Answers
The nth terms of the arithmetic sequences;
I. Tn = 3 + √2 + ( n - 1) √2
ii. Tn = 2/ √3 + ( n - 1) 1/ √3
How to determine the nth termThe formula for the nth term of an arithmetic sequence is expressed as;
Tn = a + ( n - 1)d
Where;
Tn is the nth terma is the first term n is the number of termsd is the common differencei. a = 3 + √2
d = √2
Substitute the values, we have;
Tn = 3 + √2 + ( n - 1) √2
ii. a = 2/ √3
d = 1/ √3
Substitute the value, we have;
Tn = 2/ √3 + ( n - 1) 1/ √3
Thus, the nth terms of the arithmetic sequences are Tn = 3 + √2 + ( n - 1) √2 and Tn = 2/ √3 + ( n - 1) 1/ √3 respectively
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Related Questions
what is an equivalent fraction for 6/10
Answers
Answer:
3/5, 9/15 - some equivalent fractions for 6/10
A tower has a revolving restaurant 785 feet above the ground. The restaurant makes a
complete revolution every 90 minutes. While a visitor was at the tower, the restaurant
rotated through 82°. How long was the visitor at the tower?
The visitor was at the tower for ______
minutes.
Answers
Answer:
1 revolution is 360 degrees
1 hour = 60 minutes
360/60 = 6
so it rotates 6 degrees every minute
135/6 = 22.5 minutes
What are the coordinates for the image of the figure E(0,4), F(2,2), G(0,0), D(-4,3) if it has been dilated with a scale factor of 1/4
Answers
Answers:
E ' = (0, 1)
F ' = (0.5, 0.5)
G ' = (0, 0)
D ' = (-1, 0.75)
Notes: 0.5 = 1/2 and 0.75 = 3/4
================================================
Explanation:
Assuming the origin is the center of dilation, then we multiply each coordinate by the scale factor of 1/4 = 0.25
For instance, the point E(0,4) moves to E ' (0, 1) since
x coordinate: 0*0.25 = 0y coordinate: 4*0.25 = 1Do the same for the other points.
i need help with this
Answers
Answer:
x=82
Step-by-step explanation:
Because of Supplementary angles we know that x+10 degrees and x+6 degrees is 180 degrees. We combine this to form 16+2x=180
subtract 16 from both sides. 2x=164
divide both sides by 2
x=82
Yossi used to have a square garage with 250 ft 2 of floor space. He recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side?
Answers
Answer:
5√10 ≈ 15.81 ft5√15 ≈ 19.36 ft22.47%Step-by-step explanation:
You want to know the length of the sides of a 250 ft² square, and one with an area 50% larger. You also want to know the percentage change in side length.
Side lengthThe area of a square is given by the formula ...
A = s²
Solving for the side length (s), we find ...
s = √A
The side length of a square with 250 ft² area is ...
s = √250 ft = 5√10 ft ≈ 15.81 ft . . . side length
The area of a square that has 50% more area is ...
(250 ft²) × (1 +50%) = 375 ft²
The side length of that square is ...
√375 ft = 5√15 ft ≈ 19.36 ft . . . side length
Percentage changeThe percentage change can be found from ...
percentage change = ((new value)/(old value) -1) × 100%
= ((5√15)/(5√10) -1) × 100% = (√1.5 -1) × 100% ≈ 22.47%
The percentage increase in the length of one side is about 22.47%.
In an orchard, there are 15 apple trees, 23 orange trees, and a cherry tree. What is the ratio of apple trees to orange trees?
Answers
(55 times 2) divided by 5+ 13-7= PEMDAS
55*2=110
110 divided by 5= 22
22+13=35
35-7=28
Answers
Answer:
18.33
Step-by-step explanation:
multiply 55×2 you get 110
then since it is +13-7 + is bigger than - ( positive is greater than negative)
it will be 6
so 110 ÷6 = 18.3333333 you put it into 4digits
The answer is 18.33
Hope it will help
You are buying a house and will borrow $330,000 on a 25-year fixed rate mortgage with monthly payments to finance the purchase. Your loan officer has offered you a mortgage with an APR of 4.15 percent. Alternatively, she tells you that you can “buy down” the interest rate to 3.8 percent if you pay points up front on the loan. A point on a loan is 1 percent (one percentage point) of the loan value. How many points, at most, would you be willing to pay to buy down the interest rate? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)
Answers
The number of points the borrower needs to buy down interest rate to 3.8% is 0.350 points
What is the desired annual percentage rate for the borrower?
