Write the first 5 terms of the
sequence an = 3n – 4

Answers

Answer 1

Answer:

- 1, 2, 5, 8, 11

Step-by-step explanation:

Substitute n = 1, 2, 3, 4, 5 into the n th term formula

a₁ = 3(1) - 4 = 3 - 4 = - 1

a₂ = 3(2) - 4 = 6 - 4 = 2

a₃ = 3(3) - 4 = 9 - 4 = 5

a₄ = 3(4) - 4 = 12 - 4 = 8

a₅ = 3(5) - 4 = 15 - 4 = 11

The first 5 terms are - 1, 2, 5, 8, 11

Answer 2

Final answer:

The first 5 terms of the sequence an = 3n - 4 are -1, 2, 5, 8, and 11. Each term is found by substituting the nth term number into the expression and calculating its value.

Explanation:

The student has asked to write the first 5 terms of the sequence an = 3n - 4. To find the terms of this sequence, we simply substitute the values of n (starting from 1 and going up by 1 each time) into the expression and calculate the results.

For n = 1: a1 = 3(1) - 4 = 3 - 4 = -1For n = 2: a2 = 3(2) - 4 = 6 - 4 = 2For n = 3: a3 = 3(3) - 4 = 9 - 4 = 5For n = 4: a4 = 3(4) - 4 = 12 - 4 = 8For n = 5: a5 = 3(5) - 4 = 15 - 4 = 11

Therefore, the first 5 terms of the sequence are -1, 2, 5, 8, 11.


Related Questions

-18x-17=-53
( Complete the steps:)
1. Write the original equation
2. Apply the Addition Property of Equality.
solve step by step

Answers

-18x-17=-53 /add 17 to both sides

-18x-17+17=-53+17

-18x=-36

x=(-36)/(-18)

x=2

A bag contains white marbles and red marbles, 90 in total. The number of white marbles is 6 less than 5 times the number of red marbles. How many white marbles are there?

Answers

Answer:

W = 72

Step by step explanation:

White = W

Red = R

W + R = 90

Write an equation

W = 5R - 6

Substitute

5R - 6 = 90

Add 6 to both sides of the equation

5R = 90

Simplify

90 ÷ 5 = 18

R = 18

90 - 18 = W

W = 72

Hope this was useful to you!

Final answer:

By setting up an algebraic equation, we determine that there are 74 white marbles in the bag when the total number of marbles is 90 and the white marbles count is 5 times the number of red marbles minus 6.

Explanation:

Calculating the Number of Marbles

To figure out how many white marbles are in the bag, we can set up a simple algebraic equation. Let's define the number of red marbles as x. According to the problem, the number of white marbles is 5 times the number of red marbles minus 6. We can represent this as 5x - 6. Since we know the total number of marbles is 90, we can write the equation as:

x + (5x - 6) = 90.

Combining like terms results in:

6x - 6 = 90.

Adding 6 to both sides gives us:

6x = 96.

Dividing both sides by 6, we get:

x = 16.

So, there are 16 red marbles. Now, to find the number of white marbles, we plug this back into the equation for white marbles:

5(16) - 6 = 80 - 6 = 74.

There are thus 74 white marbles in the bag.

help!! study island

Answers

It’s b, next time you can use Photomath!

Answer:

The answer is b

Step-by-step explanation:

If a bill cost $125. And they leave a $21.25 for a tip what percentage did they tip

Answers

Answer:

17%

Step-by-step explanation:

Divide $21.25 by $125

Mrs. Anderson surveyed her class and asked each student, "How many hours do you spend
playing sports per week?" The results are below.
0,0,0,0.2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,8,12
Part A: Construct a dot plot of the data and choose the best graph from the choices below.
Part B: What observations can you make about the shape of the distribution?
Part C: Are there any values that don't seem to fit? Justify your answer.

Answers

Answer: Part A is the graph with 4 dots for 0, 2 dots for 2, 10 dots for 4, 9 dots for 6, 2 for 7(in between 6 and 8) 1 dot for 8, and 1 dot for 12.

