Answer:
1.) 1.5972
2.) 11.4688
3.) 4.9725
4.) 1.81
5.) 29.3112
what is trigonometry ratio and if tan
1) sin θ + tan θ is equal to 5/6. 2) sin θ is 5/12. 3) sec θ + cosecc^2 θ = 12/√119 + 144/25 4) cot θ + sin θ is equal to 169/60.
How to answer the aforementioned question1) To find sin θ + tan θ, we need to find the value of sin θ. Using the identity tan θ = sin θ / cos θ, we can rewrite tan θ as sin θ / cos θ.
tan θ = 5/12 = sin θ / cos θ
Since we are given that 0 < θ < 90, both sin θ and cos θ are positive.
Using the Pythagorean identity[tex]{sin^2}[/tex] θ + [tex]cos^2[/tex] θ = 1, we can solve for cos θ:
[tex]cos^2[/tex] θ = 1 - sin^2 θ
[tex]cos^2[/tex] θ = [tex]1 - (5/12)^2[/tex]
[tex]cos^2[/tex]θ = 1 - 25/144
[tex]cos^2[/tex] θ = 119/144
cos θ = √(119/144)
cos θ = √119/12
Now, we can find sin θ using the relationship [tex]sin^2[/tex] θ + [tex]cos^2[/tex]θ = 1:
[tex]sin^2[/tex] θ = 1 - [tex]cos^2[/tex] θ
[tex]sin^2[/tex]θ = 1 - (119/144)
[tex]sin^2[/tex]θ = 25/144
sin θ = √(25/144)
sin θ = 5/12
Finally, we can substitute the values of sin θ and tan θ into the expression sin θ + tan θ:
sin θ + tan θ = (5/12) + (5/12) = 10/12 = 5/6
Therefore, sin θ + tan θ is equal to 5/6.
2) The value of sin θ is already calculated as 5/12.
3) To find sec θ + [tex]csc^2[/tex] θ, we need to find the values of sec θ and csc θ.
Since sec θ is the reciprocal of cos θ, we can calculate sec θ as:
sec θ = 1/cos θ = 1/(√119/12) = 12/√119
csc θ is the reciprocal of sin θ, so:
csc θ = 1/sin θ = 1/(5/12) = 12/5
Now, we can substitute these values into the expression sec θ + [tex]csc^2[/tex]θ:
sec θ + [tex]csc^2[/tex]θ = (12/√119) + [tex](12/5)^2[/tex]= 12/√119 + 144/25
4) To find cot θ + sin θ, we need to calculate the value of cot θ.
cot θ is the reciprocal of tan θ, so:
cot θ = 1/tan θ = 1/(5/12) = 12/5
Now, we can substitute the values of cot θ and sin θ into the expression cot θ + sin θ:
cot θ + sin θ = 12/5 + 5/12
To add these fractions, we need a common denominator:
cot θ + sin θ = (12/5)(12/12) + (5/12)(5/5)
= 144/60 + 25/60
= 169/60
Therefore, cot θ + sin θ is equal to 169/60.
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Mr. Gupta gave his students a quiz with three questions on it. Let
�
XX represent the number of questions that a randomly chosen student answered correctly. Here is the probability distribution of
�
XX along with summary statistics:
�
=
# correct
X=# correctX, equals, start text, \#, space, c, o, r, r, e, c, t, end text
0
00
1
11
2
22
3
33
�
(
�
)
P(X)P, left parenthesis, X, right parenthesis
0.05
0.050, point, 05
0.20
0.200, point, 20
0.50
0.500, point, 50
0.25
0.250, point, 25
Mean:
�
�
=
1.95
μ
X
=1.95mu, start subscript, X, end subscript, equals, 1, point, 95
Standard deviation:
�
�
≈
0.8
σ
X
≈0.8sigma, start subscript, X, end subscript, approximately equals, 0, point, 8
Mr. Gupta decides to score the tests by giving
10
1010 points for each correct question. He also plans to give every student
5
55 additional bonus points. Let
�
YY represent a random student's score.
