Use the equation to complete an algebraic proof that proves the answer is x = 7/6. Write your proof in your journal and upload your answer. You will be awarded 5 points for the statements and 5 points for the reasons.

I need the algebraic proofs please!!!

Answer:

cot x

Step-by-step explanation:

using the identities

csc x = [tex]\frac{1}{sinx}[/tex]

sin([tex]\frac{\pi }{2}[/tex] - x) = cos x

then

csc x × sin ([tex]\frac{\pi }{2}[/tex] - x)

= [tex]\frac{1}{sinx}[/tex] × cosx

= [tex]\frac{cosx}{sinx}[/tex]

= cot x

Answer:

4/9

Step-by-step explanation:

.44444.. = 4/9

0.nnnnnnnn.... = n/9

0.mnmnmnmnmn.... = mn/99

and so on

The new mixture exists 56.5% peanuts.

The first batch of 9 lb of mixed nuts possesses 40% peanuts.

This means the quantity of peanuts exists:

9 [tex]*[/tex] 40/100 = 3.6 lb

The second batch of 9 lb of mixed nuts possesses 73% peanuts.

This means the quantity of peanuts exists:

9 [tex]*[/tex] 73/100 = 6.57 lb

The total quantity of peanuts in the mix exists

3.6 lb + 6.57 lb = 10.17 lb

There exist 9 lb + 9 lb = 18 lb of mix.

Therefore, the percent of peanuts in the mix exists:

10.17 / 18 [tex]*[/tex] 100 = 56.5%

The new mixture exists 56.5% peanuts.

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The area of a rectangle is the amount of space it would cover on a 2-Dimensional plane. The required value of the width is 25 feet.

A rectangle is a plane shape with equal opposite sides. Its area can be determined by;

Area of a rectangle = length x width

Considering the given question, let the length of the plot be represented by l and its width as w. Given that the width of the plot should be longer than its length by 5, then we have;

w = l + 5

But,

Area of the plot = length x width

500 = l x (l + 5)

       = [tex]l^{2}[/tex] + 5l

This implies that,

500 = [tex]l^{2}[/tex] + 5l

[tex]l^{2}[/tex] + 5l - 500 = 0

Applying the quadratic formula, we have;

l = (-b  ± [tex]\sqrt{b^{2} - 4ac}[/tex]) / 2a

a = 1, b = 5, c = -500

= (-5  ±  [tex]\sqrt{5^{2} - (4*1*-500)}[/tex]/ 2

 = (-5  ± 45) / 2

l =   (40) / 2 OR l =  (-50) / 2

l = 20 OR l = - 25.5

So that,

l = 20

Therefore, the length of the plot is 20 feet.

Thus the width of the plot can be determined as;

w = l + 5

   = 20 + 5

w = 25

The width of the plot is 25 feet.

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Answer:

22, 23

Step-by-step explanation:

4x + 3(x + 1) = 157

4x + 3x + 3 = 157

7x + 3 = 157

7x = 154

x = 22

Step-by-step explanation:

1st : Vector translation.

a vector -8j ( 0 , -8 ) helped translate (x , y) => (x , y - 8)

2nd : rotation.

The only rotation that results in (-x , -y) is pi rotation.

formula : (x , y -8) => ( xcos(pi) - ysin(pi) , xsin(pi) + ycos(pi) )

substitute x & y-8 into x & y respectively of the formula above.

Answer:

2√(133)

Step-by-step explanation:

Triangle 1 = 8, 12, ?

triangle 2 = 18, x, ?

we have to find value of x which is a hypotenuse

a² + b² = c²

8² + 12² = 64 + 144 = √208 = 14.4222051019

x = 14.4222051019² + 18²

= 208 + 324

= 532

x = √532 = 2√(133)

Based on the orbital period of the planet in earth years, and the distance it is rotating, the mass of the star that the planet is orbiting is 3 solar masses.

Because the sun is so heavy, it needed to have a special unit that could adequately reflect this mass.

Solar masses was the term that scientists came up with. In terms of the Earth's mass, a single solar mass means that the body is 333,000 times the mass of the Earth.

