The exact number for tan(t + 71) is -0.5846.
To find tan(t + 71), we can use the formula for the sum of two angles:
tan(t + 71) = (tan t + tan 71)/(1 - tan t * tan 71)
Given that tan t = 5, we can substitute this value into the formula:
tan(t + 71) = (5 + tan 71)/(1 - 5 * tan 71)
To find the exact number for tan 71, we can use a calculator or a table of trigonometric values. The exact value of tan 71 is approximately 2.9042.
Substituting this value into the formula, we get:
tan(t + 71) = (5 + 2.9042)/(1 - 5 * 2.9042)
Simplifying the expression, we get:
tan(t + 71) = (7.9042)/(1 - 14.521)
tan(t + 71) = (7.9042)/(-13.521)
tan(t + 71) = -0.5846
Therefore, the exact number for tan(t + 71) is -0.5846.
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Find the value of x. (Picture attached)
DeShawn buys the following items from his grocery store.
2 boxes of cereal priced at $8.95 each
3 of a pound of cheese at $12.80 per pound
1 quart of orange juice for $5.85 per quart.
There is no sales tax on the food. DeShawn pays for the items and receives $1.65 in change.
What amount of money did DeShawn use to pay for the items?
Answer: C
Step-by-step explanation: 8.95x2=17.9, 3/4x12.80=9.6, 17.9+9.6+5.85=33.35. 33.35+1.65=35
Order the following expressions by their values from least to greatest.
-2 a+c b
The expressions ordered from least to greatest are: -2 < b < (a + c)
What is expression?In maths, an expressiοn is a cοmbinatiοn οf numbers, variables, functiοns (such as additiοn, subtractiοn, multiplicatiοn οr divisiοn etc.)
Expressiοns can be thοught οf as similar tο phrases. In language, a phrase οn its οwn may include an actiοn, but it dοesn't make a cοmplete sentence.
According to the question:
-1 < a < 0
2 < b < 3
4 < c < 5
Now, we have the expression a + c
= (-1 < a < 0) + (4 < c < 5)
= (-1 + 4) < (a + c) < (0 + 5)
= 3 < (a + c) < 5
Thus, we have the expressions ordered from least to greatest are:
-2 < 2 < b < 3 < (a + c) < 5
-2 < b < (a + c)
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Complete question:
Keri is making doll clothes for a holiday craft show. The wholesale cost of the materials for one hour of it is $9. 38. If the if she sells an outfit for $15 what is the percent of the markup
The percent of the clothe required to make doll outfit as per given cost price and selling price is equal to 59.91%.
Cost price of the material for one outfit = $9.38
Selling price of the outfit = $15
Selling price is greater than cost price
⇒Profit = Selling Price - Cost price
Substitute the value to get profit,
⇒ Profit = $15 - $9.38
⇒ Profit = $5.62
Percent Markup = (Profit / Cost price ) x 100
Substitute the value we get,
⇒Percent Markup = ($5.62 / $9.38) x 100
⇒Percent Markup = 59.9147%
⇒Percent Markup = 59.91
Therefore, the percent markup of the making doll outfit is approximately 59.91%.
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The above question is incomplete, the complete question is:
Keri is making a doll clothes for a holiday craft show. The wholesale cost of the materials for one outfit is $9.38. If she sells an outfit for $15, what is the percent of the markup?
Marco mixes 135 pounds of quartz
with some marble. If the ratio stays
the same for every bag, how many
pounds of marble will Marco need?
Marco will need 2025 pounds of marble.
What is the ratio?The ratio is defined as the relationship between two similar magnitudes in terms of the number of times the first includes the second.
Let's say that Marco mixes 1 bag of quartz with x pounds of marble. Then the ratio of quartz to marble in this bag is:
135 pounds quartz : x pounds marble
3 pounds quartz : x/45 pounds marble
Now we know that the ratio of quartz to marble in one bag is 3: (x/45). Since the ratio stays the same for every bag, we can set up a new proportion using the total amount of quartz and marble:
135 pounds quartz : x pounds marble = total pounds quartz : total pounds marble
We know the total pounds of quartz is 135. Let's call the total pounds of marble "m".
