Step-by-step explanation:
there is something severely wrong with the problem definition.
when the Hypotenuse = 9, there is no 30-60-90 triangle with a leg = 6.
and when we are just focusing that this is a right-angled triangle with the Hypotenuse = 9, then 6 cannot be the longer leg.
it is also not clear what the solution is supposed to be. the 2nd leg ? the area ? the perimeter ? the height(s) ? ...
what ?
so, all I can do here is to show you why I said what I said :
30-60-90 triangle with Hypotenuse = 9
then the longer leg is opposite of the 60° angle and therefore sin(60)×9 = 7.794228634...
the shorter leg is opposite of the 30° angle and therefore sin(30)×9 = 0.5×9 = 4.5
a right-angled triangle with Hypotenuse = 9, one leg = 6 gives us per Pythagoras for the other leg
9² = 6² + leg²
81 = 36 + leg²
45 = leg²
leg = sqrt(45) = 6.708203932...
so, you see, as stated above, there is no leg with the length 6 in such a 30-60-90 triangle.
and in a more general right-angled triangle, if one leg = 6, then the other leg is actually longer.
therefore, there is everything wrong with the problem definition.
A cabinet was ordered from a carpenter with a volume of 1.08 m³. He wrote down the following measurements: 1.2 m wide and 1.8 m high, but forgot to write down the depth. Therefore, the depth measurement is
The depth of this cabinet is equal to 0.5 m³.
VolumeVolume is a three-dimensional measure that indicates the space occupied by an object. It is a physical quantity that expresses the amount of space an object occupies in three dimensions - length, width and height.
Note that this cabinet has the shape of a parallelepiped, and its volume is found by multiplying its dimensions. Calculating the depth measurement, we have:
1,08 m³ = 1,2 m * 1,8 m * p
p = 1,08 m³/(1,2 m * 1,8 m)
p = 1,08 m³ / 2,16 m³
p = 0,5 m
What is the equation of the line thatt is parallel to the given line and passes through the point (12,-2)?
We want to write it in slope-intercept form:
y = mx + (b' = -12m - 2).
What is the parallel and perpendicular line equation?The slope of parallel lines is the same. The slopes of perpendicular lines are opposite reciprocals. To put it another way, if m=ab, then m=ba. To find the equation of a line, first determine the slope using the given information.
We can use the fact that parallel lines have the same slope to find the equation of a line that is parallel to a given line and passes through a given point.
Assume that the given line has the equation y = mx + b, where m represents the slope and b represents the y-intercept.
The slope of the line we are looking for is m because it is parallel to the given line. Because we don't know what the y-intercept of this line is, let's call it b'.
We now have two pieces of information regarding the new line:
It has the same slope as the given line (m).
It runs through the point (12,-2).
We can use this data to calculate the equation of the new line:
To begin, we can use the point-slope form of a line equation:
y - y1 = m(x - x1) (x - x1)
(x1, y1) denotes the point (12,-2) and m denotes the slope of the given line.
Substituting known values:
y - (-2) = m(x - 12) (x - 12)
Simplifying:
y + 2 = mx - 12m
We must now calculate the value of b' that makes this equation true for any point on the line. Because b' is the line's y-intercept, we can set x = 0 and solve for y:
y + 2 = m(0) - 12m
y = -12m - 2
As a result, the equation of the line parallel to the given line and passing through the point (12,-2) is:
y = mx - 12m - 2
Alternatively, we can write it in slope-intercept form:
y = mx + (b' = -12m - 2).
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Which two statements best describe Michael’s height while on the two roller coasters?
It switches between negative and positive every 40 seconds. it switches between positive and negative every 80 seconds. So correct statements are B and E.
Describe Algebra?Mathematics' branch of algebra deals with symbols and the formulas used to manipulate them. It is an effective tool for dealing with issues involving mathematical expressions and equations. In algebra, variables—which are typically represented by letters—are used to represent unknowable or variable quantities.
