Find the HCF of:
x²+5x+6, x²-4 and x³+8​

Answer:

-11.

Step-by-step explanation:

We know that the velocity function v(t) is the derivative of the position function x(t).

So, we can integrate v(t) to find x(t) up to a constant of integration:

∫v(t) dt = ∫(4 - 6t^2) dt = 4t - 2t^3 + C

where C is the constant of integration.

We can find the value of C by using the initial condition that the particle is at position x=7 at t=1:

x(1) = 4(1) - 2(1)^3 + C = 7

C = 5

So, the position function is:

x(t) = 4t - 2t^3 + 5

To find the position of the particle at time t=2, we can substitute t=2 into the position function:

x(2) = 4(2) - 2(2)^3 + 5 = -11

Therefore, the position of the particle at time t=2 is -11.

(a) The solution of the equation is √6 + 2.

(b) a = 10 and b = 2, and the solution of the equation is √10 + 7.

((a) To solve this equation, we need to isolate the term with the variable x on one side and move all other terms to the other side.

Let's start by simplifying each term using the fact that;

√24 = √(4 × 6) = 2√6,

√96 = √(16 × 6) = 4√6,

√108 = √(36 × 3) = 6√3, and

√12 = √(4 × 3) = 2√3.

Then, we have:

x√24 + √96 = √108 + x√12

2x√6 + 4√6 = 6√3 + 2x√3

2(√6 + 2√3) = (x√3 + 2x√6)

2√6 + 4√3 = x(√3 + 2√6)

Now, we can equate the coefficients of √6 and √3 on both sides to get a system of equations:

2 = x

4 = 2x

Solving this system, we find that x = 2 and therefore a = 6 and b₁ = 2.

So, the solution of the equation is √6 + 2.

(b) To solve this equation, we also need to isolate the term with the variable x on one side and move all other terms to the other side.

Let's start by squaring both sides of the equation to eliminate the square roots:

(x√40)² = (x√5 + √10)²

40x² = 5x² + 10 + 2x√50 + 10

35x² - 20 = 2x√50

Now, we can square both sides again to eliminate the remaining square root:

(35x² - 20)² = (2x√50)²

1225x⁴ - 1400x² + 400 = 0

This is a quadratic equation in x². We can solve it using the quadratic formula:

x² = (1400 ± √(1400² - 4 × 1225 × 400)) / (2 × 1225)

x² = (1400 ± 200) / 245

x² = 2 or x² = 8/7

Since x² cannot be negative, we have x² = 2 and therefore x = √2.

Substituting this value of x back into the original equation, we have:

x√40 = x√5 + √10

√80 = √10 + √10

√80 = 2√10

So, a = 10 and b = 2, and the solution of the equation is √10 + 7.

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Robert is currently 10 years old.Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation: y + 5 = 2(y)

We are given the information that Sharon is five years older than Robert, and five years ago Sharon was twice as old as Robert was then. This means we can create a system of equations to solve for Robert's age.

Let x = Robert's current age

Let y = Robert's age five years ago

Given that Sharon is five years older than Robert, we can set up the following equation:

x + 5 = Sharon's current age

Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation:

y + 5 = 2(y)

Solving the first equation for x, we get x = Sharon's current age - 5. Substituting this into the second equation, we get:

y + 5 = 2(Sharon's current age - 5)

Solving this equation for y, we get y = (Sharon's current age - 5)/2.

Since Sharon is five years older than Robert, Sharon's current age is x + 5. Substituting this into our equation for y, we get:

y = (x + 5 - 5)/2

Simplifying this equation, we get y = x/2. This means that Robert's age five years ago was half of his current age.

Since we know that Robert is currently 10 years old, Robert's age five years ago was 5. Therefore, Robert is currently 10 years old.

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Answer:

34.28 meters

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's call the horizontal distance between the boy and the pole "d". Then we can draw a right triangle with the boy's height (5m) as one leg, the distance "d" as the other leg, and the hypotenuse being the distance from the boy's eyes to the top of the pole (which we don't know yet).