The desired annual percentage rate(APR) for the borrower is 3.8% whereas the the loan officer offer is 4.15%, which means that the borrower needs to buy the interest rate from 4.15% to 3.8%
difference in interest rate=4.15%-3.8%
difference in interest rate=0.35%
We need to translate the reduction in interest rate of 0.35% to points , bearing in mind that the 1% is the same as 1 point
number of points required to buy down interest=1 point*0.35%
number of points required to buy down interest=0.350
In essence, the home loan borrower needs to buy down interest by 0.350 points in order to achieve the desired loan APR of 3.8%
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A triangle has a perimeter of 13. If it has
sides of x/2,( x – 5), and (x - 2) lengths,
then:
a) find the value of x
b)find the length of the longest side
find the value of x.
find length of the longest side.
Answers
Step-by-step explanation:
perimeter=s+s+s
p=x/2+x-5+x-2
13=x/2+x-5+x-2
26=x+x+x-10-4
26=3x-14
26+14=3x
3x/3=40/3
x=13.3cm
b.
x/2=6.65
x-5=8.3
x-2=11.3
longest side=11.3cm
Please help me! I have a fe of this for me to finish my homework! Please
Answers
Please Help Me ;-;
[tex]||3x-1|+5|\ \textless \ 1[/tex]
Answers
The value of x based on the equation illustrated as 3x - 1 + 5 < 1 is x < 1.
How to illustrate the information?It should be noted that an equation is simply used to show the relationship between the expression or variables.
From the information, 3x - 1 + 5 < 1.
Collect like terms
3x - 1 + 5 < 1.
3x < 1 + 1 - 5
3x < -3
Divide
3x / 3 < -3 / 3
x < 1
Therefore, the value of x based on the equation illustrated as 3x - 1 + 5 < 1 is x < 1.
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Factorize this does it have Any breaking form??
4a^2+4a-5
Answers
Answer:
[tex](2a + 1+\sqrt{6})(2a + 1-\sqrt{6})[/tex]==========================
Identities we will use:
[tex]a^2+2ab+b^2=(a+b)^2[/tex][tex]a^2-b^2=(a+b)(a-b)[/tex]===========================
Given expression:
[tex]4a^2+4a-5[/tex]Factorize it by completing the square and setting the difference of squares:
[tex]4a^2+4a + 1-6=[/tex][tex](2a)^2+2*1*2a + 1^2-6=[/tex][tex](2a+1)^2-6=[/tex][tex](2a + 1+\sqrt{6})(2a + 1-\sqrt{6})[/tex]Please help it’s due tomorrow
Answers
Answer:
Step-by-step explanation:
Can you please help me
Answers
Answer:1=a
2=b
3=c
Step-by-step explanation:
One bar of candy A and two bars of candy B have 770 calories. Two bars of candy A and one bar of candy B contain
784 calories. Find the caloric content of each candy bar.
Candy bar A has :
Candy bar B has:
Answers
Candy bar B has 255 calories
Work to show:
A+2B=777
2A + B =789
rearrange the first equation to solve for A:
A=777-2B
plug 777-2B in for A in the second equation, and solve for B:
2(777-2B)+B=789
1554-4B+B=789
1554-789=3B
765=3B
B=255
substitute 255 in for B in the first rearranged equation, and solve for A:
A=777-2(255)
A=777-510
A=267
So candy bar A has 267 calories, and candy bar B has 255.
Four fifths is equal to ten sixteenths of a number.
Answers
The Four-fifths is equal to ten-sixteenths of a number is x=32/25.
Given the statement is four-fifths is equal to ten-sixteenths of a number.
A mathematical statement is a meaningful component of words that can be true or false. Simply, they are known as a statement.
Let us assume the given number be x.
According to the given statement,
Four fifths means 4/5. ......(1)
And ten sixteenths means 10/16.
It is also given that ten sixteenths of a number means is (10/16)x. .......(2)
Now, we will equate equation (1) and equation (2) according to the given statement is
4/5=(10/16)x
Further, we will cross multiply both sides, we get
4×16=10x×5
64=50x
Now, we will divide both sides by 50, we get
64/50=50x/50
64/50=x
32/25=x
Hence, the number for the given statement "Four fifths is equal to ten sixteenths of a number" is 32/25.
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one mousetrap car contestant researched the speed of actual race cars. he found that when nascar drivers race on the phoenix international raceway they make 312 laps. in april 2009 the race that was held there lasted for about 3 hours. what was the approximate rate the racers were traveling one mouse trap car contestant research the speed of actual race cars he found that one NASCAR drivers race on the Phoenix International Raceway they make 312 laps in April 2009 the race that was held there lasted for about 3 hours what was the approximate right the races were traveling
Answers
Answer:
104 mph
Step-by-step explanation:
The Phoenix International Raceway is 1 Mile so they did 312 miles in 3 hours.
Rate = Distance/Time
R = 312/3 = 104/1
The racers were traveling at 104 miles per hour.
I=Prt. You borrow $10,000 from the bank at a 8% rate for 5 years. Find
the simple interest you will pay on this loan.
Answers
Answer:14 000
Step-by-step explanation:
Simple interest formula: A=P(1+in)
A= amount after interest is added
P= initial amount (10000)
i= interest rate (8%)
n= number of periods (5 years)
Now substitute what you have into the simple interest formula:
A=P(1+in)
A=10000(1+(8/100)(5))
A= 14 000
The reason why 8 is divided by 100 is that 8 is a percentage. Unless you have a percentage function on your calculator, I'd strongly encourage you to ALWAYS divide your percentages by 100.
Evalute f(x) = x² + 1 for f(10)
Answers
Answer:
101
Step-by-step explanation:
Because if f(x) = [tex]x^{2}[/tex] + 1 and f(x) is f(10), this means that x = 10. If x = 10, then you can plug that into the equation, getting you [tex]10^{2}[/tex] + 1. [tex]10^{2}[/tex] is 100, plus 1 is 101.
Hope this helps!
What is the equation of a line that is perpendicular to the line x − 2y = 4? A. y = 1/2x − 4 B. y = −1/2x + 6 C. y = 2x − 3 D. y = −2x + 8
Answers
Answer:
The answer is D. y=-2x+8
Step-by-step explanation:
Hope this helps!!
PLS HELP RUNNING OUT OF TIME
The x-intercept of a line is -5 and the y-intercept of the line is -2. What is the equation of the line?
A. y = - 5/2x -5
B. y = 2/5x + 2
C. y = 5/2x - 2
D. y = -2/5x - 2
Answers
The equation of the line is y = - (2 / 5) · x - 2. (Correct choice: D)
How to derive the equation of a line based on information about two intercepts
Lines are represented by first grade polynomials of the form y = m · x + b, where m and b are the slope and the y-intercept of the line, and x and y are the independent and dependent variables, respectively.
We can find the values of the slope and the y-intercept by knowing the location of two distinct points on Cartesian plane. If we know that (x₁, y₁) = (- 5, 0) and (x₂, y₂) = (0, - 2), then the equation of the line is:
- 5 · m + b = 0 (1)
b = - 2 (2)
The solution to the system of linear equations is (m, b) = (- 2 / 5, - 2). Lastly, the equation of the line is y = - (2 / 5) · x - 2. (Correct choice: D)
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Five pulse rates are randomly selected from a set of measurements. The five pulse rates have a mean of 74.6 beats per minute. Four of the pulse rates are
81, 54, 77, and 68.
a. Find the missing value.
b. Suppose that you need to create a list of n values that have a specific known mean. Some of the n values can be freely selected. How many of the n
values can be freely assigned before the remaining values are determined? (The result is referred to as the number of degrees of freedom.)
Answers
Part (a)
x = the missing value
The set is {81, 54, 77, 68, x}
Add up those values and divide by 5 to compute the mean. Set this equal to the 74.6 stated. Then solve for x like so:
(81+54+77+68+x)/5 = 74.6
(280+x)/5 = 74.6
280+x = 5*74.6
280+x = 373
x = 373-280
x = 93
Answer: The missing value is 93========================================================
Part (b)
In the previous part, we have n = 5 values and n-1 = 5-1 = 4 of them can be freely selected. The 5th final value is locked in based on what those previous four values are. That 5th value being x mentioned earlier.
This shows that the degrees of freedom is n-1
In other words, one value is determined by the other values in the set.
Answer: n-1Factor 2x² + 8x - 90 completely.
O a
Ob
OC
Od
(2x +9)(x - 5)
(2x-9)(x - 5)
2(x + 9)(x - 5)
2(x-9)(x - 5)
A
Please helppp
Answers
Factors of the polynomial 2x² + 8x - 90 is Option (c) 2(x + 9)(x - 5).
What is Factorization?Factorization is the method used to discover the factors of a given value or mathematical statement. A factor is an integer that is multiplied by another to create the original number. For instance, 2, 3, 6, 9, and 18 are the factors of 18. Likewise, in the case of polynomials, the factors are the polynomials that are multiplied to create the initial polynomial.
Given Equation: 2x² + 8x - 90
Step 1: Pull out like factors from the equation
⇒ 2x² + 8x - 90 = 2 • (x² + 4x - 45)
Step 2: Factorize by splitting the middle term of the equation (x² - 4x - 45)
⇒ x²+ 9x - 5x - 45
Step 3: Take Common factors from the two pairs of the equation
⇒ x(x + 9) - 5(x + 9)
Step 4: Rewrite the polynomial in factored form
⇒ 2(x + 9)(x - 5)
Therefore the factorization result is 2(x + 9)(x - 5).
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The equation that converts Celsius to Fahrenheit is C = 5/9 (F-32)
. Use it to calculate the temperature in Celsius when it is 60 degrees Fahrenheit. (Round to the nearest tenth)
Answers
Answer:
C=0
Step-by-step explanation:
C = 5/9 (60-32)
C= 5/9 (28)
C=15.55555556 (round to the nearest tenth)
C=15.6 - ANSWER
help pleaseeeeeeeeeeee
Answers
The value of h(-2) is 65
What is a function?A function can be defined as an expression, law , rule of hypothesis that explains or compares the relationship between two variables - the dependent and the independent variable.
Given the function;
h(x) = 2x^4 - x³ + 2x² - 7x + 3
To determine the function, h(-2)
We substitute the value of x as -2 into the function, we have;
h(-2) = 2(-2)^4 - (-2)^3 + 2(-2)^2 - 7(-2) + 3
expand the bracket
h(-2) = 2(16) - 2(-8) - 7(-2) + 3
h(-2) = 32 + 16 + 14 + 3
h(-2)= 65
Thus, the value of h(-2) is 65
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Last month, Alma was able to volunteer in a community pet shelter for 2,760 minutes. How many hours did she volunteer?
Answers
The number of hours Alma volunteered is 46 hours.
What is time conversion?
The process of time conversion changing or converting the unit of time from one unit to another.
For example, it can be converting seconds to minutes, converting minutes to hour or converting hours to minutes or hours to seconds.
Basically, time can be converted from one unit to another.
The number of hours Alma volunteered is calculated as follows;
60 minutes = 1 hour
2,760 minutes = ?
= (2760 x 1) / 60
= 46 hours
Thus, the number of hours Alma volunteered is 46 hours.
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Answer:
Step-by-step explanation:
46
Jasmine received a $140 paycheck from her job at the supermarket today. If she spends $10 every day at Starbucks, in how many days will she have exactly $30 left? Represent and solve this problem by creating a table graph and equation.
Answers
Type an equation for the following pattern.
Answers
Which of the following is an equivalent expression of 14x2 +18x + 5? (NEED THIS REALLY FAST)
A: 32x3 + 5
B: 14x2(18x + 5)
C: 5(14x2 + 18x)
D: 18x + 14x2 + 5
Answers
The equivalent expression of 14x2 +18x + 5 is 18x + 14x2 + 5, the correct option is D.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We are given that;
The function 14x2 +18x + 5
Now,
18x + 14x^2 + 5
This expression is equivalent to 14x^2 + 18x + 5, because it has the same terms but in a different order. You can use the commutative property of addition to rearrange the terms in any order without changing the value of the expression. For example:
14x^2 + 18x + 5 = (14x^2 + 5) + (18x)
14x^2 + 18x + 5 = (18x) + (14x^2 + 5)
14x^2 + 18x + 5 = (18x) + (5) + (14x^2)
14x^2 + 18x + 5 = (5) + (18x) + (14x^2)
All of these expressions are equivalent to each other and to the original expression.
Therefore, the equation will be 18x + 14x^2 + 5.
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13. Consider the two repeating decimals shown
below.
0.31313131...
0.02020202...
a. By simply looking at the decimal
representations, what is the sum of these
two rational numbers? Write as a decimal
and as a fraction.
b.
Verify your answer by finding fractions that
represent each decimal. Add the fractions.
c. Write the difference of the two numbers as a
repeating decimal.
Answers
1) The decimal 0.31313131...as a fraction is; 310/990
2) The decimal 0.02020202 as a fraction is; 200/9990
3) The difference of the two numbers as a repeating decimal is; 0.29292929
How to change decimal to fractions?We are given the decimals as;
0.31313131...
0.02020202...
1) The decimal 0.31313131... is repeating decimal.
If we write it as;
x = 0.31313131...
Multiply both sides by 10 to get;
10x = 3.131313 --- (1)
Multiply both sides of initial equation by 1000 to get;
1000x = 313.131313 ----(2)
Subtract eq 1 from eq 2 to get;
990x = 310
x = 310/990
2) The decimal 0.02020202 is a repeating decimal.
If we write it as;
x = 0.02020202...
Multiply both sides by 100 to get;
10x = 2.020202 --- (1)
Multiply both sides of initial equation by 10000 to get;
10000x = 202.0202 02 ----(2)
Subtract eq 1 from eq 2 to get;
9990x = 200
x = 200/9990
3) The difference of the two numbers as a repeating decimal is;
0.31313131 - 0.02020202 = 0.29292929
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