Four hundred fifty-nine

The given quadratic equation is f(x) = x³ - 3x² + 2x-1. The two solutions to the equation are x = (3x + √(9x² + 4))/2x² and x = (3x - √(9x² + 4))/2x².

A quadratic equation is written in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

To solve this equation, we will use the quadratic formula.

The quadratic formula states that for a quadratic equation of the form ax² + bx + c = 0, the solutions are given by

x = [-b ± √(b² - 4ac)]/2a.

In this equation, a = x², b = -3x, and c = -1. Plugging these values into the formula, we get x = [3x ± √(9x² - 4(x²)(-1))]/2(x²). Simplifying this, we get

x = [3x ± √(9x² + 4)]/2x².

Now, we must solve for the two solutions. The first solution is x = (3x + √(9x² + 4))/2x². The second solution is

x = (3x - √(9x² + 4))/2x².

Therefore, the two solutions to the given equation are

x = (3x + √(9x² + 4))/2x² and

x = (3x - √(9x² + 4))/2x².

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1-Is the sum of two prime numbers always a prime number?

Solution:

No. Here is an example.

3 + 7 = 10 , 3 and 7 are prime numbers but not their sum 10.

2-Is the product of two prime numbers also a prime number?

Solution:

Never because it will have 1 and itself as factors and also the two numbers involved in the product.

Example: 7 × 11 = 77 ,77 has 1, itself, 7 and 11 as factors.

3-Which is the largest 3 digit prime number?

Solution:

Start with the largest three digit number 999.

4- Which is the smallest 2 digit prime number?

Solution

Start with the smallest 2 digit number 10.

10 is not a prime number

Answer: 11 is a prime number

Therefore , the solution of the given problem of volume comes out to be a hemisphere with a 2 inch radius has a capacity of roughly 16.755 cubic inches.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Liter and in3 are these marks for cubic measurements. To compute an object's measurements, you must, however, comprehend its volume. Converting an object's weight into mass units including grams and kilograms is a common procedure.

Here,

The formula: can be used to determine the capacity of a hemisphere with a radius of 2 inches.

=> V = (2/3) * π * r³

where "π" is a mathematical constant that is roughly equivalent to 3.14159 and "r" is the hemisphere's radius.

When we substitute the radius's value, we obtain:

=> V = (2/3) * π * 2³

=> (2/3) * π* 8

=>  V = 16.755 cubic inches. (approx)

Therefore, a hemisphere with a 2 inch radius has a capacity of roughly 16.755 cubic inches.

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Answer:

The total amount of capital invested is:

N2,000 + N4,000 + N1,500 = N7,500

The proportion of the profit that each man gets is equal to the proportion of the capital that he invested. Therefore, the first man gets:

N2,000 / N7,500 * N300 = N80

The second man gets:

N4,000 / N7,500 * N300 = N160

The third man gets:

N1,500 / N7,500 * N300 = N60

Therefore, each man gets N80, N160, and N60, respectively.

Step-by-step explanation:

Answer:

N80, N160, and N60

Step-by-step explanation:

The total amount of capital invested is:

N2,000 + N4,000 + N1,500 = N7,500

The proportion of the profit that each man gets is equal to the proportion of the capital that he invested. Therefore, the first man gets:

N2,000 / N7,500 * N300 = N80

The second man gets:

N4,000 / N7,500 * N300 = N160

The third man gets:

N1,500 / N7,500 * N300 = N60

Therefore, each man gets N80, N160, and N60, respectively.

The quadratic equation has no real roots for c > 1, two roots of the same sign for c ≥ 1,  one root equal to zero & one negative root for 0 < c < 1, and two roots of opposite signs, c < 1.

What is a quadratic equation?

A quadratic equation is a polynomial equation of degree 2, which means that the highest exponent of the variable in the equation is 2. It has the general form:

[tex]ax^2 + bx + c = 0[/tex]

The quadratic equation [tex]x^2 - 2x + c = 0[/tex] has roots given by the quadratic formula:

x = (-b ±[tex]\sqrt{b^2 - 4ac}[/tex]) / (2a)

where a = 1, b = -2, and c is the unknown constant.

