Answer:
-6x + 6y = 6 (Equation 1)
-6x + 3y = -12 (Equation 2)
We can use the method of elimination, which involves adding or subtracting the equations to eliminate one of the variables.
In this case, we can start by multiplying Equation 2 by 2 to eliminate the x variable:
-6x + 6y = 6 (Equation 1)
-12x + 6y = -24 (Equation 2 multiplied by 2)
Now we can subtract Equation 1 from Equation 2:
-12x + 6y = -24 (Equation 2 multiplied by 2)
-(-6x + 6y = 6) (Equation 1, with the opposite sign)
-6x = -30
Simplifying this expression, we get:
x = 5
Now we can substitute this value of x into either Equation 1 or Equation 2 to solve for y. Let's use Equation 1:
-6x + 6y = 6
-6(5) + 6y = 6
-30 + 6y = 6
6y = 36
y = 6
Therefore, the solution to the system of equations is x = 5 and y = 6, or (5, 6) in coordinate form.
Step-by-step explanation:
Roman opened a savings account and started out the account with $45. He adds $18 each month. He currently has $207 in his account. How many months has he been saving?
Answer:
9
Step-by-step explanation: each month adding 18 starting at 45 and currently at 207 means he gained 162 and divided by 18,9 months.
The distances, in light years, of four stars from a space probe are shown. Put the stars in order from the closest one (least distance) to the farthest one (greatest distance). 0.886 0.883 1.25 0.89
A.
0.883, 0.886, 0.89, 1.25
B.
0.883, 0.886, 1.25, 0.89
C.
1.25, 0.89, 0.886, 0.883
D.
0.886, 0.883, 0.89, 1.25
The stars in order from the closest one to the farthest one are:
0.883, 0.886, 0.89, 1.25
so, the answer is A.
What is a sequence?
A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).
To put the given distances in order from the closest one to the farthest one, we need to arrange them in ascending order.
That means we need to start with the smallest value and move toward the largest value.
Looking at the given distances, we see that the smallest value is 0.883, followed by 0.886, then 0.89, and finally 1.25, which is the largest value.
Putting the given distances in ascending order, we get:
0.883, 0.886, 0.89, 1.25
Therefore, the stars in order from the closest one to the farthest one are:
0.883, 0.886, 0.89, 1.25
so, the answer is A.
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Solve For B. 47.5 degrees, 79.5 degrees
53 is the answer
47.5 + 79.5= 127
180-127=53
Scenario:
JRJ Corporation recently issued 10-year bonds at a price of $1,000. These bonds pay $60 in interest each six months. Their price has remained stable since they were issued, that is, they still sell for $1,000. Due to additional financing needs, the firm wishes to issue new bonds that would have a maturity of 10 years, a par value of $1,000, and pay $40 in interest every six months. If both bonds have the same yield, how many new bonds must JRJ issue to raise $4,000,000?
5190 new bοnds must be JRJ issued tο raise $4,000,000.
What is the interest rate?The amοunt οf interest due each periοd expressed as a percentage οf the amοunt lent, depοsited, οr bοrrοwed is knοwn as an interest rate. The tοtal interest οn a lοaned οr bοrrοwed sum is determined by the principal amοunt, the interest rate, the frequency οf cοmpοunding, and the periοd οf time the lοan, depοsit, οr bοrrοwing tοοk place.
Here, we have
Given: JRJ Cοrpοratiοn recently issued 10-year bοnds at a price οf $1,000. These bοnds pay $60 in interest every six mοnths. Their price has remained stable since they were issued, that is, they still sell fοr $1,000.
