what is the equation for this table!?

Answer:

A

Step-by-step explanation:

2x² + 5x + 2 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 2 = 4 and sum = + 5

the factors are + 4 and + 1

use these factors to split the x- term

2x² + 4x + x + 2 = 0 ( factor the first/second and third/fourth terms )

2x(x + 2) + 1(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(2x + 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 2 = 0 ( subtract 2 from both sides )

x = - 2

2x + 1 = 0 ( subtract 1 from both sides )

2x = - 1 ( divide both sides by 2 )

x = - [tex]\frac{1}{2}[/tex]

the roots are x = - 2, - [tex]\frac{1}{2}[/tex]

The function is f(x) = 4 - 4x

The domain of a function is the set of the possible values of x, while the range of a function is the set of the resulting values of the functions from the domain.

domain: {0, 1, 3, 5, 6}

range: {-20, -16, -8, 0, 4}

By using the function f(x) = 4 - 4x, you will see that the same above domain and range appear;

4 - 4(0) = 4 - 0 = 4

4 - 4(1) = 4 - 4 = 0

4 - 4(3) = 4 - 12 = -8

4 - 4(5) = 4 - 20 = -16

4 - 4(6) = 4 - 24 = -20

The value of the logarithm of the number 52.66 is 1.7215.

The value of the logarithm of the number 52.66 is calculated as follows;

Using the logarithm table, we will follow the steps below;

From the logarithm table, log 52 under 6 = 7210

mean difference of 6 = 5

The total = 7210 + 5 = 7215

0.7215 (the result is called the mantissa)

Now, we will look for the characteristics part.

Since 52 is a number between 50 and 100, the characteristic is 1

Finally, we will combine both the characteristic part and the mantissa part to get the desired logarithm value as follows;

= 1 + 0.7215

= 1.7215

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Answer:

The answer should be ( he worked 8 hours over time)

Step-by-step explanation:

a) The force in the coupling between the first carriage and the locomotive can be found by analyzing the net force acting on the train. It is determined to be 100 N.

b) The force in the coupling between the first carriage and the locomotive is a tension force.

a) To find the force in the coupling between the first carriage and the locomotive, we need to analyze the forces acting on the train.

The forces acting on the train are:

The driving force applied by the locomotive: 700 N

The resistance force of each carriage: 400 N (assuming equal resistance forces for both carriages)

The force in the coupling between the first carriage and the locomotive (unknown)

Since the train comes to rest, the net force acting on the train must be zero. We can set up the equation for the net force as:

Net force = Driving force - Resistance force - Force in coupling = 0

Substituting the given values:

700 N - 2(400 N) - Force in coupling = 0

Simplifying the equation:

700 N - 800 N - Force in coupling = 0

-100 N - Force in coupling = 0

Therefore, the force in the coupling between the first carriage and the locomotive is 100 N (opposite in direction to the driving force).

b) The force in the coupling between the first carriage and the locomotive is a tension force. Tension forces act along a string, cable, or any stretched connection. In this case, the coupling acts as a connection between the locomotive and the first carriage, so the force in the coupling is a tension force.

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The angle between 0 and 2pi in radians that is co-terminal with the angle 34/7pi in radians is 20/7π.

To find the angle between 0 and 2π in radians that is co-terminal with the angle 34/7π in radians, we need to first understand what co-terminal angles are.

Co-terminal angles are angles that share the same initial and terminal sides, but differ by a multiple of 360°. In radians, they differ by a multiple of 2π.

To find the co-terminal angle, we need to add or subtract a multiple of 2π from the given angle until we get an angle between 0 and 2π. We can do this using the following formula:

Co-terminal angle = θ ± 2nπ Where θ is the given angle and n is an integer that represents the number of full rotations (360° or 2π radians) we add or subtract.

To find the co-terminal angle with 34/7π, we need to subtract 2π until we get an angle between 0 and 2π:

34/7π - 2π = (34/7 - 14/7)π = 20/7π.

Now, we have an angle of 20/7π that is co-terminal with 34/7π and is between 0 and 2π radians.

Therefore, the answer is 20/7π.

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The quadratic equation is x² + (k - 3)x + 4 = 0.

The values of k are 7 and -1.

Given: The quadratic equation is x² + (k - 3)x + 4 = 0.

Now, we can find the possible values of k.

