You have studied polynomials consisting of constants and/or variables combined by addition or subtraction. The variables may include exponents. The examples so far have been limited to expressions such as 5x4 + 3x3 – 6x2 + 2x containing one variable, but polynomials can also contain multiple variables. An example of a polynomial with two variables is 4x2y – 2xy2 + x – 7.
Many formulas are polynomials with more than one variable, such as the formula for the surface area of a rectangular prism: 2ab + 2bc + 2ac, where a, b, and c are the lengths of the three sides. By substituting in the values of the lengths, you can determine the value of the surface area. By applying the same principles for polynomials with one variable, you can evaluate or combine like terms in polynomials with more than one variable.
The product of (7x²y³) and (3x⁵y⁸) is obtained by multiplying the coefficients and adding the exponents of like terms, resulting in c) 21x⁷y¹¹.
To find the product of the two algebraic expressions (7x²y³) and (3x⁵y⁸), we simply multiply the coefficients and add the exponents of corresponding variables:
Multiply the coefficients: 7 * 3 = 21
Add the exponents of x: x² * x⁵ = x²⁺⁵ = x⁷
Add the exponents of y: y³ * y⁸ = y³⁺⁸ = y¹¹
Therefore, the product is 21x⁷y¹¹, which corresponds to option (c).
A bank's monthly charge for maintaining an account is $.45 for each check written plus a service charge of $12.50. If x represents the number of checks written during the month, which function models this situation?
A) f(x) = x + 12.50
B) f(x) = 0.45x -12.50
C) f(x) = 12.50x + 0.45
D) f(x) = 0.45x + 12.50
The correct model for the bank service cost based on the number of checks written during a month is f(x)=0.45x + 12.50.
Explanation:The question is asking for a model that would represent the cost of a bank service based on the number of checks written during a month. The bank charges $0.45 for each check, which is a variable cost that will change depending on the number of checks, represented by x. Additionally, they also have a monthly fixed service charge of $12.50, which is paid regardless of whether or not a check is written that month.
So, the amount paid every month is $0.45 multiplied by the number of checks, plus $12.50. In function format, that will be represented as $0.45x + $12.50, which is equivalent to the option D i.e f(x)=0.45x + 12.50. So, the correct model for the situation is D.
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The area of the blue triangle, which is one-half times a base of 47 million times a height of $37.89.
A gymnasium can hold no more than 650 people. A permanent bleacher in the gymnasium holds 136 people. The event organizers are setting up 25 rows with an equal number of chairs. At most, how many chairs can be in each row?
A child designs a flag in the shape of a rhombus, as shown in the diagram below. Which expression can be used to determine the side length of the rhombus?
Answer:
A
Step-by-step explanation:
10/cos30 degree
A number has the digits 9 and 7. To the nearest 10, the number rounds to 100. what is the number?
Answer:
97
Step-by-step explanation:
The digits formed by 9 and 7 (without repetition) are 79 and 97. In rounding off a number to the nearest tens, the number in the unit position is considered.
If that number is less than 5, it is changed to 0. However, where the number is above 5, 1 is added to the number in the tens place with the number in the unit place changed to 0.
Going by the above explanation, 79 rounds off to 80 while 97 rounds off to 100.
which ratio is equivalent to 10 : 85
20/170
2/15
5/42
20/95
The volume of a cylinder is given by the formula mc021-1.jpg, where r is the radius of the cylinder and h is the height. Which expression represents the volume of this cylinder? r=x-3 h=2x+7
It can be express as follows: v = π(2x³- 5x²- 24x + 63) cubic unit
The volume of a cylinder is given as follows
volume = πr²h
where
h = height
r = base radius
Therefore,
r = x - 3
h = 2x + 7
Therefore,
The volume can be express as follows
v = π × (x-3)² × (2x + 7)
v = π × x² - 6x + 9 ×(2x + 7)
v = π × 2x³- 12x² + 18x + 7x² - 42x + 63
v = π × 2x³- 5x²- 24x + 63
v = π(2x³- 5x²- 24x + 63) cubic unit
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Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = –6. Which function could Heather be writing?