Equations represent mathematical relationships between variables in algebra. An equation is made up of two expressions, one on either side of an equal sign, separated by an equation. Algebraic expressions can involve constants, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
As we can see from the first roller coaster's graph, Michael's height changes from positive to negative after 40 seconds, whereas it was positive for the first 40. It remains negative between 40 and 80 seconds. It continues to be positive from 80 to 120, and so forth.
As a result, every 40 seconds it alternates between negative and positive.
B is accurate.
We can see from the second roller coaster's table that it stays positive from 0 to 80. It continues to be negative from 80 to 160, and so forth.
As a result, every 80 seconds it alternates between positive and negative.
E is accurate.
The complete question is:
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The surface area of a cylinder is given by the formula SA = 2r2 + 2rh. A cylinder has a radius of 12 cm and a surface area of 1,632 cm^2 . Find the height of the cylinder.
A. 52 cm
B. 56 cm
C. 59 cm
D. 34 cm
Canada had 12,968,000 visitors in 2002 while Mexico had 9,807,000 visitors. How many more people visited Canada?
Step-by-step explanation:
To find out how many more people visited Canada than Mexico, we need to subtract the number of visitors to Mexico from the number of visitors to Canada:
12,968,000 - 9,807,000 = 3,161,000
Therefore, 3,161,000 more people visited Canada than Mexico in 2002.
A young sumo wrestler decided to go on a special diet to gain weight rapidly. He gained weight at a constant rate.
The table compares the wrestler's weight (in kilograms) and the time since he started his diet (in months).
Time (months) Weight (kilograms)
1.5
1.51, point, 5
85.8
85.885, point, 8
3.0
3.03, point, 0
93.6
93.693, point, 6
4.5
4.54, point, 5
101.4
101.4101, point, 4
What was the wrestler's weight before he went on his diet?
The wrestler's weight before he went on his diet was 78.0 kilograms.
What is y-intercept?
In the context of a graph of a function, the y-intercept is the point where the graph intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is zero. Geometrically, the y-intercept is the value of the function at the point where it crosses the y-axis.
To determine the wrestler's weight before he went on his diet, we need to find the y-intercept of the linear function that represents his weight gain over time. This is because the y-intercept corresponds to the initial weight of the wrestler, i.e., his weight before he started his diet.
We can use the two data points where the time is 0 (i.e., at the start of the diet) to find the slope of the linear function:
(1.5, 85.8) and (3.0, 93.6)
The change in weight over the time interval of 1.5 to 3.0 months is:
93.6 - 85.8 = 7.8
The change in time over that interval is:
3.0 - 1.5 = 1.5
So the slope of the linear function is:
7.8 / 1.5 = 5.2
Now we can use the point-slope form of a linear function to write an equation for the wrestler's weight gain over time:
y - 85.8 = 5.2(x - 1.5)
where y represents the wrestler's weight and x represents the time in months.
To find the wrestler's weight before he went on his diet, we need to evaluate this equation at x = 0:
y - 85.8 = 5.2(0 - 1.5)
y - 85.8 = -7.8
y = 78.0
Therefore, the wrestler's weight before he went on his diet was 78.0 kilograms.
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The radius of a cylindrical water tank is 4 ft, and its height is 6 ft. What is the volume of the tank?
Use the value 3.14 for it, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
0
4 ft
6 ft
In response to the stated question, we may state that Therefore, the cylinder volume of the tank is approximately 301 cubic feet.
what is cylinder?A cylinder is a three-dimensional polyhedron made up of two congruent parallel circular bases but a curving surface linking the two bases. The bases of a cylinder are all equal to its axis, which is an artificial straight line across the centre of both bases. The volume of a cylinder is the composite of its base area and length. The volume of a cylinder is computed as V = r2h, where "V" represents the volumes, "r" represents the circle of the base, and "h" is the height of the cylinder. The formula to find the volume of a cylinder is:
[tex]V = \pir^2h[/tex]
Where V is the volume, r is the radius, h is the height, and π is a constant value that approximates to 3.14.
[tex]V = 3.14 * 4^2 * 6\\V = 3.14 * 16 * 6\\V = 301.44\\V = 301 ft^3[/tex]
Therefore, the volume of the tank is approximately 301 cubic feet.
