Answer:
We can use the formula for compound interest to find the balance in Eliana's savings account after 10 years:
A = P(1 + r/n)^(nt)
where A is the balance, P is the principal (initial deposit), r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years.
Substituting the given values, we get:
A = $700(1 + 0.04/12)^(12*10)
Simplifying, we get:
A = $700(1.0033333)^120
Using a calculator, we get:
A ≈ $1,038.81
Therefore, the balance in Eliana's savings account after 10 years is approximately $1,038.81.
CAN SOMEONE HELP WITH THIS QUESTION?
Answer:
a. Since the half-life of the isotope is 8 hours, we know that the decay rate is exponential and we can use the formula:
A(t) = A0 * (1/2)^(t/8)
where A0 is the initial amount of the substance, t is the time elapsed, and A(t) is the amount of substance remaining after t hours.
Substituting the given values, we get:
A(t) = 7 * (1/2)^(t/8)
b. To find the rate at which the substance is decaying, we need to take the derivative of A(t) with respect to t:
A'(t) = -7/8 * (1/2)^(t/8) * ln(1/2)
Simplifying, we get:
A'(t) = -ln(2) * (7/8) * (1/2)^(t/8)
c. To find the rate of decay at 14 hours, we can plug in t=14 into the equation we found in part b:
A'(14) = -ln(2) * (7/8) * (1/2)^(14/8) ≈ -0.4346 grams per hour (rounded to four decimal places)
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 82° is changed to 94°, which of the following measures changes the most and what is the new value?
IQR 34°
Range 48°
Mean 81.4°
Median 84°
Answer:
If we change the value of 82° to 94°, the new data set becomes:
58, 61, 71, 77, 91, 100, 105, 102, 95, 94, 66, 57
IQR:
To find the new interquartile range (IQR), we first need to find the new values of the first quartile (Q1) and the third quartile (Q3). The median of the original data set is 84°, which is between the 6th and 7th values when the data is ordered. So, the first half of the data set consists of the values 58, 61, 71, 77, 82, and 91, and the second half consists of the values 94, 95, 100, 102, 105.
The new Q1 is the median of the first half of the data set, which is (71 + 77) / 2 = 74. The new Q3 is the median of the second half of the data set, which is (100 + 102) / 2 = 101.
The new IQR is Q3 - Q1 = 101 - 74 = 27.
Range:
The range is simply the difference between the largest and smallest values in the data set. Before the change, the range was 105 - 57 = 48. After the change, the range is 105 - 58 = 47.
Mean:
To find the new mean, we add up all the temperatures and divide by the number of temperatures. Before the change, the sum was 980 and there were 12 temperatures, so the mean was 980/12 = 81.7° (rounded to one decimal place). After the change, the sum is 982 and there are still 12 temperatures, so the new mean is 982/12 = 81.8° (rounded to one decimal place).
Median:
The median is the middle value in the data set when it is ordered. Before the change, the median was 84°. After the change, the median is still 84°, since only one value was changed and it did not affect the position of the median.
Therefore, the IQR changes the most, increasing from 34° to 27°. The new value of the IQR is 27.
write 9 minutes and 25 seconds to 9 in the evening In analogue time
Answer:
9 minutes and 25 seconds to 9 in the evening in analogue time is represented as:
8:50:35 PM
Determina analítica y geométricamente el vector que inicia en el punto P(3,3) y termina en el punto
Q(-2,2), da el vector de igual magnitud y sentido contrario al vector anterior.
After answering the presented question, we can conclude that The vector expression of equal magnitude and opposite direction to [tex]\vec{PQ}[/tex] is the same arrow but pointing in the opposite direction: QP vector
What is expression?An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression.
Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form.
They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
To find the vector that starts at [tex]P[/tex] [tex](3,3)[/tex] and ends at [tex]Q(-2,2)[/tex] , we can subtract the coordinates of the starting point from the coordinates of the ending point:
[tex]$\vec{PQ} = \begin{pmatrix} -2 \ 2 \end{pmatrix} - \begin{pmatrix} 3 \ 3 \end{pmatrix} = \begin{pmatrix} -5 \ -1 \end{pmatrix}$[/tex]
So the vector that starts at P(3,3) and ends at [tex]Q(-2,2) is $\vec{PQ} = \begin{pmatrix} -5 \ -1 \end{pmatrix}$.[/tex]
To find the vector of equal magnitude and opposite sense to , we can simply multiply [tex]$\vec{PQ}$[/tex] by [tex]-1:[/tex]
[tex]$-\vec{PQ} = -1 \begin{pmatrix} -5 \ -1 \end{pmatrix} = \begin{pmatrix} 5 \ 1 \end{pmatrix}$[/tex]
So the vector of equal magnitude and opposite sense to [tex]$\vec{PQ}$[/tex] is [tex]$\begin{pmatrix} 5 \ 1 \end{pmatrix}$.[/tex]
Geometrically, we can represent the vectors graphic[tex]$\vec{PQ}$[/tex]ally by drawing them as directed line segments on a coordinate plane. The vector that starts at [tex]P(3,3)[/tex] and ends at [tex]Q(-2,2)[/tex] is represented by the line segment connecting [tex]P[/tex] to [tex]Q[/tex].
Therefore, The vector of equal magnitude and opposite sense to [tex]$\vec{PQ}$[/tex][tex]$\vec{PQ}$[/tex] is represented by the line segment starting at [tex]Q[/tex] and ending at the point R, which is [tex]5[/tex] units to the right and [tex]1[/tex] unit up from [tex]Q[/tex].
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Find the missing length indicated. * A) 12 C) 8 A OB D 16 24 36 B) 18 D) 15
Answer:
Is D
Step-by-step explanation:
A rectangular box has a length that is 4 feet longer than its width, w.
Write an algebraic expression, in simpliest form, to find the perimeter of the box.
Step-by-step explanation:
The length of the rectangle is 4 feet longer than its width w, which means the length is w + 4
The perimeter of a rectangle is the sum of the lengths of all four sides which can be expressed as:
Perimeter = 2(length + width)
Substituting w + 4 for length and w for width, we get:
Permiter = 2(w + 4 + w)
Simplifying this expression, we get:
Perimeter = 2(2w + 4)
Perimeter = 4w + 8
Therefore, the algebraic expression to find the perimeter of the rectangular box is 4w + 8
A bank account gathers compound interest at a rate of 5% each year. Another bank account gathers the same amount of money in interest by the end of each year, but gathers compound interest each month. If Abraham puts £4300 into the account which gathers interest each month, how much money would be in his account after 2 years and 5 months? Give your answer in pounds to the nearest 1p.
Answer:
$6235 1
' 1 . ' 8
Answer:
Step-by-step explanation:
Rhonda just got promoted in her job as a physical therapy assistant. She will now earn $20.70 per hour. This is 115% of her hourly salary before her promotion. What was her hourly salary before her promotion?
As a result, Rhonda was paid $18 per hour before to being promoted; nevertheless, she will now be paid $20.70 per hour.
what is unitary method ?Finding a single unit value and applying it to ratio and proportional problem solving is known as the unitary method in mathematics. It is frequently employed in order to resolve issues involving either direct proportion, inverse proportion, or both. In the unitary technique, the ratio of the quantities' corresponding unit values is used to indicate the relationship between the quantities. The desired value is then achieved by multiplying or dividing the unit value, as necessary.
given
Let x be the hourly wage Rhonda received prior to her promotion.
The issue states that her new hourly wage is equal to 115% of her previous wage:
20.70 = 1.15x
We can divide both sides by 1.15 to find x:
x = 20.70 / 1.15
x = 18
As a result, Rhonda was paid $18 per hour before to being promoted; nevertheless, she will now be paid $20.70 per hour.
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View the photo and solve the probability
Therefore, the probability that at least one of the next six births is a girl is 1 - 0.033 = 0.967 (rounded to three decimal places).
What is Probability?Probability is a measure of the likelihood that an event will occur. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.
To calculate the probability of an event, you divide the number of ways that event can occur by the total number of possible outcomes. For example, if you flip a fair coin, there are two possible outcomes - heads or tails - and each has an equal probability of 0.5 (or 50%) of occurring.
Given by the question.
To find the probability that at least one of the next six births is a girl, we can find the probability that all six of them are boys and subtract it from 1.
The probability that one birth is a girl is 1 - 0.513 = 0.487.
The probability that all six births are boys is. [tex]0.513^{6}[/tex] = 0.033.
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A cruise ship weighs 3.83×107 kilograms. A horse weighs 7.1×102 kilograms. Approximately how many horses weigh as much as one cruise ship?
Give your answer in scientific notation using only whole numbers.
5.394366197183099*10^4
Step-by-step explanation:1. Write the number as a decimal 53943.66197183099
2. Make it a new number between 1 and 10
Move the decimal point to make 53943.66197183099 a new number between 1 and 10. Because our number is greater than 10, we move the decimal point to the left. Drop any trailing zeros and place the decimal point after the first non-zero digit. Keep track of how many times we move the decimal point.
53943.66197183099 -> 5.394366197183099
Our new number is 5.394366197183099. We moved the decimal point 4 times.
Use a calculator and get the values from both equations, 3.83×10^7 and 7.1×10^2 then put the first value 38300000 into a calculator, then divide 38300000/710 and you will get the value 53,943.66197183099. Then run that through a scientific notion calculator to get 5.394366197183099*10^4.
There you go.
Approximately 54,000 horses weigh as much as one cruise ship.
Explanation:To find out how many horses weigh as much as one cruise ship, we need to divide the weight of the cruise ship by the weight of a horse. In scientific notation, the weight of the cruise ship is 3.83x107 kg and the weight of a horse is 7.1x102 kg.
Dividing the weight of the cruise ship by the weight of a horse, we get:
(3.83x107 kg) ÷ (7.1x102 kg) = 5.4x104
So approximately 54,000 horses weigh as much as one cruise ship.
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What is the scale factor?
The scaling factor for given transformation is 3.
What exactly is scaling factor?
The scaling factor, also known as the scale factor, is a value that indicates how much a geometric figure is enlarged or reduced. It is the ratio of the length of a side or dimension of the original figure to the length of the corresponding side or dimension of the new figure. The scaling factor can be greater than 1, which indicates an enlargement, or less than 1, which indicates a reduction. When the scaling factor is 1, the two figures are congruent, which means they have the same shape and size.
Now,
We can find the scale factor by comparing the corresponding side lengths of the two polygons. Let's start by finding the side lengths of the original polygon:
HI: √[(4-0)² + (-5+3)²] = √20
IJ: √[(6-4)² + (0-0)²] = 2
JK: √[(4-6)² + (5-0)²] = √41
KL: √[(0-4)² + (3-5)²] = √20
LH: √[(0-0)² + (-3+5)²] = 2
Now let's find the corresponding side lengths of the dilated polygon:
H'I': √[(12-0)² + (-15+9)²] = √600
I'J': √[(18-12)² + (0-0)²] = 6
J'K': √[(12-18)² + (15-0)²] = √600
K'L': √[(0-12)² + (9-0)²] = √600
L'H': √[(0-0)² + (-9+3)²] = 6
We can see that the side lengths of the dilated polygon are all 3 times as long as the corresponding side lengths of the original polygon. Therefore, the scale factor is 3.
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Henderson's Hardware has an ROA of 12%, a 8% profit margin, and an ROE of 19%. What is its total assets turnover? Do not round intermediate calculations. Round your answer to two decimal places. What is its equity multiplier? Do not round intermediate calculations. Round your answer to two decimal places.
Answer: We can use the DuPont Model to calculate the total assets turnover and equity multiplier:
ROE = ROA × Equity Multiplier
Equity Multiplier = Total Assets / Total Equity
Profit Margin = Net Income / Sales
Total Assets Turnover = Sales / Total Assets
Given:
ROA = 12%
Profit Margin = 8%
ROE = 19%
To find the Total Assets Turnover:
Profit Margin = Net Income / Sales
0.08 = Net Income / Sales
Net Income = 0.08 x Sales
ROA = 12%
ROA = Net Income / Total Assets
0.12 = 0.08 x Sales / Total Assets
Total Assets Turnover = Sales / Total Assets = 0.08 / 0.12 = 0.67
Therefore, the total assets turnover is 0.67.
To find the Equity Multiplier:
ROE = ROA x Equity Multiplier
0.19 = 0.12 x Equity Multiplier
Equity Multiplier = 0.19 / 0.12 = 1.58
Therefore, the equity multiplier is 1.58.
Note: The total assets turnover and equity multiplier are related to each other through the DuPont model. The product of these two ratios should be equal to the ROE. In this case, 0.67 x 1.58 = 1.06, which is approximately equal to 1.9 (ROE in decimal form). This confirms that our calculations are correct.
Step-by-step explanation:
Anna has one dollar she buy some candy for $.83 which shows how much change and I should get
Answer:
Anna should receive $0.17 (17 cents) in change
Step-by-step explanation:
Anna has $1, she spends $.83 on candy
To find how much change she will get, we must subtract
1 - 0.83
$0.17
Answer:$0.17
Step-by-step explanation:
A dollar is 100 cents just subtract 83 from 100 to get 17.
What is the equation of the line that passes through the point (-3,4)(−3,4) and has a slope of -2−2?
Answer:
slope intercept form= y=2x+2
point form= y+4=2*(x+3)
Step-by-step explanation:
Answer y = -2x -2 is your equation of the line crossing those points
Step by step
To find your equation of the line, use slope (-2) and the points (-3, 4) and point slope formula y- y1 = m (x - x1)
y - 4 = -2 ( x - -3)
Simplify
y - 4 = -2x -6
Add 4 to each side to isolate y
y -4 +4 = -2x -6 +4
Simplify
y = -2x -2 is your equation of the line crossing those points
Set up and solve a proportion for the following application problem. If 5 pounds of grass seed cover 355 square feet, how many pounds are needed for 6035 square feet?
Let x be the number of pounds needed for 6035 square feet.
We can set up a proportion between the pounds of grass seed and the square feet covered:
5 pounds / 355 square feet = x pounds / 6035 square feet
To solve for x, we can cross-multiply and simplify:
5 pounds * 6035 square feet = 355 square feet * x pounds
30175 = 355x
x = 30175 / 355
x ≈ 85.07
Therefore, approximately 85.07 pounds of grass seed are needed for 6035 square feet
I will mark you brainiest!
The value of M is
A) 14
B) 18
C) 20
D) 28
Answer:
I got 28
Step-by-step explanation:
use the formula k=y/x. 6/8=0.75
21/0.75=
A, B, and C started a business with Rs 60,000. Amount invested by 'A' and 'C' together is twice that of 'B', while the amount invested by 'A' and 'B' together is thrice that of 'C'. 'A' invested for 6 months, 'B' for 9 months, and 'C' for a year. Find the share of 'B' (in Rs) out of the total profit of Rs 3400.
Answer:
Step-by-step explanation:
Let the amount invested by A, B, and C be denoted by a, b, and c respectively.
From the given information,
a + b + c = 60000 ---(1)
a + c = 2b ---(2)
a + b = 3c ---(3)
Multiplying equation (2) by 3 and equation (3) by 2, we get:
3a + 3c = 6b
2a + 2b = 6c
Adding these two equations, we get:
5a + 5b + 5c = 0
a + b + c = 0
This is not possible as the sum of the investments cannot be zero. Therefore, there must be an error in the problem statement.
Without further information or correction, it is not possible to find the share of B in the profit.
Zoe's ball pool is a cylinder with height 20 cm and diameter 90 cm.
Calculate:
(a) The radius of the pool
(b) The circumference of the pool
(c) The area of the base of the pool
(d) The volume of the pool
Solution :
Zoe's ball pool is a cylinder with height 20 cm and diameter 90 cm.
Height = 20 cm
Diameter = 90 cm
Calculate :
(a) The Radius of the pool.
Answer :
We are given with Diameter of pool 90 cm.
We know that,
Radius = Diameter/2
Radius = 90/2 = 45 cm.
(b) The circumference of the pool .
Answer :
Circumference = 2 πr
[tex]2 \times \dfrac{22}{7} \times 45 \\ \\ \dfrac{ 44 \times 45}{7} \\ \\ \frac{1980}{7} \\ \\ 282.8 \: cm[/tex]
(c) The area of the base of the pool.
Answer :
Area of base = πr²
[tex] \dfrac{22}{7} \times {(45)}^{2} \\ \\ \frac{22}{7} \times 2025 \\ \\ 22 \times 289.28 \\ \\ 578.56 \: {cm}^{2} \\ [/tex]
(d) The volume of the pool
Answer :
Volume of cylinder = πr²h
[tex] \dfrac{22}{7} \times {(45)}^{2} \times 20 \\ \\ \dfrac{22}{7} \times 2025 \times 2 \\ \\ \dfrac{22}{7} \times 4050 \\ \\ \frac{89100}{7} \\ \\ 12728.57 \: {cm}^{3} [/tex]
Create a real-word mathematical problem as an equation that can be solved using all three properties
Thus, we should order two large pizzas, that will cost $22, to serve a group of 12.
What do you mean by cost?Costs in accounting are the dollar amounts paid for materials, labor, services, goods, equipment, and other purchases made for use by a company or even other accounting entity. This sum is listed as the price on invoices and is recorded as an expense of asset cost basis in bookkeeping records.
Solution:
Let x be the quantity of pizzas ordered.
12 x 2 = 24 slices are required because a large pizza contains 8 slices per slice.
As a result, the necessary quantity of pizzas is:
[tex]x\geq 3(x-1) \leq x[/tex]
In order to find the best price, we must reduce the total cost, that is determined by:
C(x) = 15x plus 5(x - 1) (x - 1) - 15
Using the cost function's derivative in relation to x, we may calculate:
C'(x) = 20 - 10[tex]/(x-1)^2[/tex]
Finding the critical points by setting the derivative to zero yields the following results:
20 - 10[tex]/(x-1)^2[/tex] = 0
Simplishing, we obtain:
[tex](x-1)^2[/tex]= 2
By solving for x using square root of the both sides, we arrive at:
x = 1 ± √2
The ideal quantity to order is two pizzas because x has to be an integer.
By adding x = 2 to the cost function, we can determine the total cost:
C(2) = 15(2) + 5(2 - 1) - 15 = 22
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Diana has watched 13 out of 25 episodes of a television series. What decimal represents the part of the series she has NOT watched yet?
Answer:
Step-by-step explanation:
16 Extend Your Thinking Suppose you cut a square shape
in half, as shown. How can you find the area of one part
of the figure?
52 yd
The function S=m^(2)+6m+8 models the growth of book sales in m months, where S is an amount in thousands of dollars. In how many months do book sales reach $80,000 ?
Answer:
We are given the function S = m^2 + 6m + 8 which models the growth of book sales in m months, where S is an amount in thousands of dollars. We want to find in how many months book sales reach $80,000.
We can set up an equation as follows:
S = m^2 + 6m + 8 = 80
Subtracting 80 from both sides, we get:
m^2 + 6m - 72 = 0
We can factor this quadratic equation as:
(m + 12)(m - 6) = 0
This gives us two possible solutions:
m + 12 = 0 or m - 6 = 0
Solving for m in each case, we get:
m = -12 or m = 6
Since we are looking for a number of months, we can discard the negative solution.
Therefore, book sales reach $80,000 in 6 months.
So, the answer is: 6 months.
Need help pls
geometry
#23
Answer: I think its C
Answer:
Step-by-step explanation:
C is false. [tex]\angle BEC = \angle AED=126[/tex] (vertically opposite).
The rest are correct.
You went out to dinner and your meal $22.00. If you want to leave a 20% tip, how much will you pay total?
You will pay a total of $26.40 including the 20% tip.
To calculate the total amount including the 20% tip, you need to add 20% of the meal cost to the original meal cost:
A gratuity or a small amount of money given to someone for their service, such as a waiter or a hairdresser.
A piece of advice or a suggestion given to someone to help them do something better or more efficiently.
A pointed or tapered end of an object, such as the tip of a pen or a needle.
Tip amount = 20% of $22.00 = 0.2 x $22.00 = $4.40
Total amount including tip = $22.00 + $4.40 = $26.40
Therefore, you will pay a total of $26.40 including the 20% tip.
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What is the fourth term of the sequence:
Write the number in the blank only.
a_1 = 5
a_n = 2a_n-1 + 3
The fourth term of the sequence with the definition of functions a₁ = 5 and aₙ = 2aₙ₋₁ + 3 is 61.
Calculating the fourth term of the sequenceGiven the following definition of functions
a₁ = 5
aₙ = 2aₙ₋₁ + 3
To find the fourth term of the sequence defined by a₁ = 5aₙ = 2aₙ₋₁ + 3, we can use the recursive formula to generate each term one by one:
a₂ = 2a₁ + 3 = 2(5) + 3 = 13
a₃ = 2a₂ + 3 = 2(13) + 3 = 29
a₄ = 2a₃ + 3 = 2(29) + 3 = 61
Therefore, the fourth term of the sequence is 61.
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Mr. Ed earns $15.50 per hour. His regular hours are 40 hours per week, and he receives
time-and-a-half overtime. Find his total pay for a week in which he works 45 hours.
Answer:
For the first 40 hours that Mr. Ed works, he earns his regular rate of pay, which is $15.50 per hour. So, his regular pay for the week is:
40 hours x $15.50 per hour = $620
For the additional 5 hours he works, he earns overtime pay at a rate of time-and-a-half, which is 1.5 times his regular pay rate. So, his overtime pay for the week is:
5 hours x $15.50 per hour x 1.5 = $116.25
Therefore, Mr. Ed's total pay for the week in which he works 45 hours is:
$620 (regular pay) + $116.25 (overtime pay) = $736.25.
Sue deposited $1,500 into two different accounts.
- She deposited $600 into an account that pays 7.5% simple interest.
- She deposited $900 into an account that pays 6% compounded annually.
If Sue does not deposit additional money into the accounts and she doesn't withdraw any
money from the accounts, which is closest to the total balance she will have in the two
accounts at the end of 5 years?
F $2,029.40
G $2,005.68
H $529.40
J $1,995.00
The total balance that Sue will have in the two accounts after 5 years can be calculated as follows:
Balance of the first account with simple interest:
FV = P(1 + rt)
FV = $600(1 + 0.075 x 5)
FV = $825
Balance of the second account with compounded interest:
FV = P(1 + r)^n
FV = $900(1 + 0.06)^5
FV = $1,286.87
Total balance = $825 + $1,286.87
Total balance = $2,111.87
The closest answer choice to this amount is F) $2,029.40, which is only off by a small margin. Therefore, the answer is F) $2,029.40.
You move up 7 units and down 4 units. You end at (-2, -2). Where did you start?
Answer:-2,-5
Step-by-step explanation:
7-4=3
You move 3 units up
You land on -2, -2
the higher units you move up, the higher the number gets to.
I need help with a problem on my test.
Write an exponential function to model the situation. Tell what each variable represents. A price of $115 increases 9% each month.
Please help
Answer: 1050$
Step-by-step explanation:
im a math teacher
i’m begging can someone PLEASE help and hurry i have to turn this in soon
Given the diagram above, which is a combination of three right triangles,
27) m∠DGE = 45°
28) m∠EDG = 85°
29) FD = 10
30) GD = 14
31) EG = 19.
What is the explanation for the above answers?27) m∠DGE = 45°
This is because m∠DGE is an alternate angle to m∠BAD which is = 45°. Recall that alternate angles are congruent.
28) m∠EDG = 85° because it is the vertical opposite of ∠ADC. Note that ∠ADC = 180 - 45 - 50
= 85°
29) and 30)
Given FG=10 and m∠DGE=45°,
FD = √DG² - FG²
Since we don't have FD
We use Cos Rule
GD = FG/cos(α)
GD = 10/Cos 45°
GD = 14.1421356237
GD [tex]\approx\[/tex] 14
Thus,
FD = √14.1421356237312 - 102
FD = √100
FD = 10
31)
EG = EF + 10
EF = √(GD² - FG²
EF = √(14² - 10²)
EF = √80.982478588641
EF = 8.99903
Hence,
EG = 8.99903 + 10
EG [tex]\approx[/tex] 19
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