NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #2

The zeros of the function are:

-¹/₂ ± √((3)/2) i, 1/3 and - 2

We want to find the Zeros of the polynomial:

f(x) = 3x⁴ + 8x³ + 6x² + 3x - 2

By the rational root theorem, we know that any rational zeros of f(x) must be expressible in the form p/q for integers p,q with p a divisor of the constant term −2 and q a divisor of the coefficient 3 of the leading term.

Therefore, the only possible rational zeros are:

±¹/₃, ±²/₃, ±1, ±2

Let's check x = 1/3 to get:

f(¹/₃) = 3(¹/₃)⁴ + 8(¹/₃)³ + 6(¹/₃)² + 3(¹/₃) - 2 = 0

f(-2) = 3(-2)⁴ + 8(-2)³ + 6(-2)² + 3(-2) - 2 = 0

Thus, x = 1/3 and - 2 are zeros of the function and (3x - 1) and (x + 2) are factors.

Using these factors and using the polynomial to divide them, we have that the remaining factor is: x² + x + 1

The zeros of x² + x + 1 are the Complex cube roots of 1, since

(x - 1)(x² + x + 1) = x³ - 1

using the quadratic formula, we have:

x = -¹/₂ ± √((3)/2) i

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If a rectangle has a perimeter of 48 in. the length and width are scaled by a factor of 2.5, the perimeter of the resulting rectangle is 225 inches.

Let L be the length of the original rectangle and W be the width. Then, the perimeter of the original rectangle is P = 2L + 2W = 48 inches.

If we scale the length and width by a factor of 2.5, we get a new length of 2.5L and a new width of 2.5W. The perimeter of the new rectangle would be:

P' = 2(2.5L) + 2(2.5W)

= 5L + 5W

To find the new perimeter, we need to find the new values of L and W. Since the length and width are scaled by the same factor, we can write:

2.5L = kL

2.5W = kW

where k is the scaling factor.

Since the new rectangle is scaled by a factor of 2.5, k = 2.5. Therefore:

L' = 2.5L = 2.5(12) = 30 inches

W' = 2.5W = 2.5(6) = 15 inches

The new perimeter is:

P' = 5L' + 5W'

= 5(30) + 5(15)

= 225 inches

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Answer:

Area of annulus is 40.85cm² to 2d.p

Step-by-step explanation:

Area of shaded part=Area of bigger circle -Area of smaler circle

Area of annulus= πR²- πr²= π(R²-r²)

A=3.142(7²-6²)

A=3.142(49-36)

A=3.142×13

A=40.846cm²

A=40.85cm² to 2d.p

a.

i. 10% of $110,000 = $11,000 down payment

ii. Loan (mortgage) = $110,000 - $11,000 = $99,000

iii. Monthly payment = P * r * (1 + r)n / ((1 + r)n - 1), where P represents the principal amount, r represents the monthly interest rate, and n represents the number of monthly installments.

First, we must determine the quantity of monthly payments. Because it is a 30-year loan, the monthly installments are 30 * 12 = 360.

The monthly interest rate of 9% divided by 12 equals 0.0075.

When we plug in the values, we get:

$793.07 monthly payment

iv. Loan total interest paid = (monthly payment * number of instalments) - principal amount = ($793.07 * 360) - $99,000 = $184,465.20

b

i. Reduction in loan balance = $99,000 - $88,536 = $10,464

ii. To date, the total amount paid to the loan firm is (monthly payment * a number of payments) = ($793.07 * 120) = $95,168.40.

We multiplied by 120 (rather than 10*12) because we're computing total payments made so far, not the total payments made over the life of the loan.

iii. Total interest paid thus far = total money given to the loan business minus principal amount = $95,168.40 - $99,000 = -$3,831.60

The negative figure shows that the interest paid thus far has been less than the principal amount. This is because, in the early phases of the loan, the majority of the monthly payment goes towards interest, with only a little portion going toward principal reduction.

iv. Home equity  = value of the home - remaining debt

= $150,000 - $88,536

= $61,464

c.

i. New monthly payment = P * r * (1 + r)n / ((1 + r)n - 1), where P represents the remaining loan value, r represents the new monthly interest rate (6% / 12 = 0.005), and n represents the number of monthly payments remaining (360 - 120 = 240).

