Answers
9514 1404 393
Answer:
∠E = ∠A = 34°; ∠AFB = ∠DFE = 107°-34° = 73°
Step-by-step explanation:
Here's where I'd go next.
73° (∠EDA) is exterior to ΔDAC, so is the sum of remote interior angles A and C. That is, ...
∠C + ∠A = 73°
∠C = 73° -∠A = 73° -39° = 34°
Triangle CBE is given as isosceles, so its base angles C and E are congruent, both 34°.
Exterior angle CDF is the sum of remote interior angles DEF and DFE, so we have ...
107° = 34° +∠DFE
∠DFE = 107° -34° = 73°
The angle we just found (∠DFE) is a vertical angle with ∠AFB, so has the same measure.
∠AFB = 73° . . . . vertical angle with ∠DFE
_____
In summary, it looks like we have added some steps to the derivation:
4. ∠A = 34° . . . . exterior angle theorem (∠A +39° = 73°)
5. ∠E = ∠A = 34° . . . . definition of isosceles triangle
6. ∠DFE = 73° . . . . exterior angle theorem (∠E +34° = 107°)
7. ∠AFB = 73° . . . . vertical angles
_____
Additional comment
Any sort of math problem solving has you work from what you know to what you need to know by making use of previously learned relationships between the bits of information you have. Here, you really only need to know (a) angles of a linear pair total 180°; (b) angles in a triangle total 180°; (c) angles opposite congruent sides in a triangle are congruent. Everything we claim above can be concluded using these facts. The various theorems we used are simply shortcuts that allow you to bypass intermediate steps in the problem-solving process.
Related Questions
Sarah has a loyalty card good for a 20% discount at her local grocery store. What would her total in dollars and cents be, after the discount and before tax, if the total cost of all the items she wants to buy is $39.25?
Answers
Evaluate the following expression 10+ 54/-6
Answers
The answer would just be 1
Hey there!
The answer to your question is [tex]1[/tex].
Let us start by dividing:
[tex]\frac{54}{-6} = -9[/tex]
Now, we do [tex]10 + -9[/tex], which is [tex]1[/tex].
Hope it helps and have a terrific day!!!
Find the sum of the interior angle measures of a convex 15-gon (a fifteen-sided polygon).
Answers
Answer:
2340 degrees.
Step-by-step explanation:
The sum of the interior angle measures of any polygon can be calculated using the following expression ([tex]n[/tex] is the number of sides the polygon has):
[tex]180(n-2)[/tex]
For a 15-sided polygon, plug in 15 for n and simplify:
[tex]180(15-2)=180(13)[/tex]
Multiply to solve:
[tex]180(13)=2340[/tex]
For a 15-sided polygon, the sum of the interior angles must be 2340 degrees. You can go a step further and divide 2340 by 15 to figure out the individual measure of each interior angle (156 degrees).
The sum of the interior angles of a fifteen-sided polygon is 2340°.
What is the formula for interior angle of a regular polygon?The formula for calculating the sum of interior angles is (n-2)×180° where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.
Given that, a fifteen-sided polygon.
Now, the sum of the interior angle measures is
(15-2)×180°
= 13×180°
= 2340°
Therefore, the sum of the interior angle measures is 2340°.
Learn more about the sum of interior angles here:
https://brainly.com/question/28793979.
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There were 45 runners to start a race. In the first half of the race 2/3 of them dropped out. In the second half 2/5 of the remaining runners dropped out. How many runners finished the race?
Answers
Answer:
18 racers finished.
Step-by-step explanation:
In the first half, 30 racers dropped out, because 2/3 of 45 is 30. In the 2nd half, 12 racers dropped out, because that is 2/5 of 30. So, in the end, 18 racers finished. (I might have done this wrong i did my best)
A rectangle has a perimeter of 30cm the width of the rectangle is n cm the length of the rectangle is n+6cm
What’s the value of n
Answers
Step-by-step explanation:
p=2(l+w)
30cm=2(n+6+n)
30cm\2=2n+6
15cm-6=2n
9cm=2n
n=4.5cm or w=4.5cm
l=w+6
l=4.5cm+6
l=10.5cm
Please help me 123 or 4........
Answers
Answer:
It's 2
Step-by-step explanation:
Hope this helps
Car A has an initial value of 30,000 and depreciates at a rate of 20% per year. Car B has an initial value of 20,000 and depreciates at a rate of 15% per year.Car B will become greater than the value of car A during the ninth,seventh,third, or fifth year
Answers
Answer:
The value of Car B will become greater than the value of car A during the fifth year.
Step-by-step explanation:
Note: See the attached excel file for calculation of beginning and ending values of Cars A and B.
In the attached excel file, the following are used:
Annual Depreciation expense of Car A = Initial value of Car A * Depreciates rate of Car A = 30,000 * 20% = 6,000
Annual Depreciation expense of Car B from Year 1 to Year 6 = Initial value of Car B * Depreciates rate of Car B = 20,000 * 15% = 3,000
Annual Depreciation expense of Car B in Year 7 = Beginning value of Car B in Year 7 = 2,000
Conclusion
Since the 8,000 Beginning value of Car B in Year 5 is greater than the 6,000 Beginning value of Car A in Year 5, it therefore implies that the value Car B becomes greater than the value of car A during the fifth year.
It’s the 7th year
Plato
Solve the system of linear equations by substitution
y-x=0
2x-5y=9
Answers
Answer:
the answer is (-3,-3)
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
1. 5(2x + 1) = 35
I need help what’s the answer showed work
Answers
Answer:
x=3
Step-by-step explanation:
5(2x+1)=35
Step 1: Simplify both sides of the equation.
5(2x+1)=35
(5)(2x)+(5)(1)=35(Distribute)
10x+5=35
Step 2: Subtract 5 from both sides.
10x+5−5=35−5
10x=30
Step 3: Divide both sides by 10.
x=3
A tree has a shadow length of approximately 9 feet. The distance from the tip of the tree to the tip of the shadow is bout 15 feet. How tall is the tree?
Please help!!!!!
Answers
so a^2 + b^2 = c^2
c^2 is the hypotenuse and the 15 feet
a^2 + 9^2 = 15^2
a^2 + 81 = 225
a^2 = 144
the square root of 144 is 12
the tree is 12 feet tall
Answer:
12
Step-by-step explanation:
if you draw the picture in your copybook you will see that there is a right triangle, we have the Pythagorean theorem i.e c=√a²+b²
15=√9²+x². the trees tall=X
15²=9²+x²
x²= 144
X= 12
hope you will understand
James earns $8.15 per hour that he works. Which algebraic equation shows the
amount of money. E, that James earns in n hours?
Answers
Answer:
e = $8.15n
Although this doesn't require an explanation, I am always open to solve any confusion.
Side Note: I used variable E assuming that the period before 'E' was supposed to be a comma which means it was a given variable.
Answer:
E= 8.15n
Step-by-step explanation:
Work out the area of a rectangle with base,
b
= 15mm and height,
h
= 12mm
Answers
Answer:
15x12=180mm
Step-by-step explanation:
A teacher has 396 pieces of candy. If there are 44 students, 6 of whom are boys, if divided evenly, how many pieces of candy will each student get?
Answers
Answer:
9 pieces of candy.
Step-by-step explanation:
The information about how many boys there are is irrelevant, so we can just ignore that.
The important information is that the teacher has 396 pieces of candy and that it is split between 44 students equally.
So, to solve, we just do 396 / 44 = 9.
Therefore, each student will get 9 pieces of candy.
Question Below please help
Answers
Choose the correct scientific notation of this number.
There are 5,280 feet in one mile.
Answers
Answer:
It's C
Step-by-step explanation:
Write an equation of a line in slope-intercept form with the given slope and y-intercept. slope: 2/3, y-intercept: −5
Answers
. Evaluate 8^0 helppp please
Answers
Answer:
1
Step-by-step explanation:
[tex] {8}^{0} = 1 \\ [/tex]
Any number raised to zero is always equal to one.
On a coordinate plane, a line goes through points (negative 4, 0) and (0, 2).
What Is the slope of the line on the graph?
Answers
Answer:
the slope is 1/2
Step-by-step explanation:
find the change in y over the change in x
2-0/0+4
you get 2/4 then simply that to 1/2
Answer:
0.5
Step-by-step explanation:
on edg
hii please please help i’ll give brainliest if you give a correct answer tyyyyy
Answers
Tommy's auto mall needs to transport 108 cars. A moving truck can fit 7 cars on each bed. How many trucks does tommy need to relocate all his car? (Do it in long division)
Answers
7|108
-7
-60
- 35
-95
Answer: 15 remainder 3.
