One solution of the following system is:
A. (–6, 0)
What is the solution for the system?The above mathematical expression requires that we use the substitution formula to obtain the correct value.
2y - 2x = 12 ... 1
x² + y² = 36 ... 2
For equation 1
2y = 12 + 2x
2
y = 6 + x ... 3
Now we substitute equation 3 in equation 2
x² + (6 + x)² = 36
= x² + 36 + 12x + x² = 36
2x² + 12x = 36 -36
2x² + 12x = 0
2x (x + 6) = 0
x = 0, -6
When we substitute x for 0 in the third equation, we will have
y = 6 + 0 = 6
If we substitute x to be -6 in the third equation, we will arrive at
y = 0.
Therefore, the two solutions that can be obtained are (0,6) and (-6,0) as seen in the first option.
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Find the area of the green shaded sector of the circle. Show all of your work. Write your answer in terms of pi.
The area of the sector with an angle of 285 degrees and a radius of 6 units is 28.5π square units.
To find the area of a sector, we can use the formula:
Area of Sector = (Central Angle / 360 degrees) × π × (Radius²)
Given that the central angle is 285 degrees and the radius is 6, we can substitute these values into the formula:
Area of Sector = (285 degrees / 360 degrees) × π × (6²)
Area of Sector = (19/24) × π × 36
Area of Sector = (19/24) × 36π
Area of Sector = (19 × 36π) / 24
Area of Sector = 684π / 24
Area of Sector = 28.5π
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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 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}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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A 12 cm by 12 cm square piece of paper has 5 holes punched out of it. 4 of the holes are circles of radius 3 cm and 1 of the holes is a circle of radius 1 cm. The paper and punched holes can be visually interpreted as below. Determine the area of paper remaining after the holes have been punched out.
5 holes have been punched into a 12 cm by 12 cm square piece of paper. The area of remaining paper will be 27.714 cm².
Firstly, we will calculate the area of the square of paper in which the holes are punched.
Side of square = 12 cm
Area of square = side²
= (12) ²
= 144 cm²
Now, we will calculate the area of the bigger punch holes
Radius of big punch hole = 3 cm
Area of 1 big punch = π (radius) ²
= 22/7 × (3)²
22 / 7 × 9
= 198 / 7 cm²
Area of 4 punches = 4 × 198/7
= 792/7 cm²
Now, we will calculate the area of smaller punch whose radius is 1cm
Area = 22/7 × 1²
= 22/7 cm²
Now, we will calculate the total area covered by circles
Total area covered by circles = area of small punch + area of 4 big punch
= 22/7 + 792/7
= 814 /7 cm²
Remaining area = area of square - area of circles
= 144 - 814/7
= (1008 - 814) / 7
= 194 / 7
= 27.714 cm²
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1. Drag the cards so that each number sentence is true. (You will have one card left over.)
2. Describe your thinking.
The figures paired are given as follows:
| -3| = 3
|-2| > 1
0 < |-1|
The left over is 2. This is based on the principle of absolute values.
What is absolute values?The absolute value (or modulus) of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5.
A number's absolute value can be conceived of as its distance from zero along the real number line.
As a result, the absolute value of -3 is 3, which suggests that |-3| = 3.
-2 in absolute terms equals 2. That is |-2| greater than 1.
the inverse value of -1 equals 1. This equals 0 |-1|.
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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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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?
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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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
A sequence can be generated by using an= 3an-1, where a1 = 10 and n is a whole number greater than 1.
What are the first 3 terms in the sequence?
A. 3, 13, 23
B. 10, 30, 90
C. 10, 13, 16
D. 3, 30, 300
Answer:
B
Step-by-step explanation:
using the recursive rule [tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] and a₁ = 10, then
a₁ = 10
a₂ = 3a₁ = 3 × 10 = 30
a₃ = 3a₂ = 3 × 30 = 90
the first 3 terms are 10 , 30 , 90
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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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 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
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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Please help quick! will mark brainliest!
Answer:
7, 14
Step-by-step explanation:
Look at the first column of numbers: 2.8 m in 2 min.
We can get a unit rate from those numbers:
2.8 m / 2 min = 1.4 m/min
He walks at a rate of 1.4 m/min
Now multiply the unit rate by each number of minutes to find the number of meter.
Let's do the second column as a check: time = 3 min
1.4 m/min × 3 min = 4.2 m
4.2 m is the number on the table, so our unti rate is correct.
5 min:
1/4 m/min × 5 min = 7 m
10 min:
1.4 m/min × 10 min = 14 m
Janet buys 4 bags of potatoes
What is the meaning of "the notational convention"?
In mathematics, notation is used to simplify and make our understanding of equations and problem statements easier.
Mathematical notation makes use of various symbols in order to represent operations, unspecified numbers, relations, and any other mathematical objects or entities, and proceeds to assemble them into understandable expressions and formulas.
A notational convention is a set of representatives consisting of symbols that are used to express mathematical equations, in this case, the notational convention adopted is that all the free variables of a formula are among u1, u2, u3 . . . un. as shown in the image provided.
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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
- Find the surface area.
40 feet
18 feet
16 feet
B cubed equals 8. Solve for b
Answer:
b=2
Step-by-step explanation:
You are given:
[tex]b^{3} =8[/tex]
What does [tex]b^3[/tex] mean?
It is simply, b·b·b
Therefore:
b·b·b=8
What number could be multiplied by itself three times and equal 8?
...
2
Yay! That's great!
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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1.2 Mr John is to deposit R 5,000 in his bank account. Deposits are calculated as follows: Cash deposit : At ATM: R4,80 +1,20% of the above value. At the Branch R8,00 + 1,50% of the above value. John claims that the difference of depositing R5 000 at ATM and at the Branch is R18, 20 Verify the stament (5) [23
The calculated difference is -R18.20, which means the deposit at the branch is higher than the deposit at the ATM by R18.20
What is simple interest?The simple interest formula is J = C ∙ i ∙ t, where J is interest, C is principal, i is interest rate, and t is time. To calculate the simple interest, just substitute the values in the formula and perform the calculation.
Calculate the deposit:
[tex]D=R4.80 + 1.20% of R5,000\\=R4.80 + (1.20/100) * R5,000\\= R4.80 + R60\\= R64.80[/tex]
Now, the deposit amount for the branch:
[tex]DB=R8.00 + 1.50% of R5,000\\= R8.00 + (1.50/100) * R5,000\\= R8.00 + R75\\= R83.00[/tex]
The difference will be:
[tex]Difference = R64.80 - R83.00\\Difference = -R18.20[/tex]
The calculated difference is -R18.20, which means the deposit at the branch is higher than the deposit at the ATM by R18.20. Therefore, John's statement is incorrect.
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A ramp has a vertical rise of 4 feet & the angle of elevation of the ramp is 12°. How long is the ramp?
Answer:
19.24 ft
Step-by-step explanation:
x = length of ramp
sin12 = 4/x
x = 4/sin12 = 19.24 ft
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.
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.
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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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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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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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].