42. Use the Quadratic Equation to find the Roots of x2 + 3x - 3=0

The fraction that should go in Box A is 9/13,the fraction that should go in Box B is 4/13.

To determine the fractions that should go in the boxes marked A and B, we need to consider the given information.

We know that there are 13 marbles in total, with 9 of them being yellow and the rest being purple. This means that there are 4 purple marbles in the bag.

For Box A, we need to find the probability of picking a yellow marble on the first draw. Since there are 9 yellow marbles and a total of 13 marbles, the probability is:

Probability of picking a yellow marble on the first draw = Number of favorable outcomes / Total number of possible outcomes

Probability of picking a yellow marble on the first draw = 9 / 13

The fraction that should go in Box A is 9/13.

For Box B, we need to find the probability of picking a purple marble on the second draw, given that a yellow marble was picked and replaced on the first draw. Since the marbles are replaced after each draw, the probability remains the same.

The probability of picking a purple marble on the second draw is the same as the probability of picking a purple marble from the original set of marbles, which is:

Probability of picking a purple marble on the second draw = Number of purple marbles / Total number of marbles

Probability of picking a purple marble on the second draw = 4 / 13

The fraction that should go in Box B is 4/13.

Box A: 9/13

Box B: 4/13

Answer:

d Because I just took the test and got it right

Answer:

A) \(f(x)=5120(1.25)^x\)

B) \(f(x)=4800(1.5)^x\)

C) see below

Step-by-step explanation:

Part A

Hopefully this formatting looks ok:

| Weeks x | Views f(x) |

| ------------ | -------------- |

|      0        |     5120     |

|       1        |     6400    |

|      2        |     8000    |

|      3        |     10000   |

|      4        |     12500   |

|      5        |     15625   |

| ------------ | -------------- |

That's my attempt at a table.

We need an equation in the form of:

\(f(x)=a(b)^x\)

where a is the starting value and b is the growth factor.

First, check the difference between each week:

\(6400 - 5120=1280\\8000 - 6400=1600\\10000 - 8000=2000\\12500 - 10000=2500\\15625 - 12500=3125\\\)

Then, check the scale factor for each of the differences:

\(16000\div 12080 = 1.25\\2000\div 1600=1.25\)

etc..

The difference grows by 1.25x each week. That is, a grow factor of 1.25.

Now that we have both the starting value and the grow factor, we can write the equation:

\(f(x)=5120(1.25)^x\)

If you want to test it, for example, calculate for the 3rd week:

\(f(3)=5120(1.25)^3\\f(3)=5120(1.953125)\\f(3)=10000\)

Part B

This is very similar to Part A. The starting value and growth factor are given this time, so all you need to do is write the equation with the new values.

\(f(x)=4800(1.5)^x\)

Part C

The initial number of video views (5120) was more than the initial number of site views (4800), and the number of video views grew (1.25) by a smaller factor than the number of site visits (1.5).

The difference between the total number of site visits and the video views after 5 weeks is 20,825.

\(f(5)=5120(1.25)^5=15625 -video\\f(5)=4800(1.5)^5=36450-site\\36450-15625=20825\)

The equation to model the relationship between the number of weeks and the number of views will be f(x) = 5120(1.25)^x

From the information given, the difference in the views will be:

6400 - 5120 = 1280

8000 - 6400 = 1600

10000 - 8000 = 2000

The scale factor will be:

= 1600/1280 = 2000/1600

= 1.25

Therefore, the growth factor is 1.25.

The equation to model the relationship between the number of weeks, x, and the number of site visits is 4800(1.5)^x.

Lastly, the difference between the total number of visits and the video views will be:

= 4800(1.5)^5 - 5120(1.25)^5

= 36450 - 15625

= 20825

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Answer:

8.33

Step-by-step explanation:

1hr=60 minutes

?hr = 500 minutes

To find how many hours, divide 500 by 60

500/60 = 8.33

500 minutes = 8.33 hours

Answer:

O AB is a major arc

Step-by-step explanation:

Circle M has the central angle LAMB with a measure of 63º

Which of the following statements does not represent the  circle M?

