classifying polynomials -8y

An equation of the parabola with focus (1, 6) and directrix y = 1 is: C. y = 1/10(x²) - 1/5(x) + 18/5

Mathematically, the standard equation of the directrix lines for any parabola is given by:

y = a(x - h)² + 2.

Where:

Since the directrix is horizontal, the axis of symmetry would be vertical. Therefore, the equation of this parabola would be modeled by this standard mathematical expression;

(x - h)² = 4p(y - k)

Where:

h = 1

In Mathematics, the focus for either a right or left parabola is modeled by this mathematical expression (h + p, k) while its directrix is modeled by this mathematical expression x = h - p;

k + p = 6

k - p = 1

Solving the set of linear equations simultaneously, we have:

2k = 7

k = 7/2

For the value of p, we have;

p = 6 - k

p = 6 - 7/2

p = 5/2

Substituting the given parameters into the formula, we have;

(x - 1)² = 4(5/2)(y - 7/2)

x² - 2x + 1 = 10(y - 7/2)

x² - 2x + 1 = 10y - 35

10y = x² - 2x + 1 + 35

10y = x² - 2x + 36

y = (x² - 2x + 36)/10

y = x²/10 - x/5 + 18/5

y = 1/10(x²) - 1/5(x) + 18/5

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The sum in simplest terms is 1/(p-6)

What is LCM?

Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least common multiple (LCM) of two numbers. It can also be computed for two or more different numbers. There are numerous ways to calculate the LCM of a given collection of numbers. Utilizing the prime factorization of each number and then calculating the product of the highest powers of the common prime factors yields the LCM of two integers in a short amount of time.

(16-p)/[ (p+4)(p-6) ] + 2/ (p+4)

Take LCM = (p+4)(p-6)

= [ 16-p + 2(p-6) ] / [  (p+4)(p-6)  ]

=  [ 16-p + 2p-12) ] / [  (p+4)(p-6)  ]

= ( p +4 ) / [  (p+4)(p-6)  ]

= 1/(p-6)

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The compound interest formula [tex]A = P(1 + r/n) ^nt[/tex] Monthly compounding is a common strategy used by interest-bearing CDs to boost returns. The annual interest rate is divided by twelve in this scenario.

After 4 years, you should have $763 in your account.After four years of saving $4 every month, your funds may reach $762.90. This includes a $500.00 initial balance and a 2.85% yearly rate of return.

Invest $500 in a 4-year certificate of deposit (CD) earning 2.85% interest compounded monthly.utilizing the compound interest formula [tex]A = P ( 1 + r / n ) ^{nt}[/tex]

The formula for calculating simple interest is S.I. = P R T, where P stands for principal, R for the annual percentage rate of interest, and T for time, which is typically expressed as the number of years. The interest rate is expressed as a percentage, or r%, and should be represented as r/100.

Many interest-bearing CDs use monthly compounding to increase returns. This model divides the annual interest rate by twelve.

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Answer:

Washer = $849

Dryer = $283

Step-by-step explanation:

Dryer = x

Washer = 3x

3x + x = 1132

Simplify:

4x = 1132

Divide both sides by 4:

x = 283

The dryer costs $283, and since the washer is three times the cost of the dryer, the washer is:

283x3 = 849

Answer:

25n+2 can be expressed as log,m^25+2.

Step-by-step explanation:

Since log,m=n, we can write 25n+2 as 25*log,m+2.

Using the property of logarithms that log,a+log,b=log,ab, we can rewrite 25*log,m as log,m^25.

The number of sets to be printed to ascertain at least 4 identical subset is there on the list when a computer is printing out subsets of a 5 element set is 97.

The total number of subset for a n element set is 2^{n}. Therefore, for a 5 element set is 2^{5} = 32.

Thus to ensure there are at least 4 identical subset, the computer should print 3 times the total number of subsets possible plus 1 additional subset, i.e. 3×32 + 1 = 97.

-- The question is incomplete, the correct question is as follows --

"A computer is printing out subsets of a 5 element set (possibly including the empty set). a. at least how many sets must be printed to be sure of having at least 4 identical subsets on the list?"

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The given statistic is said to be an "unbiased estimator". In this statistic, the mean is equal to the true value of the estimated parameter.

