what is a geometric pattern
Answers
Answer:
A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design. Any of the senses may directly observe patterns.
Step-by-step explanation:
Related Questions
I got this from Khan academy.
Rewright the equation by completing the square. x^2 −14x+33=0
(x+_)^2
HELP!
Answers
To complete the square for the equation x^2 - 14x + 33 = 0, you can follow these steps:
Take half of the coefficient of x, which is -14/2 = -7.
Square this value to get (-7)^2 = 49.
Add and subtract this value inside the parentheses of x^2 - 14x to maintain the balance of the equation: x^2 - 14x + 49 - 49 + 33 = 0
Rearrange the terms and simplify: (x - 7)^2 = 16
Take the square root of both sides: x - 7 = ±4
Solve for x: x = 7 ± 4
Therefore, the solution to the equation x^2 - 14x + 33 = 0, by completing the square, is x = 7 ± 4.
help me find the slope!
Answers
Answer:
b
Step-by-step explanation:
i think
Explanation: If you use the formula rise/run you would see the rise is -3 and the run -4 which could give you -3/4
Sales reported on the income statement were $251,370. The accounts receivable balance declined $19,310 over the year. Determine the amount of cash received from customers.
Answers
The amount of cash received from customers is $232,060
To determine the amount of cash received from customers, we need to account for the change in accounts receivable over the year. The change in accounts receivable represents the difference between the beginning balance and the ending balance.
Since the accounts receivable balance declined by $19,310, we can infer that customers paid off that amount of outstanding accounts receivable.
To calculate the cash received from customers, we add the change in accounts receivable to the sales reported on the income statement. This is because the sales reported on the income statement represent the total revenue generated from sales, including both cash and credit sales.
Cash received from customers = Sales + Change in accounts receivable
Cash received from customers = $251,370 + (-$19,310) = $232,060
Therefore, the amount of cash received from customers is $232,060. This figure represents the actual cash inflow from customers for the specified period, accounting for the change in accounts receivable.
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Select the correct answer from each drop-down menu.
Two parallel lines AB and CD are intersected by a transversal line EF that intersects AB at a point I and CD at a point K. Another transversal line GH is drawn right to GH and intersects AB at a point J and CD at point L.
In the figure, and ∠EIA ≅ ∠GJB. Complete the following statements to prove that ∠IKL ≅ ∠DLH.
∠EIA ≅ ∠IKC and ∠GJB ≅ ∠JLD because they are corresponding angles of parallel lines cut by a transversal.
So, if ∠EIA ≅ ∠GJB, then ∠IKC ≅ ∠JLD by the ________
A. Subtraction of Property
B. Substitution Property of Congruency
C. Addition Property of Congruency
D. Transitive Property of Congruency
∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs of supplementary angles by the ____
A. Vertical Angles Theorem
B. Congruent Supplements Theorem
C. Linear Pair Theorem
.
m∠IKL + m∠IKC = 180° (1)
∠IKC ≅ ∠JLD, so m∠IKC = m∠JLD (2)
Applying the _____
A. Subtraction Property of Equality
B. Substitution Property of Congruency
C. Addition Property of Congruency
D. Transitive Property of Congruency
to equations (1) and (2), we get m∠IKL + m∠JLD = 180°.
Therefore, ∠IKL and ∠JLD are supplementary angles.
We've already shown that ∠DLH and ∠JLD are supplementary angles. Therefore, ∠IKL ≅ ∠DLH by the ____
A. Vertical Angeles Theorem
B. Definition of Supplementary Angles
C. Congruent Supplements Theorem
D. Linear Pair Theorem
.
Answers
∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Transitive Property of Congruency.
∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Linear Pair Theorem.The angle is Applying the Transitive Property of Congruency and product of m∠IKL + m∠JLD = 180°.Therefore, ∠IKL ≅ ∠DLH by the Congruent Supplements TheoremWhat is the Transitive property of congruence?This states that, if a pair of lines or angles or triangles are said to be congruent to a third line or angle, therefore, the first line or angle or triangle is said to be congruent to the third line or angle.
∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Transitive Property of Congruency. because the two angles and the other side of the angle/triangle are said to be equal to two angles and other side of the other triangle.
∠IKC ≅ ∠JLD, so m∠IKC = m∠JLD and as such angle is Applying the Transitive Property of Congruency because if A =b, and b = c then A = c and therefore, the above is true.
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Wanda runs a babysitting service. She charges an hourly rate and just earned $37 for 4 hours. Create an equation that models the relationship between the total charge, y and the number of hours, h, worked
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Pls help ASAP!! Marking 50 points!
Answers
The volume of the sports drink that they have with them, in whole liters is: d. 30 liters
What is the Volume of a Rectangular Shape?The volume of a rectangular shape, just like the rectangular block in the given problem, can be calculated using the formula:
Volume = (length)(width)(height).
From the information given, the rectangular block's dimensions are:]
Length = 6.0 cmWidth = 4.0 cmHeight = 10.5 cmVolume of one rectangular block = (6.0)(4.0)(10.5)
Volume of one rectangular block = 252 cm³
Convert 252 cm³ to liters:
1,000 cm³ = 1 liters
252 cm³ = 252/1,000 = 0.252 liters
120 packs of 0.252 liters = 120 × 0.252
= 30.24 ≈ 30 liters
Therefore, the volume of the sports drink that they have with them, in whole liters is: d. 30 liters
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This year (2022), Evan graduated from college and took a job as a deliveryman in the city. Evan was paid a salary of $73,650 and he received $700 in hourly pay for part-time work over the weekends. Evan summarized his expenses as follows:
Cost of moving his possessions to the city (125 miles away) $ 1,200
Interest paid on accumulated student loans 2,890
Cost of purchasing a delivery uniform 1,490
Cash contribution to State University deliveryman program 1,345
Calculate Evan's AGI and taxable income if he files single. Assume that interest payments were initially required on Evan's student loans this year.
Answers
To calculate Evan's AGI (Adjusted Gross Income) and taxable income if he files as a single taxpayer, we need to consider his income and deductible expenses.
Calculate Evan's total income:
- Salary: $73,650
- Part-time hourly pay: $700
Total income = Salary + Part-time pay = $73,650 + $700 = $74,350
Deductible expenses:
- Moving expenses: $1,200
- Student loan interest: $2,890
- Uniform cost: $1,490
- Cash contribution: $1,345
Total deductible expenses = $1,200 + $2,890 + $1,490 + $1,345 = $6,925
Calculate AGI:
AGI = Total income - Total deductible expenses
AGI = $74,350 - $6,925 = $67,425
Evan's taxable income is equal to his AGI since there were no other deductions mentioned in the question.
Therefore, Evan's AGI is $67,425, and his taxable income is also $67,425.
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Evan's AGI is $67,425 and his taxable income is $54,875 if he files as a single taxpayer.
We have,
Income:
Salary: $73,650
Part-time work pay: $700
Total income: $73,650 + $700 = $74,350
Deductible Expenses:
Cost of moving possessions: $1,200
(This deduction applies if the move meets certain distance and time requirements. Since the move was 125 miles away, it meets the distance requirement.)
Interest paid on student loans: $2,890
Cost of purchasing a delivery uniform: $1,490
Cash contribution to State University deliveryman program: $1,345
Total deductible expenses:
$1,200 + $2,890 + $1,490 + $1,345
= $6,925
Now we can calculate Evan's AGI and taxable income:
AGI (Adjusted Gross Income)
= Total income - Deductible expenses
AGI = $74,350 - $6,925 = $67,425
Taxable Income = AGI - Standard Deduction
For a single filer in 2022, the standard deduction is $12,550.
