Write two numbers so that
The first number is less than the second number, and

The absolute value of the first number is greater than the absolute value of the second number

x = (1 ±√41)/6 is the correct answer.

To solve the equation 10 - 6x - 9x^2 = -9x, we'll use the quadratic formula. The solutions for x are (3 + √369)/18 and (3 - √369)/18.

To solve the equation 10 - 6x - 9x2 = -9x, we'll start by bringing all the terms to one side of the equation to set it equal to zero. Rearranging the equation, we get 9x2 - 3x - 10 = 0. We can then use factoring, the quadratic formula, or completing the square to solve for x. In this case, let's use the quadratic formula.

The quadratic formula states:

x = (-b ± √(b2 - 4ac))/(2a)

Using the values from our equation, we have:

x = (-(-3) ± √((-3)2 - 4(9)(-10)))/(2(9))

Simplifying further, we have:

x = (3 ± √(9 + 360))/18

x = (3 ± √369)/18

Therefore, the solutions for x are:

x = (3 + √369)/18

x = (3 - √369)/18

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Answer:

0.75

Step-by-step explanation:

Answer:

The simplest form of the ratio is: [tex]\dfrac{865}{2678}[/tex]

Step-by-step explanation:

We are given information about the buffalo in  New york in the year 2015 as:

Number of arrests= 8,625

Number of robberies=2678

Number of assaults= 865

Number of murders= 20

The population of Buffalo is 258,959.

he ratio of the number of assaults to the number of robberies in simplest form is given by:

[tex]\dfrac{865}{2678}[/tex]

As the number in the numerator and the denominator do not have a common factor. hence the simplest form of the ratio is:

[tex]\dfrac{865}{2678}[/tex]

Answer:

Speed of car on the way back = 30 mph

Step-by-step explanation:

Speed of car on the way = 45 mph = 45 x 1.6 = 72 kmph = 20 m/s

Time taken to cross bridge on the way = 40 seconds

Length of bridge = Speed of car on the way x Time taken on the way = 20 x 40 = 800 m

Time taken to cross bridge on the way back = 30 seconds

Length of bridge = Speed of car on the way back x Time taken on the way back

800 = Speed of car on the way back x 30

Speed of car on the way back = 26.67 m/s =96 kmph = 30 mph

Speed of car on the way back = 30 mph

Answer: 140 miles per hour

Step-by-step explanation:

A minute is 6 times as long as 10 seconds, so we expect Karl will ride 6 times as far.

[tex]\dfrac{120\,ft}{10\,s}=\dfrac{120\,ft}{10\,s}\cdot\dfrac{60\,s}{1\,min}=\dfrac{720\,ft}{1\,min}[/tex]

Karl rides 720 ft in 1 minute.

Answer:

720

Step-by-step explanation:

120/10 to find his feet per second which is 12 feet per second

12*60

since there are 60 seconds in a minute

= 720

Final answer:

To answer the question, we need to convert the mass from pounds to kilograms, use the ideal gas law equation to calculate the pressure in atmospheres, and then convert atmospheres to psig.

Explanation:

In this question, we are given that 100 pounds of CO2 is contained in a 10.0-ft3 tank and the safety limit of the tank is 1600 psig. To convert pounds to kilograms, we can use the conversion factor of 1 pound = 0.4536 kilograms. So, 100 pounds of CO2 is equal to 45.36 kilograms. Now, we can use the ideal gas law equation PV = nRT to find the pressure in bar. Rearranging the equation, we have P = (nRT) / V. Plugging in the values given, n = mass / molar mass, R = 0.0821 atm L / mol K, T = 273 + degrees Celsius, and V = 10.0 ft3 converted to liters, we can calculate the pressure in atmospheres. Finally, we can convert atmospheres to psig by multiplying by 14.7.

Answer:

what?

Step-by-step explanation:

Answer:

[tex]a_n=5a_{n-1}[/tex]

Step-by-step explanation:

Given fifth term of a geometric sequence is 781.25.

[tex]a_5= 781.25[/tex].

Also, each previous term is 1/5 of the value of the current term.

Therefore, common ratio would be 5.

But we just need to find the recursive formula .

Recursive formula of a geometric sequence is given by

[tex]a_n=ra_{n-1}[/tex]

Plugging value of r in above formula, we get

[tex]a_n=5a_{n-1}[/tex]

Answer: c

Step-by-step explanation:

buddy beneath me is blabbin to much

The loan amount is calculated by amortization and Brand K will be $340.32 cheaper than Brand J

Loan amortisation is the practise of making recurrent payments over time to completely pay off the principal and interest on a loan.

