Answer:
An exponential decay function has the form y = a*b^(-kt) where a is the initial value, b is the base of the exponential function (in this case, 1 - the decay rate as a decimal), k is the decay rate and t is the time.
Given that the initial value is 980, the decay rate is 1% every 2 days and the time is 5 weeks. The first step is to convert the time to the same unit of time as the decay rate, in this case, days: 5 weeks * 7 days/week = 35 days.
The decay rate per day is 1/100 because 1% as a decimal is 0.01, so the decay rate per day is 0.01/2 = 0.005
Now we can plug in the values in the function:
y = 980 * (1 - 0.005)^(-0.005*35)
y = 980 * 0.995^(-17.5)
y ≈ 574.64
So, the value of the quantity after 5 weeks to the nearest hundredth is 574.64
It's worth noting that in this case, the base (1 - decay rate) is less than 1, which implies that the value of the quantity decreases over time.
0.75 * ( x+4)=9. what does x equal?
Answer:
x = 8
Step-by-step explanation:
0.75 * ( x+4) = 9
0.75x + 3 = 9
0.75x = 9 - 3
0.75x = 6
x = 6 / 0.75
x = 8
The explicit rule for an arithmetic sequence is an = 8. 7 + (-1. 4)(n-1). What is the value of the 47th term? round to the nearest tenth, if necessary.
answer: A) -55. 7
The value of the 47th term of the given arithmetic sequence is -55.7
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is always the same.
We are given the explicit rule for an arithmetic sequence as follows -
[tex]a_n[/tex] = 8.7 - 1.4(n-1)
We have to find the value of the 47th term in the series.
So, we have the value of n = 47
The equation will become -
[tex]a_{47}[/tex] = 8.7 - 1.4(47-1)
[tex]a_{47}[/tex] = 8.7 - 1.4(46)
[tex]a_{47}[/tex] = 8.7 - 64.4
[tex]a_{47}[/tex] = -55.7
Thus, the value of the 47th term of the given arithmetic sequence is -55.7
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16 x 6 equals 92 How do I find 6?!?
The area of the rectangle would be 96 square inches.
Option (D) is correct.
What is the area of the rectangle?
The formula for the area of a rectangle is:
Area = length x width
where length is the distance along the longer side of the rectangle and width is the distance along the shorter side of the rectangle.
In the given figure,
The length of the rectangle = 8 + 8 = 16 inches.
Now by using the Pythagoras theorem, we can find the height
[tex]Height= \sqrt{(10)^2-(8)^2} \\\\=\sqrt{100-64}\\\\=\sqrt{36}\\\\=6[/tex]
So the base would be 6 inches.
Now we can find the area of the rectangle
Area = 16 * 6
Area = 96 square inches.
Hence, the area of the rectangle would be 96 square inches.
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The same type of dinner plate is sold in two different packs. Small pack contents 3 plates £5. 25. Large pack contents 12 plates £21. 24 which size packet is the better value for money?
Large pack with 12 plates has better value of money with $1.77 for each plate comparison to smaller pack with $1.75 for each plate.
Number of plates in smaller pack is equal to 3 .
Cost of smaller pack with three plates = $5.25
Cost of each plate in smaller pack = $5.25 / 3
= $1.75
Number of plates in larger pack is equal to 12 .
Cost of larger pack with twelve plates = $21.24
Cost of each plate in larger pack = $21.24 / 12
= $1.77
$1.77 is greater than $1.75.
Larger pack of plates have better value of money for each plate comparing the smaller pack.
Therefore, the larger pack has better value of money than the smaller pack .
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A form of nickel has a half life of 91 years. How much of a 90 gram sample is left after 290 years? 
