a right triangle has one side that measures 4 in. the angle opposite that side measures 80° what is the length of the hypotenuse if the triangle? round to the nearest tenth.

Answer:

What's the question? All you posted was the potential answers.

Step-by-step explanation:

This seems really easy, but

1)  0

2) 0

3) 0

Answer:

see explanation

Step-by-step explanation:

1

The cosine function in standard form is

y = acos(bx + c)

where a is the amplitude, period = [tex]\frac{2\pi }{b}[/tex] and

phase shift = - [tex]\frac{c}{b}[/tex]

here b = 2 and c = [tex]\frac{\pi }{2}[/tex], thus

phase shift = - [tex]\frac{\frac{\pi }{2} }{2}[/tex] = - [tex]\frac{\pi }{4}[/tex]

2

the amplitude = | a |

which has a maximum of a and a minimum of - a

y = 4cosx ← has a maximum value of 4

Final answer:

The phase shift of the function y = 5cos(2x + π/2) is -π/4 radians. The functions y = 4cosx and y = cosx + 4 both have a maximum y value of 4.

Explanation:

To find the phase shift of the function y = 5cos(2x + π/2), we need to look at the argument of the cosine function. The general form is y = Acos(Bx - C) where C/B is the phase shift. In this case, the argument of the cosine is 2x + π/2, thus the phase shift is -π/2 divided by the coefficient of x, which is 2, giving us a phase shift of -π/4 or -0.785 radians.

To determine which of the provided functions has a maximum y value of 4, consider the amplitude of the cosine functions. For the functions y = 4cosx, y = cos4x, and y = cos(x + 4), the amplitude is 1, and thus the maximum y value is 1 for the latter two, and 4 for the first one. However, y = cosx + 4 is a cosine function shifted upward by 4 units, and hence its maximum y value is also 5. So, the functions with a maximum y value of 4 are y = 4cosx and y = cosx + 4.

Answer: Estimates vary, but each person uses about 80-100 gallons of water per day

Explanation:

1. In order for the idea of "perpendicular distance" to make any sense in this context, the number of sides of the polygon must be even. Then the "diameter" is the diameter of the inscribed circle. As the number of sides increases, the polygon differs less and less from a circle, so the relationship of perimeter and "diameter" becomes closer to the relationship in a circle.

"As the number of sides in a regular polygon increases, the ratio of perimeter to diameter for that polygon approaches pi."

__

2. We know from the first question that ...

circumference/diameter = π

And we know that ...

diameter = 2·radius

Then the following are true:

A. circumference = π · diameter

B. circumference = (2·radius) · π

__

3. The expressions in order evaluate to approximately ...

4.0, 3.45, 3.31, 3.24

Of these, the last is closest to pi (3.14....). The appropriate choice is ...

D. (10·5)/15.4

__

4. Pi cannot be expressed as a rational number, because pi is irrational. A number of lengthy proofs have been offered to demonstrate this fact. One of them makes use of the fact that the tangent of any rational number is irrational, and the tangent of π/4 is 1. Since 1 is a rational number, π/4 cannot be, so π cannot be expressed as a rational number.

Answer:

Step-by-step explanation:

l - length

w - width

The formula of a perimeter of a rectangle: P = 2(l + w)

The formula of an area of a rectangle: A = lw

We have P = 46in and A = 76in² Substitute:

(1)     2(l + w) = 46

(2)    lw = 76

2(l + w) = 46     divide both sides by 2

l + w = 23          subtract w from both sides

l = 23 - w

subtitute it to (2):

(23 - w)w = 76              use the distributive property

23w - w² = 76              subtract 76 from both sides

-w² + 23w - 76 = 0           change the signs

w² - 23w + 76 = 0

w² - 4w - 19w + 76 = 0

w(w - 4) - 19(w - 4) = 0

(w - 4)(w - 19) = 0 ⇔ w - 4 = 0 or w - 19 = 0

w - 4 = 0           add 4 to both sides

w = 4

w - 19 = 0           add 19 to both sides

w = 19

Put the values of w to (1):

l = 23 - 4 = 19 or l = 23 - 19 = 4

Answer: Option a.

Domain: (-∞, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

We have the function [tex]f(x) = 2x + cosx[/tex]

Note that f(x) is the sum of two continuous functions [tex]h(x) = 2x[/tex] and [tex]g(x) = cosx[/tex]

The domain and range of h(x) are all real numbers

The domain of g(x) is all real numbers. The range of g(x) is [-1, 1]

Then the domain of [tex]f(x) = h(x) + g(x)[/tex] will be the intersection of the domains of the function [tex]h(x) = 2x[/tex] and the function [tex]g(x) = cosx[/tex].

