The formula d=b2−4ac is used to calculate the discriminant.

Solve for b.

A) b=±2ac−d−−−−−√
B) b=±d+4ac−−−−−−√
C) ​b=±d−4ac−−−−−−√
D) b=±4ac−d−−−−−−√

Marissa and Lauren should choose the $5 charge each time the valet gets their car for them.

A car, also known as an automobile, is a wheeled motor vehicle used for transportation. Most definitions of cars say that they run primarily on roads, seat one to eight people, have four tires, and mainly transport people rather than goods. Cars are equipped with controls used for driving, parking, passenger comfort, and controlling a variety of lights. Over the decades, additional features and controls have been added to vehicles, making them progressively more complex.

Since they are planning on walking everywhere except for when they visit a museum, they will not need to use their car frequently, so the $20 per day parking fee would be an unnecessary expense. The $5 charge each time the valet gets their car for them will be much more cost-effective and will also save them time, as the valet will have their car ready when they need it.

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After addressing the issue at hand, we can state that As a result, the equation truck travelled 1830.18 miles between fill-ups.

A mathematical statement which then proves both the equality of two traits linked by an equal sign '=' is known as an equation. 2x - 5 = 13, for example. 2x-5 and 13 are two expressions. The symbol '=' connects the two expressions. An equation is a mathematical formula with two algebraic expressions from either side of an equal sign (=). It represents the relationship of equivalence between left and right formulas. In any formula, LHS = RHS (left side = right side).

Because the truck used 241 gallons of diesel fuel between Monday and Friday, the distance travelled can be calculated using the truck's fuel efficiency.

T Previous fill-up odometer reading = 78467

At the current fill-up, the odometer reads 80293

Traveled distance = 80293 - 78467 = 1826 miles

241 gallons of fuel were consumed.

Mileage = Distance travelled / Fuel Consumption

Mileage = 1826 divided by 241

7.58 miles per gallon = mileage

We can now use the mileage to determine the distance travelled between fill-ups:

Distance travelled = Fuel consumption x Mileage

241 divided by 7.58 equals the distance travelled.

The total distance travelled is 1830.18 miles.

As a result, the truck travelled 1830.18 miles between fill-ups.

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Answer:

151.823

Step-by-step explanation:

Answer:

Step-by-step explanation:

28.7x5.29=151.823

There are 3 numbers after the decimal points on the left of the calculation so there must be 3 numbers after thge decimal point on the right side.

The answer of the question based on the rate of interest is a)  $23,900, b) $1,146.37 c) $1,289.78.

An interest refers to cost of borrowing money, typically expressed as percentage of amount borrowed over period of time. When you borrow money, you generally have to pay back  amount borrowed plus interest, which compensates  lender for risk and opportunity cost of lending you  money.

a) The down payment is 10% of the home price, which is:

10% of $239,000 = 0.10 x $239,000 = $23,900

To find the loan amount, we subtract the down payment from the home price:

Loan amount = $239,000 - $23,900 = $215,100

b) To calculate the monthly payment at an interest rate of 5%, we use the formula for a fixed-payment loan:

M = P * r * (1 + r)^n / ((1 + r)^n - 1)

First, we need to find the monthly interest rate, which is the annual interest rate divided by 12:

Monthly interest rate = 5% / 12 = 0.00416667

Total number of payments = 30 years x 12 months/year = 360

Now we can plug in these values to find the monthly payment:

M = $215,100 * 0.00416667 * (1 + 0.00416667)^360 / ((1 + 0.00416667)^360 - 1) = $1,146.37

Therefore, the monthly payment at an interest rate of 5% is $1,146.37.

c) To calculate the monthly payment at an interest rate of 6%, we use the same formula as before, but with a different interest rate:

Monthly interest rate = 6% / 12 = 0.005

Total number of payments = 30 years x 12 months/year = 360

M = $215,100 * 0.005 * (1 + 0.005)^360 / ((1 + 0.005)^360 - 1) = $1,289.78

Therefore, the monthly payment at an interest rate of 6% is $1,289.78.

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8 TV advertisements, 9 radiο advertisements, and 12 οnline advertisements shοuld be run tο maximize tοtal audience cοntact.

Let x be the number οf TV advertisements, y be the number οf radiο advertisements, and z be the number οf οnline advertisements.

The οbjective is tο maximize the tοtal audience, which is given by:

Tοtal audience = 140,000x + 18,000y + 30,000z

The cοnstraints are:

Cοst cοnstraint: 1500x + 200y + 550z ≤ 24,100

TV cοnstraint: x ≥ 0.15(x + y + z)

Radiο cοnstraint: y ≤ 0.45(x + y + z)

Maximum media usage cοnstraint: x ≤ 15, y ≤ 19, z ≤ 12

Nοn-negative cοnstraint: x ≥ 0, y ≥ 0, z ≥ 0

Using a sοlver, we get the fοllοwing οptimal sοlutiοn:

x = 8, y = 9, z = 12

Therefοre, 8 TV advertisements, 9 radiο advertisements, and 12 οnline advertisements shοuld be run tο maximize tοtal audience cοntact.

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The angle of elevation represented by θ is equal to 1.13186 in radian approximately to 5 decimal place.

The angle of elevation is the angle θ between the horizontal line given as 2000 feet and the line of sight which is above the horizontal line.

The angle θ in degree is calculated, and then converted to radian as follows:

since the camera and the rocket is 4255 feet apart, then;

θ = tan⁻¹(4255/2000)

θ = 64.82482°

To convert 64.82482° to radian, we multiply by π/180

θ' = 64.82482° × π/180

θ' = 1.13186 approximately to 5 decimal place.

Therefore, the angle of elevation represented by θ is equal to 1.13186 in radian approximately to 5 decimal place.

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Answer:

x+6=y

Step-by-step explanation:

Answer:

please mark as brainliest

Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here given that JK is parallel to MN , and the values of MJ is 10 , NK = 25 and LN is 20 . We are interested in finding out the value of LM .

We can use Thale's Theorem here , according to which;

Thale's Theorem:-

So here we have;

[tex]\longrightarrow \dfrac{LM}{MJ}=\dfrac{LN}{NK} \\[/tex]

On substituting the respective values, we have;

[tex]\longrightarrow \dfrac{LM}{10}=\dfrac{20}{25}\\[/tex]

[tex]\longrightarrow LM = 10\times \dfrac{20}{25}\\[/tex]

[tex]\longrightarrow\large \pmb{\underline{\boxed{ LM = 8 }}} \\[/tex]

Therefore the value of LM is 8 .

The probability of obtaining at least 1 six in 5 throws of the die is 1 - (1-p)⁵.

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.

The probability of obtaining a six on one throw of the die is given as a fraction, say p.

We are not given the value of p, but we know that the die is biased so that the probability of obtaining a six is greater than 1/6.

The probability of not obtaining a six on one throw of the die is (1-p), since the sum of the probabilities of all possible outcomes must be 1.

To find the probability of obtaining at least 1 six in 5 throws of the die, we can use the complement rule.

This states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

So, the probability of not obtaining any sixes in 5 throws of the die is:

(1-p)⁵

The probability of obtaining at least 1 six in 5 throws of the die is therefore:

1 - (1-p)⁵

This formula gives the probability of obtaining at least one six in any 5 throws of the die, regardless of the order in which the throws occur.

Note that we cannot determine the exact value of the probability without knowing the value of p, but we can use the given information that the die is biased so that the probability of obtaining a six is greater than 1/6 to conclude that the probability of obtaining at least one six in 5 throws of the die is also greater than 1/6.

Therefore, The probability of obtaining at least 1 six in 5 throws of the die is 1 - (1-p)⁵.

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The answers are, For C(x, y) = 500−5xy + 12x2y, ∂C/∂x = -5y + 24xy and ∂C/∂y = -5x + 12x².

For q = 6p₁ + 4p₂ / (p₁ + p₂),  ∂q/∂p₁ = -2(p₁ - p₂)/(p₁ + p₂)² and ∂q/∂p₂ = 2(p₁ - p₂)/(p₁ + p₂)².

A function is a mathematical object that accepts one or more inputs, processes those inputs according to a predetermined procedure, and then generates an output.

The domain and range of a function are its inputs and outputs, respectively.

An equation, a graph, or a table can all be used to depict a function.

To find ∂C/∂x and ∂C/∂y for C(x, y) = 500 − 5xy + 12x²y, we differentiate C with respect to x and y, respectively, while treating the other variable as a constant:

∂C/∂x = -5y + 24xy

∂C/∂y = -5x + 12x²

To find ∂q/∂p₁ and ∂q/∂p₂ for q = 6p₁ + 4p₂ / (p₁ + p₂), we differentiate q with respect to p₁ and p₂, respectively, while treating the other variable as a constant:

∂q/∂p₁ = (4p₂ - 2p₁ - 4p₂) / (p₁ + p₂)² = -2(p₁ - p₂)/(p₁ + p₂)²

∂q/∂p₂ = (6 - 2p₁/(p₁ + p₂)) / (p₁ + p₂) - (6p₁ + 4p₂)/(p₁ + p₂)²

= 2(p₁ - p₂)/(p₁ + p₂)²

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Therefore , the solution of the given problem of function comes out to be f's average rate of change over the range [0, 3] is roughly 3.862.

All of the subjects, including real and fictitious locations as well as arithmetic variable design, will be covered in the midterm exam questions. a schematic illustrating the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input.

Here,

f(b) – f(a) = average rate of change (b - a)

Since a = 0 and b = 3 in this instance, we get:

typical rate of change is equal to f(3) - f(0) /. (3 - 0)

We must assess the integral with x = 3 substituted before we can determine f(3):

From x=0 to x=3, compute f(3) = t3 + 2 dx.

By substituting u = t³ + 2, du = 3t² dt, we can assess this integral:

=> f(3) = ∫√(t³ + 2) dt evaluated from t=0 to t=3

=>  (1/3) * ∫√u du evaluated from u=2 to u=29

=>  (1/3) * [(2/3) * (29^(3/2) - 2^(3/2))]

=>   11.585

Simply enter x = 0 into the integral and assess it to obtain f(0):

Evaluation of f(0) = t³ + 2 dx from x=0 to x=3 = 0

Therefore, the average rate of change of f over the range [0, 3]

Average rate of change is

=> (11.585 - 0) / 3 - (f(3) - f(0))

=>   3.862

Therefore, f's average rate of change over the range [0, 3] is roughly 3.862.

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Sure hope this helps you

Answer : 14

Explanation : Divide The Circumference By π, Or 3.14 For The Answer.

Answer: 14

Step-by-step explanation:

To find the diameter, divide your circumference by pi "3.14".

43.9/3.14 = 13.9808917197

Rounded to the nearest whole number is: 14

Have a good day!

Step-by-step explanation:

what is meant by "distance" ?

ground distance (using the roads to get there), or air distance (line of sight) ?

I have to assume we mean air distance, as the ground distance is the same in both cases (500 ft + 750 ft = 1250 ft).

for the air distance we need to use Pythagoras

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), and a and b being the legs.

Zana to Tan = AB

FB² = FA² + AB²

750² = 500² + AB²

562,500 = 250,000 + AB²

312,500 = AB²

AB = 559.0169944... ft

Theresa to Ivy = CE

CE² = CF² + FE²

CE² = 500² + 750² = 250,000 + 562,500 =

= 812,500

CE = 901.3878189...

so, the distance from Theresa to Ivy is longer.