1) To have no real roots, the discriminant [tex]b^2 - 4ac[/tex] must be negative. So, we need:

[tex]b^2 - 4ac[/tex] < 0

[tex](-2)^2 - 4(1)(c)[/tex] < 0

4 - 4c < 0

4 < 4c

1 < c

Therefore, the quadratic equation has no real roots for c > 1.

2) To have two roots of the same sign, the discriminant [tex]b^2 - 4ac[/tex] must be negative or zero.

[tex]b^2 - 4ac[/tex] = [tex](-2)^2 - 4(1)(c)[/tex] = 4 - 4c

For two roots of the same sign, the discriminant must be negative or zero, so

4 - 4c ≤ 0

Simplifying the inequality, we get:

c ≥ 1

Therefore, for the quadratic equation, [tex]x^2 - 2x + c = 0[/tex] to have two roots of the same sign, c must be greater than or equal to 1.

3) To have one root equal to zero and one negative root, one of the roots must be zero, so we need:

x = 0 or x < 0

Setting x = 0 in the quadratic equation, we get:

c = 0

So, if c = 0, then x = 0 is the root of the quadratic equation. To find the negative root, we need:

[tex](-2)^2 - 4(1)(c)[/tex] > 0

4 - 4c > 0

1 > c

Therefore, the quadratic equation has one root equal to zero and one negative root for 0 < c < 1.

4) To have two roots of opposite signs, the discriminant [tex]b^2 - 4ac[/tex] must be positive.

So we need:

[tex]b^2 - 4ac[/tex] > 0

[tex](-2)^2 - 4(1)(c)[/tex] > 0

4 - 4c > 0

Simplifying the inequality, we get:

c < 1

Therefore, for the quadratic equation to have two roots of opposite signs, c must be less than 1.

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For c > 1, the quadratic equation has no real roots; for c ≥1, it has two roots of the same sign; for c<1, it has one root that is equal to zero and one root that is negative; and for 0 <c <1, it has two roots of the opposite signs.

The largest exponent of the variable in a quadratic equation, which is a polynomial equation of degree 2, is 2. The formula is: ax² + bx + c.

The quadratic equation x² - 2x + c has roots given by the quadratic formula:

x = (-b ±√[b²-4ac]) / (2a)

where a = 1, b = -2, and c is the unknown constant.

1) To have no real roots, the discriminant b² - 4ac must be negative.

So, we need:

b² - 4ac < 0

(-2) ² - 4(1) < 0

4- 4c < 0

1 < c

Therefore, the quadratic equation has no real roots for c > 1.

2) To have two roots of the same sign, the discriminant b² - 4ac must be negative or zero.

b² - 4ac = (-2) ² - 4(1)c = 4 - 4c

For two roots of the same sign, the discriminant must be negative or zero, so

4 - 4c ≤ 0

Simplifying the inequality, we get:

c ≥ 1

Therefore, for the quadratic equation, x² - 2x + c   to have two roots of the same sign, c must be greater than or equal to 1.

3) To have one root equal to zero and one negative root, one of the roots must be zero, so we need:

x = 0 or x < 0

Setting x = 0 in the quadratic equation, we get:

c = 0

So, if c = 0, then x = 0 is the root of the quadratic equation. To find the negative root, we need:

(-2) ² - 4(1)c > 0

4 - 4c > 0

1 > c

Therefore, the quadratic equation has one root equal to zero and one negative root for 0 < c < 1.

4) To have two roots of opposite signs, the discriminant b² - 4ac must be positive.

So, we need:

b² - 4ac > 0

(-2) ² - 4(1)c > 0

4 - 4c > 0

Simplifying the inequality, we get:

c < 1

Hence, c must be lower than 1 in order for the quadratic equation to have two roots with opposing signs.

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Answer:

False

Step-by-step explanation:

[tex](x+y)^{2} = x^{2} +2xy +y^{2}[/tex]

This means that they are not equal. For this reason, the statement is false.

