Identify intervals on which the function is (a) increasing, (b) decreasing, and (c) constant. In each case, assume that the domain of the function is (-∞, ∞) and that any characteristics of the graph continue as indicated. Q(t) = 2(2 - t) + 4t

The terminal point on the unit circle determined by 5π/6 radians is (-√3/2, 1/2).

To find the terminal point on the unit circle determined by an angle of 5π/6 radians, we need to consider the coordinates of the point (x, y) on the unit circle that corresponds to this angle.

The unit circle has a radius of 1 unit, and the terminal point can be found by using the trigonometric functions cosine and sine.

For the angle 5π/6, the cosine function gives us the x-coordinate, and the sine function gives us the y-coordinate.

Using the exact values of cosine and sine for 5π/6, we have:

cos(5π/6) = -√3/2

sin(5π/6) = 1/2

Therefore, the terminal point on the unit circle determined by 5π/6 radians is (-√3/2, 1/2).

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The end-points of the line segment will be negative 1.25 and 0.25.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The length of the line segment is 1.50 units and the midpoint of the line segment is negative 0.50. Then the end-points of the line segment are given as,

⇒ - 0.50 ± (1.50) / 2

Simplify the expression, then we have

⇒ - 0.50 ± (1.50) / 2

⇒ - 0.50 - (1.50) / 2, - 0.50 + (1.50) / 2

⇒ - 0.50 - 0.75, - 0.50 + 0.75

⇒ - 1.25, 0.25

The end-points of the line fragment will be negative 1.25 and 0.25.

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Answer:

90°

hope this helps :)

Answer:

90 degrees because when you cut each of them they will each measure 90 degrees.

The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

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

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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Answer of the given question are respectively,

\(-x^2y , 2w ,\\\\h^6 , -14a^5b^2\\x^6 , 4m^8\\9x^4/14 , y^2\\-5/x^2 , 1/2k\\7 , 1\)

Exponent:

                          A quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression.

        Example:

                             \(2^3\) = 2 × 2 × 2

Combine like term:

 1. \(9x^2y -10x^2y\) = \(-x^2y\)

 2. Subtract 6w from 8w

          8w -6w = 2w

Rule:

          \(x^{a} * x^{b} = x^{a+b} \\\\\)

1.

        \(h^2 * h^4 = h^{2+4} \\ \\\\= h^6\)              

2.  

        \((-2a^2b).(7a^3b)\\\\-14 a^{2+3} b^{1+1} \\\\= -14 a^5 b^2\)

Rule:

       \((x^a)^b = x^{ab}\)

  1.  \((x^2)^3 = x^6\)

  2.

         \((-2m^3)^2 * m^2 \\\\4m^6*m^2\\\\4m^8\)

Rule:

           \(x^a/x^b = x^{a-b}\)

1.

   \(27x^5/42x\\\\= 9x^4 /14\)

2.

          \((y^3)^2/y^4\\\\y^6/y^4\\\\y^2\\\)        

Rule:

            \(x^{-a}= 1/x^a\)

1.

    \(-5x^{-2} \\\\= -5/x^2\)

2.

    \(4k^2/8k^3\\\\= k^{-1} /2\\\\= 1/2k\)

Rule:

           \(x^0 =1\)

1.

         \(7x^0\\\\= 7\)

2.

         \((w^4)^2/w^8\\\\w^8/w^8\\\\w^0\\\\=1\)

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Answer:

m = -3

Step-by-step explanation:

First, find two clear points:

(1, -2) (0, 1)

Then, use the slope formula:

m = y2 - y1

      x2 - x1

m = 1 - (-2)

       0 - 1

   = 3  = -3

     -1

m = -3

This means that the rise-over-run is -3 over 1, or 3 over -1.

Which means three down and 1 to the right, or 3 up and 1 to the left.

Slope is the steepness of the line.

