State the domain and range of the following function using set notation. G(x)= -5x2 write the domain of the function set

Step-by-step explanation:

(cos(3A) − sin(3A)) / (1 − 2 sin(2A))

Use double angle formula:

(cos(3A) − sin(3A)) / (1 − 4 sin A cos A)

Use triple angle formulas:

(4 cos³A − 3 cos A − 3 sin A + 4 sin³A) / (1 − 4 sin A cos A)

Group and factor:

(4 (cos³A + sin³A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)

Factor the sum of cubes:

(4 (cos A + sin A) (cos²A − cos A sin A + sin²A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)

Use Pythagorean identity:

(4 (cos A + sin A) (1 − cos A sin A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)

Factor out cos A + sin A:

(cos A + sin A) (4 (1 − cos A sin A) − 3) / (1 − 4 sin A cos A)

Simplify:

(cos A + sin A) (4 − 4 cos A sin A − 3) / (1 − 4 sin A cos A)

(cos A + sin A) (1 − 4 cos A sin A) / (1 − 4 sin A cos A)

cos A + sin A

Answer:

[tex] \boxed{\sf (x + y)(6x + 5y)} [/tex]

Step-by-step explanation:

Factor the following:

[tex] \sf \implies 6 {x}^{2} + 11xy + 5 {y}^{2} [/tex]

The coefficient of x² is 6 and the coefficient of y² is 5. The product of 6 and 5 is 30. The factors of 30 which sum to 11 are 5 and 6.

So,

[tex] \sf \implies 6 {x}^{2} + (6 + 5)xy + 5 {y}^{2} [/tex]

[tex] \sf \implies 6 {x}^{2} + 6xy + 5xy + 5 {y}^{2} [/tex]

[tex] \sf \implies 6x(x + y) + 5y(x + y)[/tex]

Factor (x + y) from 6x(x + y) + 5y(x + y):

[tex] \sf \implies (x + y)(6x + 5y)[/tex]

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Explanation:

If sin(x) = 3/5, then cos(x) = 4/5 through the use of the trig identity

sin^2(x) + cos^2(x) = 1

This is assuming that x is in quadrant Q1.

Plug those values into the identity below and simplify.

sin(2x) = 2*sin(x)*cos(x)

sin(2x) = 2*(3/5)*(4/5)

sin(2x) = 24/25

Answer:

24/25

Step-by-step explanation:

Trig functions relate the angle of a triangle with the sides of that triangle (right triangle)

sin(x)= 3/5 (opposite/ hypotenuse) (25=9-x^2, using pythag. theorem, remaining side= 4)

now, cos(x)= 4/5

now, the double angle identity states:

sin2x= 2sinxcosx

so,

sin2x= 2 * (3/5) * (4/5) =

24/25

Answer: 162°

Step-by-step explanation:

Using exterior angle methods,

sum total of exterior angle of polygon =  ³⁶⁰/ₙ , where n is the size of the polygon.                                                 =   ³⁶⁰/₂₀

One exterior angle                               =  18°.

Now the interior angle                          = 180° - 18° ( angle on a straight line )

Therefore, the measure of the interior angle = 162°.

Not , Other methods can still be applied.

Answer:

-8.

Step-by-step explanation:

y = 8 - 2x.

x = 8.

y = 8 - 2(8)

= 8 - 16

= -8.

Hope this helps!

Answer:

x=5/3

Step-by-step explanation:

Answer:

5/8 of a gallon

Step-by-step explanation:

since a cup is 1/16 of a gallon and were asked what part of a gallon is 10 cups so what were going to do is....

(1/16)*10= 10/16 = 5/8

Answer:

from my calculation, the answer is B

The midpoint of the segment between the points (15,−9) and (−2,−18) will be (−13/2, −27/2). Then the correct option is C.

Let C be the mid-point of the line segment AB.

