The seaside train runs along a 156 mile route that takes 3 hours to complete. if it always runs at the same speed, write an equation to represent the distance and time.

We have proved the trigonometric expression cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A) by using C/D formula.

We are given the expression:

cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A)

We need to prove the expression.

We know that:

Cos C + Cos D = 2 cos ( C + D / 2) cos ( C - D / 2)

Using this identity, we get that:

= cos 5 A + cos A + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= 2 cos ( 5A + A / 2) cos ( 5A - A / 2) + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= 2 cos 3 A cos 2 A + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= cos 2 A ( 2 cos 3A + 1) = cos 2 A (1 + 2 cos 3 A)

= cos 2 A (1 + 2 cos 3 A) = cos 2 A (1 + 2 cos 3 A)

LHS = RHS

Hence proved.

Therefore, we have proved the trigonometric expression cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A) by using C/D formula.

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Answer:

6x-9=2

Step-by-step explanation:

Answer: B. 3x+6<6 or -2x+9>3

               C. 3x-5<10 and -2x+9>3

It is square-shaped as it is 4-straight sides with equal length, and every interior angle is right angle.

A right angle is defined as an angle in geometry and trigonometry that is exactly 90 degrees, or pi /2 radians, or one-quarter turn. The adjacent angles are right angles if a ray is positioned so that its terminus is on a line and they are equal. An interior angle is a shape's internal angle. The closed shape with sides and vertices is a polygon. All of the inner angles of a regular polygon are equal to one another. For instance, a square has interior angles that are all exactly right angles, or 90 degrees. The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.

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The number of wins is 68 ad losses is 26.

Let the number of losses = l

Therefore, the number of wins will be: = (2 × l) + 16 = 2l + 16

Total games = 94

Therefore we will add the equation

l + 16 + 2l = 94

3l + 16 = 94

3l = 94 - 16

3l = 78

Divide

l = 78/3

l = 26

Losses = 26

Number if wins = 2l + 16 = 2(26) + 16 = 52 + 16 = 68

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Answer:

C ≈ 31.42 in

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = 2πr ( r is the radius ) , then

C = 2π × 5 = 10π ≈ 31.42 in ( to 2 dec. places )

Answer:

c= 24

Step-by-step explanation:

Answer: it's 75

Step-by-step explanation:

acd= 165 bcd=90 165-90=75 therefore its a 75 degree angle

Answer:

x=3 and N is the mid-point.

Okay, so if N is the mid-point.

E D=15

E N=4 x -1

N D=4+ 2 x

6 x -3=15

Now get the 6 x by itself, so move the 3 over

So it would be: 6 x =18

So that would be 6 divided by 6 is x and then 18 divided by 6 equals 3

So, X equals 3

Answer:

2.47

Step-by-step explanation:

Perform long division.

[tex]Borrow\:8\:and\:2.\:You\:will\:see\: :)\\6 \cdot 2 = 12\\= 14 - 12 \\= 2\\Drop\:8\\= 28\\6 \cdot 4 = 24\\= 28 - 24\\= 4\\Drop\:2\\= 42\\6 \cdot 7 = 42\\= 42 - 42\\= 0\\\\= \boxed{2.47}[/tex]

➲ Hope it helps.

The product of two rational numbers is a rational number.

Definition and importance Imbalance or monetary disparity alludes to the contrast between the rich and poor, the endlessly the less wealthy it is shown by individuals' various situations inside the financial conveyance abundance, pay and pay. Imbalance is huge in a general public where hardly any individuals own a lopsided measure of the financial pie. Social imbalance alludes to the lopsided economic wellbeing in any general public, coming about because of inconsistent open doors, and lower awards for exertion. This sort of divergence is brought about by a sensation of being unjustifiably treated, or of segregation in host of regions, like restricted admittance to quality training and occupations. Notwithstanding pay imbalance, individuals who have specific individual attributes, either from birth, or which have been constrained on them by others, are in many cases the subject of inconsistent social treatment. These attributes incorporate such things as race, skin tone, and eye shape, as well as parentage, the guardians' societal position, inability, orientation and orientation character.