Taxable Income = $67,425 - $12,550 = $54,875
Therefore,
Evan's AGI is $67,425 and his taxable income is $54,875 if he files as a single taxpayer.
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find the area of the region which is bounded by the polar curves θ=π θ=π and r=10θ, 0≤θ≤1.5π r=10θ, 0≤θ≤1.5π
Answers
To find the area of the region bounded by the polar curves θ = π and r = 10θ, 0 ≤ θ ≤ 1.5π, we use the formula for the area enclosed by a polar curve: A = 1/2 ∫[θ1,θ2] (r(θ))^2 dθ,where θ1 and θ2 are the angles at which the curves intersect.
In this case, the curves intersect at θ = π and r = 10π, so θ1 = π and θ2 = 1.5π. We substitute r = 10θ into the formula and integrate:
A = 1/2 ∫[π,1.5π] (10θ)^2 dθ
= 1/2 ∫[π,1.5π] 100θ^2 dθ
= 50 ∫[π,1.5π] θ^2 dθ
= 50 [θ^3/3] [π,1.5π]
= 50 (1.5π)^3/3
= 562.5π^3
Therefore, the area of the region bounded by the polar curves θ = π and r = 10θ, 0 ≤ θ ≤ 1.5π is 562.5π^3 square units.
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A recipe calls for 2/3 cup of sugar for every 4 teaspoons of vanilla. How much vanilla should be used for every 1 cup of sugar?
Answers
Answer:
Let x = the number of teaspoons of vanilla needed
sugar/vanilla: 2/3 = 1
4 x Cross multiply
(2/3)x = 4
x = 4(3/2)
x = 6 teaspoons
Step-by-step explanation:
Answer:
x = 6 teaspoons
Step-by-step explanation:
good luck!
What is the part of line having 1 endpoint and extending in one direction?
Answers
A part of a line that has 1 endpoint and extends indefinitely in only one direction is called a ray.
A ray is named using its endpoint first, and then any other point on the ray
Properties of ray:
A line is a series of points placed together that continue infinitely.When this line is restricted from one direction and is extended in the other direction indefinitely, it forms a ray.It has just one starting point and does not have an opposite end and goes through and cuts many points and lines and is often used to draw angles, and we cannot measure the length of a ray.To know more about ray:
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10. [5pts.] cot A Prove the following identity: sin 2A = 1- cos 24
Answers
We successfully proved the given identity cot(A) = sin(2A) / (1 - cos(2A)).
To prove the identity cot(A) = sin(2A) / (1 - cos(2A)), we'll start with the left-hand side (LHS) and simplify it to match the right-hand side (RHS).
LHS: cot(A)
Using the reciprocal identity, cot(A) = 1 / tan(A), we can rewrite it as:
LHS: 1 / tan(A)
Now let's simplify the right-hand side (RHS):
RHS: sin(2A) / (1 - cos(2A))
Using the double-angle identity for sine, sin(2A) = 2sin(A)cos(A), we can substitute it into the RHS:
RHS: (2sin(A)cos(A)) / (1 - cos(2A))
Now, let's manipulate the RHS to match the LHS:
RHS: (2sin(A)cos(A)) / (1 - cos(2A))
To simplify further, we'll use the double-angle identity for cosine, cos(2A) = cos²(A) - sin²(A):
RHS: (2sin(A)cos(A)) / (1 - (cos²(A) - sin²(A)))
Simplifying the denominator:
RHS: (2sin(A)cos(A)) / (1 - cos²(A) + sin²(A))
Since cos²(A) + sin²(A) = 1 (from the Pythagorean identity), we can replace it:
RHS: (2sin(A)cos(A)) / (2 - cos²(A))
Canceling out the common factor of 2:
RHS: sin(A)cos(A) / (1 - cos²(A))
Using the identity sin²(A) = 1 - cos²(A), we can rewrite it:
RHS: sin(A)cos(A) / sin²(A)
Now, let's simplify the right-hand side further:
RHS: sin(A)cos(A) / sin²(A)
Using the identity sin(A) / sin²(A) = 1 / sin(A), we can rewrite it:
RHS: cos(A) / sin(A)
Since cot(A) = 1 / tan(A) = cos(A) / sin(A), we have:
LHS: cot(A) = RHS: cos(A) / sin(A)
Therefore, we have successfully proved the given identity cot(A) = sin(2A) / (1 - cos(2A)).
