a) f1(t) = 1 is a even function, the even part is simply 1/2, and the odd part is 0.
b) f2(t) = t^3 - 2t is odd function, the even part is t^3 - t, and the odd part is -t.
Part (a) asks us to classify the function f1(t) = I as even, odd, or neither. Here, I represents a constant, so f1(t) is a constant function.
A function f(t) is even if f(-t) = f(t) for all t in the domain of f. In other words, the function has symmetry about the y-axis.
A function f(t) is odd if f(-t) = -f(t) for all t in the domain of f. In other words, the function has rotational symmetry about the origin.
For a constant function, we have f(-t) = I = f(t) for all values of t. Therefore, f1(t) is even.
Part (b) asks us to classify the function f2(t) = t^3 - 2t as even, odd, or neither.
To determine whether f2(t) is even, odd, or neither, we need to apply the definitions of even and odd functions.
If f2(t) is even, then we have f2(-t) = f2(t) for all t.
If f2(t) is odd, then we have f2(-t) = -f2(t) for all t.
We can check these conditions as follows:
f2(-t) = (-t)^3 - 2(-t) = -t^3 + 2t
Since f2(-t) is not equal to f2(t) for all t, we know that f2(t) is not even.
We can also check if f2(t) is odd:
f2(-t) = (-t)^3 - 2(-t) = -t^3 + 2t = -f2(t)
Since f2(-t) = -f2(t) for all t, we know that f2(t) is odd.
To find the even and odd parts of a function, we use the following formulas:
even part of f(t) = (f(t) + f(-t))/2
odd part of f(t) = (f(t) - f(-t))/2
For f1(t) = I, the even part is (I + I)/2 = I/2, and the odd part is (I - I)/2 = 0.
For f2(t) = t^3 - 2t, the even part is (t^3 - 2t + (-t)^3 - 2(-t))/2 = t^3 - t, and the odd part is (t^3 - 2t - (-t)^3 + 2(-t))/2 = -t.
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question shown below
The equation of the graphed line can be found to be 2x + 2 y = 4
How to find the equation of the line ?To find the equation of the line, you first need to find the slope which requires picking two points on the line. ( 4, 0 ) and ( 0, 2 )
The slope is:
= Change in y / Change in x
= ( 0 - 2 ) / ( 4 - 0 )
= - 2 / 4
= - 1 / 2
The equation form is:
y = mx + b
m = slope
b = y - intercept which is shown on the line as 2
The equation is:
y = - 1 / 2 x + 2
To put it in the form on the question,
( y = - 1 / 2 x + 2 ) x 2
2 y = - 2 x + 4
2x + 2 y = 4
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A car tire company is testing a new tire that has proposed improved performance in wet conditions. An experiment was performed on a closed, half-mile track in wet conditions with the same car and driver. Two trials were performed with standard and new Wet Condition tires. What would the tire company MOST LIKELY infer based on this data?
Responses
A There is no hypothesis provided.There is no hypothesis provided.
B The hypothesis was neither verified or refuted.The hypothesis was neither verified or refuted.
C The hypothesis of the company is refuted.The hypothesis of the company is refuted.
D The hypothesis of the company is verified.
Answer:
B
Step-by-step explanation:
Based on the information provided, it is not possible to determine the hypothesis of the tire company. Therefore, options C and D can be eliminated.
Option A suggests that no hypothesis was provided, which may be possible. However, it is implied that the hypothesis was related to the proposed improved performance in wet conditions of the new tire. Therefore, option A may not be the best answer.
Option B suggests that the hypothesis was neither verified nor refuted. This is a common outcome in many experiments, and it is possible that the tire company may draw this conclusion based on the data. Therefore, option B is the most likely answer.
So, the tire company MOST LIKELY would infer that the hypothesis was neither verified nor refuted based on this data.
Identify the function of the figure below this is trigonometry by the way
The graph shown is the graph of the cotangent function.
What is the graph of Cotangent?
The graph of the cotangent function, cot(x), is a periodic function that has a period of 2π. The cotangent function is the reciprocal of the tangent function, so its graph is related to the graph of the tangent function.
Like the tangent function, the cotangent function has singularities at x = (n + 1/2)π where n is an integer. At these points, the function has a vertical asymptote, meaning it approaches positive and negative infinity as x approaches (n + 1/2)π from either side.
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commutative property of (32)-5+7?
Answer:
= 34
Step-by-step explanation:
(32)-5+7
32 - 5 + 7
= 32 + 2
= 34.
A group of friends’ dinner bill is $82.95 They want to leave a 15% tip. What is their total dinner bill, including tip?
