Consider the function y=z²+2x+3
Part A
What are the coordinates of the vertex of the given function? Show your work.
Part B
What is the function in vertex form? Pleaseee help!!!

Answer:

The correct answer is: domain: all real numbers, range: all real numbers greater than or equal to -5.

We can see that the function is a polynomial of degree 4, which means it is defined for all real numbers. Also, as x^4 is always non-negative, the minimum value of the function occurs when x=0, and it is f(0) = -4. Therefore, the range of the function is all real numbers greater than or equal to -4. However, since the function is increasing as we move away from 0, the range is actually all real numbers greater than or equal to the minimum value of -4 plus the vertical shift of -1, which is -5.

Answer:144

Step-by-step explanation:

Answer:144

Step-by-step explanation:

We may calculate the distance from Carlos and the tree as [tex]D = 781.23[/tex] ft using trigonometric relationships.

Many functions in trigonometry offer excellent illustrations of how calculus may be used in practical situations. By the way, basic trigonometry primarily deals with the algebraic features of circular functions, therefore basic calculus is not always simpler than basic trigonometry. On the other hand, calculus is fundamentally non-algebraic in nature.

The mnemonic SOHCAHTOA makes it simple for us to recall the three primary trigonometric ratios.

Then one of the cathetus of the triangle is equal to:

[tex]275ft - 6ft = 269ft[/tex]

That cathetus is the opposite cathetus to the angle of 19° (the elevation angle). And the adjacent cathetus is the distance between Carlos and the tree.

Then we can use the relation:

Where:

[tex]a=19^{0}[/tex]

opposite cathetus [tex]=269ft[/tex]

adjacent cathetus [tex]=D[/tex]

Replacing that, we get

[tex]tan(19^{0} ) = 269ft/D[/tex]

Solving for D, we get:

[tex]D = 269ft/tan(19^{0} ) = 781.2ft[/tex]

So we conclude that Carlos is at [tex]781.23[/tex] ft of the tree.

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The percent decrease in the amount of land that Patty owns now is approximately 15.00%. Destiny's time at yesterday's race was 187 minutes.

To find Destiny's time at yesterday's race, we can first calculate the time reduction as a percentage of her previous time, and then subtract that reduction from her previous time.

The time reduction is 15% of 220 minutes -

0.15 x 220 = 33

So, she took 33 minutes less at yesterday's race.

Her time at yesterday's race is -

220 - 33 = 187 minutes

Therefore, time value is obtained as 187 minutes.

The percent decrease in the amount of land that Patty owns can be calculated by finding the difference between her old and new land sizes, dividing that by her old land size, and then multiplying by 100 to convert to a percentage.

The difference between her old and new land sizes is -

2,220 - 1,887 = 333

Dividing that by her old land size and multiplying by 100, we get -

(333/2220) x 100 ≈ 15.00

Therefore, the percent decrease is obtained as 15.00%.

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a. The equation of the tangent plane is z = 1 + x.

b. The point (4/3, 8/3, 5) lies on both the plane T(0,1) and the line l.

c. The other points on the graph of f(x) whose tangent plane contains the line l are (-9/8, -1/2, -21/8) and (-25/32, -3/4, -47/32)

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

(a) The partial derivatives of f(x) at this point:

∂f/∂x = 2x + y²

∂f/∂y = x² + 2xy

Evaluating these at (0,1), we get:

∂f/∂x(0,1) = 1

∂f/∂y(0,1) = 0

So the equation of the tangent plane is:

z = f(0,1) + ∂f/∂x(0,1)(x-0) + ∂f/∂y(0,1)(y-1)

z = 1 + x

(b)

The plane T(0,1) contains the line l:

2x = y = (z+3)/2

Substituting y = 2x and z = 2y-3, we get:

z = 2(2x) - 3 = 4x - 3

So any point on the line l can be written as (x, 2x, 4x-3).

Substituting these values into the equation of the plane, we get:

4x-3 = 1 + x

3x = 4

So x = 4/3, y = 8/3, and z = 5.

Therefore, the point (4/3, 8/3, 5) lies on both the plane T(0,1) and the line l.

(c) To find all other points on the graph of f whose tangent plane contains the line l, we need to find the intersection of the graph of f with the plane T(0,1) + λ(2,0,1), where λ is a scalar. This gives us the system of equations:

x² + y²xy = 1 + x + 2λ

2x + y² = 0

y - 1 = λ

Solving for x and y in terms of λ, we get:

y = λ + 1

x = -(y²)/2 = -(λ+1)²/2

Substituting these values into the first equation, we get:

(λ+1)² + (λ+1)²(-(λ+1)²/2) = 1 - (λ+1)²/2 + 2λ

Simplifying and solving for λ, we get:

λ = -1/2, -1/4

Therefore, the other points on the graph of f(x) whose tangent plane contains the line l are:

(-9/8, -1/2, -21/8) and (-25/32, -3/4, -47/32)

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The solution of the equation is x = -0.21 and x = -1.79 and the steps used are from the quadratic formula.

