Answers
Answer:
transitive property
Step-by-step explanation:
This is the answer by definition.
The substitution property is demonstrated in the case of m∠AZF=m∠AZL+m∠LZF and m∠AZL+m∠LZF=m∠SZW+m∠LZF, so, m∠AZF=m∠SZW+m∠LZF.
In order to find the value of the unknown, the substitution property is a concept in algebra that is used to substitute the value of a given variable or quantity into an expression.
According to the substitution property of equality, "If two variables x and y are equal, then x can be substituted for y in any equation or expression, and y can be substituted for x in any equation or expression."
According to the question, m∠AZF=m∠AZL+m∠LZF and m∠AZL+m∠LZF=m∠SZW+m∠LZF, so by the substitution property, on substituting the value of m∠AZL+m∠LZF in the first expression, we get, m∠AZF=m∠SZW+m∠LZF.
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Related Questions
A survey was conducted among the students at Elmwood High School. What are the individuals in this study?
the types of sports
the music groups
the clubs
the students
Answers
Based on the information provided, the individuals in this study are: D. the students.
What is a study?A study can be defined as a strategic process or technique through which a scientist (researcher) observes and measures the effect of a risk factors, diagnostic test, or treatments on a particular population of interest.
What is a variable?In Mathematics, a variable can be defined as the measurable conditions, events, characteristics, individuals, or behaviors that a scientist (researcher) can control or observe when performing a study.
Based on the information provided, the individuals in this study are the students and these include the following subclasses:
FreshmenSophomoresJuniorsSeniorsRead more on variables here: https://brainly.com/question/523303
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The students are the individuals in this study and is therefore denoted as option D.
What is a Sample?This refers to a group of people which are chosen or taken from a large population for measurement or surveys.
In this scenario, the study was conducted in a school with different types of students according to their grades such as freshman, sophomore etc. This therefore makes the individuals in the study to be students and is the most appropriate choice.
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The perimeter is 54 m. The apothem is \root(3)(3) . To the nearest tenth, what is the area of this regular polygon?
Answers
The area of this regular polygon is 46.8 square units
How to determine the area of this regular polygon?The given parameters are:
Perimeter, p = 54 m
Apothem, a = √3
The area of this regular polygon is then calculated as:
Area = 0.5 * Apothem * Perimeter
Substitute the known values in the above equation
Area = 0.5 * √3 * 54
Evaluate the product
Area = 46.8
Hence, the area of this regular polygon is 46.8 square units
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Simplify 4/16 to lowest terms and find an equivalent fraction that has a denominator of 32
Answers
equivalent fraction- 8/32
find the zeros x^4-2x^3-44x^2-88x-32
Answers
The zeros which are the roots of the polynomial expressions are:
x = -4; x = - 2; x = 4 - 2√5; x = 2(2 + √5)
What are the zeros of a polynomial expression?The zeros of a polynomial f(x) are really the values of x that answer the equation f(x) = 0. Thus, f(x) is a function of x, and the polynomial zeros refer to the values of x, which makes the f(x) value equal to zero. The digit of zeros in a polynomial is decided by the degree of equation f(x) = 0.
For a polynomial, there may be specific values of the variable for which the polynomial is zero. These are known as polynomial zeros. They are also known as polynomial roots. In essence, we look for the zeros of quadratic equations to discover the solutions to the given equation.
From the given equation, the zeros of x^4-2x^3-44x^2-88x-32 can be computed as follows:
Using the rational root theorem:
[tex]\mathbf{= (x+2)\dfrac{x^4-2x^3-44x^2-88x-32}{x+2} }[/tex]
[tex]\mathbf{=(x+2) (x^3-4x^2-36x-32) }[/tex]
By factorization, we have:
= (x + 2) (x + 4) (x² - 8x - 4)
The zeros which are the roots of the polynomial expressions are:
x = -4; x = - 2; x = 4 - 2√5; x = 2(2 + √5)
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Mike drove 40 miles from his home to his office, and he then drove back home using the same route. The average speed on his return trip was 10 miles/hour more than the average speed on his trip to the office. The total time for the trip is represented by this expression, where x is the average speed on the trip from his home to his office.
