Show all work to calculate the following exactly, include any reference triangle (a) For x > 0, if y = arccot(3x/8), find cos(y). (b) Show HOW to use your TI to approximate: sec^-1 (67). Write a sentence to tell Explain what the answer tells us. (c) Show how to find the exact value of cos^-1(cos(-5phi/6)). Show reference triangles for support:

Answer:

= 42m²

Step-by-step explanation:

The ratio of two similar hexagons is 3:7

where the smaller correspond to 3

And

the bigger correspond to 7

where the area of the smaller haxagon is 18

so if 3 = 18m²

then 7 = ?

therefore

[tex] \frac{7}{3} \times 18 \\ = 42 {m}^{2} [/tex]

therefore the area of the bigger hexagon is 42m²

Lina hops linearly and Kavier hops exponentially

The equations of the functions are Lina: y = 2x + 3 and Kavier: y = 3(2)^x

Linear pattern

The table of values represent the given parameter

For Lina's distance from the tree, we can see that

As the hop increases by 1, the distance covered increases constantly by 2 feet

This represents a linear function

Exponential pattern

For Kavier's distance from the tree, we can see that

As the hop increases by 1, the distance covered doubles

This represents an exponential function

Lina Linear Function

From the question, we have the following parameters that can be used in our computation:

(0, 3) and (1, 5)

A linear function is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 3

Using the points, we have

m + 3 = 5

m = 2

So, we have

y = 2x + 3

Kavier Exponential Function

Here, we have

(0, 3) and (1, 6)

An exponential function is represented as

y = ab^x

Where

a = y when x = 0

So, we have

y = 3b^x

Using the points, we have

3b = 6

b = 2

So, we have

y = 3(2)^x

Hence, Kavier's equation is y = 3(2)^x

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The resulting polynomial in descending order is 11x7 + 5x6

To combine like terms and write the resulting polynomial in descending order, we need to first identify the like terms and then add or subtract their coefficients. Like terms are terms that have the same variable and the same exponent.

In this case, the like terms are 2x^(7) and 9x^(7).

We can combine these like terms by adding their coefficients:

2x^(7) + 9x^(7) = 11x^(7)

Now we have:

11x^(7) + 5x^(6)

Since the exponents are different, we cannot combine these terms.

Therefore, the resulting polynomial in descending order is 11x7 + 5x6

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An expression that shows the associative property has been applied to (6+8)+4 is 6+(8+4).

The associative property is a mathematical rule that states that the way numbers are grouped within an expression does not affect the final result. In other words, you can add or multiply numbers in any order, and the result will be the same.

This property is represented as (a+b)+c=a+(b+c) or (a*b)*c=a*(b*c).

In the given expression, (6+8)+4, the associative property can be applied by changing the grouping of the numbers. This can be done by moving the parentheses from the first two numbers to the last two numbers. The new expression would be 6+(8+4).

Therefore, an expression that shows the associative property has been applied to (6+8)+4 is 6+(8+4).

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Answer:

Step-by-step explanation:

There is no graph attached.  

Convert the English phrases into expressions:

1.  "A number (Let's call it x) is equal to the sum of half a second number (y) and 3"

2.  "The first number (x) is also equal to the sum of one-quarter of the second number (y) and 5"

Let's rewrite these in standard form:

x = (1/2)y+3

2x = y + 6

y = 2x - 6

and

x = (1/4)y + 5

4x = y + 20

y = 4x - 20

A plot of these two lines is attached.  Match them with the graph.

Answer:

Now, This number is neither a perfect square nor a perfect cube

So, 34 can be evaluated as, 34 = (30 + 4) (15 + 15 + 4)

Here is the evaluated form of 34.

Step-by-step explanation:

is of goggle btw so just change some of the words

Answer:

y - 8 ≤ -27

Step-by-step explanation:

The difference of y and 8 is less than or equal to -27

y - 8 ≤ -27

To solve this problem, we can use a system of equations. Let's represent the amount invested in stocks as x, the amount invested in bonds as y, and the amount invested in CDs as z.

The first equation we can create is the total amount invested:

x + y + z = 85000

The second equation is the difference between the amount invested in bonds and CDs:

y - z = 20000

The third equation is the total interest earned:

0.064x + 0.052y + 0.055z = 4780

We can use substitution to solve this system of equations. Let's rearrange the second equation to solve for y:

y = z + 20000

We can then substitute this value of y into the first equation:

x + (z + 20000) + z = 85000

Simplifying gives us:

x + 2z = 65000

Now, let's substitute the value of y into the third equation:

0.064x + 0.052(z + 20000) + 0.055z = 4780

Simplifying gives us:

0.064x + 0.107z = 3780

We can now use the first and third equations to solve for x and z. Let's rearrange the first equation to solve for x:

x = 65000 - 2z

We can then substitute this value of x into the third equation:

0.064(65000 - 2z) + 0.107z = 3780

Simplifying gives us:

4160 - 0.128z + 0.107z = 3780

Combining like terms gives us:

-0.021z = -380

Solving for z gives us:

z = 18095.24

We can now use this value of z to solve for y:

y = z + 20000 = 18095.24 + 20000 = 38095.24

And finally, we can use the value of z to solve for x:

x = 65000 - 2z = 65000 - 2(18095.24) = 28809.52

So, Maricopa Success invested $28809.52 in stocks, $38095.24 in bonds, and $18095.24 in CDs.