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Answer: A rational Number

Step-by-step explanation:

If a chip is randomly drawn from the bag, the probability it is not a red one is P(not red)  = 12/19.

Probability of an event A is the number of event A divided by all possible outcomes. Mathematically,

P(A) = n(A)/n(S)

where:

n(A) = number of event A

n(S) = number of all possible outcomes or sample space.

Suppose there 3 possible outcomes, A, B, and C, then:

n(S) = n(A) + n(B) + n(C)

1 = P(A) + P(B) + P(C)

The probability the outcome is not event A is equal to the probability of (B or C), or in other words,

However,

    P(B or C) =  P(B) + P(C)

It means,

     P(not A)  = 1 - P(A)

In the given problem:

Number of chips:

Blue = 3

Red = 7

Yellow = 4

Green = 5

Total chips = 3 + 7 + 4 + 5 = 19

If a chip is randomly drawn, the probability it will be a red one is:

P(red) = 7/19

Hence

P(not red) = 1 - 7/19 = 12/19

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Answer:

$25.23

Step-by-step explanation:

Step-by-step explanation:

Answer:

96.8 %

Step-by-step explanation:

not to bad

The inverse of y = 7x² - 10 is √(x+10)÷7

Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effects of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One is the result when a number is multiplied by its reciprocal, or inverse.

based on the available facts;

y = 7x^2 - 10

Switch y and x.

x = 7y^2 - 10

Solve for y.

Add 10 to both sides.

x + 10 = 7y^2

Divide both sides by 7.

(x + 10)/7 = y^2

√ both sides.

√(x + 10)/7 = y

Replace y with f^-1(x)

f^-1(x) = √(x + 10)/7y = 7x^2 - 10

Switch y and x.

x = 7y^2 - 10

Solve for y.

Add 10 to both sides.

x + 10 = 7y^2

Divide both sides by 7.

(x + 10)/7 = y^2

√ both sides.

√(x + 10)/7 = y

Replace y with f^-1(x)

f^-1(x) = √(x + 10)/7

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The conversion factors are used to multiply to 18 cm/s to get meters per minute is 60s/1m.

The conversion procedure depends on the unique circumstances and the targeted goal. A rule, a contract, technical requirements, or other norms that have been made public may control this. The precision of the initial measurement must not be increased or decreased during some unit conversions from one system to another. Soft conversion is another name for this. It doesn't need altering the way the thing being measured is physically constructed.

A hard conversion or an adaptable conversion, on the other hand, could not be perfect equivalents. In the new system, it converts the measurement to practical and usable numbers and units. Sometimes it entails rearranging the item's parts significantly or changing its size.

18 cm/s means 18 cm in 1 second.

You must change 1 second into a minute and 18 cm into meters when converting 18 cm/s into meters per minute. 18 cm = 18/100 meters.

1 second = 1/60 minutes.

18/100 meters per 1/60 minutes

18/100÷1/60 = 18/100 ×60/1

= 18 ×(60/100) meters per minute

The factor is 60s/100cm, which is equivalent to 60s/1m

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Here we have the quadratic function:

f(x) = 50 + 312*t - 16t²

The quadratic term:

- 16t²

Refers to the acceleration of the cannonball, in this case, caused by the gravitational force.

The linear term:

312*t

Refers to the vertical initial velocity of the cannonball (the velocity of the cannonball when t = 0)

The constant term:

50

Refers to the the initial height of the cannonball.

Now we want to graph between the boundaries "0 n", im not sure of what do you mean with that, so I will give the graph of the function in its whole domain, which can be seen below.

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Answer: 1.03(1.35x)

Step-by-step explanation:

The quadratic equation x² - 10x + 9 = 0. = 0 by completing the square, which of the following equations is a step in the process

(x – 10)2 = 34

(x – 10)2 = 16

(x – 5)2 = 34

(x – 5)2 = 16

Given that

To find

So, according to the question

We have

We have to solve that quadratic equation by completing square method.

So, we know that

In Completing square method, we have to convert this quadratic equation in square form.

So,

                  x² - 10x + 9 = 0.

