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The equation x² + 4x - 7 can be written in the form (x + a)² - b as (x + 2)² - 11.

It follows from the task content that the equation x² + 4x - 7 is to be written in the vertex form; (x + a)² - b.

Since the given equation is; x² + 4x - 7 in which case, b is a constant.

b = constant

x² + 4x - 7

We therefore have an equivalent expression using the completing the square method as follows;

(x + 2)² - 4 - 7

= (x + 2)² - 11

Hence,

x² + 4x - 7 = (x + 2)² - 11

To Check:

= (x + 2) (x + 2) - 7

= x² + 2x + 2x + 4 - 11

= x² + 4x - 7

Therefore, the obtained equation; (x + 2)² - 11 is another form the equation x² + 4x - 7 can be written.

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Carlos attempted correctly.

Formulas for converting temperature values between different units are referred to as temperature conversions. There are numerous ways to convert temperatures. The most popular units of measurement among these are Kelvin, Celsius, and Fahrenheit.

Given:

We know the formula

F= 9/5 C + 32

Now, writing in the equation form

5F = 9C + 160

5F- 9C = 160

As, per the given Information Carlos attempted the right form and

Mikala made a mistake in transferring 5/9.

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The difference between the apply and the transform function is explained below.

In order to differentiate these function, first we have to know the definition of each of the function.

The apply function is used to operate on different types of data.

Where as the transform function is used to convert an equation transforming into one equation to another whose given roots are inverse to the roots present in an equation that is given

According to the definition, the difference between these function is defined as the transform() can take a function and string function then list of functions finally a dict.

Where as the apply() is only allowed a function and on the other hand it works with multiple Series at a time. Where as the transform function is only allowed to work with a single Series at a time.

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Answer:

c + p <= 20

2c >= p

Step-by-step explanation:

We can declare our variables as:

c = pounds of chicken

p = pounds of pork

The total meat can be expressed as c + p, and at most signifies that the family needs 20 pounds or less. Putting this together, one equation becomes c + p <= 20.

The family additionally wants at least 2 * c as p, which means that 2*c is greater than or equal to p, or 2c >= p.

hope this helps :)

Answer: 95/3 gallon of paint

Step-by-step explanation:

I guess you mean each requires 5/3 gallon of paint

If so, we take 5/3 times 19 = 95/3 gallon of paint

95/3 = 31 2/3

Answer:

A. It is a decrease in assets.

Step-by-step explanation:

The business paid $700,000 to the Loans Payable via cash, reducing their assets by 700,000 dollars AND increasing the credits. The business increased its credit score since it paid the exact amount it got a loan for back to the Loan Company.

That money was the payable loan depicted in the Debit section.

Answer:

OptionA) Decrease in assets

Step-by-step explanation:

The business paid $700,000 to the Loans Payable via cash, reducing their assets by 700,000 dollars AND increasing the credits.

Answer:

Lola can buy 12 DVD's,

Step-by-step explanation:

Lola's dad gives each of his 5 children an equal part of $340, which means that each child receives $340 / 5 = $68. Lola adds $28 to her portion, so she has a total of $68 + $28 = $96 to spend on gifts.

Lola finds classic DVDs for $8 each, and she has $96 to spend, so she can buy a total of $96 / $8 = 12 DVDs. Therefore, Lola can buy 12 classic DVDs with the money she received from her dad and the additional money she added.

I did some stuff I hope you get the bar graph or a diagram of sorts

The number of DVDs Lola can buy if, Lola's dad gives each of his 5 children an equal part of $340 to buy gifts, is 12.

One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.

Given:

Lola's dad gives each of his 5 children an equal part of $340 to buy gifts,

Lola adds $28 to her portion. She finds classic DVDs for $8 each,

Calculate the money each child gets as shown below,

The money each child gets = Total money/number of children

The money each child gets = 340 / 5

The money each child gets = 68

The total money Lola has after adding extra money,

The total money Lola has = 68 + 28

The total money Lola has = 96

Calculate the number of DVDs as shown below,

The number of DVDs = total money/price of each DVDs

The number of DVDs = 96 / 8

The number of DVDs = 12

Thus, the number of DVDs Lola can buy is 12.

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The amount of ascent, or vertical distance, divided by the run, or horizontal distance, is how slope is commonly expressed as a percentage.

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Answer:

7

Step-by-step explanation:

-(-4) + 3

= 4 + 3

= 7

The graph of which the function has an axis of symmetry at x = 3 is the graph of

The axis of symmetry of a quadratic function is the line that bisects the curve into two.

The formula for the axis of symmetry is of the form

x = -b / 2a

for the function y = x² - 6x - 1

b = -6

a = 1

the axis of symmetry, x = -(-6/(2 * 1))

= - (-3)

= 3

hence the axis of symmetry is x = 3

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The tools that would be used to make header 1 appear and look like header 2 is the alignment tool icon and the Bold tool icon.

Microsoft Excel is a spreadsheet that can be used for a variety of features such as:

As a Microsoft software, Microsoft Excel can also be used to edit sheets. In the image attached, the required tool icons needed to change the header 1 into header 2 is the alignment tool icon and the Bold tool icon. The two tools can be seen in the image as the two lower left icons.

Electronic spreadsheet programs were originally based on paper spreadsheets used for accounting. As such, the basic layout of computerized spreadsheets is the same as the paper ones. Related data is stored in tables — which are a collection of small rectangular boxes or cells organized into rows and columns.

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By using several transformations, including reflection, translation, rotation, and stretching, geometry may be changed into congruent geometry.

A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.

congruence: Two forms are congruent if they have comparable sides and corresponding angles. By using transformations, including reflection, translation, rotation, and stretching, geometry may be changed into congruent geometry.

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The true values of x and y in the system of inequalities are (2/3, 10/3)

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

y ≥ 2

x + y ≤ 4

y ≤ 2x + 2

Express the inequalities as equations

So, we have the following representation

x + y = 4

y = 2x + 2

Substitute y = 2x + 2 in the equation

x + y = 4

So, we have the following representation

x + 2x + 2 = 4

Evaluate the like terms

So, the equation becomes

3x = 2

Divide by 3

x = 2/3

Substitute x = 2/3 in y = 2x + 2

y = 2 x 2/3 + 2

Evaluate

y = 10/3

In y ≥ 2, we have

10/3 ≥ 2

The above inequality is true

Hence, the values of x and y are (2/3, 10/3)

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Answer:

Step-by-step explanation:

Tangent is perpendicular to radius at point of contact.

So, ∠ABO=∠ACO=90

∘

In a quadrilateral, the sum of the angles is 360

∘

​.

∠BAC+∠BOC+∠ABO+∠ACO=360

∘

∴∠BAC+∠BOC=18​0

∘

                     ∠BOC=180

∘

−40

∘

                     ∠BOC=140

∘

So, option C is the answer

Points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.

True

A continuous function in mathematics is a function without discontinuities, or any sudden changes in value.

A function must be defined there, have a limit there, and have the value of the function there equal the value of the limit there in order for it to be continuous at that place.

Discontinuities can be categorized as being removable, jump, or infinite.

If we have a corresponding output value for any input value, the function graph will be continuous.

Without removing the pencil from the paper, we could continue the graph in both the negative and positive directions without the graph becoming broken.

Any breakage in the graph marks discontinuity

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Based on the definition of supplementary angles, the values of x and y are:

x = 17; y = 29.

If two angles are supplementary angles, then they will be equal to 180 degrees.

Since lines m and n are parallel, then:

(6x + 19) + (3x + 8) = 180 [supplementary angles]

Solve for x:

6x + 3x + 19 + 8 = 180

9x + 27 = 180

9x + 27 - 27 = 180 - 27

9x = 153

Divide both sides by 9

9x/9 = 153/9

x = 17

(6x + 19) + (2y + 1) = 180 [supplementary angles]

6x + 19 + 2y + 1 = 180

6x + 2y + 20 = 180

Plug in the value of x:

6(17) + 2y + 20 = 180

102 + 2y + 20 = 180

122 + 2y = 180

2y = 180 - 122

2y = 58

y = 58/2

y = 29

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The team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

For the team with the homecourt advantage, let [tex]Wi[/tex] and [tex]Li[/tex] denote whether the game '[tex]i[/tex]' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.

The probability that the team with the home-court advantage wins is

P [H] = P [[tex]W1W2[/tex]] + P [[tex]W1L2W3[/tex]] + P [[tex]L1W2W3[/tex]]

        = [tex]p(1-p)[/tex] + [tex]p3[/tex] + [tex]p(1-p){2}[/tex]

Note that P[H] ≤ pfor 1/2≤p≤1.

Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

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For the team with the homecourt advantage, let  and  denote whether the game '' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.

The probability that the team with the home-court advantage wins is

P[H] ≤ pfor 1/2≤p≤1.

Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

The probability of the event occurring at odds of 11 to 28 is 11/39.

The odds of an event are other way of expressing the likelihood of an event occurring. Use the below formula for converting the probabilities and odds .

Probability = odds/(1+ odds)

We have, the odds for a certain event = 11 to 28 i.e, 11/28

The probability of the event occuring say, P =

= odds/(1+ odds) = (11/28)/( 1 + 11/28 )

=> P = (11/28 )/(( 28+ 11)/28)

=> P = (11/28 )/(39/28)

=> P =( 11/28)× 28/39

=> P = 11/39

Since 11 is prime number, this fraction cannot be reduced. Hence, required fraction is 11/39.

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The balance after 5 years would be near around 5661 dollars.

What is compound interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.

First, convert R as a percent to r as a decimal

r = R/100

r = 2.5/100

r = 0.025 rate per year,

Then solve the equation for A

[tex]A = P(1 + r/n)^{nt}\\\\A = 5,000.00(1 + 0.025/2)^{(2)(5)}\\\\A = 5,000.00(1 + 0.0125)^{10}\\\\A = 5,661.35[/tex]

Hence the balance after 5 years would be near around 5661 dollars.

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Answer: x=9

Step-by-step explanation:

15-4x=42-7x

Move 15 to the right side

-4x=-7x+27

Move 7x to the left side

3x=27

3x/3=27/3

x=9

If the player do not know exactly how many times the game will be repeated the maximum level of probability can be predicted through Nash equilibria.

The concept, Nash equilibrium in game theory where the optimal outcome is when there is no incentive for players to deviate from their initial strategy. The players have knowledge of their opponent’s strategy and still will not deviate from their initial chosen strategies because it remains the optimal strategy for each player. Overall, an individual can receive no incremental benefit from changing actions, assuming that other players remain constant in their strategies. A game may have multiple Nash equilibria or none at all. The Nash equilibrium is a decision making theorem within game theory that states a player can achieve the desired outcome by not deviating from their initial strategy.

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A car is being driven at a rate of 40 mph when the brakes are applied. the car decelerates at a constant rate of 10 ft/sec2.The car will stop after 5.87 seconds.

1 mile = 5280 ft (approx)

1 hr = 3600 sec

The car is driven at a rate of 40 mph when the breaks are applied , then,

v(0)=40 m/hr

v(0)=40 5280 / 3600

v(0)=58.67 ft/sec2     [rounded to two decimal places] .............. (i)  

The car decelerate at a constant rate of 10 ft/sec²

So, acceleration function,

a(t)=-10 m/sec2  

Now, velocity function,

v(t)= a(t) dt    (ft/sec²)

v(t)= -10 dt   (ft/sec²)

v(t)=-10t+C1   (ft/sec²)   [where c is integrating constant]............ (ii)

Putting t=0 in this function,

v(o)=-10(0)+C1   (ft/sec²)    (ft/sec²)

v(0)=C1   (ft/sec²)

58.67=C1

C1=58.67

Putting this value of C1 in equation (ii) velocity function becomes,

v(t)=-10t+58.67      ......... (iii)

Car will stop when v(t) =0 . Then,

-10t+58.67=0

10t=58.67

t=58.67/10

t=5.867    [rounded to 2 decimal places]

So after 5. 87 sec the car will stop.

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To find the asymptotes and holes of a rational function, factor the denominator of the function and set it to zero. This will give you the x-values of the holes. To find the asymptotes, take the degree of the numerator and subtract it from the degree of the denominator. This will give you the degree of the asymptote.

To find the asymptotes and holes of a rational function, you must first factor the denominator of the function and set it to zero. This will give you the x-values of the holes, or the values where the function is undefined. To find the asymptotes, take the degree of the numerator and subtract it from the degree of the denominator. This will give you the degree of the asymptote. For example, if the numerator is a second degree polynomial and the denominator is a third degree polynomial, the asymptote will be a first degree polynomial. To find the equation of the asymptote, divide the numerator and denominator by the highest degree term of the denominator. The resulting quotient will be the equation of the asymptote. The asymptotes will be straight lines, so the equation will be in the form of y = mx + b. The holes will be the x-values of the points where the denominator equals zero. The asymptotes and holes will divide the graph of the rational function into distinct regions, and can be used to analyze the behavior of the function.

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To establish congruence between two geometric figures, it is necessary to have information about their size and shape. This includes information about the lengths of their sides and the measures of their angles. It may also be necessary to know the relative positions of the figures, such as whether they are oriented in the same way or whether one is a reflection of the other.

To show that two figures are congruent, it is usually necessary to use one or more of the following techniques:

Superimpose the figures: This involves placing one figure directly on top of the other so that corresponding parts are aligned. If the figures are congruent, they will fit exactly on top of each other and no gaps or overlaps will be visible.

Use a ruler or other measuring tool: By measuring the lengths of the sides and angles of the two figures, it is possible to determine whether they are congruent. If all of the measures are the same, the figures are congruent.

Use transformations: Congruent figures can be obtained from each other through translations, rotations, and reflections. By applying these transformations to one of the figures, it is possible to determine whether it can be made to match the other figure.

Use geometric principles: There are various geometric principles that can be used to establish the congruence of two figures. For example, the AA (Angle-Angle) Congruence Postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are congruent.

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The constant of proportionality for the data is 80. The correct option is B.

The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, and even the rate of change.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the points are (6,480) and (8,640). The value of the proportionality constant will be calculated as,

y =kx

480 = k x 6

k = 480 / 6

k = 80

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The optimal response is The ranges below encompass all real numbers: From 0 through all actual numbers. The domain of this function is all real numbers since x can be entered with any value.

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

answer to the question is that all real numbers or (−∞,∞)

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The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.

To find the median:

1-Arrange the data points from smallest to largest.

2-If the number of data points is odd, the median is the middle data point in the list.

3-If the number of data points is even, the median is the average of the two middle data points in the list.

Finding the middle number requires sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers).

Example: The median of 4, 1, and 7 is 4 because when the numbers are put in order (1,4,7)the number 4 is in the middle.

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With the gradient and one coordinates of the line, Using the formula of equation of line with gradient and a coordinates, The answer is

[tex](y-y_1) = m (x-x_1)[/tex] .

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.

coordinates = ([tex]x_1,y_1[/tex])

gradient =slope =m

Required equation,

[tex](y-y_1) = m (x-x_1)[/tex]

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The roots of the Given quadratic equation are 0.57 and -2.9 solved using the algebraic method.

The given equation is a quadratic equation because the degree of the given equation is 2.

How can one tell whether or not a given equation is a quadratic equation?

A quadratic equation is a two-variable polynomial equation of degree two of the form [tex]f(x) = ax^2+bx+c = 0[/tex] with the variables a, b, and c being real numbers and a not equal to 0. With "a" denoting the leading coefficient and "c" denoting the absolute term of f, it is a quadratic equation in its general form (x). The values of x that fulfil the quadratic equation are known as the roots.

The given equation is 3x²+7x - 5 =  0 a =3,b=7, c =-5

lets roots of the given equation is (α, β).

roots can be found using  Shreedhara Acharya's formula.

[tex](\alpha, \beta) = [-b \± \sqrt(b^2 - 4ac) ]/2a[/tex]

α = [-b + √(b^2 – 4ac)]/2a

β = [-b - √(b^2 – 4ac)]/2a

b^2 – 4ac = 49-4*3*(-5) = 49+60 = 109

α = (-7+[tex]\sqrt{109}[/tex])/2*3

α = (-7+10.44)/6

α = 0.57

β  = (-7 - 10.44)/6

β  = -2.9

So the roots of the Given quadratic equation are 0.57 and -2.9.

-- The given question is incomplete, the complete question is

"What will be the roots of the equation 3x^2+7x-5=0" --

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