The graph represents a quadratic function. Write an equation of the function in standard form.

Answer:

3.66666. . . = 11/3 = 3  2/3

Step-by-step explanation:

Use distributive property.

3 ⋅ x = 3x

3 ⋅ (-1) = -3

3x - 3 + 4 = 12

Add -3 to 4

1

3x + 1 = 12

Subtract 1 from both sides.

3x = 11

Divide both sides by 3

3.666666. . .

This can also be written as 11/3

11/3 can be simplified to 3  2/3

Hope I helped :)

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To find the exact length of the curve defined by the parametric equations x = 5t^2 and y = 3t^3, where 0 ≤ t ≤ 3, we can use the arc length formula for parametric curves.

The arc length formula for a parametric curve defined by x = f(t) and y = g(t) over the interval [a, b] is given by:

L = ∫[a,b] √[ (dx/dt)^2 + (dy/dt)^2 ] dt

In this case, we have x = 5t^2 and y = 3t^3, with the parameter t ranging from 0 to 3.

First, we need to find the derivatives of x and y with respect to t:

dx/dt = d/dt (5t^2) = 10t

dy/dt = d/dt (3t^3) = 9t^2

Next, we substitute these derivatives into the arc length formula:

L = ∫[0,3] √[ (10t)^2 + (9t^2)^2 ] dt

L = ∫[0,3] √(100t^2 + 81t^4) dt

Now, we can integrate the expression inside the square root with respect to t:

L = ∫[0,3] √(100t^2 + 81t^4) dt

L = ∫[0,3] t√(100 + 81t^2) dt

Unfortunately, this integral does not have a simple closed-form solution. We would need to evaluate it numerically using numerical integration techniques or computer software.

So, the exact length of the curve cannot be determined algebraically. However, it can be approximated using numerical methods.

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The positive difference between the original number of termites in the nest and the original number of ants in the box is 16

From the question, we are to determine the positive difference between the original number of termites in the nest and the original number of ants in the box

From the given information,

The number of termites is represented by the function

f(t) = 4(3)^t

The original number of termites is the number of termites present at 0 months

To determine the original number of termites, we will set t = 0

f(t) = 4(3)^t

f(0) = 4(3)^0

f(0) = 4(1)

f(0) = 4

Therefore original number of termites is 4

Now, we will determine the original number of ants in the box

From the given table,

The original number of ants is 20

Thus,

The positive difference = 20 - 4

The positive difference = 16

Hence, the positive difference is 16

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Answer: it is 16. i got it right on the test!

Si alquilas el auto por un día y recorres 50 kilómetros, el precio del alquiler es de $400

Si rentas un auto por un día y recorres 50 kilómetros, el precio de renta será

$300 por día + $2 por kilómetro recorrido * 50 kilómetros

= $300 + $100 = $400.

La función que relaciona el precio de renta con los kilómetros recorridos se puede expresar como

P = 300 + 2K,

donde P es el precio de renta en dólares y K es la cantidad de kilómetros recorridos.

Si rentas un auto por un día y deseas que el precio de renta sea de $500, podemos utilizar la función determinada en el punto 2 para calcular la cantidad de kilómetros que puedes recorrer.

Reemplazando P = 500 en la función, tenemos

500 = 300 + 2K, entonces 200 = 2K, entonces K = 100.

Por lo tanto, puedes recorrer 100 kilómetros si deseas que el precio de renta sea de $500.

La función determinada en el punto 2 es lineal, ya que relaciona una variable dependiente (el precio de renta) con una variable independiente (los kilómetros recorridos) de manera lineal. Por lo tanto, la respuesta es is Lineal.

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Answer:

Let \(\left(1+\frac{1}{\tan^{2}A} \right)\cdot \left(1+\frac{1}{\cot^{2}A} \right)\), we proceed to prove the trigonometric expression by trigonometric identity:

1) \(\left(1+\frac{1}{\tan^{2}A} \right)\cdot \left(1+\frac{1}{\cot^{2}A} \right)\) Given

2) \(\left(1+\frac{\cos^{2}A}{\sin^{2}A} \right)\cdot \left(1+\frac{\sin^{2}A}{\cos^{2}A} \right)\)   \(\tan A = \frac{1}{\cot A} = \frac{\sin A}{\cos A}\)