Substituting these values into the proportion, we get:
135 : x = 135 : m/45
To solve for x, we can cross-multiply and simplify:
135(m/45) = 135x
3m = 45x
m = 15x
So, Marco will need 15 times as many pounds of marble as he has of quartz, or:
m = 15 × 135 = 2025 pounds of marble.
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a contractor has 8 trucks. some trucks carry a load of 10 tonnes and the other trucks carry a load of 5 tonnes. when all 8 trucks are filled, they contain a total of 70 tonnes. how many of each size of truck does the contractor own?
Answer:
10 tonnes = 6 trucks, 5 tonnes = 2 trucks
Step-by-step explanation:
Total number of trucks = 8
Let number of trucks carrying 10 tonnes = x
then number of trucks carrying 5 tonnes = 8 - x
We can represent this situation as follows:
10x + 5(8 - x) = 70 tonnes
10x + 40 - 5x = 70
5x + 40 = 70
5x = 30
x = 6
Number of trucks with 10 tonnes capacity = 6
Number of trucks with 5 tonnes capacity = 2 (i.e; 8-x = 8-6)
Hope it helps.......
There are 773 different species of fish and other wildlife at an aquarium. The aquarium has advertised the addition of 32 new species of fish, 7 new species of crustaceans and 9 new species of sharks.
How many species of fish and wildlife will the aquarium be home to?
Answer:821
Step-by-step explanation:773+32+7+9=821
Rachel, Phoebe and Monica are sunflower farmers in the village of Girasol. They each have zero wealth, so their consumption is equal to the income they earn from their economic activity. Each of them must choose one (and only one) of the following three activities:
Activity 1: Full time farming. Sunflower farming is risky because of a combination of weather and pests. Under full time farming, the farmer works 7 days per week on their farm. There is a 50% probability of having a GOOD harvest and a 50% chance of having a BAD harvest. If the harvest is GOOD, the farmer earns an income of $100. If the harvest is BAD, the farmer earns an income of only $20.
Activity 2: Full time construction work. This activity has no risk. An individual who decides to work full time in construction earns $40 with certainty.
Activity 3: Part-time farming. In this third activity, the farmer works during the week as a sunflower farmer and works in construction during the weekend. Since she is not able to work full time on the farm, the probability of having a GOOD harvest and earning $100 drops to 25%, and the probability of having a BAD harvest and earning only $20 increases to 75%. The individual also earns $10 with certainty as a construction worker (the person earns this $10 from construction in addition to her farm income under both a GOOD and BAD harvest).
Q: What is the expected value of consumption for each activity?
The expected value of consumption for each activity is $60 for Activity 1, $40 for Activity 2, and $50 for Activity 3.
The expected value of consumption for each activity can be calculated using the formula: E(x) = P(x) * X, where P(x) is the probability of an event occurring and X is the value of that event.
For Activity 1: Full time farming, the expected value of consumption is:
E(x) = (0.5 * $100) + (0.5 * $20) = $50 + $10 = $60
For Activity 2: Full time construction work, the expected value of consumption is:
E(x) = (1 * $40) = $40
For Activity 3: Part-time farming, the expected value of consumption is:
E(x) = (0.25 * $100) + (0.75 * $20) + (1 * $10) = $25 + $15 + $10 = $50
Therefore, the expected value of consumption for each activity is $60 for Activity 1, $40 for Activity 2, and $50 for Activity 3.
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On a nationwide test taken by high school students, the mean score was 51 and the standard deviation was 12. The scores were normally distributed. Complete the following statements
The scores of students were normally distributed.
a)Approximately 68% of the students scored between 40 and 62 .
b) The approximately 95% of the students scored between 29 and 73.
We have a nationwide test taken by high school students, Mean score, μ = 51
Standard deviations, s = 12
The scores were normally distributed, that is
X~ N(M= 51, s = 12)
Lower bound of confidence interval= 40
Upper bound of CI = 62
As we know according to empirical rule the percentage of data falls within one,two and three
standard deviations are 68%,95% and 99.7%
respectively.
a) Mean + standard deviations = 51 + 12 = 63 close to 62
= Upper bound
For 2 standard deviations, 51 + 2×12 = 75
Mean - standard deviations= 51 - 12 = 39 close to 40 = lower bound
For 2 standard deviations, 51 - 2×12 = 27
Thus, data falls within one standard deviation
that is under 68% and so, approximately 68% of students scored between 40 and 62.
b) Similarly, the empirical rule demonstrates that 95% of scores falls within two standard deviation.
mean - 2× standard deviations= 51 - 2× 11
= 51 - 22 = 29
mean + 2× standard deviations= 51 + 2×11
= 51 + 22 = 73
Therefore, approximately 95% of students scored
between 29 and 73.