Part B: Answer: Most are clumped together and smaller than 8, with one data point far away from the others.

Part C: Answer; 12 hours seems to much higher than the other data values.

Step-by-step explanation: Hope that helped:) I just did it and checked and it’s correct. Have a good day!

What is the area of the following rectangle?
A) 18 sq ft
B) 36 sq ft
C) 80 sq ft
D) 100 sq ft

Answers

Answer:

C

Step-by-step explanation:

Because area = L x w

8 x 10 = 80

C

Answer:

A=80

Step-by-step explanation:

You find the area of rectangle using Length times width. 8 times 10 =80

HURRY!!!!!!!!!

Given P(5,10,8) and Q(7,11,10), find the midpoint of the segment PQ.

Answers

Answer:

[tex]P_{m}=(6,10.5,9)[/tex]

Step-by-step explanation:

The mid point can be found with the formula

[tex]P_{m}=(\frac{x_{1}+x_{2} }{2},\frac{y_{1} +y_{2} }{2} ,\frac{z_{1}+z_{2} }{2} )[/tex]

The given coordinates are [tex]P(5,10,8)[/tex] and [tex]Q(7,11,10)[/tex].

Replacing coordinates in the formula, we have

[tex]P_{m}=(\frac{5+7}{2},\frac{10+11 }{2} ,\frac{8+10}{2} )=(\frac{12}{2},\frac{21 }{2} ,\frac{18}{2} )\\P_{m}=(6,10.5,9)[/tex]

Therefore, the mid point of the segment PQ is [tex]P_{m}=(6,10.5,9)[/tex]

Answer:

^its C if ur too lazy to read the equation like me

Step-by-step explanation:

Kerry bought a conical tent to put on the back porch. The tent instructions reveal the height at the tallest point to be
4.5 feet and the space inside to be 10.5 cubic feet. About how many square feet of the back porch will be covered by
the tent?
Which measure of the cone needs to be calculated to answer the problem?
A. diameter
B. Radius
C. Base area
D. Volume
Which equation represents the scenario?
A. V= (1/3)(10.5)(4.5)
B. 4.5 = (1/3)(10.5)(h)
C. 10.5 = (1/3)(4.5)(h)
D. 10.5= (1/3)B (4.5)
How many square feet of the back porch will the tent cover?
A. 2.33 square feet
B. 6 square feet
C. 7 square feet
D. 15.75 square feet​

Answers

1) The measure needed is the C. Base area,  2) the scenario represents the equation D. 10.5= (1/3)B (4.5)

and 3) the tent will cover C. 7 square feet of the back porch.

Use the appropriate formulas to solve it step-by-step.

We know the height (h) of the conical tent is 4.5 feet.The volume (V) of the tent is given as 10.5 cubic feet.

The formula for the volume of a cone is:

[tex]V = \frac{1}{3} \pi r^2 h[/tex]

We need to find the base area of the cone (which is a circle) to determine the area covered by the tent on the back porch. The base area (A) of the cone is:

[tex]A = \pi r^2[/tex]

To calculate this, we must first determine the radius (r) of the cone. Let's rearrange the volume formula to solve for the radius (r):

[tex]10.5 = \frac{1}{3} \pi r^2 4.5[/tex]

Simplifying this equation, we get:

[tex]10.5 = \frac{1}{3} \pi r^2 4.5[/tex]

Multiply both sides by 3 to get rid of the fraction:

[tex]31.5 = \pi r^2 4.5[/tex]

Divide both sides by 4.5:

[tex]\frac{31.5}{4.5} = \pi r^2[/tex]

[tex]7 = \pi r^2[/tex]

Divide both sides by π:

[tex]r^2 = \frac{7}{\pi}[/tex]

Taking the square root of both sides, we find the radius (r):

[tex]r = \sqrt{\frac{7}{\pi}}[/tex]

Now we can calculate the base area (A) of the cone:

[tex]A = \pi r^2[/tex]

Substitute r^2 back into the equation:

[tex]A = \pi \left( \frac{7}{\pi} \right) = 7 \text{ square feet}[/tex]

Please answer this quickkkkkkk

Answers

Answer:

A = 12 units^2

Step-by-step explanation:

The area of a trapezoid is

A = 1/2 (b1+b2)* h where b1 and b2 are the bases (which are parallel)

b1 = AT = 4 units

b2 = SR = 2 units

The heights is along the x axis which is 4 units

A = 1/2 ( 2+4) *4

A = 1/2 (6)*4

A = 12 units^2

Find the sum of 10x^2-10x-6 and x+6.

