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The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

1st.) x = 5 /Sin(30°)

x = 10

!) sin(45°) = 4/x

x = 4/sin(45°)

x = 4√2

I) Cos(45°) = √3 / x

x = √3 / Cos(45°)

x = √6

E) Tan(60°) = 3√3 / x

x = 3√3 / 3

W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.

x = 45°

N) x² + x² = (7√2)²

x = 7

V) Tan(60°) = 7 / x

x = 7√3/3

K) x² + x² = (9)²

x = 9/√2

Y) Sin(60°) = 7√3/x

x = 14

M) Sin(30°) = x/11

x = 11/2

T) Sin(45°) = x/√10

x = √5

A) x + 2x + 90° = 180°

x = 30°

O) Sin(45°) = √2 / x

x = 2

R) Tan(30°) = x / 4

x = 4/√3 = 4√3 / 3

S) Sin(60°) = x / (10/3)

x = 5√3 / 3

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1) Because [tex]\angle AOC[/tex] is a central angle, the answer is 50 degrees.

2) By the inscribed angle theorem, the answer is 25 degrees.

The inverse of any function F(x) is also a function.

A function is an abecedarian notion in mathematics and computer programming. In both contexts, a function is a regulation or relationship that maps input values to corresponding output values. It takes one or more input values, performs a set of operations or calculations, and produces a single output value.

There are many types of functions such as trigonometric function, logarithmic function, exponential function, and so on.

If a function f(x) gives output y then its inverse will be [tex]f^{-1}(y)[/tex] and will return x as output.

So, the statement is true.

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Shape A was reflected over the y axis and translated 1 unit down to get shape B.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right on the coordinate plane.

Shape A was reflected over the y axis and translated 1 unit down to get shape B.

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Using the given exponential function, we have that:

Every minute, the number of bacteria decays by a factor of 0.98.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, the function is, for the amounts each second:

[tex]Bs(t) = 6000\left(\frac{15}{16}\right)^{t}[/tex]

The initial amount is of 6000 bacteria. After 60 seconds = 1 minute, the amount will be of:

[tex]Bs(60) = 6000\left(\frac{15}{16}\right)^{60} = 125[/tex]

The decay factor after 1 minute is:

(6000 - 125)/6000 = 98% = 0.98.

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Answer:

Step-by-step explanation:

  [tex]\sf f(x) = \dfrac{1}{Sin \ x}[/tex]

f(x) does not contain values where sin x = 0. Sin x is 0 at integral multiples of π.

Domain = R - nπ , n is integers.

The range of Sin x is [-1 , 1] and in this range we cannot find 1/sin x .

Range = (-∞, -1] U [1,∞)

[tex]\sf f(x) =\dfrac{1}{Cos x}[/tex]

f(x) does not contain values where Cos x  = 0 . Cos x is 0 at integral of multiples of (π/2)

   [tex]\sf Domiain =R -\dfrac{(2n+1)\pi }{2}[/tex]

The range of Cos x is [-1,1] and in this range we cannot find 1/Cos x.

Range =  (-∞, -1] U [1,∞)

The triangle will be computed based on the information illustrated below.

The steps needed for the construction will be:

Draw a segment XY.

Locate B, C on XY such that BC = 4.5cm.

Construct a line segment such that B = 90°.

With C as center and radius 7cm, draw a arc cutting BD at A.

Then, the required triangle ABC will be gotten.

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There is a rule for finding perimetre of all polygons that perimetre is the sum of all the side's lengths ; according to this rule add the length of the sides of this polygon and you'll get the answer , the answer is the choice that you've written ( 2+3×2+5+6+7+9 ) or ( 2+3+3+5+6+7+9 ) both are correct because 3+3 is same as 3×2

perimetre is 2+3×2+5+6+7+9 = 35 units

HOPE IT HELPS

Answer: 48

Step-by-step explanation:

By the geometric mean theorem,

[tex]\frac{x}{36}=\frac{64}{x}\\\\x^{2}=36 \cdot 64\\\\x=\sqrt{36 \cdot 64}\\\\x=\sqrt{36} \sqrt{64}=48[/tex]

The value of x from the given equation is 5/3

Since the three points are collinear to U, they are on a straight line which equals 0

Then we have,

UM + UD =  MD

5x+30 + 10x+20 = 3x+80

Collect like terms

5x + 10x + 50 = 3x + 80

15x - 3x = 80 - 50

12x = 30

x = 30/12 = 15/6 = 5/3

Thus, the value of x from the given equation is 5/3

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Answer:

357 mi²

Step-by-step explanation:

A = LW + 0.5πr²

A = (10 × 20 + 0.5 × 3.14159 × 10²) mi²

A = (10 × 20 + 0.5 × 3.14159 × 10²) mi²

A = 357 mi²

#1

No

#2

We can see f(1) has 3 values so it's not a function as it's failed in vertical line test

#3

f(10) has two values -2 and 11

So not a function

#4

As per definition of function

So it's not a function

Using it's vertex, the maximum value of the quadratic function is -3.19.