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Answer:

In order to pay Jimmy's credit card debt off in the next 12 months, then the total minimum credit card payment will be $411.25.

Step-by-step explanation:

The equation (bd)/(b-d) = c can be used to determine how many hours a day the remaining women must work in order to produce the same number of articles each day, when some of the women have been released.

An equation is an expression used to relate two or more quantities, usually by using mathematical operators such as addition, subtraction, multiplication and division. An equation typically has an equal sign (=) as its central element, with the left and right sides of the equation representing the two sides of the equation.

The answer to this question can be determined by using the following equation: (bd)/(b-d) = c. This equation is a simple ratio that takes into account the number of hours the women work per day (b), the number of women released (d), and the number of articles produced each day (c).

For example, if a factory had 10 women working 8 hours a day and produced 100 articles each day, and 5 of those women were released, then the equation (8 x 5) / (8-5) = 100 would determine that the remaining women must work 12.5 hours per day in order to produce the same number of articles.

In conclusion, the equation (bd)/(b-d) = c can be used to determine how many hours a day the remaining women must work in order to produce the same number of articles each day, when some of the women have been released.

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It's not a. If I expanded "a" I would get = (9x - 64y)(9x - 64y) hence the square root. If I did FOIL I would not get the correct answer. "A" is essentially "b" written differently.

Answer:

(3x + 8y) • (3x - 8y)

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the graph of the parent function is shifted 7 units up and is steeper than the parent function, which of these could represent the function? answer choices.

Answer:

P(4, tail) = 1/12

Step-by-step explanation:

The probability of a particular outcome when all possible outcomes are equaly likely, is the number of "desired" oucomes divided by the total number of possible outcomes.

In your case, there are 12 possible outcomes (you can count them, or calculate 6 for the dice times 2 for the coin). Only one of them is "desired", namely the combination of 4 and a tail. Hence 1 divided by 12.

Stella's family traveled 2/5 of the total distance to her aunt's house on Sunday.

What is distance ?

Distance is a physical quantity that refers to the length between two points or the amount of space between them. It is typically measured in units such as meters, kilometers, miles, or feet.

Stella's family traveled 3/10 of the distance to her aunt's house on Saturday. Therefore, the remaining distance they had to travel was:

1 - 3/10 = 7/10

On Sunday, they traveled 4/7 of the remaining distance. Therefore, the total distance traveled on Sunday is:

(4/7) x (7/10) = 4/10

Simplifying the fraction 4/10 gives 2/5.

Therefore, Stella's family traveled 2/5 of the total distance to her aunt's house on Sunday.

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Our assumption is false

We can prove this statement by contradiction. Suppose a > b and c > 0 but ac < bc.

Since a > b, then a - b > 0. Multiplying both sides by c > 0 gives (a - b)c > 0.

We can then add bc to both sides to get (a - b)c + bc > bc.

Since we assumed that ac < bc, then (a - b)c < 0, and thus (a - b)c + bc < bc, which contradicts the previous result.

Therefore, our assumption is false, and we can conclude that for a, b, and c ∈ Z, a > b and c > 0 =⇒ ac ≥ bc.

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Answer:

132, 115

Step-by-step explanation:

For the first one:

Bsc its parallelogram angle x is 132

Second one:

x + 108 + 68 + 59 = 360

x + 235= 360

x = 360 - 235

x = 115

The value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid is (2a)*(2b)*(2c).

To find the value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid, we need to use the formula for the volume of a parallelopiped. The formula is:

V = l*w*h

Where V is the volume, l is the length, w is the width, and h is the height.

Since we are looking for the largest rectangular parallelopiped, we need to maximize the volume. This can be done by finding the maximum values of the length, width, and height.

The maximum values of the length, width, and height can be found by using the semi-axes of the ellipsoid. The semi-axes of the ellipsoid are given by:

a = √(x^2/a^2 + y^2/b^2 + z^2/c^2)

Where a, b, and c are the semi-axes of the ellipsoid, and x, y, and z are the coordinates of the point on the surface of the ellipsoid.

