what is the range of the function f(x)=x^2+2x+4

Answer:

Your answer is C and D. :)

Step-by-step explanation:

The equations are solved to get

2/5 * (1 1/4 * x - 3 1/3) - 1 1/3 x here x = 1 3/5

2 1/8 x + 3/4 x + 1/6 - 7/12 x + 5 2/3 here x = 2 6/11

0.5(x + 1.6) + 1.4(3x + 2.4) = 9.8 here x = 1.2

1.

2/5 * (1 1/4 * x - 3 1/3) - 1 1/3 * x

opening the parenthesis and converting to improper fraction

1/2 x - 4/3 - 4/3 x

-5/6 x - 4/3

-5/6 x = 4/3

x = 8/5

x = 1 3/5

2.

2 1/8 x + 3/4 x + 1/6 - 7/12 x + 5 2/3

adding like terms

55/24 x + 35/6 = 0

55/24 x = - 35/6

x = 28/11

x = 2 6/11

3.

0.5(x + 1.6) + 1.4(3x + 2.4) = 9.8

removing the parentheses:

0.5x + 0.8 + 4.2x + 3.36 = 9.8

4.7x + 4.16 = 9.8

4.7x = 5.64

x = 1.2

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Answer:

9 years

Step-by-step explanation:
To determine the number of years it will take for the new furnace to pay for itself, we need to compare the cost of running the old furnace for that period with the cost of buying and operating the new furnace during the same time.

Let's calculate the cost of running the old furnace for one year:

Old furnace cost per year = $850

Now, let's calculate the savings in energy costs for the new furnace:

Savings in energy costs per year = 34% of $850

= 0.34 * $850

= $289

The total cost of buying and operating the new furnace for one year is:

New furnace cost per year = Cost of buying the new furnace + Savings in energy costs per year

= $2,500 + $289

= $2,789

To find the number of years it will take for the new furnace to pay for itself, we divide the cost of the new furnace by the annual savings:

Number of years to pay for itself = Cost of buying the new furnace / Annual savings

= $2,500 / $289

≈ 8.65

Since we cannot have a fraction of a year, we can round up to the nearest whole number. Therefore, it will take approximately 9 years for the new furnace to pay for itself.

The equation of the line that passes through the points (-2, 4) and (3, 9) is y = x + 6.To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b) using the given points (-2, 4) and (3, 9).

First, let's find the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the values from the points:

m = (9 - 4) / (3 - (-2)) = 5 / 5 = 1

Now that we have the slope, we can proceed to find the y-intercept (b). We can choose either of the given points to substitute into the equation.

Using the point (-2, 4):

4 = 1(-2) + b

4 = -2 + b

b = 6

Therefore, the y-intercept (b) is 6.Now we have the slope (m = 1) and the y-intercept (b = 6), so the equation of the line in slope-intercept form is:

y = x + 6.

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The solution to the system of equations is x ≈ -4.06 and y ≈ -2.7.

It seems you have provided a system of linear equations. The system can be represented as:

3x + 4y = -23

5x + y = -23

This system can be solved using various methods such as substitution, elimination, or matrix methods. Let's solve it using the method of substitution.

From the second equation, we can express y in terms of x:

y = -23 - 5x

Substituting this value of y into the first equation:

3x + 4(-23 - 5x) = -23

Simplifying the equation:

3x - 92 - 20x = -23

-17x - 92 = -23

-17x = 69

x = -69/17

x ≈ -4.06

Substituting this value of x back into the second equation to find y:

5(-4.06) + y = -23

-20.3 + y = -23

y = -23 + 20.3

y ≈ -2.7

Therefore, the solution to the system of equations is x ≈ -4.06 and y ≈ -2.7.

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The market equilibrium point is a supply of 1000 at $325

We have the demand of

So, the demand equation is a linear equation that passes through

(800, 350) and (1200, 300)

This equation is

d(x) = -x/8 + 450

We have the supply of

So, the supply equation is a linear equation that passes through

(700, 280) and (1400, 385)

This equation is

s(x) = 3x/20 + 175

At the market equilibrium point, we have

d(x) = s(x)

So, we have

3x/20 + 175 = -x/8 + 450

This gives

x = 1000

Also, we have

s(1000) = 3 * 1000/20 + 175

s(1000) = 325

This means that the market equilibrium point is a supply of 1000 at $325

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Complete question

A retail chain will buy 800 televisions if the price is $350 each and 1200 if the price is $300. A wholesaler will supply 700 of these televisions at $280 each and 1400 at $385 each.

