What is the average rate of change from n = 1 to n = 2 for the sequence an = 2(2)n − 1

Answer: 7

Step-by-step explanation:

[tex]A \cap C[/tex] denotes the intersection of A and C, or in other words, how many elements are shared between them.

The number of elements is 2 + 5 = 7

The ordered pairs are ( -2,0),( -1,-3),( 0,-4),(1,-3),(-2,0).

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

The ordered pairs will be calculated as:-

y = x² − 4

At  x = -2

y = ( -2)² - 4 = 4 - 4 = 0

At x = -1

y = (-1)² - 4 = -3

At x = 0

Y = 0² - 4 = -4

At x = 1

Y = 1 ² - 4 = -3

At x = 2

Y = (2)² - 4 = 0

Therefore ordered pairs are ( -2,0),( -1,-3),( 0,-4),(1,-3),(-2,0).

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Answer:

(0, 7/12)

Step-by-step explanation:

to find the y intercept we equate x to 0.

hence,

f(0) = 7/12

the coordinate is (0, 7/12)

Answer:

[tex](0,\frac{7}{12})[/tex]

Step-by-step explanation:

In order to find the y-intercept of an equation, simply plug in 0 for x, as that's where the y-axis is.

[tex]\frac{(2(0)+1)(0+7)}{((0)+3)((0)+4)}[/tex]

Simplify:

[tex]\frac{7}{(3)(4)}=\frac{7}{14}[/tex]

Therefore, the y-intercept for the equation is:

[tex]\frac{7}{14}[/tex]

I'm assuming you meant to write y = 3x-4

We know that the y-intercept of the given line is (0,-4), so we need to find the equation of the line passing through (-2,5) and (0,-4).

The slope is

[tex]\frac{-4-5}{0-(-2)}=-\frac{9}{2}[/tex]

So, this means the equation is [tex]\boxed{y=-\frac{9}{2}x-4}[/tex]

Answer:

1.  x = 55°

2.  x = 11°

3.  x = 30°

4.  x = 19°

Step-by-step explanation:

Trigonometric Identities

[tex]\sin(x)=\cos(90^{\circ}-x)[/tex]

[tex]\cos(x)=\sin(90^{\circ}-x)[/tex]

Question 1

[tex]\begin{aligned}\implies \sin(35) & =\cos(90-35)\\ & = \cos(55)\end{aligned}[/tex]

[tex]\implies x=55^{\circ}[/tex]

Question 2

[tex]\begin{aligned}\implies \cos(79) & =\sin(90-79)\\ & = \sin(11)\end{aligned}[/tex]

[tex]\implies x=11^{\circ}[/tex]

Question 3

[tex]\begin{aligned}\cos(x)& =\sin(2x)\\\implies \cos(x)& =\sin(90^{\circ}-x)\\\\\implies 2x & = 90-x\\3x & = 90\\x & = 30^{\circ}\end{aligned}[/tex]

Question 4

[tex]\begin{aligned}\sin(x+4)& =\cos(4x-9)\\\implies \sin(\theta)& =\cos(90^{\circ}-\theta)\\\\\implies x+4 & = 90-(4x-9)\\x+4 & = 90-4x+9\\5x & = 95\\x & = 19^{\circ}\end{aligned}[/tex]

Answer:

x=4y+24/5

Step-by-step explanation:

add 4y

Divide by 5

Answer:

[tex]\displaystyle{f(x+1)=|x-6|-4}[/tex]

Step-by-step explanation:

To evaluate [tex]\displaystyle{f(x+1)}[/tex], substitute [tex]\displaystyle{x}[/tex] to [tex]\displaystyle{x+1}[/tex] so we should have:

[tex]\displaystyle{f(x+1) = |x+1-7|-4}[/tex]

Evaluate the expression and finally, we have:

[tex]\displaystyle{f(x+1)=|x-6|-4}[/tex]

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Answer:

whats the question? please explain

Answer:

Step-by-step explanation:

Solution,

We use the slope formula, setting x=a :

[tex] \displaystyle{{{{ \lim_{h \to0}}}} \frac{ \frac{2}{x + h} - \frac{2}{x} }{h} = \lim_{h \to0} \frac{ \frac{2}{a + h} - \frac{2}{a} }{h} }[/tex]

[tex] \displaystyle{ \lim_{h \to0} \frac{ \frac{2a - 2(a + h)}{a(a + h)} }{h} = \displaystyle{ \lim_{h \to0} \frac{2a - 2(a + h)}{ha(a + h)} }}[/tex]

[tex] \displaystyle{ \lim_{h \to0} \frac{2a - 2a - 2h}{ha(a + h)} = \displaystyle{ \lim_{h \to0} \frac{ - 2h}{ha(a + h)} }}[/tex]

[tex] \displaystyle{ \lim_{h \to0} \frac{ - 2}{a(a + h)} = - \frac{ 2}{ {a}^{2} } }[/tex]

Therefore, The slope of the curve y=2/x at x=a is -2/a^2.

