PLEASE HURRY which expression is equivalent to -6(-2/3 + 2x)

Answer:

Irrational

Step-by-step explanation:

Answer:

Vertex is (2,1) according to your information. In general, V(h,k). Equation must be y - k =a(x-h)2 for any quadratic function (parabola). Furthermore, you know that (0,5) is a point on the curve, so substitute for h, k, x and y to determine what coefficient "a" has to be.

The equation of the parabola is y= (x+ 3)² - 1.

A quadratic function's vertex form is f(x) = a(x - h)² + k, where a, h, and k are constants of the parabola is at (h, k).

The equation in vertex form of the parabola is given by:

y= a(x- h)² + 6

Here (h, k) is the vertex of parabola which is (-3, -1).

Now, the equation can be written as

y = a (x - (-3))² + (-1)

y = a(x+ 3)² - 1

Now, substituting a point of the parabola in the equation in the form of vertex

8 = a (0 - (-3))² + (-1)

8 = 9a - 1

8 +1 = 9a

9a = 9

a= 9/9

a= 1

Then, the equation of the parabola is given by

y= (x+ 3)² - 1

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Answer:

Step-by-step explanation:

\(x^{2} + 3x - 10 = 0\\a *c = 1*-10=-10\\Find-factors-when-they- are -added= 3x -and-when-multiplied=-10\\Factors = -2x, and 5x\\x^{2} -2x+5x-10=0\\x(x-2)+5(x-2)=0\\(x-2)(x+5)=0\\(x-2)=0 ,or, (x+5)=0\\x = 0+2 , or, x =0-5\\x = 2 \\x =- 5\)

The solutions to the given quadratic equation x² + 3x - 10 = 0 are x = 2 and x = -5.

The quadratic equation is given as follows:

x² + 3x - 10 = 0

To solve the equation x² + 3x - 10 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the equation in the form ax² + bx + c.

Here, a = 1, b = 3, and c = -10, so we have:

x = (-3 ± √(3² - 4(1)(-10))) / 2(1)

x = (-3 ± √(49)) / 2

x = (-3 ± 7) / 2

So, the solutions are:

x = (-3 + 7) / 2 = 2

x = (-3 - 7) / 2 = -5

Therefore, the solutions to the equation x² + 3x - 10 = 0 are x = 2 and x = -5.

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The specific solution, without the complementary solution, is y = (-1/2 x^2 + 5/12 x - 5/12) e²x.

The given differential equation:

y = y" + 3y - 4y = (-6x² + 5x-8) e²x.

To find one particular solution of the given differential equation, the method of undetermined coefficients can be used.

This method involves the following steps:

Step 1:

Find the complementary solution of the differential equation.

That is, solve the homogeneous equation that results from setting the right-hand side to zero, y" + 3y - 4y = 0.

This gives the solution of the form,

y_c = c₁e^(-4t) + c₂e^(t),

Where c₁ and c₂ are constants.

Step 2:

Assume a specific form for the particular solution, depending on the form of the non-homogeneous term on the right-hand side. In this case, the non-homogeneous term is (-6x² + 5x-8) e²x.

Since the right-hand side contains a polynomial of degree 2 times an exponential function, the particular solution can be assumed to have the form y_p = (Ax^2 + Bx + C) e²x.

Step 3:

Substitute the assumed form of the particular solution into the differential equation and solve for the coefficients A, B, and C.

y = y" + 3y - 4y

  = (-6x² + 5x-8) e²x

Now,

y_p'' + 3y_p' - 4y_p = (-6x² + 5x-8) e²x

Taking the derivatives of y_p, we get:

y_p' = (2Ax + B + 2A) e²x

y_p'' = (4Ax + 4A + 4A) e²x

        = (4Ax + 8A) e²x

Substituting these into the differential equation, we get:

(4Ax + 8A) e²x + 3(2Ax + B + 2A) e²x - 4(Ax² + Bx + C) e²x = (-6x² + 5x-8) e²x

Grouping like terms, we get:

(4A + 6A - 4C) e²x + (6B - 8C) e²x + (4A - 4B - 6x² + 5x-8) e²x = 0

Equating coefficients of like terms, we get the following system of equations:

4A - 4B - 6 = 0 6B - 8C = 5 4A + 6A - 4C = -8

Solving for A, B, and C, we get:

A = -1/2, B = 5/12, and C = -5/12

Therefore, the particular solution is,

y_p = (-1/2 x^2 + 5/12 x - 5/12) e²x.