When we plug in the values, we get:

$63.63 is the new monthly payment.

Total interest paid on the new loan during the life of the loan = (new monthly payment * number of payments) - remaining loan balance = ($63.63 * 240) - $88,536 = $32,028.40

d.

Monthly savings = old monthly payment minus new monthly payment = $793.07 - $63.63= $729.44

Total interest paid on the new loan during the life of the loan = (new monthly payment * number of payments) - remaining loan balance = ($63.63 * 360) - $88,536 = $37,847.80

Because the new loan is being paid off over a longer period of time, the total interest paid during the life of the new loan is more than the remaining interest on the previous loan.

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Step-by-step explanation:

Using the distance formula, we know that the distance between points A and B is:

sqrt((3 - 0)^2 + (a - 4)^2) = 5

Simplifying:

sqrt(9 + (a - 4)^2) = 5

Squaring both sides:

9 + (a - 4)^2 = 25

Simplifying:

(a - 4)^2 = 16

Taking the square root of both sides (note that we can take the positive or negative square root since both will satisfy the equation):

a - 4 = ±4

Solving for a:

a - 4 = 4 or a - 4 = -4

a = 8 or a = 0

However, we need to check that these values of a actually make sense based on the given information. If a = 0, then the distance between A and B is:

sqrt((3 - 0)^2 + (0 - 4)^2) = sqrt(9 + 16) = 5

So a = 0 is a valid solution. If a = 8, then the distance between A and B is:

sqrt((3 - 0)^2 + (8 - 4)^2) = sqrt(9 + 16) = 5

So a = 8 is also a valid solution.

Therefore, the possible values of a are a = 0 or a = 8.

The value of a can be 0 or 8 if the distance between the given points is 5.

A straight line drawn between two points is the shortest distance between the two points. We can calculate the shortest distance by the distance formula.

Let A(0,4) = (x1,y1)

     B(3,a) = (x2,y2)

Using distance formula,

[tex]D = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

As distance = 5 units

Therefore,

[tex]\sqrt{(x2-x1)^2 + (y2-y1)^2} = 5[/tex]

[tex]\sqrt{(3-0)^2 + ((a-4)^2} = 5[/tex]

[tex]\sqrt{(3)^2 + (a^2 + 16 + - 8a)} = 5[/tex]

[tex]\(9 + 16 + a^2 - 8a = 25[/tex]

[tex]25 + a^2 -8a = 25[/tex]

[tex]a^2 - 8a = 0[/tex]

[tex]a(a-8) = 0[/tex]

a = 0 and a = 8

Therefore, the answer is 0 or 8.

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The graph that shows the image of ABC after a rotation about the origin is the graph d

Rotation about the origin is a transformation in which a point or object is rotated around the origin (0, 0) by a certain angle. The origin is the fixed point of the rotation, and all other points move in a circular path around the origin.

To perform a rotation about the origin, you need to know the angle of rotation, the coordinates of the point or object being rotated, and the direction of rotation (clockwise or counterclockwise).

Using the above as a guide, we have the following:

The graph after a rotation about the origin is the graph (d)

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After multiplying (−3x+4) with (2x−1) we get a quadratic equation which is equal to −6x² + 11x − 4.

To multiply the expressions (−3x+4)(2x−1), we use the distributive property of multiplication:

(−3x+4)(2x−1) = −3x(2x) + 4(2x) − 3x(−1) + 4(−1)

Simplifying the above expression, we get:

= −6x² + 8x + 3x − 4

= −6x² + 11x − 4

Therefore, the product of (−3x+4)(2x−1) is −6x² + 11x − 4.

We can also use the FOIL method to multiply the two expressions:

(−3x+4)(2x−1) = −3x(2x) −3x(−1) + 4(2x) + 4(−1)

= −6x² + 3x + 8x − 4

= −6x² + 11x − 4

Either method can be used to get the same result.

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Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by

[tex]\text{Z}=\dfrac{\text{X}-\mu}{\sigma}[/tex]

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X.

In this problem, we have that:

A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm, so [tex]\mu=49.9,\sigma=3.74[/tex].

What is the length in cm of the longest 15% of Atlantic cod in this area?

We have to find the value of X for the value of Z that has a p-value of 0.85.

