Using addition of polynomials, it is found that:
a) The total amount is: T(t) = -0.028t³ - 0.32t² + 1.6t + 59.
b) $55.5 million was spent on buying new and used vehicles in the fifth year.
How do we add polynomials?To add polynomials, we have to combine the like terms, that is, the terms that have t elevated to the same power.
For this problem, the functions are given as follows:
N(t) = -0.028t³ + 0.06t² + 0.1t + 17.U(t) = -0.38t² + 1.5t + 42.Hence the total amount is:
T(t) = N(t) + U(t)
T(t) = -0.028t³ + 0.06t² + 0.1t + 17 - 0.38t² + 1.5t + 42.
T(t) = -0.028t³ + (0.06 - 0.38)t² + (0.1 + 1.5)t + 17 + 42.
T(t) = -0.028t³ - 0.32t² + 1.6t + 59.
For the 5th year, the amount is given by:
T(5) = -0.028(5)³ - 0.32(5)² + 1.6(5) + 59 = 55.5.
$55.5 million was spent on buying new and used vehicles in the fifth year.
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If m angle A=5x +29 then what is the smallest integer value of x for which angle A would be classified as obtuse
The smallest integer value of x for which angle A would be classified as obtuse is 14°
What is an obtuse angle?An obtuse angle can be defined as an angle that is greater than 90 degrees.
This can be expressed as;
Obtuse angle > x > 90°
Given the angle as A = 5x +29
Let's assume that the value of the obtuse angle is 99 which is greater than 90 degrees.
Now, we have to equate the expression for angle A to 91 degrees.
We have;
5x + 29 = 99
collect like terms
5x = 99 - 29
subtract like terms
5x = 70
To make 'x' the subject, divide both sides by the coefficient of x
5x/5 = 70/5
x = 14°
Thus, the smallest integer value of x for which angle A would be classified as obtuse is 14°
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At the city museum, child admission is $5.50 and adult admission is $9.60. On Saturday, four times as many adult tickets as child tickets were sold, for a total
sales of $1141.40. How many child tickets were sold that day?
Number of child tickets:0
5
The number of child tickets sold that day were 26.
Here, we are given that the fees for admission into the museum is as follows-
Child admission = $5.50
Adult admission = $9.60
Let the number of children admitted on Saturday be x
then the number of adults admitted that day = 4x
Now, the total money from sale of children tickets = $5.50x
the total money from sale of adult tickets = $9.6 × 4x = $38.4x
The total money from sale of tickets = $1141.40
⇒ 5.50x + 38.4x = 1141.40
43.9x = 1141.40
x = 1141.40/ 43.9
x = 26
Thus, the number of child tickets sold that day were 26.
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Pls Helppp need it now
Answer:
down one over two( point on -8 then down one over two
Step-by-step explanation:
this might be the right answer please let me know
QUESTION BELOW SLOVE USING NTH TERM!
I found this
im using T for tails and H for heads
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
MOVE 1# TTTT
MOVE 2#THHH
MOVE 3#HTTH
MOVE4#HHHT
MOVE5#TTTH
end up like =HHHH
HOW DO I WRITE THIS OUT FOR NTH TERM.
THE QESTION IS BELOW! WILL GET 100 POINTS! PLEASE HELP BEEN STUCK ON THIS FOREVER!
Answer:
thanks bro bro
Step-by-step explanation:
anyways you gotta to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
Determine the percent change in the price of an item that was selling for $230.00 last
year, and is being sold for $184.00 this year.
Round to the nearest given place.
1.80949 thousandths
Answer:
1.809
Step-by-step explanation:
Beacuse 4 is less than 5, the number round down.
I think the answer is 1.809 though im not sure
Multiply the fractions. Select the answer that is in simplest form.
5x1 1/9
The product of the numbers 5 and [tex]1 \frac{1}{9}[/tex] will be equal to the fractional number 50/9.
What is multiplication?It is also known as the product. If the object n is given to m times then we just simply multiply them.
The numbers are given below.
5 and [tex]1 \frac{1}{9}[/tex]
The product of the numbers 5 and [tex]1 \frac{1}{9}[/tex] will be
[tex]\rightarrow 5 \times 1 \dfrac{1}{9}[/tex]
⇒ 5 x 10 / 9
⇒ 50/9
The product of the numbers 5 and [tex]1 \frac{1}{9}[/tex] will be equal to the fractional number 50/9.