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Prove the following identity cotA=sin2A/(1-cos2A)
The economy is initially in long-run equilibrium. The AD curve shifts to the right and the price level rises. Assuming that the economy is self-regulating, the SRAS curve will shift to the left and the price level will rise even further. If the price level now remains constant, what have we witnessed
Answers
We witnessed that the economy has moved from its initial short-run equilibrium to a new long-run equilibrium, where the price level has stabilized despite the changes in aggregate demand and short-run supply.
Suppose the price level remains constant despite the initial shift of the AD (Aggregate Demand) curve to the right, followed by the leftward shift of the SRAS (Short-Run Aggregate Supply) curve. In that case, it suggests that the economy has experienced a change toward long-run equilibrium.
The initial shift of the AD curve to the right causes an increase in both output and the price level. However, the subsequent leftward shift of the SRAS curve indicates that in the short run, the price level has led to higher costs for businesses, potentially due to factors such as increased wages or input prices.
As a result, with a leftward shift in the SRAS curve, the output level decreases, and the price level rises further. However, if the price level remains constant after this adjustment, it suggests that the economy has reached a new equilibrium point where aggregate demand and short-run aggregate supply are once again balanced.
In short, witnessing a constant price level after the initial shifts in the AD and SRAS curves implies that the economy has moved from its initial short-run equilibrium to a new long-run equilibrium, where the price level has stabilized despite the changes in aggregate demand and short-run supply.
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Can someone please answer questions 2 Find the circumference AND area for a circle with a radius of 5cm. Round your answer to the nearest tenth
Answers
Answer:
C=15.7cm
A=78.54cm^2
Step-by-step explanation:
C=πr = π(5cm) = 15.7cm
A=πr^2 =π (5cm)^2 =78.54cm^2
What is the factored form of the expression x^2 - 16?
Answers
Answer:
(x + 4)(x - 4)
Step-by-step explanation:
Answer:
( − 4 ) ( + 4 )
Step-by-step explanation:
x^2 - 16
x^2 + 4x - 4x = 16
x^2 + 4x - 4x - 16
( + 4 ) − 4 ( + 4 )
( − 4 ) ( + 4 )
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Help,anyone can help me do quetion,I will mark brainlest.
Answers
Answer:
I have absolutely no clue sorry buddy
Step-by-step explanation:
There is no step-by-step explanation
Answer:
Hi
Step-by-step explanation:
I can help you
2. Area of a rectangle 40 cm2
So. We know the area AND one of the sides of the rectangle.
We can calculate the area.
We know that area=length times width
so
A=lw
Rearrange that for w:
w=A/l
w=40:8
w=5
Now we know both l and w
Now we can calculate the perimeter
P=2a+2b
P=2(a+b)
P=2(8+5)
P=2(13)
P=26
I hope it is correct
PLZ HELP 100 POINTS AND DONT BE MEAN
Answers
Answer:
Full drum 80 dollars
one lid missing
earn 10 dollars less
Step-by-step explanation:
We need to find the surface area
SA = 2 pi r^2 + 2 pi rh
The diameter is 2 so the radius = 2/2 =1
SA = 2 * pi * 1^2 + 2 * pi * 1 * 3
= 2 pi + 6pi
= 8pi
Using pi = 3.14
SA = 8 *3.14 = 25.12 ft^2
We get 3.18 per ft^2
25.12 * 3.18 =79.88
To the nearest dollar
80 dollars
If one of the lids is missing
SA = pi r^2 + 2 pi rh
pi + 6pi
7 pi
Using pi = 3.14
SA = 7 *3.14 = 21.98 ft^2
We get 3.18 per ft^2
21.98 * 3.18 =69.90
To the nearest dollar
70
The difference is 10 dollars
Answer:
\(\Huge \boxed{\mathrm{a) \ \$ \ 80}} \\\\\\\\ \Huge \boxed{\mathrm{b) \ \$ \ 10}}\)
\(\rule[225]{225}{2}\)
Step-by-step explanation:
Surface area of the cylinder :
2πr² + 2πrh
The diameter is 2 ft, so the radius is 1 ft.