Mortgage amortisation is a word used in finance to describe the process of paying down your mortgage. The mortgage lender establishes a payment plan for you when you take out a mortgage. This uncomplicated plan, which includes equal payments over the course of your loan if you have a fixed-rate mortgage, is easy to understand.

The amount is calculated using the amortization formula:

P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

where:

P is monthly payment

a is credit amount

r is the interest rate

t is the time in years

n is number of times the interest is compounded

Given data ,

Let the total loan amount for the brand J be represented as J

a = $975

r = 14.55% = 0.1455

t = 8 years

n = 12

Now , the amortization formula is

P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

P = 975 ÷ {{[(1 + 0.1455/12)^12×8] - 1} ÷ [0.1455/12(1 + 0.1455/12)^12×8]}

P = $17.24

Total amount paid J = $17.24 × 96 = $1655.04

Let the total loan amount for the brand K be represented as K

a = $265

r = 14.55% = 0.1455

t = 3 years

n = 12

Now , the amortization formula is

P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

P = 265 ÷ {{[(1 + 0.1455/12)^12×3] - 1} ÷ [0.1455/12(1 + 0.1455/12)^12×3]}

P = $9.13

Total amount paid K = $9.13 × 12 × 3 × 4 = $1314.72

The difference of amount of sofa j and sofa k = D

D = J - K

D = $1 655.04 - $ 1314.72 = $ 340.32

Hence , Brand K will be cheaper than Brand J by $340.32

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Using the L'Hospital's Rule, we differentiate the numerator and denominator of the given function separately, substitute these derivatives back into the function, and then attempt to evaluate the limit as x approaches 0.

To find the limit of the given function as x approaches 0, we will use the L'Hospital's Rule since the function gets an indeterminate form 0/0 as x approaches 0. L'Hospital's Rule states that the limit of a quotient of two functions as x approaches a certain value is equal to the limit of the quotients of their derivatives.

First, we differentiate the numerator and the denominator separately. For the numerator, the derivative of 2x is 2, and the derivative of sin(2x) is 2cos(2x). So the derivative of the numerator is 2 - 2cos(2x).

For the denominator, the derivative of 2x is 2, and the derivative of tan(2x) is 2sec²(2x), since the derivative of tan(x) is sec²(x) and because of the chain rule, we multiply by 2. So, the derivative of the denominator is 2 - 2sec²(2x).

Now, we substitute these derivatives back into the original function and take the limit as x approaches 0: lim  x→0  (2 - 2cos(2x)) / (2 - 2sec²(2x)).

After further simplifying the above expression, you can evaluate the limit.

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The limit is 0.

We need to find the limit:

lim x→0 (2x − sin(2x)) / (2x − tan(2x))

Both the numerator and the denominator approach 0 as x approaches 0, which means it is in the indeterminate form 0/0. This suggests that we can use L'Hôpital's Rule.

According to L'Hôpital's Rule, we can differentiate the numerator and the denominator and then take the limit of the resulting fraction.

First, let's compute the derivative of the numerator:

Next, let's compute the derivative of the denominator:

Now, we apply L'Hôpital's Rule:

lim x→0 (2 - 2cos(2x)) / (2 - 2sec²(2x))

As x approaches 0, cos(2x) approaches 1 and sec²(2x) also approaches 1, so:

lim x→0 (2 - 2(1)) / (2 - 2(1)) = 0 / 0

This fraction again gives an indeterminate form. Applying L'Hôpital's Rule a second time will be helpful. We need to differentiate the numerator and the denominator again:

Second derivative of the numerator: d/dx [2 - 2cos(2x)] = 4sin(2x)

Second derivative of the denominator: d/dx [2 - 2sec²(2x)] = -8sec²(2x)tan(2x)

Applying L'Hôpital's Rule once more, we get:

lim x→0 (4sin(2x)) / (-8sec²(2x)tan(2x))

Substitute x = 0:

lim x→0 (4sin(2x)) / (-8sec²(2x)tan(2x)) = 0

Therefore, the limit is 0.

There are 210 different ways for the fruits can be consumed.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A student have 3 mangos, 2 papayas, and 2 kiwi fruits.

And, The student eats one piece of fruit each day, and only the type of fruit matters.

Now,

Total number of fruits = 3 + 2 + 2

                                  = 7

And, There are 3 mangos, 2 papayas, and 2 kiwi fruits.

So, Number of ways for the fruits can be consumed, is calculated as;

= 7! / 3! 2! 2!

= 7 x 6 x 5 x 4 x 3! / 3! 2! 2

= 7 x 6 x 5 x 4 / 2 x 1 x 2 x 1

= 7 x 6 x 5

= 210

Thus, There are 210 different ways for the fruits can be consumed.

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