if tanA=1/3, tanB=-1/2, find the value of A+B
​

\(\tt\displaystyle\ 3c\underline{(p-6)}+4\underline{(p-6)}=(p-6)(3c+4)\)

The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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The density of the lobster population in the area labeled NBHK is C) 9.02 lobsters/mi^2.

Population density refers to the number of people living in a given area, usually expressed as the number of individuals per square mile or kilometer.

To calculate population density, you can divide the total population of a given area by its land area. For example, if a city has a population of 1 million people and an area of 100 square miles, its population density would be 10,000 people per square mile.

The figure has two trapezoid and the areas are 306 and 756. Total area will be 1062 miles².

Lobster population will be:

= 6817 / 756

= 9

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Answer:

\(\frac{3}{5}\) and \(\frac{9}{25}\)

because you can multiply the numerator and denominator by 3 to get 9/25

and if you want to do it vice versa, divide 9/25 by 3.

Answer:

(1,1) (2,2) (1,2) (1,5) (4,4) (4,5)

there are a lot more but those are some.

Step-by-step explanation:

The round plate in the problem has a surface area of 63.754 square inches.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given, A circular plate has a circumference of 28.3 inches.

Since circumference of a circle = 2*3.14 * r

Where r is the radius

Thus,

circumference  = 28.3

6.28 * r = 28.3

r = 4.506

Radius of circle = 4.506

Since the area of the circle = 3.14 * r * r

Thus,

Area of given circle = 3.14 * 4.506 * 4.506

Therefore, the Area of the given Circular plate is 63.754 square inches.

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When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

Given,

The cost of Carpet per square foot = $4

Total cost of the carpet = $616

We know

Area of the rectangle = Length × Width

Length = 14 feet

Consider the width of the rectangular room as x

Then the area of the room = 14x

Total cost of carpet = Area of the rectangular room× Cost of carpet per foot

Substitute the values

14x×4=616

14x=154

x=11 feet

Hence, When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

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Answer:

x = 23

7x - 11 = 4x + 58

(7x - 4x) - 11 = (4x - 4x) + 58

3x - 11 = 58

3x (- 11 + 11) = 58 + 11

3x = 69

3x/3 = 69/3

x = 23

Answer:

x=23°

Step-by-step explanation:

(7x - 11)=(4x + 58)

7x-4x=58+11

3x=69

x=23

Answer:

2352071 ft ^3

Step-by-step explanation:

formula for volume of a sphere is

V= 4/3 * \(\pi\) * r ^3

V = 4/3 * \(\pi\) * 82.5 ^3 = 2352071 ft ^3

Answer:

Option (4). Rhombus

Step-by-step explanation:

From the figure attached,

Distance AB = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\)

                     = \(\sqrt{(1-4)^2+(-5+3)^2}\)

                     = \(\sqrt{(-3)^2+(-2)^2}\)

                     = \(\sqrt{13}\)

Distance BC = \(\sqrt{(4-1)^2+(-3+1)^2}\)

                     = \(\sqrt{9+4}\)

                     = \(\sqrt{13}\)

Distance CD = \(\sqrt{(-2-1)^2+(-3+1)^2}\)

                     = \(\sqrt{9+4}\)

                     = \(\sqrt{13}\)

Distance AD = \(\sqrt{(1+2)^2+(-5+3)^2}\)

                     = \(\sqrt{9+4}\)

                     = \(\sqrt{13}\)

Slope of AB (\(m_{1}\)) = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

                           = \(\frac{4-1}{-3+5}\)

                           = \(\frac{3}{2}\)

Slope of BC (\(m_{2}\)) = \(\frac{4-1}{-3+1}\)

                            = \(-\frac{3}{2}\)

If AB and BC are perpendicular then,

\(m_{1}\times m_{2}=-1\)

But it's not true.

[\(m_{1}\times m_{2}=(\frac{3}{2})(-\frac{3}{2})\) = -\(\frac{9}{4}\)]

It shows that the consecutive sides of the quadrilateral are not perpendicular.

Therefore, ABCD is neither square nor a rectangle.