The maximum values of the length, width, and height can be found by setting the derivatives of the volume with respect to x, y, and z to zero:

∂V/∂x = 0

∂V/∂y = 0

∂V/∂z = 0

Solving these equations will give us the maximum values of the length, width, and height. Once we have these values, we can plug them into the formula for the volume of a parallelopiped to find the largest volume.

The largest volume of the rectangular parallelopiped that can be inscribed in the ellipsoid is given by:

V = (2a)*(2b)*(2c)

Where a, b, and c are the semi-axes of the ellipsoid.

Therefore, the value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid is (2a)*(2b)*(2c).

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The algebraic expression represents this word description is 7(x - 10) (option D).

One way to approach this problem is to break down the phrase into its components and then use mathematical symbols to represent them.

The phrase contains the word "product," which tells us we need to multiply two quantities.

The first quantity is the number seven, and the second quantity is the difference between a number and ten.

To represent the difference between a number and ten, we can use the variable x to stand for the unknown number.

Then, the difference between x and ten can be expressed as (x - 10).

Putting it all together, the expression that represents the product of seven and the difference between a number and ten is 7(x - 10).

Hence the correct option is (D).

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Complete Question:

Which algebraic expression represents this word description?

The product of seven and the difference between a number and ten

A. 10-7x

B. 7(10 - x)

C. 7x-10

D. 7(x - 10)

Answer:

-4.4166

Step-by-step explanation:

-23/3+(-11/2)+35/4

-24/3-11/2+35/4

use bodmas

addition first then subtract and u find your LCM.

11/2+35/4=57/4 or 14 1/4

LCM=4

-23/3-57/4=-263/12 or -21 11/12.

LCM=12

final answer= -21 11/12.

-14w + 35  is the  simplified answer of  (2w-5)(-7).

The distributive property states that for two numbers a and b, a(b+c) = ab + ac. This means that multiplying a number by a sum is the same as multiplying each number in the sum by the original number.

To simplify the expression (2w-5)(-7) using the distributive property, we need to multiply each term inside the parentheses by -7.

The distributive property states that a(b + c) = ab + ac. In this case, a = -7, b = 2w, and c = -5.

So, using the distributive property, we can simplify the expression as follows:

(2w-5)(-7) = (-7)(2w) + (-7)(-5)

= -14w + 35

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the real solutions to this equation are x = 2√2 and x = -2√2.

Solution:

(a) -n + √(6n + 19) = 2

To find the solution algebraically, we need to isolate the radical on one side of the equation and then square both sides to get rid of the radical.

-n = 2 - √(6n + 19)

(-n - 2)^2 = (2 - √(6n + 19))^2

n^2 + 4n + 4 = 4 - 4√(6n + 19) + 6n + 19

n^2 - 2n - 19 = -4√(6n + 19)

(n^2 - 2n - 19)^2 = (-4√(6n + 19))^2

n^4 - 4n^3 - 18n^2 + 76n + 361 = 96n + 304

n^4 - 4n^3 - 114n^2 + 76n + 57 = 0

This is a quartic equation that can be solved using the Rational Root Theorem or by factoring. However, this equation does not have any real solutions. Therefore, there are no real solutions to this equation.

(b) x^4 - 20x^2 + 64 = 0

This equation can be factored as:

(x^2 - 8)^2 = 0

x^2 - 8 = 0

x^2 = 8

x = ±√8

x = ±2√2

Therefore, the real solutions to this equation are x = 2√2 and x = -2√2.

Remember to check your solutions by plugging them back into the original equation and seeing if they make the equation true.

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The quadrilateral formed from the points P(7, -3), Q(0,3), R(-9,5), and S(-2,-1)  is a rhombus.

To find the desired slopes and lengths, we can use the slope formula and the distance formula. The slope formula is (y₂ - y₁)/(x₂ - x₁) and the distance formula is √((x₂ - x₁)² + (y₂ - y₁)²).

Slope of PQ = (3 - (-3))/(0 - 7) = 6/(-7) = -6/7
Slope of QR = (5 - 3)/(-9 - 0) = 2/(-9) = -2/9
Slope of RS = (-1 - 5)/(-2 - (-9)) = (-6)/(7) = -6/7
Slope of SP = ((-3) - (-1))/(7 - (-2)) = (-2)/(9) = -2/9

Length of PQ = √((0 - 7)² + (3 - (-3))²) = √(49 + 36) = √85
Length of QR = √((-9 - 0)² + (5 - 3)²) = √(81 + 4) = √85
Length of RS = √((-2 - (-9))² + ((-1) - 5)²) = √(49 + 36) = √85
Length of SP = √((7 - (-2))² + ((-3) - (-1))²) = √(81 + 4) = √85

Since the opposite slopes are equal and all of the lengths are equal, the quadrilateral is a rhombus.

