The height of the trapezium is approximately 7.898 ft.
Describe Trapezium?A trapezium (also called trapezoid in some countries) is a quadrilateral with at least one pair of parallel sides. The parallel sides of a trapezium are called the bases, and the non-parallel sides are called the legs. The distance between the bases is called the height or altitude of the trapezium.
There are different types of trapeziums, such as isosceles trapeziums, where the legs are equal in length, and right trapeziums, where one of the angles formed by a base and a leg is a right angle.
The area of a trapezium is given by the formula:
Area = (1/2) × (sum of bases) × height
where the sum of bases is the sum of the lengths of the two parallel sides.
The perimeter of a trapezium is given by the sum of the lengths of all four sides:
Perimeter = length of base 1 + length of base 2 + length of leg 1 + length of leg 2
We can use the formula for the area of a trapezium to solve for its height. The formula is:
Area = (1/2) x (sum of parallel sides) x (height)
We are given the area of the trapezium as 79.395 ft, the length of one of the parallel sides (the base) as 15.1 ft, and the length of the other parallel side as 5 ft. Let's plug these values into the formula and solve for the height:
79.395 = (1/2) x (15.1 + 5) x h
79.395 = 10.05h
h = 79.395 / 10.05
h = 7.898 ft (rounded to three decimal places)
Therefore, the height of the trapezium is approximately 7.898 ft.
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Kennedy is working two summer jobs, making $11 per hour babysitting and making $8 per hour clearing tables. In a given week, she can work at most 17 total hours and must earn no less than $160. If x represents the number of hours babysitting and y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
| x+y(less than or equal to)17
| 11x+8y(greater than or equal to)160
Step-by-step explanation:
Hope this helped! ·∪·
Find an equation for the line that passes through the points (-2,-6) and (6,4).
Step-by-step explanation:
Line P passes through POINTS (-2,6) and (6,4). Using y=mx + b where m is the SLOPE(rise divided by the run), and b is the Y-INTERCEPT. Pick the POINT (6,4) and plug into the Y-INTERCEPT EQUATION above to determine the Y-INTERCEPT
fill in the next 3 numbers for this pattern 0.6, 1.2, 1.8 __ __ __
Answer:
0.6, 1.2, 1.8, _, _, _
1. 2.4
2. 3.0
3. 3.6
Step-by-step explanation:
You increase the number by .6 each time.
A person follows the recipe proportions and uses
14
cups of baking soda. Exactly how many quarts of white vinegar will the person use?
10
1
2
quarts
10 1 2 quarts
13
quarts
13 quarts
24
1
2
quarts
24 1 2 quarts
27
quarts
Step-by-step explanation:
Ans is 12ml per cup times 30
Can someone please help me with and explain this?
Answer:
A
Step-by-step explanation:
Point R is (1, 5).
The transformation (x + 1, y - 1) denotes a translation of one unit to the right and one unit downwards.
Simply add one to the x-coordinate and subtract one to the y-coordinate of R. Hence:
\(R'=((1)+1, (5) -1)=(2, 4)\)
Next, we want to dilate RUST by a scale factor of three. Since the dilation is centered on the origin, we can simply multiply each coordinate by three. This yields:
\(R'=(3(2), 3(4))=(6, 12)\)
Our answer is A.
1. Determine the measure of each unknown angle using the diagram below. h 4 a. m 2 = b. m 3 = c. m_4= 3 2 106°
From the properties of Vertically Opposite Angles we can find the value of angle 2, 3 and angle 4:
VERTICALLY OPPOSITE ANGLE : When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.
In the given figure, angle 3 and 2 are vertically opposite angle,
So, Angle 3 = Angle 2
Similarly, Angle 4 and 106º are the pair of vertically opposite angle
So, Angle 4 = 106º
The sum of all angles at point is equal to 360º
So,
\(\begin{gathered} \angle2+\angle3+\angle4+106=360 \\ \text{ Since},\text{ }\angle4=106\text{ and }\angle3=\angle2 \\ \angle2+\angle2+106+106=360 \\ 2\angle2+212=360 \\ 2\angle2=360-212 \\ 2\angle2=148 \\ \angle2=\frac{148}{2} \\ \angle2=74 \\ \text{ As, }\angle2=\angle3 \\ \angle3=74 \end{gathered}\)So, m<2 = 74º, m<3 = 74º, m<4 = 106º
Answer :
m<2 = 74º
m<3 = 74º
m<4 = 106º
you have earned $151.00 with coins that are $2.00 and $5.00. How many coins of each will you have if you have a total of 47 coins?
