The possible first mistake Noah made in the evaluation of the sine and cosine of the acute angles of a right triangle is that the acute angles are complementary and are not always congruent. The correct option is the option (A).
(A) Angles ∠B and ∠C are complementary, not congruent
What are complementary angles?Complementary angles are angles that when added together are equivalent to 90°
The possible two column table Noah used to attempt to prove that cos(θ) = sin(θ) obtained in a similar proof on the website can be presented as follows;
Statement [tex]{}[/tex] Reason
1 m∠B = θ [tex]{}[/tex] The acute angles in a right triangle are congruent
2 sin(θ) = AB/BC [tex]{}[/tex] Definition of sine
3 cos(m∠B) = AB/BC [tex]{}[/tex] Definition of cosine
4 cos(θ) = AB/BC [tex]{}[/tex] Substitution
5 cos(θ) = sin(θ) [tex]{}[/tex] Substitution
Part of the question is; What is the first mistake in Noah's statement used to prove that cos(θ) = sin(θ)
The first mistake is the statement and reason that angle m∠B = θ because all acute angles are congruent.
The acute angles in the right triangle are ∠B and ∠C
The sum of the acute angles in a right triangle is; ∠B + ∠C = 90°
Therefore the acute angles in a right triangle are always complementary, and not always congruent.
The correct option is therefore the option (A)
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Find the partial sum for the sequence.
{2, 3, 5, 8, 13, ...}; S8
S8=
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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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.
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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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
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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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
Answer:
[tex](x - \frac{4}{9} )(x - \frac{9}{2} ) = 0[/tex]
[tex] {x}^{2} - \frac{89}{18} x + 2 = 0[/tex]
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.
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.Find two numbers such that their sum is 12 and their product is 23.
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.
can someone help me with this
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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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.
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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tuesday follows monday in a week express the probability as percent
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%.
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
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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Is the factions are proportional 1/2 and 2/4?
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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Find a function of the form
or (picture) whose graph matches the function shown below:
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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pe
Q2: A total of 160 students were surveyed from the countries of Australia, Canada, and the United Kingdom. One of
the questions asked students to report which hand they considered to be their most dominant.
Results are shown in the table.
Right-Hand Dominant Left-Hand Dominant Total
79
Australia
Canada
United Kingdom 25
Total
a.
68
46
139
dominant with approximately b
b.
Australia
Canada
tinu o lo
United Kingdom
11
160
Select an option from each drop-down menu to complete the sentence.
The country a
de salle
6
4
21
52
68%
86%
120
88%
29
had the greatest percentage of its students report being right-hand
nt ont
The country that had the greatest percentage of its students report being right-hand dominant with approximately 87% is UK
How to calculate the percentageFor Australia, 79 out of 120 students reported being right-hand dominant. So, the percentage of right-hand dominant students in Australia is:
(79/120) x 100 = 65.8%
For Canada, 68 out of 80 students reported being right-hand dominant. So, the percentage of right-hand dominant students in Canada is:
(68/80) x 100 = 85%
For the United Kingdom, 139 out of 160 students reported being right-hand dominant. So, the percentage of right-hand dominant students in the UK is
(139/160) x 100 = 86.9%
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hi can someone help with this question
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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ap calculus problem
no need full detail solution
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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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.
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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What is the surface area of the figure for #11?
*with work on how to solve please!
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.
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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.
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 -
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.
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.
Find the length of the segment.
Answer:
CD = 4 , AD = 6
Step-by-step explanation:
AC is an angle bisector of ∠ BAD and divides the opposite side from the angle into segments that are proportional to the other two sides, that is
[tex]\frac{BC}{CD}[/tex] = [tex]\frac{AB}{AD}[/tex] ( substitute values )
[tex]\frac{6}{y-1}[/tex] = [tex]\frac{9}{2y-4}[/tex] ( cross- multiply )
6(2y - 4) = 9(y - 1) ← distribute parenthesis
12y - 24 = 9y - 9 ( subtract 9y from both sides )
3y - 24 = - 9 ( add 24 to both sides )
3y = 15 ( divide both sides by 3 )
y = 5
Then
CD = y - 1 = 5 - 1 = 4
AD = 2y - 4 = 2(5) - 4 = 10 - 4 = 6
Drop the ball from a height equal to one of your group member's height (high is 5.3)
Determine the amount of time the ball takes to touch the ground (with a timer)
Time to touch the ground: 1.08 seconds
Initial velocity of the ball: ) ft/sec
Plug the initial velocity and the time to touch the ground into:
-16t^2 + v X t+h=0
Solve your equation for h. Based on the height of the person you dropped the ball from, how accurate is your answer for h?
The time taken for the ball to touch the ground is 0.61 s.
What is the time of motion of the ball?The time taken for the ball to touch the ground is calculated by applying the following method.
-16t² + vt + h = 0
where;
v is the initial velocity of the ballh is the height of fall of the ballt is the time of motionwhen the height of the ball = 5.3 ft, with initial velocity = 1.08 ft/s, the time of motion of the ball is calculated as follows;
-16t² + vt + h = 0
-16t² + 1.08t + 5.3 = 0
16t² - 1.08t - 5.3 = 0
solve the quadratic equation, using formula method;
a = 16, b = -1.08, c = -5.3
t = 0.61 second.
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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?
Answer:
Yes.
Step-by-step explanation:
8:120 = 4:60 = 2:30 = 1:15
You divide by two each time to simplify.
Figure 1 and Figure 2 below are congruent. Which point corresponds to point C'?
The point in Figure 2 that corresponds to point L in Figure 1 is the midpoint of line segment NP.
When two figures are congruent, it means that they have the same shape and size. This implies that corresponding points in the two figures have the same position and distance from each other.
In Figure 1, the points I, J, L, K, N, P, and Q are labeled. To find the point in Figure 2 that corresponds to point L, we need to look for a point that has the same relative position and distance as point L in Figure 1.
From Figure 1, we can see that point L is the midpoint of the line segment JK. Therefore, to find the corresponding point in Figure 2, we need to look for a point that is the midpoint of the line segment that corresponds to JK. In Figure 2, the line segment that corresponds to JK is NP, and the midpoint of NP corresponds to the point that is equivalent to point L. Therefore, the point that corresponds to point L in Figure 2 is the midpoint of line segment NP.
It is important to note that identifying corresponding points in congruent figures is a fundamental concept in geometry and is often used to solve problems involving congruence and similarity.
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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.
Answer:
The graphs open downward.
10^-x-1=36 solve for x
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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could i have the different proofs for this thank you
The proof for the above is given as follows:
∠A ≅ ∠C - Given
BD ⊥ ∠ABC - Given
AC ⊥ BD - Angle Bisector Theorem
According to the angle bisector theorem, a triangle's opposing side is split into two segments that are proportionate to its other two sides. A ray that splits a given angle into two equal angles is known as an angle bisector.
Thus, it is correct to state that AC ⊥ BD according to the angle bisector theorem.
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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.
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°
Learn more about parallelogram on:
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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)
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).
What is the mean of the data set?
{20, 1, 14, 14, 9, 8}
Enter your answer in the box.
Find the probability that a point chosen at random would lie in the shaded area of the figure. Round to the nearest tenth of a percent.
with the steps and explanation
Answer:
Okay, let's solve this step-by-step:
The figure shows a rectangle partitioned into 6 smaller rectangles
4 of these rectangles are shaded
To find the probability a randomly chosen point lies in a shaded area, we calculate:
Probability = (Number of shaded squares) / (Total number of squares)
There are 6 smaller rectangles
4 of these are shaded
So Number of shaded squares = 4
And Total number of squares = 6
Plugging this in:
Probability = (4) / (6)
= 2/3
Converting to a percent:
2/3 = 66.7%
Rounded to the nearest tenth: 67%
So the final answer is:
The probability that a point chosen at random would lie in the shaded area of the figure is 67% (rounded to the nearest tenth of a percent).
Let me know if this helps explain the steps and solution. I can provide more details if needed.
Good luck!
Step-by-step explanation:
