Reasoning What is the height of the square pyramid? Use pencil and paper. Once you know which length represents the hypotenuse, does it matter which length you substitute for a and which length you substitute for b? Explain.
Answers
The height of the pyramid is 30.14 in
We have,
Using the Pythagorean theorem,
Hypotenuse = 32.6 in
Base = 24.8/2 = 12.4 in
Height = x
Now,
32.6² = 12.4² + x²
x² = 1062.76 - 153.76
x² = 909
x = 30.15
Thus,'
The height of the pyramid is 30.14 in
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Related Questions
A student is graduating from college in 12 months but will need a loan in the amount of $11,650 for the last two semesters. The student may receive either an unsubsidized Stafford Loan
or a PLUS Loan. The terms of each loan are:
Unsubsidized Stafford Loan: annual interest rate of 5.95%, compounded monthly, and a payment grace period of six months from time of graduation
PLUS loan: annual interest rate of 6.55%, compounded monthly, with a balance of $12,436.41 at graduation
Which loan will have a lower balance, and by how much, at the time of repayment?
O The PLUS loan will have a lower balance by $298.35 at the time of repayment.
O The Stafford loan will have a lower balance by $298.35 at the time of repayment.
O The PLUS loan will have a lower balance by $527.14 at the time of repayment.
O The Stafford loan will have a lower balance by $527.14 at the time of repayment
Answers
Based on the information, the Stafford loan will have a lower balance by $527.14 at the time of repayment
How to calculate the loanUsing the formula for compound interest, the total cost of the loan can be calculated as follows:
Total cost of Stafford loan = $11,650 x (1 + 0.0595/12)^(12*0.5) = $12,652.14
Total cost of PLUS loan = $12,436.41 x (1 + 0.0655/12)^12 = $13,179.28
Therefore, the Stafford loan will have a lower balance at the time of repayment by $527.14 ($13,179.28 - $12,652.14).
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If a fair coin is tossed twice the possible outcomes are HH, HT, TH or TT, where HH means both tosses are heads and HT means that the first toss is a head and the second toss is a tail, etc. Since the coin is fair, a 50-50 chance of getting a head or a tail, we assign a probability of 1/4 to each of the four outcomes. Assuming that a fair coin was tossed twice, find the probability that exactly one of the tosses is a head and the other toss is a tail.
Answers
Assuming that a fair coin was tossed twice, the probability that exactly one of the tosses is a head and the other toss is a tail is 1/2.
The probability of a certain event happening is the number of ways that event can occur, divided by the total number of possible outcomes. In this case, we are interested in finding the probability that exactly one of the two coin tosses results in a head and the other results in a tail.
There are two possible outcomes that satisfy this condition: HT and TH. Since the coin is fair, each of these outcomes has a probability of 1/4. Therefore, the total probability of getting exactly one head and one tail is:
P(HT or TH) = P(HT) + P(TH) = 1/4 + 1/4 = 1/2
In other words, there is a 50-50 chance of getting exactly one head and one tail when a fair coin is tossed twice.
To see why this is the case, we can think of each toss as an independent event with two possible outcomes (head or tail). There are four possible outcomes when we toss a coin twice, and two of these outcomes satisfy the condition of exactly one head and one tail. Therefore, the probability of getting exactly one head and one tail is 2/4, which simplifies to 1/2.
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Two step for T+4=-7 ?
Answers
Answer:
Step-by-step explanation:
T+4 = -7
T = -7 -4
T = -11
Isolate the variable by doing the opposite operation of the constant on the side of the variable. I this case, subtract 4 from both sides -7-4=11
Find the volume of the shape below. Round to the nearest tenth. Use
the pi button on the calculator.
Volume =
12 cm
cm³
Answers
The volume of the sphere as shown in the diagram is 904.3 cm³.
What is a sphere?A sphere is a three-dimensional round-shaped object.
To calculate the volume of the sphere, we use the formula below
Formula:
V = 4πr³/3...................... Equation 1Where:
V = Volume of the spherer = Radius of the sphereπ = PieFrom the question,
Given:
r = 12/2 = 6 cmπ = 3.14Substitute these values into equation 1
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Is the factions are proportional 1/2 and 2/4?
Answers
Yes, the fractions 1/2 and 2/4 are proportional
What is a fraction?A fraction can simply be defined as an expression that is used in the representation of the part of a whole.
This could be a whole number, a whole element, a whole material or a whole elemeent.
In mathematics, there are different types of fractions.