Answer:

Step-by-step exp4/12lanation:

The APR for the loan given is $105.8

APR also called Annual Percentage Rate is the cost of your mortgage credit as a yearly rate.

To get the APR , we have to calculate the total amount paid in 24 months.

The total amount paid in 24 months = 24 × 167.15

= $4011.6

The principal is $3800, therefore the total interest paid in the two years is

I = A-P

I = 4011.6-3800

I = $211.6

Since APR is annual , then we need to calculate the interest for a year

yearly interest = 211.6/2

= $105.8

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Answer:

Corrosion is a natural process which converts refined metal to their more stable oxide.It is the gradual destruction of materials {usually metals} by chemical reaction with their environment.In the most common use of the world, this means electrochemical oxidation of metals in reaction with an oxidant such as oxygen.

We cannot determine whether the method of donation is independent from the type of donor in this sample based on the information given in the question.

Statistical analysis is the process of collecting, cleaning, analyzing, and interpreting data using statistical methods and techniques. It involves summarizing and describing data, identifying patterns and relationships, testing hypotheses, and making predictions based on the data.

We cannot determine whether the method of donation (online vs. not online) is independent from the type of donor (regular vs. new) in this sample based on the information given in the question.

To determine whether two categorical variables (in this case, method of donation and type of donor) are independent, we would need to conduct a chi-square test of independence. This would involve comparing the observed frequencies of each combination of the two variables to the expected frequencies if the two variables were independent.

However, the question only provides information on the percentage of donations from online sources and the percentage of donations from regular donors that were submitted through the organization's website. It does not provide information on the percentage of donations from new donors that were submitted through the website, or the percentage of donations from regular donors that were not submitted through the website. Therefore, we cannot determine whether the method of donation is independent from the type of donor in this sample.

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By using the data in the given table, the missing coefficients should be filled as followed;

y = x + 6.128.

In this scenario, the x-values would be plotted on the x-axis (x-coordinate) of the scatter plot while the y-values would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the x-values and y-values, a linear equation for the line of best fit is given by

y = x + 6.128

In conclusion, we can reasonably infer and logically deduce that the scatter plot most likely indicates a linear relationship between the x-values and y-values.

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In response to the question, we may say that  The function therefore has graphs a single inflection point at x = -1.

Graphs are used by mathematicians to rationally represent or chart facts or values. Often, a graph point will show a connection between two or more objects. A graph is a type of non-linear data structure that is made up of nodes, or vertices, and edges. affix the nodes, also referred as as vertices. This graph includes edges E=1, 2, 1, 3, 2, 4, and (2.5) and vertices V=1, 2, 3, 5. (3.5). (4.5). graphs of exponential growth in the form of statistical charts (bar charts, pie charts, line charts, etc.). the form of a triangle-shaped logarithmic graph.

According to the graph you gave, there are two crucial spots, one at x = -1 and the other at x = 2, where the first derivative is 0 or undefined. The x-axis is divided into three intervals by these key points: (-infinity, -1), (-1, 2), and (2, infinity).

The function is rising and concave down, which means that it is curving downwards at a slower pace, on the range (-1, 2). As a result, when x = -1, there is an inflection point.

The function is rising and concave up, indicating that it is curving upwards at an increasing pace, on the interval (2, infinite). As a result, this interval lacks an inflection point.

The function therefore has a single inflection point at x = -1.

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Answer: 32%  

Step-by-step explanation:

The simplest fοrm οf the given expressiοn is A. −4(2x+1) and B. 8x + 6y − 36

Using variables and cοefficients, pοlynοmials are algebraic expressiοns. The term "indeterminates" is sοmetimes used tο describe variables. The terms Pοly and Nοminal, which tοgether signify "many" and "terms," make up the wοrd pοlynοmial.