The amount of the 90gram-sample that will remain after 290 years is 9.88 grams
How to determine the number of half-lives?We'll begin by obtaining the number of half lives that has elapsed. This can be obtained as follow:
Step1
Half-life (t½) = 91yearsTime (t) = 290 yearsNumber of half-lives (n) =?n = t / t½
n = 290 / 91
n = 3.1868
Step 2
determine the amount remaining:
Original amount (N₀) = 90 gramsNumber of half-lives (n) = 3.1868Amount remaining (N) =?The amount remain can be obtained as follow:
N = N₀ / 2^n
N = 90 / 2^3.1868
=9.88
N=9.88 grams
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The points on this graph represent a relationship between x
- and y
-values. Which statement about the relationship is true?
Since the points on this graph represent a relationship between x- and y-values, a statement about the relationship which is true is that: A. it cannot be proportional because a straight line through the point does not go through the origin.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x and y represents the variables or data points.k represents the constant of proportionality.Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.
In conclusion, the relationship between the x-value and y-value isn't proportional because the straight line does not pass through the origin (0, 0).
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Sandra Williams bought a home with a 10. 25% adjustable rate mortgage for 25 years. She paid $9. 27 monthly per thousand on her original loan. At the end of 3 years she owes the bank $50,000. Since then interest rates have increased to 12. 75%. The bank will renew the mortgage at this rate, or Sandra can pay the bank $50,000. She decides to renew and will now pay $11. 10 monthly per thousand on her loan. You can ignore the small amount of principal paid during the 3 years. What was the old monthly payment? $ a0 What is the new monthly payment? $ a1 What is the percent increase in her monthly payment (to the nearest tenth)? a2 %
a) The old monthly payment was = 9.27 × 50 = 463.5
b) The new monthly payment is = 11.10 × 50 = 555
c) The percent increase in his monthly payment is 1.947 %
With a 25-year, 10.25% adjustable rate mortgage, Sandra Williams purchased a property. She made monthly payments of $9.27 per thousand on his initial debt.
According to the question,
The per thousand value of $65000 is, 50000/1000 = 50
Now, the old monthly payment was = 9.27 × 50 = 463.5
She makes the decision to renew and will now make monthly loan payments of $11.10 per thousand.
So, the new monthly payment is = 11.10 × 50 = 555
The percent increase in his monthly payment is = 11.10 /9.27 - 1 × 100
⇒ 19.7411 %
And to nearest tenth it is 1.947%
Hence, the old monthly payment was = 9.27 × 50 = 463.5
The new monthly payment is = 11.10 × 50 = 555
Thus, the percent increase in his monthly payment is 1.947%.
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What is the solution to 9|x + 8| > 45?
x < –3 or x > 13
–3 < x < 13
x < –13 or x > –3
–13 < x < –3
The inequality model of the question will be -13 > x > -3
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
9|x + 8| > 45
now when we remove the modulus there will be two terms.
|x + 8| > 45/9
|x + 8| > 5
-5>x + 8>5
-5-8>x >5-8
-13 > x > -3
Hence, the inequality model will be -13 > x > -3
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2. How many points
of intersection are there
on the graph
of
y=x² + 3x-2
y -x=4
There is one point of intersection on the graph of y = x² + 3x - 2 and y - x = 4
To find the point of intersection, we need to set the two equations equal to each other and solve for x and y.
y = x² + 3x - 2
y - x = 4
x² + 3x - 2 - x = 4
x² + 2x - 6 = 0
(x-3)(x+2)=0
x =3 or x=-2
When x = 3, we substitute it into the first equation y = x² + 3x - 2
y = 3² + 3(3) - 2
y = 9 + 9 - 2
y = 16
When x = -2, we substitute it into the first equation y = x² + 3x - 2
y = -2² + 3(-2) - 2
y = 4 -6 -2
y = -4
So the point of intersection is (3,16) or (-2,-4)
Hence there is only one point of intersection on the graph of y = x² + 3x - 2 and y - x = 4
Eagle Airlines flies charter planes all over the world. Susan, one of the airlines' top pilo
routes in Europe and North Africa. Susan's plane uses 2 kilograms of fuel for every kil
she flies.
