50 Points! Multiple choice algebra question. One factor of x^3+4x^2-11x-30=0 is x+2. Find the remaining factors. Photo attached. Thank you!

(a) There are 2 sequences of length 1 that fit the bill: 0 and 1. So if \(b_n\) is the number of permissible sequences, then \(b_1=2\).

To the sequence 0, we can attach either 0 or 1 at the end, while the sequence 1 must be followed by 0. Then the permissible sequences of length 2 are 00, 01, and 10, so \(b_2=3\).

Now consider a sequence of length n + 1, of which there are \(b_{n+1}\).

• If the last digit is 0, then we got this sequence by simply joining 0 to one of \(b_n\) sequences. In other words, there are \(b_n\) permissible sequences of length n + 1 that end in 0.

• If the last digit is 1, then the previous digit must have been 0. Put another way, we join 01 to a permissible sequence of length n - 1 (there are \(b_{n-1}\) of them). So there are \(b_{n-1}\) permissible sequences of length n + 1 that end in 1.

These cases are mutually exclusive, so the number of (n + 1)-length permissible sequences is given by

\(\begin{cases}b_1 = 2 \\ b_2 = 3 \\ b_{n+1} = b_n + b_{n-2} & \text{for }n\ge2\end{cases}\)

(b) The reasoning for a permissible ternary sequence is similar. Let \(t_n\) be the number of sequences of length n not containing 11.

We first note that \(t_1 = 3\), since we can have 0, 1, or 2; and \(t_2 =  8\), since we can have 00, 01, 02, 10, 12, 20, 21, or 22.

Consider a sequence of length n + 1 (\(t_{n+1}\) of these).

• If the last digit is 0, then we joined 0 to a permissible sequence of length n. So there are \(t_n\) permissible sequences of length n + 1 ending in 0.

• If the last digit is 1, then the last two digits must be either 01 or 21. Since there are 2 choices for the n-th digit, there are \(2t_{n-1}\) permissible sequences of length n + 1 ending in 1.

• If the last digit is 2, then we essentially have the same situation as if the sequence ended in 0, so there are \(t_n\) sequences of length n + 1 ending in 2.

Then the recurrence for ternary permissible sequences is

\(\begin{cases}t_1 = 3 \\ t_2 = 8 \\ t_{n+1} = 2t_n + 2t_{n-1} & \text{for }n\ge2\end{cases}\)

Using matrices the simultaneous equation is solved to get x = 3 and y = 5

This method required finding determinants in three occasions then dividing

The given equation

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right] \left[\begin{array}{c}x\\y\\\end{array}\right]= \left[\begin{array}{c}19\\8\\\end{array}\right]\)

the determinant is

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right]\)

3 * 1 - 2 * 1 = 3 - 2 = 1

Solving for x

determinant while replacing x values

\(\left[\begin{array}{cc}19&2&\\8&1\\\end{array}\right]\)

19 * 1 - 2 * 8 = 19 - 16 = 3

solving for x = 3/1 = 3

Solving for y

determinant while replacing y values

\(\left[\begin{array}{cc}3&19&\\1&8\\\end{array}\right]\)

3 * 8 - 19 * 1 = 24 - 19 = 5

solving for y = 5/1 = 5

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The circumference of a circle is also referred to as the distance around that circle.

The circumference of the flower garden which is circular in shape is given as = 20 meters

The formula for the circumference of a circle is given as \(\bold{2\pi r}\)

We have to find the radius of the circular garden

Hence: \(\sf 2\pi r = 20 \ m\)

\(\sf \pi = 3.14\)

To find the radius, the formula would be given as

\(\bold{r = \dfrac{C}{2\pi}}\)

Where C = Circumference of the circle

\(\sf r = \dfrac{20}{2\times3.14}\)

\(\sf r = \dfrac{20}{6.28}\)

\(\sf r = 3.1847133758 \ m\)

We can find the area of the circle now

The formula for the area of the circle is given as:

\(\bold{A = \pi r^2}\)

\(\sf A = 3.14 \times 3.1847133758^2\)

\(\sf A = 31.847133758 \ m^2\)

\(\sf A\thickapprox32 \ m^2\)

Therefore, the area of the flower garden to the nearest whole number is 32m²

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The height of the can of cylinder shape is 9.14 cm.

What is a cylinder?