The quadratic formula in elementary algebra is a formula that gives the solution(s) to a quadratic problem. In addition to the quadratic formula, there are various methods for solving quadratic equations, including factoring (direct factoring, grouping, and the AC technique), completing the square, graphing, and others.

Given that, the equation is:

8x² + 16x + 3

The steps that could be used to solve the following equation are:

The quadratic formula is given as:

-b ± √b² - 4ac / 2a

Substitute the values:

x = -16 ± √(16)² - 4(8)(3) / 2(8)

x = -16 ± √256 - 96 / 16

x = - 16 ± 12.64 / 16

x = - 16 + 12.64/16 and x = - 16 - 12.64 / 16

x = -0.21 and x = -1.79

Hence, the solution of the equation is x = -0.21 and x = -1.79 and the steps used are from the quadratic formula.

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The surface area of the cone is 48π square centimeters (or approximately 150.8 square centimeters if we use a decimal approximation for π).

Calculating a cone's surface area is as follows:

[tex]\mathrm{SA = \pi r\² + \pi r \boldsumbol l }[/tex]

where l is the cone's slant height and r is the base's radius.

The radius and slant height in this instance are 4 cm and 8 cm, respectively. Therefore:

[tex]SA = \pi (4\²) + \pi (4)(8) \s= 16 \pi + 32 \pi \s= 48 \pi[/tex]

Hence, the cone's surface area is 48 square centimetres (or around 150.8 square centimetres if we round to the nearest decimal).

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The total area of the exercise room is 160 square feet.

The number of square yards equivalent to this total area is 17. 78 square yards.

Since the rubber flooring is sold in whole square yards, Juan must purchase exactly 18 square yards.

To find the area of the exercise room, you should divide it into two different rectangles and then add up their areas.

Rectangle 1 length = 16 ft

Rectangle 1 width = ( 13 - 6 ) = 7 ft

Rectangle 2 length = ( 16 - 8 ) = 8 ft

Rectangle 2 width = 6 ft

The area is therefore :

= ( 16 x 7 ) + ( 8 x 6 )

= 160 square feet

1 square yard is 9 square foot so 160 square foot is:

= 160 / 9

= 17. 78 square yards

The area of rubber flooring that Juan must purchase would then be the whole number of 18 square yards which is 17.78 rounded up.

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The relative minimum point is B. Option B is the correct option.

What is the relative minimum?

The function's graph makes it simple to locate relative minima. It is the pivotal point in the function's graph. Relative minima are locations where the function's graph shifts from decreasing to increasing. A point that is lower than the points to its left and right is said to be at its relative minima.

The points of the graph function are A, B, C, D.

The lowest point among the given points on the graph is B.

Thus the relative minimum point is B.

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Answer: To find out how much commission Yamilet will receive for selling an $8,125 ring, we need to multiply the price of the ring by her commission rate, which is 12% or 0.12 in decimal form.

Commission = Price of ring x Commission rate

Commission = $8,125 x 0.12

Commission = $975

Therefore, Yamilet will receive a commission of $975 for selling an $8,125 ring.

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

your add odd number 1,3,5,7,9,11,13...

The answer is m = 0.

The function Q(x) = 7.25x 36.25 can be used to model daily profit, Q(x), making none of the proposed answers suitable.

A function in mathematics is a relationship between a domain—a set of possible inputs—and a range—a set of potential outputs—with the property that each input is linked to precisely one output. Frequently, a mathematical expression, equation, or formula will be used to describe a function. They are a fundamental idea in calculus, algebra, and other branches of mathematics, used to explain how one quantity relies on another.

given

Let Q(x) = 7.25x 36.25 be a model for his daily earnings, where x is the quantity of bracelets he sells.

Q(5) = 23.5, which indicates that Quincy will make $23.50 if he sells 5 wristbands today.

The function Q(x) = 7.25x 36.25 can be used to model daily profit, Q(x), making none of the proposed answers suitable.

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Answer:

She read 4/5 of a book per month

Step-by-step explanation:

4/5= 4/5per month

Step-by-step explanation:

To find out how many books Tanisha read each month, we can use the formula:

books read per month = total number of books ÷ total number of months

Using the information given in the problem, we know that Tanisha read 4 books in 5 months. So we can plug those values into the formula:

books read per month = 4 ÷ 5

Simplifying the fraction by dividing the numerator and denominator by their greatest common factor, which is 1, we get:

books read per month = 4/5

Therefore, Tanisha read 4/5 of a book per month, or equivalently, 0.8 books per month.

please give me a brainliest.