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Complete question:
On a nationwide test taken by high school students, the mean score was 51 and the standard deviation was 11
The scores were normally distributed. Complete the following statements.
(a) Approximately ?% of the students scored between 40 and 62 .
(b) Approximately 95% of the students scored between ? and ?
Solve the given polynomial equation. Use the Rational Zero Theorem, Descates's Rule of Signs, and possib ald in obtaining the first root. x^(4)-4x^(3)-37x^(2)-56x-24=0
The rational root theorem, as its name suggests, is used to find the rational solutions of a polynomial equation (or zeros or roots of a polynomial function). The solutions derived at the end of any polynomial equation are known as roots or zeros of polynomials.
A polynomial doesn't need to have rational zeros. But if it has rational roots, then they can be found by using the rational root theorem.
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1. f(x) = x²+6X-11 Vertex (j)? Access of Symmetry?! X-intercept! Y-intercept! Range ? Domain:?
2. f(x) = x^3 +4x^2 + 10x+12 + Find the zeros!!!
The vertex of the function is (-3, -20), the axis of symmetry is x = -3, the x-intercepts are (-8.44, 0) and (1.44, 0), the y-intercept is (-11), the range is (-∞, -20], and the domain is (-∞, ∞).
To find the vertex, axis of symmetry, x-intercept, y-intercept, range, and domain of the function f(x) = x² + 6x - 11, we can use the following formulas:
- Vertex: (-b/2a, f(-b/2a))
- Axis of symmetry: x = -b/2a
- X-intercept: Solve f(x) = 0
- Y-intercept: f(0)
- Range: All real numbers for a parabola that opens up or down
- Domain: All real numbers
Using these formulas, we can find the following:
- Vertex: (-3, -20)
- Axis of symmetry: x = -3
- X-intercept: (-8.44, 0) and (1.44, 0)
- Y-intercept: (-11)
- Range: (-∞, -20]
- Domain: (-∞, ∞)
Therefore, the vertex of the function is (-3, -20), the axis of symmetry is x = -3, the x-intercepts are (-8.44, 0) and (1.44, 0), the y-intercept is (-11), the range is (-∞, -20], and the domain is (-∞, ∞).
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According to a survey of workers, 7/25 of them walk to work, 2/25 bike, 4/25 carpool, and 12/25 drive alone. What percent of workers walk or bike to work?
Answer:
Step-by-step explanation:
Make a model
Answer: The answer is 9/25. (36%)
Step-by-step explanation:
Since we know that 7/25 workers walk and 2/25 walk, we can do simple addition to find the total Percentage. This equals 9/25. To find the percentage, do the following:
Write 9/25 into a percentage: Divide
9 / 25 x (100%) = 36%
0.36 (100%) = 36%
Therefore 36% is your answer.
Please help me with step by step explanation, thank you
d
2/3 is the same as 4/6 and 25/100 is the same as 1/4. -1.3 is transferred to the beginning of the equation
what is the vertex for the following quadratic function?
x^2-4x-6
Answer:
vertex = (2, - 10 )
Step-by-step explanation:
given a quadratic function in standard form
ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
x² - 4x - 6 ← is in standard form
with a = 1 and b = - 4 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{-4}{2}[/tex] = 2
substitute x = 2 into the function for corresponding y- coordinate
2² - 4(2) - 6
= 4 - 8 - 6
= - 10
vertex = (2, - 10 )
The function f(x) is defined below. What is the end behavior of f(x)? f(x)=-432x^3+48x^4+7056+5544x-1984x^2+8x^5
Hence, we may conclude that function(x) behaves as though it will eventually approach infinity as x approaches infinity and will eventually approach negative infinity as x approaches negative infinity.
what is function?Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.
F(x) also approaches positive infinity as x gets closer to infinity.
F(x) also approaches negative infinity as x gets closer to its opposite.
This is due to the fact that as x increases or decreases in value, the term with the largest x power determines how the function behaves.