Slope of diagonal BD = \(\frac{4+2}{-3+3}\)

                                    = Not defined (parallel to y-axis)

Slope of diagonal AC = \(\frac{1-1}{-1+5}\)

                                    = 0 [parallel to x-axis]

Therefore, both the diagonals AC and BD will be perpendicular.

And the quadrilateral formed by the given points will be a rhombus.

Answer:

B.

Step-by-step explanation:

I used the percent button on my calculator. :)

Hope this helps

Answer:

234

Step-by-step explanation:

We know L+W=H so the easiest way to find the length would be to do 298-64 and we get 234 and we know this is right because if we add 234+64 we get 298.

Hope this helps.

Answer:

2

Step-by-step explanation:

Multiply 4 times 1/2

If you need to find the derivative the answer is 2^-1/2

The standard cell potential can be calculated by subtracting the standard reduction potential of the anode from the standard reduction potential of the cathode. In this case, the standard cell potential is 2.46 V.

The standard cell potential represents the potential difference between the anode and the cathode in a galvanic cell under standard conditions. It can be calculated by subtracting the standard reduction potential of the anode from the standard reduction potential of the cathode.

In this case, the reduction half-reaction for aluminum (Al) is Al^3+ + 3e^- → Al with a standard reduction potential of -1.66 V. The reduction half-reaction for silver (Ag) is Ag^+ + e^- → Ag with a standard reduction potential of 0.799 V.

To calculate the standard cell potential, we subtract the standard reduction potential of the anode from the standard reduction potential of the cathode:

Standard Cell Potential = E°(cathode) - E°(anode)

Standard Cell Potential = 0.799 V - (-1.66 V)

Standard Cell Potential = 2.46 V

Therefore, the standard cell potential for this reaction is 2.46 V. The positive value indicates that the reaction is spontaneous in the forward direction, and the higher the value, the stronger the driving force for the reaction.

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The amount for Emiliano tip is $1.8.

From the information, Emiliano buys two coffees for $8.98 and he tips the barista 20% of the bill.

The value of the tip will be:

= Percentage × Value of coffee

= 20% × $8.98

= 0.2 × $8.98

= $1.796

= $1.8 to the nearest cent.

This illustrates the concept of multiplication.

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The arc length is D) 3.14 meters.

What is arc length?

In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.

It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.

The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.

                                      \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

Here the give circle Radius PR = 3m and θ=60°.

Now using arc length formula then,

=> Arc length \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

=> \(A_L=\frac{60}{360} \times2\times3.14\times3\)

=> \(A_L=\frac{1}{6}\times2\times3.14\times3\)

=> \(A_L\) = 3.14 m.

Hence the arc length is D) 3.14 meters.

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Using the Pythagorean theorem, we know that the string needed to go from D to C is 3 inches and from E to D is 2.7 inches.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

So, according to the given information:

We know that:
CE = 1.1 in

EC = 2.7 in

Then,

The string needed to go from E to D is 2.7 in (Given).

String needed to go from D to C:

Using the Pythagorean theorem: c = √a² + b²

Now, calculate DC as follows:

DC = √a² + b²

DC = √1.1² + 2.7²

DC = 2.91548

Rounding off DC: 3 in

Therefore, using the Pythagorean theorem, we know that the string needed to go from D to C is 3 inches and from E to D is 2.7 inches.

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The coordinates of the geometric figure after it is reflected about the y-axis include the following:

x" = (-4, 5).

y" = (-3, 9).

z" = (-6, -11).

In Geometry, a reflection over the y-axis is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the coordinates of the object include the following:

(x, y)                               →              (-x, y)

Coordinate x' = (-4, -5)   →  Coordinate x" = (-(4), 5) = (-4, 5).

Coordinate y' = (3, 9)   →  Coordinate y" = (-(3), 9) = (-3, 9).

Coordinate z' = (6, -11)   →  Coordinate z" = (-(6), (-11)) = (-6, -11).

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Answer:

you can afford a loan of $211,204 with a total payment of $504,000 (which is $292,796‬ interest in total).

Step-by-step explanation:

Deposit, p = $1400

Rate of interest, r = 0.07 ÷ number of months in a year (12) = 0.0058

periods, n = 30 X 12 = 360‬

P =  1400 ( 1 - ( 1 + 0.0058)^- 360)  ÷ 0.0058  

= 1400 (150.86)

p = $211,204

You will pay a total of $504,000 ($1400 per month for 360 months) to the loan company.