Since she has set aside only $50 for the trip, she hasn't set aside enough money for the trip

She works 3 days in a week in the headquarter and 2 days a week at the production site.

When she works at the company headquarters, she takes a bus to and from work. The cost for using the bus is $48.00 for 10 one-way trips.

Therefore,

each one way trip = 48 / 10 = $4.8

To and from the headquarters = 4.8 × 2 = $9.6

Hence,

Therefore,

three days cost = 9.6 × 3 = $28.8

The cost of using her car she estimates at 30 cent per mile. When she goes to production sites, she uses her car and travels 52 miles per day.  Therefore,

cost of travelling to production site in a week = 2 × (52 × 0.3) = $31.2

Hence,

cost of expenses per week = 31.2 + 28.8 = $60

Since she has set aside only $50 for the trip, she hasn't set aside enough money for the trip

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Last option: (50, 30); 50 adult tickets and 30 child tickets

A linear equation is an equation in which the highest power of the variable is always 1.

We have the system of equations:

x + y = 80

6x + 4y = 420

We will use elimination method to solve it:  

Multiply the first equation by -6 and then add the equations:

- 6x - 6y = -480

6x + 4y = 420  

We get:

-2y = -60

After dividing both sides by -2 we get:

y = 30

then plugging 30 in place of y into the original first equation we get:

x+30=80

Then subtracting 30 from both sides we get:

x = 50

The solution to the system is (50, 30)

Then notice the second equation 6x+4y=420 clear indicates that x represents the tickets for adults since the price for adults $6 is the coefficient of the x-term, while the price for children which is $4 is attached as coefficient in front of the y.

Thus, x=50 means there were sold 50 adult tickets. And y=30 that there were sold 30 child tickets.

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Answer:

( 50, 30)

Step-by-step explanation:

The numeral preceding and succeeding each of the following numerals.

Now, what happens when you add 1 or subtract 1 from 100 in the familiar base 10.

Adding adds 1 to the unit digit.

Subtracting 1 gives 99 because 9 is the largest digit in base 10.

So A. 100 base 8

The largest digit in base 8 is 7, so

..., 77, 100, 101,...

B. 10000 base 7

The largest digit in base 7 is 6, so

..., 6666, 10000, 10001, ...

Next what happens when you add 1 to 509 in base 10. 9 is the largest digit in base 9, so adding 1 makes the units digit 0, and you carry a 1 to the next digit to the left:

509 + 1 = 510.

C. 305 base 6

5 is the largest digit in base 6, so

..., 304, 305, 310, ...

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should i create the world problem with 12 3 and 9?

The balance in Yolanda's saving plan after 14 years is; $9,455.36

We want to find the balance in Yolanda's saving plan after 14 years.

For Yolanda;

PV = 0

PMT = 250

i% = 4%/12 = 0.33%

N = 14 yrs * 12 = 168

FV = ?

For Zach:

PV = 0

PMT = $3300

i% = 4%

N = 14 yrs

FV = ?

From online future value calculator, we have;

Yolanda FV = $9,455.36

Zach FV = $47,204.19

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Answer:

  y ≈ 15272.9(1.06306^x) . . . . from regression tool

  y = 15300(1.0624^x) . . . . calculated "by hand"

Step-by-step explanation:

An exponential model is one that uses the exponential function ...

  f(x) = a·b^x

to model the data. The value of 'a' is the function value when x=0, the initial value. The value of 'b' is the growth factor, the multiplier between function values for successive values of x.