Hence, we may conclude that f(x) behaves as though it will eventually approach infinity as x approaches infinity and will eventually approach negative infinity as x approaches negative infinity.
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Use the given conditions to write an equation for the line in point slope form and in slope-intercept form X-intercept and y-intercept = 1 Write an equation for the line in point-slope form. 4 y 3 ** (Simplify your answer. Use integers or tractions for any numbers in the equation) Write an equation for the line in slope-intercept form. y= (Simplify your answer. Use integers or fractions for any numbers in the equation.)
The equation of the line in slope-intercept form is y = -x + 1
To write an equation for the line in point-slope form, we can use the formula y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
Since the x-intercept and y-intercept are both 1, we know that the line passes through the points (1,0) and (0,1).
To find the slope of the line, we can use the formula m = (y2 - y1) / (x2 - x1). Plugging in the coordinates of the two points, we get:
m = (1 - 0) / (0 - 1) = -1
Now we can plug in the slope and one of the points into the point-slope form equation:
y - 0 = -1(x - 1)
Simplifying, we get:
y = -x + 1
This is the equation of the line in point-slope form.
To write the equation in slope-intercept form, we can use the formula y = mx + b, where m is the slope of the line and b is the y-intercept.
We already found the slope to be -1, and the y-intercept is given as 1. So we can plug these values into the slope-intercept form equation:
y = -1x + 1
Simplifying, we get:
y = -x + 1
This is the equation of the line in slope-intercept form.
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whats find the sum mean
Answer:
To find the answer / The result you get from adding numbers
Step-by-step explanation:
when you have a problem with two or more numbers being added your answer / result to the question would be called the Sum rather then an answer
3x^(2)-27x+75=15
please help please
please help me
Answer:
36
Step-by-step explanation:
bbecause yes and because a put in my quiz and they put me a A
distribute and then combine ( 2)/(3) (3x - 1) + 4x +3^(2)-10x + 5
So, by resolving the given, we obtain the result: The final simplified expressions phrase is as follows: -4x + 38/3
what is expression ?Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression. For example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
Let's start by condensing the first expression:
(2/3) (3x - 1) = 2x - 2/3
Now, we may reformat the phrase as follows:
(2x - 2/3) + 4x + 9 - 10x + 5
Mixing related concepts gives us:
-4x + 38/3
The final simplified phrase is as follows:
-4x + 38/3
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Matt's car can travel 555 miles on 15 gallons of fuel. Work out the rate of consumption of fuel of Matt's car in mpg
The rate of consumption of fuel of Matt's car is 37 miles per gallon (mpg).
Matt's car can travel a total distance of 555 miles.
The fuel required to travel the total distance is 15 gallons by Matt's car.
Hence the rate of consumption of fuel of Matt's car can be measured in mpg (miles per gallons) as = Total distance travelled / Total gallons required to travel that distance
(that is, total distance travelled divided by the total amount of gallons to travel the same)
Thus the mpg of Matt's car is = 555 miles / 15 gallons
= 37 miles per gallon
(that is 37 mpg)
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PLEASE HELP!!!!!!! ASAP PLSSS WHICH ONE IS IT???!
Answer: y = 5/6x
Step-by-step explanation:
It is a direct variation.
in ABC m
jjj k
kkkkkkk
kkk
3a+4b-1 where a = 7 and b =2
Given:-
[tex] \frak{a = 7}[/tex][tex] \: [/tex]
[tex] \frak{b = 2}[/tex][tex] \: [/tex]
Solution:-
[tex] \frak{3a + 4b - 1}[/tex][tex] \: [/tex]
[tex] \frak{3 ( 7 ) + 4( 2 ) - 1}[/tex][tex] \: [/tex]
[tex] \frak{21 + 8 - 1}[/tex][tex] \: [/tex]
[tex] \frak{21 + 7}[/tex][tex] \: [/tex]
[tex] \underline{ \boxed{ \frak{ \purple{ \:28 \: }}}}[/tex][tex] \: [/tex]
hope it helps! :)
To indirectly measure the distance across a river, Arun stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Arun draws the diagram below to show the lengths and angles that he measured. Find
�
�
PR, the distance across the river. Round your answer to the nearest foot.
P
R
O
C
E
The distance across the river is approximately 597 feet.
