Find an equation for the nth term of the arithmetic sequence. a18 = 97, a20 = 281
Answers
Final answer:
To find the nth term equation of an arithmetic sequence, we first determined the common difference to be 92 by given terms, and then found the first term by using the formula for arithmetic sequences. The nth term equation for the sequence is: an = -1489 + (n-1)(92).
Explanation:
To find the nth term equation of the arithmetic sequence, we need to determine the common difference and the first term of the sequence. Since we know the 18th term, a18 = 97, and the 20th term, a20 = 281, we can find the common difference, d, by subtracting the two given terms and dividing by the number of terms between them:
d = (281 - 97) / (20 - 18) = 184 / 2 = 92.
Once we have the common difference, we can use the following formula to find the first term (a1):
an = a1 + (n-1)d.
Let's substitute n = 18 and d = 92 into the formula:
97 = a1 + (18-1)(92)
a1 = 97 - (17)(92) = -1489.
Now we can write the equation for the nth term of the arithmetic sequence:
an = -1489 + (n-1)(92).
Related Questions
A solution of phosphoric acid has a boiling point of 158 degrees Celsius. What is the boiling point of the solution in degrees Fahrenheit?
Answers
The boiling point of a phosphoric acid solution that is 158 degrees Celsius is 316.4 degrees Fahrenheit. This is found by using the formula F = C * 9/5 + 32.
Explanation:To convert the boiling point of a solution from degrees Celsius to Fahrenheit, we use the formula F = C * 9/5 + 32, where F represents the temperature in Fahrenheit and C represents the temperature in Celsius.
In this case, the temperature in Celsius that you want to convert is 158 degrees. So you can substitute this value in the formula as follows:
F = 158 * 9/5 + 32
When you perform the calculation, you find that the boiling point of the phosphoric acid solution is 316.4 degrees Fahrenheit.
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Find the product of (2x + 5y)2.
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A line with a slope of 3 passes through the point (2,5) what is the equation of this line?
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The equation is a horizontal line, therefore the slope is 0.
What is the taxi distance between A(2, 5) and B(7, 9)?
Answers
t=|x2-x1|+|y2-y1|
t=5+4
t=9 units
If you mean the actual distance between the two points then:
d^2=(x2-x1)^2+(y2-y1)^2
d^2=(7-2)^2+(9-5)^2
d^2=25+16
d^2=41
d=√41 units
d≈6.4 units (to nearest tenth of a unit)
Choose the correct description of the graph of the compound inequality
2x + 5 > 9 and 5x less than or equal to 30.
A) A number line with an open circle on 2, shading to the left, and a closed circle on 6, shading to the right
B) A number line with an open circle on 2, a closed circle on 6, and shading in between
C) A number line with a closed circle on 2, shading to the left, and an open circle on 6, shading to the right
D) A number line with a closed circle on 2, an open circle on 6, and shading in between
Answers
Answer:
B) A number line with an open circle on 2, a closed circle on 6, and shading in between
Step-by-step explanation:
easy answer
ROUND 43.0810194943 TO THE NEAREST TEN-THOUSANDTH HELP!
Answers
Since the hundred thousandths is a 1 which is less than a 5, you have to round down.
The original value of the car is $18,000 and it depreciates by 50% each year what is the value of the car after three years
Answers
value = 18000*(1-0.50)^3 = 2250
value after 3 years = $2250
A=p (1-r)^t
A the value of the car after 3 years?
P current value 18000
R rate of depreciation 0.5
T time 3years
A=18,000×(1−0.5)^(3)
A=2,250
Find the measure of each exterior angle of a regular polygon with 24 sides
Answers
The formula for finding the measure of each exterior angle of a regular polygon is similar to the formula for finding the measure of each interior angle. We take the sum of the measures of the exterior angles which is always 360 degrees and we divide this by the number of sides in the polygon which is n. So the formula for finding the measure of each exterior angle of a regular polygon is simply 360 over n. In this problem since the polygon has 24 sides, we simply plug a 24 in for n and we have 360 over 15. 360 divided by 24 is 15. Therefore, the measure of each exterior angle of a regular polygon that has 24 sides is 15 degrees.
What is the length of a square
Answers
The pressure P exerted by a force varies inversely as the area A on which the force is applied. If 16 N/ft2 of pressure is exerted by a force on an area of 3 ft2 , what is the pressure exerted by the same force on an area of 6 ft2?
A) 8 N/ft2
B) 16 N/ft2
C) 4 N/ft2
D) 32 N/ft2
Answers
16 = C / 3
Solve for C
C=16×3=48
Now find P if A = 6. and C=48
P = C/6
P = 48/6
P = 8 N/ft2
Answer:
A) 8 N/ft2
Step-by-step explanation:
Pressure is the normal force per unit area, that is, it is equivalent to the force acting on the surface unit, and is given by:
[tex]P=\frac{F}{A}[/tex]
Where:
[tex]P=Pressure\\F=Normal\hspace{3}force\\A=Area\hspace{3} where \hspace{3}force\hspace{3} is \hspace{3}applied.[/tex]
In the first case:
[tex]P=16N/ft^2\\A=3ft^2[/tex]
Using the previous equation and solving for [tex]F[/tex] :
[tex]F=P*A=16*3=48N[/tex]
Now, for the second case, since the force is the same applied in the first case, then:
[tex]P=\frac{F}{A} =\frac{48}{6} =8N/ft^2[/tex]
Therefore the answer is:
A) 8 N/ft2
express 3/4, 7/16,and 5/8 with the LCD
Answers
4 = 2²
16 = 2⁴
8 = 2³
Take common and non-common factors with highest exponent.