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

Considering the coefficient a, we have that:

In this problem, the equation is:

y + 4 = -x² + 1.8x

In standard format:

y = -x² + 1.8x - 4.

The coefficients are a = -1 < 0, b = 1.8, c = -4, hence the maximum value is:

[tex]y_v = -\frac{1.8^2 - 4(-1)(-4)}{4(-1)} = -3.19[/tex]

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Answer:

No this is not a function because the x-values repeat. In a function you can have the the output duplicate but not the input. The input at 3 has duplicates s o this is not a function.

Step-by-step explanation:

Definition

A relation is called to be a function if every domain has an unique range

Here

As

f(3) has 2 corresponding values it's not a function

Answer: [tex]120^{\circ}[/tex]

Step-by-step explanation:

[tex]12\pi=2(\pi)(18)\left(\frac{\theta}{360} \right)\\\\12\pi =36\pi \left(\frac{\theta}{360} \right)\\\\\frac{1}{3}=\frac{\theta}{360}\\\\\theta=120^{\circ}[/tex]

According to the central angle theorem, the measure of angle MNP = 114°.

According to the central angle theorem of a circle, the measure of central angle MNP equals the measure of intercepted arc MP.

Measure of arc MP = 114°

Measure of angle MNP = arc MP

Measure of angle MNP = 114° [central angle theorem]

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Answer:

B

Step-by-step explanation:

given a quadratic function in standard form

y = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = x² - 4x + 3 ← is in standard form

with a = 1, b = - 4 , then

x = - [tex]\frac{-4}{2}[/tex] = 2

substitute into the equation for corresponding y- coordinate

y = 2² - 4(2) + 3 = 4 - 8 + 3 = - 1

vertex = (2, - 1 )

Answer:

? = 45

Step-by-step explanation:

the inner and outer triangles are similar ( AA postulate )

Then the ratios of corresponding sides are in proportion, that is

[tex]\frac{56}{56+24}[/tex] = [tex]\frac{105}{105+?}[/tex]  , that is

[tex]\frac{56}{80}[/tex] = [tex]\frac{105}{105+?}[/tex] ( divide numerator/denominator by 8 to simplify left side )

[tex]\frac{7}{10}[/tex] = [tex]\frac{105}{105+?}[/tex] ( cross- multiply )

7(105 + ? )  = 1050 ← distribute parenthesis on left side

735 + 7? = 1050 ( subtract 735 from both sides )

7? = 315 ( divide both sides by 7 )

? = 45

Answer:

  3000/5 = 600

Step-by-step explanation:

Every multiplication fact is equivalent to two (2) division facts:

  a·b = c  ⇒  c/a = b  and  c/b = a

Multiplication or division by 10 involves moving the decimal point one place to the right or left (respectively).

The division ...

  [tex]\dfrac{3000}{5}[/tex]

is fully equivalent to ...

  [tex]\dfrac{30}{5}\times 100[/tex]

We assume your "basic fact" is 5×6 = 30. In accordance with the above equivalence to division problems, this tells you ...

  [tex]\dfrac{30}{5}=6\\\\\dfrac{30}{5}\times100 = 6\times100\\\\\dfrac{3000}{5}=600[/tex]

Answer:

4

Step-by-step explanation:

348 / 87 = 4

There are 87 Customers. The restauraunt served 348 pancakes. You divide 348 by 87 and conclude that each customer ate 4 pancakes.

Answer:

4

Step-by-step explanation:

348 ÷ 87 = 4

each person ate 4 pancakes

Answer:

151°

Step-by-step explanation:

The above shape is a quadrilateral.

The exterior angles are :

82°, 70°, 62°, and (x -5)°

Therefore,

82 + 70 + 62 + x - 5 = 360

214 -5 + x = 360

209 + x = 360

x = 360 - 209

x = 151°

The new employee should choose the second option to make the most money on a typical day. The amount that the new employee will earn 20-day at this rate is $3,100.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

For Option 1,

Receive an hourly rate of $15.25 for 8 hours plus $0.50 per bottle of wax sold to customers. Also, A typical day consists of 12 bottles of wax sold per detailer.

Earning = ($15.25 × 8) + ($0.50×12)

= $122 + $6

= $128

For Option 2,

Receive $38.75 per automobile detailed in a day. Also, 4 automobiles are detailed per employee. Therefore, the earnings are,

Earning = $38.75 × 4

= $155

For Option 3,

Receive $100 per day plus 2% of sales in a day. Also, the average daily sales are $1,500. Therefore, the earnings are,

Earning = $100 + 0.02($1500)

= $130

Hence, The new employee should choose the second option to make the most money on a typical day.