In a statistic, if the mean is equal to the estimated parameter, then that statistic is said to be an unbiased estimator. It is used to estimate a population parameter.

Consider a statistic.

"A statistic describes a portion of the target population".

"A parameter describes the whole population".

In a statistic, the mean of the sampling distribution is equal to the true value of the estimated parameter.

I.e., μ = E(x)

So, that statistic is said to be an unbiased estimator.

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The cost from company A and company B will be the same at 40 square feet of countertop

Given that:

Company A will sell Mikayla a countertop according to the given

graph, which includes a $1, 000 installation fee.

Company B will sell a countertop according to the values given in the

table, which includes an $800 installation fee and a constant rate of change

With this information, you can make cost function for both Company A and Company B

Company A

A linear function is of the form y = mx + c

where c is the y-intercept (starting point) and m is the slope (rate)

c = 1000  (from the graph)

m = 1150-1000 / 10-0  (By using the 2 points on the graph: m = y2-y1/x2-x1)

m = 15

y = mx + c

y = 15x+1000

Company B

c = 800  (given)

m = 1100-1000 / 15-10  (From table)

m = 100/5 = 20

y = mx + c

y = 20x+800

Equate the two cost functions and solve for x:

20x+800 = 15x+1000

20x-15x = 1000-800

5x = 200

x = 200/5

x = 40 square feet

Therefore, at 40 square feet of countertop, the cost from each company will be the same

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Answer:

Make the denominators equal by L.C.M

--> 8/20 + 5/20

--> 13/20

The value of x that makes the perimeters of the figures equal is; x = 3.

To find the perimeter of a figure, add all its side together. That is, the sum of all its sides will give you the perimeter.

Perimeter of the triangle = (x + 6) + 5x + (3x + 3)

Open the bracket and simplify

x + 6 + 5x + 3x + 3

Combine like terms

= 9x + 9

Perimeter of the square = 4(x + 6)

= 4(x) + 4(6)

= 4x + 24

Make both equation equal to each other and find x:

9x + 9 = 4x + 24

9x - 4x = -9 + 24

5x = 15

x = 3

The value of x is 3.

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The scale factor of triangle PQR to triangle STU is 3/2

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying.

Taking a point of reference say PR and SU

PR = 8

SU = 12

let the scale factor be r such that

8 * r = 12

r = 12 / 8

r  = 3/2

checking with other sides

PR to UT

6 * 2/3 = 9 correct

QP to TS

10 * 3/2 = 15 correct

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Answer:

the daily fee is 37 and the mileage charge is .24 per mile.

Step-by-step explanation:

256 = 450x + 4b

159 = 200x + 3b

Multiple the top equations by -3 all the way through the bottom equations by 4 all the way  through then add the equation together.

-768 = -1350x -12b

636 = 800x + 12b

-132 = -550x  Divide both sides by -550

.24 = x  This is the charge per mile.

Plug in .24 for x into either of the original 2 equations to solve for b which is the daily fee.

256 = 450(.24) = 4b

256 = 108 + 4b  Subtract 108 from both sides

148 = 4b  Divide both sides by 4

37 = b  This is the daily fee.

Compared to the graph of y = x graph y = -x/3 is a negative slope

Compared to the graph of y = x graph y = -x/3 intersects the y axis at same point

Compared to the graph of y = x graph y = x - 2 is a parallel line

Compared to the graph of y = x graph y = x - 2 intersects the y axis at 2 units down

The two graphs compared are linear function graphs

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

y = x

slope = 1

c = 0

y = -x/3

slope = -1/3

c = 0

y = x - 2

slope = 1

equal slopes means the lines are parallel

c = -2 (down 2 units)

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geologists unearth a sample of zircon that appears to be a closed system. they find 0.686 micro gram of 206 Pb for 1.000 micro gram of 238U present. approximately  3.7973 × 10⁹ years old is the sample.

The reciprocal of the time period during which the number of atoms in the radioactive element drops to almost A. 50% of its initial number is the decay constant.