The average speed on Mike’s drive home is represented by
x + 10
.
When Mike drives at an average speed of 55 mile/hour on his way home, it takes him approximately
1.6 hours
to drive to work and back.
Answers
Mike's speed driving to his office is 45 miles/hour, which is 10 miles less than his average speed driving back.
How is speed calculated?Speed is an average value of a scalar measurement of the distance covered over the time taken.
Speed is the equation, r = d/Δt, where r = speed or rate, d = distance, and Δt is the change in time.
Thus, when the distance covered by a traveler is divided by the time consumed, one can determine the average speed for the travel.
Data and Calculations:Distance from Mike's home to his office = 40 miles
Distance to and from = 80 miles (40 miles x 2)
Hours covered from office = 1.6 hours
Average speed for the trip = 50 miles/hour (80/1.6)
Average speed to return home = 55 miles/hour
Average speed to office = 45 miles/hour (55 - 10)
Thus, Mike's speed of driving to his office is 45 miles/hour.
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Question Completion:What is Mike's speed driving to his office?
A hotel builds an isosceles trapezoidal pool for children. It orders a tarp to cover the pool when not in use. What is the area of the tarp?
Trapezoid ABCD with base side AD labeled 15 feet, top side BC labeled 10 feet, and right side CD labeled 5 feet. Angle C measures 120 degrees.
To find the height, first find that is
. This means the height of the trapezoid is approximately
feet. So, the area of the tarp is approximately
square feet.
Answers
The area of the tarp is 54.125 square feet
How to determine the measure of D?From the figure in the question, we have the following angle measure:
DCE= 120
This means that:
<C = DCE - 90
Substitute the known values in the above equation
<C = 120 - 90
Evaluate the difference
<C = 30
The measure of D is then calculated as
<D = 90 - <C
This gives
<C = 90 - 30
Evaluate the difference
<C = 60
How to determine the height of the trapezoid?Represent the height with h.
This is then calculated as:
sin(D) = h/5
This gives
sin(60) = h/5
Multiply both sides by h
h = 5 * sin(60)
Evaluate
h = 4.33
How to determine the area of the tarp?This is calculated as:
A = 0.5 * (10 + 15) * 4.33
Evaluate
A = 54.125
Hence, the area of the tarp is 54.125 square feet
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Answer:
In the image
Hope this helps!
Step-by-step explanation:
To find the height, first find that ∠D is 60°. This means the height of the trapezoid is approximately 4.3 feet. So, the area of the tarp is approximately 53.7 square feet.
y = x^3 - 52x^2 + 15x^4 + 16 + 20x
Answers
The factors of the equation of power 4, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex] are x=1, -2, 4/3, -2/5.
Given equation is [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex],
By performing L-division method, we get
[tex]y = (x-1)(15x^{3} +16x^{2} -36x-16)[/tex]
Then again doing the same L-division method to the cubic equation [tex]15x^{3} +16x^{2} -36x-16[/tex], we get
[tex]15x^{3} +16x^{2} -36x-16 = (x+2)(15x^{2} -14x-8)[/tex]
Therefore, [tex]y = (x-1)(x+2)(15x^{2}-14x-8)[/tex]
Then finally the roots of the quadratic equation [tex]15x^{2}-14x-8[/tex] are (x-(4/3)) and (x+(2/5))
Hence, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x = (x-1)(x+2)(x-\frac{4}{3} )(x+\frac{2}{5} )[/tex]
Therefore, the roots of the equation of power 4, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex] are x=1, -2, 4/3, -2/5.
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Rhombus BCDE is shown below. Give the coordinates of C and D.
