if f(1) = -5 and f(n) = f(n-1) +7, find the first four terms and the common difference of the sequence

Answer:

250

75

40

Step-by-step explanation:

The pattern is 25

4*25= 100

10*25= 250

3*25= 75

40*25=1000

Answer:

4. 0|8

Step-by-step explanation:

key 3|4 = 34

The first digit is the tens place and the second digit is the ones place

8 can be represented as 08

0|8 would be 08

Answer:

4. 0 | 8

Step-by-step explanation:

Note that in the stem-and-leaf plot example given to us, 3 | 4 = 34.

From this, we can assume that the left side of | represents the tens place, while the right side of | represents the ones place value.

It is asking what the value 8 represents in 3 | 8. From the example that we see above, we know that the number given is 38. the value of 8 in this number represents the one's value.

0 | 8 is your best answer, for there is no tens place.

~

[tex]ax^2+bx+c=0\\\\x_1,\ x_2-the\ roots\\\\x_1+x_2=\dfrac{-b}{a}\\-------------------------\\\text{We have}\ 3x^2+11x-4=0\\\\a=3,\ b=11,\ c=-4\\\\\text{Substitute:}\\\\x_1+x_2=\dfrac{-11}{2(3)}=-\dfrac{11}{6}\\\\Answer:\ \boxed{-\dfrac{11}{6}}[/tex]

Answer:

There are 4 quarts in a gallon. 3x4=12. He bought 12 quarts of milk.

Step-by-step explanation:

Answer:

$3.60

Step-by-step explanation:

Answer:

$41.40

Step-by-step explanation:

You just have to do $45.00-8%

Answer:

Measurements were needed for multiple things, such as agriculture, construction, and trade. Also, many areas developed their own systems for measuring objects making it difficult as people from different places had different results. Eventually, the same system was adopted by the majority of people.

Step-by-step explanation:

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We have

[tex]y-6=-3(x+2)\to y-6=-3(x-(-2))[/tex]

Therefore

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

2x - y = 4    it's standard form Ax + By = C

y = 2x - 4     it's slope-intercept form y = mx + b

y - x = 4 → x - y = -4  t's standard form Ax + By = C

Answer:

Vertical shift is 2 units top and horizontal shift is [tex]\frac{\pi }{2}[/tex] units to the right

Step-by-step explanation:

Consider the function f(x) = a cos(bx + c) + d.

In this graph, the horizontal shift is -c/b and the vertical shift is d.

Let's compare our graph, f(x) = -3 cos(2x - π) + 2 with this graph.

Here, a = -3, b = 2, c = -π and d = 2.

So, vertical shift = d = 2 units top and

horizontal shift = [tex]-\frac{c}{b} =-\frac{-\pi }{2} =\frac{\pi}{2}[/tex] units to the right.

Answer: -1

Step-by-step explanation:

I think because if u graph it you can count the boxes down and to the side and you get -1

Answer: D) -1

Step-by-step explanation: Use the slope formula and plug in two points form tha table.

I chose the first two (3, -5) and (6, -8)

Y2-y1/x2-x1

-8--5/6-3

Hope it helps!

Answer: 0.6 (choice B)

x = number of days the book has been checked out

Check out the attached image below. I've marked 3 boxes in red to represent the bars that span from x = 9 to x = 18. The heights of these bars add up to 0.15+0.30+0.15 = 0.45+0.15 = 0.60

So if we randomly pull out a book, then the chances of picking a book that has a x value between 9 and 18 (including 9; excluding 18) is 0.60

Answer:

37.5

Step-by-step explanation

Th ratio is 2.5 to 1. So then I just multiplied 2.5 to 15 and got the answer!

Hope it helps, if it is right please tell me!

Answer: $37.50

Step-by-step explanation:

$25.00 / 10 = $2.50

$2.50 * 15 = $12.50

$12.50 + $25.00 = $37.50

Jasmine earns $4.20 per hour of work. The function that represents her earnings (c) for working h hours is c = 4.2h.

From the provided information, we know that Jasmine earns $25.20 for working for 6 hours one day, and $16.80 for working 4 hours the next day. The rate at which Jasmine is paid can be determined by dividing her earnings by the hours she works, otherwise known as her wage rate.

For the first day:
Wage rate = $25.20/6 = $4.20 per hour

For the second day:
Wage rate = $16.80/4 = $4.20 per hour

Thus, we can conclude that Jasmine earns $4.20 per hour. Therefore, the function for Jasmine's earnings (c) for working h hours is given by:
c = 4.2h
Where 'c' represents the total earnings and 'h' represents the hours worked.

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The function that shows how much Jasmine earns (c) for working (h) hours is c = 4.20h.

The function that shows how much Jasmine earns for working for a certain number of hours can be determined by finding the rate of earnings per hour. We can calculate the rate of earnings by dividing the total earnings by the number of hours worked. Let's use the given information to find the rate of earnings for Jasmine:

Rate of earnings for the first day: $25.20/6 = $4.20 per hour

Rate of earnings for the second day: $16.80/4 = $4.20 per hour

Therefore, the function that shows how much Jasmine earns (c) for working (h) hours is c = 4.20h.