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

O AB is a minor arc

O mAB=63 º

O The center of the circle is point M.

O AB is a major arc

Answer:

225 miles

Step-by-step explanation:

We will need to first find the base unit that will allow us to easily find the actual distance. For example, if 2:10, the base unit is 1:5 which allows use to easily find any other value.

There are two easy ways to solve this, the first way is always definitive regardless of the numbers

1. we do 2/180 as a fraction, then cross multiply 180 by 2.5 and divide it by 2. We are given 225 miles

2. We simplify the ratio of 2:180 to 1:90. With this, we can manipulate the value of 1 and along with it the value of 90. So 1*2.5 = 2.5, and we also need to apply this to 90. So we would do 90*2.5 giving us 225 miles.

Answer:

no. of moles = mass / molar mass

100/55

1.81 moles of iron(Fe)

Answer:

4

Step-by-step explanation:

\(3x+2+3x+3=5x+9 \\ \\ 6x+5=5x+9 \\ \\ x=4\)

Step-by-step explanation:

\(x = \frac{4}{3} \)

\(1. \: 6x + 6 = 5 + 9 \\ 2. \: 6x + 6 = 14 \\ 3. \: 6x = 14 - 6 \\ 4. \: 6x = 8 \\ 5. \: x = \frac{8}{6} \\ 6. \: x = \frac{4}{3} \)

The least positive integer we can get as the product is 2.

Here we have the following set of numbers:

{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}

And we want to take the product between 3 of them and find the least positive integer that we can get as the product.

So it makes sence to choose the smallest absolute value numbers (not zero) such that one is positive and two are negative (we want two negative ones so the signs cancell eachother)

Then we will get:

1*(-1)*(-2) = 2

That is the least positive integer we can get as the product.

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Answer:

c

Step-by-step explanation:

using the continously compounded formula, let a be unknown, p= 530, r be 0.05 and t be 12.

the equation would then be a=530e to the (0.05*12)th power, so that's why it's c

The amount of money after 12 years is $965.66. Therefore, option C is the correct answer.

Continuously compounded interest means that an account balance is constantly earning interest, as well as refeeding that interest back into the balance so that it, too, earns interest.

The continuous compound interest formula is \(P(t)=P_0e^{rt}\).

Where, P(t)=value at time t, \(P_0\) =original principal sum, r=nominal annual interest rate and t= length of time the interest is applied

Now, \(P(12)=530\times e^{0.05\times12}\)

⇒ \(P(12)=530\times e^{0.6}\)

⇒ P(12)= 530×1.822

⇒ P(12)= $965.66

The amount of money after 12 years is $965.66. Therefore, option C is the correct answer.

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Answer:

1960

Step-by-step explanation:

1880 unknown

1990 $1.23

2016 $1

1960 $8

Answer: 29

It is very simple, just substitute.

x = 9, y = 10

Replace the x and y in the expression to that.

You get: 9 + 10 + 10. Just add and you will get 29.

Answer:

9+10+10=29

Step-by-step explanation:

We know that x=9, so where ever we see x we know it is 9. We also know that y=10, so where ever we see y we know it is 10. So then we just replace the variables with our numbers then just add them.  That is I got 9+10+10=29

Hope this helps!

A neural network is a complicated set of possibly nonlinear equations. There are at least two degrees to a nonlinear equation.

This means that a variable in the equation can only be raised to the power of two or higher. A linear equation is typically represented as y = mx + c, where x and y are variables, m is the line's slope, and c is a constant. A nonlinear equation is one in which the highest degree of any term is two or greater. Since equation 1 has the highest degree of 2, and equation 2 involves variables x and y, this is an example of a nonlinear equation. + 2x + 1 = 0, 3x + 4y = 5, etc.