Answers

Answer:

10x²−9x

Step-by-step explanation:

10x²−10x−6+x+6

=10x²−10x−6+x+6

Combine Like Terms:

=10x²−10x−6+x+6

=(10x²)+(−10x+x)+(−6+6)

=10x²−9x

Hope this helps!

Final answer:

The sum of the equations 10x^2 - 10x - 6 and x + 6 is achieved by combining like terms, which results in 10x^2 - 9x.

Explanation:

To find the sum of 10x^2-10x-6 and x+6, you combine the like terms from each equations. You do this by adding the coefficients of like terms, which are terms with the same variable. In this case, the variable x is the like term. Let's do it step by step:

First, identify the like terms. In the expression 10x^2 - 10x - 6, 10x^2 is a term, -10x is a term, and -6 is a term. In the expression x + 6, x is a term and 6 is a term.Combine the terms that have similar variables. The coefficients of 10x^2 and x are 10 and 1 respectively. Since there's no like term for 10x^2, carry it as it is. The coefficients for -10x and x are -10 and 1. When you add these together, you get -9x (-10 + 1 = -9).Combine the constant terms -6 and 6. When you add these, you get 0 (-6 + 6 = 0).

The sum of the two expressions 10x^2 - 10x - 6 and x + 6 therefore is 10x^2 - 9x.

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Last month, took Lucas 32 minutes to run 3 miles. This month is took him 28 minutes. Find the percent of change.

Answers

Answer:12.5%

Step-by-step explanation:

Percentage=(32-28)/32 x 100

Percentage=4/32 x 100

Percentage=(4x100)/32

Percentage=400/32

Percentage=12.5%

What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 5:8? Round to the nearest tenth, if necessary.

x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1

y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1

(–2.2, –6.3)
(–2.4, –6.4)
(2.7, –0.7)
(1.2, –4.7)

Answers

Answer: D) (1.2,-4.7)

Step-by-step explanation:

plug in the end corrdinates like it says in the equation that the problem gives you.

The x and y-coordinates of the point C will be equal to (1.2, -4.7).

What is a coordinate system?

Using one or even more integers, or coordinates, a coordinate system in geometry establishes a unique way to locate points or other geometrical objects on a manifold, such as Euclidean space.

The order of the values is important, and they can sometimes be distinguished by their place in an arranged tuple or by a letter, such as "the x-coordinate."

As per the given information in the question,

Coordinates are the location of a point in an (x,y) plot.

The given coordinates are:

A = (7,-2)

B = (-8,-9)

m:n = 5:8

Use the formula given below,

(x, y) = 1/(m + n)(nx₁ + mx₂, ny₁ + ny₂)

(x, y) = 1/(5 + 8)[5(-8) + 8(7), 5(-9) + 8(-2)]

(x, y) = (1.2, -4.7)

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Use the multiplier method to increase £258 by 43%
You must show your working.​

Answers

Answer:£368.94

Step-by-step explanation:

258*1.43= 368.94

4x + 3y = 6
-4x + 2y = 14
Solve the system of equations.

Answers

Answer:

Systems of equations equals (-1.5, 4)

Step-by-step explanation:

1. isolate the y in both equations

2. a. 4x+3y=6

3y=-4x+6

y=-4/3x+2

    b.

