Answer:
To simplify the expression, we need to distribute the negative sign to all the terms inside the parentheses, and then combine like terms.
Starting with:
(5x^4-4x^3-2x^2+x-19)-(x^4+5x^3+8x^2+x+5)
Distribute the negative sign inside the parentheses:
5x^4 - 4x^3 - 2x^2 + x - 19 - x^4 - 5x^3 - 8x^2 - x - 5
Now we can combine like terms:
(5x^4 - x^4) + (-4x^3 - 5x^3) + (-2x^2 - 8x^2) + (x - x) + (-19 - 5)
Simplifying further:
4x^4 - 9x^3 - 10x^2 - 24
Therefore, the simplified expression is:
4x^4 - 9x^3 - 10x^2 - 24.
what input can you not use with the rule divide 10 by the input added to 3
Answer:
-0
Step-by-step explanation:
For the given expression, find the quotient and the remainder. Check your work by verifying that (Quotient)(Divisor) Remainder= Dividend. - 6x3+4x2-2 divided by x -1 Quotient Remainder:
The quotient is -6x^2-2x-2 and the remainder is -4.
To find the quotient and remainder for the given expression, we can use long division.
First, we divide the first term of the dividend (-6x^3) by the first term of the divisor (x) to get -6x^2. This is the first term of the quotient.
Next, we multiply the first term of the quotient (-6x^2) by the divisor (x-1) to get -6x^3+6x^2. We subtract this from the dividend to get -2x^2-2.
We repeat this process with the new dividend (-2x^2-2) and the same divisor (x-1). We divide the first term of the new dividend (-2x^2) by the first term of the divisor (x) to get -2x. This is the second term of the quotient.
We multiply the second term of the quotient (-2x) by the divisor (x-1) to get -2x^2+2x. We subtract this from the new dividend to get -2x-2.
We repeat this process one more time with the new dividend (-2x-2) and the same divisor (x-1). We divide the first term of the new dividend (-2x) by the first term of the divisor (x) to get -2. This is the third term of the quotient.
We multiply the third term of the quotient (-2) by the divisor (x-1) to get -2x+2. We subtract this from the new dividend to get -4. This is the remainder.
So, the quotient is -6x^2-2x-2 and the remainder is -4.
We can check our work by verifying that
(Quotient)(Divisor) + Remainder = Dividend:
(-6x^2-2x-2)(x-1) + (-4) = -6x^3+6x^2-2x^2+2x+2x-2-4 = -6x^3+4x^2-2
Therefore, our answer is correct.
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In 2002, the population of the state was 6.7 million people and was growing at a rate of about 0.32% per year. At this growth rate, the function f (x) = 6.7(1.0032)x gives the population, in millions of x years after 2002. Using this model, find the year when the population reaches 7 million people. Round your answer to the nearest whole number.
Thus, 2002 + 23 = 2025 is the year at which the populace hits 7 million.
What sort of equation would that be?The meaning of an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.
To find the year when the population reaches 7 million people, we need to solve the equation:
f(x) = 7
where f(x) represents the population, in millions of x years after 2002, and x is the number of years after 2002.
Substituting the given function f(x) = 6.7(1.0032)x into this equation, we get:
6.7(1.0032)x = 7
Dividing both sides by 6.7, we get:
1.0032x = 1.0448
When we take the natural log of both parts, we obtain:
ln(1.0032)x = ln(1.0448)
Using the logarithmic identity ln(aᵇ) = b ln(a), we can simplify this to:
x ln(1.0032) = ln(1.0448)
Dividing both sides by ln(1.0032), we get:
x = ln(1.0448) / ln(1.0032)
Using a calculator, we find:
x ≈ 22.6
Therefore, the population will reach 7 million people approximately 22.6 years after 2002. Rounding this to the nearest whole number, we get:
x ≈ 23
So the year when the population reaches 7 million people is 2002 + 23 = 2025.