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Bob Ross bought a Blackberry on the Web for $90.49. He saw the same Blackberry in the mall for $120.21. How much did Bob save by buying on the Web?
Note: Round your answer to the nearest cent.
Answer:
$29.72
Step-by-step explanation:
$120.21-$90.49=$29.72
How many integers a satisfies |2a+7|+|2a−1] =8?
Answer:
3
Step-by-step explanation:
given f(x)=3(4-x) what is the value of f(-2)
WHats this-2 1/6+(-2/3)
its 150/230, again the answer is -709/216
again the answer is -377/008. alright hope I helped you out with your question you have stated.
in Zoe's class, 4/5 of the students have pets. Of the students who have pets, 5/8 have rodents. what fraction of the students in Zoe's class have pets that are rodents?
Answer:
1/2
Step-by-step explanation:
5/8 students of the 4/5 students have rodents. The word "of" tells us to multiply. 5/8 * 4/5 is equal to 5*4/8*5, which is 20/40 and therefore simplifies to 1/2.
If Rachel were to paint her living room alone, it would take 2 hours. Her sister Fran could do the job in 5 hours. How many hours would it take them working together?
Express your answer as a fraction reduced to lowest terms, if needed.
Rachel and her sister Fran together can paint the living room in [tex]\frac{10}{7}[/tex] hours
Given that
Rachel can paint half of the living room in 1 hour
Fran can paint [tex]\frac{1}{5}[/tex]th part of the living room in 1 hour
Let's assume together they paint the living room in x hours
⇒ together they can paint [tex]\frac{1}{x}[/tex]th part of the living room in 1 hour
By proportions,
⇒[tex]\frac{1}{2}[/tex]+[tex]\frac{1}{5}[/tex]= [tex]\frac{1}{x}[/tex] {using operation proportions and addition}
⇒[tex]\frac{7}{10}[/tex]=[tex]\frac{1}{x}[/tex]
⇒x=[tex]\frac{10}{7}[/tex]
⇒ together they can paint [tex]\frac{7}{10}[/tex]th part of the living room in 1 hour
It means, Rachel and her sister Fran together can paint the living room in [tex]\frac{10}{7}[/tex] hours
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Sacha picked some apples from a tree in her garden. She then gave some to her friends. To her
first friend, she gave half the apples she had, plus 2 more. To her second friend, she gave half the apples she had left, plus 2 more. And she did the same thing for her third friend. After giving away all these apples, she had 1 apple left. Find how many apples she originally pick from the tree.
Step-by-step explanation:
x = apples picked from the tree
x1 = x/2 + 2
x2 = (x - x1)/2 + 2 = (x - (x/2 + 2))/2 + 2 =
= (x - x/2 - 2)/2 + 2 = (x/2 - 2)/2 + 2 =
= x/4 - 1 + 2 = x/4 + 1
x3 = (x - x1 - x2)/2 + 2 = (x - (x/2 + 2) - (x/4 + 1))/2 + 2 =
= (x - x/2 - 2 - x/4 - 1)/2 + 2 =
= (x/4 - 3)/2 + 2 = x/8 - 3/2 + 2 = x/8 + 1/2
x - x1 - x2 - x3 = 1
x - x/2 - 2 - x/4 - 1 - x/8 - 1/2 = 1
x/8 - 3 - 1/2 = 1
x/8 = 4 1/2 = 9/2
x = 9×8/2 = 9×4 = 36
she had originally 36 apples
x1 = 20
x2 = 10
x3 = 5
What two "rules" govern sets, and what do they imply about the nature of sets?
Two of some of the rules that govern set are:
Universality: This implies all the elements in the setintersection: This means similar elements between sets comparedWhat is universal set?The term universal set is used in set to refer to all the elements in the set that is determined, This means that any other set has their elements in the universal set, hence other sets are members of the universal set. The universal set is the set from which other sets are generated from.
What is intersect in set?Intersect as used in set refers to elements that can be seen in two or more sets that are being compared. If two sets has no intersection, then then do not have elements alike,
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My bill is normally $90 but has gone up to $108 what is the percentage it went up by
Answer:
it went up 20%
Step-by-step explanation:
If a company decides to hire more employees, then its
a. total variable cost and total cost will increase, but its total fixed cost will not change.
b. total fixed cost will increase, its total variable cost will decrease, and thus its total cost will not change.
c. total cost will increase, and its total fixed cost and total variable cost will decrease.
d. total cost will increase and total fixed cost will decrease, thus its total variable cost will not change.
