Answers
Using the prοperties οf the triangle the values are οbtained as -
m ∠DGE = 47.5°
m ∠EDG = 85°
FD = 8.30
GD = 13
EG = 20
What are triangles?Triangles are a particular sοrt οf pοlygοn in geοmetry that have three sides and three vertices. Three straight sides make up the twο-dimensiοnal figure shοwn here. An example οf a 3-sided pοlygοn is a triangle. The tοtal οf a triangle's three angles equals 180 degrees. One plane cοmpletely enclοses the triangle.
Twο triangles ADC and DEG are given.
In triangle ADC the measure οf angle A is given as 45°.
And the measure οf angle C is given as 50°.
Accοrding tο the prοperties οf a triangle, the sum οf angles οf a triangle is 180°.
So, mathematically this can be represented as -
∠A + ∠D + ∠C = 180°
Substituting the values into the equation -
45° + ∠D + 50° = 180°
∠D + 95° = 180°
∠D = 180° - 95°
∠D = 85°
The measure of angle D is obtained as 85°.
Now, since ∠ADC and ∠EDG are vertically opposite angles so they are equal.
So, mathematically this can be represented as -
∠EDG = ∠ADC
∠EDG = 85°
Also, the angle ∠EDG is bisected by the line segment BF.
So, in ΔDFG we have ∠FDG = 85/2 = 42.5°.
Now, in ΔDFG , the sum of angles of a triangle is 180°.
So, mathematically this can be represented as -
∠GFD + ∠FDG + ∠DGF = 180°
Substituting the values into the equation -
90° + 42.5° + ∠DGF = 180°
132.5° + ∠DGF = 180°
∠DGF = 180° - 132.5°
∠DGF = 47.5°
Now, in ΔDEG we have -
∠DGF = ∠DGE
∠DGE = 47.5°
Since, line segment FD is a bisector so we have -
EF = FG
EF = 10
Now, in Δ DFE Since, line segment FD is a bisector so we have -
EF = FG
EF = 10according to Pythagoras theorem we have -
ED² = EF² + FD²
Substituting the values into the equation -
13² = 10² + FD²
FD² = 13² - 10²
FD² = 169 - 100
FD = √69
FD = 8.30
Therefore, the value for FD is obtained as 8.30.
Now, in Δ DFG according to Pythagoras theorem we have -
DG² = FG² + FD²
Substituting the values into the equation -
DG² = 10² + √69
DG² = 100 + √69
DG = √(100 + √69)
DG = √169
DG = 13
Therefore, the value for DG is obtained as 13.
Since, line segment FD is a bisector so we have -
EG = EF + FG
EG = 10 + 10
EG = 20
Therefore, the value for EG is obtained as 20.
To learn more about triangles from the given link
https://brainly.com/question/25215131
#SPJ1
Related Questions
pls help
Which of the following must be true to prove AABCDEF by the AAS
theorem?
Given:
ZA ZD
AC
DF
OA. ZB LE
OB. ZC LF
OC. LB=LC
OD. ZELF
Answers
The information that must be true to prove that both triangles are congruent by triangles congruent by the AAS theorem is: A. ∠B ≅ ∠E.
What is the AAS Congruence Theorem?The AAS congruence theorem states that if two pairs of corresponding angles and a pair of non-included sides of two triangles are congruent, then both triangles are congruent triangles.
We are given the following:
∠A ≅ ∠D (one pair of congruent angles)AC ≅ DF (one pair of congruent)What will make both triangles congruent by AAS theorem is: A. ∠B ≅ ∠E.
Learn more about the AAS congruent theorem on:
https://brainly.com/question/3168048
#SPJ1
14.127 divided by 5.1 show work
Answers
9514 1404 393
Answer:
2.77
Step-by-step explanation:
Usually we like to do long division with the divisor being an integer. Here, that means the decimal points in both numbers are moved one place to the right. This makes the division be 141.27/51 = 2.77. The work is shown in the attachment.
Dan's car depreciates at a rate of 9% per year.
By what percentage has Dan's car depreciated after 4 years?