⇒ 2π(1)² + 2π(1)(3)
⇒ 8π ≈ 25.13
$3.18 is getting payed per square foot.
⇒ 25.13 × 3.18
⇒ 79.9221171073 ≈ 80
If the lid was missing:
πr² + 2πrh
π(1)² + 2π(1)(3)
7π ≈ 21.99
$3.18 is getting payed per square foot.
⇒ 21.99 × 3.18
⇒ 69.9318524689 ≈ 70
The difference :
80 - 70 = 10
$10 less if the lid is missing.
\(\rule[225]{225}{2}\)
PLS HURRY I HAVE 30 MIN
:)
which shape has the smallest perimeter?
-describe all of your work and how you derived your answers.
Answers
Answer:
Circle.among all shapes with the same area, a circle has the shortest perimeter
every sunday, devon and her cousins get together for brunch. this week, devon is in charge of making fresh-squeezed orange juice. there is a proportional relationship between the number of oranges devon squeezed, x, and the amount of juice (in ounces) she makes, y. x (oranges) y (ounces) 2 6 3 9 4 12 6 18 what is the constant of proportionality? write your answer as a whole number or decimal. ounces per orange
Answers
The constant proportionality is - 3.
Constant proportionality can be defined as the constant value of the ratio between two proportional quantities. The value of the constant of the proportionality is dependent on the type of proportion between two given quantities.
According to the question,
Devon and her cousins get together every Sunday. Devon is in charge of making fresh-squeezed orange juice this week.
A proportional relationship is being taken place between the number of oranges Devon squeezes and the amount of juice (in ounces) she makes.
By using the division method, we get
6 ÷ 2 = 3
9 ÷ 3 = 3
12 ÷ 4 = 3
18 ÷ 6=3
So, the constant proportionality is - 3.
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Answer:60????
Step-by-step explanation:
A. Show all of your work to solve each equation and to check for extraneous solutions:1. [√(x - 3)] - 7=0
Answers
Given:
\((\sqrt{x-3})-7=0\)Required:
We need to find the value of x.
Explanation:
Set x =28 and substitute in the equation.
\((\sqrt{28-3})-7=0\)\((\sqrt{25})-7=0\)\(5-7=0\)\(-2=0\)This is not true.
x=28 is an extraneous solution.
Set x =39 and substitute in the equation.
\((\sqrt{39-3})-7=0\)\((\sqrt{36})-7=0\)\(6-7=0\)\(-1=0\)This is not true.
Set x =52 and substitute in the equation.
\((\sqrt{52-3})-7=0\)\((\sqrt{49})-7=0\)\(7-7=0\)\(0=0\)This is true.
x=52 is the solution.
Final answer:
\(x=52\)How is solving 2x c= d similar to solving 2x 1 = 9 for how are they different? how can you use 2x c= d to solve 2x 1 = 9? free anser
Answers
The value of x is x = 9/4. The equation 2xc = d as follows: 2xc = d2x * 1/2 = 9/22x = 9/2 * 2x = 9/4
The equation 2xc = d and 2x + 1 = 9 are similar in that they are both linear equations and involve the variable x.
However, they are different in that they have different constants and coefficients.
