21. Which of the following is an identity? a) sin (a) cos (a) = (1/2) sin(2 a) b) sin a + cos a = 1 c) sin(-a) = sin a d) tan a = cos a / sin a

Answer:

Step-by-step explanation:

Rectangle:

length = l = 12 cm

Width = w = 0.8 cm

Use Pythagorean theorem to find the diagonal

Diagonal² =  l² + w²

                = 12² + 0.8²

                = 144 + 0.64

                = 144.64

Diagonal = √144.64 = 12.03 cm

Diagonal of square  = diagonal of rectangle

                               = 12.03 cm

To find the side of square again use Pythagorean theorem,

side² + side² = 12.03²

2 sides² = 144.64

  side² = 144.64/2

  side² = 72.32

 side = √72.32

Side = 8.50 cm

Answer:The right answer is B

Step-by-step explanation:

If it's negative then it should be on the other side with one side down on the graph and one side on the left.(hope this helped you) :)

Answer:  -1 < x < 3

Step-by-step explanation:

[tex]\dfrac{5}{(x+2)(4-x)}<1[/tex]

Step 1   The denominator cannot equal zero:

x + 2 ≠ 0    and     4 - x ≠ 0

     x ≠ -2                4 ≠ x

Place these restrictive values on the number line with an OPEN dot:

    <----------o-------------------o--------->

                -2                       4

Step 2   Find the zeros (subtract 1 from both sides and set equal to zero):

[tex]\dfrac{5}{(x+2)(4-x)}-1=0\\\\\\\dfrac{5}{(x+2)(4-x)}-\dfrac{(x+2)(4-x)}{(x+2)(4-x)}=0\\\\\\\dfrac{5-(-x^2+2x+8)}{(x+2)(4-x)}=0\\\\\\\dfrac{5+x^2-2x-8}{(x+2)(4-x)}=0\\\\\\\dfrac{x^2-2x-3}{(x+2)(4-x)}=0\\\\\\\text{Multiply both sides by (x+2)(4-x) to eliminate the denominator:}\\x^2-2x-3=0\\(x-3)(x+1)=0\\x-3=0\quad x+1=0\\x=3\quad x=-1[/tex]

Add the zeros to the number line with an OPEN dot (since it is <):

    <----------o-----o----------o----o--------->

                -2     -1            3      4

Step 3    Choose test points to the left, between, and to the right of the points plotted on the graph. Plug those values into (x - 3)(x + 1) to determine its sign (+ or -):

Left of -2: Test point x = -3: (-3 - 3)(-3 + 1) = Positive

Between -2 and -1: Test point x = -1.5: (-1.5 - 3)(-1.5 + 1) = Positive

Between -1 and 3: Test point x = 0: (0 - 3)(0 + 1) = Negative

Between 3 and 4: Test point x = 3.5: (3.5 - 3)(3.5 + 1) = Positive

Right of 4: Test point x = 5: (5 - 3)(5 + 1) = Positive

          +         +        -          +       +

    <----------o-----o----------o----o--------->

                -2     -1            3      4

Step 4  Determine the solution(s) based on the inequality symbol. Since the original inequality was LESS THAN, we want the solutions that are NEGATIVE.

Negative values only occur between -1 and 3

So the solution is:     -1 < x < 3

Answer:

2x+14

Step-by-step explanation:

(3/4)x-7.3+(5/4)x+21.3

(3/4+5/4)x+21.3-7.3

2x+14

Answer:

(1/2, [tex]\frac{\sqrt{3} }{2}[/tex])

Step-by-step explanation:

Don't totally trust me on this...

Step-by-step explanation:

[tex]2 + 8(x + 2) = 52 [/tex]

[tex]2 + 8x + 16 = 52[/tex]

[tex]8x + 18 = 52[/tex]

[tex]8x = 52 - 18[/tex]

[tex]8x = 32[/tex]

[tex]x = \frac{34}{8} [/tex]

[tex]x = 4.25[/tex]

Hope it helps u

Answer:

(2/5) * (3/4) = 3/10 = 0.3

Answer:A

Step-by-step explanation:

The phrase can be described broadly as adjusted gross income (AGI) minus allowable tax deductions.