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You want to create a simulation of the following scenario:
In country x 50% of people have blood type O, 25% have blood type A, 12.5% have blood type B, and 12.5% have blood type AB.
In country y, 60% have blood type O, 20% have type A, 10% have type B and 10% have type AB.
What is the best way to assign values for a simulation using random digits table?
Choose answer from photo below! A, B, C, or D : this is the answer I want, not just an explanation please, thank you so much! 100 points!
Thank you :)
The best way to assign values for a simulation using random digits table will be option A.
What will be the simulation?The best way to assign values for a simulation using a random digits table would be to use a table with at least 10 digits (0-9) in each row.
For Country X, we would assign Blood type O with the digits 0-5, Blood type A with digits 6-7, Blood type B with digit 8, and Blood type AB with digit 9. If a digit outside of these ranges is generated, it would be ignored.
For Country Y, we would assign Blood type O with the digits 0-5, Blood type A with digits 6-7, Blood type B with digit 8, and Blood type AB with digit 9. Again, if a digit outside of these ranges is generated, it would be ignored.
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In ΔVWX, v = 33 inches, w = 57 inches and ∠X=147°. Find ∠W, to the nearest degree.
A flower bed is 2 meters wide and 3 meters long.What is the area of the flower bed i square feet? Round your converted dimensions and your final answer to the nearest hundredth show your work.
Answer:
64.58
Step-by-step explanation:
1 meter is 3.28084 so 3 meters is 9.84252 because you multiply it by 3 or add them to each other 3 times. 2 meters is 6.56168 because you multiply it by 2 or add them to each other. now that you have 6.56168 and 9.84252 multiply them with each other and you get 64.5834666336 but it was said to round to nearest hundredth so since the 3 in front of the 8 is not a 5 and above the answer is 64.58 and not 64.89
The sum of twice a number,n, and 14 is 30. Write an equation that models this statement.Then explain how you might use reasoning to find the value of n.
Answer:
2n + 14 = 30
Step-by-step explanation:
Since you know that 2n + 14 = 30, we can determine the values by first subtracting 14 from 30. Our equation would then be 2n = 16. Divide 2 from both sides and n = 8.
This model represents the total on the top and the 2 parts on the bottom.
Find the perimeter of a rectangle with w=5 and l=9
Answer:
28 units
Step-by-step explanation:
The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width.
Substituting l = 9 and w = 5, we get:
P = 2(9 + 5) = 2(14) = 28
Therefore, the perimeter of the rectangle is 28 units.
Part D
The table in part C did not have a row for 10°. Look at the values of other powers of 10 in the table. Given the pattern of the values, what would
the value of 10° be?
Therefore, we can assume that the value of 10⁰ would be 1, based on the pattern of the other values in the table.
What is Celsius?Celsius (symbol: °C) is a temperature scale used in the metric system. It is named after the Swedish astronomer Anders Celsius, who first proposed it in 1742. The Celsius scale is based on the properties of water, with 0°C defined as the freezing point of water, and 100°C defined as the boiling point of water at standard atmospheric pressure. Celsius is widely used in many countries around the world as a unit of temperature measurement, including in scientific and everyday contexts.
Given by the question.
In the table from part C, we see that as the power of 10 decreases by 1, the value of 10 raised to that power also decreases by a factor of 10. For example, we see that 10² = 100, 10¹ = 10, and 10⁰ = 1.
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23 x _ = 23 x 4
(help me)
Answer:
4
Step-by-step explanation:
To solve for the missing value in 23 x _ = 23 x 4, you can use the property of equality to divide both sides by 23. This will give you _ = 4. Therefore the missing value will be 4.
Hope this helped :)
Answer: the answer is 4
Step-by-step explanation: u can divide both sides with 23 and that leaves u with x=4
In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.
Using trigonometric functions, we can find that the value of the angle N is 3°.