Heather's quadratic function must have a double root at x = -6, suggesting a function of the form y = a(x + 6)² here 'a' is a nonzero coefficient. The orientation and width of the parabola depend on the value of 'a'.
Since Heather's quadratic function represents a parabola that touches but does not cross the x-axis at x =
–6, her function must have a double root at x= –6. To achieve this, the quadratic function should be in the form y = a(x + 6), where a is a non-zero coefficient.
The function that Heather could be writing will have a vertex at the point (-6, 0), as the parabola touches the x-axis at this point. Thus, a possible function can be y = (x + 6), if we assume a coefficient of 1 for simplicity. If a is negative, the parabola will open downwards, while a positive a will make the parabola open upwards. However, the exact value of a will depend on other conditions Heather might have, such as the position of the parabola in relation to the y-axis or specific points it must pass through.
Charlie is trying to hold on to his toy fire truck.
His brother Noah is pulling with a force of 8 N on a bearing of 023° and his brother Jude with a force of 5 N on a bearing of 155°.
What force does Charlie need to exert to keep the toy in equilibrium?
If you could explain it using Cartesian vectors, that would be the best.
Charlie needs to apply a force in the opposite direction of the resultant vector sum of his brothers' forces. By converting the forces into Cartesian vectors based on the bearings, we can calculate the components of Charlie's required force to maintain equilibrium.
Explanation:Step 1: Break down the forces into their x and y components
The force exerted by Noah can be broken down into its x and y components using the following equations:
F_x_Noah = F_Noah × cos(θ_Noah) = 8 N × cos(023°) ≈ 7.13 N
F_y_Noah = F_Noah × sin(θ_Noah) = 8 N × sin(023°) ≈ 3.71 N
The force exerted by Jude can be broken down into its x and y components using the following equations:
F_x_Jude = F_Jude × cos(θ_Jude) = 5 N × cos(155°) ≈ -4.95 N
F_y_Jude = F_Jude × sin(θ_Jude) = 5 N × sin(155°) ≈ -0.58 N
Step 2: Sum the x and y components of the forces
To find the net force in the x-direction, we sum the x-components of the forces exerted by Noah and Jude:
F_x_net = F_x_Noah + F_x_Jude ≈ 7.13 N - 4.95 N ≈ 2.18 N
To find the net force in the y-direction, we sum the y-components of the forces exerted by Noah and Jude:
F_y_net = F_y_Noah + F_y_Jude ≈ 3.71 N - 0.58 N ≈ 3.13 N
Step 3: Calculate the magnitude of the net force
The magnitude of the net force can be calculated using the Pythagorean theorem:
F_net = √(F_x_net^2 + F_y_net^2) ≈ √(2.18 N^2 + 3.13 N^2) ≈ 3.74 N
Step 4: Find the angle of the net force
The angle of the net force can be calculated using the following equation:
θ_net = atan(F_y_net / F_x_net) ≈ atan(3.13 N / 2.18 N) ≈ 55.6°
Step 5: Calculate the force Charlie needs to exert
In order for Charlie to keep the toy fire truck in equilibrium, he needs to exert a force that is equal in magnitude and opposite in direction to the net force. Therefore, the force Charlie needs to exert is 3.74 N at an angle of 55.6° + 180° = 235.6° (since the net force is acting in the third quadrant).
Dan and Dawn purchased a house for $69,500. They had to make a down
payment of 20%. How much was the amount of the mortgage they obtained?
a. $13,900
b. $69,500
c. $55,600
d. $76,450
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One canned juice drink is 2020% orange juice; another is 1010% orange juice. how many liters of each should be mixed together in order to get 1010l that is 1212% orange juice?
cristal's gross semimonthly salary is $2968.50. What is the maximum amount she can afford to borrow for a home mortgage?