"Adjusted gross income, or AGI, is your gross income minus certain adjustments. The IRS uses this number as a basis for calculating your taxable income. AGI can also determine which deductions and credits you may qualify for."

Since, Taxable income is the portion of your gross income used to calculate how much tax you owe in a given tax year.

It can be described broadly as adjusted gross income (AGI) minus allowable itemized or standard deductions.

Taxable income includes wages, salaries, bonuses, and tips, as well as investment income and various types of unearned income.

Hence, the phrase can be described broadly as adjusted gross income (AGI) minus allowable tax deductions.

Learn more about adjusted gross income visit:

brainly.com/question/6705479

#SPJ5

Answer:

(-8,2)

Step-by-step explanation:

This is because when you reflect a point across the x-axis, the x-coordinate fo the point remains the same and the y-coordinate's sign gets switched.

(x,y) --> (x,-y)

(-8,-2) --> (-8,2)

Answer:

96 pi

Step-by-step explanation:

The formula for the volume of a cone is V=pi*r^2*h/3 the radius is 4 and the height is 18 plug in those values into the equation to get V=pi*16*6 16*=96 so the answer is 96 pi.

In this question, we given a piece-wise function, that has different definitions depending on the domain.

Evaluate the function at x = 0.

The exercise asks for us to evaluate the function at [tex]x = 0[/tex]

We have to look at the definition, and see which definition includes [tex]x = 0[/tex]. The equal sign at [tex]x = 0[/tex] is on the second definition, that is:

[tex]f(x) = 1, 0 \leq x < 2[/tex]

Thus, at [tex]x = 0[/tex], the value of the function is 1, and the correct answer is given by option A.

For another example of evaluation of a piece-wise function, you can check https://brainly.com/question/17966003

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

Explanation:

a = 200 = first term

d = -30 = common difference

Tn = nth term

Tn = a + d(n-1)

Tn = 200 + (-30)(n-1)

Tn = 200 - 30n + 30

Tn = -30n + 230

Set Tn less than 0 and isolate n

Tn < 0

-30n + 230 < 0

230 < 30n

30n > 230

n > 230/30

n > 7.667 approximately

Rounding up to the nearest whole number gets us [tex]n \ge 8[/tex]

So Tn starts to turn negative when n = 8

We can see that,

Tn = -30n + 230

T7 = -30*7 + 230

T7 = 20

and

Tn = -30n + 230

T8 = -30*8 + 230

T8 = -10 is the 8th term

and lastly

Tn = -30n + 230

T9 = -30*9 + 230

T9 = -40 is the ninth term

Or once you determine that T7 = 20, you subtract 30 from it to get 20-30 = -10 which is the value of T8. Then T9 = -40 because -10-30 = -40.

Answer:

- 10

- 40

Step-by-step explanation:

By the 7th term you should be pretty close to 0. Let's show that.

a1 = 200

n = 7

d = - 30

t7 = a1 + (n - 1)*d

t7 = 200 + (7 -1)*-30

t7 = 200 + 6*-30

t7 = 200 - 180

t7 = 20

This is the last term that is positive. when you take 30 away from t7 you are going to be in negative territory.

t8 = 200 + (8-1) * - 30

t8 = 200 + 7 * - 30

t8 = 200 - 210

t8 = - 10

Now the 9th term

t9 = 200 + (9 - 1)*-30

t9 = 200 + 8 * - 30

t9 = 200 - 240

t9 = - 40

Answer:

x≥3

Step-by-step explanation:

7x-28≥-7

Add 28 to each side

7x-28+28≥-7+28

7x≥21

Divide by 7

7x/7≥21/7

x≥3

Answer:

7x-28≥-7

7x≥21

x≥3

Answer:

(5x+2) (3x+4)

= 15x²+20x+6x+8

= 15 x²+ 26x+8

Hope this helps ^_^

Answer:

Step-by-step explanation:

Use FOIL method

(5x + 2)(3x + 4) = 5x * 3x + 5x *4 + 2*3x +2*4

                        = 15x² + 20x + 6x + 8    { now add like terms}

                       = 15x² + 26x + 8

Answer:

-k² - (7k - 5n) + 9n

-(-1)² - [7(-1) - 5(-2)] + 9(-2)

-1 - [-7 - (-10)] - 18

-1 - 3 - 18

= -22

Answer:

-9<x<31

Step-by-step explanation:

|11 – xl < 20

There are two solutions, one positive and one negative, remember to flip the inequality for the negative

11-x < 20       and 11 -x > -20

Subtract 11 from each side

11-x-11 <20-11   and 11-x-11 >-20-11

-x <9  and -x > -31

Multiply each side by -1, remembering to flip the inequality

x>-9  and x< 31

-9<x<31

Answer:

[tex]F_{1}[/tex] = 5

Step-by-step explanation:

Given [tex]F_{1}[/tex] is perpendicular to [tex]F_{2}[/tex] then Δ ABC is right

Given [tex]F_{2}[/tex] = [tex]F_{1}[/tex]

Then using Pythagoras' identity in the right triangle

[tex]F_{1}[/tex] ² + [tex]F_{2}[/tex] ² = (5[tex]\sqrt{2}[/tex] )² , that is

2[tex]F_{1}[/tex] ² = 50 ( divide both sides by 2 )

[tex]F_{1}[/tex] ² = 25 ( take the square root of both sides )

[tex]F_{1}[/tex] = 5

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

You don't get a free answer. I am, after all, a high school math teacher, so there has to be a lesson in with this.

The discriminant is part of the quadratic formula. It is:

[tex]b^2-4ac[/tex]. If this value is found to be > 0 and a perfect square, there are 2 real roots; if this value is found to >0 and not a perfect square, there are 2 complex roots; if this value is found to be = 0, then there is 1 real root with a multiplicity of 2; and finally, if this value is found to be < 0, then there are 2 imaginary roots. Also, it would help to know that, because we are dealing with the discriminant, which comes from the quadratic formula, and quadratics, by definition, have 2 solutions, you must have 2 solutions listed as the possible roots for the equation. Our equation is:

[tex]-4x^2=-8-10x[/tex] but in order to determine the a, b, and c for the discriminant, that equation has to be in standard form, set equal to 0:

[tex]-4x^2+10x+8=0[/tex]

From this we can see that a = -4, b = 10, and c = 8. Filling in the discriminant:

[tex]10^2-4(-4)(8)[/tex] which gives us a value of

100 - [4(-4)(8)] (don't forget orders of operation here!)

100 - (-128) = 100 + 128 = 228

This value is greater than 0 but is not a perfect square, so there are 2 complex roots. That means that there will be radicals in the solutions.

Answer:

2.08 meters

Step-by-step explanation:

From the diagram attached :

We can calculate the height of the shorter building using trigonometry :

s = Height of shorter building

t = height of taller building

Tanθ = opposite / Adjacent

θ = 36°

Adjacent = 12, opposite = s

Tan36° = s / 12

0.7265425 × 12 = s

s = 8.72 meters

s = height of shorter building 8.72 meters ( 2 decimal places)

Height of taller building :

Tanθ = opposite / Adjacent

θ = 48°

Adjacent = t ; opposite = 12

Tan48° = 12 / t

1.1106125 = 12 / t

1.1106125 × t = 12

t = 12 / 1.1106125

t = 10.80 meters ( 2 decimal places)

Height of Taller building = 10.80 meters

Difference in height :

(10.80m - 8.72m) = 2.08 meters

Answer:

Just one of the ones in the numerator and the one in the denominator

Step-by-step explanation:

a. Reflectional symmetry only. The mirror line is vertical along the center of the sunglasses. The left half mirrors over this line to get the right half, and vice versa. There isn't any rotational symmetry because we can't rotate the glasses (some angle between 0 and 360 exclusive of both endpoints) to have the image be the same as the preimage.

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b. Rotational symmetry only. The puzzle can be rotated 90 degrees and the before and after image will be the exact same. There isn't any reflectional symmetry here.

----------------------

c. Reflectional symmetry and rotational symmetry. Effectively a combination of parts a) and b). We have a horizontal line of symmetry to go with a vertical one. The angle of rotation is 180 degrees.