If a company decides to hire more employees, then its:(a).total variable cost and total cost will increase, but its total fixed cost will not change
What is the behavior of fixed and variable costs?
The fixed cost remains the same over a reasonable range of output whereas the variable cost is the cost that increases as output increases, such as the cost of raw materials, the more output produced, more materials would be needed.
In short, the variable increase would make the total cost, the sum of fixed cost and variable cost, to increase, so hiring more employees, would increase variable cost and total cost only.
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Help me on this question please.
Answer:
67.5
Step-by-step explanation:
Hope this Helps! Be sure to study this so you get it you really just need to subract!
Which point is a reflection of Z (5 1/2, 3) across the x-axis
The reflection of Z (5 1/2, 3) across the x-axis is (5 1/2, -3).
Here,
The given point is Z (5 1/2, 3).
We have to find the point of reflection of Z (5 1/2, 3) across the x-axis.
What is Reflection across x-axis?
A point after reflection across the x-axis, the x- coordinate remains the same but y - coordinate is taken to be the additive inverse.
Now,
Since, The given point Z (5 1/2, 3) is lie on first coordinate.
Hence, The reflection of the point Z (5 1/2, 3) is lie on the third coordinate.
And, In the third coordinate the x-coordinate is positive and y-coordinate is negative.
Since, The rule of the reflection across x- axis is,
(x, y) → (x, -y)
So, The reflection of the point Z (5 1/2, 3) across the x - axis = (5 1/2, -3)
Therefore, The reflection of Z (5 1/2, 3) across the x-axis is (5 1/2, -3).
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Please help I can’t solve 14,15,16
Answer:
chcicken
Step-by-step explanation:
A spaceship has a mass of 9000kg. The spaceship is launched from Earth and lands on a distant planet, where it has a gravity of 25 m/s2. What is the weight?
The weight of the spaceship that has a mass of 9000kg is 22936kg.
How to illustrate the information?It should be noted that the mass in a body simply means the measure of the quantity if the matter that the body has.
It should be noted that it is also the body of the inertia.
In this case, the spaceship has a mass of 9000kg. The spaceship is launched from Earth and lands on a distant planet, where it has a gravity of 25 m/s². Therefore, the weight will be:
= 9000 /9.81 × 25
= 22936kg
Therefore, the weight of the spaceship that has a mass of 9000kg is 22936kg.
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TASK CARD 17
Half of a number increased by six is
15. What is the number?
The number is 18
Let x be the number
Half of a number = x/2
Half of a number is increased by 6 = x/2 + 6
Half of a number increased by 6 is 15 = x/2 + 6 = 15
Algebra: The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division.
Solving the equation we get:
= (x + 12)/2 = 15
= x + 12 = 30
x = 18
Hence, the number is 18
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Residents of city voted on whether to raise property taxes. The ratio of yes votes to no votes was 3 to 2. If there were 1748 no votes, what was the total number of votes
tbh only answer if you are the user "beinggreat78" I dont trust the rest of yall
Answer:
hi ik you dont trust me however id like to say that the answer is A. 41.6
Step-by-step explanation:
hope this helps <3 (also i put this into a calculator to double check my work and it was still 41.6)
Answer:
41.6
Step-by-step explanation:
Move the decimal 1 place to the right according to the laws of exponents.
since the exponent is 1, that's why we move it 1 place right. if the exponent was -1, it would go to the left, and the number would become "0.416".
14 less than the product of two and number 16
Answer:
18
Step-by-step explanation:
(2 x 16) - 14 = 32 - 14 = 18
Does the given matrix, A, have an inverse? If it does, what is A-¹? (1 point)
The inverse of a matrix A is A^-1. And I, the identity matrix, is equal to A.A^-1.
The square matrix needs to be non-singular and have a non-zero determinant value in order to get the inverse matrix. Let's think about the 2 x 2 square matrix A.
Inverse of matrix:
A^(-1)=Adj A/|A|
A-1 stands for Inverse of Matrix for matrix A. There is a straightforward formula for calculating the inverse of a 2 × 2 matrix. In order to find the inverse of a matrix of order 3 or higher, we also need to be aware of the matrix's determinant and adjoint. When multiplied by the provided matrix, the other matrix that serves as the inverse of that matrix yields the multiplicative identity.
