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\( \sf \: {x}^{2} + 3x + 5 = 0\)

Solve the quadratic equation (ax²+bx+c=0) using the quadratic formula:

\( \boxed{ \bf \: x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }\)

\( \tt \: x = \frac{ - 3± \sqrt{ {3}^{2} - 4 \times 1 \times 5 } }{2 \times 1} \)

Any expression multiplied by 1 remains the same

\( \tt \: x = \frac{ - 3± \sqrt{ {3}^{2} - 4 \times 5 } }{2} \)

Evaluate the power

\( \tt \: x = \frac{ - 3± \sqrt{9 - 4 \times 5} }{2} \)

Multiply the numbers

\( \tt \: x = \frac{ - 3± \sqrt{9 - 20} }{2} \)

Calculate the difference

\( \tt \: x = \frac{ - 3± \sqrt{ - 11} }{2} \)

Calculate the square root

\( \tt \: x = \frac{ - 3± \sqrt{11}i }{2} \)

Write the solutions, one with a + sign and one with a - sign

\( \tt \: x = \frac{ - 3 + \sqrt{11} i}{2} \\ \tt \: x = \frac{ - 3 - \sqrt{11}i }{2} \)

Separate the real and the imaginary parts

\( \tt \: x = - \frac{3}{2} + \frac{ \sqrt{11} }{2} i \\ \tt \: x = - \frac{3}{2} - \frac{ \sqrt{11} }{2} i\)

∴ The quadratic equation has two solutions

\( \rm x_{1} = - \frac{3}{2} + \frac{ \sqrt{11} }{2} i, x_{2} = - \frac{3}{2} - \frac{ \sqrt{11} }{2} i\)

Answer:

\(⇒x = \frac{ - b \binom{ + }{ - } \sqrt{ {b}^{2} } - 4ac }{2a} \)

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

\(⇒ {x}^{2} + 3x + 5 = 0 \\ ⇒a = 1 \\ ⇒b = 3 \\ ⇒c = 5 \\ ⇒x = \frac{ - 3 \binom{ + }{ - } \sqrt{ {3}^{2} } - 4.1.5}{2.1} \)

▪Evaluate the exponent

▪Multiply the numbers

▪Subtract the numbers

▪Multiply the numbers

\(⇒x = \frac{ - 3 \binom{ + }{ - } \sqrt{ - 11} }{2} \)

▪The square root of a negative number is not a real number

\(⇒d = - 11\)

♧ no solution ♧

If the engine is idling at 500 rpm, the Alternator rpm is 1075 rpm

Ratio of alternator-to-engine drive = 2.15 : 1

If engine is idling at 500 rpm, alternator rpm is x

2.15 : 1 = x : 500

2.15/1 = x/500

cross product

2.15 × 500 = 1 × x

1075 = x

Alternator rpm is 1075 rpm

Therefore, the alternator will have 1075 rpm when the engine is idling at 500 rpm.

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Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

-108 is the depth of the submarine after 9 ​minutes.

An expression is combination of variables, numbers and operators.

The given expression is  -210+ 12m

This expression  represents a submarine that began at a depth of 210 feet below sea level and ascended at a rate of 12 feet per minute.

We need to find the depth of the submarine after 9 ​minutes

m=9

Now put m value in the expression

-210+12(9)

-210+108

-108

Hence, -108 is the depth of the submarine after 9 ​minutes.

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Answer: 9.77 m

Step-by-step explanation:

xyz

Answer:

heyyy thereee

4) 572 = five hundred seventy two

5) 2.897 = two and eight hundred ninety seven thousandths

6) three hundred twenty five and 10 hundredths  or three hundred twenty five and 1 tenth

glad if brainliest ig ?

Answer:

The answer is true

Step-by-step explanation:

14(-9)-17(-8)=10

11(-9)-14(-8)=13

Answer:

Hello!!

Yes, (-9,-8) is a solution to the system of equations.

\(14x-17y=10\\11x-14y=13\)

Step-by-step explanation:

Solve for the first variable in either one of the equations and then substitute the result for the other equation.

Hope this helps and let me know if you need any other help!

The cylindrical coordinates of (−7, 7, 7) are (√98, -π/4, 7). cylindrical coordinate (−7, 7 3 , 1) is  (14, -π/3, 1).

