. Why is the following arrangment of squares not an array?​

The equation for the tangent plane is 12x - y + 4z - 56 = 0 and the equation for normal line is (x - 6)/12 = (32 - y) = (z - 2)/4

Finding the Equations for Tangent Plane and Normal Line:

The given function is,

f(x, y, z) = x² - y - z² = 0

∂f/ ∂x = 2x

∂f/ ∂y = -1

∂f/ ∂z = 2z

At given point (6, 32, 2),

∂f/ ∂x = 12

∂f/ ∂y = -1

∂f/ ∂z = 4

(a) The equation of tangent plane is given as follows,

(∂f/ ∂x)(x-x₁) + (∂f/ ∂y)(y-y₁) + (∂f/ ∂z)(z-z₁) = 0

12(x - 6) - 1(y - 32) + 4(z - 4) = 0

12x - 72 - y + 32 + 4z - 16 = 0

The required tangent plane is,

12x - y + 4z - 56 = 0

(b) The equation for normal line is given as,

(x-x₁) / (∂f/ ∂x) = (y-y₁) / (y-y₁) = (z-z₁) / (∂f/ ∂z)

(x - 6)/12 = (y - 32)/(-1) = (z - 2)/4

Thus, the required equation of normal line is,

(x - 6)/12 = (32 - y) = (z - 2)/4

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Answer: See attached

Step-by-step explanation:

    Given:

y = -x² + 6x - 5

    Since this is a quadratic function, we will have a parabola.

    Because our x² value is negative, this parabola will be a "frowny face" instead of a "smiley face" like the parent function.    

    The - 5 means we shift the function 5 units to the right from the parent function.

    See attached for our graph.

    What parent function am I mentioning?

The parent function of y = -x² + 6x - 5 is y = x²

Answer:

"unit"

Step-by-step explanation:

Answer:

It is 3

•°•°•°

Math is poop

Answer:

me too (help)

Step-by-step explanation:

a. Assuming no additional restrictions, there are  800 possible three-digit area codes.

b. Considering ERCs, there are  80 ERCs.

c. For the seven digits after the area code, there are \(8 \times 10^6 = 8,000,000\)  possible seven-digit phone numbers.

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers is 800 \(\times\) 8,000,000 = 6,400,000,000.

a. For three-digit area codes, the first digit cannot be 0 or 1.

Assuming no additional restrictions, there are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining two digits (0-9). Therefore, the total number of three-digit area codes possible under this plan is \(8 \times 10 \times 10 = 800.\)

b. For an ERC (Easily Recognizable Code), the second and third digits of the area code must be the same, and the first digit cannot be 0 or 1. There are 8 possibilities for the first digit (2-9) and 10 possibilities for the third digit (0-9).

Since the second digit must be the same as the third digit, there is only 1 possibility.

Therefore, the total number of ERCs is \(8 \times 1 \times 10 = 80.\)

c. For the seven digits after the area code, the first digit of the three-digit local prefix cannot be 0 or 1.

There are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining six digits (0-9).

Therefore, the total number of seven-digit phone numbers possible is 8 * \(10\times 10 \times 10 \times 10 \times 10 \times 10 = 8,000,000.\)

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers can be calculated by multiplying the number of possibilities for each digit position.

For the area code (part a), there are 800 possibilities.

For the seven digits after the area code (part c), there are 8,000,000 possibilities.

Therefore, the total number of ten-digit phone numbers possible is 800 * 8,000,000 = 6,400,000,000.

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Bob can deduct a total of $2,210 on his Schedule C related to these expenses.

To determine the total amount Bob can deduct on his Schedule C related to these expenses, consider the specific categories that can be deducted. Based on the information provided, categorize the expenses as follows:

Course fees for continuing legal education: $1,400

Airfare and hotel room: $500

Meals provided by the hotel's restaurant: $300

Snacks from the newsstand: $10

To calculate the total amount that Bob can deduct, add up these expenses:

$1,400 + $500 + $300 + $10 = $2,210

Therefore, Bob can deduct a total of $2,210 on his Schedule C related to these expenses.

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Answer:

Prefer the attachment for ur ans.

Given:

• m∠H = 133 degrees

• m∠I = 38 degrees

• m∠J = 153 degrees

• m∠K = 36 degrees

Let's choose all answers that describe the quadrilateral.

Let's first make a sketch of the quadrilateral:

We can see the quadrilateral has four unequal angles.

Since it has four unequal angles, the possible quadrilateral which describe quadrilateral HIJK is:

Trapezoid

This quadrilateral can be called an irregular trapezoid. An irregular trapezoid has all four unequal angles and four unequal sides.