Therefore the domain of f(x) are all real numbers.  x ∈ (-∞, ∞)

The range of f(x) will be equal to the union of the range of g(x) and h(x)

Therefore the range will be all real numbers f(x) ∈ (-∞, ∞)

Answer:

A = 21.65 cm squared

Step-by-step explanation:

The basic area formula for a triangle is

[tex]A= \frac{1}{2}bh[/tex]

We have our base as 5, so we can find the height using right triangle trig.  Side BC is opposite the given angle, which is the height, and we are given side CD as 5 which is the base.  Using the tangent ratio to find side BC:

[tex]tan(60) = \frac{x}{5}[/tex] which simplifies to

5 tan(60) = x so

x = 8.66

Filling in for the area:

[tex]A= \frac{1}{2}(5)(8.66)[/tex] so

A = 21.65 cm squared

Divide 110 by 10 to get a rate if 11 feet per second. Multiply 11 by 12 seconds to get 132 feet

probability of drawing a blue marble is 1/3

Answer:

  B.  3x -2y = 10

Step-by-step explanation:

The given line rises three units for each two units of run to the right. Hence its slope is 3/2. A parallel line will also have a slope of 3/2.

Of the equations we can see, selection B has a slope of 3/2. It can be rewritten in slope-intercept form as ...

  3x -10 = 2y . . . . . add 2y-10 to isolate the y-term; next divide by 2.

  y = 3/2x -5 . . . . . the coefficient of x is the slope

Answer:

B.  3x -2y = 10

Step-by-step explanation:

The given line rises three units for each two units of run to the right. Hence its slope is 3/2. A parallel line will also have a slope of 3/2.

Of the equations we can see, selection B has a slope of 3/2. It can be rewritten in slope-intercept form as ...

  3x -10 = 2y . . . . . add 2y-10 to isolate the y-term; next divide by 2.

  y = 3/2x -5 . . . . . the coefficient of x is the slope

Answer:

V = 115.3 ft³

Step-by-step explanation:

The left part of the figure shows a cube of side length 4.2 ft.  The volume of a cube is V = s³, where s is the side length.  Hence, the volume of this particular cube is V = (4.2 ft)³ = 74.088.

The volume of a pyramid is V = (1/3)(base area)(height).

Here V = (1/3)(4.2 ft)²(7 ft) = 41.16 ft³.

Summing up the two distinct areas, we get V = 41.16 ft³ + 74.088 ft³, or

V = 115.3 ft³ after rounding up to the nearest tenth.

The volume of the composite figure is 115.2 cu.ft. , Option A is the correct answer.

Those figures that required x,y and z axis for their representation are three dimensional figures.

They have length , breadth and height.

All the object that we see around us can be categorized into Three Dimensional Figure.

In the given figure

It can be seen that it consists of a cube and a square pyramid

To determine the volume we have to determine the volume of each figure and then add

Volume of a cube =  side * side * side

Side of the cube = 4.2 ft.

Substituting the values

Volume of cube = 4.2 * 4.2 * 4.2

Volume of cube = 74.088 cu.ft

Volume of a square pyramid is given by

(1/3) * a² * h

a is the area of the base

area of the base =  area of the square = side * side

Area of the base = 4.2 * 4.2

Area of the base = 17.64 sq.ft

Height of the pyramid  = 7 ft.

Volume of  square pyramid = (1/3)* 17.64 *7

Volume of a square pyramid = 41.16 cu.ft

Total volume = 74.088 + 41.16

Total Volume = 115.2 cu.ft

Therefore , The volume of the composite figure is 115.2 cu.ft. , Option A is the correct answer.

To know more about Three Dimensional Figures

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B. Three. It is three because there is one decimal place in each factor.

Answer:

B. Three.

Explanation:

Three because there is one decimal place in each factor and there are 3 factors.

Answer:

  12 m

Step-by-step explanation:

The formula for the area of a triangle is ...

  A = 1/2bh . . . . . b represents the base; h represents the height

We are told that the height is 5 m less than the base, so we have ...

  42 = (1/2)(b)(b -5)

  84 = b(b-5) . . . . . . . . multiply by 2

We want two factors of 84 that differ by 5. The factors are ...

  84 = 1·84 = 2·42 = 3·28 = 4·21 = 6·14 = 7·12

The relevant factors are 7 and 12, so now we know b-5 = 7 and b = 12.

The length of the base is 12 m.