So LCD = 16
The new dneominator of all fractions is 16. Divide this number for the original denominators and multiply for numerator...
16/4 = 4
4*3 = 12
3/4 = 12/16
16/16 = 1
1*7 = 7
7/16 = 7/16
16/8 = 2
2*5 = 10
5/8 = 10/16
5x - 10y = 15 if 3x + 7y = 31
Answers
3x + 7y = 31
x - 2y = 3....multiply by -3
3x + 7y = 31
---------------
-3x + 6y = -9 (result of multiplying by -3)
3x + 7y = 31
---------------add
13y = 22
y = 22/13
x - 2y = 3
x - 2(22/13) = 3
x - 44/13 = 3
x = 3 + 44/13
x = 39/13 + 44/13
x = 83/13
solution is (83/13, 22/13) <=
15x-30y-15x-35y=45-155
-65y=-110
y=22/13, making 3x+7y=31 become
3x+154/13=31
39x+154=403
39x=249
x=83/13
So the solution to the system of equation is the point (83/13, 22/13)
HELP!!!!
Use the following data set and a separate piece of paper to make a line plot that will help you to answer questions 2-7.
(6, 4, 4, 5, 1, 8, 10, 7, 8, 6, 6, 7, 5, 4, 6)
Add a box and whisker plot to the graph. Clearly mark the ends of box by drawing vertical lines and labeling their values on the horizontal axis. What are the ends of the box and whisker plot?
A. 1 and 6
B. 4 and 7
C. 4 and 8
D. 5 and 7
Answers
minimum = 1
Q1 = 4
Q2 (median) = 6
Q3 = 7
maximum = 10
The beginning and end of the " box " are Q1 and Q3.....4 and 7
Joseph pays $20 for his base phone in addition to the $0.10 per text. Micki pays $10 for her phone plan plus the $0.15 per text. Write a function for Joesph's phone plan and for Micki's phone plan.
Provide the number of text messages in which the plans are the same plan.
Answers
m=10+0.15t
They wil cost the same when m=j so we can say:
10+0.15t=20+0.1t, subtract 0.1t from both sides
10+0.05t=20 subtract 10 from both sides
0.05t=10 divide both sides by 0.05
t=200
So when one texts 200 times, both plans cost the same amount.
By using the equations Cj = 20 + 0.10x for Joseph's phone cost and Cm = 10 + 0.15x for Micki's phone cost, we find their costs would both be the same if 200 text messages were sent.
Explanation:The question is asking us to create an equation for both Joseph's and Micki's texting plans. In mathematical terms, the cost for each plan would be represented by the equation Cost = base rate + (cost per letter)x, where x represents the number of texts.
So for Joseph, the equation would be Cj = 20 + 0.10x and for Micki the equation would be Cm = 10 + 0.15x.
To find out when both plans cost the same, we set the two equations equal to each other and solve for x.
20 + 0.10x = 10 + 0.15x
By subtracting 0.10x from both sides and then subtracting 10 from both sides we get:
x = 200.
This means that both plans would cost the same if both parties sent 200 texts.
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The hypotenuse of a right triangle is 3 times as long as the shorter leg. find the measure of the angle between the shorter leg and the hypotenuse
Answers
shorter leg = x
hypotenuse = 3x
[tex]cos \alpha = \cfrac{x}{3x} = \cfrac{1}{3} \ \ \to \alpha \approx70.5^o[/tex]
The measure of the angle between the shorter leg and the hypotenuse, [tex]\theta[/tex] = 70.53 °
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.
Given that:
Let us consider the shorter leg be 'x'.
and, the Hypotenuse be '3x '.
Using trigonometric functions,
[tex]cos \theta= \frac{Base}{Hypotenuse}[/tex]
cos [tex]\theta[/tex] = x /3x
cos [tex]\theta[/tex] = 1/3
[tex]\theta[/tex] = [tex]cos^{-1}[/tex] (1/3)
[tex]\theta[/tex] = 70.53 °
Hence, the measure of the angle between the shorter leg and the hypotenuse 70.53 °
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write the ordered pair that represents yz. then find the magnitude of yz. Y(-5,7), Z(-1,2)
Answers
yz = z - y = (-1 , 2) - (-5,7) = (4 , -5)
The magnitude of yz can be calculated as follows:
magnitude yz = sqrt [(4)^2 + (-5)^2]
= sqrt (41)
= 6.403
Answer: the answer is D on edge
Step-by-step explanation:
Draw a model to represent the problem 6/12 divided by 1/4
Answers
The expression 6/12 divided by 1/4 is 2 and the model is attached
Drawing a model to represent the problem
From the question, we have the following parameters that can be used in our computation:
6/12 divided by 1/4
This can be expressed as
6/12 multiplied by 4
So, we have
0.5 multiplied by 4
When the product is evaluated, we have
2
Hence. 6/12 divided by 1/4 is 2 and the model is attached
Gabriella said a triangle with an angle of 98 degrees was an obtuse angle. Cynthia said a triangle with an angle of 98 degrees was an acute triangle. Who is right and why?