Give your answer to the nearest percent.
Answers
Answer:
about 31%
Step-by-step explanation:
\(1 - {.91}^{4} = 1 - .6857 = .3143 = 31\%\)
A scale drawing of a rectangular park is 8 inches wide
and 11 inches long.
The actual park is 330 yards long. What is its area?
Use paper to help you with your thinking.
79200 square yards
240 square yards
88 square yards
2640 square yards
Answers
The area of park in terms of scale drawing is 79200 square yards with scale drawing of a rectangular park is 8 inches wide and 11 inches long.
What is area of rectangle?Area of rectangle=Length * width.
Given:
scale length of rectangular park = 11 inch =
scale width of rectangular park = 8 inch
scale length / actual length of park = scale width/ actual width of park
11/330= 8/ actual width of park
1/30 = 8/ actual width of park
actual width of park = 240
So,
Area = length* width
=330*240
= 79200 square yards
Hence, the area of the actual parking is 79200 square yards.
learn more about area of rectangle here:
brainly.com/question/20693059
#SPJ1
Someone please help
Answers
Answer:
Angle 1 and angle 8
angle 2 and angle 7
angle 3 and angle 6
angle 4 and angle 5
I think its tat.
Step-by-step explanation:
Pharmex is a chain of drugstores that operate around the country. To see how effective its advertising and other promotional activities are, the company has collected data from 50 randomly selected metropolitan regions. In each region, it has compared its own promotional expenditures and sales to those of the leading competitor in the region over the past year. There are two variables: "Promote" reflects Pharmex’s promotional expenditures as a percentage of those of the leading competitor, and "Sales" reflects Pharmex’s sales as a percentage of those of the leading competitor. A portion of the data appears below. Show all work.
Region Promote Sales Region Promote Sales Region Promot Sales
1 77 85 21 103 112 41 100 94
2 110 103 22 95 96 42 96 81
3 110 102 23 103 93 43 88 92
4 93 109 24 89 97 44 109 108
5 90 85 25 97 92 45 109 103
a. Using Excel, create a scatterplot of the data. What do you observe? What type of relationship, if any, is apparent from the scatterplot?
b. Insert a trendline (click on the scatterplot, then click the Layout tab, and choose Trendline). What type of trendline seems to fit best?
c. Under "More Trendline Options," select "Display Equation on chart" and "Display R-squared value on chart." What do you see? What do these numbers mean?
Answers
Answer:
Positive relationship exists
Linear trend line
R² = 0.3522
Step-by-step explanation:
Given the data :
Promote (X) :
77
110
110
93
90
103
95
103
89
97
100
96
88
109
109
Sales (Y) :
85
103
102
109
85
112
96
93
97
92
94
81
92
108
103
A.) From the resulting plot, tbe slope of the graph is positive, hence, we can conclude that there exist a positive relationship between the variables 'promote' and 'sale'.
The linear trend line gives the best fit for the data with a correlation Coefficient, R value of 0.5935
The R² value is 0.3522. R² is the Coefficient of determination which gives the percentage of explained variation. For this data, about 35% of variation in sales is given by the best fit line.
Determine the validity of the converse and give a counterexample if the converse is not valid.
If it is sunny, then it is 80° Fahrenheit. The converse is valid.
If it is 80° Fahrenheit, then it is sunny. The converse is valid.
If it is not sunny, then it is not 80° Fahrenheit. The converse is invalid; a counterexample is a day that is not 80° Fahrenheit and not sunny.
If it is 80° Fahrenheit, then it is sunny; The converse is invalid; a counterexample is a day that is 80° and cloudy.
Answers
Your analysis is correct. Here's a summary:
If it is sunny, then it is 80° Fahrenheit. (Original statement)
Converse: If it is 80° Fahrenheit, then it is sunny. (Valid)
If it is 80° Fahrenheit, then it is sunny. (Original statement)
Converse: If it is sunny, then it is 80° Fahrenheit. (Valid)
If it is not sunny, then it is not 80° Fahrenheit. (Original statement)
Converse: If it is not 80° Fahrenheit, then it is not sunny. (Invalid)
Counterexample: A day that is not 80° Fahrenheit and not sunny (e.g., 70° and cloudy).
