Using the simplified expression you found in the last problem, solve for x. 2(4x-3)=10+(-4x)+14

The expression, h(x), in standard form that describes the length of the top surface of the rectangular boxes can be modelled by the function

[tex]h(x) = 6x + 66x^2 + 17[/tex].

A simplified way to write an expression is to use the expression in standard form. It entails expressing the expression in terms of its highest exponent, variables, and numerical coefficients. The use of standard form is intended to simplify the reading and comprehension of an expression. As opposed to writing an expression as, [tex]3x^2 + 4x +[/tex]7, it can be written in standard form as [tex]3x^2 + 4x + 7[/tex].

The two functions, f(x) and g(x), can be combined to form a single equation that expresses the length of the top surface of the rectangular boxes, which leads to the derivation of this expression.

The top surface's area is represented by the function f(x), which has the following form: [tex]f(x) = 66x^2 + 17x + 1[/tex]. With the formula g(x) = 6x + 1, the function g(x) denotes the width of the top surface. These two functions are combined to give us [tex]h(x) = 6x + 66x^2 + 17[/tex]. As a result, this expression describes how long the top surface of the rectangular boxes is.

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1. The height of the pyramid is 3.7 inches.

2. The length of the crossbar is 2√2 feet.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.

1. We know, The height, slant height, and half of the base length form a

right-angled triangle

Therefore, h² = 4² - (3/2)².

h² = 13.75

h = 3.7 inches.

2. We know, In a 45°, 45° and 90° triangle, It is an isosceles right-angled triangle, The hypotenuse is √2 times the two similar sides.

Therefore, From the given information, The length of the crossbar is

2√2 feet.

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Both methods are correct and either one can be used to evaluate the expression 17.

Both Kode and Elijah are using the distributive property to evaluate the expression 17(4+15).

The distributive property states that a(b+c) = ab + ac.

Kode's method:

17(4+15) = (17*4) + (17*15) = 68 + 255 = 323

Elijah's method:

17(4+15) = 17*19 = 323

Both students get the same answer of 323.

Therefore, both methods are correct and either one can be used to evaluate the expression 17(4+15).

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The transformations that have been applied to the parent function y=-(1)/(2)(x-3)^(2)-5 are: horizontal shift, vertical shift, and vertical stretch.

The transformations that have been applied to the parent function y=-(1)/(2)(x-3)^(2)-5 are:

- Horizontal shift: The parent function has been shifted to the right by 3 units. This is indicated by the subtraction of 3 from x in the equation.
- Vertical shift: The parent function has been shifted downward by 5 units. This is indicated by the subtraction of 5 from the entire equation.
- Vertical stretch: The parent function has been stretched vertically by a factor of (1)/(2). This is indicated by the multiplication of the entire equation by (1)/(2).

Therefore, the correct answers are horizontal shift, vertical shift, and vertical stretch.

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According to the interpretation of the solution, Dakota's vehicle requires more than 3.6 gallons of fuel to travel the 117 miles to his brother's home.

Dakota will use x gallons of gas to travel 117 miles to his brother's home.

The following inequalities can be used to determine how many gallons of fuel Dakota requires the most:

x ≥ 117/32.5

According to this inequality, x must be more than or equal to 117 miles, which is the required driving distance for Dakota, divided by 32.5 miles per gallon, the maximum fuel efficiency for his vehicle.

After finding x, we obtain:

x ≥ 3.6

Hence, in order to go 117 miles to his brother's home, Dakota would require at least 3.6 gallons of gasoline.

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On simplifying the given expression using simplification method BODMAS, we get the answer 10. Thus, in the calculator the calculation must be done from left to right.

Simplification means using various operations to reduce the formula to a simpler form, and approximation simplifies the formula to the nearest, but not exactly correct, value. 

BODMAS in simplification stands for Bracket, Ob, Division, Multiplication, Addition, and Subtraction. BODMAS is used to describe the order of operations in formulas. In some areas, BODMAS is also known as PEDMAS. This represents parentheses, exponents, division, multiplication, addition, and subtraction. 

