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Answer questions 3-6
Answers
Answer:
3. aₙ = -9n +7
4. d = -2.4
5. a₆ = 45
6. aₙ = 133 + 4n
Step-by-step explanation:
Question 3.
a₁ = -2; aₙ = aₙ₋₁ - 9
The explicit rule for an arithmetic sequence is
aₙ = a₁ + d(n -1 )
d = aₙ - aₙ₋₁
aₙ = aₙ₋₁ - 9 Subtract aₙ₋₁ from each side
aₙ - aₙ₋₁ = -9
d = -9
For this sequence,
aₙ = -2 – 9(n - 1) Remove parentheses
aₙ = -2 - 9n + 9 Combine like terms
aₙ = -9n + 7
===============
Question 4
d = aₙ - aₙ₋₁
a₂ - a₁ = 6.2 – 8.6 = -2.4
a₃ - a₂ = 3.8 – 6.2 = -2.4, etc.
The common difference is
d = -2.4
===============
Question 5
aₙ = 8n – 3 Substitute the value of n
a₆ = 8×6 – 3
a₆ = 48 - 3
a₆ = 45
============
Question 6
a₁ = 137; d = 4
aₙ = a₁ + d(n -1 )
aₙ = 137 + 4(n -1 )
aₙ = 137 + 4n -4
aₙ = 133 + 4n
Related Questions
what is the equation of a line that has an undefined slope (vertical line) and an x-intercept of -2
Answers
The equation of a vertical line: x = a (a - any real number).
x-intercept = -2, therefore your answer is:
x = -2The ratio of yellow tulip bulb to red tulip in a package is 2 to 3. There are 100 tulip in the package. How many of each color bulbs is there.
Answers
Answer:
Yellow: 40Red: 60Step-by-step explanation:
You have to distinguish the difference between a ratio of yellow bulb to red bulb and red bulb to total and yellow bulb to total. The totals are where you start.
2 bulbs out of 5 are yellow
3 bulbs out of 5 are red
Yellow
Set up the proportion for yellow. You could start with red.
2/5 = x / 100 Cross multiply5x = 2 * 100 Combine the right.5x = 200 Divide by 55x/5 = 200/5 Simplifyx = 40 Answer 1. Yellow bulbsRed
3/5 = x / 100 Cross multiply 5x = 3*100 Simplify5x = 300 Divide by 55x/5 = 300/5 Simplifyx = 60 Answer 2. Red bulbs.Note: Yellow to red is 2/3
what is the 20th term of the arithmetic sequence 8,21,34,47,60,..
Answers
Well considering that
F (1) = 8
F (x) = f(x-1) + 13
(Meaning the previous term plus 13)
So
F (x) = 13x - 5
F (0) = -5
The 20th term of the given arithmetic sequence 8, 21, 34, 47, 60... is 255.
Explanation:In the field of mathematics, this type of problem is referred to as an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is called the common difference.
In your question, the arithmetic sequence provided is 8, 21, 34, 47, 60... Here, the common difference is 13 (i.e., every term after the first is 13 more than the preceding term).
To find any term (let's say the nth term) in an arithmetic sequence, you can use the formula:
nth term = first term + (n - 1) * common difference
Applying this formula to find the 20th term:
20th term = 8 + (20 - 1) * 13 = 8 + 247 = 255
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When 2x^2 - 20x + 49 = 19 is written in the form (x - p)^2 = q, what is the value of q? Show your work please.
Answers
Answer:
q = 10
Step-by-step explanation:
The desired form is a rearrangement of the given equation, divided by the leading coefficient.
Monic polynomialA monic polynomial is one with a leading coefficient of 1. The desired form requires that we start from that condition. In order to avoid fractions, we can begin by subtracting the constant term on the left.
2x^2 -20x +49 = 19 . . . . . . given
2x^2 -20x = -30 . . . . . . . . subtract 49
x^2 -10x = -15 . . . . . . . . . divide by 2
Completing the squareThe square of the binomial a+b is given by ...