Answers
The coordinates of C - (2n, 0) and the coordinates of D - (n, -p). The diagonals of a rhombus are perpendicular and bisect each other.
What are the properties of a rhombus?The properties of a rhombus are:
All the sides of a rhombus are congruent and equalOpposite sides are parallelOpposite angles are equalThe adjacent angles add up to 180°Diagonals perpendicularly bisect each otherDiagonals bisect opposite anglesCalculation:The given rhombus BCDE has B(n, p) and E(0, 0).
Since the diagonals of a rhombus are perpendicular bisectors,
EO = OC or BO = OD
Where O is the midpoint of EC and BD.
In the given diagram, points B and D are opposite each other. They are reflecting each other over the x-axis.
So, if B has coordinates (n, p) then its reflection over the x-axis is (x, -y) i.e., (n, -p).
Thus, we have B(n, p), D(n, -p), and E(0, 0)
Consider the coordinates of C as (x, y).
The midpoint of BD = ([tex]\frac{n+n}{2}[/tex], [tex]\frac{p-p}{2}[/tex])
⇒ coordinates of O = (n, 0)
So,
The midpoint of EC = ([tex]\frac{0+x}{2}[/tex], [tex]\frac{0+y}{2}[/tex])
⇒ coordinates of O = (x/2, y/2)
⇒ (n, 0) = (x/2, y/2)
∴ x = 2n and y = 0
Then, the coordinates of C are (2n, o)
Therefore, the required coordinates of the given rhombus are C(2n, 0) and D(n, -p).
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X
Erica works 30 hours/week for
$10/hour, but she must pay $30 in
taxes. What is her take-home income?
Answers
Answer:
$270
Step-by-step explanation:
Find her gross income....then subtract taxes:
30 hr/week * $10/hr - $ 30 = $270
Solve this system. Write your answer as an ordered pair.
-5x + y = -3
3x - 8y = 24
Answers
[tex]\begin{cases} -5x+y=-3\\ 3x-8y=24 \end{cases} \\\\\\ \stackrel{\textit{using the 1st equation}}{-5x+y=-3}\implies \underline{y=-3+5x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{3x-8(\underset{y}{-3+5x})=24}\implies 3x+24-40x=24\implies 3x-40x=0 \\\\\\ -37x=0\implies \boxed{x=0}~\hfill \underline{y=-3+5(\stackrel{x}{0})}\implies \boxed{y=-3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (0~~,~~-3)~\hfill[/tex]
Answer:
( 0, -3 )
Step-by-step explanation:
-5x + y = -3 ⇒ ( 1 )
3x - 8y = 24 ⇒ ( 2 )
We can make y the subject of equation 1.
y = 5x - 3 ⇒ ( 3 )
Now let us take equation 2.
Here we can replace y with ( 5x - 3 ) to find the value of x.
Value of x.
3x - 8y = 24
3x - 8 (5x - 3) = 24
3x - 40x + 24 = 24
-37x = 0
x = 0
Now let us take equation 3 to find the value of y.
Here we can replace x with 0.
Let us find it now.
y = 5x - 3
y = 5 × 0 - 3
y = 0 - 3
y = -3
Now, let us write the answer as an ordered pair.
( x, y )
( 0, -3 )
Which of the following number 1001,1002,1004 will be the sum of 994 and a 2 digit number
Answers
The number that will be the sum of 994 and a 2 digit number is 1004 (option 3). Details about digits of numbers can be found below.
What is a 2-digit number?A digit is the whole numbers from 0 to 9 and the arabic numerals representing them, which are combined to represent base-ten numbers.
A 2-digit number is any number between 10 and 99.
According to this question, 994 is said to be added to a 2 digit number to result into either 1001, 1002 or 1004.
1001 - 994 = 7 (1 digit)1002 - 994 = 8 (1 digit)1004 - 994 = 10 (2 digit)Therefore, the number that will be the sum of 994 and a 2 digit number is 1004.