Solution using BODMAS and simplifying it:

72÷12+9−5 = (72/12) + 9 - 5

                  =6 + 9 - 5

                  = 15 - 5

⇒72÷12+9−5 = 10

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Answer:

Total time = (length of one song) x (number of songs)

Length of one song = 3/8 minutes

Number of songs = 12

Total time = (3/8) x 12

Total time = 36/8

Simplifying the fraction, we get:

Total time = 4 and 4/8 minutes

Total time = 4 and 1/2 minutes

Therefore, Michael sang for a total of 4 and 1/2 minutes.

Answer: C.

Step-by-step explanation:

The height of the ball is represented by the equation -1(-6x^(2)+4x+2), where x is time in seconds.

We can rewrite this equation by distributing the -1 and simplifying.

First, we distribute the -1 to each term inside the parentheses:
-1(-6x^(2)+4x+2) = 6x^(2) - 4x - 2

Now, we can simplify by combining like terms:
6x^(2) - 4x - 2 = 6x^(2) - 4x - 2

Therefore, the rewritten equation for the height of the ball is:
h = 6x^(2) - 4x - 2

This equation shows the relationship between the height of the ball (h) and the time in seconds (x). As time increases, the height of the ball changes according to the equation.

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Answer:

Step-by-step explanation:

rnw

The final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly is $5386.42.

Interest is the amount a lender or financial institution receives for lending money. Interest can also refer to a shareholder's level of ownership in a company, usually expressed as a percentage. 

Interest rate indicates the cost of borrowing, or the reward for saving. So if you are a borrower, the interest rate is the amount charged to borrow money, expressed as a percentage of the total loan amount. 

Solution according to the information given in the question :

Given, Principal(P) = $5,000

          Compounding frequency(n) = 4

          Time(in years)(T) = 5  

           Interest rate = 6%

Amount = P× (1 + r/n)^t

             = 5,000 × (1 + 6/4×100)⁵

             = 5,000 × (1 + 0.015)⁵

             = 5,000 × (1.015)⁵

             = 5000 ×1.077

             = $5286.42

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The probability of landing on a 6 is 1/6. The probability of rolling a 7 is zero.

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics refers to the study of events subject to probability.

If you roll a fair number cube, The probability of landing on a 6 is 1/6.

As, all the possible outcome is 6 and favourable outcome is 1 (6), Probability = 1/6 or 16.66%

The probability of rolling a 7 is zero as there is only 6 possible out come and 7 is the 7th outcome which is not possible, therefore 0.

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Leo's balance after 8 months will be $1723.05. The solution has been obtained by using geometric progression.

What is a geometric progression?

A geometric progression, also known as a geometric sequence in mathematics, is a set of non-zero numbers where each term comes after the first by multiplying the previous term by a fixed, non-zero number called the common ratio.

We are given that bank balances at the end of months 1, 2, and 3 are $1,500.00, $1,530.00, and $1,560.60, respectively.

From this, we get the common ratio to be 51/50 i.e. 1.02.

Now, using aₓ = a₁ r⁽ˣ⁻¹⁾ , we get

⇒a₈ = a₁ r⁽⁸⁻¹⁾

⇒a₈ = a₁ r⁷

⇒a₈ = 1500 (1.02)⁷

⇒a₈ = 1500 (1.1487)

⇒a₈ = $1723.05

Hence, Leo's balance after 8 months will be $1723.05.

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Answer:

Its 48

Step-by-step explanation:

2x+4=4x-16 is your equation.

subtract 2x to both sides

4=2x-16

add 16 to both sides

20=2x

divide 2 by both sides.

10=x

Then plug in the 10.

2(10)+4+ 4(10) - 16=

24+24= 48

The zeros of the polynomial function f(x) = -8(x-1)^(3)(x+5)^(2)x^(4) are x = 1, x = -5, and x = 0. The smallest zero is x = -5 with multiplicity 2.

To find the zeros of the polynomial function f(x) = -8(x-1)^(3)(x+5)^(2)x^(4), we need to set the function equal to zero and solve for x:

0 = -8(x-1)^(3)(x+5)^(2)x^(4)

This equation will be true when any of the factors on the right-hand side are equal to zero. Therefore, we can find the zeros by setting each factor equal to zero and solving for x:

x-1 = 0 -> x = 1
x+5 = 0 -> x = -5
x^(4) = 0 -> x = 0

So, the zeros of the polynomial function are x = 1, x = -5, and x = 0.