2.)

The amount that the new employee will earn 20-day at this rate is,

Amount earned = $155 × 20 days

                           = $3,100

Hence, The amount that the new employee will earn 20-day at this rate is $3,100.

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Answer:

The equation of the line that passes through the points (2a, b) and (a, b+1) is [tex]$y=-\frac{1}{a} x+2+b$[/tex].

Step-by-step explanation:

The given points are (2a, b) and (a, b+1).

It is required to find the equation of the line that passes through the points. the slope-intercept form.

Step 1 of 4

Using the given two points, to find the slope.

Given points are (2a, b) and (a, b+1).

Substitute [tex]$x_{1}[/tex]=2a,

[tex]$$\begin{aligned}&y_{1}=b \\&x_{2}=a \text { and } \\&y_{2}=b+1\end{aligned}$$[/tex]

into the formula, [tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

Step 2 of 4

Simplify [tex]$m=\frac{b+1-b}{a-2 a}$[/tex], further

[tex]$$\begin{aligned}m &=\frac{b+1-b}{a-2 a} \\m &=-\frac{1}{a}\end{aligned}$$[/tex]

As a result, the slope is [tex]$m=-\frac{1}{a}$[/tex].

Step 3 of 4

Use the slope [tex]$m=-\frac{1}{a}$[/tex] and the coordinates of one of the points (2a, b) into the point-slope form, [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex].

Substitute [tex]$m=-\frac{1}{a}$[/tex],

[tex]x_{1}=2 a$ and$y_{1}=b$[/tex]

into the formula, [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]

[tex]$y-b=-\frac{1}{a}(x-2 a)$[/tex]

[tex]$y-b=-\frac{1}{a} x+2$$[/tex]

Step 4 of 4

Rewrite the above equation as a slope-intercept equation. So, from the above term [tex]$y-b=-\frac{1}{a} x+2$[/tex], Add b on each side.

[tex]$$\begin{aligned}&y-b=-\frac{1}{a} x+2 \\&y=-\frac{1}{a} x+2+b\end{aligned}$$[/tex]

Therefore, the equation of the line that passes through the points is [tex]$y=-\frac{1}{a} x+2+b$[/tex].

a) [tex]-3(1)+1=\boxed{-2}[/tex]

b) [tex]4=-3x+1 \longrightarrow -3x=3 \kongrightarrow x=\boxed{-1}[/tex]

If we have a function f(x), f(5) is f(x) but replacing x with 5. The result give us a value of y and a point of the function, (x, y).

[tex]f(5) = \frac{1}{4} ({2})^{5} = \frac{32}{4} = 8[/tex]

ANSWER A

Hello!

Substitute x = 5 to find f(5).

⇒ f(5) = 1/4(2)⁵

⇒ f(5) = 32/4

⇒ f(5) = 8

∴ The correct option is A.

Answer:

x=22

Step-by-step explanation:

7x+6=160.

Lets start by moving 6 over to the other side. We can do this by subtracting 6 from both sides of the equation.

7x+6-6=160-6

7x=154

Now, let's isolate x by getting rid of the 7. The 7 is being multiplied with x, so to get rid of it we have to divide both sides by 7.

7x/7 = 154/7

x=22

Look Below :

Step-by-step explanation:

160 - 6 = 7x

154 = 7x

Or

7x = 154

x = 22

Answer:

The 2 numbers are 3 and 5.

Step-by-step explanation:

x + y = 8

1/x + 1/y = 8/15

From first equation  y = 8 - x so

1/x + 1 / (8-x) = 8/15

Multiply through by the LCM 15x(8-x):-

15(8 - x) + 15x =  8x(8-x)

120 - 15x + 15x = 64x - 8x^2

8x^2 - 64x + 120 = 0

x^2 - 8x + 15 = 0

(x - 3)(x - 5) = 0

x = 3 or  5

so y = 8-3 = 5 or 3.

Answer:

Step-by-step explanation:

If she offers to 9, but 2 reject, that means she paid for 7 friends.

If each friend costs $4, multiply 4 by 7.

The answer is $28

Hope this helps! (:

The 95% confidence interval of voters not favoring the incumbent is (0.0706, 0.1294).

Sample size, n=400

Sample proportion, p = 40 / 400

= 0.1

We use normal approximation, for this, we check that both np and n(1-p) >5.

Since n*p = 40 > 5 and n*(1-p) = 360 > 5, we can take binomial random variable as normally distributed, with mean = p = 0.1 and standard deviation  = root( p * (1-p) /n )

= 0.015

For constructing Confidence interval,

Margin of Error (ME) =  z x SD = 0.0294

95% confidence interval is given by Sample Mean +/- (Margin of Error)

0.1 +/- 0.0294 = (0.0706 , 0.1294)

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