When is the Law of Cosines employed in trigonometry, and what does it mean?The Law of Cosines is a formula that connects a non-right triangle's sides and angles. When the lengths of two sides and the angle between them, or the lengths of all three sides, are known, it is used to determine the length of a side or measure of an angle.
For the given figure:
Using trigonometry, we can find the length of PR as follows:
tan(43) = QR/PS
PS = QR/tan(43)
tan(68) = QR/RU
RU = QR/tan(68)
Since PS + RU = PR,
PR = QR/tan(43) + QR/tan(68)
Since triangle PQR is a right triangle, we can use the Pythagorean theorem:
QR² = PS² + RU²
Substituting the expressions for PS and RU gives:
QR² = (QR/tan(43))² + (QR/tan(68))²
QR ≈ 325.4 feet
Now we can substitute this value into the expression for PR to get:
PR ≈ 596.7 feet (rounded to the nearest foot)
Therefore, the distance across the river is approximately 597 feet.
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The complete question is:
Solve for the exact solutions in the interval (0,2π). If the equation has no solutions, respond with DNE Cos (2x) cos(x) - sin(2x)sin(x) = - ✓3 / 2
____________
The exact solutions are x ≈ 0.590, x ≈ 2.552, and x ≈ 5.103.
The equation we are solving for exact solutions in the interval (0,2π) is Cos (2x) cos(x) - sin(2x)sin(x) = - √3 / 2.
First, let's use the double angle formula for cosine to simplify the equation:
cos(2x) = 1 - 2sin^2(x)
Substituting this into the equation, we get:
(1 - 2sin^2(x))cos(x) - sin(2x)sin(x) = - √3 / 2
Next, let's use the double angle formula for sine to simplify the equation further:
sin(2x) = 2sin(x)cos(x)
Substituting this into the equation, we get:
(1 - 2sin^2(x))cos(x) - 2sin^2(x)cos(x) = - √3 / 2
Combining like terms and rearranging, we get:
4sin^2(x)cos(x) - cos(x) = √3 / 2
Factoring out cos(x), we get:
cos(x)(4sin^2(x) - 1) = √3 / 2
Dividing both sides by (4sin^2(x) - 1), we get:
cos(x) = (√3 / 2) / (4sin^2(x) - 1)
Using the Pythagorean identity, sin^2(x) + cos^2(x) = 1, we can substitute for sin^2(x):
cos(x) = (√3 / 2) / (4(1 - cos^2(x)) - 1)
Multiplying both sides by (4(1 - cos^2(x)) - 1), we get:
cos(x)(4(1 - cos^2(x)) - 1) = √3 / 2
Expanding and rearranging, we get:
4cos^3(x) - 5cos(x) + √3 / 2 = 0
This is a cubic equation, which is difficult to solve algebraically. However, we can use a graphing calculator to find the approximate solutions. The solutions are x ≈ 0.590, x ≈ 2.552, and x ≈ 5.103.
Since all of these solutions are in the interval (0,2π), the exact solutions are x ≈ 0.590, x ≈ 2.552, and x ≈ 5.103.
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[0.05=2.26] Madhu exchanged her old car valued at 1,50,000 with a new one priced at 6,50,000. She paid x as down payment and the balance in 20 monthly equal instalments of 21,000 each. The rate of interest offered to her is 9% p.a. Find the value of x. [Given that: (1-0075)-20 = 0.86118985]
The value of x is approximately 2,04,582.80.
What is expression ?An expression is a mathematical phrase that can contain numbers, variables, operators, and functions. It can be a combination of terms and can include operations such as addition, subtraction, multiplication, division, and exponentiation.
According to given information :Given,
Value of old car = 1,50,000
Price of new car = 6,50,000
Number of monthly installments = 20
Amount of each installment = 21,000
Rate of interest offered = 9% p.a.
Let x be the down payment amount.
The total amount to be paid by Madhu for the new car will be equal to the sum of the down payment and the total of 20 monthly installments.
Total amount = x + 20 × 21,000
Since the rate of interest is 9% p.a., the effective rate of interest for 20 months can be calculated as follows:
Effective rate of interest for 20 months = (1 + 0.09/12)^20 - 1 = 0.86118985
So, the total amount to be paid by Madhu for the new car can be expressed as follows:
Total amount = x + 20 × 21,000 × 0.86118985
According to the problem, Madhu exchanged her old car valued at 1,50,000 with the new car priced at 6,50,000. Therefore, the down payment x can be calculated as follows:
x + 20 × 21,000 × 0.86118985 = 6,50,000 - 1,50,00
x + 20 × 21,000 × 0.86118985 = 5,00,000
x= 5,00,000 - 20 × 21,000 × 0.86118985
x ≈ 2,04,582.80
Therefore, the value of x is approximately 2,04,582.80.