A = (x₁, y₁)

B = (x₂, y₂)

C = (x, y)

Then the midpoint will be

x = (x₁ + x₂) / 2

y = (y₁ + y₂) / 2

The midpoint of the segment between the points (15,−9) and (−2,−18) will be

x = (15 – 2) / 2

x = –13 / 2

y = (–9 – 18) / 2

y = –27/2

Then the correct option is C.

More about the midpoint of line segment AB link is given below.

https://brainly.com/question/17410964

#SPJ5

Answer:

24.78%

Step-by-step explanation:

Initial price = $230

Final price = $287

change in price = final price - initial price

= 287 - 230

= $57

Percent change

= (change in price / initial price) x 100%

= (57 / 230) x 100%

= 24.78%

Answer:

0 => -⅘ => 1.5 => 3 => -4 => [tex]-\frac{11}{2} (-5.5)[/tex]

Step-by-step explanation:

The greater the absolute value of a slope, the steeper the slope. By absolute value, we mean the non-negative value of tthe .

To arrange the slope values, from the least steep to the steepest, ignore the negative sign in any of the slope values.

Thus, in the order from the least steep to the steepest, we have:

0 => -⅘ => 1.5 => 3 => -4 => [tex]-\frac{11}{2} (-5.5)[/tex]

The greater the absolute value of the slope, the greater the vertical movement. The greater the vertical movement, the steeper the slope.

A slope value of 0 connotes a horizontal line.

Answer:

1190

Step-by-step explanation:

Here, you need to add the squares of the measurements.

20² + 10² + 13² + 11² + 20² =

= 400 + 100 + 169 + 121 + 400

= 1190

Answer:

We have a circular track that is 1 meter wide, which would mean that the diameter is equal to 1 meter.

First, we want to define this problem as a one dimensional problem. The position 0 is in the doorway, the bedroom is the positive axis, and the hallway is the negative side.

P(t) = R*cos(c*t) + R*sin(c*t).

Where R is the amplitude, in the case of the circular motion, R is equal to the radius.

If the diameter is 1m, the radius is 1m/2 = 0.5m

The equation now is:

P(t) = 0.5m*cos(c*t) + 0.5m*sin(c*t).

We also know that for t = 0s, the train is as far into the bedroom as it can, the maximum position is P = 0.5m

Then  we have:

P(0s) = 0.5m*1 + 0.5*0 = 0.5m

And we also know that the period is t = 2seconds.

The period for the sine and cosine functions is 2*pi, then:

c*2s = 2*pi

c =pi/s

The function now is:

P(t) = 0.5m*cos(t*pi/s) + 0.5m*sin(t*pi/s)

When this function is positive, this means that the train is inside her bedroom, when the function is negative, the train is outside the bedroom, when P(t) = 0, the train is in the doorway.

Answer:

The answer is below

Step-by-step explanation:

International system of unit (SI unit) are standard units which are universally accepted. There are 7 basic SI units which are meter (m), second (s), kilogram (kg), mole (mol), ampere (A), candela (cd) and kelvin (K).

The SI unit of flow rate is the m³/s.

The conversions needed are:

1 minute = 60 seconds,

1 cm³ = 1 ml = 0.001 ml,

1000000 cm³ = 1 m³,

1 L = 0.001 m³

We have to convert 5.0 liters of blood per minute. to m³/s. Therefore:

[tex]5\ L/minute=\frac{5\ L*0.001\ m^3}{1\ min*60\ s}=8.33*10^{-5} \ m^3/s[/tex]

Answer:

e(as in variable)=1/7x+2, e(as in euler)=2.388326

Step-by-step explanation:

2.718282

7

+181−179

=2.388326

Answer: Hi!

Since this is a right triangle, we already know that one angle is 90 degrees. Since the angles of a triangle all add up to 180 degrees, and the two unknown angles will be equal, all we have to do is subtract 90 from 180 and then divide the difference by 2!

180 - 90 = 90

90 ÷ 2 = 45

The two missing angles are each 45 degrees.