If it is 80° Fahrenheit, then it is sunny. (Original statement)
Converse: If it is sunny, then it is 80° Fahrenheit. (Invalid)
Counterexample: A day that is 80° Fahrenheit and cloudy.
In cases 1 and 2, the original statements and their converses are valid because the relationship between "sunny" and "80° Fahrenheit" holds in both directions. However, in cases 3 and 4, the converses are invalid because there are counterexamples where the second part of the statement (either "not 80° Fahrenheit" or "cloudy") does not necessarily imply the first part ("not sunny" or "80° Fahrenheit").
-1 1/2 -1 -1/2 0 1/2 1 1 1/2?
Answers
Answer:
.
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
In an orchard 2/5 of the trees are banana trees, 1/4 of the trees are orange trees and the rest are apple trees. If there are 220 trees in all, find the number of each kind
Answers
Answer: banana- 88
Orange-55
Apple-143
Step-by-step explanation:
220 divided by 5, times 2,
that’s the banana trees
220 divided by 4, that’s the oranges
Add the answers together
Take the answer away from 220 that’s the apples
can someone help me with this
Answers
The other leg measures 4 centimetres in length.
The right triangle in the illustration has a hypotenuse that is 5 cm long and a leg that is 3 cm long. The length of the other leg must be determined.
Applying the Pythagorean theorem, which asserts that the square of the hypotenuse's length is equal to the sum of the squares of the two legs of a right triangle, we may write:
\(a^2 + 3^2 = 5^2\)
When we simplify this equation, we obtain:
\(a^2\) + 9 = 25
By taking 9 away from both sides, we arrive at:
\(a^2\) = 16
By multiplying both sides by their square roots and keeping in mind that a must be positive, we arrive at:
a = 4
Hence, the other leg is 4 cm long.
To know more about Length visit:
brainly.com/question/30100801
#SPJ9
on December 31st 2018 the New York state minimum wage increase from 10.40 per hour to 11.10 per hour find the percent increase .
Answers
The Solution:
The New York State minimum wage increase from 10.40 per hour to 11.10 per hour. This means the base wage is 10.40
To find the percent increase in the minimum wage , we shall use the formula below:
\(\text{ Percent Increase}\frac{\text{ increase in wage}}{\text{base wage}}\times100\)In this case,
\(\begin{gathered} \text{ Increase in wage=11.10-10.40 = 0.70} \\ \text{base wage = 10.40} \end{gathered}\)Substituting these values in the above formula, we get
\(\text{Percent increase=}\frac{0.70}{10.40}\times100=6.7308\approx6.73\text{ \%}\)Therefore, the percent increase in minimum wage is 6.73%
Thus, the correct answer is 6.73%
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 145 millimeters, and a standard deviation of 7 millimeters. If a random sample of 31 steel bolts is selected, what is the probability that the sample mean would be less than 141.5 millimeters? Round your answer to four decimal places.
Answers
Using a standard normal distribution table, we find that the probability is approximately 0.0134 (rounded to four decimal places).
What is probability?Probability is a measure of the likelihood or chance that a particular event or outcome will occur. It is expressed as a value between 0 and 1, where 0 represents an event that is impossible to occur, and 1 represents an event that is certain to occur.
According to question:To solve this problem, we can use the formula for the standard deviation of the sample mean:
Standard deviation of sample mean = standard deviation / √(sample size)
Plugging in the given values:
Standard deviation of sample mean = 7 / √(31)
Next, we can calculate the z-score, which is the number of standard deviations the sample mean is below the population mean:
z-score = (sample mean - population mean) / standard deviation of sample mean
Plugging in the given values:
z-score = (141.5 - 145) / (7 / √(31))
Using a calculator, we find that the z-score is approximately -2.22.
Finally, we can use a standard normal distribution table or a calculator to find the probability that a z-score is less than -2.22.
Using a standard normal distribution table, we find that the probability is approximately 0.0134 (rounded to four decimal places).
