X over 2 linear or nonlinear

The solution to the given quadratic equation formed is; y = -9/4 and y = -1

The given equation is expressed as;

(3 + 2y) = √(-y)

Taking the square of both sides gives us;

(3 + 2y)² = √(-y)]²

→ 9 + 12y + 4y² = -y

4y² + 13y + 9 = 0

Factoring the expression gives us;

4y² + 4y + 9y + 9 = 0

4y(y + 1) + 9(y + 1) = 0

Thus;

(4y + 9) = 0

(y + 1) = 0

y = -9/4

y = -1

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If a mill worker measures the width of a plank and the width of the plank is 15.8 dm, then the width of the plank in meters is 1.58

The width of the plank in decimeter = 15.8 dm

Conversion is the process of the converting the given measurement like length, mass etc, from one unit to another unit

We have to find the width of the plank in meter

We know that,

1 decimeter = 0.1 meter

Convert the given decimeter to meter  

15.8 decimeter = 15.8 × 0.1

Multiply the numbers

= 1.58 meters

Therefore, the width of the plank in meter is 1.58

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The given question in incomplete, the complete question is :

A millworker measures the width of a plank. The width is 15.8 dm . what is the width in meters?

The value of the probability P(2) is 0.11

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

The table of values

As a general rule:

The sum of probabilities must equal to 1

Using the above as a guide, we have the following:

0.1 + P(2) + 0.35 + 0.1 + 0.3 + 0.04 = 1

Evaluate the like terms

This gives

P(2) + 0.89 = 1

So, we have

P(2) = 0.11

Hence, the solution is 0.11

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Answer:

x=-7/2 (exact form)

x=-3.5 (decimal form)

x=-3 1/2 (mixed number form)

Step-by-step explanation: :)

Answer:

x + 3y = 9

Step-by-step explanation:

The required value of x for the diagonals of parallelogram is 8.

Let ABCD be the parallelogram, and let the diagonals AC and BD intersect at point E.

We know that in a parallelogram, the diagonals bisect each other. So, we have:

AC = 2AE and BD = 2BE

We are given that AC = 4x + 2 and BD = 5x - 6. Substituting in the above equations, we get:

2AE = 4x + 2 and 2BE = 5x - 6

Dividing both sides by 2, we get:

AE = 2x + 1 and BE = (5x - 6)/2

Since AE and BE are the same length (they are both half the length of the diagonals), we have:

2x + 1 = (5x - 6)/2

Multiplying both sides by 2, we get:

4x + 2 = 5x - 6

Subtracting 4x from both sides, we get:

8 = x

Therefore, the value of x is 8.

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Let's call the length of the longer rope piece x and the length of the shorter rope piece y. We know that:

x + y = 5 (the total length of the rope is 5 feet)

And from the problem statement, we have:

3x - 7 = 5y

Now we can use the first equation to solve for y:

y = 5 - x

Substituting this expression for y into the second equation:

3x - 7 = 5(5 - x)

Expanding the right side:

3x - 7 = 25 - 5x

Adding 5x to both sides:

8x - 7 = 25

Adding 7 to both sides:

8x = 32

Dividing both sides by 8:

x = 4

So the length of the longer rope piece is 4 feet.

Answer:

135 markers

Step-by-step explanation:

Let's call the number of markers in each large box "x."

After giving away 15 markers to each of 3 teachers, there were 90 markers left, so:

x - (15 * 3) = 90

Expanding the expression on the right side:

x - 45 = 90

Adding 45 to both sides:

x = 135

So, each large box originally contained 135 markers.

The amount for first prize is $36 and second prize is $9.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the amount for Second price be x.

Then, amount of first Prize is 4x.

So, x+ x +x + 4x + 4x = 100

11x= 100

x= $9

So, the first prize would be (9 x 4)= $36

and, the second prize is $9 each.

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Answer:

median = 95

Step-by-step explanation:

the median is indicated by the line inside the box.

each interval on the number line is 5 units.

median = 75 + 4 units = 75 + 20 = 95

The probability that the first box was the one selected given that the marble is white is [tex]\frac{7}{12}[/tex] .

Probability is the likelihood that an event will occur.

The likelihood of an occurrence A provided that an earlier event B has already happened is known as conditional probability.

the two boxes are marked as B1, B2

Number of black balls: 1

Number of white balls: 1

Number of black balls in the box: 2,

Number of white balls: 1.

B and W should stand for black and white marble.

Therefore, the likelihood that either box will be selected is [tex]\frac{1}{2}[/tex]

Probability of selecting a black ball from a box: [tex]\frac{1}{2}[/tex]

Probability of selecting a black ball from a box: [tex]\frac{2}{3}[/tex]

To determine: the likelihood that the marble is black.

Solution:

The likelihood that the marble being black is equal to

[tex]\frac{1}{2} (\frac{1}{2} ) + \frac{1}{2} (\frac{2}{3} )\\= \frac{7}{12}[/tex]

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If the sum of three successive integers even numbers is 6000, then their values must be 1998, 2000, and 2002.