(x = 45 and y = 45)

Make sure to put the degrees sign after your answers!

Hope this helps!

Answer:

45 degrees.

Step-by-step explanation:

All of the angles in a triangle is 180 degrees.

Knowing that we subtract 90 degrees, the right angle from 180 degrees.

180-90=90

Since both the angles are equal,

90/2=45

Hope this helps :)

Have a great day!

Answer:

0.049.

Step-by-step explanation:

The number after the 9 is 4 so 9 remains.

Answer:

(a) 57.8 cm²

(b) 158.7 in²

Step-by-step explanation:

(a)

The area of a circle is denoted by A = 2πr, where r is the radius.

Here the radius is r = 9.2, so plug this in:

A = 2πr

A = 2π * 9.2 ≈ 57.8 cm²

(b)

The diameter is twice the radius, so since the diameter is 50.5 inches, the radius will be 50.5/2 = 25.25 inches.

Plug this into the formula:

A = 2πr

A = 2π * 25.25 ≈ 158.7 in²

~ an aesthetics lover

The x is a placeholder for a number. Think of x like a box and inside the box will go a number. In this case, -4 will replace x

7 - 2x = 7 - 2(-4) = 7 + 8 = 15

Answer:

3m +7n  +5т

Step-by-step explanation:

6m +7n +5т — Зm

Combine like terms

3m +7n  +5т

Answer:

4255 students choose Drama

4995 students choose Other

3700 students choose Comedy

Step-by-step explanation:

18500 x _% =

Ex: 18500 x 23% = 4255.

Answer:

T = Z + pr

Z + T = pr

Z/r + T/r = p

Answer:

p = Z/r + T/r

Answer:

A

Explanation

8/11 = 8 ÷ 11

BRAINLIEST PLEASE

Question:

Suppose we want to choose 5 objects, without replacement, from 16 distinct objects.

A) How many ways can this be done, if the order of the choices is relevant?

B) How many ways can this be done, if the order of the choices is not relevant?

Answer:

A. 4368 ways

B. 524160 ways

Step-by-step explanation:

Given

[tex]Objects = 16[/tex]

[tex]Selection = 5[/tex]

Required

A & B

Solving (A)

Because the order of choice is irrelevant, this implies combination and it is calculated as follows;

[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]

Where n = 16 and r = 5

[tex]^{16}C_5 = \frac{16!}{(16-5)!5!}[/tex]

[tex]^{16}C_5 = \frac{16!}{11!5!}[/tex]

[tex]^{16}C_5 = \frac{16 * 15 * 14 * 13 * 12 * 11!}{11!5!}[/tex]

[tex]^{16}C_5 = \frac{16 * 15 * 14 * 13 * 12}{5!}[/tex]

[tex]^{16}C_5 = \frac{16 * 15 * 14 * 13 * 12}{5 * 4 * 3 * 2 * 1}[/tex]

[tex]^{16}C_5 = \frac{524160}{120}[/tex]

[tex]^{16}C_5 = 4368\ ways[/tex]

Solving (B)

Because the order of choice is relevant, this implies permutation and it is calculated as follows;

[tex]^nP_r = \frac{n!}{(n-r)!}[/tex]

Where n = 16 and r = 5

[tex]^{16}P_5 = \frac{16!}{(16-5)!}[/tex]

[tex]^{16}P_5 = \frac{16!}{11!}[/tex]

[tex]^{16}P_5 = \frac{16 * 15 * 14 * 13 * 12 * 11!}{11!}[/tex]

[tex]^{16}P_5 = 16 * 15 * 14 * 13 * 12[/tex]

[tex]^{16}P_5 = 524160\ ways[/tex]

In other words, you'll use the SAS similarity property with 3/2 as the scale factor

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

Explanation:

Choice A is not correct because we don't have enough info about all three pairs of sides.