Therefore, the quadrilateral which describes quadrilateral HIJK is:

Trapezoid

ANSWER:

Trapezoid

An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

This function is one-to-one because for every element x in P, there is a unique element 2x in Q. It is onto because every element y in Q has a preimage x in P such that f(x) = y (e.g., y/2 = x).

Furthermore, this function preserves the group structure between P and Q, as it satisfies the properties of an isomorphism. In this case, the group structure is addition, and the function f preserves addition: f(x + y) = 2(x + y) = 2x + 2y = f(x) + f(y) for all x, y in P.

Therefore, the function f: P -> Q defined as f(x) = 2x is an example of a one-to-one function that is an isomorphism between sets P and Q.

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Check the picture below.

\(\textit{Law of Cosines}\\\\ \cfrac{a^2+b^2-c^2}{2ab}=\cos(C)\implies \cos^{-1}\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C \\\\[-0.35em] ~\dotfill\\\\ \cos^{-1}\left(\cfrac{10^2+4^2-7^2}{2(10)(4)}\right)=\measuredangle A \implies \cos^{-1}\left(\cfrac{ 67 }{ 80 }\right)=\measuredangle A \\\\\\ \cos^{-1}(0.8375) = \measuredangle A \implies 33.12^o \approx \measuredangle A\)

Make sure your calculator is in Degree mode.

SOLUTION

We will use a Venn Diagram for this problem.

Let N represent those that use Netflix, R represent those that use Redbox and V represent those that use video store. The Venn Diagram is shown below

From the Venn Diagram above, the number in each part of a circle, represents the information

Now, how many people use Redbox?

The number of those that use Redbox is represented by the circle R, so we add all the numbers in this circle, we have

Hence the answer is 115

Answer:

...........................................................

Step-by-step explanation:

Answer:

A=7

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The required rate of return for the stock with a beta of 0.5 is 7.5% and for the stock with a beta of 2 is 15%.

Rate of return is the amount of profit or loss earned on an investment over a certain period of time, expressed as a percentage of the initial investment or total asset value.

A stock is a type of security that represents ownership in a company. Investors buy stocks to become shareholders and share in the company's profits and losses.

According to the given information:

The Capital Asset Pricing Model (CAPM) is expressed as:

R = Rf + beta*(Rm - Rf)

Where:

R = Required rate of return

Rf = Risk-free rate of return

beta = Beta coefficient (systematic risk)

Rm = Expected market return

Using the given values, we can compute the required rate of return for each stock:

Stock with beta of 0.5:

R = 5% + 0.5*(10% - 5%)

R = 7.5%

Stock with beta of 2:

R = 5% + 2*(10% - 5%)

R = 15%

Therefore, the required rate of return for the stock with beta of 0.5 is 7.5%, and the required rate of return for the stock with beta of 2 is 15%.

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The completed statement with regards to the area of the square and the rectangle are;

The estimated value of the length of the shaded square is 5·√5 inches. The estimated value of the area of the unshaded rectangle is 175 square inches.

The area of a square is the product of the side lengths which are congruent, therefore;

Area of a square = Side length, s × Side length, s = s²

The possible figure in the question includes;

A shaded square that is 125 square inches

An adjacent unshaded rectangle, that share a side with the square that has a side length of 7·√5 inches

Please find attached the possible drawing of the figure in the question, (not drawn to scale) obtained from a similar question posted online, created with MS Word.

Therefore;

The side length of the square = √(125) inches =  5·√5 inches

The estimated value of the side length of the square is; 5·√5 inches

The area of a rectangle = Length × Width

The length of the rectangle = 7·√5 inches

The width of the rectangle = 5·√5 inches

Therefore;

The area of the unshaded rectangle, therefore is; 5·√5 × 7·√5 = 175

The estimated area of the unshaded rectangle is 175 square inches

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By completing the square the function will be, g(x)=4(x-2)²-9

The standard form of the quadratic equation will be ax²+bx+c=0.

Equate the given equation with standard form of equation and determine the values of a, b, and c.

a=4

b=-16

c=7

For completing the square, add and subtract \(\frac{b^2}{4a}=\frac{(-16)^2}{4\times4}=16\) in the given equation.

g(x)=4x²-16x+16-16+7

g(x)=(4x²-16x+16)-9

g(x)=4(x²-4x+4)-9

The term x²-4x+4 is equivalent to (x-2)².

g(x)=4(x-2)²-9

So, the given function is same as g(x)=4(x-2)²-9.

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The sine equation for the object's height is given as follows:

d = -5sin(0.24t).

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The amplitude for this problem is of 5 inches, hence:

A = 5.

The period is of 1.5 seconds, hence the coefficient B is given as follows:

2π/B = 1.5

B = 1.5/2π

B = 0.24.

The function starts moving down, hence it is negative, so:

d = -5sin(0.24t).

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The total purchase is  $18.90.

