Write the standard form of the following polynomial.
(2x-3)²-3(x-2)(x+4)-7

X² ? X+ ?

You would need an additional $3.88 to buy the skateboard.

We need to calculate the total cost, including sales tax.

The sales tax rate is 6%, so the tax on a skateboard costing $98 would be as follows:

tax = 0.06 x $98 = $5.88

Consequently, the skateboard would have a total cost of:

total cost = $98 + $5.88 = $103.88

Since you have $100 to spend, you do not have enough money to buy the skateboard. You would need:

additional money = $103.88 - $100 = $3.88

Therefore, you would need an additional $3.88 to buy the skateboard.

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The decimals as a power of 10 are given as follows:

A number in scientific notation is given by the notation presented as follows:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.

Hence the numbers are represented as follows:

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The two roots of the quadratic equation x² - 5x + 3 = 0 are (5 + √13) / 2 and (5 - √13) / 2.

To find the roots of the quadratic equation x² - 5x + 3 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

Substituting the values of a, b, and c from the given equation, we have:

x = (-(-5) ± √((-5)² - 4(1)(3))) / 2(1)

x = (5 ± √(25 - 12)) / 2

x = (5 ± √13) / 2

Therefore, the roots of the equation are (5 + √13) / 2 and (5 - √13) / 2.

To verify that these are indeed the roots of the equation, we can substitute each of these values for x in the original equation and check if the equation is satisfied. For example, if we substitute (5 + √13) / 2 for x, we get:

(5 + √13)² - 5(5 + √13) + 3 = 0

Simplifying this equation, we get:

13 - 5√13 + 8 + 13 - 5√13 + 3 = 0

This equation is true, which means that (5 + √13) / 2 is a root of the equation x² - 5x + 3 = 0. Similarly, we can verify that (5 - √13) / 2 is also a root of the equation.

These roots can be found using the quadratic formula, which is a useful tool for solving quadratic equations.

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Answer:

exponential graph

Step-by-step explanation:

it is a exponential graph the is negative ,if you substitute x values and find the points to plot you'll see how it is plotted

Answer:

See graph

Step-by-step explanation:

The graph of any function can be identified by making an x-y table.

Choose some values for x (often -2, -1, 0, 1, 2)

f(-2) = - 2^(-2) = - 1/4

f(-1) =  - 2^(-1) = - 1/2

f(-0) =  - 2^(-0) = - 1

f(1) =  - 2^(1) = - 2

f(2) =  - 2^(2) = - 4

Answer: 25%

Step-by-step explanation:

51/204=0.25

0.25 x 100 = 25

Answer:25%

Step-by-step explanation:

Answer:

[tex]c. 1/5[/tex]

Step-by-step explanation:

You have the points (-5, 0) and (0, 1).

To find the slope, b, of the original line, you can use the formula [tex](y_{1}-y_2) /(x_1-x_2)[/tex].

[tex]b = (0-1)/(-5-0) = -1/-5 = 1/5.[/tex]

The slope of a line parallel to the original line would have the same slope as the original line, therefore [tex]1/5.[/tex]

Using the property of proportionality for the equation (6-x) : (7-x) :: (18-x) : (22-x), then, x = ⁶/₇.

Solving this problem by using the property of proportionality, which states that the ratio of the first two terms in a proportion is equal to the ratio of the last two terms. In this case:

(6-x) : (7-x) :: (18-x) : (22-x)

Solving for x, cross-multiply the ratios:

(6-x) x (22-x) = (7-x) x (18-x)

Expanding both sides:

132 - 28x + x² = 126 - 25x + x²

Simplifying, we get:

7x = 6

Therefore, x = ⁶/₇.

Thus, the solution to the proportion is:

(6-x) : (7-x) :: (18-x) : (22-x)

or

⁶/₇ : ¹/₇ :: ¹²/₇ : ¹⁶/₇

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The meauser of center is the most appropriate answer for table two is the mean.

Mean, in terms of math, is the total added values of all the data in a set divided by the number of data in the set.

Each mean serves to summarize a given group of data, often to better understand the overall value of a given data set. Pythagorean means consist of arithmetic mean, geometric mean, and harmonic mean

It is the mean because all of the data points are fairly close and there aren't any outliers (extreme values).