There is a proportional relationship between the distance Susan flies (in kilometers), x
the amount of fuel her plane uses (in kilograms), y.
Graph this relationship. Select two points to draw a line.
What is the slope of the line?
The proportional relationship that models this situation is given as follows:
y = 2x.
The graph is given by the image presented at the end of the answer.
How to model the proportional relationship?A proportional relationship is modeled as follows:
y = kx.
In which k is the constant of proportionality.
Susan's plane uses 2 kilograms of fuel for every unit she flies, hence the constant is given as follows:
k = 2.
The relationship is:
y = 2x.
The domain is:
x >= 0, as the number of units flied cannot be negative.
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three people ann, bob and colin have a total of $1.80 between them, each having a different amount. does ann have the most money? (1) ann has $0.6 (2) bob has $0.5
Compared to Ann and Bob, Colin has more. Thus, Ann is not have most money.
In the given question, we have to find Ann have the most money or not.
Three people Ann, Bob and Colin have a total of $1.80 between them, each having a different amount.
Ann has $0.6 amount and Bob has $0.5 amount.
Ann + Bob + Colin = 1.80
0.6 + 0.5 + Colin = 1.80
1.1 + Colin = 1.80
Subtract 1.1 on both side, we get
Colin = 0.70
So Colin has $0.70.
So, Colin has more amount than Ann and Bob. So Ann does not have most money.
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Translate the phrase into a variable expression. Use the letter g to name the variable. If necessary, use the asterisk (*) for multiplication and the slash (/) for division.
The total number of seagulls standing on the pier and the 51 gulls in the air
The expression that represents the ratio between the total number of seagulls standing on the pier and the 51 gulls in the air is given as follows:
g/51.
How to obtain the ratio?The ratio between two amounts a and b is found applying a proportion, which is the division between them.
The amounts for this problem are given as follows:
g is the number of seagulls standing on the pier.51 is the number in the air.Hence the ratio is given as follows:
g/51.
Missing InformationThe problem asks for the expression for the ratio the total number of seagulls standing on the pier and the 51 gulls in the air.
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Kim will choose 1 type of meat and 1 type of cheese for her sandwich. The meats offered are ham, turkey, or roast beef. The cheeses offered are American, Swiss, cheddar, or provolone. Kim dislikes roast beef and Swiss cheese. How many different possible sandwiches does that leave Kim?
5
6
8
12
_______________________________________________________
Show your work!
The number of possible sandwiches does is 6.
What is combination ?
In arithmetic, a combination is a way of choosing gadgets from a set where the order of selection does no longer count. suppose we've got a hard and fast of 3 numbers P, Q and R. Then in what number of methods we can select two numbers from every set, is described via combination.
Given ,
Kim will choose 1 type of meat and 1 type of cheese for her sandwich. The meats offered are ham, turkey, or roast beef.
The cheeses offered are American, Swiss, cheddar, or provolone. Kim dislikes roast beef and Swiss cheese.
factorial of n! = n*(n-1) !
The number of possible sandwiches does = 3!
=3*2 = 6.
Therefore, The number of possible sandwiches does is 6.
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PLEASE ANSWER DUE TOMORROW
The measurement of angles formed by intersecting line segments UT and WV are -
∠TXV = 25°
∠UXW = 25°
∠TXW = 155°
∠UXV = 155°
What is a line segment?
A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
Two line segments UT and WV are given.
The line segment UT and WV are intersecting each other at a point X.
Due to the intersection many angles are formed.
To find the measure of the angles, use the protractor.
The first angle is ∠TXV.
Keep the protractor's midpoint at point X.
Then turn the protractor so that it aligns with line UT.
The measure of ∠TXV is approximately 25°.
The second angle is ∠UXW.
Keep the protractor's midpoint at point X.
Then turn the protractor so that it aligns with line WV.
