Find the equation of the parabola with its focus at (–5,0) and its directrix y = 2.
Options:

A)

y = 1∕4(x + 5)^2 + 1

B)

y = –4(x + 5)^2 + 1

C)

y = –1∕4(x + 1)^2 + 5


D)

y = –1∕4 (x + 5)^2 + 1

Answer:

1

Step-by-step explanation:

\(1 = 1 \\ \\ 8 {c}^{3} = 1 \times 2 \times 2 \times 2 \times c \times c \times c \\ \\ common \: factor = 1 \\ \\ \implies \: greatest \: common \: factor = 1\)

Break down each expression and then look at the common terms...

\( \tt \: 1 = 1 \\ \sf \: 8 {c}^{2} = 1 \times 2 \times 2 \times 2 \times c \times c \times c\)

➪ The common factor is 1, Therefore their GCF is 1...

Answer: B

Step-by-step explanation:

The coordinates of the reflected point P' are (−5,−8).

When a point is reflected over the x-axis, the y-coordinate changes sign. Therefore, the x-coordinate remains the same while the y-coordinate changes sign. To reflect a point over the x-axis, we simply change the sign of the y-coordinate.

In this case, point P has coordinates (-5,8), so to find the coordinates of the reflected point P', we change the sign of the y-coordinate of P to get (–5,-8). This is because when reflecting over the x-axis, all points that were above the x-axis will end up below the x-axis, and vice versa.

So the x-coordinate remains the same while the y-coordinate changes sign. Therefore, the reflected point P' has coordinates (-5,-8).

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Answer:

(-11,-4) and (-5,-7)

Step-by-step explanation:

the rule (x,y)→(x−7,y+2) means the x-value of the coordinate decreases by 7, and the y-value of the coordinate increases by two.

Apply the rule to the 1st question by plugging in the coordinates:

(x,y)→(x−7,y+2)

(−4,−6)→((-4)−7,(-6)+2)

(−4,−6)→(-11,-4)

Let's use the same process for the 2nd question:

(x,y)→(x−7,y+2)

(2,−9)→((2)−7,(-9)+2)

(2,−9)→(-5,-7)

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Answer:

NO.2- SSA is not the method to show the congruency of two triangles.

Answer:

20

Step-by-step explanation:

Use the distance formula:

\(d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\\d = \sqrt{(-7 - 5)^2 + (-7 - 9)^2}\\d = \sqrt{(-12)^2 + (-16)^2}\\d = \sqrt{144 + 256}\\d = \sqrt{400} = 20\)

The distance between the points (5,9) and (-7,-7) will be 20 units.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D² = (x - p)² + (y - q)²  

The points are given below.

(5,9) and (-7,-7)

Then the distance between the points will be

D² = (5 + 7)² + (9 + 7)²  

D² = 12² + 16²  

D² = 144 + 256

D² = 400

D = 20 units

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If a population is not normally distributed, the distribution of the sample means for a given sample size n will (B) approach a normal distribution as n increases.

The correct answer is B.

As per the central limit theorem, regardless of the shape of the population, the distribution of the sample means for a given sample size n will approach a normal distribution as n increases.

This is because as sample size increases, the sample means become more representative of the population, and the effects of any skewness or non-normality in the population become less significant.

Therefore, option B is the correct answer.

Option A is incorrect because the distribution of sample means does not necessarily take the same shape as the population.

Options C and D are incorrect because the skewness of the population does not necessarily translate to the skewness of the distribution of sample means.

Finally, option E is also incorrect because option B is the correct answer.

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Answer:

-2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

-4 + (-1) - (-3) = -2

We can see here that:

A cube is a three-dimensional geometric shape that has six square faces, all of which are congruent (equal in size) and perpendicular to each other. It is a special type of rectangular prism where all edges have the same length, and all angles are right angles (90 degrees).

Cubes are commonly encountered in everyday life, such as dice, boxes, and Rubik's Cube puzzles. They have precise and uniform geometry, making them useful in various mathematical and engineering applications.

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A correlation score of 0.75 between two variables such as symptoms of anxiety and symptoms of depression indicates a strong positive relationship between these variables.

This means that as the level of symptoms of anxiety increase, there is a high likelihood that the level of symptoms of depression will also increase. Conversely, as the level of symptoms of anxiety decreases, the level of symptoms of depression is likely to decrease as well.

It's important to note that correlation does not imply causation, meaning that just because there is a strong positive correlation between two variables, it doesn't necessarily mean that one variable causes the other. Further research would be needed to establish any causal relationship between symptoms of anxiety and symptoms of depression.

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Answer:

i think 5 is the answer not sure check with other helpers or brainer

Step-by-step explanation:

The value of fraction is 6 1/4 inches are equal to 19+6/425mm.

Given that the precipitation in March was 4 3/4 inches below average and the precipitation in April was 1 1/2 inches below average.

We must determine how many inches the precipitation in March and April fell short of typical.

Add 4 3/4 inches and 1 1/2 inches to get the answer. So,

4 3/4 + 1 1/2

19+6 / 4

= + 4 312

6 1/4 inches are equal to 19+6/425mm.

six inches Therefore, the precipitation was 4 less than usual for both March and April.

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Answer:

(x+2)^2 - 6

Step-by-step explanation:

If delta and united flights are not equally on time, then the chance that we see a sample statistic of not equally or any statistic (larger or smaller) is larger, 0.05.