How to use 2xc = d to solve 2x + 1 = 9? To use 2xc = d to solve 2x + 1 = 9, you first need to rewrite 2x + 1 = 9 in the form 2xc = d.
To do this, you need to isolate x on one side of the equation. 2x + 1 = 9
Subtract 1 from both sides2x = 8. Divide both sides by 2x = 4Now, we can write 2x + 1 = 9 as 2x * 1/2 = 9/2.
Therefore, we can see that this equation is similar to 2xc = d, where c = 1/2 and d = 9/2.
We can use this relationship to solve for x in the equation 2xc = d as follows: 2xc = d2x * 1/2 = 9/22x = 9/2 * 2x = 9/4 Therefore, x = 9/4.
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In a histogram, the vertical line (dimension) shows the _____________, while the horizontal line (dimension) shows the _______________.
Answers
In the Histogram the horizontal line (dimension) represents the value of the selected collection plan element. The vertical line (dimension) represents the count or sum of occurrences of the primary collection element on the horizontal line.
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this table shows some values of an exponential function. what is the function
Answers
Answer:
there is no table so we are therefore unable to answer this question
Step-by-step explanation:
sorry
A sampling error is the result of: a. bad luck b. nontruthful responses c. measurement error d. nonresponse bias
Answers
A sampling error is the result of measurement error. What is a sampling error? The sampling error is a statistical error that arises when the sample used to estimate a population parameter differs from the actual population. When researchers obtain a random sample of individuals from a population.
The correct option is-C
They will not be able to include all individuals, resulting in a sampling error. Thus, it arises due to measurement error. What is measurement error? Measurement error is the discrepancy between an observed value and the true value of a variable. The causes of measurement errors could be: Poor measuring instruments: If a scale or a thermometer isn't calibrated correctly, the results will be incorrect.
The observer's mistake: A researcher might misinterpret the data or record it wrongly. The participant's mistake: If a participant provides inaccurate responses, it might affect the outcomes. Conclusion: A sampling error is the result of measurement error. The difference of cubes can be factored as a product of a binomial and trinomial such that the difference of cubes will have a binomial difference, multiplied by a trinomial where the first term is the cube root of the first term, the second term is the product of the square of the cube root of the first term and the cube root of the second term, and the third term is the cube root of the square of the second term.
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You have to draw two (infinite) lines parallel to the x
-axis, three (infinite) lines parallel to the y
-axis, and four (infinite) lines parallel to the line x=y
What is the smallest possible total number of crossing points among the nine lines you draw?
Answers
Answer:
ok check the attachment.
Step-by-step explanation:
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Exercises 3-33 Consider the rational function ) 1. (6 points) Find the partial fraction decomposition of f(2) 3 3X - 13 (1)(x-1) A + -15 + (X4) - 413 (x-7) (x-7) (*+) A(x-7) - B(x+1)= 3x - 13 it *---1
Answers
Partial fraction decomposition of the rational function f(x) = (3x - 13) / [(x - 1)(x - 7)] is:f(x) = A / (x - 1) + B / (x - 7)
To find the values of A and B, we can use the method of equating coefficients. Multiplying both sides of the equation by the common denominator (x - 1)(x - 7), we get: 3x - 13 = A(x - 7) + B(x - 1)
Expanding and rearranging the equation, we have:
3x - 13 = (A + B)x - 7A - B
By equating the coefficients of like powers of x, we get:
Coefficient of x: 3 = A + BConstant term: -13 = -7A - B
Solving these two equations simultaneously, we find the values of A and B. Once we have the values, we can substitute them back into the partial fraction decomposition equation:
f(x) = A / (x - 1) + B / (x - 7)
This decomposition helps in simplifying the rational function and makes it easier to integrate or perform further calculations.
