Compute the average rate of change of the function. Exercise A:

Part A: -5/9, 6/10, -7/11, 8/12

Part B:

Part C: Positive

The given sequence is:

As seen above the sequence is an alternating sequence because it changes in sign

Also, neglecting the sign chnages, we will observe, a common diffference of 1 in the numerator and denominator

a) Therefore, if the pattern continues, the next 4 terms in the sequence are:

-5/9, 6/10, -7/11, 8/12

b)

Without the sign, the explicit equation representing the numerator is calculated below:

1, 2, 3, 4......

The first term, a = 1

The common difference, d = 1

This is an arithmetic sequence

N(n) = a + (n - 1)d

N(n) = 1 + (n - 1)(1)

N(n) = 1 + n - 1

N(n) = n

The explicit equation representing the denominator is calculated below

5, 6, 7, 8........

The first term, a = 5

The common difference, d = 1

D(n) = a + (n - 1)d

D(n) = 5 + (n - 1)(1)

D(n) = 5 + n - 1

D(n) = n + 4

The alternating sequence will include the term below:

Therefore, the explicit equation for f(n) representing the sequence is:

Part C) The sign of f(56) will be:

(-1)^56 = 1

Since this gives us a positive value, the sign of f(56) is positive

It is given that an item used to be sold for $3.70 per pound.

It is required to find the current price per pound if the price was increased by 20%.

A 20% increase in the price, $3.70 is calculated as:

Hence, the current price of the item is $4.44 per pound.

The current price of the item is $4.44 per pound.

The probability that a randomly selected citizen, aged 25 or

over, had 4 years of college : 0.2458

From the table

Total number of citizens aged 25 or above = 179 million.

number of citizens aged 25 or above, had 4 years of college = 44 million

Therefore, probability = 44/179 = 0.2458

Probability is a branch of mathematics that deals with calculating the probability of a given event, expressed as a number between 1 and 0. An event with a probability of 1 can be considered certain: for example, the probability of a coin toss. a toss that results in either "heads" or "tails" is 1 because there are no other options, assuming the coin lands flat. An event with  probability 0.5 can be considered equally likely to occur or not to occur: for example, the probability that a coin toss results in heads is 0.5, because the toss is equally  likely to result in tails." An event with  probability  0 can be considered impossible: for example, the probability that the a coin lands (uniformly) without both sides up is 0, because either "heads" or "tails" must be  up.

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Answer:

D. 1/4

Explanation:

By definition, two lines are parallel if they have the same slope.

Given that lines a and b are parallel; and the slope of line a = 1/4, then:

The slope of line b = 1/4.

The correct choice is D.

The relation is 12 ounces of yellow paint with 5 ounces of blue paint. To find how many ounces of blue would be needed if you used 20 ounces of yellow, we can use the next proportion:

Solving for x,

You would need 25/3 ounces of blue paint

We can see the upper vertix of the triangle in the first figure is at the point (0,6) and after the shrink is at (0,2). So what's the number I can divide 6 to get a 2? It's 3. So the scale factor is 1/3

After solving basic fractions we have come to find that, we need 12.7 tiles to create a frieze above a Forrest.

When describing a portion or part of a whole in mathematics, a fraction is used. The equal components of the whole are represented by it. Both the numerator and denominator are components of a fraction.

Both the top and bottom numbers are referred to as the numerator and denominator, respectively. The denominator specifies the total number of equally sized pieces in the whole, whereas the numerator specifies the number of equal parts that were taken.

A fraction is something like 5/10.

The denominator in this case is 10, and the numerator is 5.

The measure of each tile = 2⅞

                                          = 23/8

Measure of doorway = 36½

                                   =  73/2

No. of tiles we need = 36½ /  2⅞

                                  = 12.7 tiles

Thus, we need 12.7 tiles to create a frieze above a Forrest.

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EXPLANATION

The reule that represents the function is y=5cos(x) + 3

There are 22 grams of fat and each gram of fat is 9 calories, then

945 calories represents 100%, then 198 represents:

21% of the calories are from g

Step1: Write out the given parameters

We are to find the area of the pool cover and it circumference

Step2: write out the formula

Hence the area of the pool cover is 254.34 square feet

The circumference of the pool cover is given by

Therefore the circumference of the pool cover is 56.52 feet

Answer:

156.4 ÷ 23 = 6.8

Step-by-step explanation:

hope this helps

D. 763 seconds

Explanation:

Data:

Seconds light travels distance between Sun and Earth : 500 seconds

Distance between Sun and Earth: 93 million miles

Distance between Sun and Mars: 142 million miles

Formula: (see image below)

Solution:

From Sun to Mars the light takes (142 * 500) / 93 = 763 seconds

NB:

The tactic is to first put the data given in a table like in the image above, to first multiply diagonally then divide horizontally. (starting from the data that his paired data).

Here the paired data missing is the time it takes for the light to travel from the Sun to Mars, therefore you'll multiply the distance between the Sun to Mars (known data missing a pair) by the time it takes light to travel from the Sun to Earth (known data with its pair), then divide the result by the distance between the Sun and earth (pair of the former mentioned known data)

Answer:

10.59480821 hours

Step-by-step explanation:

2. Now we know the percent for each surface

3. Now that we know the percent of each surface we need to find out how many km for each surface:

Uphill

Downhill

Flat

3. Now that we know all the percent and distance for each surface we need to know the km/h for each

Uphill = 24.25km/h

Downhill = x

Flat = 55.5km/h

4. Since we don't have the speed for downhill we need to know the difference between uphill and flat

5. Now we know the difference is 31.25 we can add that to the flat surface to get the downhill speed

6. Now we know all the speeds and now we can figure out how many hours it takes for each surface

( we are going to take the distance in 1 surface and then divide that by the km/h in that surface to ket how many hours)

Uphill

Downhill

Flat

7. Now we add all the hours up

Answer:

y = 0.1x + 5

Step-by-step explanation:

0.1x = the amount he pays for all his texts and 5 is a fixed amount so add them up to get y

The image of the point P(x, y) = (4, 2) by means of a translation formula is point P'(x, y) = (- 1, 4).