This is because the probability of a sample statistic being either larger or smaller (relative to the population) is always greater than the probability of it being equal. The p-value of 0.05 indicates that there is a 5% probability that the difference in on-time performance between Delta and United flights is due to chance.

The p-value of 0.05 indicates that there is a 5% chance that the observed sample statistic (of being larger or smaller than expected) is due to chance alone.

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The complete question is:

Complete the interpretation for the p-value:

If delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of ______ or any statistic (larger, smaller) is _______ .

Answer:

A. (x + 2)²(x - 2)²

Step-by-step explanation:

x⁴ - 8x² + 16 =

(x² - 4)(x² - 4) =

(x - 2)(x + 2)(x - 2)(x + 2) =

(x - 2)²(x + 2)²

Based on the provided information The right response is E, which falls between 4 and 7 x 107 meters.

Lambic pentameter, which can be discovered in English language writing from many centuries ago, is an excellent illustration of this. Iambic pentameter has ten consonants overall per line and five iambs per line. Every word with an even number is emphasised.

The meter is the fundamental measure of length inside the metric system. The metre serves as the basis for all measurement measures in the metric system. Centi signifies one tenth in the prefix. The decimal number must be shifted to the right or left in order to convert length measures in the metric system.

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Answer: A total of 30 teachers

Step-by-step explanation:

20% = 6 (science) teachers

20x5= 100

6x5=30 teachers

Hope this helps you!

Answer:

30 teachers

20% is 2/10 of 100

20 x 5 = 100

6 x 5 = 30

Therefore, 30 teachers.

Answer:

x=10.5

Step-by-step explanation:

2x+30=6x-12

30=4x-12

42=4x

x=10.5

Answer:

A

Step-by-step explanation:

They are all straight paths with end points but a line is never ending  but it is still two dimensional

Answer:

D - Are One dimensional

Step-by-step explanation:

Line , Line segments and Ray's are all one dimensional objects

Evaluating all possible values of a variable in a model is called a sensitivity analysis.

A sensitivity analysis is a technique used to assess the impact of changes in the values of input variables on the output or outcome of a model or system. It involves systematically varying the values of the variables within a defined range and observing the corresponding changes in the model's output.

The purpose of a sensitivity analysis is to understand how sensitive the model is to changes in the input variables and to identify which variables have the most significant influence on the model's results.

During a sensitivity analysis, different scenarios are created by varying one or more input variables while keeping others constant. By examining the resulting changes in the model's output, analysts can gain insights into the relationships and dependencies between the variables and assess the robustness of the model's predictions or decisions.

Sensitivity analysis helps in understanding the potential risks, uncertainties, and limitations associated with the model, and can aid in decision-making and improving the model's performance by identifying critical variables that need to be carefully monitored or controlled.

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Answer:

C >:)

Step-by-step explanation:

Answer:

25(5)+14=139

$139

Step-by-step explanation:

The approximate range is -30 to 30. Therefore, the correct answer is option D.

The correlation coefficient r measures the strength and direction of a linear relationship between two variables, x and y. The correlation coefficient can range from -1 (perfectly negatively correlated, meaning as one variable increases, the other decreases) to 1 (perfectly positively correlated, meaning as one variable increases, the other increases).

When r = -0.9, this tells us that there is a strong negative linear relationship between x and y.

The equation for a linear relationship with a correlation coefficient of -0.9 is y = -0.9x + b, where b is the y-intercept. When x = 40, plugging this into the equation gives us y = -36.

So at an x-axis value of 40, the approximate range (lowest to highest) of y-values is -36 to 36. Since 36 is further away from the y-intercept than -36, the lowest possible value of y will be -30.

So, the approximate range is -30 to 30.

Therefore, the correct answer is option D.

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Answer: 9

Step-by-step explanation: The common difference is the difference between each of the terms in an arithmetic sequence.

Let's work backwards.

First, we take the last term we are given and

subtract the second to last term.

So here, we subtract 23 - 14 to get 9.

Now, we take 14 - 5 to get 9.

Notice that 9 is our answer in both problems above.

That means it's our common difference.

The point (x, y) on the unit circle that corresponds to the real number b) (0, 1) is (1, 0).

The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the coordinate plane. It is used in trigonometry to relate angles to points on the circle. To determine the point (x, y) on the unit circle that corresponds to a given real number, we need to find the angle in radians that corresponds to that real number and locate the point on the unit circle with that angle.

In this case, the real number is b) (0, 1). Since the y-coordinate is 1, we can conclude that the point lies on the positive y-axis of the unit circle. The x-coordinate is 0, indicating that the point does not have any horizontal displacement from the origin. Therefore, the point (x, y) that corresponds to (0, 1) is (1, 0) on the unit circle.

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Find the surface area of a Cuboid of length, breadth, and height equal to 12 cm, 8 cm and 5 cm respectively.

\( \bullet \) Length (l) of a Cuboid is 12 cm.

\( \bullet \) Breadth (b) of a Cuboid is 8 cm.

\( \bullet \) Height (h) of a Cuboid is 5 cm.

The surface area of a Cuboid.

We know,

Formula of surface area of a Cuboid is 2(lb + bh + lh) sq units.

So, Surface area of a Cuboid = 2(12×8 + 8×5 + 12×5) sq cm.

= 2(96 + 40 + 60) sq cm.

= 2 × 196

= 392 sq cm

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