In mathematics, a cylinder is a three-dimensional solid that maintains two parallel bases separated by a curved surface at a specific distance. These bases frequently have a circular shape (like a circle), and an axis connects their respective centres.

We are given the diameter as 4 cm.

So, the radius is 2cm.

Also, it is given that the surface area of the can is 140 square centimeters.

So, using the surface area of cylinder, we get

⇒Area = 2πr (h + r)

⇒140 = 2π * 2 (h + 2)

⇒140 = 4π (h + 2)

⇒140 = 4 * 3.14 * (h + 2)

⇒140 = 12.56 * (h + 2)

⇒11.14 = h + 2

⇒h = 9.14

Hence, the height of the can of cylinder shape is 9.14 cm.

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Area of rectangular prism: Base x Height.

so 3x1/3x2/5=0.4 0r 2/5

Given the exponential function:

Let's substitute x by -1, 0, and 1 to compare with the graphs.

First, substituting x by -1:

Second, let's substitute x by 0:

Third, let's substitute x by 1:

So, the graph is:

Answer: A

The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

The Mean is defined as the ratio of sum of numbers present in the data to the total numbers present in the data. Median is defined as the ratio of sum of middle numbers present in the data. Mode is defined as the most recurring number present in the data. Midrange is the ratio of the largest and smallest number in the data to 2.

Let's see how to calculate Mean, Median, Mode and Midrange.

Mean = 13 + 15 + 18 + 18 + 21 / 5

Mean = 85 / 5

Mean = 17

Median = 18 (as it is the middle term of the data)

Mode = 18 (as it is most recurring number)

Midrange = 21 + 13 / 2

Midrange = 34 / 2

Midrange = 17

Therefore, The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

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Answer:

t = 15

Step-by-step explanation:

t - 12 = 3

t = 3 + 12

t = 15

Answer: 1920

Step-by-step explanation:

Answer:

50 cent

Step-by-step explanation:

Answer:

.50¢

Step-by-step explanation:

50 cents = 1 pound

$1.00 = 2 pound

$1.50 = 3 pounds

$2.00 = 4 pounds

basically adding 50 cents equals to $2

Answer:

160

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

1/2 x 1/6=

denominator(1) x denominator(1)=1

numerater (2)x numerator(6)=12

Answer:

"Que compraste para el almuerzo ayer?"

"yo me compre una torta de huevo" = i bought an egg sandwich

"yo no compre nada porque comi cereal en la manana"= I didn't buy anything since i had eaten cereal in the morning

Answer:

2c^2

simplified explanation:

(8c^3d^2)/(4cd^2)

= 2c^2

step-by-step explanation:

8/4 = 2

law of indices: (x^m)/(x^n) = x^m-n

using law of indices,

(c^3)/c = (c^3)/(c^1) = c^3-1 = c^2

(d^2)/(d^2) = d^2-2 = d^0 = 1

so,

(8c^3d^2)/(4cd^2)

= 2 × c^2 × 1

= 2c^2

The histogram appears to roughly estimate a normal distribution. The frequencies normally increase to a maximum and then​ decrease, and the histogram is symmetric.

The Graph of Normal Distribution is bell-shaped. Here the value of y is less for the lower value of x and then the value of y is increased for a larger value of x, but after some time value of y again getting decreases as the value of x increases.

For the Histogram to appear to be a normal distribution, the graph of the histogram must have the same nature. Thus, option B is only the correct option.

The histogram is made up of many columns and bars that are vertical with no gaps between bars with different labels of numeric data of different heights showing the size of the group of different labels.

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Answer:

67 marbles

Step-by-step explanation:

15+30=45

45+22=67

Step-by-step explanation:

you cannot add some simple numbers ? you don't know how to use a calculator ?

to solve this yourself is way shorter than putting this in here.

15 + 22 + 30 = 67

The simplified expression in mathematical form is -45.36.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The expression given is -

(-15 + (-1.6 + 9.34) / 6) × (3² - 5.7)

Simplifying the terms inside the parentheses first, we get -

(-15 + 7.74 / 6) × (9 - 5.7)

Next, we simplify 7.74 / 6 by dividing the numerator by the denominator -

(-15 + 1.29) × (9 - 5.7)

We add -15 and 1.29 inside the first set of parentheses -

(-13.71) × (9 - 5.7)

We subtract 5.7 from 9 inside the second set of parentheses -

(-13.71) × 3.3

Multiplying these two terms, we get -

-45.363 ≈ -45.36

Therefore, the value is obtained as -45.36.