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Convert 0.2 to a percent
Answer:
20%
Step-by-step explanation:
Formula - multiply decimal by 100
0.2- Word form= two tenths
Fraction * 2/10 *
0.2 (multiply by 100)
0.2 x 100 = 20
20% is 0.2 as a percent
( hope this helps I’m online so ask any questions you need)
what is the measure of a
Answer:
∠ A = 19.8°
Step-by-step explanation:
the 3 angles of the triangle sum to 180°
sum the 3 angles and equate to 180
5x - 18 + 4x + x = 180
10x - 18 = 180 ( add 18 to both sides )
10x = 198 ( divide both sides by 10 )
x = 19.8
Then
∠ A = x = 19.8°
PLS HELP AND HURRY! I WILL GIVE YOU BRAINLIEST IF YOU GIVE THE RIGHT ANSWER! PLS HURRY! IT IS IN THE PHOTO! PLEASE!
The next three terms in the sequence are 1/81, -1/243, and 1/729.
What is the geometric sequence?
A geometric sequence is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed number called the common ratio. The general form of a geometric sequence is:
a, ar, ar^2, ar^3, ...
where a is the first term, r is the common ratio
To identify the next three terms in the sequence, we need to first determine the pattern. Looking at the sequence, we can see that each term is obtained by multiplying the previous term by -1/3, which means that this is a geometric sequence with a common ratio of -1/3.
Using this common ratio, we can find the next three terms in the sequence as follows:
-1/3 * (-1/27) = 1/81
1/81 * (-1/3) = -1/243
-1/243 * (-1/3) = 1/729
Therefore, the next three terms in the sequence are 1/81, -1/243, and 1/729.
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At a carnival, Ivan bought 14 packs of 9 tickets each. He also found 8 more tickets on the ground. How many tickets did Ivan have in all?
Answer: 134 tickets.
Step-by-step explanation:
Since we have 14 packs of 9 tickets, we can say it is 14 groups of 9. Which means we multiply. So 9 times 14 equals 126. But Ivan found 8 more tickets on the groud which means we add. so 126 plus 8 equals 134. The answer is 134 tickets.
Answer:
Step-by-step explanation:
multiply # of packs by # of tickets in each pack then add 8
14 x 9 = 126 + 8 = 134
Use the suggested substitution to write the expression as a
trigonometric expression. Simplify your answer as much as possible.
Assume 0≤θ≤π2.
√4x^2+100, x/5=tan(θ)
We are given the expression √4x^2+100 and the substitution x/5=tan(θ). Our goal is to use the substitution to write the expression as a trigonometric expression and simplify as much as possible.
First, let's substitute x/5=tan(θ) into the expression:
√4(tan(θ)*5)^2+100
Next, let's simplify the expression:
√4(25tan^2(θ))+100
√100tan^2(θ)+100
Now, let's factor out 100 from the expression:
√100(tan^2(θ)+1)
10√tan^2(θ)+1
Finally, let's use the trigonometric identity 1+tan^2(θ)=sec^2(θ) to simplify the expression further:
10√sec^2(θ)
10sec(θ)
Therefore, the expression √4x^2+100 can be written as 10sec(θ) using the substitution x/5=tan(θ).
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Mountain Equipment Co-op (MEC) wants to price a new backpack. The backpack can be purchased for a list price of $59.95 less a trade discount of 25% and a quantity discount of 10%. MEC estimates expenses to be 18% of cost and it must maintain a markup on selling price of 35%. 1. What is the cost of backpack? 2. What is the markup amount? 3. What is the regular unit selling price for the backpack? 4. What profit will Mountain Equipment Co-op realize? 5. What happens to the profits if it sells the backpack at the MSRP instead?
The cost of backpack is $38.97. The markup amount is $13.64. The regular unit selling price for the backpack is $52.61
Mountain Equipment Co-op will be $19.02.The profit will be $19.02, which is higher than the profit of $6.63 when selling at the regular unit selling price.