Now, by multiplying both sides by the square of the x-coefficient, we get

                  x² - 10x + 9 + (-10/2)² = 0 + (-10/2)²

                       x² - 10x + 9 + (-5)² = 0 + (-5)²

Now, simplify it

                       x² - 10x + 9 + (-5)² = 0 + (-5)²

                          x² - 10x + 9 + 5² = 0 + 5²

                          x² - 2×5×x + 5² + 9 = 0 + 5²

∵ (a - b)² = a² - 2ab + b²

∴ (x - 5)² = x² - 10x + 5²

                                   (x - 5)² + 9 = 25   [since (x² - 10x + 5² = (x - 5)²]

                                        (x - 5)²  = 25 - 9

                                         (x - 5)² = 16

Answer:

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Answer:

156

Step-by-step explanation:

568-412=156

Answer:

Step-by-step explanation: 568-412=156

The value of x and BD are 29 and 62

From the diagram shown, we can see that AC and BD are diagonals of the rectangle

It is important to note that the diagonals of a rectangle are equal

Then,

AC = BD

4x - 54 =  33 + x

collect like terms

4x - x = 33 + 54

Add/ subtract like terms

3x = 87

Make 'x' the subject

x = 87/ 3

x = 29

But BD = 33 + 1x = 33 + 1(29) = 33 + 29 = 62

Thus, the value of x and BD are 29 and 62

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Answer: To graph y = x is simple, it is a line that intercepts at 0, and goes up by 1/1, or 1 (rate of change)

Step-by-step explanation:

1. For C, it's simple, it is y = -x, since the negative reciprocal slope is usually perpendicular to the original number (if not able to convert to fractions, like 1, it's just the same whole number, but a negative).

2. For the "Rotate your slope triangle 90 degrees"; seems simple, which I think you should do a reciprocal of the number, and make it a negative, for ie. 3 is a slope, when changed, it becomes -1/3. so the new slope is a negative reciprocal.

Answer:

?

Step-by-step explanation:

The inequality to represent the number of students who can attend the field trip on the bus will be C. s≤48 s is less than or equal to 48.

From the information, Mrs. Milleman's math class is planning to going on a field trip. The school bus which is taking them can hold at most 48 people.

Therefore, the inequality to represent the number of students who can attend the field trip on the bus will be C. s≤48 s is less than or equal to 48.

In conclusion, the correct option is C.

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The difference of depths between them, and which trench is deeper is (a) 2 km, and the Mariana Trench is deeper

What is the difference of depths between them, and which trench is deeper?

The given parameters are:

Mariana Trench = 11 km

Japan Trench = 9 km

The Mariana Trench is deeper because 11 is greater than 9

The difference between the depth is

Difference = 11 km - 9 km

Difference = 2 km

Hence, the difference of depths between them, and which trench is deeper is (a) 2 km, and the Mariana Trench is deeper

The equation of the absolute value function is y = -|x - 3| + 6

The given parameters are

Vertex = (3, 6)

Crosses the x-axis at (-3,0) and (9,0)

An absolute value equation is represented as

y = a|x - h| + k

Where

Vertex = (h, k)

So, we have

y = a|x - 3| + 6

At (-3, 0), we have

0 = a|-3 - 3| + 6

This gives

0 = a|-6| + 6

So, we have

0 = 6a + 6

Solve for a

a = -1

Substitute a = -1 in y = a|x - 3| + 6

y = -|x - 3| + 6

Hence, the equation of the absolute value function is y = -|x - 3| + 6

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Answer:

3pi

Step-by-step explanation:

all of the other ones are out of range

Reason:

Both have the same slope of 3/2, aka "three-halves".

The slope is the rate of change. It tells us how fast or slow a plant is growing. The larger the number, the faster the growth.

Recall that y = mx+b has,

m = slope

b = y intercept

Therefore, the slope is thee number just to the left of x.

For the given function, we have that:

The domain of a function is the set that contains all possible input values for the function. In a graph, it is given by the values of x.

In this problem, the function is defined between x = -4 and x = 4, hence the domain is [-4,4].

The zeros are the values of x for which f(x) = 0, that is, when it crosses the x-axis.

Hence, for this problem, the zero is at (0,0).

The function is positive when it is above the x-axis, and negative when it is below, hence:

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