What is a equation of line passes through the points (-6,6) and (-3,1)

Answer:

Step-by-step explanation:

ΔVWX is an isosceles triangle.

∠V ≅∠W = 20

20 + 20 + ∠X = 180

                ∠X = 180 - 40

                ∠x = 140

In ΔPQR

∠P + 20 + 80 = 180  {Angle sum property of triangle}

∠P + 100 = 180

       ∠P =  180 - 100

      ∠P = 80

In ΔSTV is an isosceles triangle.

∠S ≅ ∠T = 80°

∠V + 80 + 80 = 180

∠V + 160       = 180

            ∠V = 180 - 160

            ∠V = 20°

In ΔPRQ & ΔSTV

∠P ≅ ∠S = 80°

∠R ≅ ∠T = 80°

∠Q ≅ ∠v = 20°

ΔPRQ  ` ΔSTV  are similar by AAA congruent

Answer:

-0.08

Step-by-step explanation:

Multiply.

-0.2

x 0.4

_____

0 0 8

Each number you started out with has 1 space between the last number and the decimal, so your final answer will have 2 spaces.

Also, since you multiplied a negative and a positive, your final answer will be negative.

Answer:

Step-by-step explanation:

Rule for the dilation of a point about the origin is,

(x, y) → (kx, ky)

Here, k = scale factor

Dilating points D, E and F about the origin by a scale factor 'k' = \(\frac{1}{3}\)

D(-9, -6) → D'(-3, -2)

E(-6, -3) → E'(-2, -1)

F(0, -9) → F'(0, -3)

Now we can plot these points on graph.

Answer:

1.)

\(R = 8/17\\S = 15/17\)

2.)

\(R = 5/13\)

\(S=12/13\)

Step-by-step explanation: sin represents the ratio between a side opposite to an angle and the hypotenuse. It is important to learn these ratios as they allow for you to solve for side lengths in a triangle and angles. We were in this case finding the ratios. A lowercase letter represents a side length opposite to the angle. So to find R we would just need to divide r by t. In the first example, it would just be 16/34 which simplifies to 8/17. Do the same thing for s, and it would be for 30/34 which simplifies to 15/17. Repeat the same steps and you should get 5/13 for R and 12/13 for S.

To result in no main effect for factor B, the missing mean should be 30.

In a two-factor experiment, a main effect refers to the overall effect of one factor on the dependent variable, disregarding the other factor. In this case, factor B has two levels (B1 and B2), and the given data provide the means for each level of factor B. To have no main effect for factor B, the means for B1 and B2 should be equal.

From the given data:

B1: 20

B2: 10

To have no main effect, the means should be equal, which means the missing mean should be the average of the given means:

(20 + 10) / 2 = 30

Therefore, if the missing mean is 30, there would be no main effect for factor B in this two-factor experiment.

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A) the solution to equation A is x = 0.5465.

B) the solution to equation B is x = 0.8551.

A) To solve the equation 15 + 24x + 18 - 32 = -47x + 28 - 39x + 20, we will simplify the equation and then isolate the variable x.

Step 1: Combine like terms on both sides of the equation.

15 + 18 - 32 = -47x + 28 - 39x + 20

33 - 32 = -86x + 48

1 = -86x + 48

Step 2: Move the constant term to the right side of the equation by subtracting 48 from both sides.

1 - 48 = -86x + 48 - 48

-47 = -86x

Step 3: Divide both sides of the equation by -86 to solve for x.

-47 / -86 = -86x / -86

x = 0.5465 (rounded to four decimal places)

Therefore, the solution to equation A is x = 0.5465.

B) Let's solve the equation 45x - 30 + 43x - 15 = 18 + 19x - 32 + 14x.

Step 1: Combine like terms on both sides of the equation.

45x + 43x - 30 - 15 = 18 + 19x - 32 + 14x

88x - 45 = 19x - 14

Step 2: Move the constant term and the x terms to opposite sides of the equation.

88x - 19x = 14 + 45

69x = 59

Step 3: Divide both sides of the equation by 69 to solve for x.

69x / 69 = 59 / 69

x = 0.8551 (rounded to four decimal places)

Therefore, the solution to equation B is x = 0.8551.

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English translation of given question is below

Can you help me with the following equations? with process plsss

A) 15+24 x + 18 - 32 = - 47 x + 28 - 39 x + 20

B) 45 x - 30 + 43 x - 15= 18 + 19 x -32 + 14x

The equation of the circle graphed in this problem is:

(x - 5)² + y² = 16.

