5. An arithmetic sequence is defined by:
a₁ = -8
an = an-1+4
What is the 7th term of the sequence?
Answer: 16
Step-by-step explanation:
an = an-1+4 ==> change in every term is +4
1=1st term
7=7th term
-8+4*(7-1)=
-8+4*6=
-8+24=16
Write an equation of the line using variable x and y that passes through the given points (1,-4) and (2,-1) .
Answer:
y=3x-7
Step-by-step explanation:
Equation of a Line: y=mx + b
Slope: 3/1 or 3
Y-int: -7
The equation of a line is a form of representing the set of points, which form a line in a coordinate system.
The equation of a line that passes through the point (1, -4) and (2, -1) is
y = 3x - 7
What is equation of a line?The equation of a line is a form of representing the set of points, which form a line in a coordinate system.
The general equation of a straight line is given as:
y = mx + c,
where m = slope of the line and c = y-intercept.
We have,
Two points:
(1, -4) = (a, b) and (2, -1) = (c, d)
The equation of a line can be written in the form:
y = mx + c
Slope:
m = (d - b) / (c - a) = -1 + 4 / 2 - 1 = 3 / 1 = 3
y-intercept:
Take a point (1, -4).
-4 = 3x1 + c
-4 - 3 = c
c = -7
Now,
The equation of a line is y = 3x - 7
Thus the equation of a line that passes through the point (1, -4) and (2, -1) is
y = 3x - 7
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Write an equation of each line.slope = -3/5 , through (-4,0)
The equation of the line in point-slope form, with slope equal to -3/5 and passing through the point located at (-4 , 0), is (y - 0) = -3/5(x + 4).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the point slope form, plug in the values to set up the equation.
(y - y1) = m(x - x1)
where m = -3/5 and (x1 , y1) = (-4 , 0)
(y - 0) = -3/5(x - -4)
(y - 0) = -3/5(x + 4)
In slope-intercept form, the equation of the line is:
(y - 0) = -3/5(x + 4)
y = -3/5 x - 12/5
In standard form, the equation of the line is:
y = -3/5 x - 12/5
3/5 x + y = -12/5
Multiplying both sides by 5,
3x + 5y = -12
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HEEEEEELLLLPPPPPPP PLSSSSSSSSSSSSSS
The answer is 2 and 7/20 or the 3rd answer.
Source: Calculator soup.
Mark me Brainliest. :)
In an arithmetic sequence with a₁ =2 and d=-2 , which term is -82 ?
44th term of the sequence is -82.
What is sequence?In an arithmetic sequence with a₁ =2 and d=-2
-82 = 2 + (n-1)2
n-1 = -43
n = 44
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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Find the sum of each series. Σ⁶n=2 (-2) ⁿ⁻¹
The given series is a geometric series and its sum is -22
The summation or sigma notation is used to express long summation into a single formula.
The series, given in a summation notation, is:
[tex]\sum\limits^6_{n=2} {(-2)^{n-1}}[/tex]
The formula inside the sum notation represent the nth term, a(n).
Let evaluate the terms for some n
a(2) = (-2)²⁻¹ = (-2)¹ = -2
a(3) = (-2)³⁻¹ = (-2)² = 4
a(4) = (-2)⁴⁻¹ = (-2)³ = -8
This form a new geometric series, with the first term, let say f(1) = -2 and common ratio = -2.
The number of terms in this new geometric series is 5.
Use the sum formula for a geometric series,
S(n) = a(1) . (rⁿ - 1)/(r - 1)
Substitute n = 5, a(1) = -2, and r = -2 into the formula:
S(5) = -2 . ((-2)⁵ - 1) / ((-2) - 1)
S(5) = -2 . (-33) / (-3) = -22
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Find the value of x .
18=3 x √3
Answer:
Step-by-step explanation:
ask siri
A small can of paint was 1/2 of a liter. That was enough to fill 1/3 of a paint sprayer .How many cans of paint would it take to completely fill the sprayer
Answer:
1 1/2 small cans of paint
Step-by-step explanation:
1/2 = 1/3 of the sprayer, so I had to multiply 1/2 x 3, which is 1 1/2.
