2.2 Determine the general solution of 2.2.1 3 sin x = cos x
2.2.2 2 cos²x + 5 sin x = 4​

Answer:

Parameter

Step-by-step explanation:

A statistic is a piece of data we derive from analyzing the data from a sample, a subset of a larger population. A parameter is derived from analyzing that population. Here, we would call the mean of the sample - 4 - a statistic, and the mean of the population - 4.3 - a parameter.

The probability that the first two songs played are slow songs is approximately 0.622 or 62.2%.

To calculate the probability that the first two songs played are slow songs, we need to consider the total number of ways the first two songs can be selected and the number of ways to choose two slow songs out of the eight available.

Given:

Total number of songs = 10

Number of slow songs = 8

Step 1: Calculate the total number of ways to choose two songs out of ten (without replacement), which is represented by "10C2" (combinations of 10 things taken 2 at a time):

10C2 = (10 * 9) / (2 * 1) = 45

Step 2: Calculate the number of ways to choose two slow songs out of eight:

8C2 = (8 * 7) / (2 * 1) = 28

Step 3: Find the probability that the first two songs played are slow songs by dividing the number of favorable outcomes (choosing two slow songs) by the total number of possible outcomes (choosing any two songs from the CD):

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 28 / 45 ≈ 0.622

So, the probability that the first two songs played are slow songs is approximately 0.622 or 62.2%.

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Answer:

( 4u + a ) + ( y + 6 )

Step-by-step explanation:

4u(y+6) + a(y+6) ...

The answer is ( 4u + a ) + ( y + 6 )

Answer:

Step-by-step explanation:

x + 3 = -x - 1

2x + 3 = -1

2x = -4

x = -2

y = -2 + 3

y = 1

(-2, 1)

answer is A

Answer:

2 cups

Step-by-step explanation:

Formula: divide the volume value by 16

so its 32 divided by 16

The midpoint approximation of the area under the curve f(x) = 2x(x-4)(x-8) over the interval [0, 4] with 4 subintervals is 132.

The value of f(1/2) will be:

= 2(1/2)(1/2 - 4)(1/2 - 8)

= 105/4

The value of f(3/2) will be:

= 2(3/2)(3/2 - 4)(3/2 - 8)

= 195/4

The value of f(5/2) will be:

= 2(5/2)(5/2 - 4)(5/2 - 8)

= 165/4

The value of f(7/2) will be:

= 2(7/2)(7/2 - 4(7/2 - 8)

= 63/4

Therefore, the midpoint approximation will be:

= 1/4(105 + 195 + 165 + 63)

= 132

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Answer:

1.5 gallons

Step-by-step explanation:

(3/4) × (2 gallons) = 1.5 gallons

HOPE THIS HELPS AND HAVE A NICE DAY <3

Answer :

Explaination :

Here we are given with two equations,

So in order to calculate the number of hours (h). We would simply substitute the value of f in first equation. (i.e., keeping them equal)

>> 7h + 20 = 10h + 5

>> 10h - 7h = 20 - 5

>> 3h = 15

>> h = 15 / 3

>> h = 5

Answer:

56.31 degrees

Step-by-step explanation:

6 = opposite and 4 = adjacent

Tan = opposite over adjacent

Tan(theta)=6/4

=56.30993247

answer: 15

steps:

i means √-1

but in this problem treat

i like x

(7-i) + (5 + 3i) - (-3 + 2i) =

(7-i) + (5 + 3i) +3 - 2i

7-i + 5 + 3i +3 - 2i =

7-i + 5 + 3i +3 - 2i

7+5+3-i+3i-2i

7+5+3+2i-2i

7+5+3 =

15

Answer:

y=x-7

Step-by-step explanation:

Rise over run

-6-(-7)

---------- = 0

-4-(-4)

Point Slope form

y+7=0(x+4)

Y=MX + B

y=x-7

The equation of the line passing through the points (−4,−7) and (−4,−6) in the form of a will be a + 4 = 0.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

