Express cos S as a fraction in simplest terms.

Work Shown:

[tex]\frac{(1-\sin(\beta))(1+\sin(\beta))}{\cos^2(\beta)}\\\\\frac{1-\sin^2(\beta)}{\cos^2(\beta)}\\\\\frac{\cos^2(\beta)}{\cos^2(\beta)}\\\\1\\\\[/tex]

Therefore, [tex]\frac{(1-\sin(\beta))(1+\sin(\beta))}{\cos^2(\beta)}=1\\\\[/tex] is an identity for all values of β for which the original expression is defined. I used the difference of squares rule for the 2nd step. Then I applied the pythagorean trig identity for the 3rd step.

Answer:

x = 4

Step-by-step explanation:

7 * ( x-2) = 196/14

7x -14 = 14

7x = 28

x = 4

The equation of the line parallel to given line and passing through (-3, 1) will be y – 1 = (3/2)(x + 3). Then the correct option is D.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

The slope of the parallel lines are equal.

m = (2 + 4) / (2 + 2)

m = 6/4

m = 3/2

Then the equation of the line will be

y = (3/2)x + c

The line is passing through (-3, 1). Then the value of c will be

1 = (3/2)(-3) + c

c = 9/2 + 1

Then the equation will be

     y = (3/2)x + 9/2 + 1

y – 1 = (3/2)(x + 3)

Then the correct option is D.

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Answer:

$11.72

Step-by-step explanation:

Add: $42.29 + $87.99 = $130.28

Subtract: $142 - $130.28 = $11.72

Answer:

he would have spent 131.08 dollars meaning he has 11.72 dollars left.

Step-by-step explanation:

Based on the amount being taxed, the period of taxation, and the tax, the annual percentage of tax is 19.96%.

Assuming this rate was x, the following formula would apply:

Annual rate/ 365 days a year x number of days x amount to be taxed = Tax amount

Solving gives:

x/365 x 32 x 8,000 = 140

701.369863x = 140

x = 140 / 701.369863

= 19.96%

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Answer:

X= 5.52

Step-by-step explanation:

1. Solve the equation:

e×2x + 12= 42

x=15/e

2. Round x=15/e to the required place

x=5.52

Answer:

X=1.15

Step-by-step explanation:

Answer:

[tex]y=-\dfrac{1}{2}x+2[/tex]

Step-by-step explanation:

Define two points on the line:

  [tex]\textsf{let}\:(x_1,y_1)=(0,2)[/tex]

  [tex]\textsf{let}\:(x_2,y_2)=(4,0)[/tex]

Use the slope formula and the defined points to find the slope:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-2}{4-0}=-\dfrac{1}{2}[/tex]

Substitute the found slope and one of the points into the point-slope form of a linear equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-2=-\dfrac{1}{2}(x-0)[/tex]

Simplify:

[tex]\implies y-2=-\dfrac{1}{2}x[/tex]

[tex]\implies y=-\dfrac{1}{2}x+2[/tex]

Answer:

[tex]m \leqslant 10 \: or \: m > 4[/tex]

Step-by-step explanation:

[tex] \frac{m - 2}{3} \leqslant - 4 \\ \frac{m - 2}{3} \times 3 \leqslant - 4 \times 3 \\ m - 2 \leqslant - 12 \\ m - 2 + 2 \leqslant - 12 + 2 \\ m \leqslant 10[/tex]

OR

[tex]3m - 8 > 4 \\ 3m - 8 + 8 > 4 + 8 \\ 3m > 12 \\ \frac{3m}{3} > \frac{12}{3} \\ m > 4 [/tex]

Five factors that should be controlled are the dose of the medicine, the time the patients take this medicine, their diet, the stage of this disease and medicine composition.

This is done to avoid bias or imprecise results.

Factors related to the medicine itself and factors that can affect the results should be controlled. This includes:

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The total amount Maria ended up paying for the equipment will be $14,861.76. And The interest of Maria on the loan will be 8.48%.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

To purchase 13700 worth of restaurant equipment for her business.

Maria made a down payment of 1500 and took out a business loan for the rest, after 3 years of paying monthly payments of 371.16 she finally paid off the loan.

The total amount Maria ended up paying for the equipment will be

Total amount = 371.16 × 3 × 12 + 1500

Total amount = $14,861.76

The interest of Maria on the loan will be

Interset = [(14861.76 – 13700) / 13700] x 100

Interset = 8.48%

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Answer:

The  value comes out to be  

[tex]x=\frac{1}{2}+\frac{\sqrt{17}}{2}[/tex]

Step-by-step explanation:

The quadratic equation is an equation containing a single variable of degree [tex]2[/tex]. Its general form is [tex]ax^{2} +bx + c=0[/tex].

The discriminant is the part of the quadratic formula underneath the square root symbol: b²- 4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.