We can use the angle of elevation to find the length of this hypotenuse. The angle of elevation is the angle between the horizontal and the line of sight from the boy's eyes to the top of the pole. Since the boy is looking up at the bird, this angle is also the same as the angle between the hypotenuse and the vertical (i.e. the angle at the top of the triangle). So we have:

tan(30°) = opposite/adjacent

where "opposite" is the height of the pole (20m) and "adjacent" is the hypotenuse. Solving for "adjacent", we get:

adjacent = opposite/tan(30°) = 20/tan(30°)

We can simplify tan(30°) to 1/√3, so:

adjacent = 20/(1/√3) = 20√3

Now we can use the Pythagorean theorem to find the horizontal distance "d":

d^2 + 5^2 = (20√3)^2

Simplifying and solving for "d", we get:

d = √[(20√3)^2 - 5^2] = √(1200 - 25) = √1175

So the horizontal distance between the boy and the pole is approximately 34.28 meters (rounded to two decimal places

Alexander would have to pay $15 to buy 2 pounds of walnuts with the coupon. The expression is cost = ($8/pound) x pp - $1.

The functional connection between cost and output is referred to as the cost function. It examines the cost behaviour at various output levels under the assumption of constant technology. An essential factor in determining how well a machine learning model performs for a certain dataset is the cost function. It determines and expresses as a single real number the difference between the projected value and expected value.

Given that, the price per pound of walnuts is $8.

2 pounds x $8/pound = $16

Alexander would get $1 off the final amount.

Thus,

$16 - $1 = $15

So Alexander would have to pay $15 to buy 2 pounds of walnuts with the coupon.

The expression for the cost can be written as:

cost = ($8/pound) x pp - $1

Hence, Alexander would have to pay $15 to buy 2 pounds of walnuts with the coupon. The expression is cost = ($8/pound) x pp - $1.

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Answer:

Step-by-step explanation:

45342

Answer:

Let x be the number of hopts and y be the number of totts.

The first statement relates to the total amount of money expected to be made:

3x + 7y ≥ 84

This inequality states that the total revenue from selling hopts and totts should be at least $84.

The second statement relates to the total number of units expected to be sold:

x + y ≤ 24

This inequality states that the total number of hopts and totts sold should be at most 24 units. Therefore, the system of inequalities in standard form is:

3x + 7y ≥ 84

x + y ≤ 24

where x ≥ 0 and y ≥ 0 (since we cannot sell a negative number of hopts or totts).

Answer: Let "x" be the number of hopts that Farmer Naxvip plans to sell, and let "y" be the number of totts that she plans to sell. Then we can write the following system of inequalities to model the relationships between the amounts of hopts and totts:

3x + 7y >= 84

x + y <= 24

The first inequality represents the condition that Farmer Naxvip expects to make at least $84, while the second inequality represents the condition that she expects to sell at most 24 units.

Brainliest Appreciated! (:

Part A:

The equation Y = 10X + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Therefore, in this equation, the slope is 10 and the y-intercept is 5.

The slope represents the rate of change in the monthly rate of the gym membership. For every one unit increase in the number of months, the monthly rate will increase by $10. The y-intercept represents the initial cost of joining the gym, which is $5.

Part B:

To find out how much money Justin saves the first month by joining the gym at the discounted price, we need to calculate the difference between the regular price and the discounted price for the first month.

The regular price for the first month can be found by plugging in X = 1 into the equation Y = 15X + 20, which gives Y = 35.

The discounted price for the first month can be found by plugging in X = 1 into the equation Y = 10X + 5, which gives Y = 15.

Therefore, Justin saves $20 (35 - 15) the first month by joining the gym at the discounted price rather than the regular price.

Part C:

The system of equations is:

Y = 10X + 5 (discounted price)

Y = 15X + 20 (regular price)

The solution to the system of equations is (-3, -25), which means that if X = -3, then Y = -25 is a solution to both equations. However, this solution is not possible in this situation because X represents the number of months, which cannot be negative. Therefore, the point (-3, -25) is not a valid solution.

Answer:

Step-by-step explanation:

[tex]D=\frac{\theta}{360} \times2\times\pi \times r[/tex]

[tex]D=\frac{60}{360} \times2\times\pi \times 42[/tex]

    [tex]=\frac{1}{6} \times84\times\pi[/tex]

    [tex]=12\pi cm^2[/tex]

If the shoppers spent a total of $197 in books, the amount that Eric spend is $144.