To find the values of k, we will apply the discriminant formula of quadratic equation which is given by: [tex]$D=b^2-4ac$[/tex] ,where a,b and c are the coefficients of the quadratic equation: ax²+bx+c

Roots of the quadratic equation are given by:

[tex]$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$[/tex]

Now, let's apply these formulas to the given quadratic equation:

x² + (k - 3)x + 4 = 0

Comparing with the standard quadratic equation of the form ax² + bx + c = 0, we get:

[tex]a = 1, b = k - 3, and c = 4$\\D = b^2 - 4ac$= $(k - 3)^2 - 4(1)(4)$= $k^2 - 6k + 9 - 16$= $k^2 - 6k - 7$[/tex]

The roots of the given quadratic equation are given by:

[tex]$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$[/tex]

Substituting the values of a, b, c, and D, we get:

[tex]$x = \frac{-(k - 3) \pm \sqrt{(k - 3)^2 - 4(1)(4)}}{2(1)}$$x = \frac{3 - k \pm \sqrt{k^2 - 6k - 7}}{2}$[/tex]

Now, for the quadratic equation to have real and equal roots, the discriminant must be equal to zero, i.e., [tex]$D = 0$$\ therefore, k^2 - 6k - 7 = 0$.[/tex]

Factoring the quadratic equation, we get:

[tex]$k^2 - 7k + k - 7 = 0$$\\k(k - 7) + 1(k - 7) = 0$$\\(k - 7)(k + 1) = 0$[/tex]

So, the possible values of k are k = 7 and k = -1.

Hence, the values of k are 7 and -1.

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Answer:

Angle ACB = 44°

There are two ways to solve it. Both are right

Solution number 1

From triangle ABC

angle BAC = 180°-(102° +44°) = 36°

Because BG is parallel with AC

Another solution

The sum of angles in the shape AGBC = 360°

To evaluate the limit [tex]\sf \lim_{x,y \to \infty} \frac{x+y}{x^{2} +y^{2}-xy} \\[/tex], we can analyze the behavior of the expression as both [tex]\sf x \\[/tex] and [tex]\sf y \\[/tex] approach infinity.

Let's consider the numerator [tex]\sf x + y \\[/tex] and the denominator [tex]\sf x^{2} + y^{2} - xy \\[/tex] separately.

For the numerator, as both [tex]\sf x \\[/tex] and [tex]\sf y \\[/tex] approach infinity, their sum [tex]\sf x+y \\[/tex] will also approach infinity.

For the denominator, we can rewrite it as [tex]\sf (x-y)^2 + 2xy \\[/tex]. As [tex]\sf x[/tex] and [tex]\sf y[/tex] approach infinity, the terms [tex]\sf (x-y)^2 \\[/tex] and [tex]\sf 2xy \\[/tex] will also approach infinity. Therefore, the denominator will also approach infinity.

Now, let's consider the entire fraction [tex]\sf \frac{x+y}{x^{2} +y^{2}-xy} \\[/tex]. Since both the numerator and denominator approach infinity, we have an indeterminate form of [tex]\sf \frac{\infty}{\infty} \\[/tex].

To evaluate this indeterminate form, we can apply techniques such as L'Hôpital's rule or algebraic manipulations. However, in this case, we can simplify the expression further.

By dividing both the numerator and denominator by [tex]\sf x^{2} \\[/tex], we get:

[tex]\sf \lim_{x,y \to \infty} \frac{\frac{x}{x^{2}} + \frac{y}{x^{2}}}{1 + \frac{y^{2}}{x^{2}} - \frac{xy}{x^{2}}} \\[/tex]

As [tex]\sf x[/tex] approaches infinity, the terms [tex]\sf \frac{x}{x^{2}} \\[/tex] and [tex]\sf \frac{y}{x^{2}} \\[/tex] both approach zero. Similarly, the term [tex]\sf \frac{y^{2}}{x^{2}}[/tex] and [tex]\sf \frac{xy}{x^{2}} \\[/tex] also approach zero.

Therefore, the limit simplifies to:

[tex]\sf \lim_{x,y \to \infty} \frac{0 + 0}{1 + 0 - 0} = \frac{0}{1} = 0 \\[/tex]

Hence, the limit [tex]\sf \lim_{x,y \to \infty} \frac{x+y}{x^{2} +y^{2}-xy} \\[/tex] is equal to 0.