Add -7/8+(-2 1/6) enter your answer as a simplified fraction by filling the boxes
Answer:
-3 1/24
Step-by-step explanation:
-7/8+(-2 1/6)
=-7/8-2 1/6
=-(7/8+2 1/6)
=-(21/24+2 4/24)
=-2 25/24
=-3 1/24
Does (10, 9) make the inequality 10x + 13y > 10 true?
yes
no.
Answer:
Yes (10,9) does make the inequality 10x + 13y > 10 true
Step-by-step explanation:
Substitute (10,9) in place of x and y 10(10) + 13(9) > 10Multiply the variables 10•10=100 and 13•9=117 100 + 117 > 10Add like terms 100 + 117= 217 Compare the answer to see if your variable is true since 217 > 10 a true statement then that means yes coordinates (10,9) make the inequality 10x + 13y > 10 trueThere are 72 cars in the parking lot.If 54 leave the parking,what percentage of cars are left
Answer:
total cars= 72 cars
cars that left=54 cars
percentage of cars left=
[tex] \frac{54}{72 } \times 100 =0.75 \times 100 = 75\%[/tex]
so the answer is 75%
How many match sticks will there be in
the 6th picture?
1st
2nd
3rd
Step-by-step explanation:
1st=1 matchstick
2nd=4 matchsticks
3rd=7 matchsticks
1+4+7=12 matchsticks
Find the missing term(s) of each arithmetic sequence. 104, □, 99, ...... .
Answer:
a₂ = 101.5
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₁ = 104 and a₃ = 99 , then
104 + 2d = 99 ( subtract 104 from both sides )
2d = - 5 ( divide both sides by 2 )
d = - 2.5
then
a₂ = 104 - 2.5 = 101.5
Could anybody explain to me what both the question is asking in a simple way. For a dummy.
Research and write about the history of pi and its importance to the study of geometry.
pi or π is a Greek word and its value is approximately 3.14 and it is an irrational number.
It is given that the letter is pi or π.
We have to write the history of pi and its importance to the study of geometry.
What is pi or π ?
pi or π is the ratio of the circumference of any circle to the diameter of that circle.
We know that ;
pi or π is a Greek letter. In decimal form, the value of pi is approximately 3.14 and it is an irrational number.
According to Petr Beckmann's A History of Pi, William Jones first used this Greek letter for some purpose in 1706. Around 30 years later, it became a standard symbol for mathematical notation.
Also ; it has been known for at least 4,000 years what Pi means. According to the history of Pi , who claims that by 2000 B.C , "the Babylonians and the Egyptians were aware about the existence and significance of this constant,"
Also ; every circle has the same ratio of circumference to diameter. Both the Babylonians and the Egyptians approximated the value of pi numerically, and later mathematicians in ancient Greece, especially Archimedes, improved these approximations.
Pi is a fundamental concept that appears in all branches of mathematics. It is a crucial concept that facilitates understanding of both universal truths and some mathematical concepts.
Thus , pi or π is a Greek word and its value is approximately 3.14 and it is an irrational number.
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is 4.3239673… rational or irrational?
Answer: How do you know if its rational or irrational?
What are rational and irrational numbers? Rational numbers are the numbers that can be expressed in the form of a ratio (i.e., P/Q and Q≠0) and irrational numbers cannot be expressed as a fraction. But both the numbers are real numbers and can be represented in a number line.
Step-by-step explanation: hope this helps!!!
Find (-5.3x10<3) - (-8x10<2
-scientific notatiens
Answer:
-4500
Step-by-step explanation:
-5300 - (-800)
Step-by-step explanation:
{36+7[10÷)+9(2)]}÷4. ....
3k+10=2k-21 (2-step equation)
Find the ninth and tenth terms of each arithmetic sequence. 4,10,16,22, . . . .
The values of a9 and a10 are 52 and 58 respectively.
What is an arithmetic sequence?An ordered group of integers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.
For the arithmetic sequence,
4,10,16,22, . . . .
a = 4
d = 6
an = a + (n - 1)d
a9 = 4 + (8)6
a9 = 4 + 48
a9 = 52
a10 = a + 9d
a10 = 4 + 9(6)
a10 = 4 + 54
a10 = 58
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Hey Siri Rhea couple by basic car cost in $26, 500,000 with options costing 725,000
Ray's total cost was $28, 908.50
Ray Cupple bought a basic car costing at $26,500.00,
The options costing is $725.00.
The sales tax in the state is 6%
The combined cost for license and registration fee is $50.00
Cost price of car = $26,500 and the Cost of options= $725
Therefore, the total taxable cost=$26,500+ $725=$27225
Tax amount = 6% of Total taxable cost
=0.06 x $27225 = $1,633.5
Total cost = $27225 + $1,633.5 + $50
Total cost = $28,908.50
Therefore Ray's total cost was $28, 908.50
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Disclaimer : Your question was incomplete, the above mentioned answer is solved as per the following question "Ray Cupple bought a basic car costing $26,500.00, with options costing $725.00. There is a 6% sales tax in his state and a combined $50.00 license and registration fee. What was Ray's total cost?"
I can evaluate an algebraic expression for given values using the order of operations.
2. Evaluate x^2 + yz for x = 7, y = 5, and z = 3.
The value of the expression for x² + yz when x = 7, y = 5, and z = 3 is 64.
How to calculate the expression?It should be noted that from the information, we are to evaluate x² + yz for x = 7, y = 5, and z = 3.
This will be illustrated as:
= x² + yz
= 7² + (5 × 3)
= 49 + 15
= 64
Therefore, the value of the expression for x² + yz when x = 7, y = 5, and z = 3 is 64.
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A bouquet contains 12 roses and 10 yellow flowers. 9 of the roses are yellow. How many flowers are in the bouquet?
Answer:
31 flowers in the bouquet
What is the solution for x in the equation?
12-
1x + ² = x - 4
OA. = 3
x
OB. = -3
x
O C.
= //
OD. x = -
Suppose we have to solve this equation ,
3x - 4 = 7x + 8
would be to first subtract 3x from both sides obtaining
-4 = 4x + 8,
then subtract 8 from both sides and get
-12 = 4x.
Now divide both sides by 4 obtaining
- 3 = x or x = - 3.
If we have to find the area of trapezoid,
A trapezoid has two parallel sides and two nonparallel sides. The parallel sides are called bases.Removing parentheses does not mean to merely erase them. We must multiply each term inside the parentheses by the factor preceding the parentheses.Changing the form of an answer is not necessary, but you should be able to recognize when you have a correct answer even though the form is not the same.An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
There are three major forms of linear equations:
point-slope form, standard form, and slope-intercept form.
There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other.
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On January 1, North Country Hotel and Resort hired an independent contractor to develop scheduling software. This is a year contract for $120,000/annual. The contractor is paid bi-weekly on Fridays. The first pay period is for the week January 1-5 and January 8-12. Payday is January 19. Independent contractors are not employees, so the accounts payable department would normally issue the checks and generate a 1099 at the end of the year. Calculate the first paycheck payment to the independent contractor and record the journal entry. For our example, you can use Salaries and Wages Expense and Cash accounts.
The first paycheck payment to the independent contractor is $4,615.38
Dr. salaries and wages expense $4,615.38
Cr. salaries and wages payable $4,615.38
What is the amount of first bi-weekly pay to the contractors?
On the basis that there are 52 weeks in a year, hence, there would be 26 bi-weeks in a year, in order to determine the amount of first paycheck payment to the independent contractor, we simply divide the annual cost of contract by 26 bi-weeks in a year.
first paycheck payment =annual contract fees/26 bi-weeks
first paycheck payment =$120,000/26
first paycheck payment =$4,615.38
The paycheck refers to first 2 weeks which ends on on 12th January, whereas the actual payment would occur a week later on 19th of January, as a result, the amount is owed until 19th January, which means that salaries and wages expense would be debited and salaries and wages payable would be credited until actual payment is made on the 19th of January.
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Three competing subcontractors are reporting their average work output to a large project leader for a new housing development.
Rosk Construction provided an equation, where w represents the number of full weeks of work and a represents the estimated area of vinyl siding that can be installed in 100 ft2 units.
Equation from Rosk Construction: a = 62w
Fosbert’s Contracting provided a table indicating similar data from two jobs that had recently been completed by its crew.
Durable B Construction provided a graph showing the results of three of its recently completed jobs.
The unit rate for Rosk Construction is
The unit rate for Fosbert's Contracting is
The unit rate for Durable B Construction is
Using proportional relationships, the unit rates are given as follows:
Rosk: 62.Fosbert's: 65.Durable B: 63.What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality, also called the unit rate k, as follows:
y = kx
For this problem, the functions are given as follows:
Rask: a = 62w. (from the text).Fosbert's: a = 65w. (from the missing information section).Durable B: a = 63w. (from the missing information section).The unit rates are the constants of proportionality, respectively, given by:
k = 62, k = 65 and k = 63.
What is the missing information?The functions for Fosbert's Contracting and Durable B Construction are missing, and are given as follows:
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La razón de niños a niñas en un baile de invierno es de 5 a 6. Si hay 90 niñas, ¿cuántos niños hay en el baile?
If f(x) = 6x â€" 1 and g (x) = startfraction x 1 over 6 endfraction, which expressions can be used to verify g(x) is the inverse of f(x)? check all that apply. 6(6x â€" 1) â€" 1 startfraction (6 x minus 1) 1 over 6 endfraction 6 (startfraction x 1 over 6 endfraction) minus 1 startstartfraction (startfraction x 1 over 6 endfraction) 1 overover 6 endendfraction startfraction x 1 over 6 endfraction 6 x minus 1
The expression used to verify whether g(x) is the inverse of f(x) is 6( [tex]\frac{x+1}{6}[/tex])-1 and [tex]\frac{(6x-1)+1}{6}[/tex]
Given that f(x) = 6x-1
and g(x) = [tex]\frac{x+1}{6}[/tex]
If inverse [tex]f^{-1}[/tex] exists for a function f(x), then [tex]f(f^{-1}(x)) = f^{-1}(f(x)) = x[/tex]
So to check if g(x) is the inverse of f(x) we find f(g(x)) and g(f(x))
f(g(x)) = f( [tex]\frac{x+1}{6}[/tex]) = 6( [tex]\frac{x+1}{6}[/tex])-1 = x
and g(f(x)) = g(6x-1) = [tex]\frac{(6x-1)+1}{6}[/tex] = x
So g(x) is the inverse of f(x) and the expressions used to verify this are:
6( [tex]\frac{x+1}{6}[/tex])-1 and [tex]\frac{(6x-1)+1}{6}[/tex]
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determine whether each comparison is true or false
Only 1 > 3 / π and 6 / √34 > 0.6 are true comparisons with irrational numbers.
How to compare irrational numbers
Herein we find four cases of irrational numbers, whose quantities has to be compared with other numbers, by using algebra properties for inequalities:
Case 1
√75 > 9
√75 > √9²
√75 > √81 (FALSE)
Case 2
1 > 3 / π
π > 3 (TRUE)
Case 3
√8 > 10 /3
3√8 > 10
3√8 > √10²
√9 · √8 > √100
√72 > √100 (FALSE)
Case 4
6 / √34 > 6 / 10
10√34 > 36
√10² · √34 > √36²
√100 · √34 > √1296
√3400 > √1296 (TRUE)
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The temperature at 6:00 a.m. was 39°F. After 12 hours, the temperature had dropped by 57°F. What was the temperature after 12 hours?
Answer:
-18 Degrees F
Step-by-step explanation:
Use the equation below to find a, if b=3 and h=4 .
What is the question?
If there is a 'b' variable, switch it out with 3, so ex; 8b would then be 8(3), or 8*3. Same thing with h. If there is an 'a' variable, then you have to get everything gone but the variable. If you send over the question I can help