In the provided text is a questionnaire or form related to a research tool for assessing a campaign in the community.

The first question asks whether the campaign pursues its aims, with the options of answering "YES" or "NO." The respondent is then instructed to elaborate on their answer.

A questionnaire is a research tool   used to collect data by presenting a series of questions to respondents,typically in a written format.

Questionnaires are an important research tool as they allow researchers to gather   large amounts of data from a large number of participants in   a standardized and efficient manner.

They provide a structured approach to collecting information,allowing for easy analysis and comparison   of responses.

Questionnaires can be used in various   research settings and are particularly useful for collecting quantitative data,measuring attitudes, opinions, behaviors, and gathering demographic information.

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Answer:

x<2

Step-by-step explanation:

You're answer is wrong because the circle on the number line is not closed. If it was closed, it would be x ≤ 2 , but because it is open, it would be just be x<2

This is the absolute value function shifted to the left 2 units:

| x+2 | = {

x+2 if x >= -2,

-(x+2) if x < -2

}

In mathematics, a function is a relationship between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is a rule or a set of rules that assigns each input value exactly one output value. Functions can be represented using equations, graphs, or tables. They are used to model real-world phenomena and solve problems in various fields such as science, engineering, economics, and finance.

Here,

The absolute value function is defined as:

| x | = {

x if x >= 0,

-x if x < 0

}

To shift the function to the left 2 units, we can replace x with (x+2):

| x+2 | = {

x+2 if x+2 >= 0,

-(x+2) if x+2 < 0

}

Simplifying further, we get:

| x+2 | = {

x+2 if x >= -2,

-(x+2) if x < -2

}

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Complete question:

The absolute value function is defined as:

| x | = {

x if x >= 0,

-x if x < 0

}

Find the function when shifted to the left 2 units.

Answer:

im allergic to cookies

Step-by-step explanation:

ANSWER:

1/728

STEP-BY-STEP EXPLANATION:

The probability of drawing 544 is the same as the probability of choosing a random number from the 728 numbers in the box, since it is only one chip among the 728.

Therefore:

P = 1/728 =0.0014

Answer:

answer

A) 11.7²+X.6²

B) 7²+10² 0²

Answer:

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

3/5 part of 60 CD's were gifts.

That makes:

Answer:

the equation y=mx+b

The y intercept is the point on a line that passes through the y line.

To solve the y intercept, solve y=mx+b.

m being slope

y being a y point

x being a x point

and b being y intercept.

Step-by-step explanation:

Using the Empirical Rule, it is found that 99.7% of the weights are between 180 g and 480 g.

It states that, for a normally distributed random variable:

Hence, the bounds of the interval containing 99.7% of the weights is given by:

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Answer:$ 24,679.20 or 514.15 a month

Step-by-step explanation: 565(.09) is 50.85 which needs to be deducted from the payment of 565 because he needs to be able to pay for interest. 514.15 is then multiplied by 48 months which will bring you to 24,679.20

Answer:

The simple answer is 15 only

Answer:

f(x)=100x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

We accept Hₐ   there is enough evidence to claim that the incidence of ASD is bigger in this state than it is nationally

Step-by-step explanation:

The population follows a binomial distribution, and the fact that

p₀ = 1205/32600 = 0,03696       and then q₀  = 1-0,03696 = 0,9630

And both

p₀*n = 0,03696*32600 = 1205 > 10

q₀*n = 31395 > 10

The binomial distribution can be approximate to a Normal Distribution, then we need to develop a one tail test ( to the right) to evaluate if the claim " There is sufficient data to show that the incident rate is higher in the mentioned state than the national one.