The smallest zero is x = -5 with multiplicity 2, since it is the smallest value of x and the factor (x+5)^(2) has an exponent of 2.

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airplane A

To compare the rate of speed of Airplane A and Airplane B, we need to calculate the speed of Airplane B first.

The formula to calculate distance is:

distance = rate x time

For Airplane A, we know:

distance = 1662 miles

time = 6 hours

So, we can rearrange the formula to solve for the rate:

rate = distance / time = 1662 / 6 = 277 miles per hour

For Airplane B, we know:

y = 922/3

x = rate of speed over 6 hours

We can use the formula to solve for x:

distance = rate x time

922/3 = x * 6

x = (922/3) / 6 = 153.67 miles per hour

Comparing the rates of the two airplanes, we can see that Airplane A traveled at a faster rate with 277 miles per hour compared to Airplane B's rate of 153.67 miles per hour. Therefore, Airplane A traveled at a faster rate.

The length of TS is 30.

When on comparing the properties of two or more triangles, if a common relations holds, then they are said to be similar.

Note that similarity is NOT congruency.

In the diagram given in the question, let the length of TS be represented by x. So that;

TS/ QS = SU/ SR

But, we have;

TS = x

SU = TS - 6 = x - 6

So that;

x/ 55 = (x - 6)/ 44

44x = 55(x - 6)

      = 55x - 330

330 = 55x - 44x

330 = 11x

x = 330/ 11

 = 30

x = 30

Therefore, the length of TS is 30.

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Answer:

Step-by-step explanation:

y = [tex]\frac{1}{2}[/tex] x   (divided both sides by 2)

This is slope intercept form (y=mx+b)

Slope = [tex]\frac{1}{2}[/tex] and intercept = 0

Answer:

The factors of 899 are 1, 29, 31, 899. Therefore, 899 has 4 factors.

Step-by-step explanation:

Therefore, 899 has 4 factors. And is not prime

The firm should accept the project with an Internal Rate of Return (IRR) of 13%, as it is greater than their WACC of 8.5%.

To find the Weighted Average Cost of Capital (WACC) for the firm, we need to calculate the cost of debt, cost of preferred stock, and cost of equity:

Cost of Debt: 8% coupon bond / $1100 price = 7.2727% cost of debt

Cost of Preferred Stock: $5 dividend / $50 price = 10% cost of preferred stock

Cost of Equity: Risk-free rate + (Beta * Market risk premium) = 4% + (1.5 * 8%) = 14% cost of equity

WACC: (2 Mil * 7.2727%) + (4 Mil * 10%) + (6 Mil * 14%) / (2 Mil + 4 Mil + 6 Mil) = 8.5% WACC

The firm should accept the project with an Internal Rate of Return (IRR) of 13%, as it is greater than their WACC of 8.5%.

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Given that △ABC ≅ △XYZ which of the following are pairs of corresponding parts of the triangles ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z and  AB ≅ XY, BC ≅ YZ, AC ≅ XZ.

Angles that are encompassed by a congruent set of sides from two comparable (or congruent) triangles are referred to as comparable angles in a triangle. In a triangle, corresponding angles are of the same measure.

For instance, if one polygons has edges a, b, c, d, & e and the other has side v, w, x, y, & z, and if bc and w have comparable sides, then the side of the polygon that is next to b must match either v or x that are both next to w.

Corresponding angles: ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z.

Corresponding sides: AB ≅ XY, BC ≅ YZ, AC ≅ XZ.

Corresponding sides: AB ≅ XY.

Corresponding sides: AB ≅ ZY.

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a) The critical value of t for this question at the .05 significance level is -2.11.

b) The calculated value of t for this question at the .05 significance level is -1.47, given a standard deviation of 0.63.

c) We can reject the null hypothesis because the calculated t-value (-1.47) is less than the critical t-value (-2.11). This indicates that games are less than 3.50 hours long.

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Answer:

  B] {(6, 0), (5, 0), (4, 0)}

Step-by-step explanation:

You want to know which of the given relations is a function.

A relation is a function if its graph passes the "vertical line test." To pass that test, the graph must not intersect a vertical line more than once.

When a relation is written as a set of ordered pairs, the list of x-values (input, first in the ordered pair) must not contain any repeated values.

  A] input value 2 repeats

  B] a function

  C] input value 6 repeats

  D] input value 0 repeats

The relation of answer choice B is a function.

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Answer:

marcy added 20 instead of equating that -20

8m-20=36

8m=36+20

8m÷8=56÷8

m=7

Step-by-step explanation:

Use the Pythagorean Identity

[tex] \cos {}^{2} ( \frac{x}{2} ) = 1 - \sin {}^{2} ( \frac{x}{2} ) [/tex]

The equation that represents the amount of money Gilberto has after buying T-shirts for n sponsors at a cost of $4.75 per shirt can be written as nx - 4.75n = n² - 4.75n.

Assume count that Gilberto has n sponsors, and he plans to buy a t-shirt for each sponsor at a fee of $4.75 in step with a t-shirt. Assume also count on that every sponsor contributes x greenbacks to Gilberto's fundraising marketing campaign.

The overall amount of money Gilberto raises from all n sponsors is n instances x or nx. If Gilberto makes use of some of this cash to buy t-shirts, he may have nx - 4. 75n bucks left over.

Therefore, the equation that represents the quantity of cash Gilberto has after shopping for t-shirts is:

nx - 4. 75n = (n - 4. 75)n

simplifying this equation, we get:

nx - 4. 75n = n² - 4. 75n

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Answer:

Step-by-step explanation:

16 is diameter so r= 16/2= 8

area of circle = 3.14*r^2

therefore 3.14*8^2

which is 3.14*64=200.96cm sq

Enjoy :)

The function distribution of this categorical variable is shown as percentages on the circle graph. As a result, the data is categorical and univariate (one variable).

Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.

The right response is: The information is categorical and univariate.

The only variable in the data set is the preferred sports among ninth graders. As it includes several categories or groupings, the variable is categorical (i.e., baseball or softball, basketball, lacrosse, soccer, and field hockey). The distribution of this categorical variable is shown as percentages on the circle graph. As a result, the data is categorical and univariate (one variable).

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The journal entry to record the expenses with the annual amortization expense list is present in above figure.

a) Amortization per year = $43750 per year.

b) Amortization per year = $5230 per year.

c) Amortization per year = $14000 per year.

Amortisation of intangible assets : If any intangible assets are purchase and this will be amortized over the useful life of the assets and this will deduct the value of the intangible assets over the year completed. Now, we prepare a journal entry to record the expense:

a) A patent is a legal right granted to an individual or company to reproduce, use or sell an invention without interference from others.. A patent with 10-year remaining legal life was purchased for $350,000. Since the patent will be worthless after 8 years, the life will be considered to be 8 years. Amortization per year = $350000/8

= $43750 per year.

Amortization expense A/C.. Dr $43750 ( debit )

To Patents A/C $43750 ( credit)

b) Cost of the patent to date consisted in legal fee for handling the patent application = $52,300

Because the patent has commercial value during its remaining statutory life of 10 years. Only the original cost of patent will be amortized hence

Amortization per year = $52300/10

= $5230 per year

Amortization expense $5230 (debit)

Patents $5230 ( credit)

C) Since the additional cost will be incurred after 5 years and hence renewal is conditional , original life and cost will be considered.

Amortization per year = $70000/5 = $14000

Hence, required value is $14000.

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Complete question:

Amortization Expense : For each of the following unrelated situations, calculate the annual amortization expense and prepare a journal entry to record the expense:

a)A patent with a 10-year remaining legal life was purchased for $350,000. The patent will be commercially exploitable for another eight years. b) A patent was acquired on a device designed by a production worker. Although the cost of the patent to date consisted of $52,300 in legal fees for handling the patent application, the patent should be commercially valuable during its entire remaining legal life of 10 years and is currently worth $400,000.

c) A franchise granting exclusive distribution rights for a new solar water heater within a three-state area for five years was obtained at a cost of $70,000. Satisfactory sales performance over the five years permits renewal of the franchise for another three years (at an additional cost determined at renewal).

General Journal :

Ref. Description Debit Credit

a. To record patent amortization. ___ __

b. To record patent amortization. __ __

c. To record franchise amortization. __ ___