In addition tangere is the root of the Latin word integer, which meaning "whole" and "untouched." The word "entire" is derived from the French word entier, which also means entire and integer. The expression was once used to describe a multiple of 1 or the whole part of a mixed number. The definition of the term was given as the collection of all positive integers, which is the same as the collection of all natural numbers. The concept of integer was expanded to include negative integers as the significance of those numbers came to be realized through time. For instance, in his 1765 book Elements of Algebra, Leonhard Euler stated that integers might contain both positive and negative values. Up until about the middle of the 20th century, most European mathematicians ignored negative numbers.

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The solution of the given system of equations 6x+3y=8 and 8x+4y=-1 is x=0 and y==-8/9

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitutes solutions of the system. (5, 4) is a solution of the first equation, but not the second.

We are given that;

The equation 1;  6x+3y=8

The equation 2; 8x+4y=-1

Now,

In equation 1

6x=8-3y

x=(8-3y)/6

Substituting the value of x in equation 2

8((8-3y)/6)+4y=-1

4((8-3y)/3)+4y=-1

(8-3y)/3)+4y=-1/4

8-3y+12y=-3/4

8+9y=-3/4

9y=-3/4-8

9y=-3-32/4

9y=-35/4

y=-32/36=-8/9

Putting the value of y in equation 1

6x+3(-8/9)=8

54x-8=8

x=0

Therefore, the solution of the equations will be x=0, y=-8/9.

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The line of the best fit of the scatter plot is added as an attachment

The missing graph is added as an attachment

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

The graph

A good line of best fit would have equal number of points on either sides

To plot the graph, we draw a line that divides the points on the graph evenly

This line when drawn on the scattered points divided the points approximately evenly

Hence, the line of the best fit is attached

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Part(a), An inequality to show the number of additional minutes required to get at least 80% battery life will be 3m + 40 ≤ 80.

Part(b) The number of minutes will be 13 minutes and 20 seconds.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that according to a survey, students often have 40% of their cell phone batteries left at the end of the school day when utilizing the newest fast charger, which charges phones at a pace of 3% per minute.

Part(a) The inequality can be written as:-

3m + 40 ≤ 80.

Part(b), The number of minutes will be:-

3m + 40 ≤ 80.

3m ≤ 40

m ≤ 40 / 3

m ≤ 13.33

The time can also be written as 13 minutes and 20 seconds.

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Answer: 2707

Step-by-step explanation: just  multipli

Answer:

186m^2

Step-by-step explanation:

This compound figure will be divided to three rectangular.

1) 18x9=162

2) (18-12)x2=12

3) 2x6=12

so, total is 161+12+12=186^2

The necessary equation is [tex]L= 52+2D[/tex], and the necessary overall length is [tex]114 miles[/tex].

Given: A road is being extended by construction workers. The road already had a length of miles, and the crew is continuously extending it by miles. Let the number of days the crew has worked and the distance of the entire road (in miles) be represented by D and L respectively. Create a corresponding equation L to D.

According to the inquiry,

The road's initial length is 52 miles.

The daily length of roadways that a crew adds is 2 miles.

This number represents the number of days the crew worked.

The total length of the road that the crew built is represented by L.

A given condition-based equation can be written as [tex]L= 52+2D[/tex].

Now, the crew's total length of the road after 31 days of construction is calculated.

[tex]L= 52+2*31\\L=52+62\\L=114 miles[/tex]

As a result, the needed equation and the total length is [tex]L= 52+2D[/tex]  and 114 miles respectively.

The complete question is:-

A construction crew is lengthening a road. The road started with a length of 52 miles, and the crew is adding 2 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D . Then use this equation to find the total length of the road after the crew has worked 31 days.

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Answer:

I suppose she also paid $100 because a 20% off from Thiago could mean that the original price was 120.

Step-by-step explanation:

The probability of being assigned a general practitioner or a doctor under the age of 50 is 11/19 or approximately 0.5789 (rounded to four decimal places).

We are given that there are 5 general practitioners (GPs) out of 19 doctors in the hospital, which means that the probability of being assigned a GP is 5/19.

We are also given that there are 9 doctors under the age of 50 out of the 19 doctors in the hospital, which means that the probability of being assigned a doctor under the age of 50 is 9/19.

However, we need to subtract the probability of being assigned a doctor who is both a GP and under the age of 50 because this group is counted twice in the above probabilities.

We are given that there are 3 doctors who are both GPs and under the age of 50. Therefore, the probability of being assigned a doctor who is both a GP and under the age of 50 is 3/19.

To use the inclusion-exclusion principle, we add the probabilities of being assigned a GP and being assigned a doctor under the age of 50, and then subtract the probability of being assigned a doctor who is both a GP and under the age of 50.