Cοupοn rate = 8.0%
Face value = 1000
Year tο maturity = 10
NPER = 20
PMT = Face value × Cοupοn rate / 2 =(1000 × 0.08) / 2 = 80/2 = 40
Yield = 12%
Rate = Yield / 2 = 12% / 2 = 6%
We then calculate the net prοceeds which will be:
= PV(rate, NPER, PMT, FV)
= PV(6%, 20, 40, 1000)
= $770.60
We shοuld nοte that the amοunt that needed tο be raised is $4,000,000. Therefοre, the bοnd that will be needed tο be sοld will be:
= $4,000,000 / 770.60
= 5190bοnds
Hence, 5190 new bοnds must JRJ issued tο raise $4,000,000.
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What is the volume of the cone in cubic feet?
hope you understood the answer
option A
Determine the length of FE.
18
20
21
26
Using the concept of similar triangles, the length of FE is: 26
How to find the length of similar triangles?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Thus, if two triangles are similar, then it means that their corresponding angles are congruent and corresponding sides are in equal proportion.
Using the concept of similar triangles and trigonometric ratios, we can apply that to the given diagram and say that:
tan E = 4/8 = 1/2
tan E = DF/FE
Thus:
1/2 = 13/(FH + HE)
1/2 = 13/(FH + 8)
FH = 18
FE = FH + HE
FE = 18 + 8
FE = 26
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Find the perimeter of the triangle whose vertices are the following specified points in the plane.
(-9,-5), (-6,1) and (5,8)
After calculating the lengths of all 3 sides, we need to add them together to get the perimeter, which is 32.
Perimeter = 32
To find the perimeter of a triangle whose vertices are specified points in the plane, we need to first calculate the lengths of the 3 sides of the triangle. To do this, we need to use the distance formula, which is the square root of (x2 - x1)^2 + (y2 - y1)^2. To calculate the first side, we need to calculate the distance between (-9,-5) and (-6,1), which is 7.14. For the second side, we need to calculate the distance between (-6,1) and (5,8), which is 11.18. For the last side, we need to calculate the distance between (5,8) and (-9,-5), which is 14.86. After calculating the lengths of all 3 sides, we need to add them together to get the perimeter, which is 32.
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Can you solve this question?
A) f'(x)=?
B) slope at x=2: ?
slope at x=3: ?
C) tangent line at x=2: y= ?
tangent line at x=3: y= ?
D) value(s) of x=?
A. The derivative of f'(x) = 26x + 5is 26x + 5
B. Slope at x = 2 is 57
Slope at x = 3 is 83
c. The equation of the tangent line at x = 3 is y - 122 = 83(x - 3), or y = 83x - 179.
D. The value of x where the tangent line is horizontal is x = -5/26.
How to calculate the value(A) f'(x) = 26x + 5.
It should be noted that to find the derivative of f(x), we apply the power rule and the constant multiple rule:
f'(x) = d/dx (13x²+5x)
= d/dx (13x²) + d/dx (5x)
= 26x + 5
(B) ain this case, to find the slope of the graph of f(x) at x = 2 and x = 3, we plug these values into the derivative:
Slope at x = 2: f'(2) = 26(2) + 5 = 57
Slope at x = 3: f'(3) = 26(3) + 5 = 83
(C) Based on the information, to find the equation for the tangent line at x = 2 and x = 3, we use the point-slope form of a line:
Tangent line at x = 2:
We know the slope is 57, and the point (2, f(2)) is on the line.
Plugging in x = 2 to f(x) gives us f(2) = 13(2)² + 5(2) = 58.
So the equation of the tangent line at x = 2 is y - 58 = 57(x - 2), or y = 57x - 56.
Tangent line at x = 3:
We know the slope is 83, and the point (3, f(3)) is on the line.
Plugging in x = 3 to f(x) gives us f(3) = 13(3)² + 5(3) = 122.
So the equation of the tangent line at x = 3 is y - 122 = 83(x - 3), or y = 83x - 179.
D. In order to find where the tangent line is horizontal, we need to find where the slope is equal to zero. Setting f'(x) = 0 and solving for x gives:
f'(x) = 26x + 5 = 0
x = -5/26
Therefore, the only value of x where the tangent line is horizontal is x = -5/26.