----------------------

d. Reflectional symmetry and rotational symmetry.  Similar to part c). This time the angle of rotation is 360/3 = 120 degrees. There are 3 lines of symmetry and they all pass through a vertex of the triangle, and the symmetry lines are perpendicular to the opposite side.

----------------------

e. Reflectional symmetry and rotational symmetry. We can rotate 180 degrees and not change the image. There are two lines of symmetry which pass through the center, one line is horizontal and the other vertical.

-----------------------

f. Rotational symmetry only. We don't have reflectional symmetry due to the smaller petals not matching up when reflections happen. But we can rotate the figure 120 degrees the same way we can with figure d.

Answer:

x = 3 and y = 0

Step-by-step explanation:

3y+x=3

-2y+5x=15

Isolate y in 3y + x = 3 :

[tex]y=[/tex] [tex]\frac{3-x}{3}[/tex]

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

[tex]-2 * \frac{3-x}{3} + 5x = 15[/tex]

Simplify the equation :

[tex]\frac{-6+17x}{3} =15[/tex]

Isolate x in [tex]\frac{-6 + 17x}{3} = 15[/tex] :

Proving x = 3

Isolate y in [tex]y = \frac{3-3}{3}[/tex] :

Proving y = 0

Your solved system of equations are x being 3, and y being 0.

Answer:

kinetic energy body when it hits the ground is 98000 joule

1000joule = 1 kilojoule

, kinetic energy body when it hits the ground is 98  kilo-joule

Step-by-step explanation:

conservation of energy states that total energy of a system remains constant.

Potential energy of body = mgh

m = mass

g = gravitational pull = 9/8 m/s^2

h = height

kinetic energy = 1/2 mv^2

where v is the velocity of body

________________________________________

Total energy for this at any point is sum of potential energy and kinetic energy

total energy at height h

v= 0

PE = 250*9.8*40= 98,000

KE = 1/2 m0^2  = 0

total energy at when ball hits the ground

h=0

PE = 250*9.8*0 =

KE = 1/2 mv^2  

_______________________________________\

Applying conservation of energy

Total energy at height h = total energy at ground

98000 = KE

Thus, kinetic energy body when it hits the ground is 98000 joule

1000joule = 1 kilojoule

, kinetic energy body when it hits the ground is 98  kilo-joule

Step-by-step explanation:

1)1/2,1/5 and 0

2)In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer

Answer:

100

Step-by-step explanation:

Hey there!

First, to find the cost of one apple, 50 ÷ 25, which equals 2.

At this point, i am not very sure if you meant to say 75 apples, or $75 apples, so I am just going to give both solutions.

If you meant 75 apples: 75 x 2 = $150

If you meant $75 apples: $75 ÷ 2 = 37.5

Since it isn't realistic to buy 37 apples and one half, round it to 37 apples.

Hope this helps!

Have a great day!

Answer:

1. Surveys are used to obtain specific information from a group of people. It is administered by politicians, professionals, sociologists, and other groups to obtain data from their subjects of interest.

2. Experiments are used to establish cause-and-effect relationships. Scientists use them for highly-controlled tests to give/withdraw credence to some hypotheses.

Step-by-step explanation:

Surveys, when applied to human subjects, are used to obtain data from a selected sample of subjects. Surveys, which can be applied through mails, telephones, the internet, in-person, and through other means are aimed at getting the opinions, thoughts, and beliefs of the participants. It is administered by politicians, professionals, sociologists, and other groups to obtain data from their subjects of interest. This data can be qualitative or quantitative.

Experiments are administered to provide support or refute a given hypothesis. They establish cause and effect relationships. Scientists use them for highly-controlled tests to give/deny credence to some hypotheses. Positive controls establish the hypothesis as true. They could be conducted in the laboratory, in the field, or through observations.

Answer:

The average value of the Function f(x) by squeeze theorem states that no extreme or greater value will exist within the designated area for f(x)

Answer:

358 and remainder of 3

Step-by-step explanation:

1. Divide it like any other problem

So your remainder would be 3

Hope this helps

Answer:

75 pounds

Step-by-step explanation:

(x) + (x) + (x+20) = 185

3x + 20 = 185

3x = 165

x = 55

Large dog = 55 + 20 = 75