The coins are 19 and 28 each
How to calculate the number of coins ?Let x represent the first coin and let y represent the second coin
x + y= 47.....equation 1
2x + 5y= 151.......equation 2
From equation 1
x + y= 47
x= 47-y
Substitute 47-y for x in equation 2
2(47-y) + 5y= 151
94 - 2y + 5y= 151
collect the like terms
94 + 3y = 151
3y= 151 - 94
3y= 57
y= 57/3
y= 19
Substitute 19 for y in equation 1
x + y = 47
x + 19 = 47
x= 47-19
x= 28
Hence the coins are 19 and 28 each
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What is the value of the following function when x = 0?
A) y=-5
B) y=-2
C) y=-1
D) y=0
Answer:
maybe y = -1
cuz if it goes down it goes nearest to -1
What is the inverse of the function?
H^-1(x)=
Answer:
H^-1=2/5x-8/5
Step-by-step explanation:
interchange the variables
x=5/2y+4
so 5/2y=x-4
y=2/5x-8/5
H^-1=2/5x-8/5
Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit. Total score: ____ of 15 points (Score for Question 1: ___ of 4 points) 1. What is the value of x? Show all of your work. Answer:
To solve this equation we must find the value of x using the other values provided in the operation.
What is an equation?An equation is a type of mathematical operation that is characterized by expressing an equality between two expressions, each of these expressions involved in an equation are called members and are separated by the equal sign.
On the other hand, equations are characterized by having elements or known and unknown values related by mathematical operations.
According to the above, it can be inferred that we must use an equation to calculate the value of x using the other values provided by the situation.
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2/3 es equivalente a 4/5?
we can conclude that 2/3 is not equal to 4/5.
To determine if 2/3 is equivalent to 4/5, we can compare the fractions by checking if their ratios are equal. The ratio of 2/3 can be written as 2:3, while the ratio of 4/5 can be written as 4:5.
To check if the ratios are equal, we can cross-multiply and see if the products are equal. Cross-multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction, and the numerator of the second fraction with the denominator of the first fraction.
For 2/3 and 4/5, we have:
2 * 5 = 10
3 * 4 = 12
Since 10 is not equal to 12, we can conclude that 2/3 is not equivalent to 4/5.
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Choose the correct answer below
The correct statement is;
False, because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be x = 2π/3 + 2nx and x = 4π/3 + 2nx.
Option D
How to determine the statementFrom the information given, we have that;
All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx
There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx
Such that n is an integer.
This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.
The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.
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62x+2.63x = 1
Solve
EN
Step-by-step explanation:
answer is in photo above
Answer:
-2/5
Step-by-step explanation:
Same directions as question #1
Sn = ( -1 )n + 1
The sum of the sequence based on the function Sn = ( -1 )n + 1 will be -6.
How to depict the information?The formula for finding the nth term in an arithmetic sequence given as:
= a + (n - 1)d
Here, Sn is given as ( -1 )n + 1. This is used to illustrate the sum in the sequence. Based on the function given, let's assume that n = 5. Therefore, the 5th term will be:
= (-1)n + 1
= (-1)5 + 1
= (-1)6
= -6
Here is the complete question:
Find the 5th term of a sequence given the function Sn = ( -1 )n + 1.
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Match the prompts together.
When matched, the prompts on asymptotes would be:
Vertical asymptote at x=0: The cost of producing pills can never reach 0.Decreasing on (0,∞): As the number of pills produced gets smaller, the average cost of production greatly increases.Horizontal asymptote at y=0: The cost of producing pills cannot be negative.Positive on (0,∞): As more pills are produced, the average cost per pill decreases.How to match the asymptote statements ?The presence of a vertical asymptote at x=0 signifies that the cost of producing pills can never reach a value of 0, remaining persistently positive. Simultaneously, the horizontal asymptote at y=0 serves as a reassuring indication that the cost of producing pills cannot be negative, as it steadfastly remains at or above zero.
This crucial constraint ensures that the cost incurred in the pill production process is always a non-negative quantity. Consequently, the prompt related to the impossibility of negative costs aligns with this notion.
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3
An animal shelter spends $2.35 per day to care for each cat and $5.50 per day to
each dog. Pat noticed that the shelter spent $89.50 caring for cats and dogs on W
Pat found a record showing that there were a total of 22 cats and dogs at the she
Wednesday. How many cats were at the shelter on Wednesday?
22.
I’m
Answer:
10 cats were at the shelter on wednesday
Step-by-step explanation:
Find the value that makes each equation true.
A. 110%n=11 n=
B.
(328 x 128) x k = 328 x (82 x 128)
K=
Answer:
A. \(n=100\)
B. \(k=0\)
Step-by-step explanation:
A. The equation "110% n = 11" can be solved as follows:
110% n = 11
To solve for n, we need to get rid of the percentage sign (%). We can do this by dividing both sides of the equation by 110%, or 0.110 (since 110% is equivalent to 1.1 in decimal form).