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Answer:

Step-by-step explanation:

Good morning,

You just do it in the pathway, and there is the answer for you :D.

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

A.   (f + g)(1) = - 9

B.    (f - g)(0) = -7

C.    (fg)(3) = 0

Step-by-step explanation:

A.    (f + g)(1) = f(1) + g(1)               f(1) = 1^2 - 9 = 1 - 9 = - 8       g(1) = 1 - 2 = - 1

                    = -8 -1 = -9

B.     (f - g)(0) = f(0) - g(0)             f(0) = 0^2 - 9 = 0 - 9 =  -9      g(0) = 0 - 2 = -2

                      =  -9 + 2 = -7

C.      (fg)(3) = f(3)(g(3)                   f(3) = 3^2 - 9 = 9 - 9 = 0    g(3) = 3 - 2 = 1

                    = 0(1) = 0

There are many strategies we can use to solve a system of equations, such as elimination or substitution.

\(y=3x+6\\y=(x+4)^2-10\)

Since y has already be isolated in both equations, we can just use substitution to equate them:

\(3x+6=(x+4)^2-10\)

Now, combine like terms:

\(3x=(x+4)^2-16\)

Expand the binomial:

\(3x=x^2+8x+16-16\\3x=x^2+8x\\0=x^2+5x\)

Find the zeroes:

\(0=x(x+5)\)

Therefore, x can be 0 or -5.

Now, we can plug these values of x back into one of the equations to determine the y coordinate:

\(y=3x+6\\y=3(0)+6\\y=6\)

Therefore, one solution is (0,6).

\(y=3x+6\\y=3(-5)+6\\y=-15+6\\y=-9\)

Another solutions is (-5,-9).

(0,6), (-5,-9)

(a) Anu wants to save a certain amount each month for 60 months to accumulate at least $50,000 for starting a business. The interest payable on her savings is 0.125% per month. To find out how much she should put aside each month, we can use the concept of a geometric sequence. By calculating the monthly deposit using the formula for the sum of a geometric series, we can determine the required amount.

(b) If $100 is invested at an annual interest rate of 10%, the value of the investment after 5 years will vary depending on the compounding frequency. When compounded weekly, the investment's value can be calculated using the compound interest formula. Similarly, for semi-annual compounding, the formula will differ. By plugging in the given values and performing the necessary calculations, we can determine the investment's value in both cases.

(a) To find the monthly deposit amount, we can use the formula for the sum of a geometric series:

S = a * (1 - r^n) / (1 - r)

Here, S represents the desired sum ($50,000), a is the first term (monthly deposit), r is the common ratio (1 + 0.00125), and n is the number of terms (60 months).

By rearranging the formula and plugging in the values, we can solve for the monthly deposit:

50,000 = a * (1 - (1 + 0.00125)^60) / (1 - (1 + 0.00125))

Solving this equation will give us the required monthly deposit amount.

(b) For weekly compounding, we can use the formula:

A = P * (1 + r/n)^(n*t)

Here, A represents the final amount, P is the initial principal ($100), r is the interest rate (0.10), n is the number of compounding periods per year (52 weeks), and t is the number of years (5).

By substituting the values into the formula, we can calculate the investment's value after 5 years with weekly compounding.

Similarly, for semi-annual compounding, we use the formula:

A = P * (1 + r/n)^(n*t)

Here, n is the number of compounding periods per year (2 semi-annually).

By substituting the values into the formula, we can calculate the investment's value after 5 years with semi-annual compounding.

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The x-interval over which the function is increasing is:x < -1 or x > -1

Given function:\(y=-3x^{2} -6x+8\)

The x-interval over which the function is increasing.

The given function is a quadratic function of the form f(x) = ax² + bx + c. We will determine the intervals for which the function is increasing.

