A mechanic cuts 14 pieces of copper
tubing from a coil. Each piece is 3 1/2
inches long. What is the total length
used?

Answer:

[tex]f(n)=f(n-1)+22[/tex].

Step-by-step explanation:

Note: In the given function it should be (n-1) instead of (n=1).

Consider the given function is

[tex]f(n)=-11+22(n-1)[/tex]

It is the explicit form of an A.P.

For [tex]n=1[/tex],

[tex]f(1)=-11+22(1-1)=-11+0=-11[/tex]

For [tex]n=2[/tex],

[tex]f(2)=-11+22(2-1)=-11+22=11[/tex]

Common difference is  

[tex]d=a_2-a_1=11-(-11)=11+11=22[/tex]

The recursive formula of an A.P. is

[tex]f(n)=f(n-1)+d[/tex]

Substitute [tex]d=22[/tex] in the above formula.

[tex]f(n)=f(n-1)+(22)[/tex]

[tex]f(n)=f(n-1)+22[/tex]

Therefore, required recursive formula is [tex]f(n)=f(n-1)+22[/tex].

Answer:

First equation: 1/2

Second equation: -1/3

Step-by-step explanation:

We get the following equations:

[tex]\frac{1}{3}x+\frac{1}{6}y=2[/tex]          first equation

[tex]\frac{1}{2}x+\frac{3}{4}y=-3[/tex]       2nd equation

Then, to obtain opposite terms for the x variable, we need to identify the coefficient of the x for the 1st equation and the 2nd equation as:

The coefficient for x in the 1st equation is [tex]\frac{1}{3}[/tex] and the coefficient for x in the 2nd equation is [tex]\frac{1}{2}[/tex]

Finally, we need to multiply 1st equation with the coefficient of the 2nd equation and multiply the 2nd equation with the negative of the coefficient of the 1st equation.

We multiply by the negative of the coefficient of the 1st equation because we need to find opposite terms for x.

So, the first equation is equal to:

[tex](\frac{1}{3}x+\frac{1}{6}y)*\frac{1}{2} =2*\frac{1}{2} \\\frac{1}{6}x+\frac{1}{12}y=1[/tex]        

The second equation is:

[tex](\frac{1}{2}x+\frac{3}{4}y)*\frac{-1}{3} =-3*\frac{-1}{3} \\\frac{-1}{6}x+\frac{-1}{4}y=1[/tex]

Now, the coefficients for x, 1/6 and -1/6, are opposite terms.

Answer:3, -2

Step-by-step explanation:

Answer:

-(x+7)/6

Step-by-step explanation:

y = -6x-7

Exchange x and y

x= - 6y-7

Solve for y

Add 7 to each side

x+7 = -6y-7+7

x+7 = -6y

Divide by -6

(x+7) / -6 = -6y/-6

(x+7)/ -6 = y

The inverse is -(x+7)/6

Answer:

The answer would be, 2.75

Step-by-step explanation:

Add all the numbers up:

0+1+1+2+3+4+5+6=22

Divide the answer by the amount of numbers:

22÷8=2.75

Answer:

The mean of the following dot plot:

Mean: 3

Step-by-step explanation:

0 x 1 = 0

3 x 1 = 3

6 x 1 = 6

(we only add the numbers that only has a dot on the number in the dot plot)

So:

Mean: 0 + 3 + 6 = 9/3 = 3

Answer:

Option A.

Step-by-step explanation:

Graph of function has been given in the figure.

Coordinates of the points lying on this graph will be

x     -2        -1         0          1        2

y    -10       -3        -2         -1        6

Therefore, coordinates of the points which will lie on the inverse of this function will be

x     -10      -3        -2       -1       6

y      -2       -1         0        1       2

Therefore, Option A. will be the answer.

Answer:

B. x-intercept = 2, y-intercept = 4

Step-by-step explanation:

→The y-intercept can be found on the vertical line, while the x-intercept can be found on the horizontal line.

→Looking at the graph, you can see that the line intersects at a point on the vertical line (y-intercept), and this number is 4.

→Looking at the graph, you can see that the line intersects at a point on the horizontal line (x-intercept), and this number is 2.