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you are considering an investment into Company XYZ and need to determine the company's value and the appropriate investment amount. You have been provided with historical financial statements for the past three years in order to build a forecast model. Key assumptions to use include:
Future sales revenue is assumed to increase at 2.5% annually.
Gross margin for 2021E is assumed to be equal to the average gross margin % for 2019 and 2020, but will decrease by 2.5% (i.e. 250 bps) each year thereafter
SG&A expense is assumed to be a percentage of revenue for the forecast period. That percentage is equal to the 2018-2020 average
Depreciation expense is assumed to be a percentage of revenue for the forecast period. That percentage is equal to the 2018-2020 average
The tax rate for the forecast period is assumed to be equal to the effective tax rate for 2018
Capital expenditures for any given year in the forecast period is assumed to be 3x the prior year's depreciation expense. For example, 2021 capital expenditures is equal to 3x 2020 depreciation expense.
No new debt or equity is assumed to be issued
Download CFI_-_FMVA_Practice_Exam_Case_Study_A.xlsx and answer the following 12 questions.
1
What is Gross Profit in 2028E using the assumptions listed above and on the Control Panel?
$17,545
$30,704
$27,780
$40,938
Answers
Option A is correct. The gross profit that has been calculated for this year is given as 17545
How to solve for the gross profit22050 × 97.5%(100-2.5%) = 21498.75
= 21498.75 × 0.975 = 20961.28
= 20961.28 x 0.975 = 20437.24
= 20437.24 x 0.975 = 19926.31
= 19926.31 × 0.975 = 19428.15
= 19428.15 x 0.975 = 18942.45
= 18942.45 x 0.975 = 18468.80
= 18468.89 × 0.975 = 18017
= 18007 × 0.975 = $17545
Hence we can see at the end of the solution that the value of the gross profit in 2028 = $17545
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If the formula r=1/n-1 .....following data, what would be the value of x?
Answers
The solution or the value of x = 14 (Option C). See the explanation below.
Where x (bar) is the mean.
What is the calculation for the above?x = (12 + 13 + 14 + 15 + 16)/5
= 14
Hence option C is correct.
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can someone provide me with step by step solution of this question
Answers
Answer:
the answer is 100,008.
Step-by-step explanation:
To convert temperatures in degrees Fahrenheit to Celsius, subtract 32 and multiply by 5556
Answer: 50° F = 10° C
Step-by-step explanation:
Given information
Convert 50° Fahrenheit to Celcius
Given formula
[tex]C~=~\frac{5}{9}~ (F-32)[/tex]
Substitute values into the formula
[tex]C~=~\frac{5}{9}~ (F-32)[/tex]
[tex]C~=~\frac{5}{9}~ ((50)-32)[/tex]
Simplify values in the parenthesis
[tex]C~=~\frac{5}{9}~ (18)[/tex]
Simplify the multiplication
[tex]\Large\boxed{C=10^\circ C}[/tex]
Hope this helps!! :)
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The large rectangle was reduced to create the small rectangle.
A large rectangle has a length of 18 inches and width of 12 inches. A smaller rectangle has a length of 6 inches and width of x inches.
Not drawn to scale
What is the missing measure on the small rectangle?
2 inches
3 inches
4 inches
5 inches
Answers
Answer:
4 inches
Step-by-step explanation:
large rectangle - 18:12 ratio = 3:2
small rectangle - 6:4 = 3:2
Find the critical value. Assume that the test is two -tailed and that n denotes the number of pairs of data. n =
20, α = 0.01
A) -0.570
B) 0.570
C) +0.447
D) +0.570
Answers
Using a calculator, the critical value for the t-distribution, with a confidence level of 99%, a sample size n = 20 and a two-tailed test is of Tc = 2.8609.