The equation of a circle of center \((x_0, y_0)\) and radius r is given by:

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

For the circle graphed, we have that:

Hence the equation of the circle graphed is:

(x - 5)² + y² = 16.

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The total charges for a week = 2313.25

Given,

charges per oil change = 33.95

charges for a four-cylinder engine = 72.50

charges for a six-cylinder engine = 82.50

charges for a eight- cylinder engine = 92.50

No of oil changes done by Charlene = 35

price of 5 - four cylinder engines = 5 × 72.50

= 362.50                                .....(1)

price of 7 - six cylinder engines = 7 × 82.50

= 577.50                                ........(2)

price of 2 - eight cylinder engines = 2 × 92.50

= 185                                       ...........(3)

Now, adding (1), (2),(3)

= 362.50 + 577.50 + 185

= 1125                                        ...........(4)

Total charges for oil = 33.95 × 35

= 1188.25                                  ..........(5)

Adding (4) and (5)

= 1125 + 1188.25

= 2313.25

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Answer:

2m - 3

Step-by-step explanation:

she ran 3 miles less than twice as far as Jim

We say that there are n-1 degrees of freedom in this case.

The number of values free to vary after certain restrictions have been placed on the data is the definition of degrees of freedom (df). Degrees of freedom are a key concept in inferential statistics and are often used in hypothesis testing and the calculation of confidence intervals. In essence, degrees of freedom represent the number of values in a data set that are free to vary after the mean has been calculated.

For example, if we have a sample of n observations and we know the mean of the sample, then we can calculate the sum of the n observations. However, we cannot set the value of the last observation, as it is determined by the values of the first n-1 observations and the mean. Therefore, we say that there are n-1 degrees of freedom in this case.

Degrees of freedom are also important in the calculation of standard errors, t-tests, and F-tests. In these cases, the degrees of freedom reflect the amount of information in the sample and are used to calculate the probability of observing a particular test statistic under the null hypothesis.

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The first statement is true, while the second and third statements are false. Multicollinearity can impact the model and can lead to misleading results, even if some predictor variables are highly correlated with each other. Additionally, the significance of F-test alone cannot rule out the possibility of multicollinearity.

i. The first statement is true. The Variance Inflation Factor (VIF) can be used to measure the amount of collinearity in the model. VIF is a measure of the amount of correlation between a predictor variable and the other predictor variables in the model. Higher VIF values indicate higher levels of collinearity. Typically, a VIF value greater than 10 indicates a problematic level of collinearity.

ii. The second statement is false. If some predictor variables in the model are highly correlated with each other, it can lead to multicollinearity, which can impact the model's results. Multicollinearity can make it difficult to interpret the individual effect of each predictor variable on the outcome variable, and it can also increase the standard errors of the regression coefficients. This can result in reduced statistical power, decreased predictive accuracy, and misleading results.

iii. The third statement is also false. A significant F-test indicates that at least one of the predictor variables in the model is related to the outcome variable, but it does not rule out the possibility of multicollinearity. If none of the t-tests are significant, it could be due to a lack of statistical power or the presence of multicollinearity, which can make it difficult to detect the individual effects of each predictor variable.

To test for multicollinearity, one can examine the VIF values or use other diagnostic tests, such as the condition number or tolerance values. If multicollinearity is detected, one can consider removing one of the highly correlated predictor variables or using techniques like regularization to address it.

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We have to find horizontal component of Mayosons velocity.

#a

\(\\ \tt\bull\leadsto V_x=vsin\theta\)

\(\\ \tt\bull\leadsto V_x=2.5sin36\)

\(\\ \tt\bull\leadsto V_x=2.5(0.58)\)

\(\\ \tt\bull\leadsto V_x=1.45m/s\)

#b

Here 2 vectors A=8 and B=2.5

\(\\ \tt\bull\leadsto \overrightarrow{R}\)

\(\\ \tt\bull\leadsto \sqrt{A^2+B^2+2ABcos\Theta}\)

\(\\ \tt\bull\leadsto \sqrt{8^2+2.5^2+2(8)(2.5)cos36}\)

\(\\ \tt\bull\leadsto \sqrt{64+6.25+40(0.8)}\)

\(\\ \tt\bull\leadsto \sqrt{70.25+32}\)

\(\\ \tt\bull\leadsto \sqrt{102.25}\)

\(\\ \tt\bull\leadsto 10.15m/s\)

Answer: x = 4

Step-by-step explanation:

since it is showing us that the angles are congruent, we know that the smaller triangle is just a scaled-down version of the larger one. in other words, it is the EXACT SAME triangle, just slightly smaller.

