Find the focus and the directrix of the parabola with the equation y = -¹/2 (x-8)² -
6.
A) Focus = (-8,-5¹/2), directrix is y=-6¹/2
B) Focus = (8,-6¹/2), directrix is y= -5¹/2
○ C) Focus = (-8,-6¹⁄2), directrix is y= −5¹/2
D) Focus = (8,-5¹/2), directrix is y=-6¹/2

Using translation concepts, the y-coordinate of R' will be of -10.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the rule is given by:

(x,y) -> (x + 4, y - 7)

y -> y - 7 means that for the image, the 7 is subtracted from the y-coordinate of the pre-image. The y-coordinate of R is of -3, -3 -7 = -10, hence the y-coordinate of R' will be of -10.

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Answer: 6 hours

Step-by-step explanation: The distance is 294 miles. The speed is 49 miles per hour. In that case, we divide 294 by 49, which gives us 6.

The least amount of money you can spend to buy the same number of candles and mints is $125.

The prime factorization of 12 and 15 is:

12= 2*2*3

15= 2*5*5

Now the factor of both appears in both number's factorization so least common multiple is:

LCM of 12 and 15 = 2*2*3*5*5=300

It is given that candies come in packs of 12 and mints in packs of 50.

Hence, the total quantity of packs of each thing is:

Candles: 300÷12=25

Mints: 300÷50=6

The least amount of money to be spent is:

25×$3.50 + 6×$6.25= $87.5 + $37.5= $125

Thus, the least amount of money you can spend to buy the same number of candles and mints is $125.

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Answer:125

Step-by-step explanation: no explanations sorry but it is right thank me later

Answer:

7GB, $12

Step-by-step explanation:

I used subtraction to find the difference.

The corrected mean and median, respectively, are 557.3 and 557.

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The length of the pen in the drawing will be 2 millimeters.

As we can't create a real-life dimension in a  small sheet of paper,  we opted for a small scale that covers up the large length.As we are given, the scale of the drawing is 1 millimeter: 10 meters, which is 1 millimeter for every 10 meters

As we have been given that the  actual  size of the goat pen  is 20 meters, so the length of the pen in the drawing is =  20*(1/10)

                                                                                  =   2 millimeters

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'

3/13              least

1/7

1/4               greatest

Answer:

6 x 10^7

Step-by-step explanation:

(2x3)(10^4 x 10^3)

6 x 10^4+3

6 x 10^7

The value of 5x - 2y + 3z when x = 7 , y = 11 , z = -1 is 10.

Expression

An expression, in math, is a sentence with a minimum of two numbers and at least one math operation in it.

Given that:-

Expression : 5x -2y + 3z

x = 7, y = 11 , z = -1

We have to find the value of 5x - 2y + 3z

According to the data given in the question, we can write,

The value of the expression 5x - 2y + 3z is:-

5*(7) -2*(11) + 3*(-1) = 35 -22 - 3 = 35 - 25 = 10.

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We can the slope of the line using:

m = (y 2 - y 1)/ (x 2 - x 1) where, m is the slope of the line.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes.

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The number of people working on that day are 107 people in the staff.

According to the statement

We have to find that the number of people were working that day.

So, For this purpose, we know that the

A percentage is a number or ratio expressed as a fraction of 100.

From the given information:

a hospital day staff consists of 25 registered nurses, 75 unlicensed assistants, five phlebologists, six receptionists and office staff, and 45 physicians. one summer day the staff was at only 68% strength.

Then

Total number of staff = 25+75+5+6+45

Total number of staff = 156

Then

the staff was at strength = 68%

And then

Number of people working on that day = 68% of 156

And

Number of people working on that day = 68/100 *156

Number of people working on that day = 0.68*156

Number of people working on that day = 106.08

Approximate 107 people.

So, The number of people working on that day are 107 people in the staff.

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Answer:

1st Question 24 ÷ (-6) = -4

2nd Question -15 ÷ 0.3 = -50

3rd Question -4 ÷ (-20) = 0.2

This should be correct. I used a calculator Lol. :3.

Answer: 8 tacos

Step-by-step explanation: To turn 15 into 3 students you would divide 15 by 5. You would also have to divide 40 by 5 too so that would be 8 tacos.

Answer:

96

Step-by-step explanation:

It is a straight linek so it adds up to 189.

53+31 = 84

180-84=96

yay brainliest :D

The equation used to represent the context is 1041.50 + 62.75p = 2045.50.

From the information, they rented a bus for $1041.50 and budgeted $62.75 per player for meals.

Therefore, the equation will be:

1041.50 + (62.75 × p) = 2045.50

1041.50 + 62.75p = 2045.50

Therefore, the equation will be 1041.50 + 62.75p = 2045.50.

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Answer:

90 m

Step-by-step explanation:

a. Perimeter = 2( length + breadth) 2(x + y)

Answer: Perimeter:  2(x + y) = 420
or 2x + 2y = 420

Using the values given

b.

2x + 2y = 420 (perimeter p= 420)
2(120) + 2y = 420   (length x = 120)
240 + 2y = 420
2y =  420 - 240 = 180 (subtract 240 on both sides)

y = 190/2 = 90 m

The difference between the area of the square and the area of the circle is C. 9x²(4 - π).

The area of the square will be:

= Side ×Side

= 6x × 6x

= 36x²

The area of the circle will be:

= πr²

= 3.14 × (3x)²

= π × 9x²

= 9πx²

The difference will be:

= 36x² - 9πx²

= 9x²(4 - π)

Therefore, the correct option is C.

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The difference between the area of the square and the area of the circle is 9x²(4 - π)

area of circle = πr²

where

Therefore,

area of a square = l²

where

The circle is inscribed in the square.