Looking at the z-score table, we have that Z = 1.04 has a p-value of 0.8508. So, we have to find the value of X when .

So

[tex]\text{Z}=\dfrac{\text{X}-\mu}{\sigma}[/tex]

[tex]1.04=\dfrac{\text{X}-49.9}{3.74}[/tex]

[tex]\text{X}-49.9=3.8896[/tex]

[tex]\text{X}=53.7896[/tex]

The length of the longest 15% of Atlantic cod in this area is 53.79 cm, rounded to 2 decimal places.

Answer:

Step-by-step explanation:

To compute the break-even sales (in barrels) for the current year, we need to first determine the contribution margin per barrel, which is the amount left over from the selling price of each barrel of beer after variable costs are subtracted.

Variable costs per barrel can be calculated as 75% of the cost of goods sold per barrel, which is:

Variable cost per barrel = (75% x Cost of goods sold) / Barrels sold

Variable cost per barrel = (0.75 x $1,628 million) / 37 million barrels

Variable cost per barrel = $33.00

Similarly, the variable marketing, general, and administration expenses per barrel can be calculated as:

Variable marketing, general, and administration expenses per barrel = (50% x Marketing, general, and administration expenses) / Barrels sold

Variable marketing, general, and administration expenses per barrel = (0.50 x $592 million) / 37 million barrels

Variable marketing, general, and administration expenses per barrel = $8.00

Therefore, the contribution margin per barrel is:

Contribution margin per barrel = Selling price per barrel - Variable costs per barrel

Contribution margin per barrel = $6,512 million / 37 million barrels - $33.00 - $8.00

Contribution margin per barrel = $98.00

To compute the break-even sales (in barrels) for the current year, we can use the following formula:

Break-even sales (in barrels) = Fixed costs / Contribution margin per barrel

Fixed costs can be calculated as:

Fixed costs = Income from operations + Variable marketing, general, and administration expenses x Barrels sold - Contribution margin per barrel x Barrels sold

Fixed costs = $4,292 million + $8.00 x 37 million barrels - $98.00 x 37 million barrels

Fixed costs = $1,108 million

Substituting this into the formula, we get:

Break-even sales (in barrels) = $1,108 million / $98.00 per barrel

Break-even sales (in barrels) = 11.29 million barrels

Rounding this to two decimal places and converting to millions, we get:

Break-even sales (in barrels) = 11.29 million barrels = 11.3 million barrels (rounded)

Answer:

percentage increase: 43,75%

Step-by-step explanation:

If we want to solve thai as an equation, we can write:

800 + (x/100) * 800 = 1150

we multiply: 800 + 800x/100 = 1150

we simplify: 800+ 8x = 1150

we bring the unknown to the left, and numbers to the right:

8x = 1150 - 800

8x = 350

we find x by dividing each part by 8

x= 43,75

(note that the x/100 in the first equation is the same thing as writing x%, so 800 plus a percentage of 800 is equal to 1150)

The equation is 2m + 4s = 16 and the table of values is solved

Given data ,

Let the equation be represented as A

Now , the value of A is

2m + 4s = 16

when m = 0

4s = 16

s = 4

when s = 3

2m + 12 = 16

2m = 4

m = 2

when m = -2

-4 + 4s = 16

4s = 20

s = 5

when s = 0

2m = 16

m = 8

Therefore , the table of values for m = { 0 , 2 , -2 , 8 } and the table of values for s = { 4 , 3 , 5 , 0 }

Hence , the equation is solved

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Answer:

7,920

Step-by-step explanation:

I took test and got 100%

In the cylinder , height of the water tank is 5.5 feet.

What is volume?

The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.

Given that,

A cubic foot contains roughly 7.48 liquid gallons.

We have to find what is roughly the height of a cylindrical water tank with a capacity of 1,500 liquid gallons and a radius of 3.4 feet.

We know that,

7.48 liquid gallons are contained in one cubic foot.

The cylindrical water tank's radius is 3.4 feet.

1,500 liquid gallons are the maximum capacity.

The cylindrical water tank's volume is calculated to hold 1500 liquid gallons ,

= [tex]\frac{1500}{7.48}[/tex]

= 200.53 ft³

Volume of the cylinder= πr²h

=> 200.53= 3.14 ×3.4×3.4×h

=> 200.53 = 3.14 × 11.56 × h

=> 200.53 = 36.29 × h

=> h= 5.5

=> h= 5.5 feet (Approximately)

Therefore, height of the water tank is 5.5 feet.