The amount you pay - the amount of the loan is the interest paid. In this case, you’re paying $504,000 - $211,204 = $292,796‬ interest paid in total.

Considering it's asymptotes, the rational function shown in the graph is:

C. \(F(x) = \frac{1}{(x + 2)(x - 1)}\)

In this graph, there are vertical asymptotes at x = -2 and x = 1, hence the denominator of the function is:

(x + 2)(x - 1).

The horizontal asymptote is of y = 0, hence the function can be given by:

C. \(F(x) = \frac{1}{(x + 2)(x - 1)}\)

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There are 15 years was his money invested.

Simple Interest is an easy method of calculating the interest for a loan/principal amount.

Given

Frank invests $1,000 in simple interest investment account that pays 8% a year.

After a number of years, he withdraws his balance of $2,200.

The number of years was his money inversted is;

\(\rm I= P\times r \times t\)

Where p is the principal amount, r is the rate of interest, I is the amount and  t is the time.

Substitute all the values in the formula;

\(\rm I= P\times r \times t\\\\2200-1000= 1000 \times .08 \times t\\\\1200 = 80t\\\\t = \dfrac{1200}{80}\\\\t=15\)

Hence, in the 15 years was his money invested.

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Answer:

Step-by-step explanation:

When your desired form is expanded, it becomes ...

  a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2

This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.

a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2

b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2

c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2

d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2

_____

Additional comment

If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.

Answer:

Step-by-step explanation:

9/18 + 1/3

Find common denominators.  Since 3 can be multiplied by 6 to get 18, 18 will be the common denominator.

Multiply 1/3 by 6/6 and then add.

9/18 + 6/18 = 15/18

Simplify by dividing the numerator and denominator by 3.

15/18 ÷ 3/3 = 5/6

Answer:

I got x <= 8/7 which is none of the answer options given. Ask your professor about that.

Step-by-step explanation:

7x-1 <= 7

add 1 on each side

7x <= 8

Divide by 7 on both sides

7x/7 <= 8/7

Final answer

x <= 8/7

Answer:

Option #1, 3 and 4

Step-by-step explanation:

7x - 1 <= 7

Let's try them one by one:

1)

x <= -1

-7 - 1 = -8 is less than or equal to 7: True

There could be multiple answers, so let's do the other ones:

2)

x <= 4

28 - 1 = 27 <= 7: False

3)

x <= 1

7 - 1 = 6 <= 7: True

4)

x >= -1

-7 - 1 <= 7

-8 <= 7: True

Therefore, #1, 3, and 4 are correct.

Hope this helped!

J and K have values of 0.38 and 0.50, respectively with sampling distribution for the sample variance.

Given data;

The sampling distribution for the sample variance using the distribution;

(I) To find the value of J,

(II) To find the value of K,

We know;

⇒ ∑P(s²) = 1

⇒ J + K + 0.12 = 1

   J + K = 0.88

   K = 0.88 - K

Now K = 0.5;

J = 0.88 - 0.5

  = 0.38

Therefore, the values of J and K are 0.38 and 0.50 respectively.

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Answer:

oh come on hmm

.....The conversion factor to convert cups to liters is 0.237

Step-by-step explanation:

Given : A table showing conversions for common units of capacity.

                               Units of  capacity  

Customary System Units                             Metric System Units

         1 gallon                                                           3.79 liters

         1 quart                                                            0.95 liters

          1 pint                                                              0.473 liters

          1 cup                                                              0.237 liters

We have to find the  conversion factor to convert cups to liters.

Consider the given  table.

Since, given One cup is equal to 0.237 liters.

So , the conversion factor to convert cups to liters is 0.237

For example to convert 10 cups to liters, we can multiply the number of cups by 0.237 to get cups in liters.

That is 10 cup = 10 × 0.237 = 2.37 liters.

Thus, 10 cups is equal to 2.37 liters.

Hence, The conversion factor to convert cups to liters is 0.237

Answer:

y−5=2⋅(x−2)

Step-By-Step solution

Graph B is the answer