(x +b)^2 = x^2 +2bx +b^2
That is the constant term on the right is the square of half the coefficient of x. To achieve this perfect square trinomial in our equation, we need to add the square of half of -10.
x^2 -10x +25 = -15 +25 . . . . . . add (-10/2)^2 = 25 to both sides
(x -5)^2 = 10 . . . . . . . . . . . write in the desired form
The value of q in the form ...
(x -p)^2 = q
is 10.
Compare the graph of g(x) =x^2 +6 with the graph of f(x)=x^2
Answers
Answer:
Step-by-step explanation:
If you know what g(x) looks like, you can find f(x). Every y point of g(x) is f(x) + 6.
The general point of g(x) is (x,f(x) + 6). That is the major difference. Just so you can see it visually, the both graphs are shown below.
red: f(x) = x^2
blue: f(x) = f(x) + 6 = x^2 + 6
green: x = 2 With the two points shown that intercept the two given functions.
Purple(?): x = - 2 with the two points shown that intercept the two given functions.
The graphs of both g(x) =x² +6 and f(x)=x² are parabolas. However, while the vertex of the graph of f(x) = x^2 is at the origin, the graph of g(x) = x² + 6 is shifted upwards by six units, with the vertex of g(x) at (0,6). The shape of the two graphs is identical.
Explanation:The graphs of g(x) =x² +6 and f(x)=x² are both parabolas, but their positions differ on the coordinate plane. The function f(x) = x² is a standard quadratic function with a vertex at the origin (0,0). On the other hand, g(x) = x² + 6 is a vertical translation of the graph of f(x) = x2 upwards by six units. So, the vertex of g(x) is at the position (0, 6). Furthermore, the shape of the two graphs will remain the same as they both have the same degree and leading coefficient.
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how many meters are in 5 millimeters are in 2 kilometers?
Answers
Answer:
5 mililmiters = 0,005 meters = 0,000005 kilometers
2 kilometers = 2000 meters
Step-by-step explanation:
km / hectometer / decameter / meter / dcm / centimeter / milimeter
1000 m / 100 m / 10 m < 1 > 0,1 m/ 0,01 m / 0,0001 m
1 meter = 0, 1 decimeters / 0, 01 centimeters /0, 000 1 millimeters
1 meter = 10 decameters / 100 hectometers / 1000 kilometers
so 5 millimeters = 0,005 meters = 0, 000 005 kilometers
so 2 km = 2 000 meters = 2 000 000 millimeters
the reference unit of measure is the meter.
write the equation of the line that passes through the given points (0,-1) and (-5,-7) Simplify your answer
Answers
Answer:
y = 6/5 x-1 slope intercept form
6x-5y = 5 standard form
Step-by-step explanation:
We have the points (0,-1) and (-5,-7)
We can find the slope using
m = (y2-y1)/(x2-x1)
= (-7--1)/(-5-0)
= (-7+1)/(-5-0)
= -6/-5
= 6/5
We also have the y intercept ( when x=0) It is -1
We can use the slope intercept form of the equation y = mx+b
y = 6/5 x-1
Depending on what you mean when you say simplify your answer
We can put it in standard form ax+by = C
Multiply both sides by 5
5y =5* 6/5 x-1*5
5y = 6x-5
Subtract 6x from each side
-6x+5y = 6x-6x-5
-6x+5y = -5
Multiply by -1
6x-5y = 5
Graph the equation by plotting three points -2y=-x+8
Answers
[tex]-2y=-x+8\qquad\text{divide both sides by (-2)}\\\\y=\dfrac{1}{2}x-4\\\\for\ x=0\to y=\dfrac{1}{2}(0)-4=0-4=-4\to(0,\ -4)\\\\for\ x=2\to y=\dfrac{1}{2}(2)-4=1-4=-3\to(2,\ -3)\\\\for\ x=4\to y=\dfrac{1}{2}(4)-4=2-4=-2\to(4,\ -2)[/tex]
(4.5,-1.75) and (8,0)
Which statement is true? The initial height of the coconut is 190 feet. The coconut will hit the ground between 4 and 5 seconds after it was dropped. The values of h(t) when t = 4 and 5 should be 0. The maximum height of the coconut was 1 second after it was dropped.
Answers
Answer: Based on the given data, the coconut has a height of 210 units and it hits the ground between 4 to 5 seconds where the height is less than zero or a negative number, this means that probably the coconut was buried in the ground at these times. The correct answers are:
The values of h(t) when t = 4 and 5 should be 0. This could also be without the assumption that the coconut is buried after falling.
Answer:
its C
Step-by-step explanation:
What is the common ratio for this geometric sequence? 64,16,4,1,...
Answers
Answer:
r = ¼
Step-by-step explanation:
The formula for the nth term of a geometric sequence is
aₙ = a₁rⁿ⁻¹
We can get the value for r by dividing aₙ by aₙ₋₁.
a₄/a₃ = ¼
r = ¼
r
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Tap for more steps...
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I need the range and domain
Answers
Look at the picture.
The domain x ≥ 0 → x ∈ [0, ∞)The range y ≥ 0 → y ∈ [0, ∞)The height of the water in an a over ground pool is 3ft. As the number of water drains ,the rate of -1/2 inch per minute. Write and solve an equation to find how many minutes it will take to drain the pool
Answers
Answer:
36 - 1/2x = 0
72 minutes
Step-by-step explanation:
there is a total of 3 feet in the pool at the start, 1 ft = 12 in, and 3 ft = 36 in. the pool is losing water, so we have to subtract. it is losing water at a rate of -1/2 in per minute, and we don't know how many minutes it will take
we have to set it equal to 0 because we are trying to find out how long it will be until the pool is completely drained, which is when there will be no water left, so it will be 0
subtract 36 from both sides
-1/2x = -36
divide both sides by -1/2
x = 72
72 minutes
Jacob started that he solved the equation 2x+3=5 using addition and multiplication property of equality. Which statement is true?
A.Jacob added -3 to both sises and multiplied both sides by 1/2.
B.Jacob added -3 to both sises and multiplied both sides by 2.
C.acob added 3 to both sises and multiplied both sides by 1/2.
D.acob added 3 to both sises and multiplied both sides by 2.
Answers
Answer:
A. Jacob added -3 to both sides and multiplied both sides by 1/2.Step-by-step explanation:
To solve the equation, Jacob must add -3 to both sides, and multiply by 1/2 both of them, as it's shown below:
[tex]2x+3-3=5-3\\2x=2\\\frac{2x}{2}=\frac{2}{2}\\x=1[/tex]
So, you see, applying all operations like option A, we easily solve the equation.
Therefore, the right statement is the first one, A.Answer:
The correct option is A) Jacob added -3 to both sises and multiplied both sides by 1/2.
Step-by-step explanation:
Given :
[tex]2x+3=5[/tex] -------- (1)
Solution :
To find the value of x from equation (1) we have to first add both side -3 in equation (1), we get
[tex]2x = 2[/tex]
Now, multiply both the side of equation (1) by
[tex]\dfrac{1}{2}[/tex]
[tex]x= 1[/tex]
Therefore option A) is correct.
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The range of f(x)=5x2^x is all positive real numbers true or false
Answers
Step by step-
Nate and Laura picked apples. Laura picked 1/2 as many as Nate picked. Together they picked 90 apples. How many did each of them pick?
Let n stand for the number Nate picked.
Equation:_______
How many apples did Nate pick?_________
How many apples did Laura pick?__________
Answers
45
45 that is the problem
The answers to all the parts are -
Equation : (1/2)n + n = 90
Apples picked up by Nate : 60
Apples picked up Laura : = 30
What is a expression? What is a mathematical equation? What is Equation Modelling?
A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have Nate and Laura picked apples. Laura picked 1/2 as many as Nate picked. Together they picked 90 apples.
Let [n] stand for the number Nate picked. Then, the number of apples picked up by Laura will be (1/2)n. Then, we can write -
Equation : (1/2)n + n = 90
1.5n = 90
n = (90/1.5)
n = 60
Apples picked up by Nate : 60
Apples picked up Laura : 60/2 = 30
Therefore, the answers to all the parts are -
Equation : (1/2)n + n = 90
Apples picked up by Nate : 60
Apples picked up Laura : = 30
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find the product of 10^3 * 10^6
Answers
When multiplying the same base with exponents, you keep the base the same and then you add the exponents, so for this question you do:
10^3 x 10^6
10^9
[tex] {10}^{3} \times {10}^{6} [/tex]
[tex] = {10}^{9} [/tex]
The answer is:
[tex] {10}^{9} [/tex]
This is because of the law of indices. When multiplying indices, you add the powers.
Which of the following is an irrational number
Answers
Answer:
A
Step-by-step explanation:
Pi is a never ending number.
The answer is B) because it is not a never ending number
Also, the question in the picture asks which is a rational number, not irrational
The area of a trapezoid is given by the formula A = 1 2 h(B + b). Solved for b, this formula becomes b =
Answers
Answer:b = (2A - hB)/h
Step-by-step explanation:
See , we know area of a trapezoid is equal to 1/2*(sum of parallel sides)* perpendicular distance between parallel sides.
Here B and b are parallel sides which we know by comparing the equation.
And 'h' here is the perpendicular distance between parallel sides.
We have to write the equation in terms of one of the parallel sides 'b'
Our formula is A = 1/2*h*(B+b)
I.e. 2A = h*(B+b) (Multiplying both sides by 2)
I.e. 2A - hB = hb
I.e. b = (2A - hB)/h
Hope it helps!!!
Answer:
D) [tex]\frac{2A}{H} -b[/tex]
Evaluate for x=4 and y = -3
Answers
2y/x^2
Replace x and y with the given values:
2(-3) / 4^2
2*-3 = -6
4^2 = 16
Now you have -6/16. which can be simplifies to -3/8
Hi!! Please Help ASAP!!
Answers
Answer:
The answer is A or the first one
Answer:
it's (2,3)
because look at the intersection between 2 line, that's the solution, it said nearest, so (2,3) is the most accurate
(7.02) classify each sequence as arithmetic, geometric, or neither.
4/9,4/3,4,12,36
0,1,2,3,4,5,6
-10,-6,-2,2,6,10
Answers
Answer:
geometric
arithmetic
arithmetic
Step-by-step explanation:
1.
4/9,4/3,4,12,36
Multiply each term by 3 to get the next term. There is a common ratio between terms, so it geometric.
2.
0,1,2,3,4,5,6
Add 1 to each term to get the next term. Since there is a common difference between terms, it is an arithmetic sequence.
3.
-10,-6,-2,2,6,10
Add 4 to each term to get the next term. Since there is a common difference between terms, it is an arithmetic sequence.
A force of 250 N is applied to an object that accelerate at a rate of 5 m/s2 what is the mass of the object
Answers
Force=mass x acceleration
Plug in 250 N for the force and 5 m/s2 for the acceleration; solve for mass
250=5m
50kg=m
Hope this helps!!
what is an equivalent percent for 3/8
Answers
ANSWER: 37.5%
STEP BY STEP:
Take the fraction 3/8 and divide the numerator by the denominator ⇩
3/8= .375
Move the decimal 2 places to the right, or multiply it by 100 ⇩
.375 x 100
Enjoy your percentage! ⇩
37.5% or rounded up, 38%
How much does the bag of peanuts weigh now?
Answers
Answer:
1/12
Step-by-step explanation:
subtract the two :)
Write all factored equivalent expressions for 12z+36
Answers
The factored equivalent expression for 12z+36 is 12(z + 3) after factoring out the common factor of 12.
Explanation:When asked to write all factored equivalent expressions for 12z+36, we look for common factors. Both terms have a common factor of 12. Factoring out the 12, we get 12(z + 3). There are no other common factors, and the expression cannot be factored further as both terms within the parentheses are prime with respect to each other.
The density of apple juice is 1.04 grams per cm3. The density of fruit syrup is 1.6 grams per cms The density of sparkling water is 0.99 grams per cm3. 35 cm of apple juice are mixed with 25 cm3 of fruit syrup and 270 cm3 of sparkling water to make a drink with a volume of 330 cm3. Work out the density of the drink. Give your answer correct to 3 decimal places.