What are trigonometric functions?The six fundamental trigonometric operations make up trigonometry. Trigonometric ratios are useful for describing these methods. The sine, cosine, secant, co-secant, tangent, and co-tangent functions are the six fundamental trigonometric functions. On the ratio of a right-angled triangle's sides, trigonometric identities and functions are founded. Trigonometric formulas are used to determine the sine, cosine, tangent, secant, and cotangent values for the perpendicular side, hypotenuse, and base of a right triangle.
Here, using the cosine theorem:
CosM = n² + l² - m²/2nl
⇒ Cos 149° = 27² + 70² - m²/2 × 27 × 70
⇒ -0.981 = 729 + 4900 - m²/3780
⇒ 5629 - m² = -3708
⇒ m² = 9337.
Now Cos N = m² + l² - n²/2ml
= (9337 + 4900 - 729) / (2 × √9337 × 70)
= 0.9985
Cos N = 0.9985
Putting [tex]Cos^{-1}[/tex] on both sides:
[tex]Cos^{-1}[/tex] Cos N = [tex]Cos^{-1}[/tex] 0.9985
⇒ N ≈ 3°
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The complete question is:
In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.
Simplify 1/cos x + 1/cos x -1
Answer:
-2cotxcscx
Step-by-step explanation:
Step 1: Find a common denominator
Step 2: Simplify
A solid metal cone has radius 1.65 cm and slant height 4.70 cm. Find the angle the, slant height makes with the base of the cone.
Answer:
Step-by-step explanation:
We can use trigonometry to find the angle between the slant height and the base of the cone.
The base of the cone is a circle with radius 1.65 cm. The slant height is the hypotenuse of a right triangle whose other two sides are the height (which we don't know) and the radius (1.65 cm).
Using the Pythagorean theorem, we can find the height of the cone:
height^2 = (slant height)^2 - (radius)^2
height^2 = (4.70 cm)^2 - (1.65 cm)^2
height^2 = 19.96 cm^2 - 2.72 cm^2
height^2 = 17.24 cm^2
height = sqrt(17.24) cm
height = 4.15 cm (rounded to two decimal places)
Now we can use trigonometry to find the angle between the slant height and the base of the cone.
tan(angle) = opposite / adjacent
tan(angle) = height / radius
tan(angle) = 4.15 cm / 1.65 cm
tan(angle) = 2.515
Taking the inverse tangent (or arctan) of both sides, we get:
angle = arctan(2.515)
angle = 70.32 degrees (rounded to two decimal places)
Therefore, the angle between the slant height and the base of the cone is 70.32 degrees.
A sweater originally cost $42.75. Last week, Keisha bought it at 20% off.
What is the discount?
O A. $51.30
08 $42.95
c. $8.55
D. $42.55
Answer:
The discount is $8.55, which is option C.
Step-by-step explanation:
To find the discount, we need to calculate 20% of the original price:
Discount = 20% x $42.75
Discount = $8.55
Therefore, the discount is $8.55, which is option C.
I am struggling to correct numbers 1, 3, 4, 5, and 7. I have been working for hours on this.
Answer:
Step-by-step explanation:
1. sinL = 3/5
3. cosL = 4/5
4. sinN = 4/3
5. cos32 = x/14
x = 14(cos32) = 11.9
7. tan75 = 17/x
x = 17/tan75 = 4.56 ≈ 4.6
11 Sabina travels from London to Telford.
A ticket from London to Telford normally costs £65.25
Sabina gets off the cost of the ticket.
Amir travels by train from London to Coventry and then from Coventry to Telford.
The ticket from London to Coventry costs £23.75
The ticket from Coventry to Telford costs £14.95
Work out the difference between the cost of Sabina's journey and the cost of
Amir's journey.
