Use identities to solve each of the following. Rationalize denominators when applicable. See Examples 5-7. 65. Find cos tetha, given that sin tetha = 3/5 and tetha is in quadrant II. 66. Find sin tetha, given that cos tetha = 4/5 and tetha is in quadrant IV. 67. Find csc tetha, given that cot tetha = -1/2 and tetha is in quadrant IV.

The coordinates of the image of EB are (0, -1) and (-6, 18).

Dilation is a process for creating similar figures by changing the dimensions.

The center of dilation is given as (3, -1) and the scale factor is 3.

The distance between the center of dilation and point E is:

d = √((3-2)² + (-1-(-1))²) = 1

The distance between the center of dilation and point B is:

d = √((3-0)² + (-1-5)²) = sqrt(65)

To find the new distance, we multiply the distance by the scale factor:

For point E: 3 × 1 = 3

For point B: 3 × √(65)

Now, we can find the coordinates of the image:

For point E:

x = 3 × (2 - 3) + 3 = -3 + 3 = 0

y = 3 × (-1 -(-1)) -1 = 0 - 1 = -1

So the image of E is (0, -1).

For point B:

x = 3 × (0 - 3) + 3 = -9 + 3 = -6

y = 3 × (5 -(-1)) -1 = 18

So the image of B is (-6, 18).

Therefore, the coordinates of the image of EB are (0, -1) and (-6, 18).

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Amount of paint that should be purchased to apply one coat of paint to the side of the building is 12 gallons.

Area is the amount of space occupied by a two-dimensional shape. That is, it is a quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is the square unit, commonly expressed in square inches, square feet, and so on.

Given,

length of the wall  = 105 feet

height of the wall = 35 feet

Area of the wall

= length × height

= 105 × 35

= 3675 square feet

One gallon paints 317 square feet

Number of gallons to paint 3675 square feet

= 3675/317

= 11.59 ≈ 12

Hence, 12 gallons should be purchased to apply one coat of paint to the side of building.

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The function which represent the distance and time is y=6x-17.5.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here according to the given data, let us take to points to find linear function then,

[tex](x_1,y_1)=(0.5,3)[/tex] and [tex](x_2,y_2)=(1,6)[/tex].

Now using slope formula, m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> Slope m = [tex]\frac{6-3}{1-0.5} = \frac{3}{0.5}[/tex] = 6

Now using equation formula , [tex]y-y_1=m(x-x_1)[/tex] then,

=> y-0.5=6(x-3)

=> y-0.5=6x-18

=> y=6x-18+0.5

=> y=6x-17.5

Hence the function which represent the distance and time is y=6x-17.5.

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Step-by-step explanation:

Inverse of a Function.

To find the inverse of the function f(x) = √(x+7), we need to interchange the roles of x and y and solve for y.

Let y = f(x) = √(x+7)

To find the inverse, we need to solve for x in terms of y.

Step 1: Square both sides of the equation to eliminate the square root:

y^2 = x + 7

Step 2: Solve for x:

x = y^2 - 7

So the inverse of the function f(x) is:

f^(-1)(y) = y^2 - 7

We can also express the inverse in terms of x:

f^(-1)(x) = x^2 - 7

Note that we changed the variable from x to y, and from y to x, when expressing the inverse function.

not completely sure but i think you times the x and y numbers then draw a graph of the units

Answer:

First, we need to convert the width of the table from inches to feet to ensure that the units match. There are 12 inches in a foot, so:

42 inches ÷ 12 inches/foot = 3.5 feet

Let the length of the table be L feet. The perimeter is the sum of the lengths of all four sides of the rectangle, so:

2L + 2(3.5 feet) = 18 feet

Simplifying and solving for L:

2L + 7 feet = 18 feet

2L = 11 feet

L = 5.5 feet

Therefore, the length of the table is 5.5 feet.

Answer:

66

Step-by-step explanation:

the problem ask fr it draw out 2 rectangle

The lakefront makes angles of approximately 30 degrees and 120 degrees with the boundaries of 2.8 miles and 1.8 miles, respectively. The remaining angle is approximately 30 degrees.

