f(x) = 2x^4-8x²+5x-7
x=3

Answer:

-2.2y-1.8

Step-by-step explanation:

1.2y+4.5-3.4y-6.3

1.2y-3.4y+4.5-6.3

-2.2y+4.5-6.3

-2.2y-1.8

With the help of the given Venn diagram, the answer of n(A∪B) is 44 respectively.

A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects.

Circles that overlap share certain characteristics, whereas circles that do not overlap do not.

Venn diagrams are useful for showing how two concepts are related and different visually.

When two or more objects have overlapping attributes, a Venn diagram offers a simple way to illustrate the relationships between them.

Venn diagrams are frequently used in reports and presentations because they make it simpler to visualize data.

So, we need to find:

A ∪ B

Now, calculate as follows:

The collection of all objects found in either the Blue or Green circles, or both, is known as A B. Its components number is:

8 + 7 + 14 + 6 + 1 + 8 = 44

n(A∪B) = 44

Therefore, with the help of the given Venn diagram, the answer of n(A∪B) is 44 respectively.

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The length of the third side of the given right triangle is 6.32.

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”. The formula for the same is;

c² = a² + b², where a, b, c are sides of a right triangle.

Given that, a right triangle, with two sides 7 and 3, since, the figure is unavailable, let us assume that 7 is the hypotenuse and 3 is the other side, let the unknown side be x,

According to the Pythagoras theorem,

7² = 3² + x²

x² = 7² - 3²

x² = 49-9

x² = 40

x = √40

x = 6.32

Hence, the length of the third side of the given right triangle is 6.32.

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Step-by-step explanation:

there is the rule

outside length × (outside length + inside length) is the same for all lines originating from the same point.

so, we have

CD(CD + x) = BC(BC + AB) = 6(6+20) = 6×26 = 156

8(8 + x) = 156

8 + x = 19.5

x = 11.5

The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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You can determine the median of a triangle by looking out for the point that is 2/3 of the distance tht connects from the vertices, to midpoint and oposite sides.

The perpendicular bisector is determined by measuring the point that is equidistant from the segment.

The altitude of a triangle can be found by measiring the height of the triangle's extension that could be inside or outside the triangle. In obtsue triangles, this altitude is commonly found outside the triangle.

Also, the angle bisector of a triangle is the point that is equidistant from the angles sides. These descriptions can help in analyzing a trinagle.

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A sequence of transformations that would map PQ onto RS include the following: A. a 90° clockwise rotation about the origin, then a reflection in the x-axis.

In Mathematics and Geometry, a reflection over the x-axis is represented by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

For a 90° clockwise rotation about the origin, the new coordinates of P is given by:

(x, y)            →      (y, -x)

P (-6, 10)      →      (10, -(6)) = P' (10, -6)

Next, we would apply a reflection over or across the x-axis;

(x, y)                →      (x, -y)

P' (10, -6)       →      (10, -(-6)) = S (10, 6)

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The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Answer:

The value of a₅ is 1875.

Step-by-step explanation:

Given:

a₁ = 3

aₙ = 5aₙ₋₁

To find the value of a₅, we can apply the recursive formula to compute each term successively:

Step 1: Compute a₂

a₂ = 5a₁ = 5(3) = 15

Step 2: Compute a₃

a₃ = 5a₂ = 5(15) = 75

Step 3: Compute a₄

a₄ = 5a₃ = 5(75) = 375

Step 4: Compute a₅

a₅ = 5a₄ = 5(375) = 1875

The solution to the given algebraic expression 3(2-4x) = 5-8x is x = 1/4

3(2-4x) = 5-8x

open parenthesis

6 - 12x = 5 - 8x

combine like terms

6 - 5 = -8x + 12x

1 = 4x

divide both sides by 4

x = 1/4

Ultimately, x = 1/4 is the answer to the algebraic expression.

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Answer:x= -5+8 √2,x= -5-8 √2

For the intermediate problem: X2-4x+10=4x+10

Step-by-step explanation:

Answer:

The number of enrollments increased by 5%.

Step-by-step explanation:

Given that:

Number of students at the beginning of the year = 480

Number of students at the end of the year = 504

Change = 504 - 480 = 24

This indicates increase.

Percent of change = \(\frac{Change}{Old\ number\ of\ students}*100\)

Percent of change = \(\frac{24}{480}*100\)

Percent of change = 5%

Hence,

The number of enrollments increased by 5%.

Step-by-step explanation:

remember, a/a = 1, and it represents always a "whole" in fraction calculations.

in our case here : 4/4.

if I understand correctly, he packs 1/3 of 6 3/4 pounds into pound bags (which I assume are bags that hold 1 pound each).