These fractions are enumerates thus;
Mixed fractionsSimple fractionsProper fractionsImproper fractionsComplex fractionsFrom the information given, we have that;
If 1/2 and 2/4 are proportional, that is, if equal
2/4 = 1/2
Cross multiply the values
4 = 4
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You put $200 per month in an investment plan that pays an APR of 4.5%. How much money will you have after 23 years?
Compare this amount to the total deposits made over the time period.
After 23 years the investment plan will contain
Answers
The amount after 23 years on the investment plan is A = $358.20
Given data ,
$200 per month under a 4.5% annual percentage rate investing plan.
Now , A = P(1 + r/n)^(nt)
Where:
A is the total sum.
P stands for the initial deposit's principal.
The yearly interest rate is represented by the decimal r.
The yearly compounding rate of interest is determined by the number n.
The number of years is t.
A = 200(1 + 0.045/1)¹ˣ²³
A = 200(1.045)²³
A ≈ 200(1.791)
A ≈ $358.20
After 23 years, the investment plan will contain approximately $358.20
Total deposits = Monthly deposit amount x Number of months
Total deposits = $200 x (12 months/year) x 23 years
Total deposits = $200 x 12 x 23
Total deposits = $55,200
Consequently, $55,200 would be the total amount of deposits made during the 23-year period.
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ap calculus problem
no need full detail solution
Answers
The Taylor series for f(x) = e^2x at x = 1 is option D. Σ2ⁿ e²ˣ/n! (x - 1)ⁿ
How did we get the value?The Taylor series for a function f(x) centered at x = a is given by:
f(x) = f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...
f'(a), f''(a), f'''(a), ... depict the first, second, third, and higher derivatives of f(x) evaluated at x = a.
In this case:
f(x) = e^(2x)
The first derivative is:
f'(x) = 2e^(2x)
The second derivative is:
f''(x) = 4e^(2x)
The third derivative is:
f'''(x) = 8e^(2x) etc.
Finding the Taylor series for f(x) = e^(2x) at x = 1, evaluate each derivative at x = 1:
f(1) = e^(2)
f'(1) = 2e^(2)
f''(1) = 4e^(2)
f'''(1) = 8e^(2) etc.
Plug these values into the Taylor series formula:
f(x) = f(1) + f'(1)(x-1)/1! + f''(1)(x-1)^2/2! + f'''(1)(x-1)^3/3! + ...
f(x) = e^(2) + 2e^(2)(x-1)/1! + 4e^(2)(x-1)^2/2! + 8e^(2)(x-1)^3/3! + ...
Simplify:
f(x) = e^(2) + 2e^(2)(x-1) + 2e^(2)(x-1)^2 + 4e^(2)(x-1)^3/3 + ...
Therefore, the Taylor series for f(x) = e^(2x) at x = 1 is: Σ2ⁿ e²ˣ/n! (x - 1)ⁿ which is option D.
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can someone help me with this
Answers
The sine equation for the object's height is given as follows:
d = -5sin(0.24t).
How to define the sine function?The standard definition of the sine function is given as follows:
y = Asin(Bx) + C.
The parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: vertical shift.The amplitude for this problem is of 5 inches, hence:
A = 5.
The period is of 1.5 seconds, hence the coefficient B is given as follows:
2π/B = 1.5
B = 1.5/2π
B = 0.24.
The function starts moving down, hence it is negative, so:
d = -5sin(0.24t).
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Mary wants to hang a mirror in her room. The mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
Square with an inner frame with height of 2 ft on the left frame and width of 3 ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x.
x2 + 14x − 2 = 0
2x2 + 10x − 7 = 0
3x2 + 12x − 7 = 0
4x2 + 10x − 1 = 0
Answers
Answer:
[tex](3 + 2x)(2 + 2x) = 7[/tex]
[tex]6 + 10x + 4{x}^{2} = 7[/tex]
[tex]4 {x}^{2} + 10x - 1 = 0[/tex]
Answer:
4x2 + 10x − 1 = 0
Step-by-step explanation:
Find the partial sum for the sequence.
{2, 3, 5, 8, 13, ...}; S8
S8=
Answers
The partial sum of the sequence {2, 3, 5, 8, 13, ...} for the first 8 terms is 761/2.
