Help a girl out
Given: ray AC is parallel to ray DE, measure angle FED= measure angle GCA= 45°
Prove: ray FE is parallel to ray GC
Answers
We have proved that the ray FE is parallel to the ray GC.
What is meant by parallel lines?
In geometry, parallel lines are coplanar straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance.
Angle DEF intersects at B
which results in angle DEF corresponding to the angle ACG.
As DEF = 45 so angle ACG = 45
So by the above discussion, we can say that the ray FE is parallel to the ray GC.
Hence, we have proved that the ray FE is parallel to the ray GC.
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Related Questions
For an experiment, a scientist designs a can, 20 cm in height, that can hold water. A
tube is installed at the bottom of the can allowing water to drain out.
At the beginning of the experiment, the can is full. When the experiment starts, the
water begins to drain, and the height of the water in the can decreases by a factor of.
!
each minute.
a. Explain why the height of the water in the can is a function of time.
b. The height, h, in cm, is a function / of time t in minutes since the beginning of the
experiment, h = f(t). Find an expression for f(t).
c. Find and record the values for / when t is 0, 1, 2, and 3.
d. Find f(4). What does f (4) represent?
Answers
Step-by-step explanation:
The height of the water in the can is a function of time, because it depends on the time the water flows out each minute.
The height h in cm is a function f of time t in minutes since poking the hole, h= f(t)h=f(t). The expression for f(t) = 20. \frac{2}{3}^{t}f(t)=20.
3
2
t
The values of f -> f(0) = 20f(0)=20; f(1) = \frac{40}{3}f(1)=
3
40
; f(2) = \frac{80}{9}f(2)=
9
80
; f(3) = \frac{160}{27}f(3)=
27
160
The value of f(5) = \frac{640}{243}f(5)=
243
640
The level of water approaches close to the x-axis as time moves on. It does not completely approach zero.
Sorry if wrong answer
a. The height of the water in the can is a function of time because it changes as time progresses.
b. The exponential function for f(t) is \(f(t) = 20(1/3)^t\).
c. f(0) = 20, f(1) = 6.67, f(2) = 2.22, and f(3) = 0.74.
d. f(4) represents the height of the water in the can 4 minutes after the beginning of the experiment.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
a. The height of the water in the can is a function of time because it changes as time progresses.
As water drains out of the can through the tube, the height of the water in the can decreases over time.
b. Using the formula for exponential functions, \(f(t) = ab^t\), where a is the initial height of the water, b is the factor by which the height decreases each minute, and t is the time in minutes since the beginning of the experiment.
Here, the initial height of the water in the can is 20 cm, and it decreases by a factor of 1/3 each minute.
This means that b is 1/3, and a is 20.
Therefore, the expression for f(t) is:
\(f(t) = 20(1/3)^t\)
c. To find the values of f(t) when t is 0, 1, 2, and 3, we substitute these values into the expression for f(t):
f(0) = 20 (1/3)⁰ = 20
f(1) = 20(1/3)¹ = 6.67
f(2) = 20(1/3)² = 2.22
f(3) = 20(1/3)³ = 0.74
So, when t is 0, the height of the water in the can is 20 cm, and it decreases exponentially by a factor of 1/3 each minute.
d. To find f(4), we substitute 4 into the expression for f(t):
f(4) = 20(1/3)⁴ = 0.25
Here, f(4) represents the height of the water in the can 4 minutes after the beginning of the experiment.
At this time, the height of the water in the can have decreased to 0.25 cm, which is almost completely drained.
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The Sparrowtown Times had 8,910 subscribers last year. This year, after the paper was bought out, it had 40% fewer. How many subscribers were there this year?
Answers
24+z/10 = 31 solve for Z
Answers
Simplify both sides of the equation
Subtract 24 from both sides
Multiple both sides by 10
Use a calculator to find the trigonometric ratio. Round your answer to four decimal places
sin 98°~
Answers
Using a calculator, the trigonometric ratio of sin 98 is approximately 0.9848.
How to Find the Trigonometric Ratio?One of the trigonometric ratio we have in mathematics is the sine ratio. We can use calculator to find the sine of an angle without making use of tables. To do this on your calculator, enter the sine function followed by the degree of the angle you want to find its sine. You will get your answer.
Using a calculator, we can find the sine of 98 degrees as follows:
sin 98° ≈ 0.9848
Rounding this to four decimal places, we get:
sin 98° ≈ 0.9848
Therefore, sin 98° is approximately equal to 0.9848.
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This is just a question I had.
If Denny (random name) left to another country and he left the Tuesday of this week (June 20) and he left for a month, what day would he be back on? I though July 18 but I’m not sure. Pls help?
Answers
Answer:
Step-by-step explanation:
Well, since the length of a month can vary in the number of days, this answer can also vary.
For example, February is only 28 days long, while December is 31 days long.
That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back July 19th of July 20th.
I hope this helps!
use the prime factor method to find the greatest common factor of the group of numbers 68,170,153
Answers
The first step is to express each number in terms of its prime factors
Therefore,
68 = 2 * 2 * 17
170 = 2 * 5 * 17
153 = 3 * 3 * 17
We can see that the only factor that is common to the three numbers is 17
Therefore,
Highest common factor = 17
Help me out pls,
20 points!
Answers
Answer:
75.5 is not equivalent because 75 1/2% to a decimal is 0.775
Step-by-step explanation:
Hope this helps
Answer:
OPTION B the correct answer.
\(75 \frac{1}{2}\% = \frac{151}{200} \)
\( = 0.755\)
Let v1 = -4
-1
-2
v2 = -3
1
-2
v3= 1
-5
2
and H = Span{v1,v2,v3} . Note that v3 = 2v1 - 3v2.
Which of the following sets form a basis for the subspace H, i.e., which sets form an efficient spanning set containing no unnecessary vectors?
a. {V1, V2, V3}
b. {V1, V2}
c. {V1,V3}
d. {V2,V3}
Answers
We're told (and we can confirm) that \(v_3=2v_1-3v_2\), so \(v_3\) is a linear combination of the other two vectors.
This means H is sufficiently spanned by \(\{v_1,v_2\}\); no need for the third vector.
But this also means we can write either \(v_1\) as a linear combination of \(\{v_2,v_3\}\), and \(v_2\) as a lin. com. of \(\{v_1,v_3\}\). So any set of these three vectors taken two at a time will span the subspace H. Hence all of b, c, and d are acceptable.
Determine whether the matrix is symmetric, skew-symmetric, or neither. A square matrix is called skew symmetric when A^T -A
A= | 0 -2 3|
| 2 0 1|
| -3 -1 0|
a. symmetric
b. skew~symmetric
c. neither
Answers
By looking at the matrix, we can say that matrix A is skew-symmetric. (option b)
To check whether a matrix is skew-symmetric, we need to verify if it satisfies the condition \(A^T\) = -A.
Taking the transpose of matrix A, we get:
\(A^T\) = | 0 2 -3 |
| -2 0 -1 |
| 3 1 0 |
Subtracting A from \(A^T\), we get:
\(A^T\) - A = | 0 2 -3 | | 0 -2 3 |
| -2 0 -1 | - | 2 0 1 |
| 3 1 0 | | -3 -1 0 |
= | 0 4 -6 |
| -4 0 -2 |
| 6 2 0 |
Since \(A^T\) - A is equal to the negative of A, we can conclude that matrix A is skew-symmetric. This means that the elements on the main diagonal are all zero, and the elements below the main diagonal are the negatives of the corresponding elements above the main diagonal.
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Determine the percentile of 6.2 using the following data set.
4.2 4.6 5.1 6.2 6.3 6.6 6.7 6.8 7.1 7.2
Your answer should be an exact numerical value.
The percentile of 6.2 is |
%.
Answers
The percentile of 6.2 in the given data set is 40%.
To determine the percentile of 6.2 in the given data set, we can use the following steps:
Arrange the data set in ascending order:
4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2
Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.
Calculate the percentile using the formula:
Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100
In this case, the percentile of 6.2 can be calculated as:
Percentile = (4 / 10) × 100 = 40%
The percentile of 6.2 in the sample data set is therefore 40%.
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Annual earnings, including bonuses, for Financial Analysts and Personal Financial Advisors, are currently following a skewed to the right distribution with a mean of $66,500 and a standard deviation of $10,500. According to the 68-95-99.7 rule, it is correct to say that (select ALL that apply):______.
a. the middle 95% of all Financial Analysts and Personal Financial Advisors make between $45.500 and $77,000 annually.
b. only 2.5% of all Financial Analysts and Personal Financial Advisors make less than $45,500 annually.
c. both of the above statements are false
Answers
Answer:
c. both of the above statements are false
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Distribution skewed to the right
This means that the Empirical Rule is not applicable, and the two statements are false, and thus, the correct answer is given by option c.
The first would be false nonetheless, but the second would be true if the distribution was normal.
If mean (x) pom 15, Efx = 342 + a and N = 20 + a, find the value of a.
Answers
Answer:
a = 3
Step-by-step explanation:
mean is calculated as
mean = \(\frac{sum}{count}\)
Here mean = 15, sum = 342 + a and count = 20 + a , then
\(\frac{342+a}{20+a}\) = 15 ( multiply both sides by 20 + a )
342 + a = 15(20 + a) ← distribute
342 + a = 300 + 15a ( subtract a from both sides )
342 = 300 + 14a ( subtract 300 from both sides )
42 = 14a ( divide both sides by 14 )
3 = a
solve the equation
(x + 2)(x + 6) = 0
Answers
Answer:
The zeroes of the equation are -2 and -6.
Step-by-step explanation:
(x + 2)(x + 6) = 0
=> x = -2, -6
Hope it helps.
During the party josie decides to make some more. She has 6 litres of fruit juice left and plenty of lemonade. How much extra punch can she make
Answers
Answer:
25 extra litres
Step-by-step explanation:
Ratio 2:3
2+3=5 so 35/5 =7
7x2 means she used 14 litres of fruit juice
7x3 means she used 21 litres of lemonade
if she has 10 litres of fruit juice left then she can use 10/2=5 5x3=15 15 litres of lemonade
10+15=25 so she can make 25 extra litres
95% of what number is 114?
Answers
114 is 95% of 120
100% of 120 is 120, therefore 95 percent of 120 equals 114. To learn how to solve 114 is 95 percent of what number, see the step-by-step instructions below.
114 is 95 Percent of What Number?
Formula = Number x 100
Percent = 114 x 100
95 = 120
The following shows the steps to derive this formula and find out 95% of the number is 114.
Step 1: If 95% of a number is 114, then what is 100% of that number? Set up the equation.
114
95% = Y
100%
Step 2: Solve for Y
Using cross multiplication of two fractions, we get
95Y = 114 x 100
95Y = 11400
Y = 11400
100 = 120
HELP HOW DO I FIND THE VALUE OF X
Answers
9514 1404 393
Answer:
7. 118
8. 27
Step-by-step explanation:
Make use of the fact that the sum of angles in a triangle is always 180°.
__
7. 33 + 29 + x = 180 . . . . . numbers in degrees
x = 180 -62 . . . . . . . . . . . subtract 62 from both sides of the equation
x = 118
__
8. 21 +x + 132 = 180
x = 180 -153 . . . . . . . subtract 153
x = 27
Can someone please help me
Answers
The statements true of function f given by f(Θ) = tan(Θ):
A: f is a periodic function (True)D: The period of f is 2π. (True)How to determine functions?A: Since the tangent function has a repeating pattern, it is a periodic function.
B: The domain of the tangent function is restricted because it has vertical asymptotes at certain values of Θ (specifically, odd multiples of π/2).
C: The range of the tangent function is not all real numbers, but rather all values except for its vertical asymptotes.
D: The period of the tangent function is 2π, because the pattern repeats every 2π radians.
E: The period of the tangent function is not π.
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Which function is best represented by the graph?
Answers
Answer:This would be option letter C
Step-by-step explanation:The diagram is a gram of external geofram so the position Is fFX(4) ^N
Answer:
D
Step-by-step explanation:
f(x)= -x^2+4
Draw graph of -x^2 and shift it 4 units above
Graciela begins the month with $300 and is spending $20 per
week. Her brother Sergio begins the month with $150 and is saving $10 per week. Sergio wants to know when they will have the same amount of money.
W
Let represent the number of weeks since the beginning of the
month. Which equation represents this situation?
Answers
Answer:
300-20w=?
150+10w=?
Step-by-step explanation:
Answer:
Step-by-step explanation:
320
What is the equation of a circle with center (−8, 3) and radius 8?
(x + 8)2 + (y − 3)2 = 64
(x − 8)2 + (y + 3)2 = 64
(x − 8)2 + (y + 3)2 = 8
(x + 8)2 + (y − 3)2 = 8
Answers
Answer:
(x + 8)² + (y - 3)² = 64
Step-by-step explanation:
(x - (-8))² + (y - 3)² = 8²
(x + 8)² + (y - 3)² = 64
5) Which value of x satisfies the equation: sin (3x + 5)° = cos (4x + 1)º? A) 12 B):30 C)4 D) 24
Answers
Starting with the equation:
\(\sin (3x+5)=\cos (4x+1)\)Remember the following property:
\(\cos (90-A)=\sin (A)\)Then:
\(\sin (89-4x)=\sin (90-4x-1)=\cos (4x+1)\)Then, the given equation translates to:
\(\sin (3x+5)=\sin (89-4x)\)Then:
\(3x+5=89-4x\)Solve for x:
\(\begin{gathered} \Rightarrow3x+4x=89-5 \\ \Rightarrow7x=84 \\ \Rightarrow x=\frac{84}{7} \\ \Rightarrow x=12 \end{gathered}\)Therefore, the value of x that satisfies the equation, is:
\(x=12\)Simplify the trigonometric expression cos(2x)+1 using Double-Angle identities
Answers
9514 1404 393
Answer:
C. 2cos²(x)
Step-by-step explanation:
The relevant identities are ...
cos(2x) = cos²(x) -sin²(x)
cos²(x) = 1 -sin²(x)
__
Then the expression can be simplified to ...
cos(2x) +1 = (cos²(x) -sin²(x)) +1 = cos²(x) +(1 -sin²(x)) = cos²(x) +cos²(x)
= 2cos²(x)
What is the size of matrix A?
What are the entries of the fourth row of matrix A?
What are the entries of the third column of matrix A?
What is the entry in the (3,4)th position of matrix A?
Answers
Therefore , the solution of the given problem of matrix comes out to be matrix A's (3,4)th place is -1.
What is matrix?A matrix is a group of numbers arranged in rows and columns to form a rectangular array. The numbers make up the matrix's constituents or parts. Matrix algebra is widely used in many branches of mathematics, as well as in the sciences of architecture, physics, economics, and statistics.
Here,
Given that matrix A has 4 rows and 5 columns,
=> it has a dimension of 4 x 6.
=> -1, 2, 3, 4, and 5 are the values in the fourth row of matrix A.
=> 2, 0, 6, and -3 are the values in matrix A's third column.
The entry in matrix A's (3,4)th place is -1.
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90×4/9=40 is this equation true
Answers
The equation is correct, and the value on both sides of the equation is 40.
To verify if the equation 90 × 4/9 = 40 is true, we can perform the calculation on both sides and compare the results.
On the left side of the equation:
90 × 4/9 = (90 × 4) / 9 = 360 / 9 = 40
On the right side of the equation:
40
Both sides of the equation evaluate to 40, which means they are equal. Therefore, the equation 90 × 4/9 = 40 is indeed true.
In summary, the equation is correct, and the value on both sides of the equation is 40.
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Is (1, 8) a solution to the inequality y < 6x + 2?
yes
no
Answers
Please choose the correct answer ! I will give brainliest to the correct one.
Answers
A manufacturer has 576 square inches of material available to construct the 6 faces of a carton, which will be in the shape of a rectangular prism. To maximize the volume, the carton will have dimensions such that the length and width are each twice the height.
Answers
To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).
What is the dimension required to maximize the volume of the box?Assuming the height of the rectangular prism is h inches.
According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.
The total surface area of the rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Substituting the values, we have:
576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)
576 = 8h² + 4h² + 4h²
576 = 16h² + 4h²
576 = 20²
h² = 576/20
h² = 28.8
h = √28.8
h = 5.37
The height of the prism is approximately 5.37 inches.
The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.
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The following data set has a mode of 2, a mean of 10, and a median of 7.
Which of these three measures gives the best idea of the typical size of the
numbers in the list?
2, 2, 2, 4, 6, 8, 10, 12, 14, 60
A. Mean
B. Mode
C. Median
Answers
Answer:
Mode
Is the answer to this...
EASY MATH QUESTION pls help asap
A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and the theater collected $272.00 at the end of the day, how many
of them were adults?
A. 29 adults
B. 16 adults
C. 24 adults
D.10 adults
Answers
Answer:
b 16 adult is - 40 people end of day
Find the length of side X in simple radical form with a rational denominator
Answers
The length of side X in simple radical form with a rational denominator is 25/√3.
What is a 30-60-90 triangle?In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):
Adjacent side = 5/√3
Hypotenuse, x = 5 × 5/√3
Hypotenuse, x = 25/√3.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