To know the increasing intervals of the given function f(x), we need to determine the intervals for which f'(x) > 0 where f'(x) is the first derivative of the function.

So, Let's find the first derivative of the given function:

\(\begin{aligned}f(x)&=-3x^{2}-6x+8\\\Rightarrow f'(x)&=-6x-6=-6(x+1)\end{aligned}\)

Now, we have to check the sign of f'(x) to find the interval(s) where the function is increasing.

Sign of f'(x) changes at x = -1. If x < -1, f'(x) > 0, so the function is increasing in that interval. Similarly, if x > -1, f'(x) > 0, so the function is increasing in that interval as well.

Therefore, the x-interval over which the function is increasing is:x < -1 or x > -1

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The two triangles are similar using the AA criteria and option C is the correct answer.

If two figures share the same shape but not necessarily the same size, they are considered to be comparable.

If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same shape but may not be the exact same size.

Two triangles are said to be similar if their corresponding angles are equal.

For the first triangle the sum of interior angle is 180 thus:

60 + 53 + angle E = 180

angle E = 180 - 113

angle E = 67

From the two figures we observe that:

∠DCR = ∠GFH, and

∠DEC = ∠GHF

Hence, the two triangles are similar using the AA criteria and option C is the correct answer.

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The unit cost of pears is $1.50 per pound.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Cost for 1/3 lb of pears = $0.50

Since, 1 lb = 1 pound

Implies that,

Cost of 1/3 pounds of pears = $0.50

To find the cost of one pound of pears,

Use ratio property,

1/3 pound costs = 0.50

1 pound costs = 0.50 x 3 = $1.50

The cost of one pound of pear is $1,.50.

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Answer: Yes, the point (3,-9) is a solution to f(x) = -3x

=========================================================

Explanation:

Since y = f(x), we can say that f(x) = -3x is the same as y = -3x

The point (3,-9) means x = 3 and y = -9 pair up together

Lets plug these values into the equation

y = -3x

y = -3(3) .... replace x with 3

-9 = -3(3) .... replace y with -9

-9 = -9

We get the same thing on both sides, so the point (x,y) = (3,-9) is a solution to y = -3x. Consequently, it's also a solution to f(x) = -3x.

Answer:

Step-by-step explanation:

f(x)= -3x

-3(3)= -9

yes, (3, -9) is the solution

Answer:

x=8.5

Step-by-step explanation:

3x+31=14+5x

17=2x

x=8.5

Let's start by the formula of the average rate of change. This is the same as before:

The values of v_1 and v_2 also are the same, which is the endpoints of the given interval. So

To find

We can check the y-value that corresponds to the x-value in the graph.

We can see in the graph that for v = 0 (which is the x-value) we have k(v) = 5 (which is the corresponding y-value).

Similarly, for v = 3 we have k(v) = 0.

See here:

Now we just have to input into the formula:

Answer: 2b+12

Step-by-step explanation:

Because the number is in front of the bracket you have to times everything in the bracket by the number on the outside.

So,

2 times b is 2b

And

2 times 6 is 12

So it would be 2b+12

Answer:

0.41666666666

Step-by-step explanation:

Answer:

The value is 5/12

Answer:

That answer is $37.50

Step-by-step explanation:

You havr to multiply the 125 by .30

The evaluation of the given term in fraction is \(1/2\)

Multiplication can be regarded as an elementary mathematical operations involving arithmetic, It involves finding the products of two or more number whether in fraction or in whole number.

Given:

this can be written simply as

Then if we simplify further by dividing both the numerator and denominator by factor of 4, we have

\(=1/2\)

Therefore, the product of the terms expressed in fraction is  \(\frac{1}{2}\)

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Answer:

50°

Step-by-step explanation:

We are to find m ∠2

And lines A and B are parallel

m ∠2 and 50° are Vertical angles. This means m ∠2 is the same as 50°

Hence,

m ∠2 = 50°

Therefore, m ∠2 = 50°