"I have to say a lot of people have been asking this question. No, really. A lot of people come up to me and they ask me. They say, 'What's 2+2?' And I tell them look, we know what 2+2 is. We've had almost eight years of the worst kind of math you can imagine. Oh my god, I can't believe it. Addition and subtraction of the 1s the 2s and the 3s. Its terrible. Its just terrible. Look, if you want to know what 2+2 is, do you want to know what 2+2 is? I'll tell you. First of all the number 2, by the way I love the number 2. It's probably my favorite number, no it is my favorite number. You know what, it's probably more like the number two but with a lot of zeros behind it. A lot. If I'm being honest, I mean, if I'm being honest. I like a lot of zeros. Except for Marco Rubio, now he's a zero that I don't like. Though, I probably shouldn't say that. He's a nice guy but he's like, '10101000101', on and on, like that. He's like a computer! You know what I mean? He's like a computer. I don't know. I mean, you know. So, we have all these numbers and we can add them and subtract them and add them. TIMES them even. Did you know that? We can times them OR divide them, they don't tell you that, and I'll tell you, no one is better at the order of operations than me. You wouldn't believe it. That I can tell you. So, we're gonna be the best on 2+2, believe me. OK? Alright. Thank you." Reporter 1: "But what actually is 2+2?" Trump: "Siddown. No, siddown. I've already answered your question. Haven't I already answered your question. This is what we get from news reporters, folks. Give me a nice question. Yes - you." Reporter 2: "Is your name Donald Trump?" Trump: "Now that's a nice question, folks. That's what I want."
The difference between the cost of Sabina's journey and the cost of Amir's journey is -£38.70.
We have,
The cost of Sabina's journey is £65.25.
Since she gets off the cost of the ticket, her journey is free, so the cost is £0.
Amir's journey consists of two segments:
London to Coventry and Coventry to Telford.
The cost of the London to Coventry ticket is £23.75, and the cost of the Coventry to Telford ticket is £14.95.
Difference = Sabina's Journey Cost - Amir's Journey Cost
Difference = £0 - (£23.75 + £14.95)
Difference = £0 - £38.70
Difference = -£38.70
This means that Amir's journey is £38.70 more expensive than Sabina's journey.
Therefore,
The difference between the cost of Sabina's journey and the cost of Amir's journey is -£38.70.
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You are thinking about changing employment. Your goal is to work for three years and then return to university full-time, in pursuit of an advanced degree. A potential employer just offered you an annual salary of R55 000, R60 000, and R65 000 a year for the next three years, respectively. All salary payments will be made as lump sum payments at the end of each year. The offer also includes a starting bonus of R4 500, payable immediately. What is this offer worth to you today, at a discount rate of 8,25%?
Answer:
55K+60K+65K=184K
100% - 8.25%=91.75%
184000x91.75%=168820
Ans:168K
Answer:
Step-by-step explanation:
To determine the value of the offer today, we need to calculate the present value of all the cash flows using a discount rate of 8.25%.
First, let's calculate the present value of the salary payments.
PV(year 1 salary) = R55 000 / (1 + 0.0825)^1 = R50 760.87
PV(year 2 salary) = R60 000 / (1 + 0.0825)^2 = R51 423.95
PV(year 3 salary) = R65 000 / (1 + 0.0825)^3 = R52 110.69
Next, let's calculate the present value of the starting bonus.
PV(starting bonus) = R4 500 / (1 + 0.0825)^0 = R4 500
Finally, we can add up all the present values to find the total present value of the offer:
PV(total offer) = PV(year 1 salary) + PV(year 2 salary) + PV(year 3 salary) + PV(starting bonus)
PV(total offer) = R50 760.87 + R51 423.95 + R52 110.69 + R4 500
PV(total offer) = R158 795.51
Therefore, the offer is worth R158 795.51 to you today at a discount rate of 8.25%.
Simplify the expression to a polynomial in standard form
(x−3)(2x^2 −5x−5)
Answer:
Step-by-step explanation:
To simplify the expression, we can use the distributive property of multiplication:
(x−3)(2x^2 −5x−5) = 2x^3 −5x^2 −5x −6x^2 +15x +15
Next, we can combine like terms:
2x^3 −5x^2 −6x^2 −5x +15x +15 = 2x^3 −11x^2 +10x +15
Therefore, the simplified polynomial in standard form is 2x^3 −11x^2 +10x +15.
Natalie invests $2,000 into a savings account
which earns 11% per year. In 20 years, how
much will Natalie's investment be worth if
interest is compounded monthly? Round to the
nearest dollar.
Answer:
We can use the formula for compound interest to find the future value (FV) of Natalie's investment:
FV = P * (1 + r/n)^(n*t)
Where:
P is the principal amount (the initial investment), which is $2,000 in this case
r is the annual interest rate as a decimal, which is 11% or 0.11
n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly
t is the number of years, which is 20
Substituting the values into the formula, we get:
FV =
2
,
000
∗
(
1
+
0.11
/
12
)
(
12
∗
20
)
�
�
=
2,000 * (1.00917)^240
FV = $18,255.74
Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.
Answer:
$17,870
Step-by-step explanation:
You must use the formula for compound interest.
A = P(1 + r/n)^nt
I suggest you look it up at some point so that you can do these more easily in the future!
please hep me with these 4 questions in math!!
for the first question, the simplest way I solve reflections is by making negatives positive and positives negative.
question 2:
pi is the irrational number as it does not end
question 3:
Slope is equal to -1/2 or -0.5
as it takes 2 units right to go down by 1 unit
Question 4:
C: $11
If f(x) =X+2/x^2 -9
and g(x)=11/x^2+ 3x
(a) find f(x) + g(x)
(b) list all of the excluded values
(c) classify each type of discontinuity
The sum of the two functions f(x) + g(x) is (x+2)/(x^2 - 9) + 11/(x^2 + 3x)
Function calculation.
(a) To find f(x) + g(x), we simply add the two functions together:
f(x) + g(x) = (x+2)/(x^2 - 9) + 11/(x^2 + 3x)
(b) To determine the excluded values, we need to look for values of x that make the denominators of the two functions equal to zero. The denominators are:
x^2 - 9 and x^2 + 3x
Setting these equal to zero and solving for x, we get:
x^2 - 9 = 0 => x = ±3
x^2 + 3x = 0 => x(x+3) = 0 => x = 0 or x = -3
Therefore, the excluded values are x = ±3 and x = 0.
(c) To classify the type of discontinuity at each of the excluded values, we need to examine the behavior of the function as x approaches these values.
At x = ±3, the denominators of both functions become zero, which means that the function is undefined at these values. This creates a vertical asymptote, which is a type of infinite discontinuity.
At x = 0, the denominator of g(x) becomes zero, but the denominator of f(x) does not. This creates a removable discontinuity, because we can define f(0) separately to make the function continuous at this point. Specifically, we can set f(0) = 2/(-9) = -2/9 to remove the discontinuity.
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An old building was demolished. 5 dump trucks are used to
transport a total of 2 tons of rubble. How much rubble did each
truck carry?
HELP PLEASE
Lee puts $5,000 into a stock market index mutual fund That grew at an average of 6.5% per year for 10 years. Without any added deposits or withdrawals, about how much is in Lee's mutual fund account after only 8 years, if you ignore the come pounding?
- 1 and combining like terms
(x² - 4x+9)-(3x² - 6x-9)
Combining the like terms of the expressions (x² - 4x+9)-(3x² - 6x-9) gives -2x² + 2x + 36
What are algebraic expressions?Algebraic expressions are simply described as those mathematical expressions that are known to consist of certain variables, coefficients, terms, factors and constants.
Algebraic expressions are also identified with arithmetic operations. These arithmetic operations are;
SubtractionBracketDivisionParenthesesMultiplicationAdditionFrom the information given, we have;
(x² - 4x+9)-(3x² - 6x-9)
First, expand the bracket
x² - 4x + 9 - 3x² + 6x + 27
Now, collect the like terms
x²- 3x² - 4x + 6x + 9 + 27
Add or subtract
-2x² + 2x + 36
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how do you do this mathematics?
Answer:
What Mathematics
Step-by-step explanation:
The area of a parallelogram with base b and height h is bh. Greta is using tiles shaped like parallelograms to cover her bathroom floor. Each tile has a 4.25-inch base and is 2 inches high.
What is the area of each tile?
Write your answer as a whole number or decimal.
Answer:
Each tile would be 8.5 in
Step-by-step explanation:
Area of parallelogram is A=bh, so 4.25*2= 8.5