When given the orbital period of a planet, and the distance it is orbiting around a sun, you can find the solar mass by the formula:

= Distance planet is rotating³ - Orbital period²

Solving gives:

= 1.2³ / 0.76²

= 2.99

= 3 solar masses

In conclusion the mass of the star is 3 solar masses

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Answer:

3 solar masses

Step-by-step explanation:

just did it and got it right

======================================================

Explanation:

To go from gallons to fluid ounces (abbreviation fl oz), we multiply by 128

For example, 2 gallons becomes 2*128 = 256 fl oz as shown in the table.

Another example: 3 gallons = 3*128 = 384 fl oz.

Therefore, 6 gallons would be 6*128 = 768 fl oz.

To go in reverse, from fl oz to gallons, we divide by 128.

Using the normal distribution, it is found that:

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given, respectively, by:

[tex]\mu = 83, \sigma = 6[/tex]

The proportion of students, with a grade of at least 70 is one subtracted by the p-value of Z when X = 70, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70 - 83}{6}[/tex]

Z = -2.17

Z = -2.17 has a p-value of 0.015.

1 - 0.015 = 0.985 = 98.5% of students have at least a 70.

The proportion of students, with a grade of at least 80 is one subtracted by the p-value of Z when X = 80, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{80 - 83}{6}[/tex]

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

1 - 0.3085 = 0.6915 = 69.15% of students have an 80 or above.

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Step-by-step explanation:

x^2 +4x +4 -7 is

y=x^2+4x-3

Answer: g(x)=(x+2)²-4.

Step-by-step explanation:

g(x)=f(x)+3

g(x)=(x+2)²-7+3

g(x)=(x+2)²-4.

Using proportions, it is found that 68 more people prefer vanilla than do strawberry.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Researching this problem on the internet, it is found that, out of 400 people:

Hence the amounts are:

The difference is:

140 - 72 = 68.

68 more people prefer vanilla than do strawberry.

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The profit is Rs.4800.

When, in a transaction, the selling price is greater than the cost price, it means we earn a profit. It is calculated with the help of the formula: Profit = Selling price - Cost price.

Given that,

S.P =$6000

C.P = $6000

If, 1$ = Rs.115.4 (in cost price)

  1$ = Rs.116.20 (in selling price)

Then,

C.P =  Rs. 115.40×6000

S.P = Rs.  116.20×6000

Then,

Profit = S.P-C.P

         =  116.20×6000 -115.40×6000

         =  (116.20-115.40)×6000

         = 0.80×6000

         =  Rs.4800

Hence, The profit is Rs.4800.

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The equivalent expression to [tex](k o h)(x)[/tex]is [tex]\frac{1}{5 + x}[/tex]

Therefore  [tex](k o h)(x) = \frac{1}{5 + x}[/tex]

Given that the functions h is defined by h(x)=5+x

and k is defined by k (x) = [tex]\frac{1}{x}[/tex]

To find the composition of k and h that is: (k o h) (x)

Therefore

k (h(x)) = k (5+x)

k (h(x)) = [tex]\frac{1}{5+ x}[/tex]

The equivalent expression to is [tex]\frac{1}{5+ x}[/tex]

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Answer: H

Step-by-step explanation:

[tex]9(-3)=-27[/tex], which is an integer.

Answer: Mean = 23

Step-by-step explanation:

Given information:

35, 40, 12, 16, 25, 10

Given formula:

[tex]Mean~=~\frac{Sum~of~terms}{Number~of~terms}[/tex]

Substitute values into the formula

[tex]Mean~=~\frac{35~+~40~+~12~+~16~+~25~+~10}{6}[/tex]

Combine like terms

[tex]Mean~=~\frac{75~+~28~+~35}{6}[/tex]

[tex]Mean~=~\frac{103~+~35}{6}[/tex]

[tex]Mean~=~\frac{138}{6}[/tex]

Simplify the fraction

[tex]\Large\boxed{Mean=23}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The solution of the given logarithmic equation is x = 28.1

Here we have the logarithmic equation:

4*ln(x - 8) = 12

And we want to solve this for x.