Let's assume that Todd spent x dollars in the bookstore.

According to the problem, Eric spent $15 less than three times the amount that Todd spent, which can be written as:

3x - 15

The total amount spent by both shoppers is $197, so we can set up the equation:

x + (3x - 15) = 197

Simplifying and solving for x, we get:

4x - 15 = 197

4x = 212

x = 53

Therefore, Todd spent $53 in the bookstore.

To find how much Eric spent, we can substitute Todd's value into the expression we derived for Eric's spending:

3x - 15 = 3(53) - 15 = 144

So Eric spent $144 in the bookstore.

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In the right-angled triangle ABC the value of line segment BD is obtained as x = 21.91.

What is a right-angled triangle?

Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.

A right-angled triangle ABC with drawn with angle B = 90°.

A line BD is drawn which is perpendicular to AC.

The angle BDC is also 90 degrees.

The measure for line segment AD = 12 and CD = 40.

The measure for line segment BD is x.

The side BD is common for triangle ABC and BDC.

So, by the formula of indirect measurement we have -

DC / BD = BD / AD

Substitute the values in the equation -

40 / x = x / 12

x² = 480

x = 21.908

x = 21.91

Therefore, the value of x is obtained as 21.91.

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Answer:

Sin Q

7/25

Cos Q

24/25

Tan Q

7/24

Sin R

24/25

Cos R

7/25

Tan24/7

Step-by-step explanation:

Answer:

d. 27/4, or 6.75

Step-by-step explanation:

[tex]2( \frac{1}{8} + 4) - ( \frac{3}{16} \times 8)[/tex]

[tex]2( \frac{33}{8} ) - \frac{3}{2} [/tex]

[tex] \frac{33}{4} - \frac{3}{2} = \frac{33}{4} - \frac{6}{4} = \frac{27}{4} = 6.75[/tex]

Answer:

6.2 × 10-2

Step-by-step explanation:

Therefore, the fair price of one raffle ticket is $2.60, which is slightly less than the amount Raul paid ($3).

a) The fair price of one raffle ticket is $3. This is because 500 tickets were sold at this price and one prize of $200 is to be awarded. Therefore, the 500 tickets collected add up to $1,500, while the prize to be awarded is $200. The net amount to be divided among all the ticket holders is $1,300.

b) The fair price of one raffle ticket is $2.60. This is calculated by dividing the total prize money of $200 by the total number of tickets sold (500). Therefore, 500 tickets multiplied by $2.60 gives a total prize money of $1,300 which is equal to the total ticket sales of $1,500 less the prize money of $200.

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Answer:

Step-by-step explanation:

You want the coordinates of triangle ABC after dilation by a factor of 1/2.

When the center of dilation is the origin, each of the coordinates is multiplied by the dilation factor:

  (x, y) ⇒ (x/2, y/2)

  A(-4, 0) ⇒ A'(-2, 0)

  B(0, 2) ⇒ B'(0, 1)

  C(2, -2) ⇒ C'(1, -1)

The volume of ice cream that fills one waffle cone to the top is 13.09 cubic inches.

The waffle cone has the shape of a circular cone. The volume of a cone is given by the formula [tex]V = (1/3) * \pi * r^2 * h[/tex], where r is the radius of the circular base and h is the height of the cone.

The diameter of the cone is given as 5 inches, so the radius is half of the diameter, or 2.5 inches. The height is given as 6 inches. Substituting these values into the formula, we get:

V = [tex](1/3) * 3.14 * (2.5 inches)^2 * 6 inches[/tex]

V = 13.09 cubic inches

Therefore, the volume of ice cream that completely fills one waffle cone to the top is 13.09 cubic inches (rounded to two decimal places).

To find the volume of ice cream that fills the waffle cone completely to the top, we first note that the waffle cone has the shape of a circular cone. We use the formula for the volume of a cone, which is [tex]V = (1/3) * \pi * r^2 * h[/tex], where r is the radius of the circular base and h is the height of the cone.