To understand why, we can use the law of cosines to find the angles of the triangle. Let's call the length of the lakefront side "c", and the lengths of the other two sides "a" and "b". Using the law of cosines, we can find the angles:

[tex]cos A = (b^2 + c^2 - a^2) / (2bc)[/tex]

[tex]cos B = (a^2 + c^2 - b^2) / (2ac)[/tex]

[tex]cos C = (a^2 + b^2 - c^2) / (2ab)[/tex]

Plugging in the values we know, we get:

[tex]cos A = (1.8^2 + 4^2 - 2.8^2) / (21.84) = 0.283[/tex]

[tex]cos B = (2.8^2 + 4^2 - 1.8^2) / (22.84) = 0.717[/tex]

[tex]cos C = (2.8^2 + 1.8^2 - 4^2) / (22.81.8) = -0.283[/tex]

Using the inverse cosine function, we can find the angles:

A ≈ 75 degrees

B ≈ 43 degrees

C ≈ 62 degrees

Therefore, the lakefront makes angles of approximately 30 degrees (180 - 75 - 75) and 120 degrees (180 - 43 - 17) with the other two boundaries, and the remaining angle is approximately 30 degrees (180 - 120 - 30).

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The required fill-in-the-blanks are "same" and "line segments".

A linear relationship is a connection that takes the shape of a straight line on a graph between two distinct variables - x and y. When displaying a linear connection using an equation, the value of y is derived from the value of x, indicating their relationship.

Sometimes, the relationship between the variables doesn't stay the "same". This type of relation is called a piecewise linear relationship.

The graph of a piecewise linear relationship is made of non-overlapping "line segments", like this one.

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Step-by-step explanation:

cost1(t) = 100.25t + 6500

cost2(t) = 225.5t + 4496

both companies charge the same for the amount of t (tons), when both functions deliver the same result :

100.25t + 6500 = 225.5t + 4496

2004 = 125.25t

t = 2004/125.25 = 16

1. for the transport of 16 tons of sugar they both charge the same.

2. that charge is

100.25×16 + 6500 = $8,104

a) The cost function can be represented as C(x) = 6 + 1.180x for the first 20 units and C(x) = 6 + 1.180(20) + 0.806(x-20) for units over 20.

b) The total charge for using 15 units is C(15) = 6 + 1.180(15) = $23.70.

c) If the total charge is $73.93, we can use the cost function to solve for the number of units used.

The graph of the cost function will have a linear portion for the first 20 units and then another linear portion with a different slope for units over 20.

The average charge is $23.70/15 = $1.58 per unit.

Since the total charge is greater than the cost for the first 20 units, we know that more than 20 units were used. We can use the second part of the cost function to solve for x:

73.93 = 6 + 1.180(20) + 0.806(x-20)
73.93 = 30.6 + 0.806x - 16.12
73.93 - 30.6 + 16.12 = 0.806x
59.44 = 0.806x
x = 73.69 units
Therefore, 73.69 units were used.

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Answer:

You forgot the +- part when taking the square roots

Step-by-step explanation:

5 x^2  = -2

x^2 = -2/5

x = +- sqrt ( -2/5)       <==== note sqrt(-2/5)   NOT  sqrt (-2) / 5

x = ± i sqrt(2/5)

x^2 = 8

x = ±sqrt 8

x = ±2 sqrt (2)

The length of the diagonal is between 4 - 5 and closer to 4

First, we need to know the properties of a rectangle;

Given that the diagonal measures;

√18

Find the value

4. 2

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Answer:

Step-by-step explanation:

This expression isn't in simplest form. The terms 3x and 2x can be added, since they are like terms.

In simplest form, this expression would be 5x - 4.

Hope this helps!

The three cοrrect statements fοr the given circle are:

1)The radius οf the circle is 3 units.

2)The centre οf the circle lies οn the x-axis.

3)The radius οf this circle is the same as the radius οf the circle whοse equatiοn is x² + y² = 9.

All pοints in a plane that are at a specific distance frοm a specific pοint, the centre, fοrm a circle. In οther wοrds, it is the curve that a mοving pοint in a plane draws tο keep its distance frοm a specific pοint cοnstant. Circle's basic equatiοn is represented by:

(x-h)² + (y-k)² = r²

where the radius is r and the circle's centre's cοοrdinates are (h,k). Hence, we can quickly determine the equatiοn οf a circle if we knοw its radius and centre cοοrdinates.