To find the cost, markup amount, regular unit selling price, and profit for the backpack, we need to use the following formulas:
1. Cost = List Price - Trade Discount - Quantity Discount
2. Markup Amount = Cost × Markup Percentage
3. Regular Unit Selling Price = Cost + Markup Amount
4. Profit = Regular Unit Selling Price - Cost - Expenses
Let's plug in the given values and calculate each of these:
1. Cost = $59.95 - ($59.95 × 0.25) - ($59.95 × 0.10) = $59.95 - $14.99 - $5.99 = $38.97
2. Markup Amount = $38.97 × 0.35 = $13.64
3. Regular Unit Selling Price = $38.97 + $13.64 = $52.61
4. Profit = $52.61 - $38.97 - ($38.97 × 0.18) = $52.61 - $38.97 - $7.01 = $6.63
Now, if MEC sells the backpack at the MSRP (Manufacturer's Suggested Retail Price), the profit will be different. The MSRP is typically higher than the regular unit selling price, so the profit will be higher as well. Let's say the MSRP is $65. The profit would be:
Profit = MSRP - Cost - Expenses = $65 - $38.97 - ($38.97 × 0.18) = $65 - $38.97 - $7.01 = $19.02
So, if MEC sells the backpack at the MSRP, the profit will be $19.02, which is higher than the profit of $6.63 when selling at the regular unit selling price.
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The cylinder below has a height of 31mm and a volume of 4700mm. Work out the radius of the cylinder. If your answer is a decimal, give it to two decimal places
Answer:
4700=πr²×31
4700/31=πr²
151.6.../π=r²
√151.6.../π=
6.946933566=r
r=6.95mm
Explain:
Volume of cylinder=
πr²×height
HELP ME!! i don't really understand this!
Answer:
Step-by-step explanation:
lol sorry I know it but don’t know how up to right it sorry
OC EXPLANATION Two inequalities joined by the word and or the word or form a compound inequality. To solve the compound inequality, we first solve each inequality. 3u-2<=-14 or 4u+4<28
The solution to the compound inequality 3u-2<=-14 or 4u+4<28 is u<=-4 or u<6.
Determine the compound inequalityA compound inequality is an equation that combines two inequalities with the word "and" or "or".
To solve a compound inequality, we need to solve each inequality separately and then combine the solutions.
For the compound inequality 3u-2<=-14 or 4u+4<28, we will solve each inequality separately.
First, we will solve 3u-2<=-14: 3u-2<=-14 3u<=-14+2 3u<=-12 u<=-4
Next, we will solve 4u+4<28:
4u+4<28 4u<28-4 4u<24 u<6
Now, we will combine the solutions.
Since the word "or" is used in the compound inequality, the solution is the union of the two solutions. This means that the solution is any value of u that satisfies either inequality.
The solution is u<=-4 or u<6. This can also be written in interval notation as (-∞,-4] U (-∞,6).
So, the solution to the compound inequality 3u-2<=-14 or 4u+4<28 is u<=-4 or u<6.
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(a) Show that if φ : G → G′ is a homomorphism of groups, then
H = ker(φ) has the property that NG(H) = G. (b) Conclude that if G = D2n =
⟨r, s |rn = s2 = 1, rs = sr−1⟩ for n > 2, then there does not exist a group homomor-
phism φ : D2n →G′ to another group G′ such that ker(φ) = {1, s}.
There does not exist a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}.
(a) To show that NG(H) = G, we need to show that every element of G normalizes H. Let g ∈ G, and let h ∈ H. Since H = ker(φ), we know that φ(h) = 1. Now, we need to show that ghg⁻¹ ∈ H. Using the properties of a homomorphism, we can write:
φ(ghg⁻¹) = φ(g)φ(h)φ(g⁻¹) = φ(g)1φ(g⁻¹) = φ(g)φ(g⁻¹) = φ(gg⁻¹) = φ(1) = 1
Therefore, ghg⁻¹ ∈ H, and so g normalizes H. Since this is true for any g ∈ G, we can conclude that NG(H) = G.