(110% n) / 110% = 11 / 110%
n = 11 / 0.110
n = 100
So, the solution for n in the equation "110% n = 11" is n = 100.
B. The given equation is:
(328 x 128) x k = 328 x (82 x 128) x k
To solve for k, we can simplify the equation using the properties of multiplication.
Step 1: Perform the multiplications inside the parentheses:
41984 x k = 328 x 10576 x k
Step 2: Rearrange the equation by applying the associative property of multiplication:
41984 x k = 328 x (10576 x k)
Step 3: Divide both sides of the equation by 328:
(41984 x k) / 328 = 10576 x k
Step 4: Cancel out the common factor of k on the left-hand side:
(41984 / 328) x k = 10576 x k
Step 5: Simplify the left-hand side:
128 x k = 10576 x k
Step 6: Subtract 10576 x k from both sides of the equation to isolate k:
128 x k - 10576 x k = 0
Step 7: Factor out k on the left-hand side:
k x (128 - 10576) = 0
Step 8: Simplify further:
k x (-10448) = 0
Step 9: Divide both sides of the equation by (-10448):
k = 0
So, the solution for k in the equation "(328 x 128) x k = 328 x (82 x 128) x k" is k = 0.
PLEASE HELPPP THANKS
Answer: The last option. X is greater than or equal to -3
Step-by-step explanation:
If you are searching for all of the values highlighted in red, then it must be every single value greater than x=-3 including the value itself (the dot located on the value is shaded, therefore you must include it within the domain).
2. CTfastrak bus waiting times are uniformly distributed from zero to 20 minutes. Find the probability that a randomly selected passenger will wait the following times for a CTfastrak bus. b. Between 5 and 10 minutes. c. Exactly 7.5922 minutes. d. Exactly 5 minutes. e. Between 15 and 25 minutes.
Answer:
b. 0.25
c. 0.05
d. 0.05
e. 0.25
Step-by-step explanation:
if the waiting time x follows a uniformly distribution from zero to 20, the probability that a passenger waits exactly x minutes P(x) can be calculated as:
\(P(x)=\frac{1}{b-a}=\frac{1}{20-0} =0.05\)
Where a and b are the limits of the distribution and x is a value between a and b. Additionally the probability that a passenger waits x minutes or less P(X<x) is equal to:
\(P(X<x)=\frac{x-a}{b-a}=\frac{x-0}{20-0}=\frac{x}{20}\)
Then, the probability that a randomly selected passenger will wait:
b. Between 5 and 10 minutes.
\(P(5<x<10) = P(x<10) - P(x<5)\\P(5<x<10) = \frac{10}{20} -\frac{5}{20}=0.25\)
c. Exactly 7.5922 minutes
\(P(7.5922)=0.05\)
d. Exactly 5 minutes
\(P(5)=0.05\)
e. Between 15 and 25 minutes, taking into account that 25 is bigger than 20, the probability that a passenger will wait between 15 and 25 minutes is equal to the probability that a passenger will wait between 15 and 20 minutes. So:
\(P(15<x<25)=P(15<x<20) \\P(15<x<20)=P(x<20) - P(x<15)\\P(15<x<20) = \frac{20}{20} -\frac{15}{20}=0.25\)
can you please help me
Answer:
The answer is true!
Step-by-step explanation:
Since B is in the middle and they both are congruent.
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
9,16,23,...
Find the 46th term.
The 46th term of the sequence is 324.
We have,
To find the 46th term of the sequence, we need to determine the pattern or rule that generates the terms.
Since the difference between consecutive terms is a constant value of 7, we know that this is an arithmetic sequence with a common difference
of 7.
To find the 46th term, we can use the formula for the nth term of an arithmetic sequence:
a(n) = a(1) + (n - 1) d
where a(1) is the first term, d is the common difference, and n is the term number we want to find.
Using the given information, we have:
a(1) = 9
d = 7
n = 46
Plugging these values into the formula, we get:
a (46) = 9 + (46 - 1)7
a (46) = 9 + 45 (7)
a(46) = 9 + 315
a(46) = 324
Therefore,
The 46th term of the sequence is 324.
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solve for the missing value
1/2:4=1/3:x
Which algebraic expression is a polynomial with a degree of 2?
O4x³-2x
O 10x²-√x
O 8x³+ 5 +3
6x² - 6x + 5
6x² - 6x + 5 is the algebraic expression that is a polynomial with a degree of 2.
The algebraic expression that is a polynomial with a degree of 2 is:
6x² - 6x + 5
A polynomial expression is a sum of terms where each term consists of a coefficient multiplied by one or more variables raised to non-negative integer exponents. The degree of a polynomial is determined by the highest exponent of the variable in any term of the polynomial.