2y=4x+14

y=2x+7

3. Solve the system of equations

-4/3x+2=2x+7

2=3 1/3x+7

-5=3 1/3x

-1.5=x

4. Solve for y by plugging x into one equation

y=2x+7

y=2(-1.5) + 7

y= -3+7

y=4

5. Systems of equations equals (-1.5, 4)

6. If this was helpful for you, it would mean a lot if you could click the braniest button on my answer so I could move up in the ranks. Good luck!

Answer:

your answer would be x= -3/2

The distance between home and school is 4.5 miles. On a map it shows the distance to be 9 cm. What is the scale?

Answers

For every mile, it’s two centimeters. It’s 2 cm per mile.

The scale factor for the measurements on the map would be 11 x 10 ⁻⁵.

What is scale factor?

Scale factor is used to compare the size of two objects. Mathematically, we can write -

{K} = S{O1}/S{O2}

Given is that the distance between home and school is 4.5 miles. On a map it shows the distance to be 9 cm.

The distance between home and school : 4.5 miles.

On the map the distance between home and school is 9 cm.

We can write the scale factor as -

{K} = (9 x 5.5 x 10 ⁻⁵)/4.5

{K} = 11 x 10 ⁻⁵

Therefore, the scale factor for the measurements on the map would be 11 x 10 ⁻⁵.

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What is the point-slope form of a line that has a slope of 3 and passes through point (1, 4)? y minus 4 = 3 (x minus 1) 1 minus y = 3 (x minus 4) y 1 minus 4 = 3 (1 minus x 1) 1 minus y 1 = 3 (4 minus x 1) I NEED IT NOW PLEASEEEE!!!!

Answers

Answer:

y - 4 = 3(x - 1)

Step-by-step explanation:

It looks like you have slope 3  and a point (1, 4)

so  it should be  y - 4 = 3(x - 1)

which is your first choice:  y minus 4 = 3 (x minus 1)

The point-slope form of a line is  y - 4 = 3(x-1) which is correct option(A).

What is linear equation?

A linear equation is defined as an equation in which the highest power of the variable is always one.

GIven equation,

Slope of line (m) = 3

Slope form of a line is y-y₁ = m(x-x₁)

Line passes through point (1, 4)

⇒ y - 4 = 3(x-1)

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PLEASE help me it is about rate tables.

Answers

Answer:

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

you take 18-12 wich gives you 6, then you do 18+6 wich equals 24. hope this helps. good luck in the future :)

Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
x+5 x+4

Answers

Final answer:

The area of a rectangle is represented by the multiplication of its length and width. For a rectangle with dimensions 'x + 5' and 'x + 4', the area is given by the standard form polynomial ' [tex]x^2 + 9x + 20[/tex]'.

Explanation:

The area of a rectangle is calculated by multiplying the length by the width of the rectangle. Here, the length and width of the rectangle are given by the expressions 'x + 5' and 'x + 4'. Therefore, to find the area, you multiply those two expressions together:

(x + 5) * (x + 4)

When you multiply these two expressions, you get:
[tex]x\times x + 4\times x + 5\times x + 5\times 4 = x^2 + 9x + 20[/tex]

This is the polynomial in standard form that represents the area of the rectangle,

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Is this a piecewise graph function? Check using vertical line test.
HELP!

Answers

The answer is- Yes, the piecewise graph is a function because it passes the vertical line test.


Hope that helped!!!

What is 1 3/4 divided by 1/3 equal

Answers

5.25 and/or 21/4 i believe ?

This Question: 1 pt
Find the equation of the line that has the given properties.
Contains (-4,-2); parallel to the line y = – 5x + 3
The equation of the parallel line is .
(Type your answer in slope-intercept form.)

Answers

Answer:  y = -5x - 22

Step-by-step explanation:

Use the Point-Slope formula: y - y₁ = m(x - x₁)

m = -5      (parallel means it has the same slope)(x₁, y₁) = (-4, -2)

y - (-2) = -5(x - (-4))

y + 2  = -5(x + 4)

y + 2 = -5x - 20

y       = -5x - 22

Use the data in the table to complete the sentence.

The function has an average rate of change of....

Answers

The Average of rate is -1.