The total dinner cost, including the tip, comes at $92.40.
What is the percentage of a number explained?The definition of percentage is "out of 100." In mathematics, percentages are used to represent parts of a whole, much as fractions and decimals.A sum is considered to be made up of 100 equal parts when expressed as a percentage. Use the symbol% to denote percentages in numbers.A lunch for a few friends will set you back $82.95
They want to leave a 15% tip.
So,
Amount of tip:
15 % of 82.95 = 15*82.95 / 100
15 % of 82.95 = 12.4425
Total cost = 82.95 + 12.4425
Total cost = 95.3925
Total cost = $92.40
Thus, the total dinner cost, including the tip, comes at $92.40.
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Cual es la mitad de 183
Let A be a random variable the represents the money you earn from Job A and let B be a random variable that represents the money you earn from Job B. The mean amount earned from Job A is $220 with a standard deviation of $30. The mean amount you earn from Job B is $180 with a standard deviation of $35.
a) On average how much more do you make from Job A?
b) What is the standard deviation of the difference in the amount you make (A – B)
c) Your mom really doesn’t want you working two jobs. She offers you the following deal. If you quit Job B, in addition to what you make in Job A, she will give you half of your average Job A salary plus $100. Would you take the deal if making the most money was most important to you? Explain.
The given statement indicates that (a) Your average pay is $40 (b) The standard deviation is 45.12 (c) If you retain both positions, your anticipated income is $400.
The significance of standard deviation?Because it aids in comprehending observations when the data is dispersed, standard deviation is significant. The standard error of the data will be higher the more evenly spread the data is.
a) On average, you make $220 - $180 = $40 more from Job A.
b) The standard deviation of the difference in the amount you make from Job A and Job B is given by:
σ(A - B) = √[σ(A)² + σ(B)²]
= √[(30)² + (35)²]
≈ 45.12
c) To determine whether to take the deal, we need to compare the expected earnings from the two scenarios. If you quit Job B and accept your mom's offer, your total earnings would be:
Earnings = (1/2) × $220 + $100 = $210
On the other hand, if you keep both jobs, your expected earnings would be:
Earnings = $220 + $180 = $400
Since $400 is greater than $210, you would not take the deal if making the most money is the most important thing to you.
It is important to remember that this choice may also be influenced by aspects like the amount of time and effort needed for each work, the chance for professional advancement, job security, and other non-financial considerations.
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i need some help on this problem please
Answer:
C
Step-by-step explanation:
180-2x-2=180*7/9
x=19
he auditors for a health insurance company are reviewing the bills from client's stays at hospitals from last year. the length of stay in days for hospital visits from 20 randomly sampled bills is provided below. use excel and the quartile.inc function to construct a box and whisker plot for the dataset. what is the value of the third quartile? round your answer to two decimal places. hospital length of stay (days) 7 6 7 6 7 8 3 2 6 provide your answer below:
The value of the third quartile is approximately 7.00, rounding it up to two decimal places.
In order to construct a box and whisker plot using Excel and the QUARTILE.INC function we will follow the steps -
Enter the data into a column in Excel.Select the column of data.Click on the "Insert" tab and select "Insert Statistic Chart."Choose "Box and Whisker" from the chart types.The box and whisker plot will be displayed.Using the given data, the third quartile (Q3) can be found using the QUARTILE.INC function in Excel as follows -
Enter the data into a column in Excel.Use the formula =QUARTILE.INC(data, 3) to find the third quartile (Q3).Using this method, rounding the result to two decimal places we get,
Q3 = QUARTILE.INC({7, 6, 7, 6, 7, 8, 3, 2, 6}, 3)
Q3 ≈ 7.00 (rounded to two decimal places)
Therefore, the value of the third quartile is approximately 7.00.
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Part B
Question
To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the
average number of customers per hour. Create : inequality in standard form that represents the restaurant owner's
desired revenue.
Type the correct answer in each box. Use numerals instead of words.
The inequality in standard form that represents the restaurant owner's
desired revenue is x² + 2x - 80 ≤ -65.
What are Inequalities?Inequalities are defined as the expressions consisting of both variables and constants connected by inequality signs like ≠, >, <, ≤ and ≥.
Part A :
Cost : 10 + x
Customers : 16 - 2x
Part B :
Given that,
Hourly revenue = Price paid by each customer × average number of customers per hour.
Price paid by each customer = 10 + x
Average customers per hour = 16 - 2x
Given that the restaurant owner wants a minimum revenue of $130 per hour.
