If a parabola's focus is at (1,-1)and directrix is at
y= 7, what is the general form of the equation representing this parabola?

Answer:

x=22.5°

Step-by-step explanation:

(cos²x-sin²x)-sin4x+sin²2x=0

or, (cos2x)²-sin4x+sin²2x=0

or, cos²2x+sin²2x-sin4x=0

or, 1-sin4x=0

or, sin4x=1

or, 4x=90°

or, x=90°/4

or, x=22.5°

The appropriate measure of variability for the given data is the IQR, and its value is 16.

Based on the given stem-and-leaf plot, which represents the scores earned in a flower-growing competition, we can determine the appropriate measure of variability for the data.

The stem-and-leaf plot shows the individual scores, and to measure the spread or variability of the data, we have two commonly used measures: the range and the interquartile range (IQR).

The range is calculated by subtracting the smallest value from the largest value in the dataset. In this case, the smallest value is 20, and the largest value is 65. Therefore, the range is 65 - 20 = 45.

The interquartile range (IQR) is a measure of the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Looking at the stem-and-leaf plot, we can identify the quartiles. The first quartile (Q1) is 25, and the third quartile (Q3) is 41. Therefore, the IQR is 41 - 25 = 16.

In this case, both the range and the IQR are measures of variability, but the IQR is generally preferred when there are potential outliers in the data. It focuses on the central portion of the dataset and is less affected by extreme values. Therefore, the appropriate measure of variability for the given data is the IQR, and its value is 16.

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Answer: To find the discount, simply multiply the original selling price by the %discount:

ie:  39 x 33/100= $12.87

So, the discount is $12.87.

Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:

ie: 39- 12. 87=  26.13

So, the sale price is $26.13

Answer:

0.09381663113

Step-by-step explanation:

Answer:as a fraction it would be 11 3/5

Step-by-step explanation:

Given: Two similar triangles QRS and TRU

To Determine: The reflexive property to prove the similar triangles

Solution

We have been all that could lead to proving the similar triangles QRS and TRU

The space given has a the reason reflexive property

The reflexive property of equality states that a number is always equal to itself

From the image

Hence, the correct option is ∠QRS ≅ ∠ TRU, OPTION D

To determine the number of suppliers Witt Input Devices should use, we need to consider the probability of a "super-event" and the marginal cost of managing additional suppliers.

With a 3% probability of a total shutdown and an estimated cost of $400,000, along with a 5% "unique-event" risk per supplier, the company should aim to balance the costs and risks to make an informed decision on the number of suppliers.

Phillip Witt wants to create a portfolio of local suppliers for his keyboards. He faces the risk of "super-events" that could shut down all suppliers simultaneously for at least two weeks. The probability of such an event occurring is 3% per year, which would result in an estimated cost of $400,000 for the company.

Additionally, each individual supplier carries a "unique-event" risk of 5%. To mitigate the risks, Witt Input Devices needs to determine the optimal number of suppliers to use. However, it is stated that up to three nearly identical local suppliers are available.

To make a decision, the company needs to balance the costs and risks. Each additional supplier incurs a marginal cost of $15,000 per year. The company should evaluate the trade-off between the cost of managing additional suppliers and the risk reduction achieved by having multiple suppliers.

Considering these factors, Witt Input Devices should analyze the costs and benefits of each additional supplier and select the number of suppliers that provides an optimal balance between risk mitigation and cost management.

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Answer:

Sweet corn takes up a lot of room. To produce one to two ears of corn each stalk, each plant requires 3 square feet of area. Under ideal growth conditions, crowded corn will only produce one ear, whereas two ears will develop on stalks. A 10-by-15-foot garden area can accommodate 50 stalks of corn or around 75 ears of corn.

Step-by-step explanation:

You can thank me by marking me Brainliest maybe....Tee Hee

Answer:

Block planting works better in smaller gardens, although the corn still needs a minimum of a 4-foot-square area.

Step-by-step explanation:

Instead of side-by-side rows, plant the corn in 4-by-4 foot blocks.

Answer:

26

Step-by-step explanation:

Examples:

1 x 13 = 13

3 x 13 = 39

Second blank:

2 x 13 = 26

The regression analysis yielded a fitted line, y = 35 - 1.2x, with a coefficient of determination of 0.7632, a correlation coefficient of 0.8740, and a predicted mean of Y = 23 when X = 10.

To compute the coefficient of determination (r²), the correlation coefficient (r), and the predicted mean of Y when X = 10, we can use the given regression line y = 35 - 1.2x and the formulas related to regression analysis.