We must switch from rectangular to cylindrical coordinates in the provided problem. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)

A)(−7, 7, 7)

Given rectangular coordinates(x, y, z) =(−7, 7, 7)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²+(7)²

r = √49+49

r = √98

θ = tan⁻¹ (y/x)

θ =tan⁻¹  (7/-7)

θ =tan⁻¹  (-1)

θ = -π/4

So cylindrical coordinate = (r, θ, z) = (√98, -π/4, 7)

B) (-7,7√3,1)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²(7√3)²

r = √49+147

r = √196

r = 14

θ = (y/x)

θ = (7√3/-7)

θ = (-√3)

θ = -π/3

So cylindrical coordinate = (r, θ, z) = (14, -π/3, 1)

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Probability of the number being part of A∩B= 2/9

The Venn diagram, a style of diagram that illustrates the logical connection between sets, was created by John Venn in the 1880s. The examples are used to illustrate fundamental set connections and introduce basic set theory in the fields of probability, logic, statistics, linguistics, and computer science.

A Venn diagram is a type of visual representation that uses circles to show the relationships between various items or constrained groups of objects. Circles that coincide and those that intersect have certain properties in common. Venn diagrams are helpful for visually illustrating the relationship and differences between two ideas.

The probability of an occurrence is a figure used to indicate the likelihood that the event will occur. It is expressed as a figure between 0 and 1, or between 0% and 100%, when expressed as a percentage. The likelihood that the occurrence will occur increases with the probability.

In this question,

A∩B= 4,9

Probability of the number being part of A∩B= 2/9

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A unique solution occurs in a set of linear simultaneous equations if and only if (a) the number of unknowns and equations are equal, (b) all equations are consistent, and (c) there is no linear dependency between any two or more equations, that is, all equations are independent.

If a pair of linear equations is consistent with a unique solution, then their lines intersect.

The unique solution of a linear equation denotes the existence of just one point at which the L.H.S. and R.H.S. of an equation become equal when substituted. A linear equation with one variable always has a unique solution.

A one-of-a-kind solution is the sole solution. In your case, if (x0,y0) solves your problem, it is said to be unique if the following condition is true: if (x1,y1) solves the equation, it implies x0=x1,y0=y1.

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Answer:

c

Step-by-step explanation:

i took the test

Answer: El número de grupos de Analistas que puede realizar la inducción es de 238 y el número de grupo Ingenieros en Mantenimiento  es de 227.

Explanations: Hacemos dos ecuaciones para resolver la incógnita. Siendo X el grupo de Técnicos y Y el grupo de Ingenieros Civiles.

17X + 18Y = 423 (1)

14X + 7Y = 231 (2)

Resolvemos el sistema de ecuaciones, multiplicamos por -14 a la primera ecuación y por 17 a la segunda ecuación:

(-14) (17X + 18Y = 423)

(17)  (14X + 7Y  = 231)

Sumamos y despejamos a Y:

-238X - 252Y = -59 976

238X + 119Y = 28.322

0 + 133Y = 31 654

Y = 31 654/133

Y = 238

Entonces el número de grupo de analistas que puede realizar la inducción es 238.

Ahora sustituimos el valor de Y en cualquiera de las ecuaciones y despejamos a X:

17X + 18*231 = 423

17X + 4284 = 423

17X = 4284-423

17X = 3861

X = 3861/17

X = 227

El número de grupo de Ingenieros en Mantenimiento que realizarán la inducción es 227.

Answer:

x = ± 4

y = - 2

Step-by-step explanation:

y = 0.5x² - 10 ------------------------(I)

y = -x² + 14   ------------------------(II)

Substitute the y value in equation (II)

    0.5x² - 10  = -x² + 14           {Add x² to both sides}            

0.5x² + x² -10 = 14                  {combine like terms}

       1.5x² - 10 = 14                   {Add 10 to both sides}

               1.5x² = 14 + 10

                1.5x² = 24         {Divide both sides by 1.5}

               1.5x²/1.5 = 24/1.5

                       x² = 16

                      x = ±4

Substitute x = 4 in (I)

y = 0.5 * 4² - 10

 = 0.5*16 - 10

 = 8- 10

y = -2

Substitute x = -4 in (I)

y = 0.5 * (-4)² - 10

 = 0.5*16 - 10

 = 8- 10

y = -2

The statement that best summarizes the bounded rationality model of problem solving and decision making is 'Managers are comfortable making decisions without identifying all options'. Therefore, the correct option is B.

This is because the bounded rationality model recognizes that managers have limitations in their cognitive ability to process all information and alternatives, and therefore they use heuristics and simplified decision-making processes. However, this does not mean that they completely ignore options or do not consider the consequences of their decisions. Instead, they focus on the most relevant information and use their experience and judgment to make the best possible decision given the constraints they face.

Therefore, while option A) is partially correct, it does not capture the essence of the bounded rationality model. Option C) is too idealistic and implies that managers have unlimited time and resources to generate all possible options, which is not realistic. Option D) is not accurate as the bounded rationality model does not rely solely on statistical rules for decision making. Hence, the correct answer is option B.

Note: The question is incomplete. The complete question probably is: Which statement best summarizes the bounded rationality model of problem solving and decision making? A) Managers critically view the world as complex and multivariate. B) Managers are comfortable making decisions without identifying all options. C) Managers generate a wide array of decision options and select the one that meets all decision criteria. D) Managers follow statistical rules for decision making.

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According to the solution, the Given number is not prime (7/8 or 0.875). This doesn't qualify as a prime number.

Prime numbers are those that have just two elements, one and themselves. For instance, the first five prime numbers are 2, 3, 5, 7, and 11. Comparatively, composite numbers are defined as having more than two elements.

Try to divide the number by all the smaller numbers to see if your child can determine whether it is prime. It is a prime number if it can only be divided by itself and by one.

= 4/7+1/8+1/3

=  7/8 or 0.875

This is not a prime number.

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Answer:

a=45° because they are corresponding angles

c=135°

b=45°

Answer:

a=45°

b=45°

c=135°

Answer:

b

Step-by-step explanation:

The distance is 1,750.0 miles if a Boeing 737 airplane travels about 500 miles per hour option (D) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The function d(t) = 500t represents the number of miles traveled in t hours.

Plug t = 3.5 hours in the equation of the function.

d(3.5) = 500(3.5)

d(3.5) = 1,750.0 miles

Thus, the distance is 1,750.0 miles if a Boeing 737 airplane travels about 500 miles per hour option (D) is correct.

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Answer:

1,5,8,11,16

Step-by-step explanation:

this will be helpful and don't forget to mark me

I found this on B i n g because I don't have a map of India.

Rice is mainly grown and eaten in South and East India, while wheat is predominantly grown and eaten in North and West India.

(The first picture is top ten).

(The second one is all).

♡ Anyways I hope this helped! ♡

❀ Have an amazing day or night! ❀

Brainiest is appreciated! ♡

Answer:

To determine the speed, we can use the formula:

speed = distance / time

where distance is measured in feet and time is measured in minutes.

In this case, the distance is 264 feet and the time is 3 minutes. Plugging these values into the formula, we get:

speed = 264 feet / 3 minutes

simplifying, we get:

speed = 88 feet/minute

Therefore, the equipment is traveling at a speed of 88 feet per minute.

The rent Dan pays now is £214.5

Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.

For example, if you spent $200 to heat your home last month, but only $140 this month, the cost has decreased by $60. Therefore percentage increase= 60/200×100= 30%

Similarly 2.5=(220-x)/220 ×100

x is the new rent of Dan

2.5×220=( 220-x)100

550= ( 220-x)100

divide both sides by 100

5.5= 220-x

therefore x= 220-5.5= £214.5

therefore Dan's new rent is £214.5

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Explanatory variables in a regression model are typically considered to be random when they are subject to variability or uncertainty. There are several reasons why explanatory variables may be treated as random:

Measurement error: Explanatory variables may be measured with some degree of error or imprecision. This measurement error introduces randomness into the values of the variables. Accounting for this randomness is important to obtain unbiased and accurate estimates of the regression coefficients.

Sampling variability: In many cases, the data used to estimate the regression model are obtained through sampling. The values of the explanatory variables in the sample may differ from the true population values due to random sampling variability. Treating the explanatory variables as random helps capture this uncertainty and provides more robust inference.

Random assignment in experiments: In experimental studies, researchers often manipulate or assign values to the explanatory variables randomly. This random assignment ensures that the variables are not influenced by any underlying factors or confounders. Treating the explanatory variables as random reflects the randomization process used in the experiment.

By considering the explanatory variables as random, we acknowledge and account for the inherent variability and uncertainty associated with them. This allows for a more comprehensive and accurate modeling of the relationships between the explanatory variables and the response variable in regression analysis.

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Answer:

D

Step-by-step explanation:

When you say "and" its representing a decimal it also ends in the thousandTHS

Answer:

two and sixty three thoundths

Step-by-step explanation:

Answer:

24.99

Step-by-step explanation:

25.9-6.91=24.99

Each of the pairs of angles should be identified as follows;

Complementary angles = ∠HJ and ∠FJ

Adjacent angles = ∠LON and ∠NOM

Supplementary angles = ∠EFA and ∠EFB

Vertical angles = ∠LOP and ∠MO

In Mathematics and Geometry, a complementary angle can be defined as two (2) angles or arc whose sum is equal to 90 degrees (90°).

Mathematically, a complementary angle can be represented by using this mathematical equation:

Q + R = 90°

Where:

Q and R are measure of the angles subtended.

In Mathematics and Geometry, adjacent angles can be defined as two (2) angles that share a common vertex and a common side. This ultimately implies that, both angle LON and angle NOM are adjacent angles.

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The dimensions of the box that will have the greatest volume are:

Length and width of the base: 2√3 feet

Height: h = (36 - x^2) / 8x = (√3)/2 feet

Let the length and width of the base be x, and let the height be h.

The surface area of the top is x^2, and the surface area of the remaining four sides is \(2(xh + xh) = 4xh\).

The cost of the top is \(x^2\), and the cost of the remaining four sides is \(2(4xh) = 8xh\). Therefore, the total cost is:

\(C(x,h) = x^2 + 8xh\)

We know that the total cost is $36, so we have:

\(x^2 + 8xh = 36\)

Solving for h, we get:

\(h = (36 - x^2) / 8x\)

The volume of the box is given by:

\(V(x,h) = x^2h\)

Substituting h in terms of x, we get:

\(V(x) = x^2 ((36 - x^2) / 8x)\)

Simplifying, we get:

\(V(x) = (1/8) x (36x - x^3)\)

To find the dimensions of the box that will have the greatest volume, we need to find the value of x that maximizes V(x). We can do this by taking the derivative of V(x) with respect to x, setting it equal to 0, and solving for x:

\(V'(x) = (1/8) (36 - 3x^2) = 0\)

Solving for x, we get:

x = 2√3

Therefore, the dimensions of the box that will have the greatest volume are:

Length and width of the base: 2√3 feet

Height: \(h = (36 - x^2) / 8x\) = (√3)/2 feet

The volume of the box is:

\(V = x^2h\)= (2√3)^2 ((√3)/2) = 9√3 cubic feet

Note: To confirm that this value represents the maximum volume, we can check that V''(x) < 0, which indicates a maximum point. We have:

\(V''(x) = (1/8) (-6x) = -3x/4\)

At x = 2√3, V''(x) = -3(2√3)/4 = -3√3/2 < 0, so this is indeed a maximum point.

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The correct option is option (d).

Using Combination,

Total 120, different samples of size 3 (without replacement) can be taken from a finite population of size 10.

Population size: The population is the entire group of guesses. A sample is a specific group for which you collect data. It is denoted by N.

Sample Size: The sample size is always smaller than the total size of the population. A sample is a subset of the population set. It is denoted by n.

we have given that , n = 3 and N = 10

Using the following formula for calculating the possible number of different samples of size 3 (without replacement) can be taken from a finite population of size 10.

Number of possible different samples of size n from Population size N = NCn = N!/n! (N-n)!

then we have, 10C3 = 10!/3! × 7!

=> 10×9×8/3×2 = 15×8 = 120

Hence, 120 different samples of size 3 (without replacement) is possible from Population of size 10.

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Answer:

It is three.................

30 ÷ 3 = 3

Hope this helps :)