Answer:

x = 5

Step-by-step explanation:

3x + 7 = 22 <-- Subtract 7 on both sides

3x = 15 <-- Divide both sides by 3 to isolate x

x = 5

The value of x is:

x = 5

Work/explanation:

The objective of this problem is to solve 3x + 7 = 22 by isolating x.

I begin by subtracting 7 from each side:

3x = 22 - 7

3x = 15

Next, I divide each side by 3:

x = 5

Hence, the value of x is 5.

Answer:

4-1/4

Step-by-step explanation:

just Tixes by your denominator to get your number

Answer:

1/ 4^10

(ONE on top of a fraction. Four to the tenth power on the bottom of the fraction)

Step-by-step explanation:

When you have a power to a power the short cut (exponent rule) says to multiply the powers.

(4^-2)^5

Keep the same base, the 4

times -2 × 5, you get -10

so far after one step, you have

4^-10

Now usually, you would not leave an exponent negative. So to "fix" the negative exponent, you change it to positive by "pushing it" across the fraction bar.

4^-10

becomes:

1/ 4^10

This is a ONE on top of a fraction and FOUR to the tenth power on the bottom of the fraction.

The answer is:

1/4¹⁰

Work/explanation:

For this problem, I'm going to use the following exponent law:

[tex]\boxed{\!\!\boxed{\quad\sf{(x^m)^n=x^{mn}}\quad}\!\!}[/tex]

So if we have "a power to a power", we multiply the powers.

And now that we're familiar with this property let's apply it.

[tex]\sf{(4^{-2})^5=4^{-2\times5}=4^{-10}}[/tex]

Here the next exponent law comes into play.

______________________

[tex]\boxed{\!\!\boxed{\quad\sf{x^{-m}\:\:=\:\:\dfrac{1}{x^m}\quad}}\!\!}[/tex]

So if we have a number raised to a negative power, we flop it over.

Let's apply the law to our problem now.

Our problem is:

[tex]\sf{4^{-10}[/tex]

According to the law above, we should do the following:

[tex]\sf{4^{-10}=\dfrac{1}{4^{10}}}[/tex]

It's better to leave the answer as it is.

Hence, the answer is 1/4¹⁰

Answer: (-5, -7)

Step-by-step explanation: To find the intersection of two functions, you need to set them equal to each other and solve for x.

In this case, we have:

2x + 3 = -4x - 27

Adding 4x to both sides, we get:

6x + 3 = -27

Subtracting 3 from both sides, we get:

6x = -30

Dividing both sides by 6, we get:

x = -5

Now that we have the value of x, we can find the corresponding value of y by plugging it into either of the original equations. Let's use f(x) = 2x + 3:

f(-5) = 2(-5) + 3 = -7

Therefore, the intersection of the two functions is (-5, -7).

Answer:

2π/3 + 2πn or 4π/3 + 2πn radians

Step-by-step explanation:

Think of this as a quadratic function: replace the cos(x) with “x”.

2x^2 - 7x - 4 = 0

Now factor it

(2x + 1)(x - 4) = 0

Now, replace the “x” with cos(x) and solve

(2cos(x) + 1)(cos(x) - 4) = 0

2cos(x) + 1 = 0

cos(x) = -1/2

x = 2π/3 + 2πn or 4π/3 + 2πn radians

cos(x) = 4

x is undefined here

Set A and Set R do not have one-to-one correspondence in terms of their elements. Therefore, the correct answer is no, because each element in set R is not represented in set A.

Set A is defined as the set of odd integers, while set R is defined as the set containing the elements 3, 7, 11, and 27. Since set R contains specific elements, it is not possible for every element in set A to be represented in set R.

For example, there are odd integers such as 5, 9, and 13 that are not included in set R. On the other hand, if the question was asking if set A is a subset of set R, then the answer would be no as well.

A subset relationship implies that every element in set A is also in set R, but since set R contains specific elements (3, 7, 11, 27), it does not include all the odd integers.

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5√27 can be written in the form of k√3 as 15√3, where k = 15.

To simplify the expression 5√27, we can first break down 27 into its prime factors.

The prime factorization of 27 is 3 * 3 * 3, which can be written as 3^3.

Now, we rewrite 5√27 as 5√(3^3).

Using the property of surds that √(a * b) = √a * √b, we can split the surd as follows:

5 * √(3^3) = 5 * √(3 * 3 * 3)

Next, using the property of surds that √(a^2) = a, we simplify the expression:

5 * √(3 * 3 * 3) = 5 * (3 * √3)

Finally, multiplying the constants together, we have:

5 * (3 * √3) = 15√3

Therefore, 5√27 can be written in the form of k√3 as 15√3, where k = 15.