so, i redrew them next to each other, so i could compare them easily.

i looked at the corresponding sides that were given, and realized that the side that is 10 on the larger triangle is equal to 5 on the smaller triangle. the side that is equal to 6 on the larger triangle is equal to 3 on the smaller triangle. this concludes that the smaller triangle is exactly half the size of the larger triangle!

so, i figured (using logic) that x must equal 4, simply dividing its corresponding side (with a measure of 8) in half.

hope this helps! xoxo

Answer:

4,2 1/2

Step-by-step explanation:

Q is located to theight of the x-axis, meaning the first number is a positive, and going up a little past 2 but not past 3. and in the middle so 2 1/2.

According to the question, the statement "In an alternating treatments design, the baseline is implemented for a long period of time and then the treatment is implemented for a long period of time" is false.

In an alternating treatments design, the baseline and treatment conditions are alternated in a systematic manner. This design is used to compare the effects of different treatments or interventions on a target behavior. The key characteristic of the alternating treatments design is that the baseline and treatment conditions are implemented in a rapid and alternating fashion, rather than for long periods of time.

During an alternating treatments design, multiple conditions (baseline and treatment) are applied interchangeably across different time periods, often within the same session or day. This allows for the comparison of the effects of the different conditions on the target behavior within a relatively short timeframe.

The purpose of this design is to determine the differential effects of the treatments by directly comparing their effects in a more controlled manner. By rapidly alternating between conditions, it becomes possible to evaluate the immediate impact of the treatment and establish a causal relationship between the treatment and the observed changes in behavior.

Therefore, the statement "In an alternating treatments design, the baseline is implemented for a long period of time and then the treatment is implemented for a long period of time" is false.

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600 kcal, when converted, is equivalent to 2380 BTU, 2.51 x 10^6 joules, and 0.70 kwh.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume, etc. to another.

A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.

kcal, BTU, joules, and kwh are all units of energy. To convert kcal to these units, we can use the following conversions:

1 kcal = 3.96567 BTU

1 kcal = 4184 joules

1 kcal = 0.00116222 kwh

Converting 600 kcal to BTU, joules and kwh:

1 kcal = 3.96567 BTU

600 kcal = 600(3.96567 BTU)

600 kcal = 2379.4 BTU ≅ 2380 BTU

1 kcal = 4184 joules

600 kcal = 600(4184 joules)

600 kcal = 2.51 x 10^6 joules

1 kcal = 0.00116222 kwh

600 kcal = 600(0.00116222 kwh)

600 kcal = 0.697333 kwh ≅ 0.70 kwh

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Question 16:

\(\alpha\) and \(\beta\) are the roots of the equation.

That means \((x-\alpha )(x-\beta ) = 2x^{2} -6x+5 = 0\\\)

\((x-\alpha )(x-\beta ) = 2x^{2} -6x+5 = 0\)

          \(2x^{2} -6x+5 = 0\\x^{2} -3x+\frac{5}{2} =0\)

          \((x-\alpha )(x-\beta ) =x^{2} - (\alpha +\beta )x +\alpha \beta\)

So,

\(x^{2} - (\alpha +\beta )x +\alpha \beta = x^{2} -3x+\frac{5}{2}\)

Compare coefficient

\(\alpha +\beta = 3\\\alpha \beta = \frac{5}{2}\)

Consider \(\frac{\beta }{\alpha } + \frac{\alpha }{\beta }\)

\(\frac{\beta }{\alpha } + \frac{\alpha }{\beta } =\frac{ \alpha ^{2} +\beta ^{2}}{\alpha \beta }\)

\(= \frac{(\alpha +\beta )^{2} -2\alpha \beta }{\alpha \beta } \\= \frac{3^{2} -2*\frac{5}{2} }{\frac{5}{2} } \\= 4*\frac{2}{5} \\=\frac{8}{5}\)

Ans: 8/5

Question 19:

\(f(x+2) = 2x^{2} +5x-3\\\)

Substitute x with -1

So,

\(f(1) = 2(-1)^{2} +5(-1)-3\\=2-5-3\\=-6\)

Ans: -6

Answer:

see image

Step-by-step explanation:

see image. Simplify each expression, then put them in order from smallest to biggest and put them on the numberline. See image.

Answer:

See below

Step-by-step explanation:

A line that passes only two quadrants must have either 0 slope or undefined slope.

An example of a line with 0 slope is the equation y=5 since there's just a constant and there is no change in y as x changes.