3) \(\left(\frac{\sin^{2}A+\cos^{2}A}{\sin^{2}A} \right)\cdot \left(\frac{\cos^{2}A+\sin^{2}A}{\cos^{2}A} \right)\)    

4) \(\left(\frac{1}{\sin^{2}A} \right)\cdot \left(\frac{1}{\cos^{2}A} \right)\)    \(\sin^{2}A+\cos^{2}A = 1\)

5) \(\frac{1}{\sin^{2}A\cdot \cos^{2}A}\)

6) \(\frac{1}{\sin^{2}A\cdot (1-\sin^{2}A)}\)    \(\sin^{2}A+\cos^{2}A = 1\)

7) \(\frac{1}{\sin^{2}A-\sin^{4}A}\) Result

Step-by-step explanation:

Let \(\left(1+\frac{1}{\tan^{2}A} \right)\cdot \left(1+\frac{1}{\cot^{2}A} \right)\), we proceed to prove the trigonometric expression by trigonometric identity:

1) \(\left(1+\frac{1}{\tan^{2}A} \right)\cdot \left(1+\frac{1}{\cot^{2}A} \right)\) Given

2) \(\left(1+\frac{\cos^{2}A}{\sin^{2}A} \right)\cdot \left(1+\frac{\sin^{2}A}{\cos^{2}A} \right)\)   \(\tan A = \frac{1}{\cot A} = \frac{\sin A}{\cos A}\)

3) \(\left(\frac{\sin^{2}A+\cos^{2}A}{\sin^{2}A} \right)\cdot \left(\frac{\cos^{2}A+\sin^{2}A}{\cos^{2}A} \right)\)    

4) \(\left(\frac{1}{\sin^{2}A} \right)\cdot \left(\frac{1}{\cos^{2}A} \right)\)    \(\sin^{2}A+\cos^{2}A = 1\)

5) \(\frac{1}{\sin^{2}A\cdot \cos^{2}A}\)

6) \(\frac{1}{\sin^{2}A\cdot (1-\sin^{2}A)}\)    \(\sin^{2}A+\cos^{2}A = 1\)

7) \(\frac{1}{\sin^{2}A-\sin^{4}A}\) Result

The fraction of the material that each strip represents is 1/12 of a yard.

Susan bought 1/3 of a yard of material to use for the border for the blanket. She cut the material into 4 same-size strips. The problem is asking for the part of a whole yard that each strip represents.

Since Susan has 1/3 of a yard of material and she cut it into 4 same-size strips, we can use division to find the fraction of the material that each strip represents.

Therefore, the fraction of the material that each strip represents is 1/3 ÷ 4.

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

The reciprocal of 4 is 1/4, so we can rewrite the expression as:

1/3 ÷ 4 = 1/3 × 1/4

Now we can multiply the fractions:

1/3 × 1/4 = 1/12

Therefore, each strip represents 1/12 of the whole yard of material.

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Answer:

x=−7

Solving for X:

Step 1: Simplify both sides of your equation.

5x−22=7x−8

Step 2: Subtract 7x from both sides.

5x−22−7x=7x−8−7x

−2x−22=−8

Step 3: Add 22 to both sides.

−2x−22+22=−8+22

−2x=14

Step 4: Divide both sides by -2.

-2x/-2 = 14/-2

^ x = -7

THEREFORE:

x is −7

Answer:

22.50 per 3 wristbands is the cost

The value of probability P (even | less than 3) is, 1/3.

The term probability refers to the likelihood of an event occurring. 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.

Given that;

A 6-sided die is tossed.

Here, Two numbers 1 and 2 are less than 3.

Hence, The value of P (even | less than 3) is,

⇒ 2 / 6

⇒ 1 / 3

Thus, The value of P (even | less than 3) is, 1/3.

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To calculate the optimal profit, we need to find the value of D when the total cost is \($30,500\) and then substitute it into the given equation.

To find D, we can rearrange the equation to solve for D: Given:\(p = 180 - 0.2D\) and total cost =\($30,500\) Now, substitute the total cost ($30,500) into the equation to find D:

Since D cannot be negative in this context, it means that the given equation is not applicable for a total cost of \($30,500\). it is not possible to calculate the optimal profit using the given equation and the total cost of \($30,500\).

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The nurse should teach the parents to administer 2.5 teaspoons of the acetaminophen liquid suspension per dose.