The equation of the line passing through the points (−4,−7) and (−4,−6) will be

y + 6 = [(−6 + 7) / (−4 + 4)] (x + 4)

y + 6 = (1/0)(x + 4)

x + 4 = 0

Put x = a, then the equation will be

x + 4 = 0

a + 4 = 0

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The area of the training field to the nearest whole number is 8719 msq. meter

The given field is made up of a rectangle and 2 semi circles. The formula for calculating the area of the field is:

Area of the field = area of circle + area of rectangle

Area of field = 3.14(32)² + (86)(64)
Area of field = 3215.36 + 5504

Area of the field = 8719 msq. meter

Hence the area of the training field to the nearest whole number is 8719 msq. meter

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Answer:

Because -4 is 4 units away from 0.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

Geary street :D

they intersect here

click on the photo. it's not a link it's a screenshot of where they intersect

Answer:

D.

Step-by-step explanation:

it should be the sales tax because you pay a little bit more.

Answer: -17/4

Step-by-step explanation:

The solutions to the equations are (1.702,4.7) and (-4.7,-1.7).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The two given equations ( x + 3 ) and ( 13 ( x+5)(x-1) intersects at the ponits (1.702,4.7) and (-4.7,-1.7).

The graph of the above equations is attached with an answer.

Therefore the solutions to the equations are (1.702,4.7) and (-4.7,-1.7).

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Answer:

1) As it is the coeficient of x² is 1, we need to find two numbers whose Sum S(x)=3 and the same numbers whose product is 2, P(x)= 2

S(x) = (  ) + (  ) =3

P(x) = (   )  *  (   ) =2

S(x) = ( 2 ) + ( 1 ) =3

P(x) = (  2 )  *  ( 1  ) =2

These numbers in bold will be coeficients of x.

Rewrite the Trinomial x²+ 3x +2 as x² +2x+1x+2

So x²+3x+2 =x²+2x+1x+2

x² +2x+x+2   Put the x in evidence

x(x+2)+1(x+2)  Find the Maximum Common Divider

(x+1)(x+2)

2) x²+x-6=0

Applying the same procedure. Which two integer number whose sum is 1 and whose Product is -6?

S(x) = ( 3  ) + ( -2  ) =1

P(x) = ( 3  )  * ( -2  ) =-6

Rewrite

x²+x-6

x²+3x-2x-6      Group them

x(x+3)-2(x+3)   Common Term

(x+3)(x-2)

3) Since the a coeficient is ≠ 1, a little adjustment must be made on our algorithm for -2x²+4x+30=0

Firstly multiply a*c, in this case -2 * 30 = -60

Which two numbers multiplied by themselves will turn out to be -60 and whose sum is -60? Since we're working with integers factoring out may be very helpful.

P(x)=  ( 10  )  *   ( - 6 )  = -60

S(x) = (  10 )  +  (  -6 )  = 4

Rewriting

-2x²+10x-6x+30   Group them

2x(x+5) -6(x+5)

(2x-6)(x+5)   Inserting the -1 to finally adjust

-1(2x-6)(x+5)

4) Explanation is the same principle as a≠1

3x²+4x-4=0

P(x) = ( 6  )  *  (-2  ) = -12

S(x) = (  6 ) +  ( -2  )  = 4

3x²+4x-4 = 3x²+6x-2x-4

3x²+6x -2x+4

3x(x+2)-2(x-2)

(3x-2)(x+2)

The other ones are just applications of these, above.