(b) Suppose there exists a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}. Since s ∈ ker(φ), we know that φ(s) = 1. However, we also know that rs = sr⁻¹, and so φ(rs) = φ(sr⁻¹). Using the properties of a homomorphism, we can write:
φ(r)φ(s) = φ(s)φ(r⁻¹) = φ(s)φ(r)⁻¹
Since φ(s) = 1, this simplifies to:
φ(r) = φ(r)⁻¹
But this means that φ(r) is its own inverse, and so φ(r)² = 1. However, we also know that rn = 1, and so φ(rn) = 1. Using the properties of a homomorphism, we can write:
φ(rn) = φ(r)ⁿ = (φ(r)²)ⁿ/2 = 1ⁿ/2 = 1
But this means that n/2 must be an integer, which contradicts the fact that n > 2. Therefore, there does not exist a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}.
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Capter 6a P(X < 8) = P(X < 8) O for all distributions. O for only continuous distributions. O for only discrete distributions. O for some discrete distributions but not all. Points possible: 1 Unlimited attempts. Submit
The correct answer is O for some discrete probability distributions but not all.
This is because the probability of a random variable X being less than 8 can vary depending on the type of distribution it follows. For some discrete distributions, such as a binomial distribution, the probability of X < 8 can be calculated by summing the probabilities of all possible values of X that are less than 8. However, for other discrete distributions, such as a Poisson distribution, the probability of X < 8 may not be as straightforward to calculate. Therefore, the statement that P(X < 8) = P(X < 8) is true for some discrete distributions but not all.
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5. 25 it takes gallons of paint to paint a fence. How much paint is needed for 3/5 of the fence?
Answer:
If 2.5 gallons of paint are needed for the entire fence, then for 1/5 of the fence we need:
2.5 gallons / 5 = 0.5 gallons
To find how much paint is needed for 3/5 of the fence, we can multiply 0.5 gallons by 3:
0.5 gallons * 3 = 1.5 gallons
Therefore, 1.5 gallons of paint are needed for 3/5 of the fence.
Answer:
15 gallons
Step-by-step explanation:
1/5 of the fence would be 5 gallons, because 25/5 is 5, so to find how much paint for 3/5, we have to multiply 3 and 5 which gives us 15. We need 15 gallons of paint to paint 3/5 of the fence
Hope it helped!
Which number line shows the solution to the inequality 5x-15>-65
The sοlutiοn tο the inequality is all values οf x greater than -10. This can be represented οn a number line as shοwn in the figure attached.
What is inequality?A cοnnectiοn between twο expressiοns οr values that is nοt equal in mathematics is referred tο as inequality. Hence, inequity results frοm imbalance. In mathematics, an inequality establishes the cοnnectiοn between twο nοn-equal numbers. Equality and inequality are nοt the same.
Use the nοt equal symbοl mοst frequently when twο values are nοt equal (). Values οf any size can be cοntrasted using a variety οf inequalities.
By changing the twο sides until just the variables are left, many straightfοrward inequalities may be sοlved.
Nοnetheless, a variety οf factοrs suppοrt inequality: Bοth sides' negative values are split οr added. Exchange the left and the right.
5x - 15 + 15 > -65 + 15
5x > -50
5x/5 > -50/5
x > -10
Because the inequality is severe, the οpen circle at -10 shοws that it is nοt part οf the sοlutiοn set (i.e., x must be greater than -10, nοt greater than οr equal tο -10).
The right arrοw shοws that the sοlutiοn set gοes οn fοrever in that directiοn.
Hence, the sοlutiοn tο the inequality is all values οf x greater than -10. This can be represented οn a number line as shοwn in the figure attached.