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Give one example of matrix of order 2 and 3 in which industrial
World problem is mentioned. Also solve them by using matrix
Inversion method.
It would take 90 hours on the first machine, 20 hours on the second machine, and 0 hours on the third machine to produce 100 units of Product A and 50 units of Product B.
What is matrix ?
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.
Here is an example of a 2x3 matrix that represents a problem in industrial engineering:
Suppose a company produces two types of products, Product A and Product B, and they use three different machines to manufacture these products. The number of hours required to produce each unit of each product using each machine is given by the following matrix:
| 2 3 4 |
| 4 2 3 |
This matrix represents a system of linear equations that can be solved using matrix inversion to find the number of hours required to produce a given number of units of each product. For example, suppose the company needs to produce 100 units of Product A and 50 units of Product B. To find the number of hours required for each machine, we can set up the following system of equations:
2x + 3y + 4z = 100
4x + 2y + 3z = 50
where x, y, and z represent the number of hours required for each machine.
To solve this system of equations using matrix inversion, we can first write the system in matrix form:
| 2 3 4 | | x | | 100 |
| 4 2 3 | * | y | = | 50 |
| 0 0 0 | | z | | 0 |
Next, we need to find the inverse of the coefficient matrix:
| 2 3 4 |^-1 = 1/10 | -6 12 -3 |
| 4 2 3 | | 9 -6 4 |
| 0 0 0 | | 0 0 0 |
Finally, we can solve for x, y, and z by multiplying both sides of the equation by the inverse of the coefficient matrix:
| x | | -6 12 -3 | | 100 | | 90 |
| y | = | 9 -6 4 | * | 50 | = | 20 |
| z | | 0 0 0 | | 0 | | 0 |
Therefore, it would take 90 hours on the first machine, 20 hours on the second machine, and 0 hours on the third machine to produce 100 units of Product A and 50 units of Product B.
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help now pls !!!!!!!!!!!!!!!!!!!!!
Answer: it was another reason for the United States to join the war in the side of the Allie’s.
Step-by-step explanation:
The circle below is centred at O.
a) Work out the size of angle X.
b) Which of the circle theorems below allows you to calculate this angle?
Answer:
61∘
Step-by-step explanation:
Isosceles triangle property:
The triangle in the circle is an isosceles triangle, so that means the lateral sides of the triangle are equal, and so are the angles;
x = 90∘ - 29∘ = 61∘ (90∘, because the tangent and the radius form a right angle (that the b) part, I think))
Find the solution of
{Y≤-x² - 4x +3
Y>x^2+3
Thus, shaded region bounded between the interval (-2,7) and (0,3) are the solution of the given linear inequalities.
Explain about the graphical method?The 2 linear programming is optimised using the graphical approach. Finding the ideal answer is best done using a graphical approach when there are two choice factors in the problem. The collection of inequalities are bound by limitations in this method. The disparities are then shown using an XY plane graphic.
To represent the data visually, there are two different sorts of graphs. As follows: Time Series Graphs - Line Graph as an example. Frequency Polygon Graph is an illustration of a frequency distribution graph.For charting linear functions, there are three fundamental techniques. The first method involves tracing a line through a set of points that have been plotted. The second method makes use of the slope and y-intercept. The third method involves changing the identity function f(x)=x.Given linear inequalities are:
Y ≤ -x² - 4x +3
Y > x² + 3
Plot the graph of each equation using the graphing tool to get he solution.
From the graph:
Blue Region : Y ≤ -x² - 4x +3
green region: Y > x² + 3
Thus, shaded region bounded between the interval (-2,7) and (0,3) are the solution of the given linear inequalities.
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Work out the highest common factor (HCF) of 8 and 20.
Answer: The HCF of 8 and 20 is 4. The factors of 8 are 1, 2, 4, 8, and the factors of 20 are 1, 2, 4, 5, 10, 20.
Step-by-step explanation: Please give Brainlist.