A) $71,244
B)$124,336
C)$142,488
D)$154,362
Answer:
C) 142,488
Step-by-step explanation: by adding up here semimonthly, also took test.
The maximum amount she can afford to borrow for a home mortgage is: C)$142,488.
Home mortgageAn employees who receive semimonthly salary will get 24 (12months×2) paychecks per year as the salary is paid twice per year.
Using this formula
Maximum amount= Gross semimonthly salary×24 paychecks×2
Let plug in the formula
Maximum amount=($2968.50×24)×2
Maximum amount=$71,244×2
Maximum amount=$142,488
Inconclusion the maximum amount she can afford to borrow for a home mortgage is: C)$142,488.
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Jan has a box of magnets. She finds 21 more magnets. She now has a total of 33 magnets. How many magnets did Jan have to start?
12 magnets
21 magnets
45 magnets
33 magnets
I need help w/ this problem...please don't answer if you don't know and PLEASE answer as fast as you can...I'm desperate.
Using the formula v= l x w x h find the volume of a right rectangular prism when the length of the prism is 45cm the width is 12cm and height is 10cm
The volume of the right rectangular prism is 5400 cubic centimeter.
What is right rectangular prism?
A right rectangular prism is a three dimensional object with six faces, twelve edges, and eight vertices.
Formula for the volume of right rectangular prism:volume of right rectangular prism = length × width × height
According to the given question we have,
length of the prism = 45cm
width of the prism = 12cm
height of the prism = 10cm
Therefore,
The volume of the right rectangular prism = length × width × height
⇒ volume of prism = 45 × 12 × 10 = 5400 cubic centimeter.
Hence, the volume of the right rectangular prism is 5400 cubic centimeter.
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21x^3 - 2x^2 + 20x +11 / 7x+4
Factor this equation
Answer:
9x(x-3y)
Step-by-step explanation:
to factor, you need to take the greatest common factor out. with this one, the greatest common factors are 9 and x
answer would be...
9x(x-3y)
The distance between 2 points is found by ________ the x terms and squaring the result, _________ the y terms and squaring the result, taking the sum of the results and then finding the square root of the sum.
subtracting; subtracting
adding; adding
adding; subtracting
subtracting; adding
Answer:
A)
subtracting; subtracting
Step-by-step explanation:
Which is a way to borrow money from a bank or financial institution to pay for a car?
car loan
car lease
car rental
Complete the following statement of congruence: MON~= .
A. STR
B. TRS
C.RTS
D.RST
Answer:
∵ MON ≅ RTS
∴ The answer is C. RTS.
Step-by-step explanation:
When two triangles are congruent, they will have congruent pairs of vertices. Each vertex in one triangle will have a partner in the other triangle.
Congruent vertex pairsIf we look at ΔMON, we can see it is almost like a right triangle, with:
'M' as the almost-right angle;'O' at the end of the long side, and;'N' at the end of the short side.In the next triangle, each letter has to be in the same order as the congruent vertex in ΔMON.
This triangle is ΔRTS, with:
'R' as the almost-right angle;'T' at the end of the long side, and;'S' at the end of the short side.Thus, the pairs of congruent angles are:
M ≅ RO ≅ TN ≅ SWhen we write the statement of congruence, we order the letters by their congruent pair.
∴ MON ≅ RTS
Tell whether each sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a function rule to represent it. A. 128, 64, 32, 16, ... B. 3, 3.25, 3.5, 3.75, ...
to convert 45000 inches into miles which two ratios could you multiply by
What are the first 35 digits of pi?
Here are the first 3000 digits of pi.