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Answer:

The correct answer is D. 5.4% after rounding my answer off to the nearest tenth of a percent.

The graph of your equation is a parabola with x-intercepts at x = -8.75 and x = 7.25.

x = -8.75; x = 7.25

2(x + ¾)² - 5 = 123

Add 5 to each side:                     2(x+ ¾)² = 128

Divide each side by 2:                   (x+ ¾)² = 64

Take the square root of each side: x + ¾ = 8       x + ¾ = -8

Subtract ¾ from each side:                     x = 8 - ¾        x = -8 - ¾

Convert to decimal fraction:                    x = 8 - 0.75    x = -8 – 0.75  

Subtract:                                                   x = 7.25           x = -8.75

The graph of your equation is a parabola with x-intercepts at x = -8.75 and x = 7.25.

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The graph of your equation is a parabola with x-intercepts at x = -8.75 and x = 7.25.

x = -8.75; x = 7.25

2(x + ¾)² - 5 = 123

Add 5 to each side:                     2(x+ ¾)² = 128

Divide each side by 2:                   (x+ ¾)² = 64

Take the square root of each side: x + ¾ = 8       x + ¾ = -8

Subtract ¾ from each side:                     x = 8 - ¾        x = -8 - ¾

Convert to decimal fraction:                    x = 8 - 0.75    x = -8 – 0.75  

Subtract:                                                   x = 7.25           x = -8.75

The graph of your equation is a parabola with x-intercepts at x = -8.75 and x = 7.25.

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The adjascent angles to angle EDC is angle EDI and CDH.

Two angles are said to be adjacent angles when they share the common vertex and side. The sum of adjascent angles is 180°. This means that adding two adjascent angles together will give 180°. Adjascent angles are also called supplementary angles.

Examples of adjascent angles in the diagram include;

AEB Is adjascent to AED

and also there are two angles that are adjascent to angle EDC. They are;

angle ED1 and CDH

Therefore the adjascent angles to angle EDC is angle EDI and CDH.

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We can see here that the triangle is a right-angle triangle.

The fundamental geometric shape of a triangle has three straight sides and three angles. It is a triangular polygon with three edges.

We can see here that the triangle is a right-angle triangle because using Pythagoras Theorem, we will see the following:

Hypotenuse = c = 30

Adjacent = b = 24

Opposite = a = 18

c² = a² + b²

Hyp² = Opp² + Adj²

30² = 18² + 24²

324 + 576 = 900.

Thus, it is a right-angle triangle.

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Answer:

8

Step-by-step explanation:

12 ÷ 3 = 4

2 x 4 = 8

Hope I could help :)

The area of a sector of a circle is calculated as approximately 44.24 square units.

The area of the sector of a circle can be calculated by applying the given formula below:

Area of sector = ∅/360 * π * r², where: r is the radius of the circle and ∅ is the central angle or reference angle of the sector.

Given the parameters of the sector of the circle as:

Central angle (∅) = 30 degrees

Radius (r) = RS = 13 units

Plug in the values:

Area of sector = 30/360 * π * 13²

Area of sector ≈ 44.24 square units.

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Answer:

c. 8 2/8

Step-by-step explanation:

12 1/2 - 4 7/10 = 12 5/10 - 4 7/10 = 8 2/10 = 8 1/5 = 8.2

Therefore, the answer is option c. 8 2/8

Hope this helps!

Answer:

To determine the fluid replacement rate for a burn patient in the first 8 hours, we can use the Parkland formula:

Fluid (in liters) = 4 mL × body weight in kg × % total body surface area (TBSA) burned

First, we need to calculate the TBSA burned. We can use the Rule of Nines to estimate this:

Head: 9%

Left Arm: 9%

Right Arm: 9%

Upper Front Torso: 0%

Upper Back Torso: 0%

Lower Front Torso: 18%

Lower Back Torso: 18%

Upper Left Leg: 0%

Upper Right Leg: 0%

Lower Left Leg: 0%

Lower Right Leg: 9%

Total TBSA burned = 9 + 9 + 9 + 18 + 18 + 9 = 72%

Now we can plug in the values into the Parkland formula:

Fluid (in liters) = 4 mL × 50.9 kg × 72% = 14,694.72 mL

To convert mL to liters, we divide by 1000:

Fluid (in liters) = 14,694.72 mL ÷ 1000 = 14.69 L

This is the total amount of fluid the patient needs in the first 8 hours. To determine the hourly rate, we divide by 8:

Hourly fluid rate = 14.69 L ÷ 8 = 1.84 L/hour

Therefore, the patient should receive approximately 1.84 liters of fluid per hour in the first 8 hours of their care.