According to the radioactive decay law, a nucleus's likelihood of decaying is a constant that is independent of time.

t1/2 of U₂₃₈ is 4.5 × 10⁹ years

moles of U₂₃₈ : (1 × 10⁻⁶ / 238) moles

moles of Pb₂₀₆ : (0.686 × 10⁻⁶ / 206) moles

Now, U₂₃₈ → Pb₂₀₆

As Pb₂₀₆ comes from U₂₃₈ hence,

moles of  U₂₃₈ decayed = moles of  Pb₂₀₆

                                        = (0.686 × 10⁻⁶ / 206) moles

Therefore, initial moles of U₂₃₈:

N₀ = [(1 × 10⁻⁶ / 238) + (0.686 × 10⁻⁶ / 206)] moles

and N = (1 × 10⁻⁶ / 238) moles

Now, λ (decay constant) = 0.693 / (t1/2)

                                        = 0.693 / ( 4.5 × 10⁹ years)

So,

t = 2.303 / λ × log (N₀ / N)

t = 2.303 / [0.693 / ( 4.5 × 10⁹ years)] × log [1 + (0.686/206)/(1/238)]

t = 14.95 × 10⁹ × 0.254

t = 3.7973 × 10⁹ years.

Thus, the sample is: 3.7973 × 10⁹ years old.

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The algebraic expression that can be represented by the statement is  43y + 16

From the question, we have the following statement that can be used in our computation:

16 more than the product of 43 and a number

Represent the variable with y

So, we have the following representation

16 more than the product of 43 and y

Express the product as an actual product

So, we have the following representation

16 more than  43y

more than as used here means addition

So, we have

43y + 16

Hence, the expression is (d) 43y + 16

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Answer: 43y + 16

Step-by-step explanation:

i did the test

The minimum value of the function y = 2(x - 3)² - 4 is -4. Domain of the function is set of all real numbers and the range is all real numbers ≥ -4.

Domain of a function y = f(x) is the set of all the values of x where the function is defined.

The range of the function is the set of all values of the function on the defined domain.

The given function is,

y = 2(x - 3)² - 4

y = 2(x² - 6x +9) - 4

y = 2x² - 12x + 14

This is a quadratic function and the graph of the function will be a parabola.

The parabola is directed upwards if the coefficient of x² in a quadratic equation is positive and so will be having a minimum value.

The parabola is directed downwards if the coefficient of x² is negative and so will be having the maximum value for the function.

Here, coefficient of x² = 2, is positive.

So there will be a minimum value.

The value of [tex]\frac{-b}{2a}[/tex] in the quadratic equation ax² + bx + c, is the x value of the vertex of the parabola.

x = - (-12) / (2 × 2) = 3

∴ Minimum value, y = 2 (3 - 3)² - 4 = -4

Domain of the function will be the set of all real numbers because the function is defined for all real numbers.

The range will be all real numbers ≥ -4, because any values of x in the function does not make the value of the function less than -4.

Hence the minimum value of the function is -4 and the domain and the range of the function is set of all real numbers and all real numbers ≥ -4 respectively.

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Dean will take a total time of 3 hours and 10 minutes to complete the race and will beat his personal best time

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the personal best time of Dean be = A

Now , the value of A = 3 hours 14 minutes 45 seconds

And ,

The time taken by Dean to complete 1 km = 9 minutes 30 seconds

Now , the total distance of the race lap = 20 km

So , the equation will be

Total time taken by Dean to complete 20 km race B = 20 x time taken by Dean to complete 1 km

Substituting the values in the equation , we get

Total time taken by Dean to complete 20 km race = 20 x 9 minutes 30 seconds

Total time taken by Dean to complete 20 km race = 20 x 9 minutes + 20 x 30 seconds

Total time taken by Dean to complete 20 km race = 180 minutes + 600 seconds

1 hour = 60 minutes

1 minute = 60 seconds

180 minutes = 3 hours

600 seconds = 10 minutes

So , the equation is

Total time taken by Dean to complete 20 km race B = 3 hours 10 minutes

So , the value of B < value of A

Therefore , the Dean will beat his personal best time and the race is completed in 3 hours 10 minutes

Hence , Dean will take a total time of 3 hours and 10 minutes to complete the race and will beat his personal best time

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Answer:

statements 2 and 3 are true

Step-by-step explanation:

using the rule of exponents

[tex]a^{0}[/tex] = 1

then

1 [tex]a^{0}[/tex]≠ a ← lie

2 [tex]x^{0}[/tex] = 1 ← true

3 [tex]5^{0}[/tex] = 1 ← true

The total of his sales for that week is $49,500.

Given :

Nate Belloir earns a weekly commission of 2. 5% on sales of $50,000 or less and 3. 0% on sales in excess of $50,000. One week Nate's commission was $2,135.

Let x be the total sales.

2135 = 2.5 % * 50000 + 3 % (x - 50000 )

= 2.5 * 50000 / 100 + 3/100 ( x - 50000 )

1235 = 2.5 * 500 + 0.03x - 0.03 * 50000

1235  = 1250 + 0.03x - 1500

0.03x = 1235 - 1250 + 1500

0.03x = -15 + 1500

0.03x = 1485

multiply by 100 on both sides

0.03x * 100 = 1485 * 100

3x = 148500

x = $49500

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The probability that a child chosen at random from the school arrives by car is the total of the column Car 74%.

Describe probability using an example?

By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained.

                           The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.

You can build a two-way relative frequency table to represent the data:

These are the columns and rows:

              Car         No car      Total

Boys

Girl

Total

Fill the table

30% of the children at the school are boys

            Car         No car      Total

Boys                                       30%

Girl

Total

60% of the boys at the school arrive by car

That is 60% of 30% = 0.6 × 30% = 18%

            Car         No car      Total

Boys      18%                         30%

Girls

Total

By difference you can fill the cell of Boy and No car: 30% - 18% = 12%

            Car         No car      Total

Boy       18%           12%         30%

Girl

Total

Also, you know that the grand total is 100%

            Car         No car      Total

Boy       18%           12%         30%

Girl

Total                                     100%

By difference you fill the total of Girls: 100% - 30% = 70%

            Car         No car      Total

Boy       18%           12%         30%

Girl                                         70%

Total                                     100%

80% of the girls at the school arrive by car

That is 80% of  70% = 0.8 × 70% = 56%

            Car         No car      Total

Boy       18%           12%         30%

Girl       56%                         70%

Total                                     100%

Now you can finish filling in the whole table calculating the differences:

            Car         No car      Total

Boy       18%           12%         30%

Girl        56%         14%         70%

Total     74%          26%      100%

Having the table completed you can find any relevant probability.

The probability that a child chosen at random from the school arrives by car is the total of the column Car 74%.

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Answer:

The number is 15

Answer:

15

Step-by-step explanation:

The number is between 10 and 20.

10 11 12 13 14 15 16 17 18 19 20

The number is composite or have more than 2 factors.

10 12 14 15 16 18 20

The number is odd.

15

Answer:2p

Step-by-step explanation:

Answer: it is 8103.38

Step-by-step explanation:

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$120000\\ r=rate\to 11.5\%\to \frac{11.5}{100}\dotfill &0.115\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &7 \end{cases}[/tex]

[tex]A=120000\left(1+\frac{0.115}{1}\right)^{1\cdot 7} \implies A \approx 257101.92 \\\\\\ \underset{earned~interest}{\stackrel{257101.92 - 120000}{\text{\LARGE 137101.92}}}\hspace{10em}\underset{adjusted~balance}{\stackrel{257101.92 - 25000}{\text{\LARGE 232101.92}}}[/tex]

Given that he is running on a treadmill at a pace of 7.2 miles per hour, the necessary expression will be y=7.2x.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.

Here,

Speed of him=7.2 miles/hour

Let y be the total distance and x be the number of hours,

speed=distance/time

7.2=y/x

y=7.2x

The required expression will be y=7.2x as he is running on a treadmill at a speed of 7. 2 miles per hour.

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The percent increase is 56%

The percent increase if the airline charges an additional $50 baggage fee with the new ticket price is 76%

The formula for determining percent increase is expressed as;

Percent increase = x₂ - x₁/x₁  × 100/ 1

Where;

Now, substitute the values, we have;

Percent increase = $320 - $210/$210  × 100/ 1

Find the difference

Percent increase = $110/$210  × 100/ 1

Percent increase = 0. 52  × 100/ 1

Multiply through

Percent increase = 52%

If there is an increase of $50

Percent increase = $370-210/210 × 100/ 1

= 160/210 × 100/ 1

= 76%

Hence, the values are 52% and 76% respectively,

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Answer:

It would be most appropriate to use the mode for categorical data, such as favorite ice cream flavor. This is because you can't use mean or median for flavors such as chocolate or vanilla, so mode would make the most sense there.