How to find the critical value of the t-distribution?It is found using a calculator, with three inputs, which are given by:
The confidence level.The number of degrees of freedom, which is one less than the sample size.The tail.In this problem, the inputs are given as follows:
Confidence level of 99%, as 1 - 0.01 = 0.99 = 99%.19 df, as 20 - 1 = 19.Two-tailed test, as stated in this problem.Hence, using a calculator, the critical value is of is of Tc = 2.8609.
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A large bakery buys flour in 20-pound bags. The bakery uses an average of 1050 bags a year. Preparing an order and receiving a shipment of flour involves a cost of $15 per order. Annual Carrying costs are $ 55 per bag. a) Determine the economic order quantity? b) What is the average number of bags on-hand? c) How many orders per year will there be? d) Compute the total cost of ordering and carrying flour? e) If holding costs were to increase by $5 per year, how much would the minimum total annual cost?
Answers
Given the following:
Demand = 1050Ordering cost = 15Holding cost = 55The economic order quantity is 24.
What is the economic order Quantity?Eoq = √2 * demand * ordering cost / holding cost)
= √(2 * 1050 * 15 / 55)
EOQ = 24
What is the average number of bags on-hand?The Average inventory = EOQ / 2
= 24 / 2
= 12
How many orders per year will there be?Expected number of orders = demand / EOQ
= 1050 / 24
= 44
What is the total cost of ordering and carrying flour?Annual holding cost (AHC) = (EOQ / 2) * Holding cost
= (24 / 2) * 55
= 660
Annual ordering cost (AOC) = (demand / EOQ) * ordering cost
= (1050 / 24) * 15
= 656
Thus,
Total cost of managing = AHC + AOC
= 660 + 656
TCM = 1,316
If holding costs were to increase by $5 per year, how much would the minimum total annual cost?5. For holding cost of 60
EOQ= √(2 * demand * ordering cost / holding cost)
= √(2 * 1050 * 15 / 60)
= 23
Annual holding cost = (EOQ / 2) * holding cost
this gives us
= (23 / 2) * 60
= 690
Annual ordering cost = (demand / EOQ) * ordering cost
= (1050 / 23) * 15
= 685
Total cost of managing = AHC+ AOC
= 690 + 685
= 1375
Change in total annual cost = new - old
= 1375 - 1316
= 59
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If 2/3x − 1 = 4, then x=
Answers
Answer: 15/2 or 7.5
Step-by-step explanation:
2/3x = 5
5 divided by 2/3 or 5 x 3/2
= 15/2 or 7.5
Answer: 15/2
Step-by-step explanation:
[tex]\frac{2}{3} x-1=4\\\\\frac{2}{3}x=5\\ \\x=5(\frac{3}{2})\\\\x=\frac{15}{2}[/tex]
rearrange the equation a = 1/2 b to make b the formula
Answers
Answer:
b = 2a
Step-by-step explanation:
a = [tex]\frac{1}{2}[/tex] b ( multiply both sides by 2 to clear the fraction )
2a = b
Answer: b = 2a
Step-by-step explanation:
Original equation
a = (1/2) b
Multiply 2 on both sides
a * 2 = (1/2) b * 2
[tex]\Large\boxed{b=2a}[/tex]
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A 22-ft ladder leans against a building so that the angle between the ground and the ladder is 64°. How high does the ladder reach on the building?
Answers
The height of the ladder on the building is 19.77 feet
How high does the ladder reach on the building?Represent the height of the ladder on the building with h
So, the given parameters are:
Angle, x = 64 degrees
Length of ladder, l = 22 feet
The height of the ladder on the building is calculated using
sin(x) = h/l
Substitute the known values in the above equation
sin(64) = h/22
Multiply both sides by 22
h = 22 * sin(64)
Evaluate the product
h = 19.77
Hence, the height of the ladder on the building is 19.77 feet
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Sue has sourced four wholesalers from where she will buy most of her stock, including arrangements with two suppliers for 30 days credit, while the others are Cash on Delivery (COD).