P(GP or Under 50) = P(GP) + P(Under 50) - P(GP and Under 50)

= 5/19 + 9/19 - 3/19

= 11/19

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Total ways can 4 seniors and 2 juniors be chosen to participate in a charity event is 1,91,100.

There are 16 seniors and 15 juniors in a particular social organization and

4 seniors and 2 juniors had to be chosen to participate in a charity event.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by [tex]^nC_r[/tex] and it is given by,                   [tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex] , where 0 ≤ r ≤ n.

Therefore the total ways that 4 seniors and 2 juniors be chosen to participate in a charity event = [tex]^{16}C_{4}.^{15}C_{2}[/tex]

= [tex]\frac{16!}{4!(16-4)!}$\times \frac{15!}{2!(15-2)!}[/tex]

= 1820 × 105

= 1,91,100

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The complete question is:

There are 16 seniors and 15 juniors in a particular social organization. In how many ways can 4 seniors and 2 juniors be chosen to participate in a charity event?

Answer:

Step-by-step explanation:

The required equation that can be used to determine the price of each gallon of gas is 8.4x = 23.94. Option A is correct.What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.here,Let the cost of gas per gallon be x,Now according to the question,Cost of 8.4 gallons of fuel = 8.4xfrom the question,8.4x = 23.94Thus, the required equation that can be used to determine the price of each gallon of gas is 8.4x = 23.94. Option A is correct.

Answer:

$19.29

Step-by-step explanation:

We know

Marisol buys a souvenir cup for $14.97 and a book of postcards for $4.32.

How much does Marisol spend?

14.97 + 4.32 = $19.29

So. Marisol spend $19.29

According to the given information the formula for f(x) in term of x is  f(x) = (4/5)x - 4.

A function is a relationship between a number of inputs and outcomes. Simply described, a function is an association between inputs where each input is linked to exactly one output. There is a range, codomain, as well as domain for every function. A function is commonly referred to as f(x), where x is in fact the input.

When looking at a graph, we use a procedure known as the Vertical Line Test to determine whether a function is indeed a function. Simply drawing a vertical line will reveal if the graph is a function if it touches it once.

4x - 5y = 20

Subtracting 4x from both sides

-5y = -4x + 20

Dividing 5 from the both sides

y = (4/5)x - 4

The formula for f(x) in terms of x is:

f(x) = (4/5)x - 4

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The length of the ramp that must cover the horizontal distance is 13.13 feet.

Given the data in the question, this forms a right-triangle.

To solve for the length of the ramp, we use  trigonometric ratio

Cosine = Adjacent / Hypotenuse

Plug in the values

cos( 8° ) = 13ft / hypotenuse

Hypotenuse = 13ft / cos( 8° )

Hypotenuse = 13.13 ft

Therefore, the ramp's length is 13.13 ft.

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The solution is, (-1, -7), (0, -4), (1, -1), satisfies the graph function, the coordinates did we plot when we graphed the function y = 3x - 4

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

we graphed the function y = 3x - 4

now, the required coordinates are, which satisfies the graph function.

as, we get,

(-1, -7), satisfies the graph function

(0, -4) , satisfies the graph function

(1, -1), satisfies the graph function

Hence, The solution is, (-1, -7), (0, -4), (1, -1), satisfies the graph function, the coordinates did we plot when we graphed the function y = 3x - 4

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The statement which is not true is a. Passive political risk management discourages managers from fully or partially hedging their bets against exposure to political hazards

Passive political risk management does not deter managers from fully or partially hedging their bets against political risk exposure. This management describes a strategy for controlling political risk that involves altering how a firm carries out a business to reduce political risk. This is generally performed without necessarily using financial instruments to safeguard against any degree of political risk.

It may entail taking necessary steps to spread the firm's operations across other geographies and regions, choosing joint venture partners with strong political influence, determining local contacts, and preserving strong ties with local individuals associated with politics. Even if a firm doesn't use active hedging tactics, these activities can efficiently assist it to lessen its exposure to political risk.

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Melissa earned [tex]$152.84\\[/tex] this week. This means that she earned a total of [tex]$174.49[/tex] over the two week period.

To determine how much Melissa earned last week, we can subtract the [tex]$21.65[/tex] that she earned more this week from the total amount earned over the two week period. Therefore, Melissa earned [tex]$152.84[/tex] this week, and [tex]$21.65[/tex] more than she earned last week. Subtracting [tex]$21.65[/tex]from [tex]$174.49[/tex] gives us [tex]$152.84[/tex], which is the amount Melissa earned last week. This means that Melissa earned [tex]$152.84[/tex] last week .To summarize, Melissa earned $152.84 this week, which was[tex]$21.65[/tex] more than she earned last week. This means that Melissa earned a total of [tex]$174.49[/tex]over the two week period, and by subtracting [tex]$21.65[/tex] from the total amount earned over the two week period, we can determine that Melissa earned[tex]$152.84[/tex] last week.

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