There are two ways to find a matrix's inverse. Through the use of an adjoint of a matrix and simple processes, it is possible to derive the inverse of a matrix. Row or column transformations can be used to carry out the basic operations on a matrix. Additionally, the adjoint and determinant of the matrix can be used to apply the inverse of matrix formula in order to get the inverse of a matrix.
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3. Bryan spent $13.00 of the $25.00 he got for his birthday. What decimal represents the fraction of birthday money Bryan spent?
===================================================
Explanation:
Use your calculator to type in either 13/52 or 13 ÷ 52
The calculator should display 0.52 as the answer. The decimal 0.52 converts to 52%
The steps for the long division are shown below.
Ahmad and Dante wash cars in the neighborhood and charge $5 per car. Last year, they worked very hard and were able to wash 450 cars in the year. They have done a little market research and found that for every $0.20 that the price is reduced, they can get 50 more customers.
How much did Ahmad and Dante earn last year?
The amount earned by Ahmad and Dante as at last year as required in the task content is; $2,250.
In order words, the total amount of money which was both earned by Ahmad and Dante is $2,250.
What is the amount earned by Ahmad and Dante last year according to the task content?
It follows from the task content that the amount earned by Ahmad and Dante last year is to be determined.
Since, the charge was still $5 per car last year and the washed 450 cars.
Their total earnings last year is therefore;
= 450 × $5
= $2,250.
Ultimately, they earned $2,250 last year from washing cars.
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Find the length indicated FIND IK HELP
Answer:
Here is the answer, let me know if I did it wrong.
Answer:
IK = 13 and x = - 12
Step-by-step explanation:
Let's write down each segment and if available express it in terms of x which has to be determined in order to find length of segment IK
We have IK = x + 25 (to be determined)
JK = 2x + 30 (1)
KL (unknown)
IL = x + 34 (2)
JL = 15 (3)
The entire segment
IL = IJ + JL
Substituting for JL = 15 we get IL = IJ + 15
But we are given IL = x + 34
IJ + 15 = x + 34
IJ = x + 34 -15 = x + 19 (4)
IK = IJ + JK
Substituting for IJ = x + 19 from equation (4) and JK = 2x + 30 from equation (1) we get IJ + IK = x + 19 + 2x + 30 = 3x + 49
But we are given that IK = x + 25
So
3x + 49 = x + 25
Moving x from the RHS to the LHS and 49 from the LHS to the RHS we get
3x-x = 25 - 49
2x = -24
x = -12
IK = -12 + 25 = 13
We can verify this by finding the lengths of each segment and seeing they are consistent
We have
IJ = x + 19 = -12 + 19 = 7
JK = 2x + 30 = 2(-12) + 30 = -24 + 30 = 6
IL = x + 34 = -12 + 34 = -23
We also have the fact that JK + KL = JL = 15
Substituting for JK we get
6 + KL = 15
KL = 15-6=9
Total segment length = 7+6 + 9 = 22
x + 34 = -12 + 34 = 22
So it is consistent
Katrina practices violin 4 times per week for 2/3 hour each time.Jeremy practices guitar for 3 times per week for 45 minutes each time.who practices more each week?how much more?
Katrina practices violin per week more than Jeremy by 25 minutes.
How is the practice time determined?The practice time can be determined by converting the fractional hours to minutes for each practice so that like is compared to like.
Converting 2/3 hours gives 40 minutes.
Ordinarily, Jeremy spends more time each time than Katrina. However, Katrina adds an additional practice time, which heightens her total practice time each week.
Data and Calculations:The number of times that Katrina practices per week = 4 times
The time she practices each time = 2/3 hours or 40 minutes (2/3 x 60)
The total time she practices each week = 160 minutes (40 x 4)
The number of times that Jeremy practices per week = 3 times
The time he practices each time = 45 minutes or 3/4 hours
The total time he practices each week = 135 minutes (45 x 3)
The difference in practice time per week = 25 minutes (160 - 135)
Katrina Jeremy
Number of practices times 4 3
Minutes practiced (2/3 hours) 40 min 45 minutes
Total practice time 160 min 135 min
Thus, we can conclude that Katrina practices violin per week more than Jeremy by 25 minutes.
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