Hope this helps!!!!
Replace each * with a digit that makes the solution of the equation a whole number. Find all possibilities.
5x – 124=10*
Answer:* = 50
Step-by-step explanation:
x = 75.2 5x -124 =500
10 times 50 =500
A packaging employee making $20
per hour can package 160 items
during that hour. The direct
material cost is $.50 per item. What
is the total direct cost of 1 item?
Answer:
To find the total direct cost of one item, we need to calculate the sum of the direct labor cost and the direct material cost.
Direct labor cost per item = (hourly rate)/(number of items per hour) = $20/160 = $0.125 per item
Direct material cost per item = $0.50 per item
Total direct cost per item = direct labor cost per item + direct material cost per item
= $0.125 + $0.50 = $0.625
Therefore, the total direct cost of one item is $0.625.
A company starts to track the number of phone calls recived each month. Infromation about the number of phone calls the company recived the first three months of tracking is listed below.
-During the first month, the company recieved 4,264 phone calls.
-during the second months, the company recieved 25% more phone calls than in the first month.
-during the third month, the company recived 6,396 phone calls
What was the percent in crease in the number of phone calls from the second month to the third month?
The number of phone calls received in the second month is 25% more than the first month, which means:
Number of phone calls in second month = 1.25 x 4,264 = 5,330
To find the percent increase from the second month to the third month, we can use the percent increase formula:
Percent increase = (New value - Old value) / Old value x 100%
Using this formula, the percent increase from the second month to the third month is:
Percent increase = (6,396 - 5,330) / 5,330 x 100%
= 20%
Therefore, the percent increase in the number of phone calls from the second month to the third month is 20%.
In a cross-country race, Duante took 8/9 as long as James to finish. Kofi took 7/8 as long as James to finish. Who took the longest to finish the race?
Using the LCM formula, it is deduced that James took the longest to finish the race.
What is LCM?
In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple. The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers.
Let's assume that James took time "J" to finish the race. Then -
Duante took 8/9 of James' time, which is (8/9)J
Kofi took 7/8 of James' time, which is (7/8)J
To determine who took the longest to finish the race, we need to compare their times.
Let's start by comparing Duante and James -
Duante's time = (8/9)J
James' time = J
Since Duante took less time than James, we can conclude that James did not take the longest to finish the race.
Now let's compare Kofi and James -
Kofi's time = (7/8)J
James' time = J
To compare these times, we need to express them with a common denominator.
The least common multiple of 8 and 1 is 8, so we can rewrite James' time as (8/8)J:
Kofi's time = (7/8)J
James' time = (8/8)J
Now we can compare the times -
Kofi's time = (7/8)J < (8/8)J = James' time
Therefore, Kofi took the least time to finish the race, and James took the longest.
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WILL MARK AS BRAINLIST PLEASE HELP!!
Answer:
a = 125°
Step-by-step explanation:
Angle a and 55° together make up a straight angle (a straight line) that is 180°.
Write an equation.
a + 55° = 180°
subtract 55° from both sides.
a = 180°- 55°
a = 125°
find the area of the figure helppp end of the quarter
Answer:
Step-by-step explanation:
if the front says 5ft+5ft so it equals 10ft
12ft+12ft it equals 24ft
the missing area looks alot like the 5ft+5ft so we measure it...
both sides of the back equals to 5ft each 5ft+5ft=10ft
so just put in the end of the quarter equals 10ft
and if he/she wants you to add it all together it all adds up to 44ft...
What is the value of the expression below when w=4
Answer:2(3)
Step-by-step explanation: 3w-3w+8
2with a power 3
Answer:
= 44
Step-by-step explanation:
3w² - 3w + 8
When
w = 4
Then:
3*4² - 3*4 + 8
= 3*16 - 12 + 8
= 48 - 12 + 8
= 48 + 8 - 12
= 56 - 12
= 44
Circular sector with a radius of 12 inches and a central angle of 120 degrees
Answer:
hope this helps
Step-by-step explanation:
Find the quotient. 98.3÷7 7598.3
a 3.75 kg stone hanging from a rope
vector or scalar? and why?