The equation we are given is :[tex]x+4=x^{2} \\x^{2} -x-4=0\\[/tex]

We know the formula as :

[tex]x=[-b[/tex]±[tex]\sqrt{b^{2}-4ac}][/tex] ×[tex]\frac{1}{2a}[/tex]

[tex]x=[-(-1)[/tex]±[tex]\sqrt{(-1)^{2} -4(1)(-4)}][/tex]×[tex]\frac{1}{2(1)}[/tex]

[tex]x=\frac{1}{2}[/tex] ±[tex]\frac{\sqrt{17} }{2} }[/tex]

Since [tex]x[/tex]≥[tex]0[/tex]

Other negative option is neglected

[tex]x=\frac{1}{2}+\frac{\sqrt{17}}{2}[/tex]

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The length of each leg and the hypotenuse of this triangle will be:

AD = 2 units.

AE = 2 units.

DE = 2.8 units

From the information given and the attached diagram, the value or AD and AE are 2 units respectively.

The value of DE will be calculated as the square root of 2² + 2². This will be:

= 2² + 2² = 8

= ✓8 = 2.8

Therefore, the correct options are 2, 2, and 2.8 units.

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The complete question is

"Write the inequality when 3 is less than w and 9 is greater than w."

The inequality become as 3 < w < 9.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

Given information ;

when 3 is less than w and 9 is greater than w.

Thus, the inequality will be ;

3 < w < 9

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[tex]f(x)-g(x)=(2x^{2}-1)-(3x-5)=2x^{2}-1-3x+5=\boxed{2x^{2}-3x+4}[/tex]

The answer is simple

First find the angle measures of first triangle:

statement:

we know that the sum of 45 and 30 sums up to the opposite angle and that is equal to 75, then to find the next remaining angle:

180-(75+20)=85

The you find the supplement of 85:

180-85=95

so x = 95

Hope it helps

3779.309 is the answer....

The diagram shows that ∠2 and ∠4 are the vertical angles.

Vertical angles are the angles that are opposite of each other when two lines cross.

The statements are:

1. < 2 & < 4 are vert. angles

2. Lines M & N intersect at P

3. < 2 & < 3 are a linear pair

4. m < 2 + m < 3 = 180

5. <3 and < 4 are a linear pair

6. m < 3 + m <4 =180

7. m < 2 + m < 3 = m < 3 + m < 4

8. m < 2 = m < 4

9. < 2 =~ <4

Here are the reasons:

1. Given

2. Def of vertical angles.

3. Def of. Linear pair

4. Angle addition postulate

5. Def of a linear pair

6. Angle addition postulate

7. Substitution property

8. Subtraction property

9. Def of =~ angles.

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Answer: View the picture below!

Step-by-step explanation: Just did the assignment!

Answer:

The sum of the numbers is 132

Step-by-step explanation:

First find the smallest number

Thus, you found the smallest number

then there sum given as 96+36=132

The zero of the equation is 0. Since degree of denominator is greater than degree of numerator, therefore, the horizontal asymptote is y=0

The zero of the function is the point where the function is zero

Given the function below

f(x) = 4x/x-16

For the zeros

0 = 4x/x -16

4x = 0

x = 0

Hence the zero of the equation is 0

The vertical asymptote is the point where the denominator is zero

x - 16 = 0
x = 16

Since degree of denominator is greater than degree of numerator, therefore, the horizontal asymptote is y=0

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Answer:

22 cm

Step-by-step explanation:

First we need to know that The golden number

= (1+√(5))÷2

= 1.61803398875 (in decimal)

………………………………………………

We get the length of a golden rectangle

by multiplying its width by the golden number itself.

Then

The width = 35÷ 1.61803398875

                 =21.631189606245

Answer: 1

Step-by-step explanation:

Substituting in the given values,

3a-5b=3(-3)-5(-2)=-9+10=

Answer:maybe c or d??

Step-by-step explanation:

The total amount of money that Denise and Stacey spent at the carnival is 12 + 14c + 5g dollars.

What is total amount?

The amount that you get when you add several numbers or things together.

The total amount of money that Denise and Stacey spent at the carnival will be money spent on admission + ride + game.

Total amount = 2 * 6 + 2 ( 7 * c ) +  ( 3 * g + 2 * g )

                      = 2 * 6 + 14 * c + 5 * g

                      = 12 + 14c + 5g dollars.

Therefore, the total amount of money that Denise and Stacey spent at the carnival is 12 + 14c + 5g dollars.

The questions seems incomplete, its option could be:

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Answer:

Step-by-step explanation:

Answer: QN=19

Step-by-step explanation:

Diagonals of an isosceles trapezoid are congruent, so NQ=PM.

By the segment addition postulate, NQ=QR+RN=3x+7.

So,

[tex]6x-5=3x+7\\\\3x-5=7\\3x=12\\\\x=4[/tex]

So, [tex]QN=3(4)+7=\boxed{19}[/tex]