Therefore, the difference in area of the square and circle is as follows:

area of circle = π × (3x)² = 9x²π

area of the square = (6x)² = 36x²

Hence,

difference in area = 36x² - 9x²π

difference in area = 9x²(4 - π)

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Using the function rule y=2x -2 the values in the given table are as follow:

x        y

0      -2

1       0

2       2

3       4

4       6

As given,

Given function:

y=2x - 2

Substitute the value of x in the given function y=2x - 2

x=0

⇒y=2(0) -2

      =-2

x=1

⇒y=2(1) -2

      =0

x=2

⇒y=2(2) -2

      =2

x=3

⇒y=2(3) -2

     =4

x=4

⇒y=2(4)-2

     =6

Therefore, using the function rule y=2x -2 the values in the given table are as follow:

x        y

0      -2

1       0

2       2

3       4

4       6

The complete question is :

Fill in the table using this function rule.

y=2x-2

x      y

0

1

2

3

4

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For the given condition- If the earth reversed its direction of spin. Then,

The Earth is constantly in motion. Every day, the Earth completes one full rotation around its axis. The axis is an imaginary line that runs through the earth from the North Pole to the South Pole.

Some key features regarding the Earth's rotation are-

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The complete question is -

If you are standing at the Earth's North Pole.

For this question choose as many answers as are correct. if the earth reversed its direction of spin

The number of times that blue will be expected will be 100 times.

It should be noted that from the information given, the spinner is divided into four equal sections labeled yellow, green, red, and blue.

It simply means that each color has a 1/4 chance for each scenario.

Therefore, the number of times that blue will be expected will be:

= 1/4 × 400

= 100 times

Therefore, the number of times that blue will be expected will be 100 times.

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A spinner is divided into four equal sections labeled yellow, green, red, and blue. If the spinner is spun 400 times, how many times would you expect to get blue?

Jack has left with the 19/8 yards fraction part of material.

In mathematics, yard is the unit of length. we can say that yard is the one of the measurement of length. Conversion of yard in various quantities is as below:

        1 yard = 36 inches

        1 yard = 3 feets

        1 yard = 0.914 meters

For the question given,

If we have to find the remaining material that has been left we must find the difference between the two i.e. used and purchased material by simply subtracting them.

So, Material purchased = 3 yards

      Material used = 5/8 yards

now, material left = Material purchased - material used

                             =  3 - 5/8

                             = 19/8 yards

Thus, Jack has left with the 19/8 yards material.

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Answer:

-3.4 or -17/5

Step-by-step explanation:

3 and 2/5= 17/5 or 3.4

-7 and 1/5 = -34/5 or -6.8

There are 11 questions worth 5 points and 3 questions worth 15 points.

To find the correct number of questions:

Let, 5-point questions are x and 15 marks questions are y.

The total points are 100 so the other equation will be:

Now, multiply equation (1) by 5 and then subtract it by equation (2) as follows:

Therefore, there are 11 questions worth 5 points and 3 questions worth 15 points.

Now,

So, questions worth 15 marks are 3 then, and questions worth 5 marks will be 14 - 3 that is 11.

Therefore, there are 11 questions worth 5 points and 3 questions worth 15 points.

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Answer:

3.435973837*10^10

Step-by-step explanation:

4 to the 7th power is 16384

and 8 to the 7th power is 2097152

multiplied by each other is 3.435973837*10 to the 10th power

if you have to round to the nearest 10th the answer is 3.44

The perimeter of a square is proportional to the sides of its length

The statement is given as

The perimeter of a square is four times as great as the length of any of the sides

The above statement can be represented as

P = 4L

Where P represents the perimeter and L represents the side length

A proportional equation is represented as

y = kx

Where k a constant

By comparing y = kx and P = 4L, we have

y = P, k = 4 and x = L

Hence, the perimeter of a square is proportional to the sides of its length

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The solution to the give inequality is x < d-a/c

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given the inequality expression

d - cx < a

Make x the subject of formula to have:

-cx < a - d

Divide both sides by -c

-cx <(a-d)/-c
x < -(a-d)/c

x < d-a/c

Hence the solution to the give inequality is x < d-a/c

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The percentage of vacationers who spent less than $1,200 per 12-day vacation is 7.78%.

The normal distribution, also recognized as that of the Gaussian distribution, would be a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far away from the mean. The normal distribution is represented graphically as a "bell curve."

Now, according to the question;

The formula for finding the z-score is;

z = (x - μ)/σ

where,

x is the score

μ is the mean

σ is the standard deviation.

Summer vacation costs $1,755 for the average local family.

The distribution is normal, with a standard deviation of $390.

We need to figure out what percentage of families took vacations less than $1200.

The mean is $1,755

∴ μ = $1,755

∵ The standard deviation is $390

∴ σ = 390

∵ The vacation cost is under $1200

∴ x = $1200

Substitute the values in the formula of z score.

z-score = (1200 - 1,755)/390 = -1.42

Use the negative normal distribution table of z

P(z < 1,200) = 0.07782

P(x < 1,200) = P(z < 1,200)

P(x < 1,200) = 0.07782

P(x < 1,200) = 7.78%

Therefore, the percentage of vacationers who spent less than $1,200 per 12-day vacation is 7.78%.

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The complete question is -

International travel is usually more expensive than domestic travel. A recent survey found that the average per-person cost of a 12-day international vacation is  $1,755. This includes transportation, food, lodging, and entertainment.

a. if the data are normally distributed with standard deviation $390, find the percentage of vacationers who spent less than $1,200 per 12-day vacation. round to the nearest hundredth of a percent.