The equatiοn οf the circle is given as:

x² + y²– 2x – 8 = 0

This can be cοnverted tο the standard fοrm.

Fοr that, we add and subtract 1 in the abοve equatiοn.

x² + y²– 2x – 8 +1 - 1  = 0

Rearranging,

x² – 2x + 1 + y²– 8 -1 = 0

(x - 1)² + y² = 8+1 = 9

Sο the equatiοn οf the circle in the standard fοrm is:

(x - 1)² + y² = 9

Nοw we will lοοk intο the given statements.

1) The radius οf the circle is 3 units.

This is true because radius = √9 = 3 units.

2) The centre οf the circle lies οn the x-axis.

The centre οf the given circle is (1,0).

Sο it dοes lie οn the x-axis.

3) The centre οf the circle lies οn the y-axis.

The centre is (1,0).

Sο this is nοt true.

4)The standard fοrm οf the equatiοn is (x – 1)² + y² = 3.

This is false.

5)  The radius οf this circle is the same as the radius οf the circle whοse equatiοn is x² + y² = 9

This is true because bοth equatiοns have 9 οn the right side οf the equatiοn.

Therefοre the three cοrrect statements fοr the given circle are:

1)The radius οf the circle is 3 units.

2)The centre οf the circle lies οn the x-axis.

3)The radius οf this circle is the same as the radius οf the circle whοse equatiοn is x² + y² = 9.

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Answer:

what about you read well and stop cheating

Check the picture below.

[tex]\tan(62^o )=\cfrac{\stackrel{opposite}{h}}{\underset{adjacent}{120}}\implies 120\tan(62^o )=h\implies 225.69\approx h[/tex]

Make sure your calculator is in Degree mode.

The height of the tower is 226 feet.

One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.

We have,

A tower with height labeled h.

The tower is the height of a right triangle with base of length 120 feet.

Now using Trigonometry

tan 62 = P / B

tan 62 = h / 120

h = 120 tan 62

h = 225.69

h = 226 feet

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To summarize, the correct answer is:
"If all features are scaled by the same factor λ∈R>0, i.e., xi is replaced by λxi for all i=1,…,N, then λβ^,β^,ξ^ solves SVM for penalty parameter λ2C."

The correct answer is "If all features are scaled by the same factor λ∈R>0, i.e., xi is replaced by λxi for all i=1,…,N, then λβ^,β^,ξ^ solves SVM for penalty parameter λ2C."

This is because scaling all features by the same factor λ does not change the relative importance of each feature in the classification problem. Therefore, the optimal solution for the scaled features will be the same as the optimal solution for the original features, but scaled by λ. The penalty parameter C will also need to be scaled by λ^2 to account for the scaling of the features.

To summarize, the correct answer is:
"If all features are scaled by the same factor λ∈R>0, i.e., xi is replaced by λxi for all i=1,…,N, then λβ^,β^,ξ^ solves SVM for penalty parameter λ2C."

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[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=196\pi \\ r=7 \end{cases}\implies 196\pi =\cfrac{\pi (7)^2 h}{3}\implies 196\pi =\cfrac{49\pi h}{3} \\\\\\ \cfrac{3}{49\pi }\cdot 196\pi =h\implies 12=h[/tex]

Number of years = 4

Hi there! To answer your question, Doug needs to deposit $2226.19 into a savings account that earns 2.9% interest compounded continuously. This amount was calculated using the formula P = Pe^rt, where P is the final amount Doug will have after 4 years, e is the natural logarithm constant (2.71828), r is the interest rate (2.9%), and t is the number of years (4).

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Answer: 36

Step-by-step explanation:

(a) The probability that X = n is 2^n-1 / 2^N - 1.

(b) ɸ(t) = E[2^tx] = ∑_{n=1}^N 2^tx P(X=n) = ∑_{n=1}^N 2^tx (2^n-1 / 2^N - 1) = (2^t / 2^N - 1) ∑_{n=1}^N 2^(n-1)t = (2^t / 2^N - 1) (2^Nt - 1) / (2^t - 1) = 2^Nt / (2^N - 1)

(c) The probability that X = n and Y = m is 2^(n-m-1) / 2^N - 1.