Remember the relations:

[tex]ln(e^x) = x\\e^{ln(x)} = x[/tex]

First, we divide both sides by 4:

[tex]ln(x - 8) = 12/4 = 3[/tex]

Then, if we apply the exponential equation to both sides of our equation, we get:

[tex]e^{ln(x - 8)} = e^{3}\\\\x - 8 = e^3\\\\x = e^3 + 8 = 28.1[/tex]

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The matrix for the linear transformation for which rotates every vector in r2 is [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex].

In this question,

The angle is -π/3 = -60°

Clockwise rotations are denoted by negative numbers.

Matrix for counter-clockwise direction for an angle α is

[tex]\left[\begin{array}{cc}cos\alpha &-sin\alpha \\-sin\alpha &cos\alpha \end{array}\right][/tex]

Then, matrix for clockwise direction for an angle α

Put α = -α in the above matrix,

⇒ [tex]\left[\begin{array}{cc}cos(-\alpha) &-sin(-\alpha) \\-sin(-\alpha) &cos(-\alpha) \end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{cc}cos\alpha &sin\alpha \\sin\alpha &cos\alpha \end{array}\right][/tex]

Now substitute α = 60°

Then matrix becomes,

⇒ [tex]\left[\begin{array}{cc}cos60 &sin60 \\sin60 &cos60 \end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex]

Hence we can conclude that the matrix for the linear transformation for which rotates every vector in r2 is [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex].

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The linear function of best fit for the information on the graph is:

f(x) = 200x + 100.

A linear function is modeled by:

y = mx + b

In which:

The function on the graph goes through points (3,700) and (4,900), that is, when x changes by 1, y changes by 200, which means that the slope is of 200 and the function is:

f(x) = 200x + b.

When x = 3, f(x) = 700, hence we use it to find b.

700 = 200(3) + b

b = 100.

Hence the function is:

f(x) = 200x + 100.

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To estimate that table given in Option (4) will define the quadratic relationship.

Therefore, the table of Option (5) will describe the quadratic relationship.

By estimating the second difference, if the second difference in a table exists equivalent, the table will define the quadratic relationship.

In the given option, we estimate that table given in Option (4) will define the quadratic relationship.

x       y      I st difference       II nd difference

0      4           -                               -

1      -4      -4 - (4) = -8                    -  

2     -4      -4 - (-4) = 0                0 - (-8) = 8

3      4       4 - (-4) = 8                 8 - 0 = 8

The second difference between the terms in y exists exactly as 8.

Therefore, the table of Option (4) means the quadratic relationship.

Similarly, in Option (5) we will estimate the second distinction of y terms.

x        y             I st difference       II nd difference

0      -4                     -                          -

1       -8               -8 - (-4) = -4              -

2     -10             -10 - (-8) = -2      -2 - (-4) = 2  

3     -10             -10 - (-10) = 0       0 - (-2) = 2

Here the second difference exists identical to 2.

Therefore, the table of Option (5) will describe the quadratic relationship.

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Her business will break even when she contains sold 1740 bottles of her lotion.

Given: She invests $15,225 in equipment to manufacture and package her lotion each bottle costs $3.25 to manufacture and sells for $12.

"Break even" occurs when Revenue = Costs.

($12/bottle)x = $15225 + ($3.25)x

Simplifying the above equation, we get

$8.75x = $15225

Diving both sides of the equation by 8.75, we get

$8.75x/8.75 = $15225/8.75

x = 1740 bottles

Therefore, the value of x = 1740 bottles.

Her business will break even when she contains sold 1740 bottles of her lotion.

Therefore, the correct answer is option b. 1740 bottles.

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Using proportions, the value of y is of 100º.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In a circle, the measure of an arc is twice the measure of it's equivalent internal angle. The internal angle is of 50º, hence the measure of the arc, given by y, is found as follows:

y = 2 x 50º = 100º.