6 3/4 = (6×4)/4 + 3/4 = 24/4 + 3/4 = 27/4 pounds.

1/3 of x means multiplying x by 1/3.

this is the same as dividing x by 3.

so, in our case 1/3 of the candy to be packed is

27/4 × 1/3 = 27/(4×3) = 9/4 = 8/4 + 1/4 = (2×4)/4 + 1/4.

that means he can fill 2 whole pound bags and has 1/4 pound left.

your answer is 3.375

Answer:

8.52

Step-by-step explanation:

add the two 3.99 making 7.98 then add 3.50 making 11.48 then substract that from 20.00 making the final answer 8.52

The linear and exponential equations for the amount of money in the banks indicates;

TCF Bank Equation

y = 100·x + 1000

Well Fargo Bank Equation

y = (1.06)ˣ

The number of years it will take for both accounts to have the same amount of money is about 17 years

An exponential equation is an equation of the form; y = a·bˣ, where the input variable, x is an exponent.

The equation for calculating the amount in each bank, based on the details are;

TCF Bank;

Amount invested = $1,000

Amount added each year = 100·x

Well Fargo Bank Equation

The percentage of the amount earned as interest each year = 6% = 0.06

The exponential equation for compound interest amount is; y = 1000·(1 + 0.06)ˣ

Therefore; y = 1000·(1.06)ˣ

When the amount in the two accounts have the same amount of money, we get;

1000·(1.06)ˣ = 100·x + 1000

Therefore; (1.06)ˣ = (100·x + 1000)/1000 = 0.1·x + 1

(1.06)ˣ = 0.1·x + 1

Solving the above equation using the substitution method and graphing indicates that we get;

x = 0, and x ≈ 17.125732

Therefore, it takes about 17 years for the two accounts to have the same amount of money

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Answer:

\(\frac{\sqrt{3} }{2}\)

Step-by-step explanation:

edge 2020

The value of sin(80) cos(20°) - cos(80°) sin(20°)= √3/2

Trigonometry the area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations.

Given:

sin(80) cos(20°) - cos(80°) sin(20°)

Using Trigonometric identity

sin ( A- B) = sin A cos B - cos A sin B

So, sin(80) cos(20°) - cos(80°) sin(20°)

= sin (80 - 20)

= sin 60

= √3/2

Hence,  sin(80) cos(20°) - cos(80°) sin(20°)= √3/2

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Answer:

Part A: $3,415.50

B: 11.34%

Step-by-step explanation:

Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50

Part B: For the effective tax rate, divide the amount in part A by the taxable income

Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.

To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.

Part A:

To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:

f(x) = 0.12 * 31000 - 205.50 = $3,574.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.

Part B:

To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:

Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%

Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.

Part C:

The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.

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Answer:

Step-by-step explanation:

To determine the number of subjects needed to estimate the mean number of books read the previous year within six books with 90% confidence, you would need to use a sample size calculation. There are several factors that can affect the sample size needed, including the desired level of confidence, the desired level of precision, the variability of the population being sampled, and the size of the population.

One way to calculate the sample size is to use a sample size calculator, which can be found online or in statistical software. These calculators typically ask for the desired level of confidence, the desired level of precision, and the estimated standard deviation of the population being sampled.

Alternatively, you can use a sample size formula to calculate the sample size. For example, the formula for calculating the sample size for a simple random sample with a known population standard deviation is:

n = (Z*sigma / E)^2

where n is the sample size, Z is the z-score corresponding to the desired level of confidence (e.g., for a 90% confidence level, Z would be 1.645), sigma is the population standard deviation, and E is the desired level of precision (e.g., 6 books in this case).

To use this formula, you would need to know the population standard deviation, which may require collecting data from a pilot study or using estimates based on similar populations.

It's important to note that sample size calculations are based on statistical assumptions, and the actual sample size needed may vary depending on the specific characteristics of the population being sampled. Additionally, sample size calculations are based on estimates, so the actual level of precision may differ from the desired level.

Answer:

1.5 teaspoons

Step-by-step explanation:

1/(3/4)

=4/3

9/8*4/3

=1.5 teaspoons

PLS GIVE BRAINLIEST

Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: \(g(x) = -\sqrt{9(x - 1)} + 2\)

In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.

Where:

In this context, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;

f(x) = √x

g(x) = -√9(x - 1) + 2

\(g(x) = -\sqrt{9(x - 1)} + 2\)

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Answer:

x < -2

Step-by-step explanation:

subtract 6 from each side

-3x > 6

divide both sides by -3

x < -2

(with inequalities you must flip the sign if you divide by a negative number)

1) if to substitute the given coordinates and slope into the common form of equation (it is y=s*x+i), then 0=3*1+i, ⇒ i= -3. The required equation is y=x-3.

C. y=x-3.

2) according to the condition coordinates of R are (x;0). Then it is possible to calculate the x-coordinate of R after substitution into the slope-interception form (it is y=s*x+i): 0=2x-8; ⇒ x=4. The coordinates of R are (4;0).

A. (4;0).

Answer:

#1 is 5

#2 is 4

#3 is 3

#4 is 6

Step-by-step explanation:

I used a graphing calculator called Desmos.

The required answer are :

a. Odds in favor of drawing a spade: 13:39 or simplified as 1:3.

b.the odds against drawing a five are:

Favorable outcomes: 4 Unfavorable outcomes: 48

Odds against drawing a five: 48:4 or simplified as 12:1.

Given that, suppose one card is drawn at random from a standard deck.

To find the odds in favor of drawing a spade, we need to determine the number of favorable outcomes (spades) and the number of unfavorable outcomes (non-spades).

In a standard deck of 52 cards, there are 13 spades (A♠, 2♠, 3♠, ..., 10♠, J♠, Q♠, K♠) and 39 non-spades (all other cards).

The odds in favor of drawing a spade can be expressed as the ratio of favorable outcomes to unfavorable outcomes. Therefore, the odds in favor of drawing a spade are:

Favorable outcomes: 13 Unfavorable outcomes: 39

Odds in favor of drawing a spade: 13:39 or simplified as 1:3.

(b) To find the odds against drawing a five, we need to determine the number of favorable outcomes (non-fives) and the number of unfavorable outcomes (fives).

In a standard deck of 52 cards, there are 48 non-fives (all cards except 5♠, 5♥, 5♦, and 5♣) and 4 fives (5♠, 5♥, 5♦, and 5♣).

The odds against drawing a five can be expressed as the ratio of unfavorable outcomes to favorable outcomes.

Therefore, the odds against drawing a five are:

Favorable outcomes: 4 Unfavorable outcomes: 48

Odds against drawing a five: 48:4 or simplified as 12:1.

Hence, the answer are:

a. Odds in favor of drawing a spade: 13:39 or simplified as 1:3.

b.the odds against drawing a five are:

Favorable outcomes: 4 Unfavorable outcomes: 48

Odds against drawing a five: 48:4 or simplified as 12:1.

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Answer:

110/250

Step-by-step explanation:

If the fraction goal is 250 then put the 250 as the denomanator and the 110 as the top common denomanator.

Percentage of funds raised is 44 % , Fraction of funds raised is (11/25) and Fraction of funds raised in decimal form is 0.44.

To find the % of a number, divide it by its value, then multiply the result by 100. Percentage is a relative value that denotes one tenth of any quantity. As one percent (symbolised as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

As per the given data:

In the diagram given, we can find the total amount of funds to be raised and the amount of fund which is raised currently.

Total amount to be raised = $250,000

Amount already raised = $110,000

Percentage of funds raised = (110,000/250,000) × 100 = 44 %

Fraction of funds raised = (110,000/250,000) = (11/25)

Fraction of funds raised in decimal form = 0.44

Hence, Percentage of funds raised is 44 % , Fraction of funds raised is (11/25) and Fraction of funds raised in decimal form is 0.44

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(The question is incomplete, the complete question is given below.)

Assuming you are an employee, the three necessary ways in which you can file your income taxes includes:

Filing of income taxes refers to the process of submitting a tax return to the relevant government authority, usually the Internal Revenue Service (IRS) in the United States, which details an individual or organization's income and taxes paid for a given year.

Income taxes are typically assessed on an annual basis, and individuals and businesses are required to report their income and calculate their tax liability based on the relevant tax laws and regulations. The tax return typically includes various forms, schedules, and supporting documentation that provide details on the taxpayer's income, deductions, credits, and other relevant financial information.

The filing deadline for income taxes is typically April 15th in the United States, although extensions may be granted under certain circumstances. Failure to file income taxes or pay taxes owed can result in penalties, interest charges, and other legal consequences.

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The equation 6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31 has no solution for the variable x.

Given the equation in the question:

6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31

To solve the equation 6(3x + 4) + 2(2x + 2) + 2 = 22x + 31 for the variable x, we will simplify and solve for x.

Apply distributive property:

6 × 3x + 6 × 4 + 2 × 2x + 2 × 2 + 2 = 22x + 31

18x + 24 + 4x + 4 + 2 = 22x + 31

Collect and combine like terms on both sides:

22x + 30 = 22x + 31

Next, we want to isolate the variable x on one side.

22x - 22x + 30 = 22x - 22x + 31

30 = 31

However, we notice that the x terms cancel out when subtracted:

30 ≠ 31

This means that there is no solution.

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\(-16=k\cdot2^2\\4k=-16\\k=-4\)