We are given the diameter of the cone, which is 5 inches, and we find that the radius is half of the diameter, or 2.5 inches. We are also given the height of the cone, which is 6 inches. Substituting these values into the formula, we can calculate the volume of the cone as 13.09 cubic inches (rounded to two decimal places). Therefore, the volume of ice cream that completely fills one waffle cone to the top is 13.09 cubic inches.

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Due to Alex's salary falling inside the 22% tax bracket, his short-term capital gains would be subject to the same rate of taxation as his income.

A profit realized from the sale of a capital asset, such as a piece of personal or investment property, that has been possessed for one year or less is referred to as a short-term gain.

These profits are classified as ordinary income subject to tax at your personal income tax rate. Gain earned by selling assets that are held for a year or less are called short-term capital gains.

Alex is a single taxpayer who has taxable income of $80,000.

His investment income is made up of $2,000 in short-term capital gains and $500 in qualifying dividends.

As a result of his tax rate income falling between 38,601 and 425,800, which is below 15%, his qualifying dividends would be subject to a 15% tax.

Hence, we must deduct 15% of 500 and 22% of 2000 before combining them.

15% x 500

= 15 x 5

=  75

22% x 2000

= 22 x 20

= 440.

The total is = 75 + 440 = 515.

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Answer:

Step-by-step explanation:

You ask yourself, "600 is 30% of how many students?". In equation form this looks like:

600 = .30x

Divide both sides by .30 and you'll get that the number of students is 2000

Answer:

13/20 written as a decimal is 0.65 and as a percent is 65%

1) Make the denominator 100 (20 x 5)

2) Multiply by five from the numerator too (13 x 5 = 65)

When we simplify the equation, we obtain: 2y + 20 = 56 2y = 36 y = 18 Hence, mL = 140 – 2y = 104°, mP = 104°, and mN = mO = (180° – mL – 84° – (4y–4)°)/2 = 76°.

The base angles are equivalent because the LNOP is an isosceles trapezoid. As a result, mP = mL. Since we now know that a quadrilateral's total angles equal 360°, we can say. 360° = mL + mN + mO + mP Inputting the values provided yields: m∠L + 84° + (4y-4)° + m∠L = 360° When we simplify the equation, we obtain: 2m∠L + 4y + 80 = 360 2m∠L = 280 - 4y m∠L = 140 - 2y The non-parallel sides of LNOP are congruent since it is an isosceles trapezoid. As a result, mN = mO. We are aware of: 180° - mL = mN + mO Inputting the values provided yields: 84° + (4y-4)° = 180° - (140-2y)° When we simplify the equation, we obtain: 2y + 20 = 56 2y = 36 y = 18 Hence, mL = 140 – 2y = 104°, mP = 104°, and mN = mO = (180° – mL – 84° – (4y–4)°)/2 = 76°.

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Answer:

The remainder when 5x3 + 2x2 - 7 is divided by x + 9 is -692.

Explanation:

We can use long division to divide 5x^3 + 2x^2 - 7 by x + 9:

-5x^2 + 43x - 385

x + 9 | 5x^3 + 2x^2 + 0x - 7

5x^3 + 45x^2

--------------

-43x^2 + 0x

-43x^2 - 387x

--------------

387x - 7

Therefore, the remainder when 5x^3 + 2x^2 - 7 is divided by x + 9 is 387x - 7.

Hope this helps, sorry if this is wrong! :]

Answer:

8 apples

Step-by-step explanation:

Step-by-step explanation:

n = Nancy's apples.

j = Jay's apples.

a = Ava's apples.

n = 22

n = j × 2

j = n / 2 = 22/2 = 11

j = a + 3

a = j - 3 = 11 - 3 = 8

Ava has 8 apples.

The simplified difference quotient for the function [tex]\(f(x)=6\) is \(\frac{x+h-1}{h/6}\).[/tex]

The difference quotient for the function \(f(x)=6\) is given by the formula \( \[tex]frac{f(x+h)-f(x)}{h}\)[/tex]. To simplify this difference quotient, substitute the given value of \(f(x)\) into the equation:

[tex]\( \frac{f(x+h)-f(x)}{h} = \frac{f(x+h)-6}{h} \).[/tex]  Next, substitute the value of \(f(x)\) into the numerator:

[tex]\frac{6(x+h-1)}{h} \\[/tex]  .