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The truth statements about the function f(x) = 14(0.87)^x is Growth; y = 0

From the question, we have the following parameters that can be used in our computation:

f(x) = 14(0.87)^x

An exponential function is represented as

y = ab^x

Where

a = initial value

b = growth/decay factor

In this case, the exponential function is a decay function

This means that

The value of b is less than 1 i.e.

b = 0.87 and 0.87 < 1

Hence, the function is a decay function

Recall that

f(x) = 14(0.87)^x

So, we have

y = 0 as the the equation of the asymptote

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Answer:  (5, -1)

Step-by-step explanation:

format:  f(x)

in  f(5)=-1       x=5

also sometimes f(x) is called y so  y= -1

put into ordered pair format

(5, -1)

The following are stated goals for this class:

1. Help students develop their ability to apply math concepts to real-world problems.

2. Increase your knowledge of consumer applications and personal financial management.

3. Explain the basics of home mortgages.

These goals are aimed at providing students with practical skills and knowledge that can be applied to their everyday lives, such as managing personal finances, understanding the mortgage process, and planning for retirement.

By learning math concepts in the context of real-world situations, students are better equipped to make informed decisions and solve problems that they may encounter in their personal and professional lives.

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Answer:no image

Step-by-step explanation:

Step-by-step explanation:

No image is overe there please add the image

The values that fit in the solution are -4, -3, -2, -1 , 0

g > - 5

Inequalities are described as expressions that are used to represent an unequal relationship between numbers or variables.

They are represented with the symbols;

From the information given, we have that;

4 - 5g > 39

collect the like terms, we get;

-5g > 39 - 4

subtract the values

-5g > 35

Divide by the coefficient of g, we get;

g > -5

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Answer: the answer to be smart is to learn

Step-by-step explanation:

if you learn then you can understand the u are not smart

The value of function g (5) is,

⇒ g (5) = 30/13

We have to given that;

Function is,

g (x) = {(x² + 5) / (x + 8)   if x ≠ - 8

      = { x - 1   ; if x = - 8

Hence, The value of function g (5) is,

⇒ g (5) = (x² + 5) / (x + 8)

⇒ g (5) = (5² + 5) / (5 + 8)

⇒ g (5) = (30) / (13)

Thus, The value of function g (5) is,

⇒ g (5) = 30/13

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Answer:

10868

Step-by-step explanation:

11x26=286

286x38=10868

According to the given question, Alice should use this equation f(t) = [tex]24,000(0.945)^t[/tex] to represent the value of the car after t years.

Depreciation is the expected decrease in the value of fixed assets over the course of a fiscal year. For physical assets like real estate, machinery, vehicles, and other items, large lump sum acquisitions are made.

The equation[tex]f(t) = 24,000(0.945)^t[/tex] represents the value of the car after t years, where 0.945 represents the remaining value of the car after one year of depreciation at a rate of 5.5%.

To calculate the value of the car after two years, for example, we would substitute t = 2 into the equation:

f(2) = [tex]24,000(0.945)^2[/tex]

f(2) = 24,000(0.893025)

f(2) ≈ 21,433.80

Therefore, the value of the car after two years would be approximately $21,433.80.

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The functions that have a range of all real numbers include the following:

Option 1; f(x) = -x + 2

Option 3; [tex]h(x) = 2^x +1[/tex]

In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range for f(x) and h(x):

Range = {-∞, ∞}, y|y ∈ R, or all real numbers.

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[tex][D]= \begin{bmatrix} 5&0&-8\\ 10&-2&7\\ -3&-9&6 \end{bmatrix}\implies 2[D] \stackrel{ \textit{scalar multiplication} }{\begin{bmatrix} (2)5&(2)0&(2)-8\\ (2)10&(2)-2&(2)7\\ (2)-3&(2)-9&(2)6 \end{bmatrix}} \\\\\\ ~\hspace{12.5em} 2[D]= \begin{bmatrix} 10&0&-16\\ 20&-4&14\\ -6&-18&12 \end{bmatrix}[/tex]

Answer:

A) angle 1 is congruent (equal size) to angle 4.

Step-by-step explanation:

when 2 lines intersect, then the intersection angles are the same on both sides of any of the lines. they are only left-right mirrored.

Answer:

A) angle 1 is congruent (equal size) to angle 4.

Step-by-step explanation:

Answer:

The item when it is costs $50 and there is a 55% item, as the cost would be $22.50

Step-by-step explanation:

Whenever a discount is offered on a certain item, we can find the new price of the item using the formula.

[tex]N(P)=O-(P*O)[/tex], where N(P) is the new price (price when discount is applied), P is the percentage (converted to a decimal to simplify the problem), and O is the old price (price before discount is applied)

First store:  Since the item costs $60 (O) at this store and there is a 60% discount (60% becomes 0.60 and is our P value), we can find the new price aka N(P):

[tex]N(0.60)=60-(0.60*60)\\N(0.60)=60-36\\N(0.60)=24[/tex]

Second store:  For this store, our O value is $50, and our P value is 0.55 (55% becomes 0.55):

[tex]N(0.55)=50-(0.55*50)\\N(0.55)=50-27.50\\N(0.55)=22.50[/tex]

Thus, the second store has the better price

Answer:

[tex]v = \pi {r}^{2} h[/tex]

[tex] {r}^{2} = \frac{v}{\pi \times h} [/tex]

[tex]r = \sqrt{ \frac{v}{\pi \times h} } [/tex]

D is the correct answer.

Answer:

Step-by-step explanation:

Angle KEF and JEK

Answer:

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

Complementary angles are the angles that together form a right angle.

In the picture we see two right angles:

The first one, ∠DEJ has a pair of complementary angles:

The second one, ∠JEF has a pair of complementary angles:

If Jared uses two theorems together to make a conjecture about the sum of the interior angles of pentagons, Jared is using deductive reasoning. Correct option is B.

Deductive reasoning is a logical process in which a conclusion is reached by applying general principles or known information to specific situations. In this case, Jared is using two theorems, which are general principles that have been proven to be true, to make a conclusion about a specific situation, the sum of interior angles of pentagons.

The conclusion that Jared makes is a conjecture, which is a hypothesis or a tentative conclusion that is based on limited evidence or observation.

In contrast, inductive reasoning is a logical process in which a conclusion is reached based on a series of observations or specific instances. Inductive reasoning involves making generalizations based on specific observations, which can lead to a hypothesis or a theory.

Therefore, Jared's use of two theorems to make a conclusion is an example of deductive reasoning. Correct option is B.

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Answer:

it is 0.94 miles

Step-by-step explanation:

that is because to make a mile you need 63,360 but since you have 60,000 it is not technically a mile

Squaring a number implies increasing it by itself. In case the number being squared is negative, the result will continuously be positive. Increasing a number by 2 implies multiplying it, which is not linked to squaring a number.

To square a number, one must raise it to the power of two, that is different from carrying out its multiplication with itself. One way of squaring a value is shown by taking the number 3 and raising it to the power of 2.

3² = 3 x 3 = 9

By the same way , if we raise -2 to the power of 2, the result will be a positive value of four.

Raising numbers to the power of two is a frequent mathematical procedure use in numerous academic fields such as algebra, geometry, physics, and statistics.

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The mapping of the function f(x) given as 3x⁴ - 4x³ + 3x² - 5x - 3 is define at;

-3, f(-3) = 390 and at 4, f(4) = 537

A function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers

By substitution:

For x = -3;

f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3

f(-3) = 3(81) + 4(27) + 3(9) + 15 - 3

f(-3) = 243 + 108 + 27 + 15 - 3

f(-3) = 390

For x = 4;

f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3

f(4) = 3(256) - 4(64) + 3(16) - 20 - 3

f(4) = 768 - 256 + 48 - 20 - 3

f(4) = 537

Therefore, the mapping of the function f(x) = 3x⁴ - 4x³ + 3x² - 5x - 3 for the values of x: -3 and 4 we have the results 390 and 537 respectively.

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As per the given variables, the rate at which they earn credits is 8 credits per semester

Total number of credits = 19

Total number of semesters = 6

Credits after six semesters = 67

Calculating the change in credits -

Change in credits -

Credits after six semesters - Inital credits

= 67  - 19

= 48 credits

Total time = 6 semesters

Calculating the change in credits over the six semesters and dividing by the total time to get the pace at which the college student is acquiring credits.

Therefore, the rate at which the college student is earning credits is:

Rate = Change in credits / Total time

= 48 credits / 6 semesters

= 8 credits per semester

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