An example of a line with an undefined slope is the equation x=3 since there's just a constant and there is no change in x as y changes, but the change in y divided by the change in x is undefined.

1. (c) labor rate variance and (d) labor efficiency variance
2. (a) materials price variance and (g) fixed overhead budget variance
3. (e) variable overhead spending variance
4. (e) variable overhead spending variance
5. (g) fixed overhead budget variance
6. (a) materials price variance, (b) materials quantity variance, and (f) variable overhead efficiency variance
7. (d) labor efficiency variance
8. (b) materials quantity variance and (f) variable overhead efficiency variance
9. (d) labor efficiency variance
10. (c) labor rate variance and (d) labor efficiency variance

Overall, standard cost variances can be affected by various factors such as changes in labor costs, raw material prices, production efficiency, overhead costs, and external factors such as utility rates. To accurately track and manage standard cost variances, it's important for companies to regularly review and adjusadjustt their standards to reflect changes in the  business environment.

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To construct an outlier (modified) boxplot for the Fiber Content data, the lines coming out of the box (box whiskers) would extend to the values of 3 and 17.

:

To construct an outlier (modified) boxplot, we need to determine the lower and upper whiskers. The lower whisker extends to the smallest value that is not considered an outlier, while the upper whisker extends to the largest value that is not considered an outlier.

For the Fiber Content data, the smallest value is 3, and the largest value is 17. These values represent the minimum and maximum values within the data set that are not considered outliers. Therefore, the lines coming out of the box (box whiskers) would extend to the values of 3 and 17. Option (d) correctly represents these values: 3, 17.

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Answer:

A

Step-by-step explanation:

The dot at A is an outlier because it is far outlying the skewed pattern of the data, and is basically isolated from the rest of the data.

Explanation:

For any 30-60-90 triangle, the hypotenuse is always twice as long compared to the short leg. The short leg is always opposite the 30 degree angle.

The length of x is 6.

'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the perpendicular and the base.'

According to the given problem,

Perpendicular = 3

Hypotenuse = x

We know,

sin∅ = \(\frac{perpendicular}{hypotenuse}\)

∅ = 30°

⇒ sin30 = \(\frac{3}{x}\)

⇒ \(\frac{1}{2}\) = \(\frac{3}{x}\)  [ sin30 = \(\frac{1}{2}\) ]

⇒ x = 3 * 2

⇒ x= 6

Hypotenuse = 6

Applying Pythagoras theorem:

⇒ Hypotenuse² = Perpendicular² + Base²

⇒ 6² = 3² + Base²

⇒ 6² - 3² = Base²

⇒ Base² = 25

⇒ Base = √25

⇒ Base = 5

Hence, we can conclude the value of x to be 6.

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The theoretical capacity of the roller coaster system  in number of passengers per hour at Treasure Island Amusement Park is 170 passengers per hour, based on 17 cars that carry two passengers each, with a run time of 5.5 minutes and load/unload time of 6.5 minutes.

The theoretical capacity of the roller coaster system in number of passengers per hour can be calculated as follows:

There are 17 cars, and each car can carry up to two passengers. So, the total number of passengers per run is 17 x 2 = 34.

Each run takes 5.5 minutes, and the time to unload and load riders is 6.5 minutes, for a total cycle time of 5.5 + 6.5 = 12 minutes.

To calculate the theoretical capacity in passengers per hour, we need to convert the cycle time to hours and then divide by the cycle time. There are 60 minutes in an hour, so the cycle time in hours is 12 / 60 = 0.2 hours.

The theoretical capacity in passengers per hour is then calculated as:

Capacity = (Number of passengers per run) x (Number of runs per hour)

To find the number of runs per hour, we need to divide the total available time per hour (60 minutes) by the cycle time:

Number of runs per hour = 60 / 12 = 5 runs per hour

Now we can calculate the theoretical capacity as:

Capacity = 34 x 5 = 170 passengers per hour

Rounding this down to the nearest whole number, we get the final answer:

The theoretical capacity of the roller coaster system in number of passengers per hour is 170.

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Answer:

7.2

Step-by-step explanation:

So it says they all have the same area

6 * 6 = 36

4 * 9 = 36

So now you can divide to find the answer of Figure 2

36 divided by 5 is 7.2

You can check you your answer by multiplying

5 * 7.2 = 36

Answer:

x = 7.2

Step-by-step explanation:

you would divide 5 by 36 because each of the other shapes are equivalent to each other :D

Answer:

The answer is DF

Step-by-step explanation:

The opposite side is 4 or EF, so the ADJACENT side would be 3 or DF according to SOH CAH TOA.