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Actividades que te gusta hacer solo/a:

1. Leer en mi dormitorio.

2. Escuchar música en mi dormitorio.

3. Dibujar en mi dormitorio.

Actividades que te gusta hacer con amigos:

1. Jugar videojuegos en la casa de un amigo.

2. Ir al cine.

3. Comer comida nueva en diferentes restaurantes.

4. Jugar voleibol en el gimnasio.

Actividades que te gusta hacer con familia:

1. Ver películas en casa.

2. Visitar la casa de los abuelos.

3. Comprar ropa en el centro de la ciudad.

Activities that are on all three lists:

Step 2: Where could one go to do the following activities?

1. Ver películas → al cine, a mi casa, a la casa de un amigo.

2. Estudiar para los regents → a la biblioteca, a mi casa.

3. Dibujar → a mi dormitorio, a la escuela.

4. Comer comida nueva → a diferentes restaurantes, al centro de la ciudad.

5. Jugar videojuegos → a la casa de un amigo, a mi casa.

6. Jugar voleibol → al gimnasio, a la escuela.

7. Practicar español → a la escuela, a mi casa.

8. Comprar ropa → al centro de la ciudad, a diferentes tiendas de ropa.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer: A

Step-by-step explanation:

for a function y = Asin(bx + c), an amplitude equals to |A| (10 in this case), and the period equals to 2π/b (1/2 * π in this case).

Answer:

[tex]\textsf{A)} \quad \rm amplitude = 10, \; period=\dfrac{1}{2}\pi[/tex]

Step-by-step explanation:

The sine function is periodic, meaning it repeats forever.

The general formula for a sine function is:

[tex]\boxed{y = A \sin(B(x + C)) + D}[/tex]

where:

Given function:

[tex]y=-10\sin 4x[/tex]

Comparing the given function with the general formula:

Therefore, the given function has no horizontal or vertical shift.

The amplitude of the function is 10.

The period of the function is:

[tex]\textsf{Period}=\dfrac{2\pi}{B}=\dfrac{2\pi}{4}=\dfrac{1}{2}\pi[/tex]

Thus,$248 = Principal × 0.18 × 1Principal = $248 ÷ 0.18Principal = $1,377.78, the principal at the beginning of July was $1,377.78.

Evander Holyfield is an ex-boxer, a former world champion in multiple weight classes, who had part of his ear bitten off by Mike Tyson.

Despite the fact that he made over $290 million over the course of his career as a professional boxer, he declared bankruptcy due to poor financial choices. Evander's principal at the beginning of July was $1,377.78, based on the information given in the problem. Let's go through the solution in steps

.Step 1: Calculate the yearly interest rateDivide the monthly interest rate by 100 and multiply by 12 to convert it to a yearly interest rate.18% / 100 = 0.18 (monthly interest rate)0.18 * 12 = 2.16 (yearly interest rate)

Step 2: Calculate the principal using the simple interest formulaSimple interest = Principal × Rate × TimeSimple interest = $248Rate = 2.16 / 12 = 0.18 (monthly interest rate)Time = 1 month (since the interest is for the month of July)

Therefore,$248 = Principal × 0.18 × 1Principal = $248 ÷ 0.18 Principal = $1,377.78

Thus, the principal at the beginning of July was $1,377.78.

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Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

To find the percentage by which Sara needs to reduce the price to provide the same value for money as Zak's idea, we need to compare the original price and the new price under Zak's idea.

Let's assume the original price of a box of pet food is P and the original amount of pet food in each box is A.

According to Zak's idea, the company will put 50% more pet food into each box without changing the price. Therefore, the new amount of pet food in each box will be 1.5A.

To calculate the value for money under Zak's idea, we divide the amount of pet food by the price:

Value for money (Zak's idea) = (1.5A) / P

Now, let's consider Sara's idea. She wants to reduce the price but keep the amount of pet food unchanged. Let's assume Sara reduces the price by a percentage represented by x.

Under Sara's idea, the new price of a box of pet food will be P - (x/100)P = P(1 - x/100).