The sequence given is a Fibonacci sequence, where each term is the sum of the previous two terms. To find the partial sum for the first 8 terms, we can use the formula for the sum of a finite geometric series:
Sₙ = a(1 - rⁿ)/(1 - r),
where Sₙ is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 2, r = 3/2 (since each term is 1.5 times the previous term), and n = 8. Plugging these values into the formula, we get:
S₈ = 2(1 - (3/2)⁸)/(1 - (3/2))
Simplifying the expression, we get:
S₈ = 761/2
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tuesday follows monday in a week express the probability as percent
Answers
The probability that Tuesday follows Monday in a week is 100%, or 1/1, since it is always true that Tuesday comes after Monday in a week. Expressed as a percentage, the probability is 100%.
Answer:
100%
Step-by-step explanation:
because according to our calendars, Tuesday is always after monday so the probability as percent is 100%.
PLEASE HELP ITS DUE TODAY
For the quadratic equations shown here, which statement is true?
Question 2 options:
The graphs open downward.
The graphs open upward.
The graphs are listed from narrowest to widest.
The graphs are symmetric about the x-axis.
Answers
Answer:
The graphs open downward.
Find a function of the form
or (picture) whose graph matches the function shown below:
Answers
The sinusoidal function of the form y = A·sin(k·x) + C that matches the function in the graph is; y = 4·sin((π/5)·x) - 1
What is a sinusoidal function?A sinusoidal function is a periodic function based on the sine or cosine functions.
The form of the function is y = A·sin(k·x)
The peak and trough of the graph are; (-7.5, 3), (-2.5, -5)
The amplitude of the function is therefore; A = (3 - (-5))/2 = 4
The vertical shift of the function is; C = (3 + (-5))/2 = -1
The period of the graph (Number of input x-values required to complete a cycle) = 2.5 - (-7.5) = 10 = 2·π/k
Therefore; k = 2·π/10 = π/5
The horizontal shift can be found as follows;
When x = 0, y = -1, therefore;
-1 = 4 × sin(π/5 × (0 - θ)) - 1
arcsin(0/4) = π/5 × (- θ)
θ = 0
The sinusoidal function is therefore;
y = 4·sin((π/5)·x) - 1
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hi can someone help with this question
Answers
Based on the information, we can infer that the investment was made 11.53 years ago.
How to calculate how many years ago was the investment made?To calculate how many years ago was the investment mafe we have to can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount invested)
r = the interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Let's start by finding the initial principal (P) by working backwards from the final amount (A):
A = P(1 + r/n)^(nt)
31372.0 = P(1 + 0.022/1)^(14)(1 + 0.022+0.007/1)^(1(t-4))
Simplifying, we get:
31372.0 = P(1.093248)(1.029)^(t-4)
P = 27500 euros (initial investment)
Now we can solve for t:
31372.0 = 27500(1.093248)(1.029)^(t-4)
1.1412 = (1.029)^(t-4)
log(1.1412) = log(1.029)^(t-4)
t - 4 = log(1.1412)/log(1.029)
t = log(1.1412)/log(1.029) + 4
t = 11.53
Therefore, the investment was made about 11.53 years ago.
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Use one of the triangles to approximate
�
�
EFE, F in the triangle below.
Triangle D E F has a height of six units, which is side DF. Both the base, side EF, and the hypotenuse, side DE, are unknown. Angle D F E is a right angle and angle F D E measures twenty degrees.
Answers
Basd on the information about the triangle, DF is approximately 5.68 units long.
How to calculate the valueFirst, let's find the length of EF using the sine function:
sin 20° = EF / DE
cos 20° = 6 / DE
DE = 6 / cos 20°
Now that we know DE, we can solve for EF:
sin 20° = EF / DE
EF = DE * sin 20°
EF = (6 / cos 20°) * sin 20°
EF ≈ 1.95
DF^2 = DE^2 - EF^2
DF^2 = (6 / cos 20°)^2 - (1.95)^2
DF ≈ 5.68
DF is approximately 5.68 units long.
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Find a quadratic equation which has solutions x=4/9 and x=9/2. Write the quadratic form in the simplest standard form x^2+bx+c
Answers
Answer:
[tex](x - \frac{4}{9} )(x - \frac{9}{2} ) = 0[/tex]
[tex] {x}^{2} - \frac{89}{18} x + 2 = 0[/tex]
Ivy Tech Tuition was $88.34 per credit hour in 2006. Use the CPI values to determine what the school would be charging in 2013 if they only increased tuition based on inflation.
Answers
Answer: they would be charging $102.66 per credit hour in 2013.
Step-by-step explanation:
To determine what Ivy Tech would be charging in 2013 if they only increased tuition based on inflation, we need to use the CPI values to adjust for inflation between 2006 and 2013.
First, we need to calculate the inflation rate between the two years:
Inflation rate = CPI in 2013 / CPI in 2006
Inflation rate = 234.531 / 201.6 = 1.162
This means that the cost of living increased by 16.2% between 2006 and 2013.
Next, we can use this inflation rate to calculate the adjusted tuition cost for 2013:
Tuition in 2013 = Tuition in 2006 x (CPI in 2013 / CPI in 2006)
Tuition in 2013 = $88.34 x (234.531 / 201.6)
Tuition in 2013 = $102.66 (rounded to the nearest cent)
Therefore, if Ivy Tech only increased tuition based on inflation, they would be charging $102.66 per credit hour in 2013.
what is the surface area of a sphere with a radius of 12 centimeters
A) 302cm^2
B) 452cm^2
C) 576cm^2
D) 1810cm^2
Answers
The surface area of the sphere is 1810 cm²
What is a sphere?A sphere is a three-dimensional object that is round in shape. Examples of object with spherical shape is a ball, an egg e.t.c.
The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of sphere is expressed as;
A = 4πr². where r is the radius.
A = 4 × 3.14 × 12²
A = 1809.7 cm²
approximately to the nearest whole number
A = 1810 cm²
Therefore the surface area of the sphere to the nearest whole number is 1810 cm².
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10^-x-1=36 solve for x
Answers
The solution to the exponential equation 10^(-x - 1) = 36 is given as follows:
x = -2.5563.
How to solve the exponential equation?The exponential equation in the context of this problem is defined as follows:
10^(-x - 1) = 36
The log10 operation is the inverse of the power of 10 operation, hence we can isolate the variable x as follows:
-x - 1 = log10(36)
-x - 1 = 1.5563
x = -1.5563 - 1
x = -2.5563.
Which is the solution to the exponential equation in the context of the problem.
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ABCD is a parallelogram. P is a point on AB such that LPAD = 110° and PC = BC. Calculate (a) LABC, LDCP
please do it with explanation.
Answers
The value of the angles in the parallelogram are:
∠ABC = 70°
∠DCP =70°
How to calculate the angles in the parallelogram?Recall that two adjacent angles in a parallelogram add up to 180 degrees. We can say:
∠BAD + ∠ABC = 180° (Where ∠BAD = 110°)
∠ABC = 180 - 110 = 70°
Since PC = BC, ∠BPC = 70°
Also, ∠BCP = 180 - 70 - 70 = 40° (Sum of angles in a triangle)
∠ACB = ∠BAD (opposite angles of parallelogram are equal)
Where ∠BAD = 110°
Thus, ∠ACB = 110°
∠ACB = ∠DCP + ∠BCP
110 = ∠DCP + 40
∠DCP = 110 - 40
∠DCP =70°
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A sample of bacteria is decaying according to a half-life model. If the sample begins with 500 bacteria, and after 20 minutes there are 100 bacteria, after how many minutes will there be 20 bacteria remaining? When solving this problem, round the value of k to four decimal places and round your final answer to the nearest whole number.
Answers
The constant k is 0.08
The time taken is 40 minutes
What is the half life?The half-life of a specific radioactive substance is determined by its decay constant, which is a measure of how quickly the substance decays.
Given that;
P= Poe^-kt
P = population at time t
Po = initial population
k = rate of decay
t = time taken
Then;
100 = 500e^-k20
100/500 = e^-k20
0.2 = e^-k20
ln0.2 = e^-k20
k = ln0.2/-20
k = 0.08
We know that;
20 = 500e^-0.08t
20/500 = e^-0.08t
0.04 = e^-0.08t
ln 0.04 = e^-0.08t
ln0.04 = -0.08t
t = ln0.04/-0.08
t = 40 minutes
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Sally owns a restaurant in Wooville. The city is trying to get a minor league team to move there in 2021, either to location A (near her restaurant) or location B. The team might stay in location C in another city. The probability of these events, and her estimated annual profit in 2021 are shown in the table below.
Answers
The standard deviation of the restaurant profits in 2021 is given by $71181.
Restaurant profit for outcome 'move to A' = $ 260000
Restaurant profit for outcome 'move to B' = $ 120000
Restaurant profit for outcome 'stay in C' = $ 100000
The mean of restaurant profits = $(260000 + 120000 + 100000)/3 =$ 160000.
Standard deviation of the restaurant profits in 2021 is given by
= $ √({(260000 - 160000)² + (120000 - 160000)² + (100000 - 160000)²}/3)
= $ √(((100000)² + (40000)² + (60000)²)/3)
= $ √(15200000000/3)
= $ √5066666667
= $ 71181 (rounded to the nearest dollar)
Hence standard deviation of the restaurant profits in 2021 is given by $71181.
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The question is incomplete. The complete question will be -
Consider the equation that gives the volume of a square pyramid, where
• V represents the volume in cubic feet,
• b represents the length of each side of the pyramid's base in feet, and
• h represents the height of the pyramid in feet.
V= 1²
3
Enter an equation for which the solution is the height of a pyramid, in feet, when its volume is 48 cubic feet and the
length of each side of its base is 4 feet.
Answers
An equation for which the solution is the height of a pyramid, in feet, when its volume is 48 cubic feet and the length of each side of its base is 4 feet is h = 3(48)/4².
How to calculate the volume of a square pyramid?In Mathematics and Geometry, the volume of a square pyramid can be calculated by using the following formula:
Volume of a square pyramid, V = 1/3 × a² × h
Where:
h represent the height of a square pyramid.a represent the side length of the base of a square pyramid.By making "h" the subject of formula, the side length of the base of a square pyramid can be determined as follows;
V = 1/3 × a² × h
3V = a²h
Height, h = 3V/a²
Height, h = 3(48)/4²
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Find two numbers such that their sum is 12 and their product is 23.
Answers
Let's call the two numbers we're trying to find x and y. We know that x + y = 12 and xy = 23. From the first equation, we can solve for one of the variables in terms of the other. So if we subtract x from both sides, we get y = 12 - x. Now we can substitute this expression for y into the second equation to get x(12 - x) = 23. Expanding this out, we get 12x - x^2 = 23. Rearranging, we get x^2 - 12x + 23 = 0. This quadratic equation can be factored as (x - 2)(x - 10) = 0. So either x = 2 and y = 10, or x = 10 and y = 2.
Answer:
The two numbers are 2 and 10.
Five friends order food and want to split the bill. They order two large cheese pizzas
for $10 each, wings for $18.99, and breadsticks for $5.59. Determine how much each
person owes.
Answers
Answer:
$8.92 each
Step-by-step explanation:
The pizzas cost $10 x 2 = $20The wings cost $18.99The breadsticks cost $5.59When you add all of these together, you get $20 + $18.99 + $5.59 = $44.58.To spilt the bill, you need to divide the cost equally between the 5 friends which is $8.916. You cannot pay 0.916 of a dollar so you round the bill to the nearest two decimal places.120 students
and 8 teachers go on a school trip.
The recommended ratio of adults to students is 1:15.
Is the ratio of adults to students correct?
Answers
Answer:
Yes.
Step-by-step explanation:
8:120 = 4:60 = 2:30 = 1:15
You divide by two each time to simplify.
Find the polar coordinates of a point with Cartesian coordinates (x,y)=(2√3,2).Select the correct answer below:
(4,π/6)
(2,2π/3)
(4,2π/3)
(2,7π/6)
(4,7π/6)
(2,π/6)
Answers
Answer:
(4,π/6)
Step-by-step explanation:
The correct polar coordinates of the point (2√3, 2) are (r, θ) = (4, π/6).
Explanation:
Using the formulas for converting Cartesian coordinates to polar coordinates:
r = √(x^2 + y^2)
θ = atan2(y, x)
Plugging in the given values:
r = √((2√3)^2 + 2^2)
= √(12 + 4)
= √16
= 4
θ = atan2(2, 2√3)
≈ 0.5236 radians
However, in the polar coordinate system, angles are typically expressed in radians between 0 and 2π. The angle π/6 is equivalent to 0.5236 radians, so the correct polar coordinates of the point (2√3, 2) are (r, θ) = (4, π/6).
Brooke believes she's getting a great deal on a car - zero down and
payments of only $260 per month for 6 years (72 months). She estimates
the additional costs of owning a car: insurance - $960 per year, registration
- $240 per year, and gas and maintenance of $175 per month.
How much will this car cost her over the life of the loan?
Answers
Answer:
First, you need to calculate the total cost of the loan. The monthly payment is $260, and there are 72 payments over 6 years. The total cost of the loan is 72 months * $260/month = $18,720
Next, you calculate the total cost of owning the car for 6 years. The insurance will cost $960 per year, so over 6 years it will cost $960/year * 6 years = $5,760
The registration will cost $240 per year, so over 6 years it will cost $240/year * 6 years = $1,440
The gas and maintenance will cost $175 per month, so over 6 years it will cost $175/month * 72 months = $12,600
Now you can add up all the costs to find the total cost of owning the car over the life of the loan:
Loan cost + insurance cost + registration cost + gas/maintenance cost
= $18,720 + $5,760 + $1,440 + $12,600
= $38,520
Therefore, the car will cost Brooke $38,520 over the life of the loan, including all additional costs of owning the car.
Answer:
$38,520
Step-by-step explanation:
To calculate the total cost of the car, we need to consider the following expenses:
Monthly payments:
$260/month x 72 months = $18,720
Insurance:
$960/year x 6 years = $5,760
Registration:
$240/year x 6 years = $1,440
Gas and maintenance:
$175/month x 12 months/year x 6 years = $12,600
Therefore, the total cost of the car over the life of the loan is:
$18,720 (monthly payments) + $5,760 (insurance) + $1,440 (registration) + $12,600 (gas and maintenance) = $38,520
So, while Brooke may think she's getting a good deal with zero down and low monthly payments, the total cost of the car over the life of the loan is quite high. It's important to consider all the additional costs associated with owning a car before making a decision to purchase one.
What is the surface area of the figure for #11?
*with work on how to solve please!
Answers
The surface areas of the figures are:
10. 1,376 ft² or F 1,344 ft²11. B. 1,058.4 in².How to determine surface area?10.To find the surface area of this rectangular prism, find the area of each face and then add them together.
Face 1: The front and back faces both have dimensions of 12 ft by 14 ft, so the area of each is:
12 ft × 14 ft = 168 ft²
Two of these faces, so the total area is:
2 × 168 ft² = 336 ft²
Face 2: The top and bottom faces both have dimensions of 20 ft by 14 ft, so the area of each is:
20 ft × 14 ft = 280 ft²
Two of these faces, so the total area is:
2 × 280 ft² = 560 ft²
Face 3: The left and right faces both have dimensions of 12 ft by 20 ft, so the area of each is:
12 ft × 20 ft = 240 ft²
Two of these faces, so the total area is:
2 × 240 ft² = 480 ft²
Now add up the areas of all the faces:
336 ft² + 560 ft² + 480 ft² = 1,376 ft²
11. To find the surface area of the figure, add the areas of all six faces.
Find the area of the rectangular faces:
The front and back faces both have dimensions of 14 in by 14 in, so each has an area of 14 in x 14 in = 196 in².
The top and bottom faces both have dimensions of 13 in by 8.9 in, so each has an area of 13 in x 8.9 in = 115.7 in².
Find the area of the triangular faces. Use the Pythagorean theorem to find the length of the third side of each triangle:
The two side faces are congruent triangles with legs of 14 in and 13 in.
Using the Pythagorean theorem, find the length of the hypotenuse to be √(14² + 13²) ≈ 19.14 in. The area of each triangle is then 1/2 base x height = 1/2 x 19.14 in x 8.9 in ≈ 85.3 in².
Using the Pythagorean theorem, find the length of the hypotenuse to be √(8.9² + 13²) ≈ 15.8 in. The area of each triangle is then 1/2 base x height = 1/2 x 15.8 in x 14 in ≈ 110.6 in².
Finally, add up the areas of all six faces:
Front and back faces: 2 x 196 in² = 392 in²
Top and bottom faces: 2 x 115.7 in² = 231.4 in²
Side faces: 2 x 85.3 in² = 170.6 in²
End faces: 2 x 110.6 in² = 221.2 in²
The total surface area is the sum of these areas:
392 in² + 231.4 in² + 170.6 in² + 221.2 in² ≈ 1,015.2 in²
Therefore, the answer is B. 1,058.4 in².
Find out more on surface area here: https://brainly.com/question/76387
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Polygon ABCD is drawn with vertices at A(1, 5), B(1, 0), C(−1, −1), D(−4, 2). Determine the image vertices of A′ if the preimage is rotated 270° counterclockwise.
A′(−1, −5)
A′(−1, 5)
A′(−5, 1)
A′(5, −1
Answers
Answer:
(d) A'(5, -1)
Step-by-step explanation:
You want the coordinates of A(1, 5) after it has been rotated 270° CCW about the origin.
RotationThe transformation for rotation 270° CCW is the same as that for rotation 90° CW:
(x, y) ⇒ (y, -x)
For the given point, this is ...
A(1, 5) ⇒ A'(5, -1)
The image of A is A'(5, -1), choice D.