To know more about probability visit:
https://brainly.com/question/30034780
#SPJ1
One evening, a restaurant served a total of 1/2 of a loaf of wheat bread and 7/8 of a loaf of white bread. How many loaves were served in all?
Answers
Answer:
\(\dfrac{11}{8}\)
Step-by-step explanation:
A restaurant served a total of 1/2 of a loaf of wheat bread and 7/8 of a loaf of white bread.
We need to find how many loaves were served in all. It is equal to the sum of the fraction of 1/2 and 7/8.
Sum of these two fractions :
\(\dfrac{1}{2}+\dfrac{7}{8}\\\\=\dfrac{4+7}{8}\\\\=\dfrac{11}{8}\)
So, a total of 11/8 were served in all.
Condense each Logarithm
Answers
The equation of logarithm are solved and
a) A = 2 + 3 log x + 4 log b
b) B = ( 36 + x + y ) ( log 6 )
c) C = ( 1/2 )x log 5
d) D = ln ( x⁴ / y² )
Given data ,
Let the logarithmic equation be represented as A
Now , the value of A is
a)
A = 2 log 10 + 3 log x + 4 log b
The base of the logarithm is 10 , so
A = 2 + 3 log x + 4 log b
b)
B = log 6³⁶ + log 6ˣ - log 6^ ( y )
From the properties of logarithm , we get
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
B = 36 log 6 + x log 6 + y log 6
On taking the common term , we get
B = ( 36 + x + y ) ( log 6 )
c)
C = ( 1/2 )log 5ˣ
From the properties of logarithm , we get
C = ( 1/2 )x log 5
d)
D = 4 ln x - 2 ln y
From the properties of logarithm , we get
D = ln x⁴ - ln y²
On further simplification , we get
D = ln ( x⁴ / y² )
Hence , the logarithmic equations are solved
To learn more about logarithm click :
https://brainly.com/question/12049968
#SPJ1
True or False. If the statement is false, explain why. The factored form of 7x + 21 + xy + 3y is
7(x + 3) + y(x + 3).
А
True
B
False
Briefly explain your answer
Answers
7(x+3) + y(x+3)
Split the two up and multiply them separately.
7(x+3)
7x+21
y(x+3)
xy+3y
Then put them back together.
7x+21+xy+3y
A farmer sold 53.2 pounds of carrots and 29.4 pounds of green beans to a restaurant. How many pounds of these two vegetables did the restaurant buy? Explain your thinking. *
Answers
Answer:
just add up the 2 numbers pretty simple
Step-by-step explanation:
53.2 plus 29.4
Answer: 82.6 lb
Step-by-step explanation:
Since the restaurant is buying the pounds given from the farmer, add the pounds together.
Add
53.2 + 29.4 = 82.6
Hence, the restaurant bought 82.6 pounds of vegetables.
Determine the constant of proportionality for the graph.
Answers
The constant of proportionality is 5
Answer:
I think it's B
Step-by-step explanation:
There are 9 players on a youth baseball team. To create the lineup, the coach chooses three players to play pitcher, catcher, and first base. How many ways can the coach choose these three positions?
Answers
Step-by-step explanation:
how many ways can the coach make out the batting order? 9! = 9 · 8 · 7 · 6 · 5 ·4 · 3 · 2 · 1 = 362,880 .
what is 3 3/5 x (-8 1/3)?
Answers
Answer:
The answer is negative thirty
Answer:
The answer is -450/15 = -30
Step-by-step explanation:
3 3/5 and -8 1/3 are numbers in mixed fractions. For getting the answer, the numbers must be converted into improper fractions with the formula =
Quotient * Divisor + Remainder = Dividend
Therefore;
=> 3 3/5 = 3 * 5 + 3 = 18/5
=> -8 1/3 = -8 * 3 + 1 = -25/3
Now, we multiply the improper fractions.
=> 18/5 * (-25/3)
=> -450/15
=> -30 is the final answer
Hope this helps you!