The coefficient of determination (r²) represents the proportion of the total variation in the dependent variable (Y) that can be explained by the independent variable (X). It is calculated by dividing the explained sum of squares (SSR) by the total sum of squares (SSY).

[a] To compute r²:

SSR = SSY - SSE

SSR = 2758 - 652 = 2106

r² = SSR / SSY

r² = 2106 / 2758 = 0.7632

Therefore, the coefficient of determination (r²) is 0.7632 (rounded to four decimal places).

[b] To compute the correlation coefficient (r):

We can use the formula:

r = √(r²)

r = √(0.7632) = 0.8740

Therefore, the correlation coefficient (r) is 0.8740 (rounded to four decimal places).

[c] To compute the predicted mean of Y when X = 10:

We can substitute the value of X = 10 into the regression line equation y = 35 - 1.2x:

y = 35 - 1.2(10)

y = 35 - 12

y = 23

Therefore, the predicted mean of Y when X = 10 is 23.

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Step-by-step explanation:

a.

x = number of matching questions

y = number of essay questions

x >= 3

x <= 12

y >= 4

y <= 15

x + y <= 20

the delimiter lines are therefore

x = 3

x = 12

y = 4

y = 15

y = 20 - x

when you graph these lines, the corners (intersection points) of the inner shaded area are

(3, 4)

(12, 4)

(3, 15)

(12, 8)

(5, 15)

the other intersection points

(12, 15)

(3, 17)

(16, 4)

are outside the inner shaded area.

b.

10x + 25y = score

and this we want to maximize.

we have to try the 5 corners from a. and see, which one gives the maximum score.

(3, 4) gives

10×3 + 25×4 = 30 + 100 = 130

(12, 4) gives

10×12 + 25×4 = 120 + 100 = 240

(3, 15) gives

10×3 + 25×15 = 30 + 375 = 405

(12, 8) gives

10×12 + 25×8 = 120 + 200 = 320

(5, 15) gives

10×5 + 25×15 = 50 + 375 = 425

that is the most.

so, Phil should do 5 matching questions and 15 essay questions for maximum score.

Shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

To find the shortest distance between a point and a plane, we can use the formula:

distance = |ax + by + cz + d| / √(a² + b² + c²)

where a, b, and c are the coefficients of the plane's equation, d is the constant term, and (x, y, z) is the coordinates of the point.

In this case, the plane is x + y + z = 1, so a = 1, b = 1, c = 1, and d = -1. The point is (2, 0, -3), so x = 2, y = 0, and z = -3. Plugging in these values, we get:

distance = |1(2) + 1(0) + 1(-3) - 1| / √(1² + 1² + 1²)

= 3 / √3

= √3

Therefore, the shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

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Answer:

Slope of dotted lines: 3/1 or 3

Slope of reflected line: 1/3

Step-by-step explanation:

Rise and run

Answer:

Step-by-step explanation:

1 ounce = 28.3 gm

2 ounce =x

x =2*28.3

x = 56.6 gm  

a)

It crosses the x-axis 3 times, at x = -3 and x = 1 (multiplicity 2)

Therefore, it has 3 zeros, one of them is repeated

The zeros are:

-3 , 1, 1

b)

Since it has 3 zeroes, the degree is 3

c)

The function tends to infinity as x approaches to infinity

d)

-3 : Multiplicity 1

1 : Multiplicity 2

e)

The y-intercept is the point where the graph crosses the y-axis, as we can see, the point is:

f)

Using the zeros, we can write the equation as:

The number of nickels and the number of dimes that Violet has is 10 nickles and 11 dimes.

Given:

Violet has $1.60 worth of nickels and dimes. She has a total of 21 nickels and dimes altogether.

Let nickles be n and dimes be d.

From statement given:

n + d = 21

n = 21 - d

1 dimes = 10 cents , 1 nickle = 5 cents and $1 = 100 cents.

n + d = $1.60

convert into cents

5n + 10d = 160

divide by 5 on both sides

n + 2d = 32

n = d - 21 substitute in n + 2d = 32

21 - d + 2d  = 32

d + 21 = 32

d = 11

Hence number of dimes = 11

substitute d = 11 in n = 21 - d

n = 21 - 10

n = 10

Hence number of nickles = 10

Therefore the number of nickels and the number of dimes that Violet has is 10 nickles and 11 dimes.

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Answer:

The value of x is 70°

Step-by-step explanation:

(2x – 5)° + 45° = 180°

2x – 5° + 45° = 180°

2x + 40° = 180°

2x + 40° – 40° = 180° – 40°

2x = 140°

2x/2 = 140°/2

x = 70°

Thus, The value of x is 70°

-TheUnknownScientist 72

Answer:???