The object represented by a 3..75 kg stone is scalar object
How to determine if the object is scalar or vectorThe quantity "3.75 kg" is a scalar because it is a single value that only has magnitude, and it does not have a direction associated with it.
On the other hand, the force of gravity acting on the stone and the tension force of the rope holding the stone up are vector quantities because they have both magnitude and direction.
It is important to note that the stone itself does not have a direction associated with it, but the forces acting on it do have direction.
Therefore, when describing the motion of the stone, both scalar and vector quantities are involved.
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1/3 ÷ 4 show your work
Answer:
Forma exacta:
1
12
Forma decimal:
0.083
Step-by-step explanation:
Answer:
[tex] \frac{1}{12} [/tex]
[tex]0.8333... [/tex]
as decimal form
slove the trig problems using the ratios. Remember to use SOH-CAH-TOA
1. solve for side x x = ___
2.solve for side x x = ___
3. solve for angle x x = ____
4. solve for angle x x = ____
thank you
Answer:
Step-by-step explanation:
Hunter's math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. Based on the line of best fit, what quiz score should someone who studied 6 hours expect?
Therefore, we can say that after studying 2.5 hours, a student should expect a quiz score of 81.6 based on the line of best fit.
What is line of best fit?A line of best fit, also known as a trend line, is a straight line that is drawn through a scatter plot to represent the general trend or pattern of the data. It is used to show the relationship between two variables, usually the independent variable (x) and the dependent variable (y), by fitting a line that comes as close as possible to all the data points. The line of best fit can be used to make predictions about future data points or to estimate values of the dependent variable for certain values of the independent variable. The most common method for finding the line of best fit is the method of least squares, which minimizes the sum of the squared differences between the actual data points and the predicted values of the dependent variable on the line.
Here,
The point (2.5, 81.6) represents a data point on the coordinate axes, where the x-coordinate of 2.5 represents the number of hours studied and the y-coordinate of 81.6 represents the quiz score earned by a student who studied for 2.5 hours.
Based on the line of best fit that the math teacher drew, we can use this point to estimate the quiz score for other students who also study for 2.5 hours. The line of best fit is a straight line that passes through the average point of all the data points and is used to predict one variable (quiz score) based on another variable (hours studied).
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Complete question:
Hunter's math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. What does the point (2.5,81.6) represent?
After studying 81.6 hours, a student should expect a score of 2.5. A student who actually spent 81.6 hours studying and got a score of
2.5. A student who actually spent 2.5 hours studying and got a score of 81.6. After studying 2.5 hours, a student should expect a score of 81.6.
.The regression coefficient of Y on X = 1.2 . If
=
−100
2
=
−100
3
, find .
For the regression coefficient, the value of bvu is 0.8.
How to find bvu?Regression coefficient is a measure of the relationship between two variables in a regression analysis. It represents the degree of change in one variable for a unit change in another variable.
Recall that:
u = (x – a)/p
v = (y – c)/q
b[tex]_{yx}[/tex] = q/p × bvu
Given: u = (x-100)/2 and v = (y-200)/3
Thus, q = 3 and p = 2
Since the regression coefficient of Y on X = 1.2.
Thus, b[tex]_{yx}[/tex] = 1.2
b[tex]_{yx}[/tex] = q/p × bvu
1.2 = 3/2 * bvu
bvu = 1.2 * 2/3
Therefore, the value of bvu is 0.8
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Complete Question
The coefficient of regression on Y on X = 1.2.
If U = (x-100)/2 and V = (y-200)/3 .
Find bvu.
area of a triangle vertices are (-3,1), (1,1) and (1,4)
The area of the triangle is 3 square units whose vertices are (-3,1), (1,1) and (1,4). We will use distance formulae in this question.