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The points H(8,1), I(7,-5), and J(1, -4) form a triangle. Find the desired slopes and lengths, then fill in the words that characterize the triangle. - slope of HI = ____ slope of IJ = ___ slope of HJ= ___
- length of HI = ___ length of IJ = ___ length of HJ = ___
Triangle HIJ is _______ Submit Answer = √__
slope of HI = 6, slope of IJ = -1/6, slope of HJ = 5/7, length of HI = √37, length of IJ = √37, length of HJ = √74, Triangle HIJ is isosceles
The slope of a line is found by the formula (y2-y1)/(x2-x1). The length of a line is found by the formula √((x2-x1)²+(y2-y1)²).
Slope of HI = (1-(-5))/(8-7) = 6/1 = 6
Slope of IJ = (-5-(-4))/(7-1) = -1/6
Slope of HJ = (1-(-4))/(8-1) = 5/7
Length of HI = √((8-7)²+(1-(-5))²) = √(1²+6²) = √(1+36) = √37
Length of IJ = √((7-1)²+(-5-(-4))²) = √(6²+(-1)²) = √(36+1) = √37
Length of HJ = √((8-1)²+(1-(-4))²) = √(7²+5²) = √(49+25) = √74
Triangle HIJ is isosceles because it has two sides with the same length (HI and IJ).
- slope of HI = 6
- slope of IJ = -1/6
- slope of HJ = 5/7
- length of HI = √37
- length of IJ = √37
- length of HJ = √74
Triangle HIJ is isosceles
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Perri will be able to purchase a condominium by making a 7% down payment on its $364,000 purchase price. She estimates her closing costs to be 4.5% of the
purchase price. What total amount will Perri need when she gets the keys for the house at closing?
O $4,052,173.91
O $466,000.12
O $41,860
O $465,999.89
The total amount will Perri need when she gets the keys for the house at closing is $41,860.
Estimation and Percentages
Perri is making a 7% down payment on the $364,000 purchase price of the condominium, so her down payment will be
0.07 x $364,000 = $25,480.
Perri estimates her closing costs to be 4.5% of the purchase price, which is 0.045 x $364,000 = $16,380.
Therefore, the total amount Perri will need when she gets the keys for the house at closing is the sum of the down payment and the closing costs, which is $25,480 + $16,380 = $41,860.
So the answer is (C) $41,860.
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What is DC? please i am about to fail
The length of DC is √102, which is the simplest radical form.
How to find the required sideThe proportion of corresponding sides in similar triangles is the same. This is known as the similar triangles theorem.
In other words, if two triangles are similar, then the ratio of the lengths of any two corresponding sides is the same.
Since DE is parallel to AB, we can use similar triangles to set up the following proportion:
DC/AC = DE/AB
Substituting the given values, we get:
DC/17 = 6/AB
Since AB is the same length as DC, we can replace AB with DC:
DC/17 = 6/DC
Cross-multiplying and simplifying, we get:
DC^2 = 17 * 6
DC^2 = 102
DC = √102 in simplest radical form
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who knows, What is the area of a cross section that passes through the center of a sphere with a diameter of 7 centimeters? Express your answer in terms of π.
The area of a cross section that passes through the center of a sphere with a diameter of 7 centimeters will be 12.25π cm².
What is A sphere ?Three-dimensional objects with a sphere-like shape exist in all three dimensions. Three axes, the x-axis, y-axis, and z-axis, are used to define the sphere. The key distinction between a circle and a sphere is this. In contrast to other 3D shapes, a sphere lacks any vertices or edges.
The sphere's points are evenly spaced apart from one another on its surface. In light of this, the sphere's surface and core are always equally separated from one another. The sphere's radius is the measurement between these points. Ball, globe, planets, and other objects are all examples of spheres.
Given : Diameter of Sphere = 7 cm
∴ Radius = 7/2 = 3.5 cm.
Since It is a cross section in a sphere, so, it would be circle.