Since Sara wants her idea to provide the same value for money as Zak's idea, we can equate the two value for money expressions:

(1.5A) / P = (A) / (P(1 - x/100))

Cross-multiplying and simplifying the equation:

1.5A * P(1 - x/100) = A * P

1.5(1 - x/100) = 1

Simplifying further:

1 - x/100 = 2/3

-x/100 = -1/3

x/100 = 1/3

x = 100/3

Therefore, Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

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To subtract the mixed number 2 1/4 from the fraction 385/132, we first need to convert the mixed number to an improper fraction.

2 1/4 can be written as (2 * 4 + 1) / 4 = 9/4.

Now, we have the subtraction expression: 385/132 - 9/4.

To subtract fractions, we need to have a common denominator. The least common multiple (LCM) of 132 and 4 is 132.

We can convert both fractions to have a denominator of 132:

385/132 - 9/4 = (385/132) * (4/4) - (9/4) * (33/33)

= 1540/528 - 297/132

Now that both fractions have a common denominator of 132, we can subtract them:

1540/528 - 297/132 = (1540 - 297) / 132

= 1243/132

The resulting fraction is 1243/132.

However, we can simplify this fraction further by finding the greatest common divisor (GCD) of the numerator and denominator, which is 17.

Dividing both the numerator and denominator by 17, we get:

1243/132 = (1243/17) / (132/17)

= 73/8

Therefore, the fraction 385/132 - 2 1/4 is equal to 73/8.

Answer:

The exact value of the other leg is 10.

Step-by-step explanation:

Finding the exact value of x given a 45 degree angle and a side length of 10 can be done using trigonometry. In a 45-45-90 right triangle, the two legs are congruent and the hypotenuse is equal to the square root of 2 times the length of the legs.

Therefore, if one leg is 10, the hypotenuse is 10 times the square root of 2. To find the length of the other leg, we can use the Pythagorean theorem:

c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the legs of the right triangle.

Substituting known values, we get:

(10√2)^2 = 10^2 + b^2

200 = 100 + b^2

b^2 = 100

b = 10

Therefore, the exact value of the other leg is 10.

C. √ab = √a . √b

This is because the product property of square roots states that the square root of the product of two numbers is equal to the product of their square roots. In other words, √ab = √a . √b. This property holds true for both negative and non-negative numbers a and b.

Based on the given graph, the equation that best represents it is:

y = ln(x) + 4

Here, we have,

given that,

from the given information, we get,

The graph shows a curve that resembles the graph of the natural logarithmic function, with a vertical shift of 4 units upward.

so, we get,

equation is represented by the graph is:

y = ln(x) + 4

Hence, Based on the given graph, the equation that best represents it is:

y = ln(x) + 4.

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a. Assuming no additional restrictions, there are  800 possible three-digit area codes.

b. Considering ERCs, there are  80 ERCs.

c. For the seven digits after the area code, there are [tex]8 \times 10^6 = 8,000,000[/tex]  possible seven-digit phone numbers.

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers is 800 [tex]\times[/tex] 8,000,000 = 6,400,000,000.

a. For three-digit area codes, the first digit cannot be 0 or 1.

Assuming no additional restrictions, there are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining two digits (0-9). Therefore, the total number of three-digit area codes possible under this plan is [tex]8 \times 10 \times 10 = 800.[/tex]

b. For an ERC (Easily Recognizable Code), the second and third digits of the area code must be the same, and the first digit cannot be 0 or 1. There are 8 possibilities for the first digit (2-9) and 10 possibilities for the third digit (0-9).

Since the second digit must be the same as the third digit, there is only 1 possibility.

Therefore, the total number of ERCs is [tex]8 \times 1 \times 10 = 80.[/tex]

c. For the seven digits after the area code, the first digit of the three-digit local prefix cannot be 0 or 1.

There are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining six digits (0-9).

Therefore, the total number of seven-digit phone numbers possible is 8 * [tex]10\times 10 \times 10 \times 10 \times 10 \times 10 = 8,000,000.[/tex]

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers can be calculated by multiplying the number of possibilities for each digit position.

For the area code (part a), there are 800 possibilities.

For the seven digits after the area code (part c), there are 8,000,000 possibilities.

Therefore, the total number of ten-digit phone numbers possible is 800 * 8,000,000 = 6,400,000,000.

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Answer:

a) 80 mm²

b) 28 cm²

Step-by-step explanation:

a) Area of parallelogram = base*height

= 10 * 8

= 80 mm²

b) Area of trapezium = height(base₁ + base₂)/2

= 4(5+9)/2

= 2(14)

= 28 cm²