For Christmas you want to get your parents a framed family picture. At the framing store, there are 4 different styles each available in 5 different colors. You decide to use a blue mat board and there are 3 different shades of blue to choose from. How many different frames can you create?
Answers
The number of different frames you can create, if There are 4 different styles, each available in 5 different colors, there are 3 different shades of blue to choose from, is 12.
What is the combination?A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.
Given:
There are 4 different styles, each available in 5 different colors, there are 3 different shades of blue to choose from,
Calculate the total number of frames, we can create as shown below,
The number of frames = different styles available for blue color × shades of blue
The number of frames = 4 × 3
The number of frames = 12
Thus, the number of frames you can create is 12.
To know more about the combination:
https://brainly.com/question/29594894
#SPJ1
20 = 2(n – 3) solve.
Answers
explanation:
20 = 2(n - 3)
•first distribute
2xn= 2n
2x-3= -10
20 = 2n - 10
•add 10 to both sides (since the sign is negative do the opposite.)
30 = 2n
•divide both sides by 2.
Answer: 15
Marie made the box plot below to display a set of data. Which set of data could the box plot represent?
Answers
Answer:
see below
Step-by-step explanation:
First of all, you want to find the data set the matches the extreme values of 5 and 35. That eliminates the 2nd and 4th choices.
Then you want to find the data set that has a median of 15. The first data set has a middle value (median) of 20, so that choice is eliminated.
The data set of the 3rd choice matches the box plot extremes, median, and quartile values.
Answer:
The third choice, (5, 6, 10, 12, 13, 15, 17, 25, 30, 35) would be your best answer.
Step-by-step explanation:
The sum of three numbers is 89 the second number is 3 times the third the first number is 9 more than the third what are the numbers
Answers
According to the given data we have the following:
sum of three numbers=89
second number=3 times the third, so second number=3x
let the third number be equal x
first number=9 more than the third, so first number=x + 9
So, if sum of three numbers=89, then:
x+9 + 3x +x=89
5x=89-9
5x=80
x=80/5
x=16
So, if x=16, then, first number=x + 9=16+9=25
second number=3(16)=48
third number=16
What are equivalent expressions for
3 (y + 1) + 4 + 3y
Answers
Answer:2yu
Step-by-step explanation:if you see this hi
14x7y + 2xy + y2 + 7x
Answers
Answer:
21x+9y+2xy or 2xy+21x+9y
A swimming pool is open for 7 1/2hours during a day. The pool keeps one lifeguard on
duty at a time, and each lifeguard's shift is 2 1/2hours long. How many shifts are there
per day?
7 shifts
5 shifts
3 shifts
4 shifts
Answers
Answer:
3 shifts a day
Step-by-step explanation:
7 1/2 hours = 7.5 2 1/2 hours = 2.5
7.5 divided by 2.5 = 3
Answer:
3 shift
Step-by-step explanation:
7 1/2 / 2 1/2
(15/2) / (5/2)
keep, change, flip
(15/2) x (2/5)
30/10 = 3 shifts
what is the value of the expression shown below
2 3/5 - 1 3/5
^ ^
TWO THREE-FIFTHS MINUS ONE THREE-FIFTHS
THE NUMBERS ARE MIXED FRACTIONS
Answers
Answer:
1
Step-by-step explanation:
1. One way to do this is converting both into improper fractions. To do this, multiply the whole number by the denominator and add that to the numerator.
2 3/5 --> 2*5 is 10 --> 10+3 is 13. --> 13/5
2. This leaves us with 13/5 - 8/5
3. Subtract the numerators
13/5 - 8/5 = 5/5
4. Simplify. If the numerator is the same number as the denominator, it's a whole number.
5/5 = 1
Factor of 14a–35? Pls Ty
Answers
1 ÷ 8, or 1/8, is 0.125
Answers
Answer:
both
Step-by-step explanation:
Answer:
true! :)
Step-by-step explanation:
Please ANSWER!!!!!!!
Answers
Answer:
See explanation
Step-by-step explanation:
It appears that the second graph is better since it seems to be rather consistent. The graph of the first one seems out of place. Therefore it seems to be confusing and could be misleading.