In this question we find the coordinates of a point set on Cartesian plane which is modified by using a translation, a kind of rigid transformation. Rigid transformations are transformations applied on geometric loci such that Euclidean distances are conserved.

Vectorially speaking, translations are described by the following formula:

P'(x, y) = P(x, y) + T(x, y)

Where:

If we know that P(x, y) = (- 9, - 3) and P'(x, y) = (- 14, - 1), then the translation vector is:

T(x, y) = P'(x, y) - P(x, y)

T(x, y) = (- 14, - 1) - (- 9, - 3)

T(x, y) = (- 5, 2)

Then, the image of the point (4, 2) is:

P'(x, y) = (4, 2) + (- 5, 2)

P'(x, y) = (- 1, 4)

The image of the point (4, 2) by using a translation formula is (- 1, 4).

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Whenever we multiply a decimal number by 10, we are shifting the decimal point one digit to the right. For example, if we compute

the answer is

We moved the decimal point one digit to the right; therefore, we can say moving the decimal point to the right foot places in a number is the same as multiplying by 10.

Hence, the correct answer choice is 2

Answer:

-2

Step-by-step explanation:

This is where the line crosses the y axis.  It is at point (0,-2)

The true statement is g(-13)= 20.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. Mapping or transformation is used to denote a function in math. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

domain = -20 ≤ x ≤ 5

and a range = -5 ≤ g(x) ≤ 45

and g(0) = -2 and g(-9) = 6

First, g(-13)= 20

x=-13 is in our domain  and 20 is also in our range .

So this is true for g(-13)= 20.

Now, g(-4) = -11

-11 does not comes under the range.

So this statement is not true.

Again,  g(0) = 2 is false because  g(0) = - 2.

and,  g(7) = -1 D

7 is not in our domain .

So g(7) is not possible

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To find the value of x we need to write the equation in another form that tells us what to do; both sides of the equations are ratios then we have:

Then the equation is:

Solving for x we have:

Therefore, the value of x is 8/3

6 is adding on the right, then it will subtract on the left

4 is dividing on the right, then it will multiply on the left

Answer:

Step-by-step explanation:

The least common denominator of a and b is the smallest multiplier that is divisible by both a and b. In this case, for:

The set is linearly dependent.

To explicitly prove this, we need to show there is at least one choice of constants [tex]c_1,c_2,c_3,c_3\in\Bbb R[/tex] such that

[tex]c_1 u + c_2 v + c_3(v-w) + c_4(u+v+w) = 0[/tex]

or equivalently,

[tex](c_1 + c_4) u + (c_2 + c_3 + c_4) v + (-c_3 + c_4) w = 0[/tex]

which is the same as solving the system of equations

[tex]\begin{cases} c_1 + c_4 = 0 \\ c_2 + c_3 + c_4 = 0 \\ -c_3 + c_4 = 0 \end{cases}[/tex]

From the first and last equations, we have [tex]c_1=-c_4[/tex] and [tex]c_3=c_4[/tex]. Substituting these into the second equation leaves us with [tex]c_2-2c_1=0[/tex], and so the overall solution set is

[tex]c_1 = \dfrac12 c_2 = -c_3 = -c_4[/tex]

for which there are infinitely many not-all-zero solutions.

Complete question is:

The function f(x) = 600 - 100x models the value, f(x), of a video game system x years after purchase. Which choice represents the most appropriate domain of the function?

Answer and explanation:

The domain of a function is the values you can plug into the function, the possible values for x.

While x could take any value, there are a range of apropiate values that it can take.

For example, since x represents years after purchase, x can not be a negative number, because that would represent negative years, thus x must be greater or equal to 0.

Domain:

The expression in the form of 5ⁿ is 5⁻¹³

An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.

Given:

F(x) = 5⁻⁵/5⁸

F(x) = 5⁻⁵⁻⁸

F(x) = 5⁻¹³

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Answer:

Recall that the binomial theorem states that:

Then:

Therefore:

Answer:

6

Step-by-step explanation:

You replace the x’s with 2 and then solve the problem like you would do with any other problem.

2(3)+2(0)

2(3)=6

2(0)=0

6+0=6

Please correct me if i’m wrong. I just finished this lesson!

The correct answer is: " 9 " .
_______

Step-by-step explanation:

Given:  " x³ +  x⁰ " ;  Evaluate for "x = 2 ".

Plug in 2 for the x values; and solve:
  " 2³ + 2⁰ " ;
Note:  " 2³ = 2 * 2 * 2 = 8 " ;

           " 2⁰ = 1 " .

Note: Any 'non-zero' value, raised to the 'zeroth' [0°]' exponential power, is equal to 'one' [ 1 ].

So: " x³ + x⁰ =  2³ + 2⁰ = 8 + 1 = 9 ."

The answer is:  " 9 ".
_______
Hope this is helpful!  Best wishes to you!

_______

The slope is calculated by findidng the ratio of the vertical change (change in y) to the horizontal change (change in x) between any two distinct points.

Then the slope formula is:

Answer:

-12

Step-by-step explanation:

explanation in the picture bruv

Given:

The radius of the circle is 6.48 in.

To find:

We need to find the arc length of RS.

Explanation:

Consider the formula to find the length of the arc.

Remember that

when solving a system by graphing, the solution is the intersection point both graphs

Looking at the graph

The intersection point is (5,6)

therefore