She has purchased her store fittings and has $15000 of stock (Stock at Valuation - or SAV), with a further $10000 on 30-day credit). The business has an operating cash reserve of $20000.
How many wholesalers require terms of cash on delivery?
Answers
The difference between the total number of wholesalers and those that supply on 30-day credit, gives the number that require cash on delivery as 2
How can the question be analyzed to find the required number of wholesalers?The number of wholesalers Sue has sourced = 4
Terms of two suppliers = 30 days credit
Amount of stock Sue has = $15000
Amount of stock on credit = $10000
Operating cash reserve of the business = $20000
Required:
The number of wholesalers that require terms of cash on delivery
Solution:
Given that the number of wholesalers = 4
The number number of suppliers (wholesalers) that supply on 30-day credit = 2
Therefore;
The number of wholesalers that require terms of cash on delivery = 4 - 2 = 2
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Can someone explain the steps I’m confused
Answers
Answer:
x = 8 ± [tex]\sqrt{10}[/tex]
Step-by-step explanation:
x² - 16x + 54 = 0 ( subtract 54 from both sides )
x² - 16x = - 54
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 8)x + 64 = - 54 + 64
(x - 8)² = 10 ( take the square root of both sides )
x - 8 = ± [tex]\sqrt{10}[/tex] ( add 8 to both sides )
x = 8 ± [tex]\sqrt{10}[/tex]
then
x = 8 - [tex]\sqrt{10}[/tex] , x = 8 + [tex]\sqrt{10}[/tex]
1. In a class of 60 students, a survey was conducted, 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities. Find number of students that applied at most two universities.
Answers
The number of students who applied at most two universities is 26 students.
How is the calculation for the number done?The population of students in a class = 60 students
Number of students who applied for Addis Ababa University = 30 students
Number of students who applied for Bahir Dar University = 25 students
Number of students who applied for Wachemo University = 24 students
Number of students who applied for Addis and Bahir = 11 students
Number of students who applied for Addis and Wachemo = 6 students
Number of students who applied for Wachemo and Bahir = 9 students
The number of students who applied at most two universities is 26 (11+ 6 + 9).
Thus, the number of students who applied at most two universities is 26.
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A fish can swim at 14m/s with the current and at 6m/s against it. Find the speed
of the current and the speed of the fish in still water.
Answers
Answer:
10 m/s
Step-by-step explanation:
Let x = speed of fish and y = speed of current. When swimming with current, the fish's speed is x + y. When swimming against it, the speed is x - y. Therefore, we can set up a system of linear equations to solve for x, the speed of fish.
x + y = 14
x - y = 6
2y = 8
y = 4
x - 4 = 6
x = 10
The speed of fish in still water is 10 m/s, and the speed of current is 4 m/s.
Answer:
Speed of fish in still water = 10 m/s
Speed of current = 4 m/s
Step-by-step explanation:
Let the speed of the fish in still water = x m\s
Let the speed of the current = y m/s
Speed of the fish with the current = x + y
x +y = 14 m/s ------------------(I)
Speed of the fish against current = x -y
x - y = 6 m/s ----(II) &
Add the equations (I) & (II) and 'y' will be eliminated and we can find the value of 'x'.
x + y = 14
x - y = 6 {Now, add)
2x = 20
x = 20/2
x = 10
[tex]\sf \boxed{\text{\bf Speed of fish in still water = 10 \ m / s}}[/tex]
Plugin x = 10 in equation (I)
10 + y = 14
y = 14 - 10
y = 4
[tex]\sf \boxed{\text{\bf Speed of the current = 4 \ m/s}}[/tex]
A triangle with a base of 16 cm and a height of 9 cm.
Answers
Answer: 288
Step-by-step explanation:
(16x9)x2
Which of the following is not true about two integers p and q, where p is even and g is odd? A p+q is odd. B. pq is even C q +1 even. D. q + 5 is odd.
Answers
Answer:
The statement "q + 5 is odd" is FALSE.