Answer:

$0.81

Step-by-step explanation:

We know

A grocery store sells a bag of 3 oranges for $2.43.

What is the unit cost?​

We take

2.43 / 3 = $0.81

So, the answer is $0.81

The given function does not satisfy the condition for an odd function (f(-x) = -f(x)), we can conclude that -6.66 is not an odd function

Hi there! An odd function is a mathematical function that satisfies the condition f(-x) = -f(x) for all values of x in its domain. In simpler terms, an odd function exhibits symmetry with respect to the origin in a coordinate plane.

Now, let's analyze the given function: -6.66. This function represents a constant function since it has no variables (e.g., x or y). Constant functions have a graph that appears as a horizontal line on the coordinate plane.

For constant functions, f(-x) will always equal f(x) because the function's value doesn't change regardless of the input.

In this specific case, the function value is -6.66,

so f(-x) = f(x) = -6.66 for all x.

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Answer:

The maximum height occurs at the vertex of the parabolic equation, which is given by the formula:

t = -b/2a

where a = -16 and b = 20. Substituting these values, we get:

t = -20 / (2 * -16) = 0.625 seconds

To find the maximum height, we can substitute this value of t back into the original equation:

h = -16(0.625)^2 + 20(0.625) + 19

h = -6.25 + 12.5 + 19

h = 25.25 feet

Therefore, the maximum height the ball reaches is 25.25 feet.

Answer:

h=16(t+5/8)^2+51/4

h=25.25

Answer:

To find out which two students have the same median score, we need to find the median score for each student and compare them.

For James, the median score is 82 (the middle score when the scores are arranged in order).

For Rodney, the median score is 78 (the middle score when the scores are arranged in order).

For Traci, the median score is 82 (the middle score when the scores are arranged in order).

For Maddi, the median score is 67 (the middle score when the scores are arranged in order).

Therefore, the two students who have the same median score are James and Traci, as they both have a median score of 82.

Answer:

3

Step-by-step explanation:

21 is 7 times the number three. You can get this answer by dividing 21 by 7 (answer is 3). You can check your work by multiplying 7 x 3 (you would get 21)

Answer: W = 357.2

Step-by-step explanation:

x/38 * 940/100

100x * 35,720

x=357.2

Answer:

7/9

Step-by-step explanation:

Find the reciprocal of the divisor

Reciprocal of 3/4 : 4/3

Now multiply it with the dividend..

so, 7/12 ÷ 3/4 = 7/12 × 4/3

=7/12×4/3 = 28/36

And after reducing the fraction, the answer is 7/9

Answer:

10 small, 5 large

Step-by-step explanation:

if they were all small cars, 5x15 would be 75. there need to be 15 more spots, and each large can hold an extra 3. 15/3 is 5. so there are 10s and 5l

students would need to rent 5 small cars and 8 large cars

After addressing the issue at hand, we can state that Hence, x = 5.5 and rectangle m El H = 180.

In Euclidean geometry, a rectangle is a parallelogram with four small angles. Alternately, it might be regarded as a hexagon with a fundamental rule or one with equal angles. Another option for the parallelogram is a straight angle. Four vertices in a square have equal lengths. Four 90° angle vertices and equal parallel sides make up a quadrilateral with a rectangular cross section. Because of this, it is occasionally referred to as a "equirectangular rectangle". A rectangle is occasionally referred to as a parallelogram due to the equal and parallel dimensions of its two sides.

El = 3x + 5, EG = 5x + 16, and m IF G = 270 are all known values. We also understand that a rectangle's diagonals are of equal length. Hence, we can write:

El = HG

EG = IF

From the knowledge provided above, we can formulate two equations in terms of x:

3x + 5 = HG

5x + 16 = IF

90 m HG F and 90 m EFG

Since we know that GH is a straight line because m GHE = 0, m El G must be 180 degrees.

Now that the formulas for HG and IF are equivalent to one another, we may find x:

3x + 5 = 5x + 16

2x = 11\sx = 5.5

Hence, x = 5.5 and m El H = 180.