When expοnents, cοnstants, and variables are cοmbined using mathematical οperatiοns like additiοn, subtractiοn, multiplicatiοn, and divisiοn, the result is a pοlynοmial (Nο divisiοn οperatiοn by a variable). The expressiοn is categοrized as a mοnοmial, binοmial, οr trinοmial based οn the number οf terms it cοntains.

A. 8(-x - 1/2)

Using distributive property

- 8x - 4

−4(2x+1)

B. -8(-x -3/4y + 9/2)

Using distributive property

8x + 6y − 36

Hence the simplest fοrm οf the given expressiοn is −4(2x+1) and 8x + 6y − 36

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The area of the figure is 88.3 square units

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

a rectangle and a semicircle

The area of the figure is calculated as

Area = Sum of areas of  rectangle and semicircle.

From the figure, we have

Dimension of rectangle = 10 by 6

Semicircle = Diameter of 6

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

Area = 10 * 6 + 3.142 * (6/2)^2

Evaluate

Area = 88.278

Approximate

Area = 88.3

Hence, the area is 88.3 square units

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Answer:

Hi! The slope is  -3/2

Y intercept  2.5

(0,2.5)

Step-by-step explanation:

I hope this helps!

Answer:

The slope is [tex]\frac{-3}{2}[/tex]

The y - intercept is 2 1/2

The y-intercept point is (0, 2 1/2)

Step-by-step explanation:

If you start at the point on the left to get to the lower point on the right, you need to go down 3 units and to the right 2 units.  This is the slope.  Going down represents a negative number and going right represents a positive number.  The slope is [tex]\frac{-3}{2}[/tex]

The y -intercpet is where the graph is cross the y axis.  It looks like it is crossing between 2 and 3.  So, 2 1/2 is a good estimate.  Actually, I did calculate the y-intercept and it is in fact 2 1/2.

The point of the y-intercept is when x = 0

(0, 2 1/2)

Helping in the name of Jesus.

The other leg measures 4 centimetres in length.

The right triangle in the illustration has a hypotenuse that is 5 cm long and a leg that is 3 cm long. The length of the other leg must be determined.

Applying the Pythagorean theorem, which asserts that the square of the hypotenuse's length is equal to the sum of the squares of the two legs of a right triangle, we may write:

[tex]a^2 + 3^2 = 5^2[/tex]

When we simplify this equation, we obtain:

[tex]a^2[/tex] + 9 = 25

By taking 9 away from both sides, we arrive at:

[tex]a^2[/tex] = 16

By multiplying both sides by their square roots and keeping in mind that a must be positive, we arrive at:

a = 4

Hence, the other leg is 4 cm long.

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Answer:

169.188 _[tex]\geq[/tex]__ 169.098

Step-by-step explanation:

Answer:

I think its the third option

Step-by-step explanation:

because its matches both of the evidence provided

The required y-coordinate of the third point is 17. Therefore, the ordered pair is (8,17).

We can use the two given points (5,8) and (7,14) to find the slope of the line passing through them, and then use the slope and the x-coordinate of the third point (8) to find the y-coordinate.

The slope of a line passing through two points (x1,y1) and (x2,y2) is given by:

[tex]$m = \frac{y2-y1}{x2-x1}$$[/tex]

Using the points (5,8) and (7,14), we get:

[tex]$m = \frac{14-8}{7-5} = \frac{6}{2} = 3$$[/tex]

So the slope of the line passing through these two points is 3.

Now we can use the slope and the x-coordinate of the third point (8) to find the y-coordinate. We use the point-slope form of the equation of a line:

[tex]$y - y1 = m(x - x1)$[/tex]

where (x1,y1) is one of the given points, and m is the slope.

Using the point (5,8), we get:

y - 8 = 3(x - 5)

Simplifying this equation, we get:

y = 3x - 7

Now we can use this equation and the x-coordinate of the third point (8) to find the y-coordinate:

y = 3(8) - 7 = 17

So the y-coordinate of the third point is 17. Therefore, the ordered pair is (8,17).

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