Assuming that the supply and demand functions are linear, find the market equilibrium point

The inequality in slope - intercept form is,

⇒ y ≤ x + 5

We have to given that;

The graph of the inequality is shown in image.

Let two points on the line is,

⇒ (- 5, 0) and (0, 5)

Hence, The equation of line is,

⇒ y - 0 = (5 - 0) / (0 + 5) (x + 5)

⇒ y = x + 5

Thus, The inequality in slope - intercept form is,

⇒ y ≤ x + 5

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The value of r which is the decay rate is calculated as: -0.0203

The equation for "continual" growth (or decay) is given by the expression:

[tex]A = Pe^{rt}[/tex]

where:

A is the ending amount,

P is the beginning amount (principal, in the case of money)

r  is the growth or decay rate (expressed as a decimal),

t is the time (in whatever unit was used on the growth/decay rate).

We are given that:

A = 70000

P = 93000

t = 14

Thus:

70000 = 93000 * [tex]e^{14r}[/tex]

70/93 = * [tex]e^{14r}[/tex]

14 r = In (70/93)

14r = -0.2841

r = -0.0203

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Answer:

The relationship between the number of faces, vertices, and edges of a three-dimensional object is described by Euler's formula, which states that for any polyhedron (a solid object bounded by flat faces), the number of faces (F), vertices (V), and edges (E) satisfy the equation F + V - E = 2. This formula is true for any convex polyhedron, such as a cube or a regular tetrahedron.

The formula is based on the fact that every face of a polyhedron is bounded by a closed loop of edges, and each vertex is where three or more edges meet. The total number of edges is the sum of the number of edges around each face, which is equal to twice the number of faces since each edge is shared by two faces, and the number of edges meeting at each vertex, which is equal to the degree of the vertex (the number of edges meeting at the vertex).

Therefore, by knowing the number of faces, vertices, and edges of a three-dimensional object, we can determine if it is a convex polyhedron and use Euler's formula to check if the numbers are consistent with a solid shape.

The scale factor used to create the image is given as follows:

k = 1/4.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The equivalent segment lengths for the original figure and the image are given as follows:

Hence the scale factor used to create the image is given as follows:

k = 2/8

k = 1/4.

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Answer:

its A

Step-by-step explanation:

The customer would pay a net price of $760 per item after all discounts have been applied. It's important to note that the Actual discount percentage and net price per item may vary depending on the terms of the sale and the specific furniture center's policies.

Furniture centers often offer trade discounts to their customers to encourage orders. A trade discount is a reduction in the listed price of a product or service that is offered to trade customers, such as retailers, wholesalers, or other businesses. The discount is usually a percentage of the list price, and the actual amount of the discount depends on the quantity of the product ordered and the terms of the sale.

In addition to trade discounts, furniture centers may offer additional discounts to their customers who meet certain criteria. For example, they may offer a percentage discount for orders over a certain amount or for customers who pay in full at the time of purchase. These additional discounts are intended to encourage customers to place larger orders and to reward them for their loyalty to the furniture center.

To calculate the net price per item, you need to know the list price of the item, the trade discount percentage, and any additional discounts that may apply. For example, let's say that the list price of a piece of furniture is $1,000, and the trade discount offered by the furniture center is 20%. If the customer's invoice total is high enough to qualify for an additional discount of 5%, the net price per item would be calculated as follows:

List price: $1,000

Trade discount: 20% x $1,000 = $200

Price after trade discount: $1,000 - $200 = $800

Additional discount: 5% x $800 = $40

Net price per item: $800 - $40 = $760

So, the customer would pay a net price of $760 per item after all discounts have been applied. It's important to note that the actual discount percentage and net price per item may vary depending on the terms of the sale and the specific furniture center's policies.

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The value of the functions are;

a. x = 5/6

b. x> 5/6

c. x = 1

d. x ≤ 1

Note that functions are defined as laws or rules showing the relationship between two variables

From the information given, we have that;

f(x) = 6x - 5

g(x) = -5x + 6

To determine the functions, we have;

f(x) = 0

6x - 5 = 0

collect like terms

6x = 5

x = 5/6

f(x) > 0

6x - 5> 0

6x > 5

x> 5/6

f(x) = g(x)

6x - 5 = -5x + 6

collect like terms

11x = 11

x = 1

f(x) ≤ g(x)

6x - 5 ≤ - 5x + 6

collect like terms

11x ≤ 11

x ≤ 1

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The base angles are of 25 degree.

Given that

Two sides are equal

And one angle of triangle = 130 degree

We know that,

Triangles are three-sided polygons that can be categorized as equilateral, isosceles, or scalene depending on how long their sides are.

And triangles with two equal sides are known as isosceles triangles and

it has two equal angle also.

Therefore,

let the angle is x degree

And we know that sum of interior angles of triangle is 180 degree.

Then,

x + x + 130 = 180

              2x = 50

                x = 25

Hence the required angles are of 25 degree.

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Answer:

2.

Step-by-step explanation:

The data is skewed towards 1-25. From this we can conclude that patients only call the doctor once or twice when they are sick.

Calculus a broad subject that covers many topics such as derivatives, integrals, limits, and functions.

Calculus is a branch of mathematics that focuses on the study of change and motion. It provides a framework for understanding and analyzing quantities that vary continuously. The two main branches of calculus are differential calculus and integral calculus.

Differential calculus deals with the concept of derivatives. A derivative measures how a function changes as its input (usually denoted as x) changes. Geometrically, the derivative represents the slope of a function at a particular point. It can also be interpreted as the instantaneous rate of change of a function at a given point. Derivatives have various applications, such as determining the maximum or minimum values of functions, analyzing the behavior of functions, and solving optimization problems.

Integral calculus, on the other hand, focuses on the concept of integrals. An integral is a mathematical operation that measures the accumulation of quantities or the area under a curve. It essentially reverses the process of differentiation. Integrals can be used to compute the total change or accumulation of a quantity over a given interval, find the area of irregular shapes, and solve problems involving rates of change.

Calculus plays a fundamental role in many scientific and engineering disciplines. It is used extensively in physics, engineering, economics, computer science, and many other fields to model and solve real-world problems involving continuous change. The study of calculus also forms the basis for higher-level mathematics such as differential equations, vector calculus, and multivariable calculus.

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The derivative of [tex]f(x) = \sinh{(7e^x + 2)}[/tex] is given as follows:

B. [tex]7e^x\cosh{(7e^x + 2)}[/tex]

The function in this problem is given as follows:

[tex]f(x) = \sinh{(7e^x + 2)}[/tex]

This function is a composite function, hence we use the chain rule for derivatives, which state that:

If f(x) = f(g(x)) then f'(x) = g'(x)f'(g(x)).

The inner and outer functions are given as follows:

The derivative of the hyperbolic sine is given as follows:

cosh(x).

(derivative of the outer function).

The derivative of the exponential is given as follows:

[tex](7e^x + 2)^{\prime} = 7e^x[/tex]

(derivative of the inner function).

Hence the derivative of the function is given as follows:

[tex]7e^x\cosh{(7e^x + 2)}[/tex]

(application of the chain rule).

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Answer:

The two is in the hundredths place

Step-by-step explanation:

369.425

hundreds  tens ones. tenths hundredths thousandths

3                   6      9    .   4             2                   5

The two is in the hundredths place

Answer:

The place value of 2 in 369.425 is hundredths.

The number 369.425 is a decimal number. It has a whole number part (369) and a decimal part (0.425). The decimal part is divided into tenths, hundredths, thousandths, and so on. The 2 is in the hundredths place.

Step-by-step explanation:

The solutions to the equations are;   x = = √5+3 and x= -√5 + 3

The given equation is 4x²2²-12x+9=5

we get, 4x²2²-12x+9=5

Dividing both sides by 25, we get

4x²2²-12x= -4

Taking square root on both sides, we get

x= -√5 + 3

x =  √5+3

Therefore,  x = = √5+3 and x= -√5 + 3

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The number of unique 8-card hands to be dealt are752,538,150.

The number of different 8-card hands that can be dealt from a standard 52-card deck is given by the combination formula:

[tex]C(n, k) = n! / [(n-k)! * k!][/tex]

C(52, 8) = 52! / [(52-8)! * 8!] = 52! / [44! * 8!]

Evaluating this will give the total number of different 8-card poker hands that can be dealt from a standard deck.

Using these calculations, you would find the number of unique 8-card hands to be 752,538,150.

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Time is usually represented by the x axis

In the graph, differential is 4 or (p+k)-p = k as well as difference is -2 when y = 7 or y = 5, respectively.

A graph comprises a visual representation and diagram that displays facts or values in an organised manner in mathematics. The points of a graph are widely used to depict the connections between various objects. A. The difference between y = 7 or y = 5 is 4 and -2, respectively B. 4 is the difference, so (p+k)-p = k C. It differs by -2 D. Part C depends on 'k' rather than 'p,' not 'p'.

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A) The present value of the lease payments can be computed as $255,294.44, using the lease period, borrowing rate, and the monthly lease payments in the online finance calculator as parameters.

B) The journal entry for the lease on September 1, 2024 is as follows:

September 1, 2024:

Debit Lease Expense $8,000

Credit Lease Payable $8,000

(To record the lease liability, payable on September 30, 2024.)

The present value of the lease payments can be computed using an online finance calculator as follows:

N (# of periods) = 36 months (3 years x 12)

I/Y (Interest per year) = 8%

PMT (Periodic Payment) = $8,000

FV (Future Value) = $0

Results:

Present Value (PV) = $255,294.44

Sum of all periodic payments = $288,000.00

Total Interest = $32,705.56

September 1, 2024:

Lease Expense $8,000 Lease Payable $8,000

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The sentences in this paragraph best support the idea that the printing press was an important invention A. They provide examples showing the impact of the printing press on varied groups of people.

With the greater availability of books, people were spurred to develop necessary skills in reading, thus resulting in higher literacy rates and a enhanced societal benefit.

Subsequently, due to simpler, more exact shares of data through printing, scientific progress was greatly boosted. Moreover, churches had the chance to further propagate their supernatural ideas with the aid of the printing press.

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There is not enough information to answer the first question.

For the second question, first term = 2, common ratio = 2

A geometric sequence is a set of numbers where each term following the first is obtained by multiplying the term before it by a fixed quantity, called the common ratio. In other terms, a geometric sequence is one in which every term's ratio to the term before it is constant.

We know that;

T5/T3 = 4

T5 =[tex]ar^4[/tex]

T3 = [tex]ar^2[/tex]

Then;

4 = [tex]ar^4/ar^2[/tex]

4 =[tex]r^2[/tex]

r= 2

Again we have that;

T4 = 16

T4 =[tex]ar^3[/tex]

16 = [tex]a(2)^3[/tex]

a = 2

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The method of bar chart is appropriate for representation.

According to the given data,

The most effective way to present the data is in a bar chart.

An effective visual representation of categorical data that shows the frequency or count of each category is a bar chart.

The length of each bar would reflect the frequency or count of each score, and the categories would be the test results in this instance.

It would be a simple and unambiguous approach to compare the various test results.

These are the three key characteristics of bar graphs:

The bar graph makes it simple to compare various sets of data among various groups.

The relationship is depicted using two axes, with the discrete values on one axis and the categories on the other.

The graph displays the key alterations in the data over time.

Hence,

Bar chart method should be used.

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One serving of tomato juice has mg of more vitamin C per serving is 90mg.

We are given that;

Tomato juice percentage of vit c

Now,

The Daily Value (DV) for vitamin C is 90 mg for adults and children aged 4 and older. This value is used to calculate the percent DV that you see on nutrition labels. So, if one serving (1 cup or 240 ml) of 100% canned tomato juice contains 74% of the DV for vitamin C, this means that one serving contains approximately 66.6 mg of vitamin C

Solving this calculation;

0.74 x 90 mg = 66.6 mg

The DV for vitamin C=90 mg.

Therefore, by percentage the answer will be 90mg.

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If bought a variety of fruits to bring to a party, the probability that Johnny chooses an apple or a pear after making a random selection from the bag is 0.066 or 6.6%.

The probability that Johnny chooses an apple or a pearl is the chance that either an apple or a pearl is chosen from the 50 pieces of fruits, which is determined by the multiplication of the two probabilities.

Probability refers to the likelihood of achieving an expected outcome or result amid the possibility of many outcomes.

Fruits      Units

Bananas   24

Apples      15

Pear           11

Total        50

The Probability of choosing a banana = 0.48 (24 ÷ 50)

The chance of choosing an apple = 0.3 (15 ÷ 50)

The likelihood of choosing a pear = 0.22(11 ÷ 50)

The probability of choosing an apple or a pear = 0.066 (0.3 x 0.22)

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