(d) This is the same as finding the probability that the difference between the maximum and minimum elements of a subset of {1,...,N} is k. If k = 0, then the only subsets with maximum and minimum elements differing by k are the single-element subsets, so P(W=k) = N / 2^N - 1. If k > 0, then there are (N-k) choices for the minimum element m and 2^(k-1) subsets of {m+1,...,m+k-1}, so P(W=k) = (N-k) 2^(k-1) / 2^N - 1.

To find the probability mass function of X, we need to find the probability that X = n for each n ∈ {1,...,N}. This is the same as finding the probability that the maximum element of a subset of {1,...,N} is n. There are 2^n-1 subsets of {1,...,n-1}, and each of these subsets can be combined with n to form a subset of {1,...,N} with maximum element n. Therefore, the probability that X = n is 2^n-1 / 2^N - 1.

To find the value of ɸ(t) for any t ∈ R, we need to compute the expected value of 2^tx. Using the formula for expected value, we get:

ɸ(t) = E[2^tx] = ∑_{n=1}^N 2^tx P(X=n) = ∑_{n=1}^N 2^tx (2^n-1 / 2^N - 1) = (2^t / 2^N - 1) ∑_{n=1}^N 2^(n-1)t = (2^t / 2^N - 1) (2^Nt - 1) / (2^t - 1) = 2^Nt / (2^N - 1)

To find the joint probability mass function of (X,Y), we need to find the probability that X = n and Y = m for each n,m ∈ {1,...,N}. If n = m, then the only subset of {1,...,N} with maximum element n and minimum element m is {n}, so P(X=n, Y=m) = 1 / 2^N - 1. If n ≠ m, then there are 2^(n-m-1) subsets of {m+1,...,n-1}, and each of these subsets can be combined with m and n to form a subset of {1,...,N} with maximum element n and minimum element m. Therefore, the probability that X = n and Y = m is 2^(n-m-1) / 2^N - 1.

To find the probability mass function of W = X - Y, we need to find the probability that W = k for each k ∈ {0,...,N-1}. This is the same as finding the probability that the difference between the maximum and minimum elements of a subset of {1,...,N} is k. If k = 0, then the only subsets with maximum and minimum elements differing by k are the single-element subsets, so P(W=k) = N / 2^N - 1. If k > 0, then there are (N-k) choices for the minimum element m and 2^(k-1) subsets of {m+1,...,m+k-1}, so P(W=k) = (N-k) 2^(k-1) / 2^N - 1.

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Answer:

144

Step-by-step explanation:

6*6=36

36*4=144

The values of the other trigonometric functions are:

sinα =√6/3

tanα=√2

cosecα=3/√6

secα=√3

cotα=1/√2

Given that cosα=√3/3

By definition cosine function , it is a ratio of adjacent side and hypotenuse.

So, adjacent side  =√3

Hypotenuse = 3

Let us find the third side of a triangle, by using pythagoras theorem.

√3²+x²=3²

3+x²=9

x=√6

So opposite side is √6.

Now let us find the other trigonometric values

Sinα= opposite side/hypotenuse

Sinα=√6/3

Tanα=opposite side/adjacent side

=√6/√3

Tanα=√2

Cosecα = hypotenuse/opposite side

=3/√6

Cosecα=3/√6

secα=hypotenuse side/adjacent side

=3/√3

=√3

secα=√3

cotα=Adjacent side/opposite side

=√3/√6

cotα=1/√2

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The compete question is given in attachment.

Answer:

Step-by-step explanation:

It seems like the problem is asking about a sequence of shapes rather than a sequence of matches, so I will assume that the correct information for the problem is:

Number of shapes:

n=1 n=2 n=3

m-4 m=7 m+2

i) Sequence table for the first six patterns:

Pattern number Number of shapes

1                               m-4

2                               m

3                               m+2

4                               m+6

5                               m+10

6                               m+14

ii) Formula for the number of shapes in terms of the pattern number:

From the table, we can see that the number of shapes used in each pattern is increasing by a constant amount of 4. Therefore, we can write the formula as:

Number of shapes = (pattern number - 1) * 4 + m

where m is the number of shapes in the first pattern.

iii) Number of shapes used in the 300th pattern:

To find the number of shapes used in the 300th pattern, we can use the formula and substitute pattern number = 300:

Number of shapes = (300 - 1) * 4 + m

Since we don't know the value of m, we can't determine the exact number of shapes. However, we do know that the number of shapes in the first pattern is either m-4, m, or m+2, depending on the value of m. If we assume the smallest possible value of m, which is 1 (since the number of shapes can't be negative), then the number of shapes in the 300th pattern would be:

Number of shapes = (300 - 1) * 4 + 1-4 = 1195

Therefore, if m = 1, then the number of shapes used in the 300th pattern is 1195. However, if m is greater than 1, then the number of shapes in the 300th pattern would be higher.