Step-by-step explanation:
Let p = 2 and q = 3.
A. p + q is odd ... 2 + 3 = 5 TRUE
B. pq is even ... 2*3 = 6 TRUE
C. q + 1 is even ... 3 + 1 = 4 TRUE
D. q + 5 is odd ... 3 + 5 = 8 FALSE
Pls help w this question
Answers
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
According to given figure,
Angle 11, Angle 20 and Angle 16 forms angles of a triangle,
so, by angle sum property of a triangle :
[tex]\qquad❖ \: \sf \: \angle11 + \angle20 + \angle16 = 180 \degree[/tex]
[tex]\qquad❖ \: \sf \: \angle11 +66 + 43 = 180 \degree[/tex]
[tex]\qquad❖ \: \sf \: \angle11 +109 = 180 \degree[/tex]
[tex]\qquad❖ \: \sf \: \angle11 = 180 \degree - 109[/tex]
[tex]\qquad❖ \: \sf \: \angle11 =71 \degree [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Option B is correcta swimming pool charges £3.60 for entry. you can save 1/3 of entry fee with a membership card. on his first visit, ken spends £5 on a membership card plus the reduced entry fee. how many times does ken visit before he gets back his £5
Answers
The number of times Ken visits, given the £3.6 pool charge, and 1/3 savings per visit is 5 times.
Which method can be used to find the number of times Ken visits the pool to get back his £5?The entry fee = £3.60
Amount saved on entry fee by having a membership card = 1/3 of the entry fee
Amount Ken spends on the membership card and the reduced entry fee = £5
Therefore;
Reduced entry fee = £3.60×(1 - 1/3) = £2.4
Amount saved per visit = £3.6 - £2.4 = £1.2
The number of visits, n, before he gets back his £5 is therefore;
n = £5/(£1.2/visit) ≈ 4.17 visitsKen has to visit the swimming pool more than 4 times to get his £5 back.
Rounding to the next larger whole, therefore;
The number of visits, n, before he gets back his £5 is 5 visitsLearn more about fractions here:
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A certain brand of coffee comes in two sizes. A 12.3-ounce package costs $2.99 . A 33.9-ounce package costs $8.74 . Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
Answers
Answer:
[tex]12.3 - 33.9 = 21.6 \div 10 = 2.16[/tex]
A) 12.3-ounce package costs $2.99 .
B) 33.9-ounce package costs $8.74 .
Find the unit price for each size.
A) 2.99 / 12.3 = .34 per ounce
B) 8.74 / 33.9 = .26 per ounce
The 33.9 ounce size is the better buy based on the unit price of .26 per ounce
what is the length of the hypotenuse of a right triangle whose legs have lengths 12 cm and 16 cm?
Answers
In Pythagorean Theorem, the hypotenuse of a right triangle is always the longest side and is representative of a variable we know as c^2, or c squared. Since we know that the right triangle in this problem has lengths 12 cm and 16 cm, we know that a^2 equals 12 squared and b^2 equals 16 squared. Because the formula for Pythagorean Theorem is a^2 + b^2 = c^2, we can write our problem out:
12^2 + 16^2 = c^2
12^2 (or 12 squared) equals 144 since 12 x 12 = 144
16^2 (or 16 squared) equals 256 since 16 x 16 = 256
Since we know what a squared and b squared equal, we can add them to find what our hypotenuse squared is.
144 + 256 = 400
We now know that our hypotenuse squared equals 400. To find c, we can simply find the square root of 400. You can keep this question in mind when doing it: “What number can be multiplied by itself to get 400?”
When calculating, we will find that the square root of 400 is 20. To verify, we can multiply 20 by itself to see what we get.
20 x 20 = 400
Our equation is true! Therefore, here is your final equation:
12^2 + 16^2 = 20^2
The length of the hypotenuse is 20 cm. If you need any extra help, let me know and I will gladly assist you.