Step-by-step explanation:

Everytime it goes up by one the y goes down by 1 so it would be -1.

The function has an average rate of change of -1. It is denoted by R.

What is the average rate?

The single rate applies to property in several locations and is a weighted average of the separate rates that apply to each place.

The function has an average rate of change of -1.

[tex]\rm R = \frac{4-5}{1-0} \\\\ R=-1[/tex]

Hence, the function has an average rate of change of -1.

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Find the slope of the line on the graph below:
Slope = [ ]

Answers

Answer:

slope =0

Step-by-step explanation:

its on the point (4,0) its not moving up and down therefor there's no slope

Answer:

0

Step-by-step explanation:

Hello!

Slope can be calculated using the formula [tex]\frac{Rise}{Run}[/tex]

Rise is the change in y between two pointsRun is the change in x between two points

The two points I'll pick are (0,4) and (1,4).

The change in y (4 and 4)  is 0.

The change in x (0 and 1) is 1.

Put it into the slope format and you get a slope of [tex]\frac01[/tex] or [tex]0[/tex].

When a movie is released to theaters, production companies monitor revenues from individual cities for that movie on its release date. Below is a scatter plot that shows 10 different movie revenues from opening night in both Tallahassee and Gainesville. Revenue is reported in millions of dollars.

Part B: According to the model found in Part A, if a movie brought in $32.2 million in total revenue in Tallahassee, what would the expected revenue be for Gainesville? (Round your answer to the nearest thousandths *three decimal places*)

Answers

Answer:

$13.299 million

Step-by-step explanation:

We need the model from Part A to answer Part B to three decimal places,

The point marked by the blue arrow is clearly an outlier. I ignored it in "eyeballing" the best-fit line.

My line has four points above and five points below the line,

You probably had to use a statistical calculator to get the equation for the line of best fit.

Assume it was

y = 38.9016 - 0.7951x

You would use that equation to predict y when x = 32.2.

y = 38.9016 - 0.7951 × 32.2 = 39.1588 - 25.6022 = 13.299

If a movie brought in $32.2 million on opening night in Tallahassee, it should bring in $13.299 million in Gainesville.

The  expected revenue be for Gainesville is $13.299 million.

Calculation of the expected value:

here we assume that

y = 38.9016 - 0.7951x

Here that equation to predict y

when x = 32.2.

So,

y = 38.9016 - 0.7951 × 32.2

= 39.1588 - 25.6022

= 13.299

hence, The  expected revenue be for Gainesville is $13.299 million.

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Nick is practicing kicking field goals. His first kick is modeled by the parabola that passes through (0,0), (1,6.86), and (2,3) where x is the number of seconds that the ball is in the air, and y is the height of the ball in yards.

Answers

Answer:

6.3 yards high

Step-by-step explanation:

The three given points are (0,0), (1,6.86), and (2,3). Use these values in f(x) = ax2 + bx + c.

For (0,0), 0 = 0 + 0 + c.

So, c = 0.

For (1,6.86), 6.86 = a + b + c. Since c = 0:

a + b = 6.86(equation 1)

For (2,3), 3 = 4a + 2b + c. Since c = 0:

4a + 2b = 3(equation 2)

Multiply equation 1 by 2, and subtract the result from equation 2:

2a + 2b  = 13.72

4a + 2b - (2a + 2b)  = 3 - 13.72

2a  = -10.72

a  = - 5.36

Plug this value into equation 1:

-5.36 + b  = 6.86

b  = 12.22

So the function is f(x) = -5.36x2 + 12.22x.

When the ball hits the ground, the height is 0, or f(x) = 0:

Use the function to determine the height of the ball, f(x), after x = 1.5 seconds.

f(x) = -5.36x2 + 12.22x

= -5.36(1.5)2 + 12.22(1.5)

= 6.27

0 = -5.36x2 + 12.22x

0 ≈ x − 2.27(Divide both sides by -5.36x.)

x ≈ 2.27 ≈ 2.3

So, the ball will be about 6.3 yards high after 1.5 seconds.