The measure of ∠UXW is approximately 25°.
The third angle is ∠TXW.
Keep the protractor's midpoint at point X.
Then turn the protractor so that it aligns with line WV.
The measure of ∠TXW is approximately 155°.
The fourth angle is ∠UXV.
Keep the protractor's midpoint at point X.
Then turn the protractor so that it aligns with line UV.
The measure of ∠UXV is approximately 155°.
Therefore, all the four angles are obtained.
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A bakery sells different packages of muffins. The number of muffins, , and the price in dollars, , of their packages of muffins are given in the ordered pairs below. The set of ordered pairs is a relation that is also a function.
The bakery is considering adding a new package of muffins. Which of these combinations would make the relation NOT a function? Select TWO that apply.
A relation might or might not be a function. The connection would cease to be a function because of b. (6, 8) and d. (4, 3).
What are combinations?Combinations are mathematical procedures that count how many different ways a collection of items could be arranged when the order in which they are chosen is immaterial.
Combos' components can be chosen in any hierarchy.
Combinations and permutations can coexist.
Hence, the ordered pair is given:
(x, y) = (1, 2); (2, 3); (4, 5); (6, 7); (12, 13)
For a relation to be a function, all of the x-values must be unique (i.e. no repetition)
From the list of alternatives, options (b) and (d), with x values (6, 7) and (d), already exist in the ordered pair (4,5)
In light of this, (b) and (d) would stop the connection from being a function.
Therefore, a relation might or might not be a function. The connection would cease to be a function because of b. (6, 8) and d. (4, 3).
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Correct question:
A bakery sells different packages of muffins. The number of muffins, x, and the price in dollars, y, of their packages of muffins are given in the ordered pairs below. The set of ordered pairs is a relation that is also a function.
{(1,2),(2,3),(4,5),(6,7),(12,13)}
The bakery is considering adding a new package of muffins. which ordered pairs would make the relation NOT a function? Choose all that are correct.
a. (10,13)
b. (6,8)
c. (8,12)
d. (4,3)
e. (24,18)
Here is some information about the goals scored in some hockey games.
Each game has four quarters.
Goals in hockey games
9
8
7
Number
6
of goals 5
4
3
2
1
The mean number of home
goals scored is 2. 5
The mean number of away
goals scored is 1. 8
How many home and away
games have been played
in total?
0
1st
3rd
4th
+
2nd
Quarter
Away goals
Key:
Home goals
If the mean number of home goals is 2.5 and away goals is 1.88 , then the number of home and away games have been played in total is 32 games .
From the histogram , we get that ,
the total number of home goals is = 9 + 6 + 8 + 7 = 30 goals ;
the total number of away goals is = 2 + 7 + 4 + 5 = 18 goals ;
the mean number of home goals is = 2.5 ;
the mean number of away goals is = 1.8 ;
we know formula that⇒ Mean Goal = (total goals)/(number of games) ;
For Home goals :
⇒ 2.5 = 30/n ⇒ n = 30/2.5 = 22 games .
For Away goals :
⇒ 1.8 = 18/n ⇒ n = 18/1.8 = 10 games .
So , total number of games is = 10 + 22 = 32 games ,
Therefore , In total the total number of home and away games played is 32 games .
The given question is incomplete , the complete question is
Here is some information about the goals scored in some hockey games. Each game has four quarters. the histogram is given below :
The mean number of home goals scored is 2.5 ;
The mean number of away goals scored is 1.8 ;
How many home and away games have been played in total ?
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Josh drank 70 ounces of water yesterday.how many cups of water did he drink
Answer:
8.75
Step-by-step explanation:
Find two numbers that the quotient is between.
4,096 divided by 61
The quotient is between _ and _
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
see image
The quotient from 4,096 divided by 61 is between 66 and 67.
Jude types 1,281 characters in 7 minutes. What is her typing rate in characters per minute?
