On a quiz show, the contestant who gets the answer correct in the shortest amount of time wins. The host asks for the solution to 49+83+51. Contestant number one quickly found the sum of 49 and 51 to be 100, then added 83 to get 183. Which property did the contestant use?

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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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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Answer:

A) 9

B) 53

Step-by-step explanation:

A:

-6 + 15 = 9

- - - - - -

+++++++++++++++

There are 9 more +  signs then - signs.

B:

37 - -16

37 + 16 = 53

+++++++++++++++++++++++++++++++++++++

We want to take away 16 negative signs, but we do not have any negative signs, so we add 16 zero pairs.  A zero pair has a value to zero

++++++++++++++++

- - - - - - - - - - - - - - -   If we now take away the 16 - signs, we are left with 53 + signs.

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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By factorizing x² + 16  we get the factors as (x + 4i) • (x − 4i).

Here given the equation x² + 16 .

To factor x² + 16 with our imaginary number, we will use the sum of squares formula:

a2 + b2 = (a + bi) • (a − bi)

We begin by defining our problem in mathematical terms, as follows:

x² + 16

As you can see, our problem does not match the left side of the formula, so we must first convert it to match the left side, as follows:

x² + 16 = x² + 4²

Now that it corresponds, we can simply enter x for a and 4 for b into the formula to obtain the factors of x² + 16:

(x + 4i) • (x − 4i)

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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

A reflection preserves the size and shape of the prior original image, acting as a congruence transition.

A reflection in mathematics is a mapping from a Euclidean space to itself that is an isometry with a set of fixed points known as the hyperplane, also known as the axis or plane of reflection.

The mirror image of a figure in the axis or plane of reflection is the image produced by a reflection.

A reflection keeps the pre-original image's size and shape, making it a congruent transition.

A figure that has been flipped over a line of reflection is a reflection.

The position of the x- and y-coordinates simply changes in a reflection across the line y = x.

Consider the case when the point (6, 7) is reflected across the line y = x. The reflected point's coordinates are (7, 6).

Therefore, a reflection preserves the size and shape of the prior original image, acting as a congruence transition.

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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 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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If the function f(x) = x² - 2x + 3  and g(x) = log(x) + 3 , then f(x) is a polynomial function and g(x) is the logarithmic function .

A Polynomial Function is defined as a function that involves only non-negative integer powers of a variable in equation ,

For Example : quadratic equation , cubic equation .

By the definition of polynomial function ,

we can say that the given function f(x) = x² - 2x + 3 is a polynomial function , that is having degree 2 .

A Logarithmic function is defined as a function that involves log in the equation , such as log x , ln x .

According to the definition of Logarithmic function , the given function g(x) = log(x) + 3 is a type of Logarithmic function .

Therefore , f(x) is a polynomial function and g(x) is a logarithmic function .

The given question is incomplete , the complete question is

If the function f(x) = x² - 2x + 3  and g(x) = log(x) + 3 , then what kind of function is f(x) and g(x) ?

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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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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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A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test.  r = 0.91; There is a significant linear correlation. Option A

Generally, The value of the linear correlation coefficient r is given in the display as 0.91. To determine whether there is significant linear correlation between years of study and test scores, we need to conduct a hypothesis test.

The null hypothesis for this test is that there is no linear correlation between years of study and test scores, and the alternative hypothesis is that there is linear correlation.

To test the null hypothesis, we can use the value of r and the sample size (10 pairs of data) to calculate a p-value. If the p-value is less than our significance level of 0.05, we can reject the null hypothesis and conclude that there is significant linear correlation between the variables.

Since r is given as 0.91 and the sample size is 10, we can conclude that there is significant linear correlation between years of study and test scores.

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Answer:

16

Step-by-step explanation:

because 8 x 2 is 16

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

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

True

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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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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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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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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Answer:

7

Step-by-step explanation:

-(-4) + 3

= 4 + 3

= 7

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 :)

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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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 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 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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