ONE way

This is a RIGHT triangle, so you can use the Pythagorean theorem

  c^2 = a^2 + b^2    

      where c = hypotenuse ( long side) and a and b are the other two sides (legs)

So for this triangle :

15^2  =   x^2 + 12^2

15^2 - 12^2 = x^2

225  - 144 = x^2

81 = x^2

x = 9  cm  ( the missing side length)

The correct expressions that could represent the price of the item after the discount are (1-0.20)x and 0.80x. So, correct options are C and E.

When a 20% discount is applied to an item that costs x dollars, the price of the item after the discount can be represented as:

x - 0.20x = 0.80x

This means that the price of the item after the discount is 80% of its original price.

Now let's look at the given expressions and see which ones could represent the price of the item after the discount:

a. 20/100x - This expression represents the amount of the discount, not the price of the item after the discount.

b. X-20/100x - This expression represents the original price minus the discount, not the price of the item after the discount.

c. (1-0.20)x - This expression simplifies to 0.80x, which is correct.

d. 100-20/100x - This expression represents 100 minus the discount, not the price of the item after the discount.

e. 0.80x - This expression is correct, as we already determined that the price of the item after the discount is 0.80x.

f. (100-20)x - This expression represents the original price minus the discount as a percentage of the original price, not the price of the item after the discount.

Therefore, Correct options are C and E.

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The profit function of the company is given by P(x)=-4x^3 + 32x^2 - 64, where x is the number of toys sold in hundreds, and P(x) is the profit in thousands of dollars.

The key features of the graph of the profit function are the following:

The degree of the polynomial function is 3, which means that the graph is a cubic curve.

The coefficient of the leading term is negative (-4), which means that the graph opens downwards.

The coefficient of the quadratic term is positive (32), which means that the graph is concave up.

The y-intercept of the graph is -64, which means that the company will incur a loss of $64,000 if it does not sell any toys.

It should be noted that to find the maximum profit, we need to evaluate the profit function at x = 5.33:

P(5.33) = -4(5.33)^3 + 32(5.33)^2 - 64 = 23.78

Therefore, the maximum profit that the company can make is $23,780.

In summary, the graph of the profit function reveals that the company will incur a loss if it does not sell any toys, but it can make a profit if it sells at least some toys. The profit function has a cubic shape that opens downwards, indicating that the profit decreases as the number of toys sold increases beyond a certain point. The maximum profit occurs at x = 5.33, where the profit is $23,780.

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the value of the car decreases by 15 percent each year. This means that the value of the car decreases to 85% of its previous year's value every year.

what do you mean by term  decreases  ?

In this context, "decreases" means that the value of the car is getting smaller over time. The term "decrease" is often used in mathematics to describe a decrease in the numerical value of a quantity. In this case, the value of the car is decreasing by 15% each year, which means that its value is getting smaller by 15% of the previous year's value.

In the given question,

The given function for the value of the car is:

v(t) = P(0.85)ⁿ

Here, P is the initial purchase price of the car, and t is the time in years since the car was purchased.

To find the percent that the value of the car decreases by each year, we need to find the ratio of the decrease in value to the initial value, and express it as a percentage.

Let's consider the value of the car after one year, i.e., when t=1. The value of the car after one year is:

v(1) = P(0.85)¹ = 0.85P

The decrease in value from the initial value P is:

P - v(1) = P - 0.85P = 0.15P

Therefore, the ratio of the decrease in value to the initial value is:

(0.15P/P) = 0.15

To express this ratio as a percentage, we multiply by 100, which gives:

0.15 x 100% = 15%

Therefore, the value of the car decreases by 15% each year. This means that the value of the car decreases to 85% of its previous year's value every year.

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The principal advantage of the Dodge-Romig tables is their simplicity. Therefore, the correct answer is D. simplicity.

The Dodge-Romig tables are statistical sampling tables used in quality control to determine the acceptance or rejection

of a production lot based on sample size and the number of defects found in the sample.

The principal advantage of the Dodge-Romig tables is their simplicity.

They provide a quick and easy method for determining the acceptability of a production lot, without the need for

extensive calculations or statistical knowledge.

This means that they can be used by personnel with limited training in quality control.

The principal advantage of the Dodge-Romig tables is their simplicity. While they can be used for receiving inspection,

their main benefit is in minimizing inspection time and effort by providing clear guidelines for lot sampling and

acceptance based on size and level of defects.

Additionally, their use can facilitate smaller lot sizes and more efficient quality control processes.

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Therefore, the slope of the line represented by this equation is -3.

An equation is a mathematical statement that shows that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc. An equation can also be seen as a balance scale, where both sides of the equation must be equal in order for the equation to be true.

Here,

Now let's look at the given equations:

y=-3x+10

The equation is in slope-intercept form, y=mx+b, where m is the slope of the line. Therefore, the slope of the line represented by this equation is -3. To determine the relationship between this line and line p, we need to know the slope of line p.

y-5=-(2+2)

Simplifying this equation, we get y-5=-4 or y=-4+5 or y=1. This equation represents a horizontal line passing through y=1. A horizontal line has a slope of 0, which is neither parallel nor perpendicular to line p.

-3x+y=1

Rewriting this equation in slope-intercept form, we get y=3x+1. Therefore, the slope of the line represented by this equation is 3. To determine the relationship between this line and line p, we need to know the slope of line p.

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a) Year 1: 1.00,Year 2: 1.10,Year 3: 1.21,Year 4: 1.33,Year 5: 1.46, Year 6: 1.60, Year 7: 1.76, Year 8: 1.94, Year 9: 2.13 ,Year 10: 2.34, Year 11: 2.46, Year 12: 2.59.

b) The actuarial expression for the present value of the perpetuity immediate can be written as:

[tex]PV = (1/0.10) \times [1 - (1/1.10^{10})] + (1/0.05) \times [1/1.10^{10}] \times [1 - (1/1.05^∞)][/tex]

a) The first 12 payments for the perpetuity immediate with annual payments of 1, 3, 5, 7, 9, 11,……. and interest rate of 10% for the first 10 years and 5% after that are:
Year 1: 1.00
Year 2: 1.10
Year 3: 1.21
Year 4: 1.33
Year 5: 1.46
Year 6: 1.60
Year 7: 1.76
Year 8: 1.94
Year 9: 2.13
Year 10: 2.34
Year 11: 2.46
Year 12: 2.59
b) The actuarial expression for the present value of the perpetuity immediate can be written as:

[tex]PV = (1/0.10) \times [1 - (1/1.10^{10})] + (1/0.05) \times [1/1.10^{10}] \times [1 - (1/1.05^∞)][/tex]

where PV is the present value of the perpetuity, 0.10 is the interest rate for the first 10 years, 0.05 is the interest rate

after the first 10 years, and ∞ represents infinity (i.e., the perpetuity continues forever).

This formula takes into account the different interest rates for the two periods and discounts the future payments to

their present value.

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Answer:

a. f(x)

b. (2, -1)

c. f(x); y= -2

   g(x); y= -5.1

   h(x); y= -5

d. h(x)

Step-by-step explanation:

a. greatest y-intercept :

set x = 0

f(x) = 7

g(x) = -2

h(x) = -4

b. (2, -1)

c. minimum value (The minimum value of a function is the place where the graph has a vertex at its lowest point.)

f(x); y= -2

g(x); y= -5.1

h(x); y= -5

d. largest ROC = largest rate of change

h(x)

Answer:

3. 2(x - 3) = x + 4

2x - 6 = x + 4

x = 10

4. 3x = 2(x - 1)

3x = 2x - 2

x = -2