Answer:
183 charters
7 goes into 12 1 time so 12-7=5
bring down the 8 so 7x8=56 so 58-56=2
being down the 1 and you have 21. 7 goes into 21 three times.
Answer:
183 characters per minute
Step-by-step explanation:
1281 divided by 7
A movie club surveyed 200 high school students. The students were asked how often they go to the movies and whether they prefer action movies or dramas. Their responses are summarized in the following table
The percentage of students that prefer drama is 52%.
The percentage of students that go to the movies three times or more is 34%.
What are the percentages?
Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %. In order to change a number to percentage, multiply the number by 100.
The percentage of students that prefer drama = (total number of students that prefer drama / total number of students surveyed) x 100
= [(70 + 34) / 200] x 100
= (104 / 200) x 100 = 52%
The percentage of students that go to the movies three times or more = (total number of students that go to the movies three times or more / total number of students surveyed) x 100
[(34 + 34) / 200] x 100
(68 / 200) x 100 = 34%
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complete the description of the piecewise function graphed below
The supplied input should simply be replaced in the function definition for that precise interval.
What best describes a piecewise function?An equation or set of equations, rather than a single equation, defines a piecewise-defined function. For a specific interval, each equation is valid.
Find out to which of the above intervals (or inequalities) the supplied input belongs before evaluating a piecewise function at any given input. The function definition for that specific interval should therefore just have the specified input replaced.
When a rule or relationship changes as an input value passes specific "boundaries," we refer to these instances as piecewise functions. For instance, scenarios where the price per piece of a specific item is decreased once the quantity requested exceeds a given amount are frequent in business.
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Does someone mind helping me with this problem? Thank you!
Answer:
x=71; y=19
Step-by-step explanation:
x+y = 90 so x =90-y = 14+3y
so 90=14+4y
90-14 = 4y
76=4y
y=19
x=71
Answer:
x = 71
y = 19
Step-by-step explanation:
I solved by graphing and got (71,19) as included in the image. A more mathematical way to solve is by substitution. You try to find x with one of the equations, plug in x and then solve for y.
x + y = 90
x = 90 - y
90 - y = 14 + 3y
90 - y + y= 14 + 3y + y
90 = 14 + 4y
90 - 14= 14 + 4y - 14
76= 4y
19 = y
x + y = 90
x + (19) = 90
x + 19 - 19= 90- 19
x = 71
Students will present a play in an
auditorium that has 550 seats. Each
student performing in the play must
sell 12 tickets to the performance.
The remaining 370 tickets will be
sold by other students in the school.
Which equation could be used
to
find x, the number of students
performing in the play?
Answer:
550 - 12x = 370
what is the measure of arc BC?
130 degrees
180 degrees
65 degrees
32.5 degrees
The angle subtended by arc BC on center of circle is of 2 times 65 = 130
What is Area of circle ?
Area of circle can be defined as the product of pi and the square of radius of a circle.
Using the property that angle subtended by an arc on center is double than on circumference, you can find measure of arc BC.
The angle subtended by arc BC on center of circle is of 2 times 65 = 130
Given,
The angle subtended by arc BC on circumference is 65 degrees.
We have to find Length of arc BC
Relation between angle at center and angle at circumference by an arc:
"Angle subtended by an arc of a circle on its center is double than angle subtended by it on circumference"
Therefore , angle subtended by arc BC on center of circle is of 2 times 65 = 130 .
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At the nearest wholesale store, 3 bags of cereal cost $21.75. Which equation represents the proportional relationship?
please help
The equation that represents the proportional relationship is: k = 7.25.
What is a Proportional Relationship Equation?A proportional relationship is a relationship between two variables such that one variable is a constant multiple of the other. A proportional relationship can be represented by an equation of the form y = kx where y and x are the variables, and k is the constant of proportionality. This equation can also be written as y/x = k.