__

An exponential regression tool makes short work of this. Such tools are available on some calculators, apps, and spreadsheets. All that is required is entering the data into a table and invoking the tool. The one shown in the attachment tells you the model is approximately ...

  y ≈ 15272.9(1.06306^x)

__

We can average the growth rate factors a couple of different ways. When we think of "averaging," we usually think of the arithmetic mean, the sum of values divided by their number. If we average the growth rates in this way, we get ...

  average rate of growth =

  ((161/153) +(173/161) +(184/173) +(196/184) +(207/196) +(220/207))/6 ≈ 1.0624

Using the first table value as the initial value, the model formed this way is ...

  y = 15300(1.0624^x)

__

For exponential growth it may make more sense to compute the geometric mean. This is the n-th root of the product of n numbers. In this case, it reduces to the 6-th root of the ratio of the last to the first:

  average rate of growth = (220/153)^(1/6) ≈ 1.0624

This gives the same growth factor as above, hence the same model.

The second attachment shows the application of this model to the domain used in the table. We see there are some minor differences when rounding the function value to the nearest hundred.

The differences in our two models seem to arise from rounding the data values in the table to the nearest hundred.

__

The values given in the table can be used in different ways to arrive at two similar, but different exponential models of the table data:

Interestingly, the function calculated "by hand" has a very slightly better correlation with the table data. The difference in correlation coefficients is in the 6th decimal place.

Answer:

A = 5, B = 9, C = 6

Step-by-step explanation:

let me know if you want an explanation :))

Based on the amount being taxed, the period of taxation, and the tax, the annual percentage of tax is 19.96%.

Assuming this rate was x, the following formula would apply:

Annual rate/ 365 days a year x number of days x amount to be taxed = Tax amount

Solving gives:

x/365 x 32 x 8,000 = 140

701.369863x = 140

x = 140 / 701.369863

= 19.96%

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The remaining elements if Venn diagram is  S= { 4, 9}

A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.

Given:

E = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }

S = square numbers

E = even numbers

Element in set S= { 4, 9}

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Answer:

  $385.50

Step-by-step explanation:

The amount of commission is found by multiplying the commission rate by the value of the sale.

  1.5% × $25,700 = $385.50

A commission of $385.50 is made on an average car sold.

Answer:

x/ 3x + 2

x approach 1

1/3 (1) + 2

1/ 5.

Answer:

212

Step-by-step explanation:

Simple addition and subtraction is to be used here.

5, 3 = 28

5-3 = 2 , 5+3 = 8

9 , 1 = 810

9-1 = 8 , 9+1 = 10

8 , 7 = 115

8-7= 1 , 8+7 = 15

6 , 2 = 48

6-2 = 4 , 6+2 = 8

7 , 5 = 212

7-5 = 2 , 7+5 = 12

Answer:

212

Step-by-step explanation:

Rule

5 - 3 = 2

5 + 3 = 8

Therefore: 28

9 - 1 = 8

9 + 1 = 10

Therefore: 810

8 - 7 = 1

8 + 7 = 15

Therefore: 115

6 - 2 = 4

6 + 2 = 8

Therefore: 48

7 - 5 = 2

7 + 5 = 12

Therefore: 212

Answer:

No solution

Step-by-step explanation:

the end behavior is:

If we have a polynomial of even degree, then the end behavior in both ends is the same one.

Particularly, in these cases (even degree) we only need to look at the leading coefficient. If it is positive, then as x tends to infinity and negative infinity, the function tends to infinity.

In this case, the polynomial is:

y = 9x⁴ + 8x - 2

Notice that the degree is 4, even, and the leading coefficient is 9 (positive).

Then the end behavior is:

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Answer:

p^2/r

Step-by-step explanation:

so I have shown every work in the picture attached

please let me know if this doesn't help

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: a = -1[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

For a function f(x) = y,

x represents the value ( x - coordinate ) at which the function has a value y.

[tex]\qquad \tt \rightarrow \: f(x) = a {x}^{2} + 2[/tex]

for point (-1 , 1) to satisfy the equation, we have to calculate the value of a

[tex]\qquad \tt \rightarrow \: f( - 1) = a( - 1) {}^{2} + 2[/tex]

[tex]\qquad \tt \rightarrow \: 1 = a + 2[/tex]

[tex]\qquad \tt \rightarrow \: a = 1 - 2[/tex]

[tex]\qquad \tt \rightarrow \: a = - 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Substitute -1 into x

Substitute 1 into y

f(x)= a (-1) ^2+2=1

       a=-1

Answer:

Vertical angles are angles opposite of each other. hope it helps

Answer:

which p? there isn't any p in above equation