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Answer:

3. 9n + 6 = 78

5. see below

Step-by-step explanation:

3.

Let the number of adults be n. Each adult ticket costs $9, so the cost of n adult tickets is 9n. There is only one child, and a child's ticket is $6, so the cost of the child's ticket is 6. Adding the costs, you get 9n + 6. The total cost is $78, but the expression representing the total cost is 9n + 6, so 9n + 6 must equal 78. That is the equation.

9n + 6 = 78

5.

Sam bought equal gifts for his two children. The two gifts had the same price, x. He received a discount of $125. How much did each of the two gifts cost before the discount?

Answer:

0.783

Step-by-step explanation:

To find first r and then r square for the data

n statistics, the coefficient of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

correlation coefficient of x and y = Cov (x,y)/std dev x * std dev Y

Cov (x,y) = E(xy) -E(x)E(y)

Hence calculations would be as follows:

x y xy

1 2 2

2 10 20

5 5 25

7 18 126

10 25 250

Mean 5 12 84.6

Cov E(xy)-E(x)E(y)  24.6

r 0.884640297

r^2 0.782588454

so answre is 0.783 after rounding off.

Answer:

0.783

Step-by-step explanation:

Answer:

min = 67, Q1 = 68, median = 70,

Q3 = 76, max = 78

We have 9 observations.

The correct set of data is:

67, 74, 78, 69, 78, 70, 67, 72, 69

When we rearrange this set of data in numerical order, we have:

67, 67, 69, 69, 70, 72, 74, 78, 78

Answer:

a) x=38

b) x=19

Step-by-step explanation:

a) The interior angles at L and M can be found by subtracting 134 and 84 from 180 respectively:

∠L = 180 - 134 = 46

∠M = 180 - 84 = 96

The angles of a triangle sum up to 180, so x + 46 + 96 = 180.

From this you find that x = 180 - 46 - 96 = 38

b) Because YZ and XW are parallel, ∠Y=∠W = 2x

The sum of the angles in the triangle must be 180, so

3x-5 + 90 + 2x = 180

Which simplifies to

5x +85 = 180

5x = 95

x = 19

Answer:

a) x = 38°; b) x = 19°  

Step-by-step explanation:

a)

∠OLM = 180 - 134 = 46°     Supplementary angles

∠OML =180 -   84 = 96°     Supplementary angles

         x + 46 + 96 = 180     Interior angles of triangle

                x + 142 = 180

                          x =   38°

===============

b)

∠XWY + 3x - 5 + 90 = 180         Interior angles of triangle

     ∠XWY + 3x + 85 = 180

(1)          ∠XWY + 3x = 95

                         ∠XWY = 2x

(2)           ∠XWY - 2x = 0           Alternate interior angles

                                5x = 95     [2 subtracted from (1)]

                                  x = 19°

Answer:

First box:  A straight line measures 180 degrees

Second box: Alternate interior angles theorem

Step-by-step explanation:

All lines are straight, and therefore measure 180 degrees

You can see that the red line is parallel to the line with angles 2 and 3. Alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal. Which justifies step 2

Answer:

1.A straight line measures 180 degrees

2.Alternate interior angles theorem

Step-by-step explanation:

We have to prove that

Sum of interior angles of any triangle =180 degrees

Proof:

1.[tex]m\angle 1+m\angle 4+m\angle 5=180^{\circ}[/tex]

Reason: A straight line measures 180 degrees

2.[tex]\angle 4\cong\angle 2[/tex]

[tex]\angle 5\cong \angle 3[/tex]

Reason:Alternate interior angles theorem

3.[tex]m\angle 4=m\angle 2,m\angle 3=m\angle 5[/tex]

Reason: by definition of congruent angles.

4.[tex]m\angle 1+m\angle 1+m\angle 3=180^{\circ}[/tex]

Reason: By substitution

Hence, proved.

[tex]w(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0[/tex]

The posible rational zeros of w(x) are:

[tex]\pm\text{dividers of}\ a_0\ \text{and}\ \pm\dfrac{\text{dividers of}\ a_0}{\text{dividers of}\ a_n}[/tex]

[tex]f(x)=x^4+6x^3-3x^2+17x-15\to a_n=1,\ a_0=-15[/tex]

[tex]\text{dividers of}\ a_0= 15:\ \ 1,\ 3,\ 5,\ 16\\\text{dividers\ of}\ a_n=1:\ \ 1[/tex]

Answer:

[tex]\{\pm1,\ \pm3;\ \pm5;\ \pm15\}[/tex]

Answer:

7 miles

Step-by-step explanation:

Four miles plus 3 miles = 7 miles

The shortest driving distance from the animal shelter to the stadium can be found using a map or a GPS system, which considers all possible routes and chooses the one with the least distance.

The shortest driving distance between two locations, in this case, from an animal shelter to a stadium, can be discovered by using geographical tools such as a map or GPS system. These tools can provide data on distance with respect to various routes, allowing you to choose the shortest one.

For example, assume the animal shelter is at Place A, and the stadium is at Place B. The GPS system will analyze all possible routes from A to B, consider traffic conditions, road detours, and provide you with the option that covers the least amount of miles/kilometers and saves the most time. This is considered the shortest driving distance.