Answer:

8

Step-by-step explanation:

h(t) = -t + 3;

h(-5)

Let t = -5

h(-5) = - -5 +3

       = 5+3

       = 8

Answer:

8

Step-by-step explanation:

h(t) = -t + 3

Put t as -5 in the function.

h(-5) = -(-5) + 3

The negative signs cancel.

h(-5) = 5 + 3

Add both the terms.

h(-5) = 8

Answer: See bolded below

Step-by-step explanation:

Average rate of change is the slope. To find that, we would need the equation [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

Reminder: The scale fo the graph goes by 2. You need to make sure you are looking at the right coordinates.

1. The coordinate points are (1, 2) and (2, 4).

[tex]m=\frac{4-2}{2-1}=\frac{2}{1} =2[/tex]

The average rate of change is 2.

2. The coordinate points are (2, 4) and (3, 8).

[tex]m=\frac{8-4}{3-2} =\frac{4}{1} =4[/tex]

The average rate of change is 4.

3. The coordinates are (3, 8) and (4, 16).

[tex]m=\frac{16-8}{4-3} =\frac{8}{1} =8[/tex]

The average rate of change is 8.

Answer:

f(x) = -1/2x + 2

Step-by-step explanation:

f(x) = ax + b

x = 0 , y = 2

y = 0 , x = 4

[tex]a = \frac{y'' - y'}{x'' - x'}\\a= \frac{2 - 0}{0 - 4} \\a= \frac{2}{-4} = \frac{-1}{2}[/tex]

[tex]0 = \frac{-1}{2} . 4 + b\\0 = -2 + b\\b = 2[/tex]

f(x) = -1/2x + 2

Answer:

12

Step-by-step explanation:

Answer:

(-1,1)

Step-by-step explanation:

The solution to the system of equations is where the two lines cross

They cross at x=-1 y=1

(-1,1)

Answer:

The answer is (-1,1)

Step-by-step explanation:

First of all, you can see where the two lines intersect.

Also, if there was no graph, then you could solve by substitution:

1. Substitute y from y = 2x + 3 to -x

2. Then simplify

-x = 2x + 3

subtract 2x from each side

-3x = 3

divide -3 from each side

x = -1

3. To solve for the value of y, you can plug -1 for x and solve.

y = -(-1)

y = 1

Answer:

3.1

Step-by-step explanation:

15.7 - 12.6 = 3.1

Pls mark me brainliest !!

Step-by-step explanation:

Basically plug in all X values given on the table into the graph to get the y values. Now you have a coordinate that you can plot on the graph given.

The answer is √32 units.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

It is 3.

Step-by-step explanation:

By looking at the sentences, you can translate the sentences to equations.

The sum of two numbers is 90, so this involves addition because the sum is the answer of an addition problem. x+y=90.

x is the larger number

y is the smaller number

The larger number is 14 more than or addition sign 3 times or multiplying the smaller number (y).

The equation would be x=14+3y because it is 3 times the smaller number.

Hope this helps!

Answer:

[tex]9^{-7}, 9^{-2}[/tex]

Step-by-step explanation:

[tex]\frac{9^5\times9^{-9}}{9^3}\\\frac{9^{-4}}{9^3}\\ 9^{-7}[/tex]

When you multiply like terms, you add their powers. When dividing like terms, you subtract their powers (subtract the power in the denominator from the one in the numerator).

[tex](9^4)^3\times9^{-14}\\9^{12}\times9^{-14}\\9^{-2}[/tex]

Answer:

The probability of rolling a 3 is 1/6 as there is only one face labeled "3" out of 6 total.

Multiplying the two probabilities gives (1/2)*(1/6) = (1*1)/(2*6) = 1/12 (Correct Answer)

The two events are independent from one another.

Answer:

Step-by-step explanation:

20 x 15%

is equal too...

20 x 0.15

and that is equal to

...

3

Answer:

x = 180

Step-by-step explanation:

We can use ratios to solve

2 chocolates        5 chocolates

--------------------- = ------------------

72 calories                x calories

Using cross products

2 *x = 5*72

2x = 360

Divide each side by 2

2x/2 = 360/2

x = 180

Set up a ratio 2/72 = 5/x.

Now use cross-products.

(2)(x) = (5)(72).

2x = 360.

Now divide both sides by 2.

This gives us x = 180.

So, Jodi consumes 180 chocolates when she eats 5 chocolates.