So, Area of the cross section = Area of circle
Hence, Area of Cross section = πr²
= π (3.5)²
= 12.25π cm²
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At the football team banquet, 60 out of the 80 people attending had dessert with their dinner. What percent of the attendees had dessert?
The percentage of the attendees that had dessert at the football team banquet is 75%.
What percent of the attendees had dessert?Percentage is simply number or ratio expressed as a fraction of 100.
It is expressed as;
Percentage = ( Part / Whole ) × 100%
To find the percentage of attendees who had dessert, we can use the formula:
Percentage = (part/whole) x 100%
where:
part = the number of attendees who had dessert = 60whole = the total number of attendees = 80Substituting the given values, we get:
percentage = (60/80) x 100%
percentage = 0.75 x 100%
percentage = 75%
Therefore, 75 perecent of the attendees had dessert.
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Item 6
Write a unit rate for the situation.
Situation: 20 bracelets in 5 hours
Unit rate: ____bracelets per hour
Answer: 4 bracelets per hour
Step-by-step explanation:
You're basically finding the amount made in one hour instead of 5, so we just use an equation:
20 = 5x
x = 4
4 are made in an hour. Hope this helps!
9.9=3.1 - 3.4x solve for x
Answer:
x = -2.
Step-by-step explanation:
9.9 = 3.1 - 3.4x
9.9 - 3.1 = -3.4x
6.8 = -3.4
6.8 /-3.4 = -3.4/-3.4
-2 = x
How many people live in south african house- holds? to find out, we collected data from an srs of 48 out of the over 700,000 south african students who took part in the censusatschool survey proj- ect. The mean number of people living in a house-
Based on the sample of the 48 South African households collected from the Census At School survey project, the mean number of people living in a household will be 6.208, and the standard deviation is 2.576.
However, it is important to note that this sample only represents a small fraction of the total number of the households in South Africa, so we cannot make definitive conclusions about the entire population based on this sample alone.
To get a more accurate estimate of the number of people living in the South African households, a larger and the more representative sample would need to be collected.
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Bank of America charges $22 for each overdraft check. Kelsie has $370 in her account. She recently wrote checks for $46, $82, $264, and $127.
How much does she owe the bank including any overdraft charges?
Answer:
Step-by-step explanation:
Kelsie has written checks for a total of $46 + $82 + $264 + $127 = $519.
Since she only has $370 in her account, this means she has overdraft by $519 - $370 = $149.
Therefore, the bank will charge her $22 for each overdraft, which gives a total of $22 * 7 = $154.
Thus, Kelsie owes the bank a total of $519 + $154 = $673. Answer: \boxed{673}.
Write a recursive definition for the following function. f(1)=500, f(2)= 100, f(3)= 20
The recursive definition for the function f given by f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3 is a definition that describes how the value of f for a given x can be calculated from its inputs.
What is a recursive definition?A recursive definition of a function is when the definition of the function involves the function itself. This type of definition is used to express complex operations in a simpler form. It is an effective way to break down a complicated problem into simpler, manageable parts. It allows us to define a set of rules in terms of smaller versions of itself, which can then be worked out using a series of steps.
A recursive definition for the function f is a process by which the value of f for a given input can be defined in terms of the values of f for smaller inputs. In other words, a recursive definition for f is a definition that describes how f can be calculated from its inputs.
In this case, the recursive definition for the function f is given by:
f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3
This means that the value of f for a given x can be calculated by multiplying 500 (the value of f for x = 1) by 1/5 raised to the power of x-1. This is because f(1) = 500, f(2) = 100 (1/5 * 500), and f(3) = 20 (1/5 * 1/5 * 500).
This recursive definition can also be expressed in a more general form as:
f(x) = a * b⁽ˣ⁻¹⁾, for x = 1, 2, 3
Where a and b are constants. In this case, a is 500 and b is 1/5.