(10 + x) (16 - 2x) ≥ 130
(10 × 16) + (16x) - (10 × 2x) - 2x² ≥ 130
160 + 16x - 20x - 2x² ≥ 130
-2x² - 4x + 160 ≥ 130
Dividing the equation throughout by -2,
x² + 2x - 80 ≤ -65
The inequality sign changes as we multiply or divide with a negative number.
Hence the required inequality is x² + 2x - 80 ≤ -65.
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The complete question is given below.
Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.
Part A
Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that the x represents the number of $1 increases in the cost of buffet.
Part B
To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create inequality in standard form that represents the restaurant owner's desired revenue.
create a file lab2.py and define three classes, polygon, rectangle, triangle (see next page for a visual representation)
Lab2.py is a Python script that creates and manipulates three custom classes. The classes are as follows:
1. Person: This class stores information about a person, such as their name and age.
2. Student: This class inherits from the Person class and adds additional information, such as the student's major and GPA.
3. Instructor: This class also inherits from the Person class and adds additional information, such as the instructor's department and course load.
A file lab2.py and define three classes, polygon, rectangle, triangle is:
class Polygon:
def __init__(self, number_of_sides):
self.number_of_sides = number_of_sides
class Rectangle(Polygon):
def __init__(self, length, width):
Polygon.__init__(self, 4)
self.length = length
self.width = width
def area(self):
return self.length * self.width
class Triangle(Polygon):
def __init__(self, base, height):
Polygon.__init__(self, 3)
self.base = base
self.height = height
def area(self):
return 0.5 * self.base * self.height
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Craig forgot to record the amount of the check he wrote to the hardware store. The statement from his bank shows an ending balance
of $521.60. What is the amount of the check Craig wrote to the hardware store? Define a variable for the unknown quantity. Write and
solve an equation to answer the question.
Answer: Let's call the amount of the check Craig wrote to the hardware store "x".
According to the problem, the statement from Craig's bank shows an ending balance of $521.60. This means that his balance before writing the check was $521.60 + x.
So, we can write the equation:
$521.60 + x = $521.60
Subtracting $521.60 from both sides:
x = 0
This means that Craig's check was for $0.
Step-by-step explanation:
Solve the inequalities
Answer:
m ≥ 6
Step-by-step explanation:
The question asks us to solve the following inequality:
[tex]8m - 8 \geq 40[/tex].
To solve it, we need to make m the subject of the inequality:
[tex]8m - 8 \geq 40[/tex]
⇒ [tex]8m - 8 + 8 \geq 40 + 8[/tex] [Adding 8 to both sides of inequality]
⇒ [tex]8m \geq 48[/tex]
⇒ [tex]\frac{8}{8}m \geq \frac{48}{8}[/tex] [Dividing both sides of inequality by 8]
⇒ [tex]m \geq \bf 6[/tex]
Therefore, the solution to the inequality is m ≥ 6.
a cyclist is riding their bicycle on flat terrain at a speed of 22 miles per hour. the wheels on the bike have a diameter of 26 inches.
The angular speed in radians per minute of the cyclist riding a bike with wheels of diameter 26 inches at a speed of 22 miles per hour is approximately 1124.65 radians per minute.
The formula for the angular speed is:
angular speed = linear speed / radius
where the radius is half the diameter of the wheel. We need to convert the units to be consistent, so let's convert the speed from miles per hour to inches per minute and the diameter from inches to feet:
22 miles per hour = 22 * 5280 feet per hour / 60 minutes per hour
≈ 2437.3 inches per minute
26 inches = 26/12 feet = 2.1667 feet
Now we can calculate the angular speed:
angular speed = 2437.3 / 2.1667 ≈ 1124.65 radians per minute
Your question is incomplete, most likely it was:
A cyclist is riding their bicycle on flat terrain at a speed of 22 miles per hour. the wheels on the bike have a diameter of 26 inches.
Find the angular speed in radians per minute.
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A line passes through point (-6, 1)and has a slope of 3. Write an equation in Ax+By=Cform for this line. CO Use integers for A, B, and C.
An equation in Ax + By=C form for this line include the following: -3x + y = 19.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represents the data points.At data point (-6, 1), a linear equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (1) = 3(x - (-6))
y - 1 = 3x + 18
y = 3x + 18 + 1
y = 3x + 19
In standard form, we have:
-3x + y = 19.
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If one dose of elixir is 6 mL, how many doses are there in 500 mL?
Answer:
83 There is an elixir
total quantity of elixir = 500 mL
quantity of elixir use in one dose = 6 mL
number of dose in 500 mL = 500/6
83.333
Which of the following are like terms?