In the expression 6x² - 6x + 5, the highest exponent of the variable x is 2 in the term 6x². The other terms have lower exponents, with -6x having an exponent of 1 and 5 having an exponent of 0. Therefore, the degree of the polynomial is 2, which is the highest exponent in the expression.
Hence, 6x² - 6x + 5 is the algebraic expression that is a polynomial with a degree of 2.
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Shawn wants to paint all the surfaces of the table shown below.
A. the volume of 3 rectangular prisms
B. the surface area of 1 triangle and 4 cylinders
C. the volume of 1 rectangular prism and 3 cylinders
D. the surface area of 2 triangles and 1 rectangular prism
What's the answer? How do I solve for this?!
the answer is D
The figure can be divided into a rectangle and 2 triangles
calculate standard deviation of these:
88
100
85
82
The standard deviation of the given set of numbers is calculated as: 6.833
How to calculate the standard deviation?Standard deviation is defined as a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
We are given the data as: 88, 100, 85, 82
Thus:
To find the standard deviation of a set of numbers, first find the mean (average) of the set of numbers:
(88 + 100 + 85 + 82)/4 = 88.75
Second, for each number in the set, subtract the mean and Add the square the result:
(88 - 88.75)² + (100 - 88.75)² + (85 - 88.75)² + (82 - 88.75)² = 186.75
Standard deviation = √(186.75/4)
= 6.833
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4x(x + 1) − (3x − 8)(x + 4)
The simplified form of the expression 4x(x + 1) − (3x − 8)(x + 4) is -3x^2 - 4x - 32.
To simplify the expression 4x(x + 1) − (3x − 8)(x + 4), we can expand the parentheses and combine like terms.
Expanding the first term, we get 4x^2 + 4x.
Expanding the second term, we have -(3x)(x) - (3x)(4) - (-8)(x) - (-8)(4), which simplifies to -3x^2 - 12x - (-8x) - (-32), further simplifying to -3x^2 - 12x + 8x - 32.
Combining like terms, we obtain -3x^2 - 4x - 32.
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Cómo se hace y cómo es el proceso ayuda porfaaaaa
Answer:
30: 100
31: -13
32: -45
33: 14
34: -32
35: -22
36: 17
Pls help, answer within 5 minutes
Answer: I thin it’s Opposite of 2
Step-by-step explanation:
Answer:
The distance between A and D
Step-by-step explanation:
when it is |-2| (in the box) it changes to 2
Becky spends 10% of her day eating, 15% free time, 10% homework, 25% school, and 40% sleeping. How many hours does Becky spend doing homework and eating, together?
Answer:
20%, which is 4.8
Step-by-step explanation:
Answer: 4.8 hours
Step-by-step explanation: To get the decimal equivalent of 20 percent of 24 hours, the percentage of how much time Becky spent eating and doing homework, you have to multiply 24 by 0.2, since 0.2 is 20 percent of 1, which gives you 4.8 hours.
Optimal Chapter-Flight Fare If exactly 212 people sign up for a charter flight, Leisure World Travel Agency charges $292/person. However, if
more than 212 people sign up for the flight (assume this is the case), then each fare is reduced by $1 for each additional person. Determine how
many passengers will result in a maximum revenue for the travel agency. Hint: Let x denote the number of passengers above 212. Show that the
revenue function R is given by R(x) = (212+x)(292-x).
passengers
What is the maximum revenue?
$
What would be the fare per passenger in this case?
dollars per passenger
Answer:
Dollars per passenger would be $252.
The maximum revenue is $63,404.
Step-by-step explanation:
Let's define the number of passengers above 212 as x.
The revenue function is given by R(x) = (212 + x)(292 - x).
We can expand and simplify the revenue function:
\(R(x) = 212 * 292 + 212 * (-x) + x * 292 + x * (-x)\)
= \(61804 - 212x + 292x - x^2\)
= \(-x^2 + 80x + 61804\)
The revenue function is a quadratic function in the form\(R(x) = -x^2 + 80x + 61804\), representing a downward-opening parabola.
To find the x-coordinate of the vertex (which gives the number of passengers for maximum revenue), use the formula \(x = -b/2a\), where \(a = -1\) and \(b = 80\).
\(x=\frac{-80}{2*(-1)}\)
\(= \frac{80}{2}\)
\(= 40\)
Therefore, the number of passengers above 212 for maximum revenue is 40.
Substitute x = 40 into the revenue function to find the maximum revenue:
\(R(x) = -(40)^2 + 80(40) + 61804\)
\(= -1600 + 3200 + 61804\)
\(= 61804 + 1600\)
\(= 63404\)
Hence, the maximum revenue is $63,404.
To determine the fare per passenger, subtract x from the base fare of $292:
Fare per passenger = Base fare - x
\(= 292 - 40\)
\(= 252\) Dollars per passenger.