Step-by-step explanation:

Step-by-step explanation:

that kind of wording is always misleading.

please give my regards and comments to your teacher.

a square root has ALWAYS 2 solutions : a positive AND a negative one.

in that sense the negative solution to a square root is NOT an extraneous solution.

only any value of x < -10 (to make the argument of the square root negative) as solution would be extraneous.

so, if your teacher wants to say that only the positive solutions of a square root are allowed, it has to be said as an extra definition or by applying the "+" sign to the square root.

so,

x + 4 = sqrt(x + 10)

since the 2 solutions are already given to us, we only need to use them in the equation and see what happens.

x = -1

-1 + 4 = sqrt(-1 + 10)

3 = sqrt(9) = 3 (actually, it is ±3)

so, x = -1 is a real solution.

x = -6

-6 + 4 = sqrt(-6 + 10)

-2 = sqrt(4) = 2 (actually, it is ±2)

so, based on your teacher's expectation of only positive results of the square root (even though it was not stated),

x = -6 is an extraneous solution.

therefore, the third answer (c) is the "correct" answer.

but actually, formally, the second answer (b) is the truly correct answer.

Answer:

f'(x) = 2x - 20

Step-by-step explanation:

f(x) = 1/2 x + 10

Switch x and y.

y = 1/2 x + 10

Solve for y by itself.

x = 1/2 y + 10

x - 10 = 1/2 y

y = 2 * (x - 10)

f'(x) = 2x - 20

Two polygonal regions are similar with scale factor 7, if the area of the smaller region is 490 cm² then the area of the larger region would be 3430 cm²

An equation is an expression that shows the relationship between two or more numbers and variables.

Dilation is the increase or decrease in the size of a figure by a scale factor.

Two polygonal regions are similar with scale factor 7. The area of the smaller region is 490 cm², hence:

Area of larger region = 7 * 490 cm² = 3430 cm²

Two polygonal regions are similar with scale factor 7, if the area of the smaller region is 490 cm² then the area of the larger region would be 3430 cm²

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Volume of a Rectangular Prism = length x width x height

Length = 4

Width = 2

Height = a

Volume = 7.2

7.2 = 4 x 2 x a

7.2 = 8 x a

a = 0.9

Answer: a = 0.9

Hope this helps!

Answer:

a = 0.9 cm

Step-by-step explanation:

Volume of a rectangular prism: L*W*H

Substitute the values above into the formula:

V = L*W*H

7.2 = 4*2*a

7.2 = 8a

/8     /8

0.9 = a

Therefore, the value of a is 0.9 cm.

Hope this helps!

Answer:

y = -2x

Step-by-step explanation:

From the figure, the given line passes through the points (0, 0) and (-4, 8).

Recall that the equation of a straight line is given by

Thus, the equation of the given figure is given by

-4y = 8x

Therefore, the answer is y = -2x.

Answer:

V = 2143.57

Step-by-step explanation:

To find the volume of a sphere you need to use this formula:

[tex]V = \frac{4}{3}\pi r^{3}[/tex]

r = radius

Solve:

You need the radius from the diameter. Divide 16/2 which is

8.

[tex]V = \frac{4}{3}(3.14) 8^{3}[/tex]

V = 2143.57

Answer: (a) 8 : 15 (b) 8 : 7

Step-by-step explanation: all marbles is 8+7 = 15

ratio of blue marbles to ALL marbles

8 : 15

ratio of blue marbles to red

8 : 7

Answer:

  33°

Step-by-step explanation:

Where a transversal crosses parallel lines at right angles, all of the angles at their points of intersection are right angles.

__

Angles at U are right angles, congruent to ∠UXZ. So, acute angle UXW in right triangle UXW is the complement of acute angle UWX:

  ∠UXW = 90° -57° = 33°

Using a system of equations, it is found that they expect to sell 175 adult tickets and 350 student tickets.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

They expect that twice as many students as adults will attend, hence:

s = 2a.

Their goal is to earn $1,500 from ticket sales, hence:

10a + 5s = 1500.

10a + 5(2a) = 1500.

20a = 1500.

a = 1500/20.

a = 175.

s = 2a = 2 x 175 = 350.

They expect to sell 175 adult tickets and 350 student tickets.

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Answer: 3 hours

Step-by-step explanation:

Bottle = 3.6 liters / 3600 milliliters

Rate = 20 ml a minute

3600 / 20 = 180 minutes

60 minutes = 1 hour

180 / 60 = 3 hours