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Answer: May 7th i believe

Step-by-step explanation: If they both pick up on may 4th and then they pick up every 3-4 days it would be 7-8 but 3 to 4 it is 3 and a half so the answer would be May 7th. Hope this helps...

Roselyn can drive a distance until she runs out of fuel for a time of 2.5 hours or until she spends all the fuel, whichever comes first.Roselyn can travel 120 km before running out

Distance travelled with 20 l of petrol in solution and final answer.

Roselyn's average speed is 60 kilometers per hour, and she needs to travel 150 kilometers to reach her family's place. Therefore, she will require a total of 150/60 = 2.5 hours to complete the journey.

The car's fuel efficiency is 6 kilometers per liter, meaning it consumes 1/6 liters of fuel per kilometer. To determine the total fuel required, we multiply the fuel consumption rate by the total distance: 150 * (1/6) = 25 liters of fuel.

Since the car's tank has 20 liters of fuel at the beginning of the drive, Roselyn will need an additional 25 - 20 = 5 liters of fuel to complete the journey.

As fuel costs 0.60 dollars per liter, Roselyn will need to spend a total of 5 * 0.60 = 3 dollars to purchase the necessary fuel.

Therefore, Roselyn can drive until she runs out of fuel for a time of 2.5 hours or until she spends all the fuel, whichever comes first.

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Step-by-step explanation:

50-3n

or,50=3n

or,50/3=n

or,n=16.67

Thus,the value of n is 16.67.

Answer:

X = 12

Step-by-step explanation:

the total degree of any triangle is 180.

therefore I took (7x + 4) + (5x + 3) + ( 2x + 5) = 180

I replace the Xs with 12 and then the answer is 180

(7(12) + 4) + (5(12) + 3) + ( 2(12) + 5) = 180

Answer:

29.16 grams

Step-by-step explanation:

To solve this, you have to use the weight of cocoa formula. So the weight of cocoa = 54% percent of chocolate bar's weight which is 54 gram. So weight of cocoa = 54/100*54. This will give you 29.16 grams.

The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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The contribution margin ratio is 37%, unit contribution margin is $12.95, whereas the operating income is $297,950

What is the contribution margin ratio?

The contribution margin ratio compares the contribution margin per unit to the selling price per unit whereby contribution margin is the selling price minus the variable cost per unit

unit contribution margin=$35-$22.05

unit contribution margin=$12.95

Contribution margin ratio=$12.95/$35

Contribution margin ratio=37%

operating income=(unit contribution margin*sales units)-fixed costs

sales units=39000

fixed costs= $207,100

operating income=($12.95*39000)-$207100

operating income=$297,950

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Answer:

1/12 or 0.0833

Step-by-step explanation:

1/2 divided by 6

1/2x6

1/12!

Answer: Fraction Form: 1/12

              Decimal Form: 0.0833

              Expanded Decimal Form: 0.08333333333

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Answer:

-12

Step-by-step explanation:

What you have to do is plug -4  into the function as a puzzle. So, replace all x with -4.

f(-4) = 7(-4) - 4(-4) = -28 + 16 = -12

f (-4) = 7x ( 1-4 ) - 4 (-4)

       = -28 + 16

      = -12

An equation is a mathematical statement this is made from two expressions related by an equal sign. for instance, 3x – 5 = 16 is an equation. solving this equation, we get the fee of the variable x as x = 7.

A declaration of the equality of mathematical expressions. An expression representing a chemical reaction by using chemical symbols. equation.

Conclusion: There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.

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Answer:

The answer is -73x.

Answer:

-73x

Step-by-step explanation:

Since you dont know what the number is you use a variable in place of it.

Answer:

To find the square root of 27 over m to the fifth power, we can break it down into two separate parts: the square root of 27 and the square root of m to the fifth power.

First, we can simplify the square root of 27 to get √27 = √(9 x 3) = √9 x √3 = 3√3.

Next, we can simplify the square root of m to the fifth power to get (√m)^5 = m^(5/2).

Putting it all together, we get:

√(27/m^5) = √27/√m^5 = 3√3/m^(5/2)

Therefore, the square root of 27 over m to the fifth power is 3√3/m^(5/2).