Step-by-step explanation:

Answer:

x=2 y= -4

Step-by-step explanation:

set each to 0 to find the other

Answer:

A, C

Step-by-step explanation:

Only B is containing a variable .

The  -5 is not variable.

We have given that,

A.3x2

B. y

A

C. -5

In the expression 3x^2 + y -5

We have to determine which of the following terms does not have a variable.

variable, In algebra, a symbol stands in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).

Only C contains a variable.

The  -5 is not variable.

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Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

The cost for her to purchase the fence is $108.

Since she wants to put a wire fence around her garden which is 12 feet long and 6 feet wide, the total perimeter will be:

= 2(length + width)

= 2(12 + 6)

= 36 feet

Therefore, the cost will be:

= Total feet × Amount

= 36 × $3

= $108

Therefore, the cost for her to purchase the fence is $108.

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By applying the law of cosine, the length of side BM is equal to 7.05 cm..

A polygon can be defined as a two-dimensional geometric shape that comprises straight line segments and a finite number of sides. Also, some examples of a polygon include the following:

Note: The number of sides (n) of a pentagon is 5.

In Geometry, the interior angle of both a regular and irregular polygon is given by this formula:

Interior angle = 180 × (n - 2)/n

Interior angle = 180 × (5 - 2)/5

Interior angle = 180 × 3/2

Interior angle = 108°.

For the central angle, we have:

Central angle, O = 360/5

Central angle, O = 72°.

By applying the theorem of intersecting secants, angle OCB will be given by this formula:

<OCB = ½ × (180 - 72)

<OCB = ½ × 108

<OCB = 54°.

In order to determine the length of side BM, we would apply the law of cosine:

cos(θ) = Adj/Hyp

cos54 = BM/12

BM = 12 × cos54

BM = 12 × 0.5878

Side BM = 7.05 cm.

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Step-by-step explanation:

A. Each point in the image has the same x-coordinate as the corresponding point

in the figure.

D. Each point in the image moves the same distance and direction from the

figure.

These two statements are true about a figure and an image created by a translation. When a figure is translated, every point in the figure is moved the same distance and direction. This means that each point in the image has moved the same way as its corresponding point in the figure. Additionally, since a translation only involves moving a figure without changing its shape or size, the image and figure are the same shape and size, but just in different positions. As such, statement B and C are not true for figures and images created by translation.

To graph the image G'R'A'M', we need to add 10 to each x-coordinate and subtract 2 from each y-coordinate:

G': (-9+10, -9-2) = (1,-11)

R': (-8+10, -6-2) = (2,-8)

A': (-4+10, -6-2) = (6,-8)

M': (-5+10, -9-2) = (5,-11)

Graphing these points and connecting them gives us parallelogram G'R'A'M'.

The value of x will be;

⇒ x = 50

Parallel lines are those lines that are equidistance from each other and never intersect each other.

Given that;

Two parallel lines cut by a transversal.

Now,

Since, Two parallel lines cut by a transversal.

Hence, By definition of co-interior angle, we get;

The sum of co-interior angle in supplementary.

Hence, We get;

⇒ (2x + 10)° + (2x - 30)° = 180°

⇒ 4x - 20 = 180

⇒ 4x = 180 + 20

⇒ 4x = 200

⇒ x = 200/4

⇒ x = 50

Thus, The value of x = 50

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Answer:

what is the question in this picture

Answer: Given two points on a line, we can write an equation for that line by finding the slope between those points, then solving for the y-intercept in the slope-intercept equation y=mx+b.

Step-by-step explanation:

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Igraine is incorrect in stating that a rectangular prism is the best model for approximating the surface area of a fire extinguisher. The fire extinguisher has a curved surface, which cannot be properly approximated by a rectangular prism.

The curved surface of the fire extinguisher indicates that a cylindrical model would be more appropriate for approximating its surface area.

A cylindrical model would consist of a curved lateral surface area and two circular bases. While a rectangular prism could be used to approximate the volume of the fire extinguisher, it would not be the best model for approximating the surface area.

It is important to choose an appropriate model for accurate calculations and analysis.

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The simplified expression is 26 - 4x.

To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.

6 - 4(x - 5)

First, distribute -4 to the terms inside the parentheses:

6 - 4x + 20

Now, combine like terms:

(6 + 20) - 4x

Simplifying further:

26 - 4x

Therefore, the simplified expression is 26 - 4x.

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