Answer:

Final answer in simplified form is [tex]3x^2-17x-30[/tex]

Step-by-step explanation:

Given expression is [tex](3x^2-8x-24)-(9x+6)[/tex]

Now we need to find an equivalent expression for [tex](3x^2-8x-24)-(9x+6)[/tex]

First we can distribute the negative sign and remove the parenthesis the combine like terms

[tex](3x^2-8x-24)-(9x+6)[/tex]

[tex]=3x^2-8x-24-9x-6[/tex]

[tex]=3x^2-17x-30[/tex]

Hence final answer in simplified form is [tex]3x^2-17x-30[/tex]

there are two ways you can do

[tex]y = 5x + 15 \\ \\ 1. \: y - 15 = 5x \\ 2. \: \frac{y - 15}{5} = x \\ 3. \: x = \frac{y - 15}{5} \\ \\ \\ 1. \: 5x + 15 = y \\ 2. \: 5x + 15 + - 15 = y + - 15 \\ 5x = y - 15 \\ 3. \: \frac{5x}{5} = \frac{y - 15}{5} \\ x = \frac{1}{5} y - 3[/tex]

A solution of the equation y = 5x + 15 represents a specific moment during Kenneth's experiment, where 'x' is the time elapsed since he started adding the blue liquid, and 'y' is the total volume of the liquid mixture in the beaker.

The equation y = 5x + 15 provided is a linear equation, which is a mathematical expression showing a constant rate of change. In this context, Kenneth's experiment in the laboratory, 'x' is the number of minutes since Kenneth began adding drops of blue liquid to the beaker, and 'y' is the total amount of liquid, in milliliters, in the beaker.

A solution to this equation refers to specific values for 'x' and 'y' which make this equation true. For instance, if we choose x = 1 minute, then we can calculate 'y' by substituting 'x' into the equation which gives y = 5*1 + 15 = 20 mL. This means that after 1 minute, Kenneth has 20 mL of liquid in his beaker. Indeed, every solution to this equation reflects a specific moment (x, or number of minutes) in Kenneth's ongoing experiment and the corresponding total volume (y) of the mixture in the beaker.

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Answer:

$36.00

Step-by-step explanation:

The cost performance index (CPI) is a measure of the financial effectiveness and efficiency of a project. As a ratio it is calculated by dividing the budgeted cost of work completed, or earned value, by the actual cost of the work performed, that is to say:

CPI = Budgeted cost of work / Actual cost of work

From the statement we know that:

CPI = 1.94

Budgeted cost of work= $69.85

Cost of work in 1983 = Budgeted cost of work / CPI

Cost of work in 1983 = $69.85 / 1.94 = $36.00

Answer:

The answer is C

Step-by-step explanation:

Answer:

The radius is r=5 units

Step-by-step explanation:

we know that

The equation of the circle in standard form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

where

(h,k) is the center and r is the radius

we have

[tex]x^{2}+y^{2}-12x+6y+20=0[/tex]

Convert to standard form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](x^{2}-12x)+(y^{2}+6y)=-20[/tex]

Complete the square twice. Remember to balance the equation by adding the same constants to each side

[tex](x^{2}-12x+36)+(y^{2}+6y+9)=-20+36+9[/tex]

[tex](x^{2}-12x+36)+(y^{2}+6y+9)=25[/tex]

Rewrite as perfect squares

[tex](x-6)^{2}+(y+3)^{2}=5^{2}[/tex]

therefore

The center is the point (6,-3) and the radius is r=5 units

Answer:

A' because it is translated to another position.

Hope this helps

Answer: A'

Step-by-step explanation:

From the given figure , it can be seen that the quadrilateral ABCD is translated to produce A'B'C'D' by some distance in a particular direction.

We can see that the point A' in the image is corresponding to the point A in the pre-image.

Hence, the image of point A is A' .

Answer: 5 Vertices

Step-by-step explanation: I believe if it had 4 faces and 8 edges it would have 5 vertices.

Answer:

See below.

Step-by-step explanation:

Values are excluded if they make the denominator zero, so one rational expression could be:

(x^2 - 9) /  (x + 4)(x + 7)

- when x = -4 or -7 then the denominator is zero so the values of the function is undefined for these values.

Answer:

No, it is not safe

Answer:

Hello!

The answer is no, he will not be safe. I had a similar problem on a test and got the answer correct. The only difference was they used slightly different numbers, so I am pretty sure this is correct. I hope this helps!

Step-by-step explanation:

Okay, so you are looking for x.

sin x= [tex]\frac{16.5}{17}[/tex]

x=[tex]sin^{-1}[/tex]([tex]\frac{16.5}{17}[/tex])

x≈76.07

76.07>70

The yellow and orange triangle is AA

It is AA because the orange triangle has two angles listed and, the yellow triangle has two angle listed.

Answer:

AA

Step-by-step explanation:

For the 2 triangles to be similar we require 2 corresponding angles to be congruent.

There are 2 angles of measure 30°

If we consider the yellow triangle the the third angle is

180° - ( 41 + 30)° = 180° - 71 = 109°

The 2 triangles have therefore 2 corresponding congruent angles

Hence the triangles are similar by the postulate AA

Answer:

559.2 yards.