Step 4:

The general solution of the differential equation is given by,

y = y_c + y_p.

Since we are only interested in finding one particular solution, we can ignore the complementary solution and write the answer as:

y = (-1/2 x^2 + 5/12 x - 5/12) e²x.

The method of undetermined coefficients has been used to find one particular solution of the given differential equation.

The specific solution, without the complementary solution, is y = (-1/2 x^2 + 5/12 x - 5/12) e²x.

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Answer: C.

Step-by-step explanation: As shown by the data, there is a single outlier that is leading the averages to be so high, when in reality none of the tires are close enough to the average in order for the company to advertise. The other reasons are not applicable to this scenario and therefore C will be the right answer.

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The statement is misleading: "Our tires last an average of 28 months." so the correct one is C. 5 of the 6 tires lasted less than 20 months.

The average can be calculated by dividing the sum of observations by the number of observations.

Average = Sum of observations/the number of observations

We are given that study of 6 bicycle tires found that they lasted 19, 16, 15, 82, 17, and 19 months.

Based on the data, there is a single outlier that is leading the averages to be so high, when in reality none of the tires are close enough to the average in order for the company to advertise.

The other reasons are not applicable to this scenario and therefore C will be the correct answer.

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When x = 4, y is equal to 2.25. The correct answer is: C) 2.25

If y varies inversely as x, it means that as x increases, y decreases, and vice versa, while their product remains constant.

We can set up an equation to represent the inverse variation:

y = k/x

Where k is the constant of variation.

To find the value of k, we can use the given information that when x = 3, y = 3:

3 = k/3

Multiplying both sides by 3, we get:

9 = k

Now we can use this value of k to find y when x = 4:

y = 9/4

Simplifying, we have:

y = 2.25

Therefore, when x = 4, y is equal to 2.25.

The correct answer is:

C) 2.25

It's important to note that in an inverse variation, as x increases, y decreases, and as x decreases, y increases. The relationship is not linear, but rather, the product of x and y remains constant. Option C.

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∠1 and ∠2 are right angles because the measure of both angles is 90° and supplementary angles because the sum of both angles is 180°.

A triangle is a polygon that has three sides and three angles and the sum of the angle of the triangle is 180 degrees.

The figure is attached in the picture, please refer to the attached picture.

Given that:

So,

\(\angle2 = 90^\circ\) (vertically opposite angles are equal)

\(\angle1 + \angle2 = 180^\circ\) (Linear Pair)

\(\angle1 = 180 - 90\)

\(\angle1 = 90^\circ\)

\(\angle1 = \angle2 = 90^\circ\)

So, ∠1 and ∠2 are right angles because measure of both angles is 90°.

Adjacent angles because both a common arm and a common vertex.

Thus, ∠1 and ∠2 are right angles because the measure of both angles is 90° and supplementary angles because the sum of both angles is 180°.

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Answer

-4

Step-by-step explanation:

Therefore, slope of the line that passes through points ( -10, -8 ) and ( -8, -16 ) is -4.

the area of triangle $AMN$ is 8 square cm.

To find the area of triangle $AMN$, we need to determine the lengths of its base and height.

In square $ABCD$ with side length 4 cm, $N$ is the midpoint of side $BC$, so $BN = NC = \frac{1}{2} \cdot 4 = 2$ cm.

Similarly, $M$ is the midpoint of side $CD$, so $CM = MD = \frac{1}{2} \cdot 4 = 2$ cm.

Now, we can see that $AM$ is the height of triangle $AMN$ and has a length of 4 cm, as it is parallel to side $AD$ of the square.

$AN$ is the base of triangle $AMN$ and has a length of $BN + CM = 2 + 2 = 4$ cm.

Therefore, the area of triangle $AMN$ is given by:

$A_{AMN} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 4 = 8$ square cm.

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Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

The proper way to report the groups' mean and standard deviation of independent sample t test is  

Group 1 (M = 11.6, SD = 3.1) Group 2 (M = 13.24, SD = 2.9).

The APA style guide provides detailed instructions for referencing statistical test results, so in addition to following the basic format correctly, you must pay attention to details like punctuation, bracket placement, italicization, and other formatting elements.

Given, that the independent samples t test is conducted, where we have two groups.

Group 1- mean= 11.6 and SD=3.1

Group 2- mean=19 and SD=2.9

We have to write the values in the APA format for a report.