What are the mean and standard deviation of
�
YY?
The mean score of a random student (YY) is 574.5. the standard deviation of the random student's score (YY) is 8.
How to answer the aforementioned questionGiven:
- Each correct question is worth 10 points.
- Every student receives an additional 555 bonus points.
Let's calculate the mean and standard deviation of YY:
Mean of YY:
The mean score, denoted as μY, can be calculated using the mean of XX (μX) and the scoring scheme:
μY = μX * 10 + 555
Substituting the value of μX from the given information:
μY = 1.95 * 10 + 555
μY = 19.5 + 555
μY = 574.5
Therefore, the mean score of a random student (YY) is 574.5.
Standard Deviation of YY:
The standard deviation of YY, denoted as σY, can be calculated using the standard deviation of XX (σX) and the scoring scheme:
σY = σX * 10
Substituting the value of σX from the given information:
σY = 0.8 * 10
σY = 8
Therefore, the standard deviation of the random student's score (YY) is 8.
Complete question: Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions
that a randomly chosen student answered correctly. Here is the probability distribution of X along with
summary statistics:
0
1
2
2.
3
X = # correct
P(X)
0.05
0.20
0.50
0.25
Mean: Hex = 1.95
Standard deviation: Ox 0.8
Mr. Gupta decides to score the tests by giving 10 points for each correct question. He also plans to give
every student 5 additional bonus points. Let Y represent a random student's score.
What are the mean and standard deviation of Y?
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The diagram represents the trajectory of an airplane at take off. The angle that represents the
trajectory of a jet is 15% greater than the trajectory of the airplane.
The diagram represents the trajectory of an airplane at take off the angle representing the airplane's trajectory is approximately 147.83 degrees.
To solve this problem, let's denote the angle of the airplane's trajectory as x degrees. According to the given information, the angle representing the trajectory of the jet is 15% greater than the airplane's trajectory.
The angle representing the trajectory of the jet can be calculated as:
x + 0.15x = 1.15x
Therefore, the angle representing the trajectory of the jet is 1.15x degrees.
Given that the airplane's trajectory is at 170 degrees, we can set up the following equation:
1.15x = 170
To solve for x, divide both sides of the equation by 1.15:
x = 170 / 1.15 ≈ 147.83
Thus, the angle representing the airplane's trajectory is approximately 147.83 degrees, and the angle representing the jet's trajectory is approximately 1.15 * 147.83 ≈ 170 degrees.
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Kyle's current credit card balance is $3,109.87 with a minimum payment of $159.00. Over the next month he spends $532.42. If the APR is 27.99% (billed monthly), what will Kyle's new balance be, with interest? (4 points) $3,404.65 $3,564.54 $3,606.84 $3,789.03
Answer:
(b) $3564.54
Step-by-step explanation:
You want the new balance showing on a credit card statement if the APR is 27.99%, the old balance is $3109.87, a payment of $159 was made, and purchases were made totaling $532.42.
SubtotalApparently, the new balance is computed by subtracting payments, and adding new charges to the old balance, then computing and adding the finance charge on this sum.
balance before finance charge: $3109.87 -159.00 +532.42 = $3483.29
Finance chargeThe finance charge is 1 month's interest at the annual rate:
I = Prt = $3483.29×0.2799×(1/12) = $81.25
New BalanceThe new balance is the subtotal above, with the finance charge added:
new balance = $3483.29 +81.25 = $3564.54
Kyle's new balance will be $3564.54.
__
Additional comment
This is a very expensive credit card. Not only is the interest rate of 27.99% very high, but also finance charges are charged on new purchase in the month they are purchased.
Some cards these days have interest rates of 12.75% or lower, with no finance charge for purchases made during the month. Some cards offer a rebate of up to 1.5% of purchases, so a net "negative" finance charge if you pay off the card every month.
Given: AB is parallel to BC
DC is parallel to BC
Angle 1 is congruent to Angle 2
Prove: AC is congruent to DB
Angles 1 and 2 are congruent and AB is parallel to DC, so by the Corresponding Angles Theorem, AC is congruent to DB.