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Answer:

380

Step-by-step explanation:

To find out what number is 600% of another number, we need to divide that number by 600% (or 6).

So:

x = 2,280 ÷ 6

x = 380

Therefore, 600% of 380 is equal to 2,280.

Hope this helped !

Answer:     7 .

Step-by-step explanation:

The middle term is, +7x its coefficient is 7 . Step-2 : Find two factors of -8 whose sum equals the coefficient of the middle term, which is

The areas of the triangle with length of two side are 3cm and 4cm and the angle included between these sides is 30° is equals to the (3√3/2) cm².

Area is defined as a measure the space inside a two-dimensional shapes, like square, triangle, etc. Area is denoted by square units, like cm², m², etc. Area of triangle is equals to the (1/2)× base length × height. We have a triangle with side lengths. Let triangle be named as ABC. Let

Base length of triangle, BC = 3 cm

Other side of triangle ABC, AC = 4 cm

Angle included between these sides is

= 30°

Now, the above assumption results a right angled triangle ABC, with base 3 cm and hypothenuse 4 cm. We have to calculate the area of triangle ABC. First we determine the height of ∆ABC. Using the Trigonometric functions,

tan 30° = AB/BC

=> tan 30° = AB/3

=> AB = 3 tan 30°

=> AB = 3(1/√3) = √3 cm

Now, area of triangle ABC = (1/2)× base length × height.

= (1/2) × √3 cm × 3 cm

= 3√3/2 cm²

Hence, the required area is 3√3/2 cm².

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Answer:

Réponse :Explications étape par étapea) Le vecteur AC(xc-xa;yc-ya)vecteur AC(-6;-3

Step-by-step explanation:

Les coordonnées d'un vecteur dans un r.o.n. décrivent le déplacement qu'il représente. Ainsi, un déplacement de « 3 ...

The identity \[ \frac{1}{\tan x(1+\cos 2 x)}=\csc 2 x \] is proved.

To prove the identity \[ \frac{1}{\tan x(1+\cos 2 x)}=\csc 2 x \], we can use the Double Angle Formula for Cosines and the Pythagorean Identity.

Using the Double Angle Formula for Cosines, we get:
$\cos2x = 2\cos^2 x - 1$

We can then substitute this into the original identity and simplify:
$\frac{1}{\tan x(1+\cos 2 x)}=\frac{1}{\tan x(1+2\cos^2 x - 1)}$

Using the Pythagorean Identity, $\cos^2 x + \sin^2 x = 1$, we get:
$\frac{1}{\tan x(1+\cos 2 x)}=\frac{1}{\tan x(\sin^2 x)}$

Using the inverse tangent function, $\tan^{-1}x = \frac{\pi}{2}-\sin^{-1}x$, and since $\sin 2x = 2 \sin x \cos x$, we can rewrite this as:
$\frac{1}{\tan x(1+\cos 2 x)}=\frac{1}{2 \sin x \cos x}$

Finally, using the definition of cosecant, $\csc x = \frac{1}{\sin x}$, we get:
$\frac{1}{\tan x(1+\cos 2 x)}=\csc 2 x$

Therefore, the identity \[ \frac{1}{\tan x(1+\cos 2 x)}=\csc 2 x \] is proved.

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The concession stand made 18 fewer cups of coffee than cups of hot chocolate.

To find out how many fewer cups of coffee they made than cups of hot chocolate, we need to add together the number of cups of hot chocolate with marshmallows and the number of cups without marshmallows:

20 cups + 15 cups = 35 cups of hot chocolate

Now, we can subtract the number of cups of coffee from the number of cups of hot chocolate to find out how many fewer cups of coffee they made:

35 cups - 17 cups = 18 cups

So, the concession stand made 18 fewer cups of coffee than cups of hot chocolate.

In conclusion, the concession stand made 18 fewer cups of coffee than cups of hot chocolate.

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Answer:

Step-by-step explanation:

The volume of the parallelepiped determined by the vectors u, v, and w is 20.

To calculate the volume of the parallelepiped determined by the vectors u, v, and w, we need to use the scalar triple product. The scalar triple product of three vectors is defined as the dot product of one vector with the cross product of the other two vectors. In this case, the volume of the parallelepiped is given by:

Volume = |u . (v x w)|

Where "." represents the dot product and "x" represents the cross product.

First, let's calculate the cross product of v and w:

v x w = (2i + k) x (4j) = 8k - 4i

Next, let's take the dot product of u and the result of the cross product:

u . (v x w) = (i - 2j + 3k) . (8k - 4i) = -4 + 24 = 20

Finally, we take the absolute value of the result to get the volume of the parallelepiped:

Volume = |20| = 20

Therefore, the volume of the parallelepiped determined by the vectors u, v, and w is 20.

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