Answer: he invested $120000 at 6% and $281000 at 9%

Step-by-step explanation:

Let x represent the amount invested at 6%

Let y represent the amount invested at 9%

The Actor invest some money at 6% and $41000 more than twice the amount at 9%. This means that

y = 2x + 41000- - - - - - - - - 1

The interest gotten from x is

6/100 × x = 0.06x

The interest gotten from y is

9/100 × y = 0.09y

The total annual interest earned from the investment is $32490. It means that

0.06x + 0.09y = 32490- - - - - - - - -2

Substituting equation 1 into equation 2, it becomes

0.06x + 0.09(2x + 41000) = 32490

0.06x + 0.18x + 3690 = 32490

0.06x + 0.18x = 32490 - 3690

0.24x = 28800

x = 28800/0.24

x = 120000

Substituting x = 120000 into equation 1, it becomes

y = 2(120000) + 41000

y = 281000

Answer:

The minimum number of letters John has to send to be sure that Peter receives his letter is 127 letters

Step-by-step explanation:

The four digit numbers that are multiples of 5 and 7 with the last digit = 0 is found as follows  

Since the last digit of the house number = 10, then the house number is divisible by 10 which also meets the condition that the house number is divisible by 5

We have the four digit numbers from 1000 to 9999

Hence the numbers divisible by both 7 and 10 are from (1000/70 (Which is 14 + 2/7) - 2/7)×70 + 70 = 1050 to (9999/70 (Which is 142 + 59/70)- 59/70)×70= 9940

Which gives 142 - 15 =  127 numbers which are four digit number multiples of 5 and 7 with the last digit = 0

Hence the minimum number of letters John has to send to be sure that Peter receives his letter = 127 letters.

The minimum number of letters that John will have to send to ensure Peter receives his letter is : 127 letters

Applying the given information;

size of house number = Four digits which is a multiple of 5 and 7

House number ends with 0

given that the last number has a 0 digit the house number is divisible by 5 because it is divisible by 10

The Four digit house number will fall between : 1000 to 9999

    ( 1000 / 70 ) = [tex](14 + 2/7) - 2/7)*70 + 70 = 1050[/tex]

    ( 9999 / 70 ) = [tex]( 142 + 59/70)- 59/70)*70= 9940[/tex]

∴ The minimum number of letters of a four digit number that is a multiple of    5 and 7 and whose last digit = 0 will be

     142 - ( 14 + 1 ) = 127 letters

Learn more : https://brainly.com/question/9215444

Answer:

subtract 2x on both sides

Step-by-step explanation:

Answer:

x= -3

Step-by-step explanation:

Move The Terms:

8x -2x =3 = -15

Collect like terms and calculate:

6x = -15-3

Divide both sides of the equation by 6:

x = -3

Final answer:

x= -3

Hope this helped have a good day

Answer: (9 - 2) ⋅ 180 ° = 7 ⋅ 180 ° = 126 0 °

Step-by-step explanation:

Answer:

1. $3.85 per gallon

2. $1.59

3. 7/12

Step-by-step explanation:

1. Jayden spent $46.20 on 12 gallons of gasoline. The price per gallon can be gotten by dividing the total price paid by the total number of gallons bought:

46.20 / 12 = $3.85 per gallon

The price per gallon is $3.85

2. Jayla buys 1.2 pounds of bananas and they cost $1.29 per pound. The total amount paid for the bananas is:

1.2 * 1.29 = $1.59

3. Billy ate 1/4 of a pizza, and Wi ate 1/3 of the same pizza. The total fraction of the pizza ate is:

1/4 + 1/3 = 7/12

They ate 7/12 of the pizza

Answer:

associative property with respect to addition and subtraction

3+[7+(-4)]=(3+7)+(-4)

3+[7-4]=10+(-4)

3+3=10-4

6=6

Step-by-step explanation:

i hope it will help you

Answer:

75 km / h = 1250 m / m;

Solution ⇒ 1250 meters / minute

Step-by-step explanation:

Take a look at the explanation below;

[tex]75 km / hour - m / minute,\\75 km = 75 * 1000 meters = 75000 meters,\\\\1 hour = 60 minutes,\\75 kilometers / hour = 75000 meters / 60 minutes,\\\\75000 meters / 60 minutes = 1250 meters / minute\\[/tex]

Conclusion; 1250 meters / minute

Answer:

$1.24

Step-by-step explanation:

5% of 6.24 x 4 .If you're rounding then it's $1.25 (but also who's letting someone open an account with 6 dollars)

(edit:forgot the explaination)