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Classify the states of the following Markov chain and select all correct statements. [1 0 0 0 0 0 0 ]
[7/8 1/8 0 0 0 ]
[0001/3 1/2 1/6]
[0 0 1/3 2/3 0]
a)State 1 is absorbing b) States 4 and 5 are periodic c) State 1 is transient d) State 1 is recurrent e) States 3, 4 and 5 are recurrent f) Only state 3 is recurrent
Answers
In the given Markov chain, State 1 is absorbing, State 4 is periodic, State 1 is recurrent, and States 3, 4, and 5 are recurrent.
A Markov chain is a stochastic model that represents a sequence of states where the probability of transitioning from one state to another depends only on the current state. Let's analyze the given Markov chain to determine the properties of each state.
State 1: This state has a probability of 1 in the first row, indicating that it is an absorbing state. An absorbing state is one from which there is no possibility of leaving once it is reached. Therefore, statement a) is correct, and State 1 is absorbing.
State 2: There are no transitions from State 2 to any other state, which means it is an absorbing state as well. However, since it is not explicitly mentioned in the question, we cannot determine its status based on the given information.
State 3: This state has non-zero probabilities to transition to other states, indicating that it is not absorbing. Furthermore, it has a loop back to itself with a probability of 1/6, making it recurrent. Hence, statements c) and e) are incorrect, while statement f) is correct. State 3 is recurrent.
State 4: State 4 has a transition probability of 1/3 to State 3, which means there is a possibility of leaving this state. However, there are no outgoing transitions from State 4, making it an absorbing state. Moreover, since there is a loop back to itself with a probability of 2/3, it is also recurrent. Therefore, statement b) is correct, and State 4 is periodic and recurrent.
State 5: Similar to State 4, State 5 has a transition probability of 2/3 to State 3 and no outgoing transitions. Hence, State 5 is also an absorbing and recurrent state. Consequently, statement e) is correct.
To summarize, State 1 is absorbing and recurrent, State 4 is periodic and recurrent, and States 3 and 5 are recurrent.
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Algebra 2
—————
y = -2(x - 3)^2 + 4
Factor and Solve.
Answers
y=-2*(x^2-6x+9)+4
y=-2x^2+12x-18+4
y= -2x^2 + 12x -14
Write and graph an inequality for the given solution set.
{n ∣ n≥−2}
Answers
how do you factor the expression 51xy − 34xy2
Answers
The simplified expression is 17xy( 3 - 2y).
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
51xy − 34xy²
Now, factorizing
51xy= 3 x 17 × x × y
34xy² = 2 ×17 × x × y ×y
So, the simplification can be
51xy − 34xy²
= 3 x 17 × x × y- 2 ×17 × x × y ×y
= 17xy( 3 - 2y)
Hence, the simplified expression is 17xy( 3 - 2y).
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. An elevator in a building starts with five passengers and stops at seven floors. Say every passenger is equally likely to get off at each floor and all the passengers leave independently of each other. a. How many ways are there for the passengers to be assigned a floor? b. How many ways are there for the passengers to be assigned a floor but no two passengers are on the same floor?
Answers
There are 16807 number of ways the passengers to be assigned a floor and there are 2520 number of ways the passengers to be assigned a floor but no two passengers are on the same floor.
Given that an elevator starts with five passengers and stops at the seven floors of a building.
From the given information, the total number of floors n=7.
The number of passengers r = 5.
(a) Compute the number of ways that 5 passengers can be assigned to seven floors.
Here, repetition is allowed.
From the known information, if r numbers are selected from n number of observations then the total number of observations that can be drawn from n number of observations is \(n^r\).
If 5 passengers can be assigned to seven floors is 7⁵ = 16807.
(b) Compute the number of ways that the passengers to be assigned a floor but no two passengers are on the same floor.
Here, repetition is not allowed.
If 5 passengers can be assigned to seven floors but no two passengers are on the same floor is 7x6x5x4x3 = 2520.
Hence, the number of ways that 5 passengers can be assigned to seven floors is 16807, and the number of ways that the passengers to be assigned a floor but no two passengers are on the same floor is 2520.
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