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Answer:

90ft

Step-by-step explanation:

43,560ft² = L × l

43,560ft² = 484ft × l

43,560ft² ÷ 484ft = l

l = 90ft

0.0016

reduce expression if possible by canceling the common factors

By direct comparison and definition of line segment  we notice that the point (x, y) = (- 6, 0) lies on the line segment AB as each AP is a multiple of former. (Correct choice: C)

According to linear algebra, a point lies in a line segment if its vector is a multiple of the vector that generates the line segment itself, that is:

AB = k · AP        (1)

The vector that generates the line segment is:

AB = (2, 6) - (- 2, 3)

AB = (4, 3)

And the vectors related to each point are:

Case A

AP = (- 2, 12) - (- 2, 3)

AP = (0, 9)

Case B

AP = (6, 12) - (- 2, 3)

AP = (8, 9)

Case C

AP = (- 6, 0) - (- 2, 3)

AP = (- 4, - 3)

Case D

AP = (- 6, 6) - (- 2, 3)

AP = (- 4, 3)

By direct comparison and definition of line segment  we notice that the point (x, y) = (- 6, 0) lies on the line segment AB as each AP is a multiple of former. (Correct choice: C)

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Answer:

Step-by-step explanation:

Comment

The sum of the remote interior angles = The exterior angle not connected to them

What that means is that

<C + <D = <KEB

Givens

<C = 60

<KED = <C + <D

Solution and answer

<KED = <C + <D                      Substitute the givens into this equation

100 = 60 + <D                         Turn this around

<60 + <D = <100                     Answer first equation

Subtract 60 from both sides

<60-<60 + <D = <100 - 60

<D = <40                                   Answer second Equation

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

Given:

▪ [tex]\longrightarrow \sf{KED = 100^\circ}[/tex]

▪ [tex]\longrightarrow \sf{\angle ECD = 60^\circ}[/tex]

[tex]\leadsto[/tex] According to the triangle angle sum theorem, the sum of interior angles of a triangle is 180°.

[tex]\leadsto[/tex] We can find the value of ∠E if we know the sum of two supplementary angles is equal to 180°

[tex]\longrightarrow \sf{m \angle E+ m \angle K=180^\circ}[/tex]

[tex]\longrightarrow \sf{m \angle E+ 100^\circ =180^\circ}[/tex]

[tex]\longrightarrow \sf{m \angle E= 80^\circ}[/tex]

As we find the value of ∠E, we can replace it in the initial formula. [tex]\downarrow[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\bm{m \angle C + m \angle \boxed{\bm D} = m \angle \boxed{\bm E}}[/tex]

[tex]\bm{m \angle D= \boxed{\bm{ 40^\circ}}}[/tex]

By working with percentages, we will see that they served 56 salmon filets.

Here we know that the restaurant served 70 specials in total, such that 80% of these were salmon filets.

So we just need to calculate what is the 80% of 70.

This is just given by:

70*(80%/100%) = 70*0.8 = 56

This means that they served 56 salmons filet.

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The dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.

Let the dimension of the rectangle be x and y m.

According to the given question.

The area of the rectangle is 1728 square meter.

⇒ x × y = 1728

⇒ x = 1728/y

Since, the perimeter of the rectangle is the sum of the length of its boundary.

Therefore,

Perimeter of the recatngle with dimensions x and y is given by

Perimeter of the rectangle, P = 2(x + y)

⇒ P = 2(1728/y + y)

⇒ P = 3456/y + 2y

Differentiate the above equation with respect to y

⇒ [tex]P^{'} = -\frac{3456}{y^{2} } + 2[/tex]

For the minimum(small) perimeter equate the above equation to 0.

⇒ [tex]-\frac{3456}{y^{2} } + 2 = 0[/tex]

⇒ [tex]2y^{2} =3456[/tex]

⇒ [tex]y^{2} = \frac{3456}{2}[/tex]

⇒ y^2 = 1728

⇒ y = √1728

⇒ y = 41.56 m

Therefore,

x = 1728/41.56

⇒ x = 41.57 m

Hence, the dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.

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