The prescribed dosage of acetaminophen is 300 mg every 4 hours as needed. The liquid suspension provides 120 mg of acetaminophen per 5 mL (1 teaspoon). To determine the number of teaspoons required for the prescribed dosage, we can set up a proportion:

120 mg / 5 mL = 300 mg / x mL

Cross-multiplying, we get:

120 mg * x mL = 5 mL * 300 mg

Simplifying, we have

120x = 1500

Dividing both sides by 120, we find:

x = 1500 / 120 = 12.5 mL

Since there are 5 mL (1 teaspoon) in each dose, we can convert 12.5 mL to teaspoons:

12.5 mL / 5 mL = 2.5 teaspoons

Therefore, the nurse should teach the parents to administer 2.5 teaspoons of the acetaminophen liquid suspension per dose to ensure the child receives the prescribed dosage of 300 mg.

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Answer: 10+2t

Step-by-step explanation: I guess not sure sorry

Answer:

b. 31.

Step-by-step explanation:

The other 2 angles in the triangle are congruent so they are:

(180 - 118) / 2

= 31 degrees.

The possible measure of two similar angles in an isosceles triangle could be b. 31 °

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know in an isosceles triangle two sides are equal and angles opposite sides to the equal side are also equal.

We also know that the sum of all the interior angles in a triangle is 180°.

Let, The similar angles be 'x'.

Therefore,

x + x + 118 = 180

2x = 62.

x = 31°.

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Answer:

According to Angle Bisector Theorem, if Ray YZ is an angle bisector, then MZ and NZ are congruent.

EH= 23. It is shown that ray FH bisects EFG, EF and EH are perpendicular, FG and HG are perpendicular. Then EH and GH are congruent. Therefore since GH= 23, then EH= 23

Answer:

B. 47.8% increase

Step-by-step explanation:

34-23= 11

11/23= 0.478 or 47.8%

The solution to the initial value problem is √x = (1/3) \(y^{\frac{3}{2} }\) + 2/3.

Given: dx/dy = -2y, y = 3 when x = 0

To solve this, we'll separate the variables and integrate:

dx = -2y dy

Integrating both sides:

∫ dx = ∫ -2y dy

x = - \(y^{2}\) + C

Now we can apply the initial condition y = 3 when x = 0:

0 = - \(3^{2}\) + C

C = -9

Therefore, the solution to the initial value problem is x = - \(y^{2}\) - 9.

Given: dx/dy = xy, y = 1 when x = 0

We'll again separate the variables and integrate:

dx = xy dy

Integrating both sides:

∫ dx = ∫ xy dy

x = (1/2)\(y^{2}\) + C

Applying the initial condition y = 1 when x = 0:

0 = (1/2) \(1^{2}\) + C

C = -1/2

Thus, the solution to the initial value problem is x = (1/2)\(y^{2}\) - 1/2.

Given: dx/dy = \(e^{x+y}\), y = 0 when x = 0

Separating the variables and integrating:

dx = \(e^{x+y}\) dy

∫ dx = ∫ \(e^{x+y}\) dy

x = \(e^{x+y}\) + C

Using the initial condition y = 0 when x = 0:

0 = \(e^{0+0}\) + C

C = -1

Hence, the solution to the initial value problem is x = \(e^{x+y}\) - 1.

Given: dx/dy = √(y/x), y = 1 when x = 1

Again, separating the variables and integrating:

dx/√x = √y dy

Integrating both sides:

2√x = (2/3)\(y^{\frac{3}{2} }\) + C

Simplifying:

√x = (1/3)\(y^{\frac{3}{2} }\) + C

Applying the initial condition y = 1 when x = 1:

1 = (1/3)\(1^{\frac{3}{2} }\) + C

C = 2/3

Therefore, the solution to the initial value problem is √x = (1/3) \(y^{\frac{3}{2} }\) + 2/3.

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Answer:

6x^2 -9x  -2x-3

6x^2 -11x +3

Step-by-step explanation:

Answer: -5x+3 hope this helps

Step-by-step explanation:

Answer:

the answer for this question isnparallelogram

Answer:

Parallelogram

Step-by-step explanation:

The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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Answer:

2.12 kilometers

Step-by-step explanation:

Manuel needs to run a total of 4.06 kilometers. He only has 1.94, so to find the amount he still needs, we can make an equation of 4.06-1.94 = x. Solve that and we get x = 2.12, so Manuel still needs to run 2.12 kilometers to run 4.06 kilometers.