Therefore, AC is congruent to DB.
How to explain the congruenceGiven: AB is parallel to BC
DC is parallel to BC
Angle 1 is congruent to Angle 2
Prove:
AC is congruent to DB
Proof: AB is parallel to BC and DC is parallel to BC.
Therefore, AB is parallel to DC.
Angle 1 is congruent to Angle 2.
Angles 1 and 2 are alternate interior angles, so they are congruent.
Angles 1 and 2 are congruent and AB is parallel to DC, so by the Corresponding Angles Theorem, AC is congruent to DB.
Therefore, AC is congruent to DB.
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Find domain+range
Thank you for the help :-)
Domain: {-15, 0, 9, 33, 44, 45}
Range: {15, 21, 33, 46, 57, 97}
Step-by-step explanation:The domain and range describe the x and y-values of a function.
Domain
The domain of a function shows the x-values covered by a function. Since the function cannot be proved to be continuous, we have to list the domain as a discrete list of values. We cannot say that the values between the listed x-values are a part of the domain. Any x-value included in the function is a part of the domain. As stated in the question, we should list our answer as an ordered list with braces.
Domain: {-15, 0, 9, 33, 44, 45}Range
The range of a function shows the y-values covered by the function. Similar to the domain, we cannot assume that the y-values between those listed are included in the range. This means that the range will also be a list of values. Range and domain should be listed from least to greatest. So, we can create a list of all the y-values in numerical order.
Range: {15, 21, 33, 46, 57, 97}100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer: 127
Step-by-step explanation:
360 - 70 - 36 = 254
254/2 = 127
D = 127
Rhett made a simple drawing of his house. It is a three dimensional figure with four faces that are rectangular and two that are square what kind of figure is it?
Rhett's house is a rectangular prism
Given data ,
Let the figure be represented as A
Now , the value of A is
Rhett made a simple drawing of his house.
And , It is a three dimensional figure with four faces that are rectangular and two that are square
So , the figure is represented as a rectangular prism
A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.
Hence , the figure is rectangular prism
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During the repair, the mechanics will need to
connect a cable between chairs B and J, and then
continue that cable to chair G. What is the angle
formed by the cable?
The angle formed by the cable between chairs B and J, and then
continue chair G is
75 degrees
How to determine the angleThe angle is determined with the knowledge of the total angle in a circle which is 360 degrees. Also, intercepted arc = 2 * inscribed angle
Assuming each chair is equal distance apart, then they will subtend equal angle.
The number of chairs for A to L is 12
angle per chair = 360 / 12 = 30 degrees
number of chairs from B to G = 5 and angle intercepted arc = 30 * 5 = 150 degrees
Inscribed angle = 1/2 * intercepted arc
Inscribed angle = 1/2 * 150
Inscribed angle = 75 degrees
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Tom is ordering 5 bags of cat food from Canada. Each bag has a mass of 6 kg . To determine the shipping costs, Tom needs to know the total weight in pounds. What is the weight of the cat food in pounds? Use 1kg= 2.2 lb and do not round any computations.
Answer:
6* 2.2lb = 13.2 lb
Step-by-step explanation:
If 1 bag weights 2.2lb than 6 bags will weight 6 times more or:
2.2 lb * 6 = 13.2 lb
We can use the provided conversion factor, which states that 1 kg is equal to 2.2 pounds, to determine the weight of the cat food in pounds.
Since each bag of cat food weighs 6 kg, we can calculate the weight of 5 bags as follows.
5 bags of 6 kg each equal the total weight = 30 kg.
Now, we can convert the total weight from kilograms to pounds using the conversion factor:
Total weight multiplied by the conversion factor equals total weight in pounds.
= 30 kg x 0.2 lb/kg.
= 66 lbs.
Consequently, the cat food has a 66-pound weight when measured in pounds.
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The triangle below is isosceles. Find the length of side x to the nearest tenth.
Answer: x=15.6
Step-by-step explanation:
An isosceles triangle has two congruent sides. (1 pair). So, the other side (not x) must equal 11.