Answer:

Step-by-step explanation:

If two bakers can make 30 loaves in 1 hour, then we can use proportionality to find how many hours it would take for 3, 5, 6, and 15 bakers to make 30 loaves.

Let h be the number of hours needed for a given number of bakers to make 30 loaves. Then we have:

2 bakers can make 30 loaves in 1 hour, so 1 baker can make 15 loaves in 1 hour.

Therefore:

3 bakers can make 45 loaves in h hours, so 45/3 = 15 loaves can be made in 1 hour. Thus, 3 bakers can make 30 loaves in 2 hours.

5 bakers can make 75 loaves in h hours, so 75/5 = 15 loaves can be made in 1 hour. Thus, 5 bakers can make 30 loaves in 2 hours.

6 bakers can make 90 loaves in h hours, so 90/6 = 15 loaves can be made in 1 hour. Thus, 6 bakers can make 30 loaves in 2 hours.

15 bakers can make 225 loaves in h hours, so 225/15 = 15 loaves can be made in 1 hour. Thus, 15 bakers can make 30 loaves in 2 hours.

Therefore, regardless of the number of bakers, it would take 2 hours to make 30 loaves of bread.

The expression that describe the area of the shaded part is 1/3 × 1/2 (optionD)

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.

therefore the area of the shaded part is l× w

On the vertical row 3 boxes are shaded out of 6

and on the horizontal 3 are shaded out of 9 boxes

A = 3/6 × 3/9

A = 1/2 × 1/3

therefore the area of the shaded part = 1/3 × 1/2

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The algebraic expression for Thabo is, Thabo's age in 6 years' time is x + 6.

There are three primary categories of algebraic expressions, including:

Numeral Expression. Binary Expression. Expression of a Polynomial

Monomial Expression: A monomial is an algebraic expression that only has one term.

Monomial expressions include 3x4, 3xy, 3x, 8y, etc. as examples.

A binomial expression is an algebraic expression with two terms that are opposite each other.

Binomial examples are 5xy + 8; xyz + x3; etc.

Polynomial Expression: In general, a polynomial expression is one that has several terms with non-negative integral exponents of a variable.

Given that, Thabo is x years old and Lizzie is y years old.

In 6 years, Thabo's age will be:

x + 6

Hence, Thabo's age in 6 years' time is x + 6.

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The relative maximum from the given graph is (2, 0). Therefore, options B, C, D and E are the correct answers

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

From the given graph,

The zeros of function are x=-3, x=2 and x=5.

So, the number of zeros are 3 and the degree of the polynomial is 3.

The relative maximum from the given graph is (2, 0).

The leading coefficient test tells us that the graph rises or falls depending on whether the leading terms are positive or negative.

Here, the leading coefficient is negative.

The edge multiplicity of a given end vertex in a multigraph is the number of multiple edges sharing that end vertex. The maximum edge multiplicity in such a graph is known as the graph multiplicity.

Here, the multiplicity is 2.

Therefore, options B, C, D and E are the correct answers

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Most nations adopt the international standard ISO 216, which specifies the dimensions of an A4 sheet.

ISO (International organization fr Standardization) is an independent, non-governmental body that develops standards to ensure the effectiveness, safety, and quality of goods, services, and systems.

Obtaining an ISO quality management certification can greatly benefit your company by increasing productivity, efficiency, and customer satisfaction.

The international standard ISO 216, which is widely used worldwide, specifies the dimensions of an A4 sheet. A4 paper measures 210 x 297 mm r 21 x 29.7 cm.

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Answer:

To compare the times of Paul and Jeff, we need to convert Paul's time to seconds.

Paul's time = 2 minutes 2 seconds = (2 x 60) + 2 = 122 seconds

Now we can compare their times:

Paul's time: 122 seconds

Jeff's time: 121 seconds

Jeff finished first since he has the lowest time.

Answer: To compare the times of Paul and Jeff, we need to convert Paul's time to seconds:

2 minutes and 2 seconds = 2 × 60 seconds + 2 seconds = 122 seconds

Now we can compare their times:

Paul finished in 122 seconds

Jeff finished in 121 seconds

Since Jeff's time is lower than Paul's time, Jeff finished first.