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Answer:

x < 5 because any value of x must have a bigger negative number than 5. In this case, formally you say that all x values must be less than 5.

Therefore, the value of x is -4 if A= B and AB= 3x-5 BC= 5x-6 and AC = 2x-9.

An equation is a mathematical statement that shows the equality of two expressions. It is composed of two sides, separated by an equals sign (=), indicating that the two sides are equivalent in value. An equation may contain variables, which are unknown values represented by letters, as well as constants, which are known values. Equations are used in many areas of mathematics and science to model and solve problems. For example, the equation y = mx + b is a linear equation that describes the relationship between the variables x and y in a straight line, where m is the slope of the line and b is the y-intercept. Equations can be solved by manipulating the variables and using mathematical operations to isolate the unknown value.

Here,

Since A = B, we know that AB = B². So, we can rewrite the equation AB = 3x - 5 as B² = 3x - 5.

Similarly, we can rewrite BC = 5x - 6 as B² = 5x - 6, and AC = 2x - 9 as A² - B² = (2x - 9) - (B^2).

Since we know that A = B, we can substitute B for A in the last equation to get:

B² - B² = (2x - 9) - (B²)

Simplifying this equation, we get:

0 = 2x - 9 - B²

Now we can substitute the equation B² = 3x - 5 into the above equation to get:

0 = 2x - 9 - (3x - 5)

Simplifying this equation, we get:

0 = -x - 4

Solving for x, we get:

x = -4

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The possible lengths for AC are any values greater than the square root of 51.2 (approximately 7.15 feet).

If triangle ABC is isosceles, then AC must be equal to BC. Let's call the length of AC "x".

Using the Pythagorean theorem, we can find the length of the diagonal line segment BD (which is also the height of the peaked roof):

BD^2 = AB^2 - (AC/2)^2

BD^2 = 8^2 - (x/2)^2

BD^2 = 64 - x^2/4

To ensure that the roof is peaked, we need BD to be less than x (otherwise, the roof would be flat). So we can set up an inequality:

BD < x

√(64 - x^2/4) < x

64 - x^2/4 < x^2

256 - x^2 < 4x^2

5x^2 > 256

x^2 > 51.2

x > √(51.2)

Therefore, the possible lengths for AC are any values greater than the square root of 51.2 (approximately 7.15 feet).

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Answer:

C: y=2x-4

Step-by-step explanation:

pls mark brainliest

Based on the given information, you would be giving $5 per month or $60 per year to charity.

Starting with a monthly gross income of $5,000, we can calculate the amount set aside for family activities as 10% of the gross income, which is:

= $5,000 x 0.10

= $500

Now, we will calculate the monthly allowance as 10% of the family activity money, which is:

= $500 x 0.10

= $50

Since you give 10% of your monthly allowance to support a charity organization, you will be giving:

= $50 x 0.10

= $5 per month

Now, in order to calculate how much you would give to charity in one year, we simply multiply the monthly amount by 12 which gives us:

= $5 x 12

= $60 per year

Therefore, the amount we would be giving to the charity is $5 per month or $60 per year.

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Answer:

Step-by-step explanation:

Let's call the average yearly salary of an architect "A" and the average yearly salary of a lawyer "L".

From the first sentence, we know that:

L = 2A - 25

From the second sentence, we know that:

A + L = 209

We can substitute the first equation into the second equation:

A + (2A - 25) = 209

Simplifying:

3A - 25 = 209

Adding 25 to both sides:

3A = 234

Dividing both sides by 3:

A = 78

Now we can use the first equation to find L:

L = 2A - 25 = 2(78) - 25 = 131

Therefore, the average yearly salary of an architect is $78,000 and the average yearly salary of a lawyer is $131,000.

Answer:

10 2/3 kg

8 X 1 1/3 kg = 10 2/3 kg

Nate made 18 loaves of bread and gave an equal number to each of his 9 neighbors, resulting in each neighbor receiving 2 loaves of bread.