Finally, divide both sides of the equation by 6 to simplify the equation:

[tex]\( \frac{6(x+h-1)}{h} = \frac{x+h-1}{h/6} \)[/tex]

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Answer:

Tip is $34

Round up bill amount $170

Step-by-step explanation:

20/ 100 x 170 = $34

Tip is $34

BILL plus tip is $204

90% people entering the emergency department is within the interval of [0.1559, 0.2933].

The confidence interval of the percent of patients entering the emergency department who are admitted to the hospital is [0.1763, 0.3137]. It is not reasonable for the hospital to assume that 25% of people who enter the emergency department are admitted to the hospital. Here's why.How to calculate a 90% two-sided confidence interval for p, the percent of people entering the emergency department who are admitted to the hospital:$$CI_p =\bigg(\hat{p}-Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}, \hat{p}+Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\bigg)$$ where $\hat{p} = \frac{x}{n}$, $\alpha = 0.10$, $Z_{\alpha/2} = 1.645$ (for a 90% confidence interval), and $n = 187$. The margin of error is given by $$ME = Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$Plugging in the values, we get $$\hat{p} = \frac{42}{187} = 0.2246$$$$ME = 1.645 \cdot \sqrt{\frac{0.2246\cdot 0.7754}{187}} \approx 0.0687$$Therefore, the confidence interval for $p$ is $$CI_p = (0.2246-0.0687, 0.2246+0.0687) = (0.1559, 0.2933)$$The 90% two-sided confidence interval for the percent of people entering the emergency department who are admitted to the hospital is [0.1559, 0.2933].Since the interval doesn't include 0.25, the hospital should not use the assumption that 25% of people who enter the emergency department are admitted to the hospital. This is because the interval does not overlap with the value of 0.25. As a result, we are 90% confident that the true proportion of people who are admitted to the hospital after entering the emergency department is within the interval of [0.1559, 0.2933].

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Answer: 3000m

Step-by-step explanation:

Half of 6 km is 3 km

To convert to meters multiply 3 times 1000

That will give you 3000m=3km

If a square base has a volume of 4 cubic feet, the dimensions that minimize the surface area are: x = 2√2 and h = 4/x^2 = 1/2.

Let x be the side length of the square base and h be the height of the box. Since the volume is 4 cubic feet, we have:

V = x^2h = 4

Solving for h, we get:

h = 4/x^2

The surface area of the box, A, is given by:

A = x^2 + 4xh

Substituting h in terms of x, we get:

A = x^2 + 4x(4/x^2) = x^2 + 16/x

To minimize A, we take the derivative with respect to x and set it equal to zero:

dA/dx = 2x - 16/x^2 = 0

Solving for x, we get:

x = 2√2

To ensure that this is a minimum, we take the second derivative:

d^2A/dx^2 = 2 + 32/x^3

At x = 2√2, this is positive, indicating a minimum.

The box has a square base with side length 2√2 feet and height 1/2 feet.

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Therefore , the solution of the given problem of probability comes out to be there is a 37.5% chance of thunderstorms occurring on at least three of the next four days.

The primary goal of the form of patterns defined as hyper parameters is to calculate the likelihood that a remark is accurate or a specific event will occur. Any number between 0 but instead 1, where 1 usually denotes assurance and range 0 typically connotes possibility, can be used to represent chance. A probability diagram shows the chance that a specific event will occur.

Here,

We must count the number of outcomes in which there are 3 or 4 thunderstorms in order to calculate the chance that a thunderstorm will occur on at least 3 of the following 4 days using the simulation.

We can see from the programme that there are 6 scenarios where there are at least 3 thunderstorms:

=>  1-2-3-4

=>  1-2-4-3

=>  1-3-2-4

=>  1-3-4-2

=>  1-4-2-3

=>  1-4-3-2

Since there are a total of 16 potential outcomes (since a thunderstorm can occur every day or not), the likelihood of at least 3 thunderstorms is:

=> 6/16 = 0.375

This means that there is a 37.5% chance of thunderstorms occurring on at least three of the next four days.

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