Answer:

every other 3

Step-by-step explanation:

The following are solutions to the given problems given f(x)=x²- 5x+7 and g(x)=3x² + 4x - 2;

(f- g)(x) = -2x² - 9x + 9

(g-f)(x) = 2x² + 9x - 9

(f + g)(x) = 4 x² - x + 5

A function can be defined as a relation between a set of inputs having one output each. In other words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain (range). A function is generally denoted by f(x) where x is the input.

here, we have,

The general mathematical representation of a function is y = f(x).

f(x)=x²- 5x+7

g(x)=3x² + 4x - 2

so, we get,

(f- g)(x) = x²- 5x+7 - (3x² + 4x - 2)

(f- g)(x) = x²- 5x+7 - 3x² - 4x + 2

(f- g)(x) = -2x² - 9x + 9

(g-f)(x) = 3x² + 4x - 2 - (x²- 5x+7)

(g-f)(x) = 3x² + 4x - 2 - x² + 5x - 7

(g-f)(x) = 2x² + 9x - 9

(f + g)(x) = x²- 5x+7 + 3x² + 4x - 2

(f + g)(x) = 4 x² - x + 5

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The mixed integer would be 2 3/4.

A mixed integer is a number that includes both a whole number and a fraction. For example, 2 1/2 is a mixed integer because it includes the whole number 2 and the fraction 1/2.

To rewrite a fraction as a mixed integer, you need to divide the numerator (the top number) by the denominator (the bottom number) and find the quotient and remainder. The quotient will be the whole number part of the mixed integer and the remainder will be the numerator of the fraction part. The denominator will stay the same.

For example, if you have the fraction 11/4, you can divide 11 by 4 to get a quotient of 2 and a remainder of 3. So the mixed integer would be 2 3/4.

Here are the steps to rewrite a fraction as a mixed integer:
1. Divide the numerator by the denominator.
2. Write the quotient as the whole number part of the mixed integer.
3. Write the remainder as the numerator of the fraction part of the mixed integer.
4. Keep the denominator the same.
5. Simplify the fraction if necessary.

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A correct 2-column proof include the following: B. table B.

In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Since line segment r is parallel to line segment s, the 2-column proof to justify that angle b and angle h are supplementary angles should be written as follows;

Statement                                             Reasons_________________

r║s                                                            Given

∠b ≅ ∠c                                                Vertical angles

∠c and ∠e are supplementary           Same-side interior angles

∠e ≅ ∠h                                                Vertical angles

∠b and ∠h are supplementary            Substitution

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No change is needed. The underlined text is grammatically correct and conveys the intended meaning clearly.

The underlined text "Taking up to six months, hikers who plan to complete the entire journey" means that the journey being referred to may take up to six months to complete, and it is being undertaken by hikers who have planned to complete the entire journey.

The text suggests that the journey is a long and challenging one that requires careful planning and preparation by the hikers.

Therefore, the correct answer is as given above. It could then be concluded that the underlined text does not need to change.

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To find the zeros, set the function equal to 0.  In other words, solve f(x)=0.

             f(x) = 0

x^2 +6x + 8 = 0

 (x+4)(x +2) = 0

x = -4 and x = -2

The vertex will happen when x = -b/2a:

    [tex]x=\dfrac{-6}{2(1)} = -3[/tex]
Then use this x-value of –3 to find the y-value of the vertex:

   y = (-3)^2 + 6(-3) + 8 = 9-18+8 = -1

The vertex is (-3,-1).

Side note: The x-value of the vertex can also be found by finding the average of the two zeros:

    (-4 + (-2)) / 2 = -6/2 = -3