Solve the following radical equation.

6y2−22y+16⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√+4=4y
Write your answer(s) beginning with the first answer box. If applicable, the second answer box may be left blank.

The equation of the quartic function is f(x) = x⁴ - 18 · x² + 6 · x + 72.

Herein we must construct at least a polynomial that satisfies all conditions described in the statement. According to the fundamental theorem of algebra, quartic functions may have no real roots, two real roots or four real roots, which means that one of the roots must have a multiplicity of 2.

The root with a multiplicity of 2 is x = 3 and both x = - 4 and x = - 2 have only a multiplicity of 1, then we have the following expression by using the factor form of the definition of polynomials:

f(x) = (x - 3)² · (x + 4) · (x + 2)

Now we expand the expression to get the standard form:

f(x) = (x² - 6 · x + 9) · (x² + 6 · x + 8)

f(x) = x⁴ - 6 · x³ + 9 · x² + 6 · x³ - 36 · x² + 54 · x + 8 · x² - 48 · x + 72

f(x) = x⁴ - 18 · x² + 6 · x + 72

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Answer:

Assume you are working with a standard deck of 52 cards. There are 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace) in each of four suits

and spades).

What is P(Jack Heart) if you draw one card? 13

None of the equation of the line is parallel because there slope are not equal.

Parallel line have the same slope.

Therefore, using slope intercept equation,

y = mx + b

where

Hence,

y = −5x − 5 , slope = -5

x + 12y = −4; y = -1 / 3 - 1 / 12 x, slope = 1 / 12

y = −2x + 4: slope = -2

y + 8 = -15x + 135; y  = -15x + 127, slope  = -15

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The current yield of the bond is 9.27%.

What is current yield?

Current yield is the bond rate of return computed as the annual coupon divided by the current price of the bond

The annual coupon is the coupon rate of 10% multiplied by the bond's par value of 100

annual coupon=10%*100

annual coupon=10

current bond price=107.87

current yield=annual coupon/current bond price

current yield=10/107.87

current yield=9.27%

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Answer:  [tex]y=\frac{13}{2} x+3[/tex]

Step-by-step explanation:

Remember the point-slope equation which is [tex]y-y_{1} = m(x-x_{1} )[/tex]  where[tex](x_{1} , y_{1} )[/tex] is your point and [tex]m[/tex] is your slope.

Given that we substitute what you have:

[tex]y-(-10) =\frac{13}{2} (x - (-2))[/tex]

Minus and minus give us positive:

[tex]y+10 =\frac{13}{2} (x +2)[/tex]

Multiply slope into the parenthesis:

[tex]y+10= \frac{13}{2}x + \frac{13}{2}*2\\[/tex]

Calculate it:

[tex]y+10= \frac{13}{2}x +13[/tex]

Isolate the [tex]y[/tex] by subtracting 10 from both sides:

[tex]y=\frac{13}{2} x + 13 -10[/tex]

Your final equation is:

[tex]y=\frac{13}{2} x +3[/tex]

Hope this makes sense!

And here's the graph to prove that the line actually goes through the point [tex](-2,-10)[/tex]:

The price elasticity of demand is 1.90.

Price elasticity of supply measures the responsiveness of quantity supplied to changes in price of the good. It is expected that quantity supplied would be positively related to the price of the good.

Price elasticity of supply = percentage change in quantity supplied / percentage change in price

55% / 29% = 1.90

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Answer:

-8 x^2
1.25 x^2
1/2 x^2

Step-by-step explanation:

They are like terms because they have the same variable x^2, yx^2 is not the same because it has the variable y

Answer:

the 2nd, 3rd and 4th options (all with x²)

Step-by-step explanation:

"like terms" means the exactly same variable(s) with exactly the same exponents of these variables.

constants in the terms can be different and even have different signs.

5yx² is not "like", because of the additional y variable.

The story problem that aligns with the division problem is A. A whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the whiteboard?

From the information given, it can be seen that 1/2 is divided by 2/5.

In this case, the story that aligns with it is that a whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the whiteboard?

In this case, the length is multiplied by width to get the area.

Therefore, the correct option is A.

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Answer:

305.25

Step-by-step explanation:

18.5 for one floor, multiply by 15 to get the amount for 15 floors: 18.5*15 = 277.5 sheets

We need to add 10% for waste, meaning 277.5 plus the waste: 1.1*277.5 = 305.25

The drywaller needs to order 306 core boards for the 15-story elevator shaft, considering the 10% waste.

calculate the number of core boards needed for the 15-story elevator shaft, we can follow these

Calculate the total number of sheets for all floors:

Total sheets = Number of floors × Sheets per floor

Total sheets = 15 floors × 18.5 sheets per floor

Total sheets = 277.5 sheets

Add 10% of the total for waste:

Waste percentage = 10% = 0.10 (in decimal form)

Waste sheets = Total sheets × Waste percentage

Waste sheets = 277.5 sheets × 0.10

Waste sheets = 27.75 sheets

Calculate the final number of boards needed (including waste):

Number of boards = Total sheets + Waste sheets

Number of boards = 277.5 sheets + 27.75 sheets

Number of boards = 305.25 sheets

Since you can't have a fraction of a sheet, we need to round up to the nearest whole number.

Therefore, the drywaller needs to order 306 core boards for the 15-story elevator shaft, considering the 10% waste.

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The information given about the landscape is illustrated below:

a. You'll need a measuring tape, two range poles, pegs, and three people.

The first person holds the zero mark between their thumbs and fingers, the second person holds the 3m mark on the tape between their thumbs and fingers, and the third person holds the 8m. When all sides of the rope are stretched, a triangle is created, and an angle near one is a right angle.

Wrap one loop of the rope around peg A with a peg through the other loop, draw a circle on the ground, place pegs B and C where the circle crosses the base line, and place peg D half way between pegs B and C, allowing pegs D and A to form lines perpendicular to the base line, forming a right angle.

B. Method 1; Take a measurement of the distance between both trees and divide by 2 to get the midpoint.

Method 2; By use of a compass to bisect the distance between both points.

Method 3; By using a protractor to mark the 90° vertical point when placed between the two endpoints.

C The three different ways he can do this.

1) by using a protractor

2) by finding a point

3) by extending the line of the angle until it reaches the other side of the field.

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Substitute [tex]u=x^2+4[/tex] and [tex]du=2x\,dx[/tex]. Then the integral transforms to

[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \int \frac{du}{u^3}[/tex]

Apply the power rule.

[tex]\displaystyle \int \frac{du}{u^3} = -\dfrac1{2u^2} + C[/tex]

Now put the result back in terms of [tex]x[/tex].

[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \left(-\dfrac1{2u^2} + C\right) = -\dfrac1{4u^2} + C = \boxed{-\dfrac1{4(x^2+4)^2} + C}[/tex]

Answer: False

Step-by-step explanation:

G(x) is not a one-to-one function (since it fails the horizontal line test). Therefore, it doesn't have an inverse.

Answer:

A) 69

Step-by-step explanation:

• First , we put the numbers of the distribution in order:

60 , 66 , 72 , 78 , 80 , 82 , 88 , 90

• Notice that the set has 8 numbers which is an even number.

Then

→ the lower quartile is the mean of the set :

60 , 66 , 72 , 78

Which is the average of the two middle numbers 66 and 72.

Then

[tex]\text{the lower quartile}=\frac{66+72}{2} = 69[/tex]

Answer:

150 student tickets and 375 adult tickets

Step-by-step explanation:

Let x = # of student tickets sold, and y = # of adult tickets sold.

Total of 525 tickets were sold, so the first equation is x + y = 525. The register gained $8325, so 10.50x + 18y = 8235 is the second equation.

x + y = 525

10.50x + 18y = 8325

18x + 18y = 9450

10.50x + 18y = 8325

7.5x = 1125

x = 150

150 + y = 525

y = 375

The solution to the system of inequalities is (0.667, 5.333)

The system of inequalities is given as:

y > 2x + 4

x + y ≤ 6

Next, we plot the graph of the system using a graphing tool

From the graph, both inequalities intersect at

(0.667, 5.333)

Hence, the solution to the system of inequalities is (0.667, 5.333)

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Answer:

A. The reference angle measures 78 degrees

Using proportions, it is found that they must win 19 of their next 30 games.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

We want a win-to-loss proportion of 2:1, which is equivalent to a win-to-total proportion of 2:3. We have that:

Hence:

[tex]\frac{5 + x}{36} = \frac{2}{3}[/tex]

3(5 + x) = 72

15 + 3x = 72

3x = 57

x = 19.

The Rangers must win 19 of their next 30 games.

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Based on the calculations, all of the numbers belong to this arithmetic sequence.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

[tex]a_n = a_1 +(n-1)d[/tex]

Where:

Next, we would determine the common difference as follows:

d = a₂ - a₁

d = 105 - 99 = 6.

d = a₃ - a₂

d = 111 - 105 = 6.

d = a₄ - a₃

d = 117 - 111 = 6.

Based on the calculations, all of the numbers belong to this arithmetic sequence.

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Complete Question:

What is the number that does not belong to this sequence 99, 105, 111, 117, 123, 129, 135, 141, 147, 153

The amount that will be in the account after 30 years is $162,272.32.

When an amount is compounded annually, it means that once a year, the amount deposited and the interest already accrued increases in value. Compound interest leads to a higher value of deposit when compared with simple interest, where only the amount deposited increases in value once a year.

The formula that can be used to determine the future value of the yearly deposit of $4,000 in 30 years is : annuity factor x yearly deposit

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$4000 x [{(1.02^30) - 1} / 0.02] = $162,272.32

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The quantity of each concentrations of 3% and 9% needed to get the desired concentration is 54 milliliters and 27 milliliters respectively

Let

x + y = 81

0.03x + 0.09y = 81 × 5%

0.03x + 0.09y = 4.05

x + y = 81

0.03x + 0.09y = 4.05

From (1)

x = 81 - y

0.03x + 0.09y = 4.05

0.03(81 - y) + 0.09y = 4.05

2.43 - 0.03y + 0.09y = 4.05

- 0.03y + 0.09y = 4.05 - 2.43

0.06y = 1.62

y = 1.62/0.06

y = 27

x = 81 - y

x = 81 - 27

x = 54

Simultaneous equation:

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The equation that shows the relationship between the number of paragliding trips, adventure tours, and his total pay is 55a + 75p = 2725

An equation is an expression that shows the relationship between two or more numbers and variables.

Let a represent the number of adventure tours and p represent the number of paragliding trip, hence:

55a + 75p = 2725

The equation that shows the relationship between the number of paragliding trips, adventure tours, and his total pay is 55a + 75p = 2725

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The points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24))

The circle equation is given as:

(x-3)^2 +(y+2)^2= 49

Rewrite as:

(y+2)^2= 49 -(x-3)^2

Take the square root of both sides

y+2= ±√[49 -(x-3)^2]

Subtract 2 from both sides

y = -2 ± √[49 -(x-3)^2]

Next, we determine the points

Set x = 3

y = -2 ± √[49 -(3-3)^2]

Evaluate

y = -2 ± 7

Solve

y = 5 and y = -9

So, we have

(x, y) = (3, 5) and (3, -9)

Set x = 8

y = -2 ± √[49 -(8-3)^2]

Evaluate

y = -2 ± √24

Solve

y = -2 - √24 and y = -2 + √24

So, we have

(x, y) = (8, -2 + √24) and (8, -2 - √24)

Hence, the points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24)

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Using the Fundamental Counting Theorem, it is found that:

The 2 people can arrange themselves in 40 ways.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

With one people in the aisle and one in the normal seats, the parameters are:

n1 = 4, n2 = 7

With both in the aisle, the parameters is:

n1 = 4, n2 = 3

Hence the number of ways is:

N = 4 x 7 + 4 x 3 = 28 + 12 = 40.

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The zeros of the polynomial function are -1.728, 0.56 and 5.167

The polynomial function is given as:

x^3 - 4x^2 - 7x + 5

Next, we plot the graph of the polynomial

From the graph, the polynomial cross the x-axis when

x = -1.728, 0.56 and 5.167

Hence, the zeros of the polynomial function are -1.728, 0.56 and 5.167

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[tex]x {}^{(1)} = - 3 \: \: \: \: \: \: x {}^{(2)} = - 1[/tex]

The explicit formula that can be used to determine the number of wolves is w = 210 (1.0692^t) .

The first step is to determine the growth rate of the wolf species.

Growth rate = [(future population / present population)^(1/number of years)] - 1

[(410 / 210)^(1/10)] - 1 = 6.92

The exponential function would have the form:

FV = P (1 + r)^t

w = 210 (1.0692^t)

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In the given diagram, the length of CD is 12.7 cm

From the question, we are to determine the length of CD

First, we will calculate the length of CB

From the Pythagorean theorem,

|CA|² = |CB|² + |BA|²

12² = |CB|² + 6²

144 = |CB|² + 36

|CB|² = 144 - 36

|CB|² = 108

|CB| = √108

|CB| = 6√3 cm

Now, to find CD

Using SOH CAH TOA

sin55° = |CB| / |CD|

sin55° = 6√3 / |CD|

|CD| = 6√3 / sin55°

|CD| = 12.7 cm

Hence, the length of CD is 12.7 cm

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Using the z-distribution, it is found that she should take a sample of 46 students.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence, by the Empirical Rule the standard deviation is found as follows:

[tex]6\sigma = 800 - 200[/tex]

[tex]6\sigma = 600[/tex]

[tex]\sigma = 100[/tex]

The sample size is n when M = 29, hence:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]29 = 1.96\frac{100}{\sqrt{n}}[/tex]

[tex]29\sqrt{n} = 196[/tex]

[tex]\sqrt{n} = \frac{196}{29}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{196}{29}\right)^2[/tex]

n = 45.67.

Rounding up, a sample of 46 students should be taken.

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Answer: B

Step-by-step explanation: Trust me bro