To find the area of a triangle whose vertices are (-3,1), (1,1), and (1,4), we can use the formula for the area of a triangle:
Area = 1/2 * base * height
where the base and height are perpendicular and are formed by any two sides of the triangle.
To apply this formula, we can choose the line segment between (1,1) and (1,4) as the base of the triangle, since it is a vertical line and therefore has a length equal to the height of the triangle. The length of this line segment is 4 - 1 = 3 units.
Next, we need to find the length of the perpendicular segment from the point (-3,1) to the line containing the base. To do this, we can use the formula for the distance between a point and a line:
distance = [tex]|ax + by + c| / \sqrt{(a^2 + b^2)[/tex]
where a, b, and c are the coefficients of the equation of the line and x, y are the coordinates of the point.
In this case, the equation of the line containing the base is x = 1, so a = 1, b = 0, and c = -1. Plugging in the coordinates of (-3,1), we get:
distance = [tex]|1*(-3) + 0*(1) - 1| / \sqrt{(1^2 + 0^2)} = 2[/tex]
Therefore, the height of the triangle is 2 units.
Finally, we can plug these values into the formula for the area of a triangle to get:
Area = 1/2 * base * height = 1/2 * 3 * 2 = 3
So the area of the triangle is 3 square units.
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Helpppp
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.
What is exponential decay?
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
To find the annual rate of change between 1992 and 2006, we can use the formula:
r = [tex](V_2/V_1)^{1/n}-1[/tex]
where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.
=>r = -0.0839
Therefore, the rate of change between 1992 and 2006 is -0.0839.
To express the rate of change in percentage form, we can multiply the result from part A by 100:
=>r = -0.0839 x 100
=> r = -8.39%
Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.
To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.
From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:
where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.
=>V = 11792.51
Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).
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Type the correct answer in each box.
Compete the statement about these similar cylinders.
Figure 1
D.
9 in
E 4.5 in
5 in
Figure 2
P.
R
The circumference of the base of figure 2 is
(Hint: The circumference of a circle = 2rr and the area of a circle = n², where r is the radius.)
and the area of a
It inches, and the area of the base of figure 2 is
[]
π square inches.
Therefore, the completed statement is: The circumference of the base of Figure 2 is 9π inches, and the area of the base of Figure 2 is 20.25π square inches.
What is area?Area is a measure of the size of a two-dimensional surface or region, typically expressed in square units. It is the amount of space inside a closed shape, such as a square, rectangle, triangle, circle, or any other shape with a well-defined boundary. The concept of area is used in many areas of mathematics, science, and engineering, such as geometry, calculus, physics, and architecture. For example, engineers need to calculate the area of materials, such as the cross-sectional area of a pipe or the surface area of a building, in order to design structures that are strong, efficient, and safe.
Here,
The missing information in the statement can be found by using the given dimensions of the cylinders.
Figure 1 has a height of 9 inches and a radius of 4.5 inches.
Figure 2 is similar to Figure 1, so its height and radius are proportional to those of Figure 1. Let the height of Figure 2 be h inches and the radius be r inches. Then we have:
h/r = 9/4.5 = 2
So the height of Figure 2 is twice the radius.
The circumference of the base of Figure 2 is 2πr, which is equal to 2π(4.5) = 9π inches.
The area of the base of Figure 2 is πr², which is equal to π(4.5²) = 20.25π square inches.
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Answer:
The circumference of the base of figure 2 is 5 π inches, and the area of the base of figure 2 is 6.25 π square inches.
Hope this helps!
Step-by-step explanation:
The cylinders are similar, not congruent. That means the shape is the same but the values are not. The radius of figure 1 ( 4.5 in ) is half of figure 1's height ( 9 in ). That means we can figure out that figure 2's radius will also be half its height ( 5 in ), figure 2's radius is 2.5 in. Plug 2.5 into the circumference and area formulas and you have figure 2's circumference and circle area.