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Which expression shows the result of applying the distributive property to 1/5(−3x+4)?
Therefore, -3/5x + 4/5 is the expression that represents the outcome of applying the distributive principle to 1/5(3x+4).
what is expression ?An expression in mathematics is a grouping of digits, variables, and mathematical signs (like +, -, +, +, and =) that denote a mathematical relationship or computation. Expressions can be made up of a single number or variable or they can be intricate arrangements of different words and mathematical processes.
given
According to the distributive principle, a(b + c) = ab + ac. We can distribute the 1/5 to both terms inside the parentheses in order to apply the distributive principle to the expression 1/5(3x+4):
1/5(-3x + 4) = 1/5(-3x) + 1/5(4) (4)
If we simplify, we get:
1/5(-3x) + 1/5(4) = -3/5x + 4/5
Therefore, -3/5x + 4/5 is the expression that represents the outcome of applying the distributive principle to 1/5(3x+4).
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Tanya can bike 9 miles in 1.5 hours.
How long will it take Tanya to bike 12 miles?
Enter your answer as a whole number in the box.
__ hours
Use polynomial fitting to find the formula for the nth term of the sequence (an)nzo which starts,
4, 15, 44, 109, 228, 419,...
an=
The formula for the nth term of the sequence is:
an = 1n^5 - 5n^4 + 9n^3 - 7n^2 + 3n + 3
To find the formula for the nth term of the sequence 4, 15, 44, 109, 228, 419,... using polynomial fitting, we need to follow the following steps:
1. Identify the degree of the polynomial: Since the sequence has 6 terms, the degree of the polynomial is 5.
2. Create a system of equations: Use the given terms of the sequence to create a system of equations with the polynomial coefficients as unknowns.
3. Solve the system of equations: Use any method to solve the system of equations to find the values of the polynomial coefficients.
4. Write the formula for the nth term: Use the values of the polynomial coefficients to write the formula for the nth term of the sequence.
The system of equations is:
a5n^5 + a4n^4 + a3n^3 + a2n^2 + a1n + a0 = an
Plugging in the values of the terms of the sequence, we get:
a5(1)^5 + a4(1)^4 + a3(1)^3 + a2(1)^2 + a1(1) + a0 = 4
a5(2)^5 + a4(2)^4 + a3(2)^3 + a2(2)^2 + a1(2) + a0 = 15
a5(3)^5 + a4(3)^4 + a3(3)^3 + a2(3)^2 + a1(3) + a0 = 44
a5(4)^5 + a4(4)^4 + a3(4)^3 + a2(4)^2 + a1(4) + a0 = 109
a5(5)^5 + a4(5)^4 + a3(5)^3 + a2(5)^2 + a1(5) + a0 = 228
a5(6)^5 + a4(6)^4 + a3(6)^3 + a2(6)^2 + a1(6) + a0 = 419
Solving this system of equations, we get:
a5 = 1
a4 = -5
a3 = 9
a2 = -7
a1 = 3
a0 = 3
Therefore, the formula for the nth term of the sequence is:
an = 1n^5 - 5n^4 + 9n^3 - 7n^2 + 3n + 3
So, the formula for the nth term of the sequence 4, 15, 44, 109, 228, 419,... using polynomial fitting is an = 1n^5 - 5n^4 + 9n^3 - 7n^2 + 3n + 3.
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Kent is walking in a race and the equation that describes the relationship between his distance (meters) and time (seconds) is d = 2t + 15.
The coefficient is and, in the situation, it represents
The coefficient is 2 and, in the situation, it represents the number of meters that Kent walks per second.
What is the coefficient?In mathematics, the coefficient is a numerical or constant quantity or the multiplicative factor in an expression.
The coefficient multiplies its attached variable to determine a value in the algebraic expression.
For instance, from the equation describing the relationship between his distance (meters) and time (seconds) is d = 2t + 15, 2 is the coefficient of t.
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