Answers
so if we see gabby's statement, ,98>90 so tecnically, she is correct
cynthya's statement is false because 98>90 so it is an obtuse angle
There are 50 jelly beans. if 7 of them are red, and 23 are black, what percentage of the jelly beans are not reed
Answers
([solve by writing an equation])
A pair of jeans costs 75% as much as a pair of corduroy pants. what is the cost of each if the total cost for the jeans and cords is $42?
I know the answer is Jeans: $18 and Cords: $24 but how do I write that in an equation to solve??
thank you!!!
Answers
"A pair of jeans costs 75% as much as a pair of corduroy pants."
this means [tex] x=\frac{75}{100}*y [/tex], simplifying by 25:
[tex]x= \frac{3}{4} y[/tex] (equation 1)
"the total cost for the jeans and cords is $42?"
x+y=42 (equation 2)
substitute x form equation 1, in equation 2
x+y=42
[tex] \frac{3}{4} y+y=42[/tex]
[tex] \frac{3}{4} y+ \frac{4}{4} y=42[/tex]
[tex]7y=4*42 [/tex]
y=4*6=24
substitute y=24 in either of equations 1 or 2:
x+y=42 (equation 2)
x+24=42
x=42-24=18
Answer: Jeans cost 18$, Cords cost 24$
The janitor found that it was leaking at a rate of 13 fl oz per minute How fast was the pipe leaking in gallons per hour?
Answers
16cup=1gal
so
16*8=128oz per gallon
13oz/min
alrighty
13oz=13/128gal
1min=1/60hr
(13/128gal)/(1/60hr)=(13/128gal)(60hr/1)=78hr/128gal
128gal/78hr=64gal/39hr≈6.09375
about 6 gallons per hour
Determine the number of possible triangles, abc, that can be formed given c = 85°, a = 10, and c = 13.
Answers
a/sin A=c/sin C=d/sin D
thus the value of angle A will be:
10/sin A=13/sin 85
10/sin A=13.05
sin A=10/13.05
sin A=0.7663
A=arcsin 0.7663
A=50
thus the n=value of angle B will be:
B=180-(85+50)
=45
The triangle formed will be an acute triangle
what is f^-1(1)? inverse function
Answers
f⁻¹(x) = x = y
If x = 1 → f(1) = y =1
if x = 1 → f⁻¹(1) = x = 1
PLZ I NEED HELP ASAP
Annie has a compost pile that produces 12 pounds of compost a day from yard waste. Which function expresses the amount of compost (c) as a function of the number of days (d)? The function representing the relationship between the amount of compost and the number of days is__, with the input as__.
Answers
Answer: number of days: c=f(d) =12d
Imput:12
Step-by-step explanation:
Use 1% or 10% to estimate 8% of 310
Answers
10% of 310 = 310÷10 = 31
1% of 310 = 310÷100 = 3.1
2% of 310 = 2×3.1 = 6.2
8% of 310 = 31 - 6.2 = 24.8
Two cards are drawn at random from a standard deck of cards without replacement. What is the probability that both cards will be from the clubs suit?
Answers
Answer:
The answer is 1/17.
Step-by-step explanation:
You will draw one club which will be 13/52. You will NOT replace it so you will draw a second card 12/51.
You will need to multiply them to find the probability.
First simplify your two fractions.
13/52 = 1/4 AND 12/51= 4/17
Multiply the two together and you will get 4/68 = 1/17
Hope this helps :)
Which property is demonstrated by this equation? 3 + 2x = 2x + 3
Answers
answer Commutative Property
The commutative property is demonstrated in your equation.
An example of this property could be: a+b = b+a or 23+15 = 15+23.
It is the result of changing the order of the operands without changing the result. (whether sum, difference, product, or quotient)
Hope this helps! (Don't forget Brainliest!) :)
Can someone help me plz!!!
Answers
. If ON = 4x – 6, LM = 3x + 5, NM = x – 4, and OL = 4y – 3, find the values of x and y for which LMNO must be a parallelogram.
Answers
This means that
LM = ON
NM = OL
Using the equations, find x and y:
4x - 6 = 3x + 5
4x = 3x + 11
1x = 11
x = 11
x - 4 = 4y - 3
x - 1 = 4y
-1 = 3y
-1/3 = y
The values are:
x = 11
y = -1/3
Help me with this please!!!
Answers
do a ratio
11/2=X/24
24*11 = 264
264/2 = 132
X= 132
so 132 students