A discount would reduce the cost of the purchase. A tax increases the cost of the purchase.

The first step is to determine the total cost of the items purchased.

Total cost = (cost of lb of cheese x lb bought) + (cost of sliced ham x lbs bought) + (cost of bread x loaves bought) + (cost of a bag of potato chips x number of bags bought) + (cost of one salsa container x number of containers bought)

(1.99 x 1/2) + (3 x 3.29) + (1.59 x 2) + (2 x $3) + (1.39 x 1) = $20.39

Since, the total cost is greater than $20 she qualifies for the 10% discount

Total cost after the discount = (1 - 0.1) x $20.39

0.9 x $20.39= $18.35

Cost after the tax = (1 + 0.03) x $18.35

1.03 x $18.35 = $18.90

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The limit for this problem is given as follows:

\(\lim_{x \rightarrow 3} \frac{\sqrt{x + 2}}{x - 4} = -\sqrt{5}\)

The limit for this problem is defined as follows:

\(\lim_{x \rightarrow 3} \frac{\sqrt{x + 2}}{x - 4}\)

The point that is excluded from the domain of the function is given as follows:

x - 4 = 0 -> x = 4.

The limit is calculated at:

x = 3.

As the function is in fact defined at x = 3, we just obtain the numeric value of the function at x = 3, replacing each instance of x by 3, hence:

\(\lim_{x \rightarrow 3} \frac{\sqrt{x + 2}}{x - 4} = \frac{\sqrt{3 + 2}}{3 - 4} =  -\sqrt{5}\)

(positive divided by -1 is negative).

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To find:-

Answer:-

Here we need to find out the following limit ,

\(\implies \displaystyle \lim_{x\to 3}\dfrac{\sqrt{x+2}}{x-4} \\\)

We start by substituting x = 3 in the given limit as ,

\(\implies \displaystyle \dfrac{\sqrt{3+2}}{3-4} \\\)

Simplify,

\(\implies \displaystyle \dfrac{\sqrt{5}}{-1} \\\)

Multiply Numerator and Denominator by -1 ,

\(\implies \displaystyle -\sqrt{5}\\\)

Therefore,

\(\implies\underline{\underline{\green{ \displaystyle \lim_{x\to 3}\dfrac{\sqrt{x+2}}{x-4} =-\sqrt5}}} \\\)

and we are done!

Answer:

Sydney, Nova Scotia

Step-by-step explanation:

Out of all 3 Sydney, Nova Scotia would be the coldest because -23 degrees is lower than -21 and -22. When using a thermometer the lower it is the colder, so Nova Scotia would be your answer.

Answer:

Charlottetown, Prince Edward Island, is the warmest. Sydney, Nova Scotia is the coldest. The larger the negative number the more cold it is while the lower the negative number, it becomes warmer.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want a graph and a description of the triangle whose vertices are Q(2, 2), R(4, 8), and S(8, 5).

See the attachment for the correct graph. Plotting points on a graph should be no mystery: the first coordinate tells you how far to the right of the y-axis; the second coordinate tells you how far up from the x-axis. (The coordinates are (right, up).)

You can look at the differences between coordinate pairs to get an idea whether sides are the same length. Or you can go to the trouble to actually figure out the lengths.

  R -Q = (4-2, 8-2) = (2, 6)

  S -R = (8-4, 5-8) = (4, -3)

  Q -S = (2-8, 2-5) = (-6, -3)

The ratios of the y-difference to the x-difference are ...

  QR: 6/2 = 3

  RS: -3/4

  SQ: -3/-6 = 1/2

None of these is the opposite reciprocal of another, so no segments are perpendicular. The triangle is not a right triangle.

You can look at the sums of squares of these number to get an idea about length relationships:

  QR² = 2² +6² = 40

  RS² = 4² +(-3)² = 25

  SQ² = (-6)² +(-3)² = 45

These are all different, so the triangle is scalene.

__

Additional comment

You can tell whether the triangle is acute, right, or obtuse by looking at the value of the expression a²+b²-c², where a, b, c are the side lengths from smallest to largest. Here, that value is 25+40-45 = 20. It is greater than 0, so the triangle is acute. (=0: right; <0: obtuse)

Lines with opposite reciprocal slopes are perpendicular. For example, a line with a slope of -3/4 is perpendicular to one with a slope of 4/3.

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Answer:

the answer to that question is 12,600 rupees

Answer:

1 1/3

Step-by-step explanation:

take the denominator and times it to the mixed number.

so 3*1 = 3

then add the numerator to that, so

3 + 1 = 4

making it, 4/3

Answer:

The answer is 56°. Angle B is an exterior angle of triangle ABC, which means it is equal to the sum of the two remote interior angles (angles A and C). Angle A is 35°, angle C is 121°, so angle B is 56°.