Select 3 correct answer(s)
Question 1 options:
3x2 & 3x4
3x4 & 2x4
3y2 & 3x2
2x2 & 3x2
x2 & y2
2x & 3x
4x2 & 4x
The like terms in the given options are 3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x
What is like terms?Terms whose variables (such as x or y) with any exponents (such as the 2 in x²) are the same are called like terms,
Examples: 7x and 2x are like terms because they are both "x".
Given are some pairs of expressions, we are asked to identify which are like terms,
We know that, according to the definition of the like terms,
Like terms are those terms which contain the same variable which is raised to the same power,
Therefore, the expressions showing the like terms are,
3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x
Because, they have same variable with same powers.
Hence, the like terms in the given options are 3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x
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a hotel is looking over its occupancy, the number of rooms sold, over the course of the last 20 days. the data are provided below. use excel and the quartile.inc function to construct a box and whisker plot for the dataset. what is the interquartile range? round your answer to two decimal places. hotel occupancy 131 135 139 124 124 121 124 135 124 helpcopy to clipboarddownload csv provide your answer below:
The interquartile range is 16.00
To construct a box and whisker plot in Excel using the Quartile.INC function for the given data, follow these steps:
1) Enter the data into a column in Excel.
2) Select the data column and click on the "Insert" tab in the top menu.
3) Click on "Insert Statistic Chart" and select "Box and Whisker" from the dropdown menu.
4) In the "Chart Elements" menu on the right, click on the arrow next to "Axis Titles" and select "Primary Vertical Axis Title" to add a title for the y-axis.
5) Label the y-axis "Number of Rooms Sold".
6) Right-click on the y-axis and select "Format Axis" from the dropdown menu.
7) In the "Number" menu, select "Number" as the category and set the number of decimal places to 0.
8) In the "Chart Elements" menu, click on the arrow next to "Chart Title" and select "None" to remove the chart title.
9) The resulting box and whisker plot should show the quartiles, the median, and any outliers.
To find the interquartile range, subtract the first quartile (Q1) from the third quartile (Q3). The Quartile.INC function in Excel returns the exclusive quartiles (i.e., does not include the median in either quartile), so the interquartile range is calculated as:
IQR = Q3 - Q1
Using the Quartile.INC function with the given data, we get:
Q1 = 78.5
Q3 = 94.5
Therefore, the interquartile range is
IQR = Q3 - Q1 = 94.5 - 78.5 = 16
Rounding to two decimal places, the interquartile range is 16.00.
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Find a quadratic equation with integer coefficients that has the given solution set.
{-10, 9}
The quadratic equation with integer coefficients that has the given solution set {-10, 9} is x² + x - 90 = 0.
What is a polynomial?Polynomial is an equation written with terms of the form kx^n.
where k and n are positive integers.
There are quadratic polynomials and cubic polynomials.
Example:
2x³ + 4x² + 4x + 9 is a cubic polynomial.
4x² + 7x + 8 is a quadratic polynomial.
We have,
If the given solution set is {-10, 9}.
Then the quadratic equation can be written in factored form as:
(x + 10) (x - 9) = 0
Expanding the product,
x² + x - 90 = 0
Therefore,
The quadratic equation with integer coefficients that has the given solution set {-10, 9} is x² + x - 90 = 0.
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Let t
be the time in weeks. At time t=0
, organic waste is dumped into a pond. The oxygen level in the pond at time t
is given by
f(t)=t2−t+1t2+1
.
Assume f(0)=1
is the normal level of oxygen.
(a) On a separate piece of paper, graph this function.
(b) What will happen to the oxygen level in the lake as time goes on?
The oxygen level will eventually return to its normal level in the long-run.
(c) Approximately how many weeks must pass before the oxygen level returns to 75
% of its normal level?
weeks (Round to at least two decimal places.)
The graph is plotted and attached
The oxygen level will be increasing as time goes on
In 0.5 weeks the oxygen level will return to 75% of its normal level
What will happen to the oxygen level in the lake as time goes on?This is the end behavior of the graph, of the function f(t) = t^2 − t + 1, the graph shows that as t tends to infinity. the oxygen level will continue to increase.
The graph is plotted and attached
From the problem. the normal level of oxygen is at f(0) = 1
75% of 1 = 0.75
From the graph, the oxygen level will return to normal level in 1 week(1, 1) and at 0.5 the oxygen level is 0.75, (0.5,0.75). This is the vertex of the graph.
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(15x²+x²+7)-(6x² - 2x³)-7x²
Answer:
= 3x² + 7 +2x³.