Step-by-step explanation:

The present value of the annuity is $189,468.24 if the initial payment is $1,000 and the monthly interest rate is 0.3333%.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To solve this problem, we need to first find the monthly interest rate since the payments are made monthly. The monthly interest rate can be found by dividing the annual interest rate by 12:

i = 4% / 12 = 0.3333% per month

Next, we need to find the present value of the annuity. We can use the formula for the present value of an annuity-immediate:

[tex]PV = P * (1 - (1 + i)^{-n}) / i[/tex]

where PV is the present value, P is the monthly payment, i is the monthly interest rate, and n is the number of payments.

The first year, the payments are level, so we can use the formula with n = 12 to find the present value of the payments for the first year:

[tex]PV1 = 1000 * (1 - (1 + 0.003333)^{-12}) / 0.003333 = \$11,887.87[/tex]

For the second year, the payments increase by 2%, so the monthly payment for the second year will be:

P2 = 1000 * 1.02 = $1,020

We can then use the formula again with n = 12 to find the present value of the payments for the second year:

[tex]PV2 = 1020 * (1 - (1 + 0.003333)^{-12}) / 0.003333 = \$12,061.92[/tex]

We can continue this process for the remaining 18 years, increasing the payment by 2% each year. The total present value of the annuity is the sum of the present values of each year's payments:

PV = PV1 + PV2 + ... + PV20 = $189,468.24

Therefore, the present value of the annuity is $189,468.24 if the initial payment is $1,000 and the monthly interest rate is 0.3333%.

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Answer:

number is 8

Step-by-step explanation:

let the number be n then trebling it ( multiplying it by 3 ) is 3n, then subtracting 6 from this is 3n - 6 , so

3n - 6 = 18 ( add 6 to both sides )

3n = 24 ( divide both sides by 3 )

n = 8

that is the number thought of is 8

By answering the above question, we may infer that As a result, (x, y) = is the answer to the system of equation (3, 0).

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The equations in the system are:

x + 2y = 3 ... (1)

x - 3y = 3 ... (2)

We may use equation (2) to solve for x in terms of y:

x = 3 + 3y

If this value of x is substituted into equation (1), the result is:

(3 + 3y) + 2y = 3

If we simplify this equation, we get:

5y = 0

Hence, y = 0. Inputting y = 0 into the equation we found for x results in:

x = 3 + 3(0) = 3

As a result, (x, y) = is the answer to the system of equations (3, 0).

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Answer:1004.8

Step-by-step explanation:

divide 8 by 2 since we need the radius which gives us 4. Then square it by the second power which will give you 16 since 4x4 equals 16. Then multiply 16 by pie/3.14 and you should get 50.24. then multiply it by the height which is 20in and you should get the answer which is 1004.8

The worker worked 38 + 5 = 43 hours that week.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let's break this problem down into two parts.

Part 1: Calculating the base pay for the 38 hours worked

The worker earned #80 per hour for a 38-hour week, so the base pay for those 38 hours would be:

Base pay = #80/hour x 38 hours = #3040

Part 2: Calculating the overtime pay for the additional hours worked

To find out how many hours were worked beyond the 38-hour week, we can use the fact that the total pay for the week was #3640. We know that the base pay for 38 hours was #3040, so the remaining #600 must be the overtime pay.

Since the company pays overtime at a time and a half, we can use this to find out how many hours were worked beyond the 38-hour week:

Overtime pay = (#80/hour x 1.5) x (number of overtime hours)

We can rearrange this equation to solve for the number of overtime hours:

Number of overtime hours = Overtime pay / (#80/hour x 1.5)

Number of overtime hours = #600 / (#80/hour x 1.5) = 5

Therefore, the worker worked 38 + 5 = 43 hours that week.

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Atul's father is mistaken, and Atul's request for an increase in his allowance may be valid based on the information given.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

To determine whether Atul's allowance is above or below the average, we need to calculate the average allowance for all the friends, including Atul.

To do his, we add up all the amounts and divide by the total number of friends:

Average allowance = (120+180+100+50+250+200+200+220+150+100+100+150+130+200+180+100+150+100+180+150+120+150+100+150+100+120+180+200+50) / 29

Average allowance = 162.07

So, the average allowance for Atul's friends, including himself, is Rs. 162.07 per day.

Since Atul's allowance is Rs. 120 per day, we can see that his allowance is actually less than the average.

Therefore, Atul's father is mistaken, and Atul's request for an increase in his allowance may be valid based on the information given.

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The food will last the other scouts for 8 days

At a scout's camp, the food will last 72 scouts for 6 days

The first step is to multiply both values(the number of scouts and the number of days spent in the camp)

= 72 × 6

= 432

The number of scouts at the camp can be calculated by subtracting the number of scouts present from the number of days the scouts spent at the camp

= 72-18

= 54

The amount of food left can be calculated as follows

= 432/54

= 8

Hence the food will last for 8 days

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