Answers
Answer:
Density = 1.042 grams /cm^3
Step-by-step explanation:
Work out the mass of each of three in a unit volume (cm^3)
Givens
Apple Juice = 1.04 grams / cm^3Fruit Syrup = 1.6 grams / cm^3Sparkling water = 0.99 grams / cm^3Mixture
35 cm^3 Apple Juice = 1.04 grams / cm^3 * 35 cm^3 = 36.4 grams
25 cm^3 Fruit = 1.6 grams/cm^3 * 25 cm^3 = 40 grams
270 cm^3 water = 0.99 * 270 267.3 grams
Total Mixture
Volume = 25 + 35 + 270 = 330 cm^3Mass = 36.4 + 40 + 267.3 = 343.7 gramsDensity
Density = mass / volume = 343.7 / 330 = 1.0415
Answer
1.042 grams / cm^3
The density of the resulting drink is; 1.042 grams per cm³.
To find the density of the resulting drink, we need to first determine the mass of each of the constituents.
The masses of the constituents can be found as follows;
Mass = density × volumeFor apple juice;
Mass(a) = 1.04 × 35 = 36.4gramsFor fruit syrup;
Mass(f) = 1.6 × 25 = 40grams.For sparkling water;
Mass(s) = 0.99 × 270 = 267.3gramsTherefore, the total mass of the drink is;
= 36.4 + 40 + 267.3 = 343.7 grams.And, since the total volume of the drink is 330cm³
Density of the drink = 343.7 grams/ 330 cm³Density of the drink = 1.042 grams per cm³.
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What type of graph is best to use to graph data about the favorite sport for seniors and juniors? A. Bar Graph B. Double Bar Graph C. Line Graph D. Double Line Graph
Answers
Answer:
Bar Graph
Step-by-step explanation:
A bar graph would be best.
B.Double Bar Graph
There are TWO types of people so it needs to be a two type Bar Graph as in double Bar Graph. A line graph is not right because it is changes over time.
Natasha was thinking of a number. Natasha subtracts 16 from it and gets an answer of 18.2. What was the original number?
Answers
Answer:
34.2
Step-by-step explanation:
Pink is shoe is 20.4 cm long Rajesh shoe is 7 mm longer than pinky shoe how long is Rajesh shoe in cm
Answers
To find the length of Rajesh's shoe, convert the additional length from millimeters to centimeters and add it to Pinky's shoe length. Rajesh's shoe is 21.1 cm long.
Explanation:The subject of this question is Mathematics and it is suitable for a Middle School student. To find the length of Rajesh's shoe, we need to add the length of Pinky's shoe to the additional length that Rajesh's shoe has. Pinky's shoe is 20.4 cm long, and Rajesh's shoe is 7 mm longer.
Firstly, we need to convert millimeters to centimeters since 1 cm equals 10 mm. Therefore, 7 mm is equivalent to 0.7 cm (since 7 divided by 10 equals 0.7).
Next, we add this length to Pinky's shoe length:
20.4 cm (Pinky's shoe length)+ 0.7 cm (additional length)Rajesh's shoe length equals 21.1 cm.
25 POINTS PLEASE HELP How do I solve
{y=2x-4; x+2y=12}
Answers
Substitute y = 2x - 4 to x + 2y = 12:
x + 2(2x - 4) = 12 use distributive property
x + (2)(2x) + (2)(-4) = 12
x + 4x - 8 = 12 add 8 to both sides
5x = 20 divide both sides by 5
x = 4
Put the value of x to the first equation:
y = 2(4) - 4
y = 8 - 4
y = 4
Answer: x = 4 and y = 4Answer:
x=4, y=4
Step-by-step explanation:
y=2x-4;
x+2y=12
We can use substitution since the first equation is solved for y
Where ever you see y in the second equation, replace it with 2x-4
x + 2(2x-4) = 12
Distribute the 2
x+4x-8 = 12
Combine like terms
5x-8=12
Add 8 to each side
5x-8+8=12+8
5x=20
Divide by 5
5x/5 = 20/5
x =4
We still need to solve for y
y = 2x-4
We know x =4
y = 2(4) -4
y = 8-4
y=4