Step-by-step explanation:
Here is my solution to my answer.
A jug contained314 pints of milk at the start of a baking class. At the end of the class, only 3 fluid ounces were left.
How many fluid ounces of milk were used during the class?
Responses
10 fl oz
10 fl oz
23 fl oz
23 fl oz
49 fl oz
49 fl oz
101 fl oz
Answer:
311 fl oz only were used, that is what I got for your answer..
The answer is 49 fl oz
Identifying a Graph from an Equation
Which graph represents a function with amplitude 4 and period pi?
The graph of the function f(x) = 4sin(2x) is illustrated in the image.
What are periodic functions?A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.
Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.
We know sin(x) is a periodic function with amplitude 1 and a period of 2π.
Therefore, A periodic function with amplitude 4 and period π would be,
f(x) = 4sin(2x).
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If △ EFG ∼ △ ABC
, What value of x will make the two triangles similar?
Answer:
the value of x will be 9 they all are similar so we will just take ratios and do cross multiplication
What is the volume of this right cone?
O 40 cm³
O 300 cm³
O 400 cm³
O 480 cm³
15.6 cm
12 cm
10 cm
The volume of the right cone is (c) 400π cm cube
How to determine the volume of the coneFrom the question, we have the following parameters that can be used in our computation:
Radius = 10 cm
Height = 12 cm
The volume of the cone is calculated as
Volume = 1/3πr²h
Substitute the known values in the above equation, so, we have the following representation
Volume = 1/3π * 10² * 12
Evaluate
Volume = 400π
Hence, the volume is 400π cm cube
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The value of the equation is 4.19p = -6.1
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
2.3p - 10.1 = 6.5p - 4 - 0.01p
On simplifying , we get
Adding 4 on both sides , we get
2.3p - 6.1p = 6.49p
Subtracting 2.3p on both sides , we get
4.19p = -6.1
Now , the value of the equation similar to 4.19p = -6.1 is 2.3p - 6.1p = 6.49p
Hence , the equation is 4.19p = -6.1
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How do you find a percentile of normal distribution (probability, probability theory, probability distributions, normal distribution, math)?
To find the percentile of a normal distribution, first determine the mean, then convert the interested value to a standard score, look-up the normal distribution table to find the area to the left of the normal score. Finally, multiply the area by 100.
Steps to find the percentile of a normal distributionDetermine the mean (μ) and standard deviation (σ) of the normal distribution.Convert the value you are interested in (i.e., the score) to a standard score (z-score) using the formula:z = (x - μ) / σ
where x is the value of interest.
Look up the z-score in a standard normal distribution table to find the area (probability) to the left of the z-score.Multiply the area by 100 to get the percentile.For example, suppose you want to find the percentile of a test score of 85, which comes from a normal distribution with a mean of 75 and a standard deviation of 10.
The mean (μ) is 75 and the standard deviation (σ) is 10.The z-score for a test score of 85 is:z = (85 - 75) / 10 = 1
Using a standard normal distribution table, we can find that the area to the left of a z-score of 1 is 0.8413.To find the percentile, we multiply the area by 100:0.8413 * 100 = 84.13
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Stacy says there is not enough information to prove that ACXBCX. Explain why Stacy's statement is incorrect.
Stacy's statement is incorrect because Stacey did not consider the side common side to both triangles such that by Reflexive Property of Congruence.
Reflexive Property of Congruence:
An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry.Stacey did not consider the side common side to both triangles such that by Reflexive Property of Congruence. Together with the two given angle congruencies, we can conclude that by ASA.Stacey did not consider the side common side to both triangles such that by Reflexive Property of Congruence.
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The area of this triangle is 64.8 km². Find the height h.
18 km is the base.
The height of the triangle is?
Answer: 16.2 km
Step-by-step explanation:
The height of the triangle can be found using the area formula for triangles:
Area = (1/2) × base × height
Rearranging the formula to solve for the height gives:
height = (2 × Area) / base
In this case, the area of the triangle is 64.8 km² and the base is given as 8 km. So, the height of the triangle can be calculated as:
height = (2 × 64.8 km²) / 8 km
height = 16.2 km
Answer:
7.2 km
Step-by-step explanation:
the formula for the area of a triangle is 1/2*b*h where b is its base and h is its height. now let's solve for the height
64.8=1/2*18h
64.8=9h
64.8/9=h
7.2 km=h
What can be combined with 2x2? Select
all that apply.
Answer:
its only -11x^2
Step-by-step explanation:
2x^2 and -11x^2 have the same variable.