The APA formatting to represent the mean and SD of two groups is as follows, Mean and standard deviation are denoted by the letters M and SD, respectively.

Group 1 (M = 11.6, SD = 3.1) Group 2 (M = 13.24, SD = 2.9).

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Answer:

2/3

Step-by-step explanation:

The rate of change is the same thing as the slope of a line

From the total amounts, the correct option regarding the association between owning a dog and owning a cat is given by:

There is a strong, positive association.

Whether the association is strong or weak depends on the rate of change, the rate of increase or decrease.

From the amounts in the table, we have that:

Having a cat increases the likelihood of having a dog and vice-versa, hence there is a strong, positive association and the first option is correct.

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Answer:

-1

A 52-card deck is made up of an equal number of diamonds, hearts, spades, and clubs. Because there are 4 suits, there is a 1/4 chance to draw one of them, in our case, spades.

There are 4 aces in a 52-card deck, so the chance of drawing one is 4/52, or 1/13.

The question asks for the probability of drawing an ace or a spade. Because it uses the word "or," we add the probabilities together. This is because there is a chance of drawing either of the cards; it doesn't have to meet both requirements to satisfy the statement.

However, if the question were to say "and," we would multiply the two probabilities.

Let's add 1/4 and 1/13. First, we can find a common denominator. We can use 52 because both fractions can multiply into it (since the ratio came from a deck of 52 cards as well).

\(\frac{1}{4} -- > \frac{13}{52}\)

\(\frac{1}{13} -- > \frac{4}{52}\)

Now we can add them together.

\(\frac{13}{52} + \frac{4}{52} = \frac{13+4}{52} = \frac{17}{52}\)

This cannot be simplified further, so the probability is 17 in 52, or 33%.

hope this helps!

Answer:

Step-by-step explanation:

4/13

The difference between the actual value of the response variable and the corresponding predicted value(regression error) using the multiple regression model is the correct option.

A residual is a measurement of the vertical distance between a point and the regression line. It is just the discrepancy between an actual value observed and a value that was projected.

To ensure that the requirements for making conclusions about the coefficients in a linear model have been met, one should always perform a residual analysis.

In regression analysis, a residual is the discrepancy between an observed value and a predicted value.

It is determined by,

Residual = Observed value – Predicted value

The residual is the discrepancy between the expected value and the actual value.

Observed value minus predicted value equals residual.

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Answer:

43 I think

Step-by-step explanation:

Answer:

Not sure how you got 114, but SRU is equal to 70, and TRV is equal to 44, so if you do 180-70-44, you will get X which is 66

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

when you do 225/5, you find out that the number has been multiplied 45 times, so you should multiply 45 by 2 which is 90

The mean for Mai's data is 8.9167.

To find the mean of the data given by Mai for the past 12 school days, we need to add all the values together and then divide by the total number of values.

Here is the solution: Given data are: 9, 12, 6, 9, 10, 7, 6, 12, 9, 8, 10, 10

To find: The mean for Mai's data

To calculate the mean, we will add up all the values and then divide by the total number of values.

Mean (average) = sum of values / total number of values

Sum of values = 9 + 12 + 6 + 9 + 10 + 7 + 6 + 12 + 9 + 8 + 10 + 10= 107

Total number of values = 12

Therefore, Mean (average) = sum of values / total number of values

= 107 / 12

= 8.9167 (rounded to four decimal places)

Hence, the mean for Mai's data is 8.9167.

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The value of the given function f(4 + h) - f(4) is 5h(x)² + 40h(x)

A function is a mathematical concept that maps a set of inputs to a set of outputs with a definite rule. In mathematics, a function is a set of ordered pairs (input, output) where each input is associated with exactly one output. The input is usually referred to as the argument of the function and the output is the value of the function at that argument.

f(x) = 5x²

f(4 + h) - f(4)

f(4 + h(x)) = 5(4 + h(x))²

f(4) = 80

Substituting the values into each other;

5(4+h(x))² - 80

f(4 + h) - f(4) = 5h(x)² + 40h(x)

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Answer:

=2x-2

Step-by-step explanation:

The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2/3x + 5/2y = 15

4x + 15y = 12

Multiply the first equation by 6, to eliminate the fractions.