Instead we'll go with SAS similarity. This is the idea where we'll use two pairs of sides to see if they are in the same proportion, and we'll also use the included angle between the two sides. The angles ABE and DBC are congruent as they are vertical angles. So that's where the "A" comes from in "SAS".

As for the S terms, we divide the corresponding sides like so

DB/AB = 9/6 = 3/2

BC/BE = 1.5/1 = 15/10 = 3/2

The scale factor as a fraction is 3/2, which converts to the decimal form 1.5

This says that triangle DBC has sides that are 3/2 = 1.5 times longer than corresponding sides in triangle ABE.

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

If you're curious how the sides correspond, then look at the ordering of ABE and DBC. The order is important when it comes to similar triangles.

AB and DB are the first two letters of ABE and DBC respectively. So we have AB pair up with DB.

Similarly, BE and BC pair up because they are the last two letters of ABE and DBC respectively.

We divide sides of DBC over sides of ABE to get the scale factor from ABE to DBC. The scale factor must be some result larger than 1 do indicate an enlargement is going on.

Answer:

[tex]A(L) = 4L - L^2[/tex]

Step-by-step explanation:

Given

Perimeter = 8m

Required

Determine its area as a function of length

Represent Length and Width with L and W, respectively;

Perimeter (P) is calculated as thus;

[tex]P = 2(L + W)[/tex]

Substitute 8 for P

[tex]8 = 2(L + W)[/tex]

Divide both sides by 2

[tex]4 = L + W[/tex]

Make W the subject of formula

[tex]W = 4 - L[/tex]

Area (A) of a rectangle is calculated as thus:

[tex]A = L * W[/tex]

Substitute 4 - L for W

[tex]A = L * (4 - L)[/tex]

Open bracket

[tex]A = 4L - L^2[/tex]

Represent as a function

[tex]A(L) = 4L - L^2[/tex]

Area of rectangle in terms of length L is

[tex]A(L)= 4L-L^2[/tex]

Given :

A rectangle has perimeter 8 m. Express the area A of the rectangle as a function of the length, L, of one of its sides

We know that the perimeter of rectangle formula is

[tex]perimeter = 2(length)+2(width )[/tex]

perimeter is 8m

Let the length of rectangle is L

[tex]P=2L+2W\\8=2(L+W)\\4=L+W\\W=4-L[/tex]

so width is 4-L

Now we use area formula

Area of rectangle = length times width

[tex]A=L(W)\\A=L(4-L)\\A= 4L-L^2[/tex]

Area of rectangle in terms of length L is

[tex]A= 4L-L^2[/tex]

Learn more : brainly.com/question/5085323

Answer:

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

liked- brought

Complete Question

In a random sample of

five mobile​ devices, the mean repair cost was $75.00 and the standard deviation was ​$11.50

Assume the population is normally distributed and use a​t-distribution to find the margin of error and construct a 95​%

confidence interval for the population mean. Interpret the results.

Answer:

The margin of error is  [tex]E = 10.1[/tex]

The 95% confidence interval  is [tex]64.9 < \mu < 85.1[/tex]

Step-by-step explanation:

From the question we are told that

  The sample mean is  [tex]\= x = \$ 75.00[/tex]

   The  standard deviation is  [tex]\sigma = \$ 11.50[/tex]

   The sample size is  n = 5

Given the that the confidence level is  95% then the level  of significance is mathematically represented as

            [tex]\alpha = 100 -95[/tex]

            [tex]\alpha = 5\%[/tex]

            [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is  

         [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]

substituting values

         [tex]E = 1.96* \frac{11.50 }{ \sqrt{5} }[/tex]

        [tex]E = 10.1[/tex]

The 95% confidence interval  is mathematically represented as

        [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

        [tex]75 - 10.1< \mu < 75 + 10.1[/tex]

        [tex]64.9 < \mu < 85.1[/tex]

Answer:

The answer is A

Its A.

Reasoning: Because I Took The Test