Step-by-step explanation:

the perimeter (the way one time around it) of a rectangle is

2×length + 2×width

length = 3×width

2×(3×width) + 2×width = 160

6×width + 2×width = 160

8×width = 160

width = 160/8 = 20 ft

length = 3×width = 3×20 = 60ft

When the simultaneous equation is solved, we have that;  x = 2 and y = 3

Simultaneous equations are a set of two or more equations that are solved together to find the values of the variables that satisfy all of the equations at the same time.

We have the equations;

9x - 7y = -3 --- (1)

-3x + 5y = 9 ---- (2)

Multiply (1) by 1 and (2) by (3)

9x - 7y = -3  ---- (3)

-9x + 15y = 27 ----- (4)

Add (3) and (4)

8y = 24

y = 3

Substitute y = 3 into (1)

9x - 7(3) = -3

9x - 21 = -3

9x = -3 + 21

9x = 18

x = 2

Thus the solution is x = 2 and y = 3

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Answer :

Answer : 1.796

The explanation is in the pictures.

The statements that are true about the scatter plot graph are;
1. The line of best fit should have the same number of points above and below it.

2. There is a moderate positive correlation.

3. The line of best fit will have a positive slope.

Some facts about scatter plot graphs:

Scatter plots are used to show the correlation or relationship between two variables. The variables are plotted on the x and y-axes, and each point represents a pair of values for the two variables.

Scatter plots can show different types of relationships between two variables, including positive, negative, or no correlation.

The shape of a scatter plot can provide insights into the strength and direction of the relationship between the two variables. For example, if the points on the scatter plot form a linear pattern, this indicates a strong correlation.

Scatter plots can be used to identify outliers or anomalies in the data that do not fit the general pattern of the relationship between the two variables.

The above answer is based on the following options provided in the picture.

Tick all the statements that applies

The y intercept of the line  of best fit would be around 45

The line of best fit should have the same number of points above and below it

The slope of the line of best fit could be around -1/20000

The line of best fit must pass through at lest 2 points on the scattered plot

There is no correlation between happiness and income

There is a moderate positive correlation

The line of best fit will have a positive slope

As a person's income goes up, their happiness trends down

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Answer:

First, we need to put the equation in standard form, which is ax^2 + bx + c = 0. So, we have 2x^2 + 6x + 3 = 0.

Using the Quadratic Formula, x = (-b ± sqrt(b^2 - 4ac)) / 2a, we can plug in the values for a, b, and c:

x = (-6 ± sqrt(6^2 - 4(2)(3))) / 2(2)

x = (-6 ± sqrt(36 - 24)) / 4

x = (-6 ± sqrt(12)) / 4

Simplifying further, we have:

x = (-6 ± 2sqrt(3)) / 4

x = (-3 ± sqrt(3)) / 2

To the nearest hundredth, the solutions are:

A. 2.37 and 0.63

Answer:

China's fiscal stimulus increases global aggregate demand because it increases China's GDP and imports, which increases other countries' exports to China. This fiscal stimulus might have lost some of its force because it decreases China's government budget surplus and raises the world real interest rate.

Step-by-step explanation:

hope this helps

The confidence interval is given as (38.811,43.829)

In statistics, a margin of error refers to the degree of imprecision that can be projected in survey or polling outcomes due to random sampling involved in such studies.

This indicator serves as both the measure for the accuracy of results and an assurance of confidence in them. The percentage rate expressing the magnitude of the latter varies inversely with the former and depends on the sample size, desired level of confidence, and cumulative trends in feedback obtained from respondents.

Thus, surveys featuring minimal margins of error are considered substantively accurate while ones plagued by larger margins signal a lack thereof.

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