Answer:

A

Step-by-step explanation:

Find the rise over run (gradient) between two points. Choosing x=-2 and x=1 we get (1 - - 2) / (4 - 7) = -3/3 = -1. This means that m in y=mx+c is -1 so it is either A or C. If we then try a pair of x and y with y = -x + c we can get c. Using the first pair: 7=-1*-2+c = 2 + c so c = 5, leaving us with y = -x + 5.

Alternatively try all 4 with the numbers, if plugging in that value of x gives you that value of y then it is the correct equation.

Answer:

a

Step-by-step explanation:

The expressions (a) 3 / -0 and (c) 3 / 0 are undefined.

To determine which of the following expressions are undefined, let's analyze each expression:

a. 3 / -0:

Division by zero is undefined in mathematics. Therefore, the expression 3 / -0 is undefined.

b. 0 / 3:

This expression represents the division of zero by a non-zero number. In mathematics, dividing zero by a non-zero number is defined and yields the value of zero. Thus, the expression 0 / 3 is defined.

c. 3 / 0:

Similar to expression (a), division by zero is undefined in mathematics. Therefore, the expression 3 / 0 is also undefined.

In conclusion, the expressions that are undefined are (a) 3 / -0 and (c) 3 / 0.

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Answer:

Answer to the following question is as follows;

Step-by-step explanation:

Given:

Amount invested by Mr. Mohit = Rs. 50,00,000

Computation:

Books of (...... LTD)

Journal entries

Date                         Particular                        Debit        Credit

March 1         Cash                     A/C Dr.     50,00,000

                     To Capital            A/C Cr.                         50,00,000

(Being Amount invested in new business)

Answer:

m < 49/12

Step-by-step explanation:

The portion of the quadratic formula under the square root sign is the discriminant.

If the discriminant is > 0 then there are two real roots.

b² -4ac > 0

-----------------------------

7² - 4(3)m > 0

49 - 12m > 0

Subtract 49 from both sides

-12m > -49

Divide both sides by -12

(when multiplying or dividing by a negative the inequality must be reversed)

m < 49/12

Answer:

SAS similarity

Step-by-step explanation:

The two triangles MON and MQP are such that

Angle M = Angle M

MO/MQ = MN/MP

Therefore, Triangle MON ~ Triangle MQP (SAS similarity)

The answer to the questions on instrument are:

True

True

True

True

False

True

True: A survey timeline typically includes various dates related to the survey administration, such as the start and end dates for participant recruitment, the date for activation of the measurement instrument, and the deadline for completing the survey. The date for activation of the measurement instrument refers to the date on which the survey respondents can begin answering the questions.

True: Instrument disposition refers to the process of distributing and collecting the measurement instruments. This can involve various methods, such as mailing the instruments to the participants or delivering them to a dropbox for paper-and-pencil instruments.

True: Participant data entry can increase the accuracy of a data record because it eliminates the need for manual data entry, which can introduce errors. With participant data entry, the participants themselves enter their responses directly into a computer or mobile device, ensuring that the data is accurate and complete.

True: A significant number of "Don’t Know" responses to a closed measurement question may indicate that the measurement instrument failed to provide appropriate response categories. If the survey respondents are unsure about how to answer a question and there is no appropriate response option available, they may select "Don’t Know" instead.

False: Cross-tabulation in CFA (Confirmatory Factor Analysis) is typically used to examine the relationship between two or more variables, and it is not called a contingency table. A contingency table is a table used to display the frequencies and/or percentages of two or more categorical variables.

True: Percentages are a way of expressing data in relation to a base of 100, making it easier to compare variables. For example, if 80 out of 100 respondents answered "Yes" to a question, we can say that the percentage of respondents who answered "Yes" is 80%. This allows us to compare the percentage of "Yes" responses to other questions or variables in the survey.

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Answer: y = 3

Step-by-step explanation:

Answer: The student wins 15 rounds.

Step-by-step explanation:

The number of rounds the student won is required.

The number of rounds the student won was 15.

The total number of rounds played is \(20\).

The percentage the student wins is \(75\%\)

The number of times he won was

\(20\times 75\%\\ =20\times \dfrac{75}{100}\\ =20\times 0.75\\ =15\)

The number of rounds the student won was 15.

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