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Answer:

Step-by-step explanation:

If answer A works then so will Answer A. The reason is because 1/4 and 0.25 are equal to one another. The only comment you should recognize is that

5/0.25 is a whole lot easier to do than 5/(1/4)

B is the same thing as C when you apply the division by fractions rule.

D is the odd method out. Instead of 20 games (5 * 4) she will only get to play 4. That because she has 5 dollars and if you multiply by 0.25 you get 1.25 games

Answer:

A. 180°+z−w

Step-by-step explanation:

We know that x  + w = 180  because they are same side exterior angles and a and b are parallel.

z=y  because they are alternate interior angles and a and b are parallel.

x  + w = 180

Solve for x by subtracting w from each side

x = 180-w

y =z

Lets find x+y

x+y

(180-w) +z

Rewriting

180+z-w

Answer:

A. 180º + z - w

Step-by-step explanation:

x + w = 180, because they are same side exterior angles, and are on opposite sides.

z = y, because if you move z down, then you will see that they overlap.

From x + w = 180, you can get x = 180 - w.

We are trying to find x + y in terms of w and z, so:

x = 180 - w

y = z

With that, you can assemble the expression, 180 - w + z.

If you re-arrange, you will get 180 + z - w.

Therefore, A is the answer.

Answer:

Step-by-step explanation:

You really don't have enough information to solve this with one answer. You want a value for y and there is no what to limit it to just 1 set of values. For example if x = 23 then

x = y + y - 3

x = 2y - 3

23 = 2y - 3           Add three to both sides

23+3 =  2y           Combine

26 = 2y                Divide by 2

26/2 = 2y/2          Do the division

13 = y

The smaller number is 13 - 3 = 10

Their sum is 13 + 10=23           But that answer is not unique.

====================

Suppose x = 13

13 = 2y - 3              Add 3

13 + 3 = 2y

16 = 2y

y =8

The larger number = 8

The smaller number = 5

=======================

The best I can do is give you the equation which is

x = 2y - 3

Answer:

the solution os 3p+2≥-10 is p≥-4

Step-by-step explanation:

So.... 3p+2≥-10

            -2   -2

             3p≥-12

and then you divide...... 3p≥-12

                                       3      3

                                       p≥-4

Answer:  30 percent of 20 is 6.

_______________________________________________

Step-by-step explanation:

_______________________________________________

(n/100)  * 20 = 6  ?  

Solve for "n"  .

_______________________________________________

Divide each side of the equation by "20" :

{ (n/100) * 20 }  / 20  = 6 / 20 ;

to get:

n/100  = 6/20 ;  

↔ 6/20 = n/100 ; solve for "n" ;

Look at the denominators:

20 * ? = 100 ?

  100/ 20 = ?  ;

  100/20 = 5 ;

So, 20 *  " 5" = 100 ;

Then 6* 5 = "n"  (for the numerator, "n";  in  :   "n /100" ) ;

                  →  6 * 5 = 30 ;

                  →  n = 30 .

_______________________________________________

 Answer:  30 percent of 20 is 6.

_______________________________________________

What we know here is that the pattern subtracts 6 every nth value progression.

We can create a explicit formula for this sequence.

let the output be f(n)

let term # = n

so the formula would be...

[tex]f(n)=10-6(n-1)[/tex]

If we plug in the value 41 for n

[tex]f(n)=10-6(41-1)\\f(n)=10-6(40)\\f(n)=10-240\\f(n)=-230[/tex]

41st term of the sequence is -230

Answer:

Step-by-step explanation:

1. Divide the numerator by the denominator.

2. Write down the whole number answer.

3. Write down any remainder above the denominator.

Answer:

Not sure but i think its C. y=-2x-3

Answer:

y = 2x - 3

Step-by-step explanation:

Given : The Total Bill at the Restaurant is $84.99

Given : The Additional Tax is $5.10

⇒ Total Bill Including the Tax is : (84.99 + 5.10) = $90.09

Given : Three Friends decide to evenly split their Bill

⇒ $90.09 should be Divided into 3 Equal Parts

[tex]\mathsf{\implies The\;Amount\;each\;person\;should\;owe\;is = (\frac{90.09}{3})}[/tex]

[tex]\mathsf{\implies The\;Amount\;each\;person\;should\;owe\;is = 30.03\;Dollars}[/tex]

His Friend Calculation is not Reasonable

The friend's calculation of each person owing $45.04 is not reasonable as the correct amount should be $30.03 per person when evenly splitting a bill of $84.99 with an additional $5.10 tax.

To determine whether the friend's calculation of $45.04 each for splitting a bill of $84.99 with an additional $5.10 tax is reasonable, let's calculate the correct amount each person should owe. First, we combine the total bill and tax: $84.99 + $5.10 = $90.09. Then, we divide this total by three, as there are three friends: $90.09 / 3 = $30.03 per person.

The friend's calculation is not reasonable because each person should owe about $30.03, not $45.04. The estimate of $45.04 is significantly higher than the accurate calculation.