Therefore:

Hypothesis Test                    H₀    ⇒    p₀ = p

Alternative Hypothesis        Hₐ   ⇒     p₀ > p

p is the population proportion mean

p = 1/88  =  0,011

We must test having a very wide Confidence Interval since the matter we are trying is public health then we choose CI = 95 %

CI = 95 %     α = 5 %    α = 0,05    

Critical value for 0,05  is from z-table  z(c) = 1,64

We compute z(s)

z(s) =( p₀ - p )/ √ p₀*q₀/n

z(s) = 0,03696 - 0,011 / √ (0,03696*0,9630)/ 32600

z(s) =  0,02596* 180,55/ √ 0,0356

z(s) = 4,687 / 0,189

z(s) = 24,9

Comparing  z(s) and z(c)   24,9 > 1, 64

z(s) is out of the acceptance region and we have to reject H₀

We accept Hₐ   there is enough evidence to claim that the incidence of ASD is bigger in this state than it is nationally

Answer:

20

Step-by-step explanation:

E:S

4:3

4u+3u=140

7u=140

u=20

According to the information provided, 4.5 litres of red paint and 1400 ml of blue paint are required to manufacture the paint mixture.

Red paint requires 3/4 x 6 = 9/2 = 4.5 litres.

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Answer:

the top empty box is 5 the second down box is 4 the box under 6 is 8

Step-by-step explanation:

None of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

To find the slope of the red line given that it is perpendicular to the green line with a slope of 2, we can use the property that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the green line is 2. To find the slope of the red line, we take the negative reciprocal of 2. The negative reciprocal is obtained by taking the reciprocal (flipping the fraction) and changing the sign.

Reciprocal of 2: 1/2

Negative reciprocal: -1/2

Therefore, the slope of the red line is -1/2.

However, none of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

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Answer: t<40

8p+<184

Step-by-step explanation:

The inequalities representing the given condition will be \(t\leq40\) and \(8p+t\leq184\).

Given information:

A baker makes apple tarts and apple pies each day.

The baker receives a shipment of 184 apples every day.

A tart requires 1 apple and a pie requires 8 apples.

Let t be the number of tarts made each day and p be the number of pies made each day.

The baker makes no more than 40 tarts per day. So, the condition can be written as,

\(t\leq40\)

And the condition for each day apple delivery can be written as,

\(8p+t\leq184\)

Therefore, the inequalities representing the given condition will be \(t\leq40\) and \(8p+t\leq184\).

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Answer:

The two numbers are 17 and 7

Step-by-step explanation:

Translate this word problem into a math equation

If we let x and y be the two unknown numbers

One-half the sum of two numbers is 12 ==>

So one equation is 1/2(x + y) =12

Multiplying throughout by 2 gets rid of the denominator:
2 x 1/2 x (x + y) = 2 x 12

x + y = 24   (1)

One of the numbers is three more than two times the other number:
x = 2y + 3

or

x - 2y = 3  (2)

Equation (2) - Equation (1) =>

x + y - (x -2y) = 24 - 1
x + y - x + 2y = 21

3y = 21

y = 21/3

y = 7

With y = 7, substituting in equation 1 gives

x + y = 24

x + 7 = 24

x = 24-7

x = 17

The two numbers are 17 and 7

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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The mass of the load in kilogram is an illustration of subtraction operation

The mass of the load in kilogram is (b) 1645 kg

The complete mass is given as:

\(\mathbf{m_t = 2.87\ tonnes}\)

The mass of the lorry is given as:

\(\mathbf{m_l = 1.225\ tonnes}\)

The mass of the load is calculated by subtracting the mass of the lorry from the mass of the lorry and its load.

So, we have the following equation:

\(\mathbf{m_{load} = m_t - m_l}\)

Substitute known values

\(\mathbf{m_{load} = 2.87\ tonnes- 1.225\ tonnes}\)

Subtract

\(\mathbf{m_{load} = 1.645\ tonnes}\)

Convert to kilogram

\(\mathbf{m_{load} = 1.645 \times 1000kg}\)

Multiply

\(\mathbf{m_{load} = 1645 kg}\)

Hence, the mass of the load in kilogram is (b) 1645 kg

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