The problem provides us with some information about Nate's bread-making and bread-giving activities. We know that he made 8 loaves of bread on Monday and 10 more on Tuesday, for a total of 18 loaves. We also know that he gave an equal number of loaves to each of his 9 neighbors.

To find out how many loaves each neighbor received, we need to divide the total number of loaves (18) by the number of neighbors (9). This gives us:

18 loaves / 9 neighbors = 2 loaves per neighbor.

This means that each neighbor received 2 loaves of bread from Nate. We can check this by multiplying 2 (the number of loaves per neighbor) by 9 (the number of neighbors):

2 loaves/neighbor x 9 neighbors = 18 loaves

So, we can see that the math checks out and each neighbor received 2 loaves of bread from Nate.

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The linear regression line is:Y = 0.51X - 14.05

Number is a mathematical object used to count, measure, and label. It is a fundamental concept in mathematics, and is used in nearly every branch of the discipline. In everyday life, the notion of number is used to count objects, keep track of scores, measure amounts, and label objects.

City TV Commercials Car Sales
A 60 20
B 50 15
C 70 25
D 45 17
E 55 19

Calculating the linear regression line:

m = Slope = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2)
= (5(1475) - (325)(95)) / (5(5850) - (325)2)
= (7375 - 30875) / (29250 - 105625)
= -38500 / -75375
= 0.51

b = Intercept = (ΣY - m(ΣX)) / N
= (95 - 0.51(325)) / 5
= (95 - 165.25) / 5
= -70.25 / 5
= -14.05

Therefore, the linear regression line is:
Y = 0.51X - 14.05.

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The probabilities are given as follows:

a) All 10: 0.0163 = 1.63%.

b) Exactly eight: 0.3483 = 34.83%.

c) At least nine: 0.1518 = 15.18%.

The mass probability formula, giving the probability of x successes, is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are listed as follows:

The parameter values for this problem are given as follows:

N = 20, k = 15, n = 10.

Hence the probability of answering all 10 is given as follows:

[tex]P(X = 10) = h(10,20,10,15) = \frac{C_{15,10}C_{5,0}}{C_{20,10}} = 0.0163[/tex]

The probability of exactly 8 is given as follows:

[tex]P(X = 8) = h(8,20,10,15) = \frac{C_{15,8}C_{5,2}}{C_{20,10}} = 0.3483[/tex]

The probability of nine successes is of:

[tex]P(X = 9) = h(9,20,10,15) = \frac{C_{15,9}C_{5,1}}{C_{20,10}} = 0.1355[/tex]

Hence the probability of at least nine successes is of:

P(X >= 9) = P(X = 9) + P(X = 10) = 0.1355 + 0.0163 = 0.1518 = 15.18%.

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The wrapping paper used by Aaron is 9 and 2/3 feet of paper

To solve this problem, use the given information about how much wrapping paper is needed for each game and gaming console, and then multiplied by the number of games and consoles that Aaron wraps in one hour. For simple calculation convert mixed fractions into an improper fraction and solve the problem.

Here we have

Aaron wraps present in a store. In one hour, he wraps 8 games and one console.

From the given figure,

Each game takes 2/3 foot of wrapping paper

Each gaming console takes 4 1/3 feet of wrapping paper

From the data

Aaron wraps 8 games in 1 hour

The wrap is used for 8 games = 8 × [ 2/3 foot ] = 16/3 foot

He wraps one console.

The wrap used for 1 console = 4 1/3

Here 4 1/3 = 13/3  [ Converting mixed fraction to improper fraction ]

Hence,

Total amount of wrap used = 16/3 + 13/3

= [ 16 + 13]/3 = 29/3 = 9 2/3  

Therefore,

The wrapping paper used by Aaron is 9 and 2/3 feet of paper

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For the given situation the probability event can be denoted mathematically as P(V|W).

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The event we are interested in is "a randomly chosen person has varicose veins" (V), given that "the person drinks sixty-four ounces of water per day" (W).

So, we can write this as -

P(V|W)

which is the conditional probability of event V given event W.

Therefore, the event can be denoted as P(V|W).

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Answer: (1/10, 9/10)

Step-by-step explanation: