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The intersection of equations y=2x-2 and y= -2x^2 +4x+ 3 is y = 3

The general formula for the equation of a line is expressed as;

y = mx + c

Where the parameters are;

From the information given, we have the equation of the lines as;

Now, equate the lines, we have;

2x - 2 = -2x² + 5x + 3

collect the like terms

2x -5x + 2x² - 2 - 3 = 0

add the iike terms

2x² -3x - 5 = 0

Factorize the quadratic equation

2x² - 5x + 2x - 5 = 0

Group in pairs

(2x² - 5x) + (2x-5) = 0

x(2x -5) + 1(2x - 5) = 0

The intersection for when  x = 5/2

y = 2x - 2

y = 2(5/2) - 2

y = 3

Hence, the value is 3

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The gallons consumed when car A travels 300 mi of city driving plus 100 mi of highway driving is 12.66 gallons

The gallons consumed when car B travels 300 mi of city driving plus 100 mi of highway driving is 13.37 gallons

The gallons consumed when car A travels 100 mi of city driving plus 300 mi of highway driving is 13.74 gallons

The gallons consumed when car B travels 100 mi of city driving plus 300 mi of highway driving is 12.54 gallons

Gallons consumed when car A travels 300 mi of city driving plus 100 mi of highway driving = (300 / 33) + (100 / 28)

= 9.09  + 3.57 = 12.66 gallons

Gallons consumed when car B travels 300 mi of city driving plus 100 mi of highway driving = (300 / 29) + (100 / 33)

= 10.34 + 3.03 = 13.37 gallons

Gallons consumed when car A travels 100 mi of city driving plus 300 mi of highway driving = (100 / 33) + (300 / 28)

= 3.03 +  10.71 =13.74 gallons

Gallons consumed when car B travels 100 mi of city driving plus 300 mi of highway driving = (100 / 29) + (300 /33)

= 3.45 + 9.09 = 12.54 gallons

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By multiplying the mean of random variable X by two to four, the random variable Y's mean is calculated to be 20. (5). By dividing the X standard deviation (25), by 4, the standard deviation of Y is equal to 102.

The random variable X has a mean of 5 and a standard deviation of 25. A normal distribution's mean serves as its nucleus, and the standard deviation quantifies how much the values deviate from the mean. Y = 2 + 4X is the definition of the random variable Y. By adding 2 to the mean of X (5), we can determine the mean of Y, which equals 20. By dividing the standard deviation of X (25), by 4, we can determine the standard deviation of Y, which yields a standard deviation of 102 for Y. As a result, the standard deviation is 102 and the mean of Y is 20.

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Answer:true

Step-by-step explanation:

The door frame is not rectangular.

If the door frame is rectangular, the sum of the square of the height and the width would be equal to the square of the diagonal.

Height² + width = diagonal²

213² + 92²

45,369 + 8,463 = 53,833

231² = 53,361

53,833 ≠ 53,361

The door frame is not rectangular because the sum of the height and the width is not equal to the diagonal.

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Answer: x = 13

Step-by-step explanation:

First you have to move 15+ to the other side to 28.Then when 15+ moves to the other side it will be 15-. After that you subtract 28 with 15 that will make 13. So x is equal to 13.

By numbers:

15+x=28

x=28-15

x=13

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

As it is a triangle , so we know that sum of all angles of a triangle = 180°

=> 44 + 53 + x = 180

=> 97 + x = 180

=> x = 180 - 97

=> x = 83°

Answer: a. The equation using the information as it is given above that can be solved to answer this question is:

distance = speed x time

Let t be the amount of time Krystal spent driving from Houston to Philadelphia.

distance = 50t + 60(46 - 25 - t)

b. To find the distance between Houston and Philadelphia, we can substitute the known values into the equation and solve for t.

distance = 50t + 60(46 - 25 - t)

distance = 50t + 60(21) - 60t

distance = 50t + 1260 - 60t

distance = -10t + 1260

To find the total distance, we can set t = 25

distance = -10(25) + 1260

distance = -250 + 1260

distance = 1010

Therefore, Houston is 1010 miles from Philadelphia, to the nearest mile.

Step-by-step explanation:

The length of the perimeter will be 121/7 cm.

Given is that a soda company would like to replace the label on a can of soda with a radius of 2 and three fourths cm. The label touches end to end with no overlap.

The length of the label will be its perimeter. We can write -

P = 2πr

P = 2 x 22/7 x 11/4

P = 2 x 22/7 x 11/4

P = 22/7 x 11/2

P = 11 x 11/7

P = 121/7

Therefore, the length of the perimeter will be 121/7 cm.

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The triangles are congruent by AAS (Angle-Angle-Side) and not by ASA (Angle-Side-Angle)

When the corresponding length of sides or measure of the internal angles of two or more triangles are equal, then the triangles are said to be congruent. The congruency can be expressed in terms angles, sides, or the combination of sides and angles. An example is the SAA (Side-Angle-Angle) property which implies that a side that is not an included angle and other angles are congruent.

Considering triangles ABC and CDE, it can be seen that two angles are congruent and a side of both are congruent. Since the congruent side is not an included angle, then the congruent relations is AAS (Angle-Angle-Side).

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The two triangles are not congruent

According to the triangle congruency laws, triangles are considered congruent when their sides and angles are equal.

The rules include

Side - Side - Side = SSS

Side, Angle, and Side = SAS

Angle Side Angle = ASA

Angle, Angle, and Side. = AAS

Hypotenuse and one leg. = HL

In the problem no information is given about the sides and just one angle is given.

Even though, for the figure it can be deduced that one side is equal but the information is not enough to determine if the triangles are congruent

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Answer: 14

Step-by-step explanation:

Given expression ?/(2/5)=4 where ?=x gives x=8/5.

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given expression ? ÷ 2/5 = 4

let x=?

Therefore,

              x=4*2/5

             x=8/5

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The 100th derivative of P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷) will be zero.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given:

A polynomial,

P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷).

To find the degree:

(x⁷)¹⁰(x²)¹¹(x⁷) = x⁹⁹.

The polynomial has a degree of 99.

If we think about it intuitively,

Therefore, if we were to multiply it all out,

the leading word would be x⁹⁹.

The term's first derivative is 99x⁹⁸,

followed by 99(98)x⁹⁷,

and 99(98)(97)x⁹⁶.

And finally,

the 99th derivative is 99×98×97×96×...4×3×3×2×1× (x⁰)

=99!

So, the 100th derivative will be zero.

Therefore, by the 100th derivative, all terms will cancel out.

100th derivative will be zero.

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The two lines are perpendicular because the product of their slopes is equal to 1

The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line

Given here: The two lines  x-3y =15 and y = -3y + 4

Rewriting the given expressions in slop-intercept form we get

y=x/3-5

y = -3y + 4

The respective slopes are given as 1/3 and -3

Thus the product of the two slopes is 1/3×-3=-1

Hence, The given lines are perpendicular.

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The triangles are congruent if two of one triangle's sides and its included angle are the same as the corresponding sides and angles of another triangle.

The complete question is,

To what extent can the congruence of the triangles be demonstrated?

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The decimal expansion of the following fraction 1/3 would be; 0.33

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

We need to find the expression of  1 divided by 3.

A negative divided by a negative is positive, then;

1/3 = 0.33

Therefore, The value of expression 1/3 would be; 0.33

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The area of triangle with three sides a,bc is equals to  

√[s × (s – a) × (s – b) × (s – c)].

What is triangle ?

Triangle can be defined as in which it consists of three sides, three angles and sum of the three angles are 180 degrees always.

Given

in the triangle with three sides a,b,c.

Let ABC be a triangle such that the length of the 3 sides of the triangle is AB = c, BC = a and CA = b.

The semi-perimeter of triangle ABC = s = (a + b + c)/2

Then, the area of triangle ABC = √[s × (s – a) × (s – b) × (s – c)].

Therefore, The area of triangle with three sides a,bc is equals to  

√[s × (s – a) × (s – b) × (s – c)].

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A compound event is a combination of multiple simple events that can occur simultaneously or independently. When talking about coin flipping, the sample space is the set of all possible outcomes of the experiment, which in this case is flipping a coin 3 times. In this case, the sample space is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}.

Option A, You get exactly 2 tails, is a compound event because it consists of three simple events, THT, HTH, and TTH. These events can happen independently of one another and therefore, it is a compound event.

Option B, You get exactly 3 tails, is not a compound event because it only consists of one simple event, TTT. This event is not a combination of other simple events and is, therefore, not a compound event.

Option C, This is not an event, is not a valid option as it is not a possible outcome.

Option D, You get exactly 3 heads, is also a compound event because it consists of one simple event, HHH. This event can happen independently of other simple events and it is, therefore, a compound event.

Hence, options A and D are compound events as they are a combination of multiple simple events that can happen independently or simultaneously.

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Answer: In a real-life representation of the multiplication problem "15 (2/5) = 6," we can imagine a bag of 15 items, each of which is 2/5 of a whole. To find out how many whole items are in the bag, we can multiply 15 (the number of items) by 2/5 (the fraction of each item that is a whole).

The result of 6 represents the number of whole items in the bag.

Step-by-step explanation:

Using the disk method, it can be concluded that the volume of the solid is 125π /3 cubic units.

Disk Method is a method used to determine the volume of a solid formed by revolving the region about the x-axis and the interval [a, b]. The volume of the solid is the integral of the area of the base times dx.

V = π ∫ Ax dx

From the question, we know that the base of the figure is a triangular region and the coordinates are (0,0), (5,0), and (0,5).

The square is perpendicular to the x-axis. Thus, we can find the side of the square, that is the straight line passing through (5,0) and (0,5) which meet the y = mx + b equation.

First, we determine the slope of the line (m).

m = (y₂ - y₁) / (x₂ - x₁)

   = ( 5 - 0 ) / ( 0 - 5 )    

   = 5 / -5

   = -1

To find b, we input the value of m into the equation for point (5,0):

y = mx + b

0 = -1*5 + b

0 = -5 + b

b = 5

So we got the side of the square:

y = mx + b

y = -x + 5

y = 5 - x

Thus the area of the square is:

A = side²

  = (5 - x)²

  = 25 + x² - 10x

The volume of the solid can be calculated as follows:

   V = π ∫ Ax dx

      = π ∫₀² (25 + x² - 10x) dx

      = π (25x + 1/3x³ - 5x² |₀⁵)

      = π (25*5 + 1/3*5³ - 5*5² - 0)

      = π (125 + 125/3 - 125 - 0)

      = 125π /3 cubic units

Thus, the volume of the solid is 125π /3 cubic units

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Answer:

the equivalent algebraic expression is -2x -8 after applying the distributive property.

Step-by-step explanation:

The distributive property states that for any real numbers a, b, and c, a(b+c) = ab + ac.

To apply the distributive property to the expression -2(x-4), we can distribute the -2 across the parenthesis, like this:

-2(x-4) = -2x + (-2)(-4)

Simplifying the last part of the expression:

-2(x-4) = -2x -8

So, the equivalent algebraic expression is -2x -8 after applying the distributive property.

The Range  and standard deviation of the set of data 11, 8, 5, 11, 25 is 20 and 7.68 respectively.

What is mean ?

Mean can be defined as the ratio sum of the observations and total number of observations.

Given

set of data,

11, 8, 5, 11, 25

we have to find the range and standard deviation,

We know that,

range = max - min

here max = 25

min = 5

range = 25-5

range = 20

Standard deviation ,

= √( ( Σx^2 - (Σx)^2 / n ) / (n-1)  )

= √( ( Σ11^2+8^2+5^2+11^2+25^2 - (Σ60)^2 / 5 ) / (5-1)  )

= √( ( 956 - (3600)^2 / 5 ) / (5-1)  )

= √( ( 956 - 720) / 4  )

= √( 59 )

=  7.68

Hence, The Range  and standard deviation of the set of data 11, 8, 5, 11, 25 is 20 and 7.68 respectively.

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By constructing 95% confidence intervals for each simulation, we can be 95% confident that the true proportion of wins lies within the range of each interval.

A confidence interval is a set of values that, given a specific level of certainty, are likely to include a population parameter like a mean or proportion.

The interval is derived using data drawn from a sample of the population and is frequently presented as a range of values with a 95% confidence level.

The probability that the range of values contains the genuine population parameter is quantified by the confidence level.

In the case of a 95% confidence interval, for instance, it means that 95% of the intervals would contain the real population parameter if we sampled the same population more than once and calculated a confidence interval each time.

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The system of inequalities is:

x + y ≥ 16

x*0.75 + y*2 ≤ 20

And its graph can be seen below, there we can see that one possible solution is (14, 2)

Let's define the variables:

x = number of apples.

y = number of mangos.

Kayden needs to buy not less than 16 items, so the first inequality is:

x + y ≥ 16

And he can spend at most $20, then:

x*0.75 + y*2 ≤ 20

The system of inequalities is then:

x + y ≥ 16

x*0.75 + y*2 ≤ 20

To graph it just graph the two lines and shade the region correspondent, for the first inequality shade the region above the line, for the second one shade the region below the line.

You should get.

The solution set is the region where both shaded areas intercept. Then a possible solution is:

x = 14

y = 2

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Answer:

A is ST, PR, and UV

B is rays SQ and QT

C is point Q

D is Points S, Q, and T

The angle θ measures 53.13⁰ with the east direction.

The tangent of an angle is a trigonometric function that is defined as the ratio of the side opposite the angle to the side adjacent to the angle in a right triangle. In other words, it is a measure of the steepness of a line that is tangent to a point on a function's graph and is represented by the symbol tan. It is one of the three main trigonometric functions, along with sine and cosine. The value of tangent is always positive in the first and fourth quadrants.

let the angle made be θ degree to the north of east from the post office to the grocery shop

so tan θ = p/b

where p is perpendicular , b is base of the triangle

so tan θ = 3/4

=> θ = 53.13 degree

so the angle θ measures 53.13⁰ with the east direction.

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Complete question :

what is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.

When looking east, the angle is 53.[tex]13^{0}[/tex] degrees.

What does a tangent to any angle mean?

The ratio of a right triangle's side opposite to its side next to the angle is known as the tangent of an angle, which is a trigonometric function. It is a measurement of the steepness of a line that is tangent to a point on the graph of a function, and it is denoted by the symbol tan. One of the three primary trigonometric functions, together with sine and cosine, is it. In the first and fourth quadrants, tangent's value is always positive.

Let the angle formed between the post office and the grocery store be degrees to the north of east.

so tan θ = p/b

where p is perpendicular , b is base of the triangle

so tan θ = 3/4

=> θ = 53.13 degree

so the angle θ measures 53.13⁰ with the east direction.

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Complete question :

What is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.

The mixture is 78.25% copper for the given alloy.

The percentage is defined as a ratio expressed as a fraction of 100.

To solve the given situation, we utilize material balancing before and after mixing.

Let the total amount of material after mixing is 320.

Let x be the percent copper of the mixture and applying copper balance,

⇒ (0.42)(120 g) + (1)(200) = 320x

Solving the above equation, we get the value as

⇒ x = 0.7825

Thus, the mixture is 78.25% copper.

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Answer: Income Statement:

Revenue: _________

Expenses: _________

Net Income: _________

Statement of Stockholders' Equity:

Beginning Balance:

Common Stock: $550,000

Retained Earnings: $46,000

Total: $596,000

Additions:

Common Stock: $32,000

Total: $628,000

Deductions:

Dividends: $24,000

Total: $604,000

Ending Balance:

Common Stock: $550,000

Retained Earnings: $50,000

Total: $600,000

Note: I've left the Revenue, Expenses and Net Income section in the income statement blank as it is not provided in the question. It is also important to note that these are just examples and the numbers may not match with the actual financial statement.

Step-by-step explanation: