3.x2 + 42x = -24
Solve the equation by completing the square

We have to find the probability of randomly drawing a chip number that is smaller than 213.

As the chips are numbered from 1 to 348,this probability will be equal to the proportion of chips that have a number that is less than 213.

We have 212 chips in the bag that have a number less than 213, so we can calculate the probability P as:

Answer: the probability is 53/87 or approximately 0.6092.

Answer:

1 2 3 4 5 6

Step-by-step explanation:

1. x = 100

180 - (55 + 25) = 180 - 80 = 100

2. x = 20

360 - (127 + 54 + 119) = 360 - 300 = 60

60/3 = 20

3. x = 136

94 + 42 = 136

4. x = 116

63 + 53 = 116

5. x = 50

180 - 155 = 25

105 + 25 = 130

180 - 130 = 50

6. x = 20

180 - 100 = 80

80 + 80 = 160

180 - 160 = 20

Answer:

x=2 x=-4

Step-by-step explanation:

x2+2x−8=0

Step 1: Factor left side of equation.

(x−2)(x+4)=0

Step 2: Set factors equal to 0.

x−2=0 or x+4=0

x=2 or x=−4

Answer:

x=2 or x=−4

Answer:

x=2 or x=-4

Step-by-step explanation:

ax^2+bx+c=0

when solving this equation you should find two numbers that if we multiply them we get c and when we subtract them we get b so in this equation we get 2 and -4

Answer:

VU < US < SR by the hinge theorem.

Step-by-step explanation:

Did quiz on edge

Answer:

A. VU < US < SR  

Step-by-step explanation:

I got a 100 on the test

Answer:

The answer is D.

Step-by-step explanation: Because It makes sense.

Step-by-step explanation:

I believe the answer is C.

Depending on whether the movement is along the x-axis or the y-axis, the ordered pair would be either (0.25, 0) or (0, 0.25).

To plot an ordered pair starting from the origin and moving 0.25, we need both an x-coordinate and a y-coordinate.

We are starting from the origin (0, 0), we can apply the movement of 0.25 to either the x-axis or the y-axis.

If we move 0.25 units on the x-axis, the x-coordinate of the ordered pair would be 0.25, and the y-coordinate would remain 0 since there is no movement on the y-axis. Therefore, the ordered pair would be (0.25, 0).

Similarly, if we move 0.25 units on the y-axis, the x-coordinate would remain 0 since there is no movement on the x-axis, and the y-coordinate of the ordered pair would be 0.25. In this case, the ordered pair would be (0, 0.25).

So, depending on whether the movement is along the x-axis or the y-axis, the ordered pair would be either (0.25, 0) or (0, 0.25).

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Answer:

−16x²

Step-by-step explanation:

Simplifying!

Answer:

-14

Step-by-step explanation:

Remove the parentheses

(11-18)2

multiply

-7x2=

-14

Answer: 84000

Step-by-step explanation:

Format:

{Expression} = {Rewritten} = {Value}

Answer:

3/8 * 24 = 72/8 = 9

5/9 * 18 = 90/9 = 10

11/12 * 36 = 396/12 = 33

Answer:

5:7

Explaintion

20÷4=5

28÷4=7

Answer:

The answer is (-9, 5). Hope this helps.

i think by x2 you meant x²

(-3x² + 2x + 1) + (-8x² + 3x + 2)

-11x² + 5x + 3

To solve the given differential equation by separation of variables, we'll rearrange the equation and integrate both sides.

Starting with the given differential equation:

dy - (y - 2)^2 dx = 0

Rearranging the terms:

dy = (y - 2)^2 dx

Now, we can separate the variables:

dy / (y - 2)^2 = dx

Integrating both sides:

∫ dy / (y - 2)^2 = ∫ dx

Let's evaluate the integrals separately.

For the left-hand side:

∫ dy / (y - 2)^2

Using a substitution, let u = y - 2. Then, du = dy.

The integral becomes:

∫ du / u^2

Integrating, we have:

-1 / u = -1 / (y - 2)

Now, for the right-hand side:

∫ dx = x + C

Combining the results:

-1 / (y - 2) = x + C

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The three major chords built on white notes without accidentals are:

1. C major chord (C, E, G)

2. F major chord (F, A, C)

3. G major chord (G, B, D)

These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.

Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.

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Answer: 8

Step-by-step explanation:

Answer:

If i'm not wrong 8 minutes.

Step-by-step explanation:

If you add all the meters together its adds up to 1600. It says you run 200 meters per minute so it will take 8 minutes to run around the track 4 times.

Teniendo en cuenta el mínimo común múltiplo, considerando que hoy coincidieron, dentro de 135 días Juan y Alfredo volverán a encontrarse.

El mínimo común múltiplo de dos o más números es el múltiplo más pequeño que esos números tienen en común.

En otras palabras, el mcm es la cifra más pequeña que satisface la condición de ser múltiplo de todos los elementos de un conjunto de números.

El mínimo común múltiplo se suele expresar como m.c.m. (a, b), siendo a y b los números.

Para calcular el mínimo común múltiplo de dos o más números, debes:

En este caso debes encontrar el mínimo común múltiplo entre 15 y 27, correspondientes a los días que Juan y Alfredo asisten a la misma cafetería.

Descomponiendo cada número en factores primos se obtiene:

15= 3× 5

27= 3× 3× 3= 3³

Escogiendo los factores (comunes y no comunes), elevados a la máxima potencia, y multiplicándolos se obtiene:

m.c.m(15,27)= 3³× 5= 135

Finalmente, considerando que hoy coincidieron, dentro de 135 días Juan y Alfredo volverán a encontrarse.

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False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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Answer:

k=6.5

Step-by-step explanation:

by the graph, when x=0, y=-3

y = 2x+c

-3=2(0)+c

then,

c=-3

for y = 10,

10=2(k)-3

k=6.5

The volume of the cube is 1 cubic foot.

Given that, each side of cube is 1 inch.

When dilation of the cubic inch by a factor of 12. Then each side of cube became 12 inches.

As we know that,

            \(12inch=1 foot\)

So that, each side of cube become 1 foot.

   Volume of cube \(=(side)^{3}\)

               \(Volume=1^{3}=1ft^{3}\)

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Answer:

its 1728

Step-by-step explanation:

The largest value that f(4) can possibly be is 29.

The mean value theorem states that for a function f(x) that is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), there exists a number c in the open interval (a, b) such that:

f(b) - f(a) = f'(c)(b - a)

In this case, we are given that f(0) = -3 and that f'(x) ≤ 8 for all values of x. To determine how large f(4) can possibly be, we can use the mean value theorem with a = 0 and b = 4:

f(4) - f(0) = f'(c)(4 - 0)

Substituting the given values:

f(4) - (-3) = f'(c)(4)

f(4) + 3 = 4f'(c)

Since f'(x) ≤ 8 for all values of x, we can say that f'(c) ≤ 8. Therefore:

f(4) + 3 ≤ 4f'(c) ≤ 4(8) = 32

Therefore, we have:

f(4) ≤ 32 - 3 = 29

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Step-by-step explanation:

\(distance = \sqrt{ {( - 1 - 9)}^{2} } + { ( - 2 + 4) }^{2} \\ = \sqrt{ { - 8}^{2} } + {2}^{2} \\ = \sqrt{68} \\ = 2 \sqrt{17} unit\)

The average rate of inflation over the period from 1980 to 2000 can be calculated by determining the percentage increase in the cost of the market basket of goods. The correct answer is 60%, which represents the percentage increase from $250 to $400.

To calculate the average rate of inflation, we need to determine the percentage increase in the cost of the market basket of goods over the given period.

In 1980, the basket cost $250, and in 2000, it cost $400. To find the percentage increase, we calculate the difference between the final and initial values and divide it by the initial value, then multiply by 100.

Percentage increase = [(Final value - Initial value) / Initial value] * 100

= [(400 - 250) / 250] * 100

= (150 / 250) * 100

= 0.6 * 100

= 60%

Therefore, the average rate of inflation over this period is 60%, indicating that the cost of the market basket of goods increased by 60% from 1980 to 2000.

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Answer:

\(\frac{1}{4}\) is larger than \(\frac{3}{14}\)

\(\frac{1*14}{4*14}\) = \(\frac{14}{56}\)

\(\frac{3*4}{14*4}\) = \(\frac{12}{56}\)

i cant tell if it is \(\frac{1}{4}\) or 2 \(\frac{1}{4}\)

but if it is 2 \(\frac{1}{4}\) that mean this is a mixed number

and \(\frac{3}{14}\) is a proper fraction

The quadratic residues for the given integers are as follows: a) For the integer 3, the quadratic residues are 0 and 1.

b) For the integer 5, the quadratic residues are 0 and 1.

c) For the integer 13, the quadratic residues are 0, 1, 3, 4, 9, and 10.

d) For the integer 19, the quadratic residues are 0, 1, 4, 5, 6, 7, 9, 11, 16, and 17.

In number theory, a quadratic residue of an integer n is an integer x such that there exists an integer y satisfying x^2 ≡ y (mod n), where "≡" denotes congruence.

To find the quadratic residues of a given integer, we can calculate the square of each integer between 0 and n-1 (inclusive) and check if the result is congruent to a residue modulo n.

For example, let's consider the integer 13. We calculate the squares of integers from 0 to 12:

0^2 ≡ 0 (mod 13)

1^2 ≡ 1 (mod 13)

2^2 ≡ 4 (mod 13)

3^2 ≡ 9 (mod 13)

4^2 ≡ 3 (mod 13)

5^2 ≡ 12 (mod 13)

6^2 ≡ 10 (mod 13)

7^2 ≡ 10 (mod 13)

8^2 ≡ 12 (mod 13)

9^2 ≡ 3 (mod 13)

10^2 ≡ 9 (mod 13)

11^2 ≡ 4 (mod 13)

12^2 ≡ 1 (mod 13)

From these calculations, we can see that the quadratic residues of 13 are 0, 1, 3, 4, 9, and 10.

Similarly, we can apply this process to the other given integers (3, 5, and 19) to determine their quadratic residues.

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Answer: A

Step-by-step explanation:

If people prefer a choice with risk to one with uncertainty, they are said to be averse to uncertainty.

Uncertainty and risk are related concepts in decision-making under conditions of incomplete information. However, they represent different types of situations.

- Risk refers to situations where the probabilities of different outcomes are known or can be estimated. In other words, the decision-maker has some level of knowledge about the possible outcomes and their associated probabilities. When people are averse to risk, it means they prefer choices with known probabilities and are willing to take on risks as long as the probabilities are quantifiable.

- Uncertainty, on the other hand, refers to situations where the probabilities of different outcomes are unknown or cannot be estimated. The decision-maker lacks sufficient information to assign probabilities to different outcomes. When people are averse to uncertainty, it means they prefer choices with known risks (where probabilities are quantifiable) rather than choices with unknown or ambiguous probabilities.

In summary, if individuals show a preference for choices with known risks over choices with uncertain or ambiguous probabilities, they are considered averse to uncertainty.

If people prefer a choice with risk to one with uncertainty, they are said to be averse to uncertainty.

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The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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According to the information, the jet has traveled 4400 miles.

To find how many miles the jet has traveled, we need to know the total time it has been in the air. Since the jet left the airport 4 hours ago, and assuming it has been flying at a constant speed of 600 mph ever since, we have:

Total time in air = 4 hours + time since reaching top speed

We can convert this total time to minutes by multiplying by 60:

Total time in air = 4 × 60 + time since reaching top speed

Total time in air = 240 + time since reaching top speed (in minutes)

Now, we can use the equation:

distance = speed × time

to find the distance traveled by the jet. The speed is 600 mph, but we need to convert it to miles per minute by dividing by 60:

speed = 600 mph ÷ 60 = 10 miles per minute

The time is the total time in air we just calculated. Therefore:

distance = 10 miles per minute × (240 + time since reaching top speed)

We don't know the exact value of the time since reaching top speed, but we know it is less than 4 hours (since the jet reached top speed 7 minutes after takeoff and has been flying at a constant speed of 600 mph ever since). Therefore, we can assume it is less than 240 minutes. Let's take a conservative estimate and assume it is 200 minutes:

distance = 10 miles per minute × (240 + 200) = 4400 miles

Therefore, the jet has traveled 4400 miles.

 600|            .__

     |          .     \

     |        .        \

     |      .            \

     |    .                \

     |  .                    \

     |________________________

         0       7 min     t

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Answer:

<EFG

Step-by-step explanation:

Answer:

1.

Step-by-step explanation:

+ (-4) = - 4 so we have

-2 + 7 - 4

= 5 - 4

= 1.