The n th term of the series is 3n where n is the term of reference
As we can see that there is constant difference in the terms
12-9=3
9-6=3
6-3=3
We are made sure that it is the arithmetic progression
Common difference is the difference that is constantly subtracted or added to each term after the first term
Thus the common difference 'd' is 3 as per the calculations above
Now the first term is 3
We know that any N th term of arithmetic progression is given by the formula
Tn= a+ (n-1)*d
where a is the first term of the progression and n is the term of reference and d is the common difference
a=3
d=3
Therefore, nth term of the series is = Tn= 3 + (n-1) *3
Tn= 3+3n-3
Tn = 3n
Hence the n th term of the series is 3n where n is the term of reference
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Simplify the following expression:
2y-7x + 4x² + 3y + 7x
A. 4x214x + 5y
B. 4x² - 14x
C. 4x² + 14x + 5y
D. 4x² + 5y
The simplified expression for the expression 2y - 7x + 4x² + 3y + 7x is
D. 5y + 4x²
Option D is the correct answer.
We have,
To simplify the expression 2y - 7x + 4x² + 3y + 7x, we combine like terms:
The like terms are:
2y and 3y
-7x and 7x
Group the terms with "y" together: 2y + 3y = 5y
Group the terms with "x" together: -7x + 7x = 0
Combining (1) and (2) for the expression.
Now the expression becomes:
5y + 4x²
Thus,
The simplified expression for the expression 2y - 7x + 4x² + 3y + 7x is
D. 5y + 4x²
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Write a number to represent the quantity.
a loss of five yards
Answer:
6-1
Step-by-step explanation:
Commission is based on a percentage of sales. Nia sells cars and earns 4% commission on
each car or truck sold. How much will Nia earn if she sells 4 trucks for $18,434 each?
Answer:
2949.44 Step-by-step explanation: 18,434x4 - four trucks = 73736 73736x.04-2949.44
Find a vector function that represents the curve of intersection of the two surfaces. the paraboloid z = 8x 2 y 2 and the parabolic cylinder y = 3x 2 r(t) = t i j
The vector function, r(t) that represents the curve of intersection of the two surfaces, the paraboloid and the parabolic cylinder is given by < t, 3t2, 8t2 + 9t4 >. It is attained by applying the concept of vectors to the assigned problem.
What is a vector?
A vector is any quantity that contains both magnitudes as well as direction. Geometrically, one can imagine a vector as a directed line segment, whose length denotes the magnitude of the vector and the direction is shown by the arrow, which is generally taken from its tail to its head. Using an arrow with a line specifies that it is not only scalar but also has some direction.
Calculation of the vector function representing the curve of intersection of the paraboloid and parabolic cylinder
A vector function r(t) is represented as: r(t) = < x, y, z >
Given: y = 3x2 – 1
z = 8x2 + y2 – 2
Let,
x = t
Using x = t in equations 1 and 2
y = 3t2
z = 8t2 + y2
Putting the value of y in z, we get,
z = 8t2 + (3t2)2
z = 8t2 + 9t4
Substitute these values of x, y, and z in vector representation to obtain the result, i.e. < t, 3t2, 8t2 + 9t4 >
Hence, the value of vector function r(t) is: < t, 3t2, 8t2 + 9t4 >
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Round 91584.3774339 to 2 decimal places.
Answer:
To 2 decimal places, we have 91584.38.
can anyone help me find the answer to the attatched question
Answer:
Angle BOC = 120°
Angle DOC = 60°
Angle ODC = 90°
Step-by-step explanation:
Triangle ABC is an equilateral triangle, therefore Angle BAC = 60°.
Now that we know Angle BAC, we can find Angle BOC: 2 × 60 = 120°
Angle DOC = ½ Angle BOC ( Radius drawn from centre to midpoint of chord, bisect the angle)
So Angle DOC = ½ (120) = 60°
Angle = 90° because D is the midpoint of chord BD and OD is a radius.
Ratios Equivalent to 15:6 (not 6:15)
Pls tell me what ratios they are
Answer:
30/32
Step-by-step explanation:
15×2=30
16×2=32
30/32
Answer:
5:2 , 30:12 , 60:24 , etc.
Step-by-step explanation:
To identify ratios equivalent to 15:6, all you need to do is multiply or divide both numbers in the ratio by the same amount to find an equivalent ratio.
So, for example:
1:2 --> 1*2 : 2*2 = 2:4 Both one half, so equal.
Now for 15:6...
Let's divide by the least common denominator ( 3 )
15 / 3 and 6 / 3 = 5 and 2
So 15:6 = 5:2
And we can also multiply the ratio by any constant as well...
For example 15 * 2 and 6 * 2
So 30:12 = 15:6
Hope this helped!
What is the best estimate for the area of the triangle, in square units?
y
OA) 5.25 square units
O B) 10.5 square units
OC) 21 square units
OD) 42 square units
The best estimation for the area of the triangle is option (C) 21 square units
The base of the triangles = 6 units
The height of the triangle = 7 units
We know,
The area is the total space taken by the surface of an object.
Area of the triangle is the half the product of its base length and height.
The area of the triangle = (1/2)×b×h
Where b is the base of the triangle
h is the height of the triangle
Substitute the values in the equation
The area of the triangle = (1/2)× 6× 7
= (1/2)× 42
= 21 square units
Hence, the best estimation for the area of the triangle is option (C) 21 square units
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22. Pamela is making the legs for a three-legged stool from two pieces of scrap wood. The lengths of the two pieces of wood are 36 inches and 21 inches. Each leg is 16 inches long. a. Pamela cuts one leg from each piece of wood. Write and evaluate two expressions to show how much of each piece of wood is left over. b. Will Pamela have enough wood for a third leg? Explain.
Pamela will have enough wood for making the third leg as she has a 20 inch piece still left with her.
We are given that:
Pamela wants to make a three legged stool.
She has two pieces of wood: 36 inches and 21 inches.
Length of each leg = 16 inches.
Now, she cut 1 leg from each piece of the wood.
Length of wood pieces left will be given by the expression:
36 inches - 16 inches = 20 inches
and
21 inches - 16 inches = 5 inches.
Yes, Pamela will have enough wood for making the third leg as she has a 20 inch piece still left with her.
Therefore, Pamela will have enough wood for making the third leg as she has a 20 inch piece still left with her.
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An analysis of variance produces ssbetween = 30, sswithin = 60, and an f-ratio with df = 2, 15. for this analysis, what is the f-ratio?
For this analysis, 4/25 is the f-ratio.
What is f- ratio?
In the psychosocial, behavioral, and health sciences, the F-ratio is frequently employed in study on quality of life. In order to compare two or more groups, it often refers to a statistic that is produced by dividing two sample variances that are supposed to come from normally distributed populations.SS between = 30
SS within = 60
Mean square of regression = 30/2 = 15
Mean square of error = 60/15 = 4
So f ratio = 15/4 = 3.75
So it's answer is D.
Solution(15)
Df between = Df total - Df within = 29-27 = 2
So it's answer is b. I.e. 2
Solution(16)
If Df = 18 and there are two independent sample than total sample size = 18+2 = 20
So it's answer is A
Solution(17)
N1=10
N2 = 15
So DF = 10+15-2 = 23
So it's answer is C. I.e. 23
Solution(18)
D = (M1-M2)/spooled = (35-31)/25 = 4/25
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over which interval is the graph of f(x)=-(x+8)^2-1 decreasing
The interval at which the function f ( x ) = - ( x + 8 )² - 1 is decreasing is [-8, ∞).
We are given the function:
f ( x ) = - ( x + 8 )² - 1
We will first simplify the expression:
f ( x ) = - x² - 64 - 16 x - 1
f ( x ) = - x² - 16 x - 65
Now, we will plot the function on a graph.
Now, we can see that, the function is decreasing at [-8, ∞) from the graph of the function.
Therefore, the interval at which the function f ( x ) = - ( x + 8 )² - 1 is decreasing is [-8, ∞).
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Need help 5th grade math
Answer:
99
Step-by-step explanation:
9 × 11 = 99
Answer:99 you got it right.
Step-by-step explanation:
its easy for a seventh grader.
For+a+first+order+reaction,+how+many+half-lives+are+required+for+the+concentration+of+reactant+to+decrease+to+1.56%+of+its+original+value?
6 half-lives are required for the concentration of reactant to decrease to 1.56% of its original value.
Using integrated rate law for first order kinetics as:
[tex][A_t]=[A_0]e^{-kt}[/tex]
Where
[tex][A_t][/tex]is the concentration at time t
[tex][A_0][/tex] is the initial concentration.
Given,
Concentration is decreased to 1.56 % which means that 0.0156 of [tex][A_0][/tex] is decomposed. So,
=> [tex]\frac{[A_t]}{[A_0]}[/tex] = 0.0156
Thus
=> 0.0156 = [tex]e^{-kt}[/tex]
When we simplify it,
Then we get,
kt = 4.1604
k = 4.1604/t
The expression for the half life is:-
Half life = 15.0 hours
[tex]t_{1/2}=\frac{ln2}{k}[/tex]
Where, k is rate constant
So,
[tex]k=\frac{ln2}{t_{1/2}}[/tex]
Apply the value of k then.
[tex]\frac{4.1604}{t}=\frac{ln2}{t_{1/2}}[/tex]
Therefore,
[tex]t=6\times t_{1/2}[/tex]
Therefore, 6 half-lives are required for the concentration of reactant to decrease to 1.56% of its original value.
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the answers for 22, 24,and 25?
Answer:
22) -3jk+12k^2---------24)-3xy^4-7xy^3
Step-by-step explanation:
Solve the system of equations 2x+y=-2 and -9x-3y=18 by combining the equations.
Answer:
2x+y=-2
-9x-3y=18
So what you would do is see which one you would like to get rid of (either x, or y in this situation get rid of y)
multiply y by postive 3
3(2x+y=-2)
6x+3y=-6
-9x-3y=18 (both y's cross out since 3y+-3y is equal to zero)
-----------------
-3x=-24 (divide both sides by -3)
--- ---
-3 -3
x= 8 (neg/neg=positive)
Then figure out the x so use either the first or second equation
so in this case I will use the first equation (plug in the x for 8)
2(8)+y=-2
16+y=-2
-16 -16
---------------
y=-18
Check:
2x+y=-2
2(8)+y(-18)=-2
16+-18=-2
-2=-2 (therfore you know that you are right)
Ansers:
y=-18
x=8
Hope this helps!
9 is subtracted from the product of 9 and a number.
The numerical form of the statement the product of 9 and a number is
9n - 9.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The given statement is 9 is subtracted from the product of 9 and a number.
Let the number be 'n'.
Therefore, The statement 9 is subtracted from the product of 9 and a number can be numerically written as,
9n - 9.
We can also take 9 as a common factor,
9(n - 1).
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Find the distance between -2 3/5 and -1 on a number line. Write your answer as a mixed number.
The distance between -2 3/5 and -1 on a number line is -1 3/5.
What is the distance?A mixed number is a fraction that is made up of a whole number and a proper fraction. A proper fraction is a fraction in which the numerator is less than the denominator. An example of a mixed number is -2 3/5.
In order to determine the distance, -1 would be subtracted from -2 3/5
[tex]-2\frac{3}{5} - (-1)[/tex]
[tex]-2\frac{3}{5} + 1[/tex]
[tex]-\frac{13}{5} + \frac{5}{5}[/tex]
[tex]\frac{5 - 13}{5}[/tex]
-8/5 = -1 3/5
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how do i write four more than p
Answer:
p+4
Step-by-step explanation:
you can determine the rate of calcification at any given carbonate ion concentration as follows: draw a vertical line up from the x-axis at that concentration value until it intersects the red linear regression line; then draw a horizontal line from the intersection over to the y-axis to see what the calcification rate is at that carbonate ion concentration. if the seawater carbonate ion (co3 2-) concentration is 270 µmol/kg, a) what is the approximate rate of calcification, and b) approximately how many days would it take 1 square meter of reef to accumulate 30 mmol of calcium carbonate (caco3)? you can determine the rate of calcification at any given carbonate ion concentration as follows: draw a vertical line up from the x-axis at that concentration value until it intersects the red linear regression line; then draw a horizontal line from the intersection over to the y-axis to see what the calcification rate is at that carbonate ion concentration.if the seawater carbonate ion (co3 2-) concentration is 270 µmol/kg, a) what is the approximate rate of calcification, and b) approximately how many days would it take 1 square meter of reef to accumulate 30 mmol of calcium carbonate (caco3)? 10 mmol caco3 per m2 per day; 3 days 20 mmol caco3 per m2 per day; 0.67 days 20 mmol caco3 per m2 per day; 1.5 days 20 mmol caco3 per m2 per day; 600 days
For Part F- Option C is correct.
1.5 days for 1 m2 of reef to accumulate 30 mmol of CaCO3
Graph of carbonate concentration versus time calcification rate.
At 270 umol/kg of seawater carbonate ion concentratio the approximate rate of calcification will be 20 mmol CaCO3 per m2 per day.
So it will take 1.5 days for 1 m2 of reef to accumulate 30 mmol of CaCO3
For Part G-
At 250 umol/kg of seawater carbonate ion concentratio the approximate rate of calcification will be 10 mmol CaCO3 per m2 per day.
So it will take 3 days for 1 m2 of reef to accumulate 30 mmol of CaCO3
What is the calcification rate?The rate at which corals that form reefs lay down their calcium carbonate skeleton is known as coral calcification. It serves as a gauge of coral growth, which is crucial for the sustainability of reef ecosystems.
The long-term biodiversity, and possibly the existence, of coral reefs depends on significant reductions in global CO2 emissions as well as good management of water quality to lessen macroalgal competition and aid coral recovery.
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danielle’s mistake subtract x3 - 2x2 from x2-6
we get - x³ + 3 x² - 6 after subtracting x³ - 2 x² from x² - 6.
We are given two expressions:
x³ - 2 x²
x² - 6
We need to subtract x³ - 2 x² from x² - 6
We get the expression as:
x² - 6 - (x³ - 2 x²)
Opening the brackets, we get that:
= x² - 6 - x³ + 2 x²
Combining the like terms, we get that:
= 3 x² - x³ - 6
Simplifying the expression, we get that:
= - x³ + 3 x² - 6
Therefore, we get - x³ + 3 x² - 6 after subtracting x³ - 2 x² from x² - 6.
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I really need some help
Answer:
a
Step-by-step explanation:
The commutative property is related to both addition and multiplication. It means that changing the order or position of two numbers while adding or multiplying them does not change the end result.
Since the question specifically asked for multiplication, the answer is a.
Find the distance between the two points in simplest radical form. (0, -3) (8,2)
Answer:
Step-by-step explanation:
[tex]\frac{3}{5}x+22=28
The value of x is 1/ 5
What are algebraic expressions?
Algebraic expressions are expressions that comprise of variables, factors, coefficients, terms and constants.
They are also made up of mathematical operations such as addition, division, multiplication, subtraction, etc
Given the expression:
3/ 5x + 22 = 28
collect like terms
3/ 5x = 28 - 22
3/ 5x = 6
cross multiply
5x × 6 = 3
30x = 6
Makr 'x' the subject
x = 6/ 30
x = 1/ 5
Thus, the value of x is 1/ 5
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The photo is of the rotunda in the capitol building in St. Paul, Minnesota. A rotunda is a round buildiug, usually covered by a domc. Use, Postulate 2.1 to help you answer parts a-c.
c. What term describes the shortest distance from the center of a circle to a point on the circle?
The shortest distance from the center of a circle to a point on the circle is the radius.
What is a circle?The circular line is drawn equidistant from the center point of a circle, which is a two-dimensional geometry object on a plane.
Any line segment connecting a circle's center to its perimeter is considered a circle's or sphere's radius, and in more recent usage, their length is also considered.
The radius of a circle is the shortest path between any two points on the circle.
Therefore, the shortest distance from the center of a circle to a point on the circle is the radius.
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Zahra Buys eggs and oranges at the stores she pays a total of $30.01 she pays a total of $5.30 for the eggs she buys seven bags of oranges that each cost the same amount how much does each bag of oranges cost
Answer:
$3.53
Step-by-step explanation:
$30.01- the eggs $5.30= $24.71
24.71÷7= 3.53
-2(X - 5) - 3(4x +4)
I know the evaluation is -14x - 2 but I need to explain why this is correct.
In the expression:
[tex] - 2(x - 5) - 3(4x + 4)[/tex]
Apply the rule of BODMAS which states that bracket comes first, and we know that when a number is outside a bracket, it means the number will multiply the number(s) in the bracket. Infact, bracket means multiplication. So, -2 will multiply the values in the bracket beside it, and -3 will multiply the values in the bracket beside it. When that is done, combine everything together (always observe the mathematical signs)
[tex] - 2x + 10 - 12x - 12[/tex]
Now, collect like terms.
[tex] - 2x - 12x + 10 - 12[/tex]
Therefore, final answer is:
[tex] - 14x - 2[/tex]
I hope this helps(URGENT)Trinity walked to town at a rate of 4 mph. She rode the bus back at 40 mph. The town is 2 miles away. How long did it take Trinity to travel to town and back?
Based on the fact that town is 2 miles away, the time it took Trinity to travel to town and back was 33 minutes
How long did Trinity travel?The time taken can be found as:
= Distance / Speed
Trinity's trip to town took:
= 2 / 4
= 0.5 hours
Trinity's trip back took:
= 2 / 40
= 0.05 hours
The total time it took Trinity to travel to and from town was:
= (0.5 + 0.05) x 60 minutes per hour
= 0.55 hours x 60
= 33 minutes
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Write 6,750,000,000 in scientific notation.
O 6.75 × 10⁹
O 675 x 107
675 x 10-7
06.75 × 10-9 question 13
The proper format for scientific notation is a x 10^b , 6.75 × 10⁹ is the scientific notation for 6,750,000,000.
What is Scientific Notation?The proper format for scientific notation is a x 10^b where a is a number or decimal number.
Given number is 6,750,000,000, we need to write in scientific notation.
To write the number to scientific notation, we need to follow few rules, Move the decimal so there is one non-zero digit to the left of the decimal point.
The number of decimal places you move will be the exponent on the . If the decimal is being moved to the right, the exponent will be negative.
If the decimal is being moved to the left, the exponent will be positive.
6,750,000,000 = 6.75 × 10⁹
Therefore 6.75 × 10⁹ is scientific notation for 6,750,000,000.
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Info
On the coordinate plane, what are the coordinates of the
point that is halfway between (4,-1) and (3,-2)?
0 (7,-3)
○ (1, 1)
o (3.5, 1.5)
○ (3.5, -1.5)
The coordinates of the mid point of the given points (4,-1) and (3,-2) is found as (x,y) = (3.5, -1.5).
What exactly is the Mid - Point Theorem?The midpoint of a line segment is referred to by the midpoint theorem. It describes the coordinate points of the line segment's midpoint and can be found by averaging the coordinates of a given endpoints.It also states that a line with endpoint coordinates - [x(1), y(1)] and [x(2), y(2)] has its mid - point just at coordinate.In response to the question, we have -
A (4,-1)and B(3,-2) are our two coordinate points.
We must determine the midpoint of the this line AB.
x(m) = [x(1) + x(2)]/2
y(m) = [y(1) + y(2)]/2
A is the first coordinate point (4,-1).
Point B is the second coordinate (3,-2).
Put the given points;
x(m) = [4 + 3)]/2
x(m) = 7/2 = 3.5
Now, for y;
y(m) = [y(1) + y(2)]/2
y(m) = [-1 -2]/2
y(m) = -3/2 = -1.5
Therefore, we get - using the Mid - Point formula (x,y) = (3.5, -1.5).
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HELPPP 15 pointssssss mathhh