3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 003137838752886587533208381420617177669147303598253490428755468731159562863882 353787593751957781857780532171226806613001927876611195909216420198938095257201 065485863278865936153381827968230301952035301852968995773622599413891249721775 283479131515574857242454150695950829533116861727855889075098381754637464939319 255060400927701671139009848824012858361603563707660104710181942955596198946767 837449448255379774726847104047534646208046684259069491293313677028989152104752 162056966024058038150193511253382430035587640247496473263914199272604269922796 782354781636009341721641219924586315030286182974555706749838505494588586926995 690927210797509302955321165344987202755960236480665499119881834797753566369807 426542527862551818417574672890977772793800081647060016145249192173217214772350 141441973568548161361157352552133475741849468438523323907394143334547762416862 518983569485562099219222184272550254256887671790494601653466804988627232791786 085784383827967976681454100953883786360950680064225125205117392984896084128488 62694560424196528502221066118630674427862203919494504712
Turning of the water while brushing your teeth saves 379 centiliters off water . how many liters of water can you save if you turn of the water while you brush three times'
Which point is on the line that passes through (0,6) and is parallel to the given line
Points depends on the value of slope for the parallel line y = m₁ x + 6.
What are parallel lines?
" Parallel lines defined as two different lines lie in the same plane and never intersect with each other in that plane. Distance between parallel lines remain constant."
According to the question,
Let y = m₁ x + d be the given line.
Slope of parallel lines are equal and line passes through (0, 6)
Therefore,
6 = m₁ (0) + d
⇒ 6 = d
Required line parallel to the given line is
y = m₁ x + 6
Hence, points depends on the value of slope for the parallel line
y = m₁ x + 6.
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Factor the trinomial
x^2 − 7x + 10
What is the factored form of the trinomial, and why?
A. (x−2)(x−5). The product of –2 and –5 is –10, and their sum is 7.
B. (x−2)(x−5). The product of –2 and –5 is 10, and their sum is –7.
C. (x+2)(x+5). The product of 2 and 5 is 10, and their sum is 7.
D. (x+2)(x+5). The product of 2 and 5 is 10, and their sum is –7.
The factored form of the trinomial (x − 2) (x − 5):
The product of –2 and –5 is –10, and their sum is 7.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
(x − 2) (x − 5)
When factoring a trinomial in the form of ax² + bx + c, we look for two numbers whose product is equal to a x c and whose sum is equal to b.
In this case,
We need two numbers whose product is (1)(10) = 10 and whose sum is -7. These numbers are -2 and -5, so the factored form is (x-2)(x-5).
Thus,
(x − 2) (x − 5)
The product of –2 and –5 is –10, and their sum is 7.
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You work as a coordinator for data entry projects. On one project, the status report shows that 15% of the work was completed in 6 days. If the work progresses at the same rate, how many more days will be required to complete the remainder of the project?
Answer: They need 34 more days to complete the remainder of the project.
Step-by-step explanation:
Since we have given that
Number of days the work was done = 6 days
Part of work is completed in these days = 15%
If the work is done at the same rate,
then the remaining part of work is done in how many days.
Remaining part of work is 100% - 15% = 85 %
So, it becomes,
[tex]\dfrac{6}{0.15}=\dfrac{x}{0.85}\\\\x=\dfrac{6\times 0.85}{0.15}=34\ days[/tex]
Hence, they need 34 more days to complete the remainder of the project.
I need help in the problem
some people can help me plz
Estimate the percent of decrease.
Original population: 1,503
New population: 1,356
a. 1%
b. 10%
c. 13.5%
d. 15%
Answer:
Percentage in decrease = 10 %
Step-by-step explanation:
Given : Original population: 1,503 and New population: 1,356.
To find : Estimate the percent of decrease.
Solution : We have given
Original population: 1,503
New population: 1,356.
Value decrease = original population - new population.
Decrease = 1,503 - 1,356
Decrease population = 147
Percentage in decrease = [tex]\frac{decrease\ value}{original}*100[/tex].
Percentage in decrease = [tex]\frac{147}{1503}*100[/tex].
Percentage in decrease = [tex]\frac{14700}{1503}[/tex].
Percentage in decrease = 9.78 %
Estimate = 10 %.
Therefore,
Percentage in decrease = 10 %
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The answer is measure of A is 137