Step-by-step explanation:
Mike recorded the number of hours he slept each night for a period of 5 days as shown in the table below.
Based on the information in the table, what was the total number of hours that Mike slept from Monday through Friday?
Answers
Step-by-step explanation:
8+9= 17
7 3/4 + 7 1/4= 15
15 + 5 1/2= 20 1/2
17 + 20 1/2 = 37 1/2
I have a math question
Answers
Answer:
D. RS = DQ
Step-by-step explanation:
SSS = Side-side-side congruence criteria!
One is given, other is common, and we have RS=DQ
Answer/Step-by-step explanation:
According to the Side Side Side rule (SSS) Side RQ is congruent to side DS.
RQ ≅ DS.
This means that in order to complete the chart:
RS ≅ DQ
A recent poll found that 76% of a random sample of 100 American movie goers thought the popcorn sold at the movie theatre was overpriced.
If the sample size was increased to 10,000 American movie-goers, what effect would this have on the estimated percentage of American movie-goers who
think the popcorn is overpriced?
Answers
Answer:
Step-by-step explanation:
Given that:
percentage of sample proportion = 76%
sample size = 100
Given that the sample proportion estimate is unbaised of the population proportion, then the percentage of all American movie-goers who think popcorn is overpriced is = 76%. Also, the mean of the sampling distribution appears to be independent of the sample size. Then, the estimate of the percentage will equally remain the same regardless it is even a sample of size 10000.
Item 2 What is the value of the function at x=−2? y=−4 y = 0 y = 2 y = 3
Answer fast please!!!
Answers
Answer:
ok
Step-by-step explanation:
38=p−15
PLEASE HELP MEHHHHH
Answers
Answer:
p=23
Step-by-step explanation:
Answer:
P=23
Step-by-step explanation:
38-15=23
p=23
Hope this helps
Have a great day!
A suitcase measures 21 inches by 16 inches. What is the length of the diagonal of the suitcase to the nearest tenth of an inch?
Answers
Answer:
Step-by-step explanation:
we have a rectangle that measure 21 inches by 16 inches
to find the rectangle(which is the hypotenuse) we will use Pythagorean theorem
c^=a^2+b^2
c^=21^2+16^2=697
c=[tex]\sqrt697}[/tex] =26.40 which rounded to the nearest tenth =26
The system shown is blank.
a.) inconsistent
b.) equivalent
c.) consistent
Answers
Answer:
I think it's consistent
Step-by-step explanation:
Can u help me please
Answers
I'll help
The sum of the prices for the items(That's 2large baskets and small gift baskets) for the first customer is $57. So assuming the price of a large basket is x and small basket is y, then an expression for the first sentence is;
2x + 5y= 57
The sum of the prices for the second customer is $6 less than the first customer ( that's 57-6 which is $51). Since he bought 1 large basket and 10 small baskets and the price of each large basket is the same and the price of each small basket is the same they assume the same variable of x and y. So the expression of the second sentence is;
x+10y=51.
So the expressions will be;
2x+5y=57
x+10y=51
That's Option C
Find the slope of the line through (9, 4) and (0, 5).
Answers
Answer:
It's just y2-y1 over x2-x1
Step-by-step explanation:
so pick a coordinate and make it 1 and make the other one 2 and put in the numbers.
The slope of the line will be m = -1/9.
What is the general equation of a Straight line?The general equation of a straight line is -y = mx + c
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis
Other possible equations of line are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}We have a line through (9, 4) and (0, 5).
The slope of the line will be -
[m] = (4 - 5)/(9 - 0)
[m] = - 1/9
Therefore, the slope of the line will be m = -1/9.
To solve more questions on straight line, visit the link below-
brainly.com/question/20400984
#SPJ2
A nonstop flight from Albuquerque, NM to Atlanta, GA takes 3 hours. If the plane flies a total of 1,269 miles, what is the plane’s unit rate in miles per hour?
A. 3,807 mph
B. 1,266 mph
C. 432 mph
D. 423 mph
Answers
Answer:
423 mph
Step-by-step explanation:
To find the answer, you have to divide 1,269 by 3 since we want to find how many miles the plane travels in one hour. Doing this, we end up with 423 which is the answer.
Step-by-step explanation:
A nonstop flight from Albuquerque, NM to Atlanta, GA takes 3 hours. If the plane flies a total of 1,269 miles, what is the plane’s unit rate in miles per hour?
1,269 % 3 = 423
ITS RIGHT