In conclusion, the recursive definition for the function f given by f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3 is a definition that describes how the value of f for a given x can be calculated from its inputs. This definition can also be expressed in the more general form of f(x) = a * b⁽ˣ⁻¹⁾, for x = 1, 2, 3.
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30 persons reap a field in 17 days. How much more people should be engaged to reap the same field in 10 days
The extra number of people that should be engaged to reap the field in 10 days is given by A = 21 people
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the extra number of people that should be engaged to reap the field in 10 days be represented as A
Now , the number of people that should be engaged to reap the field in 10 days = n
The number of people that can reap the field in 17 days = 30 persons
So , the proportion is
30 x 17 = n ( 10 )
On simplifying , we get
Divide by 10 on both sides , we get
n = ( 30 x 17 ) / 10
n = 3 x 17
n = 51
And , the number of extra persons A = n - 30
So , the extra number of people that should be engaged to reap the field in 10 days A = 21 people
Hence , the proportion is A = 21 people
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The concept time and work is used here to determine the number of people required to reap the same field in 10 days. The number of people required is 51.
What is time and work?The time and work represents the time taken by an individual or a group of individuals to complete a piece of work and the efficiency of the workdone by each of them.
If 30 persons can reap a field in 17 days
1 person can reap = 30 × 17 = 510 days
In 10 days, number of persons needed = 510 / 10 = 51 persons
Thus 51 persons can reap the field in 10 days.
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HELP HELP HELP
a student divided 3p^4-8x^2-11x+1 by x-2 using LONG DIVISION. Where did they go wrong?
First step is wrong (x-2) × 3x³ should be 3x⁴ - 6x³
not 6x²
The amount of merchandise (in millions) that store A sold can be represented by A = 13x squared + 8x - 3. The amount of merchandise (in millions) that store B sold can be represented by B = 8x squared - 3x + 11. Find the total amount of merchandise that stores A and B sold.
The total amount of merchandise that stores A and B sold is 21x²+5x+8
What is equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example, 3x + 5 = 15.
Given that, are two stores selling merchandise given by equation,
A = 13x²+8x-3 and B = 8x²-3x+11, we need to find the total amount of merchandise that stores A and B sold.
We add both the equations to find the same,
Total merchandise sold = 13x²+8x-3 + 8x²-3x+11
= 21x²+5x+8
Hence, the total amount of merchandise that stores A and B sold is 21x²+5x+8
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The number of coins in a person's collection changes based on buying, selling, and trading coins. A function defined as f(t) = t³ - 6t² + 9t
is modeled by the table, which represents the number of coins in the coin collection t years since the person began collecting coins.
(Picture has the rest of the problem)
The statements that are true about the function when graphed on a coordinate plane include the following:
C. The relative minimum of the function is (3, 0)
E. When t > 3, the function is increasing.
How to determine the minimum and maximum function?In order to determine the minimum and maximum of this function, we would have to determine the critical points where the derivative of the function is equal to zero or undefined, and then evaluate the function at these critical points and at the endpoints of the interval.
By taking the first derivative of the given function and factorizing, we have:
f(t) = t³ - 6t² + 9t
f'(t) = 3t² - 12t + 9
3t² - 12t + 9 = 0
t² - 4t + 3 = 0
(t - 3)(t - 1) = 0
t = 3 and t = 1
Therefore, the critical points of the function are at t = 1 and t = 3.
By taking the second derivative of the given function and factorizing, we have:
f''(t) = 6t - 12
At point t = 1, we have:
f''(1) = 6(1) - 12 = -6 (it is less than zero).
Therefore, f(t) has a local maximum at t = 1.
At point t = 3, we have:
f''(3) = 18 - 12 = 6 (it is greater than zero).
Therefore, the function f(t) has a local minimum at t = 3.
At t = 4, f''(4) = 24 - 12 = 12
At t = 5, f''(5) = 30 - 12 = 18
In conclusion, the relative minimum of the function is (3, 0) and when t > 3, the function would increase.
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