6 * (2/3x + 5/2y = 15)

This gives

4x + 15y = 90

Subtract the equation 4x + 15y = 90 from 4x + 15y = 12

4x - 4x + 15y - 15y = 12 - 90

Evaluate the difference

0 + 0 = -78

Evaluate the sum

0 = -78

The above equation is the same equation as option (b) 0 = 26

This is so because they both represent that the system of equations have no solution

Hence, the equation that could represent a linear combination of the system is 0 = 26

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Complete question

The system of equations below has no solution.

2/3x + 5/2y = 15

4x + 15y = 12

Which equation could represent a linear combination of the system?

The learning rate in gradient descent determines the step size and should be not too small or too large, as it can cause the algorithm to converge slowly or overshoot the minimum; adjusting the value of the learning rate can fix the problem, but the optimal value depends on the problem and data set.

According to the given information:

When running gradient descent,

The learning rate α determines the step size taken in each iteration toward the optimal solution.

If α is too small, the algorithm will take small steps and will converge slowly, or may even get stuck in a local minimum.

If α is too large, the algorithm may overshoot the minimum and diverge, or bounce back and forth without converging.

In the scenario described, the learning rate α of 0.5 appears too large, causing J(θ) to increase over time.

This suggests that the algorithm is not converging and is overshooting the minimum.

To fix this,
The value of α can be adjusted by reducing it to a smaller value,

Such as 0.1 or 0.01.

This should allow the algorithm to take smaller steps towards the minimum and eventually converge to a lower value of J(θ).

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Answer:

Mean= 13.38

Median= 15

Step-by-step explanation:

The mean can be calculated by getting the sun of the 8 scores and then dividing it by the number of students

Mean= 7 + 18 + 18 + 15 + 17 + 10 + 15 + 7/8

= 107/8

= 13.38

The median can be calculated by first rearranging the numbers from the lowest to the highest and then calculating the average of the two middle numbers

7 , 7, 10, 15, 15, 17, 18, 18

Median = 15+15/2

= 30/2

= 15

Hence the mean is 13.38 and the median is 15

Answer:

42 ft

Step-by-step explanation:

\( - 120 + 13m \\ = - 120 + 13 \times 6..(plug \: m = 6 )\\ = - 120 + 78 \\ = - 42 \: ft\)

(Negative sign symbolises that the submarine is below the sea level or depth of the submarine.)

Hence, the depth of the submarine after 6 minutes was 42 ft.

The events U and V are mutually exclusive, which means they cannot occur at the same time. Therefore, the probability of both events happening together, P(U and V), is 0. On the other hand, to calculate the probability of either U or V occurring, we can add the individual probabilities of U and V. Given that P(U) is 0.26 and P(V) is 0.37, we can determine that the probability of either U or V happening, P(either U or V), is 0.63

Mutually exclusive events are events that cannot occur at the same time. In this case, U and V are mutually exclusive events. When two events are mutually exclusive, the probability of both events occurring together (P(U and V)) is always 0 because they cannot happen simultaneously. Therefore, the probability of U and V occurring together is 0.

To calculate the probability of either U or V occurring (P(either U or V)), we need to add the individual probabilities of U and V. In this case, P(U) is given as 0.26 and P(V) as 0.37. By adding these probabilities, we get 0.26 + 0.37 = 0.63. So, the probability of either U or V occurring is 0.63.

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Answer:

x = 107 , y = 60

Step-by-step explanation:

Each lower base angle is supplementary to the upper base angle on the same side, then

x + 73 = 180 ( subtract 73 from both sides )

x = 107

and

y + 2y = 180

3y = 180 ( divide both sides by 3 )

y = 60

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Overall, search and indexing tools are essential components of information retrieval systems. They enhance the accessibility and usability of data by enabling users to locate, retrieve, and analyze information quickly and accurately.

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Answer:

The answer is supposedly 0.25

\(\qquad\) According to the question :-

\(\qquad \pmb{\sf\longrightarrow \dfrac{2}{3 }x= x-20}\)

\(\qquad \pmb{\sf\longrightarrow \dfrac {2}{3}x-x=-20}\)

\(\qquad \pmb{\sf\longrightarrow \dfrac{ 2x-3x}{3}=-20}\)

\(\qquad \pmb{\sf\longrightarrow \dfrac{ -1x}{3}=-20}\)

\(\qquad \pmb{\sf\longrightarrow -1x=-20\times 3}\)

\(\qquad \pmb{\sf\longrightarrow -1x=-60}\)

\(\qquad \longrightarrow {\pink{\underline{\underline{\pmb{\sf{ x= 60}}}}}}\)

Therefore–

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