Step-by-step explanation:

Let the height of the mountain be x yards and the distance from the second location to the base of the mountain be y yards.

Then we have the equations:

tan 27 = x/y

tan 23 = x / (220 + y)

From the first equation  y =  x/ tan27 so substituting in the second one we have:

tan 23 =  x / (220 + x / tan 27)

Cross multiply:

x = 220 tan23 +  x tan 23 / tan 27

x =  93.384 + 0.833 x

x - 0.833x = 93.384

x = 93.384 / 0.167

x = 559.2 yards to 1 dec place (answer).

Answer:

The answer is 1/4.

Step-by-step explanation:

5 rock CDs, plus 3 country CDs, plus 4 movie sound track CDs, equal 12 CDs in total. To find the odds of choosing a country CD, you divide the total number of CDs, by the number of what you choose (3/12).

Answer:

The odds that he choose a country CD is 1/3

Step-by-step explanation:

12/12 ÷ 3 = 1/3

Answer:8462

Step-by-step explanation:

Answer:

8862 feet

Explanation:

The formula for circumference is C=pi*diameter. So, by substitution we can use 26586=(3)d and solve by dividing 26586 by 3 which gives us d=8862 feet.

Answer:

15 g

Step-by-step explanation:

30% · 50 g = 30/100 · 50 g = 1500/100 g = 15 g

Answer:

15g

Step-by-step explanation:

20% off, means that 20% of the regular price is how much you would save.

Multiply the original price by 20%

18 x 0.20 = 3.6

The discount is $3.60

Answer:

Option 1.

[tex]P(A) = \frac{1}{8},\ P(A|B) = \frac{1}{3}[/tex]     Dependent

Option 2

[tex]P(A) = \frac{1}{4},\ P(A|B) = \frac{1}{4}[/tex]    Independent

Option 3

[tex]P(B) = \frac{1}{8},\ P(B|A) = \frac{1}{4}[/tex]    Dependent

Option 4

[tex]P(B) = \frac{1}{4},\ P(B|A) = \frac{1}{4}[/tex]     Independent

Step-by-step explanation:

Two events A and B are independent if the occurrence of A does not affect the probability of B.

On the other hand The probability of A given B is defined as:

[tex]P (A | B) = \frac{P (A\ and\ B)}{P (B)}[/tex]

When two events are independent then:

[tex]P (A\ and\ B) = P (A) * P (B)[/tex]

So if the two events A and B are independent this means that:

[tex]P (A | B) = \frac{P (A) * P (B)}{P (B)}[/tex]

[tex]P (A | B) = P (A)[/tex]

Which makes sense because if the events are independent then the probability of A not being affected by B.

So to solve this problem identify in what cases

[tex]P (A | B) = P (A)[/tex] or [tex]P (B | A) = P (B)[/tex]

When this happens those events are independent

Option 1.

[tex]P(A) = \frac{1}{8},\ P(A|B) = \frac{1}{3}[/tex]     Dependent

Option 2

[tex]P(A) = \frac{1}{4},\ P(A|B) = \frac{1}{4}[/tex]    Independent

Option 3

[tex]P(B) = \frac{1}{8},\ P(B|A) = \frac{1}{4}[/tex]    Dependent

Option 4

[tex]P(B) = \frac{1}{4},\ P(B|A) = \frac{1}{4}[/tex]     Independent

Answer: 1) Quadrant: I, reference angle: [tex]\dfrac{2\pi}{5}[/tex]

              2) Quadrant: III, reference angle: 85°

              3) Quadrant: IV, reference angle: [tex]\dfrac{\pi}{4}[/tex]

Step-by-step explanation:

Reference angle is the angle closest to the x-axis

1) The given angle is (2/5)π. The first quadrantal (π/2) would be (2.5/5)π

Since (2/5)π < (2.5/5)π then it must be in Quadrant 1.

The angle closest to the x-axis is the same as the given angle.

2) The given angle is -95°. It is measured clockwise since it is a negative angle.  Since it is greater than 90°, it is greater than the 270° quadrantal. So it must be in Quadrant III.

The angle closest to the x-axis is 85°.

3) The given angle is (23/4)π.  Since (8/4)π is one rotation, this is greater than one rotation. (23/4)π - (8/4)π - (8/4)π = (7/4)π. So, it rotates two complete rotations and lands at coterminal angle (7/4)π.

The angle closest to the x-axis is π/4

Answer:

(-5 +/- sqrt(65))/2

Step-by-step explanation:

To solve this, we can use the quadratic formula!

So,

x = (-b +/- sqrt(b^2-4ac))/2a

x = (-5 +/- sqrt(25+40))/2

x = (-5 +/- sqrt(65))/2

So (-5 +/- sqrt(65))/2  is our answer.