From the given information, we have:
Constant of proportionality (k) = 21.75 / 3
k = 7.25
To write the equation, substitute k = 7.25 into y = kx:
y = 7.25x
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Analysis A question on a test asks students to find the speed at which a car
travels. The graph shows a proportional relationship between the distance traveled
in miles and time in hours. Anna incorrectly says that the speed of the car is 59
mile per hour. What is the speed of the car? What error might Anna have made?
The speed of the car is 59 miles per hour. Anna might have made an error by using change in y-coordinates/change in x-coordinates to find a unit rate, instead of change in x-coordinates/change in y-coordinates.
What is defined as speed?Speed is a measure of how quickly something is moving, or how quickly something can be done. It is usually measured in terms of distance traveled per unit of time, such as miles per hour or kilometers per hour. The unit of speed is Miles per hour (mph).Speed can also be measured in terms of the rate of change of a certain quantity. For example, speed can be used to measure acceleration, which is the rate of change in velocity. Speed can also be used to describe the rate of flow of a certain quantity, such as the rate of water flow in a river. Speed is also used to measure the rate at which a certain process is taking place, such as the rate at which a person is typing words. In many cases, speed is used to describe how quickly something is happening relative to something else, such as the speed of light relative to the speed of sound. Speed is an important concept in many fields, including physics, engineering, and sports.To learn more about speed refer to:
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the value of philipine peso is less than the value of one US dollar
The mathematical statement that accurately depicts how value of philipine peso is less than the value of one US dollar is: p < d. The Option C is correct.
What is Less than Symbol all about?The Less-than symbol is used to compare two values where the first number is less than the second number, for example, in ascending order. The opening angle bracket is approximated by the less than symbol.
"<" is the symbol used to represent the less than inequality. The less than sign is a universally recognized math symbol composed of two equal measure strokes intersecting in an acute angle at the left.
For example: If given 2< 5: 2 is less than 5
Missing options "Which of the following mathematical statement represents the given situation? a. d = p b. p>d c. p <d d. none of these
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A boss wants to estimate the proportion of her employees who are satisfied with the company's
parking policy. She puts all 600 employees' names into a hat and picks 50 different names out of
the hat. Of the 50, 47 are satisfied with parking policy and 3 are not satisfied with it.
Which condition for constructing a l-sample z-interval for proportions has the boss failed to
satisfy?
For the given case The boss has failed to satisfy the condition of random sampling without replacement. This condition states that the samples must be taken randomly and with replacement, meaning that each sample is replaced after it has been selected.
In this case, the boss picked the 50 names out of the hat without replacing them, which means that the same names could have been picked more than once. This can lead to a sample bias, as the same names may be overrepresented in the sample. This lack of randomness can lead to an inaccurate estimate of the proportion of employees who are satisfied with the company's parking policy.
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U.S. inflation is intentionally kept at a steady 5%, for a variety of economic reasons. Because of this, the cost
of most things is expected to increase by 5% per year, with few exceptions.
In 2009, minimum wage was set to 7.25, and has not changed since. If it had risen to meet the intended
inflation, what would minimum wage be now in 2023?
A$21.16
B $14.35
C$15.05
D$2,116,.49
Use your formula 1/2(a+b)h, to determine the height of a trapezoid with an area of
24 cubic centimeters and base lengths of 9 cm and 7 cm
The height of the trapezoid that has an area of 24 cubic cm is: 3 cm.
How to Calculate the Height of a Trapezoid?The formula for the area of a trapezoid is 1/2(a+b)h, where a and b are the lengths of the bases and h is the height.
Given that the area of the trapezoid is 24 cubic centimeters and the base lengths are 9 cm and 7 cm, we can plug in those values to the formula and solve for h:
24 = 1/2(9+7)h
24 = 1/2(16)h
24 = 8h
To find h, we divide both sides of the equation by 8:
h = 24/8
h = 3
So the height of the trapezoid is 3 cm.
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