What is 5 log 3 + log 4 written as a single logarithm?

Answers

exact form: log (972)

decimal form: 2.98766626...

hope this helps !

The range of a projectile that is launched with an initial velocity v at an angle of with the horizontal is given by R-
where g is the acceleration due to gravity or 9.8 meters per second squared. If a projectile is launched with an initial velocity of 15
meters per second, what angle is required to achieve a range of 20 meters? Round answers to the nearest whole number.

Answers

Answer: theta ≈ 30°

Step-by-step explanation:

It said on the "show me" box at the bottom of the screen :)

The required angle of the projectile motion having range 20 m and initial velocity 15 m is 30.29°

Range of the projectile motion:

The formula for finding projectile motion is given by

Range R = [tex]\frac{v^2sin2\theta}{g}[/tex]

where v is the initial velocity and g is acceleration and [tex]\theta[/tex] is the projectile angle of the object

How to calculate angle ?

If we have given range and initial velocity with acceleration then by substituting above range formula we can find angle of the projectile

Here we have given that

R = 20 m

v = 15 m/s

g = 9.8 m/s^2

Therefore

[tex]20=\frac{15^2sin2\theta}{9.8}[/tex]

[tex]sin2\theta=\frac{20(9.8)}{225}[/tex]

[tex]\theta[/tex] = 30.29

This is the required angle of the projectile

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Tacy deposited $6900 into a savings account that earns 3.1% simple interest
each year, calculated annually. What will be the value of Tacy's account after
9 years?
O A. $1925.10
O B. $8825.10
Oc. $71,113.90
OD. $19,251.00
SUBMIT

Answers

Answer:

$8825.10

Step-by-step explanation:

Interest total= P x r x t

P = principal amount, or $6900

r= interest rate, or 0.031

t = time, or 9 years

6900 x 0.031 x 9 = 1925.10

You now add this to the original amount

6900 + 1925.10 = $8825.10

Boxes A and B contain some counters.is
8y + 1
counters
6y + 9
counters
Box A
Box B
The number of counters in each box is the same.
Work out the value of y

Answers

Answer: y=4

Step-by-step explanation:

8y+1=6y+9 -Because y is equal the equations are as well.

2y+1=9- Take 6y to the other side by -6y

2y=8-Take one over by -1

y=4-Divide 8 by 2 to get y=4

Answer:

The value of y is 4

Step-by-step explanation:

If the some of the counters in each box are the same, then A = B

If A is 8y + 1 and B is 6y + 9

Since A = B, we can say

8y + 1 = 6y + 9

Collecting like terms, we will have

8y - 6y = 9 - 1

2y = 8

Dividing both sides by 2, we will have

y = 8/2

y = 4

Water flows at a constant rate out of a faucet. Suppose the volume of water that comes out in three minutes is 10.5 gallons. How many gallons of water come out of the faucet in any number of minutes?

Answers

Answer:

3.5 Gallons Per Minute or 3.5m

Step-by-step explanation:

Since there is 10.5 Gallons in 3 minutes, do

10.5/3 = 3.5

(please mark brainliest if this helps!)

Final answer:

The flow rate from the faucet is 3.5 gallons per minute. To determine the amount of water that comes out in any number of minutes, we multiply the flow rate by the number of minutes desired.

Explanation:

Given that 10.5 gallons of water are dispensed in three minutes, we can calculate the rate of flow, which will allow us to determine how many gallons of water would come out of the faucet in any other number of minutes.

We start by finding the flow rate per minute by simply dividing the volume of water dispensed by the number of minutes it took. So, the flow rate is 10.5 gallons / 3 minutes = 3.5 gallons per minute. Now, to find out how many gallons flow in any number of minutes, we multiply the flow rate (3.5 gallons per minute) by the number of minutes.

For example, if we want to know how much water comes out in 5 minutes, we calculate it as follows: Flow rate x Time = 3.5 gallons/minute x 5 minutes = 17.5 gallons. Therefore, 17.5 gallons of water would come out of the faucet in 5 minutes.

Other Questions
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