Using the Pythagorean Theorem; a^2+b^2=c^2, you can substitute the values in as follows
11^1+11^2=x^2
121+121=x^2
242=x^2
15.55634918610405=x
round to the nearest tenth as said in the question...
x=15.6
Tyrell is traveling to Chicago, Illinois. He takes a cab service from the airport to his hotel. The table shows the linear relationship between the number of miles the cab travels, x, and the total fee, y.
Cab Fare
Number of Miles Total Fee
2 $13.00
5 $17.50
7 $20.50
10 $25.00
15 $32.50
What does the y-intercept mean in this situation?
For every additional mile the cab travels, the total fee increases by $10.00.
For every additional mile the cab travels, the total fee increases by $1.50.
When the cab travels 0 miles, the total fee will be $1.50.
When the cab travels 0 miles, the total fee will be $10.00.
Answer:
When the cab travels 0 miles, the total fee will be $10.00.
Step-by-step explanation:
We Know
2 miles = $13.00
5 miles = $17.50
3 miles = 17.50 - 13.00 = $4.50
1 mile = 4.50 / 3 = $1.50
So, for every 1-mile go, the cost is increasing by $1.50; this is the slope.
What does the y-intercept mean in this situation?
It is the total fee that Tyrell pays when the cab goes 0 miles (when he first steps in the cap).
So, the answer is D. When the cab travels 0 miles, the total fee will be $10.00.
Carter is going to invest in an account paying an interest rate of 4.3% compounded daily. How much would Carter need to invest, to the nearest ten dollars, for the value of the account to reach $174,000 in 19 years?
Carter would need to invest approximately $76,869.06 to reach a value of $174,000 in 19 years with a 4.3% annual interest rate compounded daily.
What is the principal that needs to be invested?The formula accrued amount in a compounded interest is expressed as;
[tex]A = P( 1 + \frac{r}{n})^{(nt)}[/tex]
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Accrued amount A = $174,000
Compounded daily n = 365
Time t = 19 years
Interest rate r = 4.3%
Principal P = ?
First, convert R as a percent to r as a decimal
r = R/100
r = 4.3/100
r = 0.043
Plug these values into the above formula and solve for principal P.
[tex]A = P( 1 + \frac{r}{n})^{(nt)}\\\\A = 174,000( 1 + \frac{0.043}{365})^{(365\ *\ 19)}\\\\A = \$ 76,869.06[/tex]
Therefore, the principal that needs to invested is $76,869.06.
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100 Points! Geometry question. Photo attached. Determine whether the pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Please show as much work as possible. Thank you!
Answer:
∆SMK is similar to ∆RMT by AA.
Please help I am struggling thank you, have a great day
Answer:
24
Step-by-step explanation:
For this problem, substitute the value -3 for x and solve. It would look like this:
[tex]4(-3)^2+2(-3)-6[/tex]
Using the order of operations (PEMDAS) we solve the exponent first.
[tex]-3^2=9[/tex]
Then solve the multiplication parts.
[tex]4(9)+2(-3)-6\\4*9=36[/tex]and [tex]2*(-3)=-6[/tex]
Finally subtract to get the answer.
[tex]36-6-6=24[/tex]
please answer i would appreciate it thank you
a) The triangles are congruent by the AAA criterion.
b) The triangles are congruent by the SAS criterion.
a) In the first triangle the interior angles are 40 degrees and 30 degrees.
The other interior angle would be 180 - (40 + 30) = 110 degrees.
As per the diagram, the triangles have equal proportionate-sized side lengths.
Therefore, the triangles are congruent by the AAA criterion.
b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.
Therefore, the triangles are congruent by the SAS criterion.
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Find the area of the following figure. Round to the nearest hundred if necessary.
14 m
9.5 m
17 m
The area of the given figure is 133 m²
Given is quadrilateral with sides 17m and 9.5m with height of 14m we need to find its area,
The given quadrilateral is a parallelogram, we know that area of the parallelogram is = base x height
Therefore,
The area of the given figure = 9.5 x 14 = 133
Hence, the area of the given figure is 133 m²
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In circle S, a sector is shaded. ZTSU measures 40°.
C
T
40°
(47)
S
What fraction of the interior of the circle is shaded?
Simplify your answer.
4 cm
Which expression represents the area of the shaded sector in square centimeters
(4x)
(16)
(167)
Given that in circle S, a sector is shaded and ZTSU measures 40°. We are to find out what fraction of the interior of the circle is shaded and simplify the answer.The correct answer is 16π/9 cm².
To find out the fraction of the interior of the circle that is shaded, we need to determine the measure of the central angle that intercepts the entire circle.The total measure of a circle is 360 degrees.
To find the fraction of a circle shaded, divide the number of degrees in the sector by
360.4x = (40/360) × πr² = (1/9) × πr².
We simplify the answer: 4x = πr²/9 Fraction of the interior of the circle that is shaded = 40/360 = 1/9.Expression for the area of the shaded sector in square centimeters is:
A = (40/360) × πr² = πr²/9 = π(4²)/9 = 16π/9 cm²
Therefore, the correct answer is 16π/9 cm².
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6 sin =5 solve to the nearest 0.1
Step-by-step explanation:
sin Φ = 5/6 = .8333
Arcsin ( sin Φ) = arcsin (.8333)
Φ = 56.4 degrees
50 POINTS!!!
Math...Money...Interest...
Please give the correct answers and show the steps. I will report your account if I find an error. Thank you for your help.
Answer:
2.
Quarterly:
100000 = 60000(1 + 0.075/4)^4tt ≈ 6.87466382 yearsMonthly:
100000 = 60000(1 + 0.075/12)^12tt ≈ 6.83227061 yearsContinuously:
100000 = 60000e^0.075tt ≈ 6.811008 years3.
Twice a year:
300 = 100(1 + 0.1025/2)^2tt ≈ 10.99053398 yearsEight times a year:
300 = 100(1 + 0.1025/8)^8tt ≈ 10.78668624 yearsContinuously:
300 = 100e^0.1025tt ≈ 10.718169 yearsStep-by-step explanation:
The formula for compound interest is:
A = P(1+r/n)^nt
The formula for compounded continuously is:
A = Pe^rt
Where:
A = the future value of the investment
P = the principal balance
r = the annual interest rate (decimal)
n = number of times interest is compounded per year
t = the time in years
Using that we can plug the formula in for each question:
2.
Quarterly:
100000 = 60000(1 + 0.075/4)^4tCompounded quarterly means in a year, it is compounded 4 timesNote that the question is asking to find how much time it takes so t is the thing we need to solve fort ≈ 6.87466382 yearsMonthly:
100000 = 60000(1 + 0.075/12)^12tt ≈ 6.83227061 yearsContinuously:
100000 = 60000e^0.075tWe are now using the compounded continuous formulat ≈ 6.811008 years3.
Twice a year:
Since the question does not give us a starting amount but it gives us a goal of tripling the money, we can substitute any amount of money for P and A as three times PFor now, let's say P is 100 and A is 3 times 100 so A is 300300 = 100(1 + 0.1025/2)^2tt ≈ 10.99053398 yearsEight times a year:
We will continue to place hold P as 100 and A as 300300 = 100(1 + 0.1025/8)^8tt ≈ 10.78668624 yearsContinuously:
We will now use the compounded continuous formula300 = 100e^0.1025tt ≈ 10.718169 years- Find the surface area.
40 feet
18 feet
16 feet
The point (2, 1) is the turning point of the graph with equation y = x² + ax + b,
where a and b are integers.
Find the values of a and b.
Optional working
+
a
b =
Step-by-step explanation:
This is a quadratic with vertex at (2,1) ....write the equation first in vertex form, then expand to the form requested
y = ( x -2)^2 + 1
y = x^2 -4x +4 + 1
y = x^2 -4x + 5 Done. a = -4 b = 5
For a charity drive, each classroom is given a coin box made of cardboard like the one shown. The student council wants to construct a version of the coin box that has a scale factor of 3 times the classroom coin box. Is 100 square feet of cardboard enough to build the new coin box? Select the response with the correct answer and an argument that can be used to defend the solution
The classroom coin box required less than 11.11 Square feet of cardboard (100 square feet divided by 9), then 100 square feet would be sufficient
The 100 square feet of cardboard is enough to build the new coin box with a scale factor of 3 times the classroom coin box, we need to consider the relationship between the areas of the two boxes.
The area of the original classroom coin box is unknown, as it is not given in the problem. However, since we know that the new coin box has a scale factor of 3 times the original, we can infer that its area will be 3^2 = 9 times greater than the original.
Let's assume that the area of the classroom coin box is A square feet. In that case, the area of the new coin box would be 9A square feet.
Now, we are given that 100 square feet of cardboard is available. To determine if it's sufficient, we need to compare this value to the area of the new coin box, which is 9A.
If 100 square feet is greater than or equal to 9A, then it would be enough to build the new coin box. Conversely, if 100 square feet is less than 9A, it would not be enough.
Since we do not have a specific value for A, we cannot determine the exact answer. However, we can provide the argument to defend our solution.the classroom coin box required less than 11.11 square feet of cardboard (100 square feet divided by 9), then 100 square feet would be sufficient.
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Note the question be like :
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn from the bag without replacement, what is the probability that both marbles are red?
Janet buys 4 bags of potatoes
6x + y = 8
y= -6x + 8
Answer:
y = -6x + 8
Step-by-step explanation:
\begin{bmatrix}6x+y=8\\ y=-6x+8\end{bmatrix}
I don't know why it came out like this
18/5 divided by 3/25 in simplest form
Answer: 30
Step-by-step explanation:
18/5 divided by 3/25 is the same thing as multiplying 18/5 with the reciprocal of 3/25 (25/3).
[tex]\frac{18}{5} *\frac{25}{3} =\frac{450}{15}[/tex]
And when multiplying out you get 450/15.
Simplifying (by dividing 450 by 15) this you will get 30.
Could i get some help in answering this question?
The value of the variable x in the right angle triangle is: 9
How to use Pythagoras theorem?Pythagoras Theorem is defined as the way in which we can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
The tangent forms a right angle with the circle and as such using Pythagoras theorem, we have:
8 + x = √(15² + 8²)
8 + x = √289
8 + x = 17
x = 17 - 8
x = 9
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Tiffany drew the design below that she is going to use on a stained-glass window, above her front door. Identify all the rays in Tiffany’s design
The rays in Tiffany’s design are EA, FB, GC, GH, ED
Identifying all the rays in Tiffany’s designFrom the question, we have the following parameters that can be used in our computation:
Tiffany’s design
By definition, the rays in Tiffany’s design are lines that have one fixed endpoint and the other endpoint extends indefinitely
Using the above as a guide, we have the following:
The rays in Tiffany’s design are EA, FB, GC, GH, ED
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You are given a map with a number scale 1:60 you must measure a length on the map of 10cm
The measure of a length of 10cm on the scale is 1/6 units
How to determine the measure of a length on the map of 10cmFrom the question, we have the following parameters that can be used in our computation:
Scale = 1 : 60
For a length of 10 cm, we have
Actual length = 10 cm
This means that
Scale ; 10 cm = 1 : 60
Express as fraction
So, we have
Scale/10 cm = 1/60
When evaluated we have
Scale = 1/6 units
Hence, the measure of a length of 10cm on the scale is 1/6 units
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Can someone help me find the surface area of these 2 prisms?
Step-by-step explanation:
1) the 1-st prism is cube. Then its surface area can be calculated as:
A=5*5*6=150 [ft²];
2) A=[Perimeter of triange]*height+2*[Area_of_triangle];
according to the formula above height=3; Perimeter of triangle=9+12+15=36; Area of triangle=12*9*0.5=54;
Finally, A=36*3+2*54=108+108=216 [cm²].