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
Dale buys candy that costs $8 per pound. He will buy at least 7 pounds of candy. What are the possible amounts he will spend
on candy?
Use c for the amount (in dollars) Dale will spend on candy,
Write your answer as an inequality solved for c.
Answers
Answer:
66
Step-by-step explanation:
The line plots shows the weights of 9 grapefruits. What is the difference in the total weight of all the 1 1/2 lb grapefruits and the total weight of all the 1 1/4 lb grapefruits? A 1/4lb B 2 lb C 4 1/2lb D 7 lb
Answers
Answer:
The difference of weight is [tex]2[/tex] pounds.
Step-by-step explanation:
Given: The line plots shows the weights of [tex]9[/tex] grapefruits
To find: The difference in the total weight of all the [tex]1\frac{1}{2} lb[/tex] grapefruits and the total weight of all the [tex]1 \frac{1}{4}lb[/tex] grapefruits.
Firstly, we need to convert the given mixed fractions as following:
[tex]1\frac{1}{2} lb=\frac{2+1}{2}=\frac{3}{2}lb[/tex]
[tex]1\frac{1}{4} lb=\frac{4+1}{4}=\frac{5}{4}lb[/tex]
Now, we know that,
Point diagrams divide a sample into different classes, and allow to observe the frequencies of each class.
In this case, the different weights of the grapefruit constitute the classes. From a sample of 10 grapefruit, some will weigh others weigh.
We need to observe the dot diagram to know how many grapefruit we have of weight [tex]\frac{3}{2} lb[/tex] and how many grapefruit we have of weight [tex]\frac{5}{4} lb[/tex]. In other words, we need to know, in the diagram, how many points there are about class of [tex]\frac{3}{2} lb[/tex] and how many points there are about class of [tex]\frac{5}{4} lb[/tex].
Then, the total difference between all grapefruit of pounds and all grapefruit of pounds is calculated as follows:
[tex]x (1\frac{1}{2} ) - y (1\frac{1}{4} ) = Z[/tex]
Where
[tex]Z[/tex]: Weight difference
[tex]x[/tex]: Quantity of [tex]1\frac{1}{2} lb[/tex] grapefruit
[tex]y[/tex]: Quantity of [tex]1\frac{1}{4}lb[/tex] grapefruit
Suppose that of the [tex]10[/tex] total grapefruits, [tex]3[/tex] of them weigh [tex]1\frac{1}{2} lb[/tex] and [tex]2[/tex] of them weigh [tex]1 \frac{1}{4}[/tex] pounds. This is: [tex]x=3[/tex] and [tex]y=2[/tex]
Now,
[tex]3(\frac{3}{2} )-2(\frac{5}{4} )[/tex]
[tex]=\frac{9}{2} -\frac{5}{2}[/tex]
[tex]=\frac{4}{2}[/tex]
[tex]=2[/tex]
Hence, for this case, the difference of weight is [tex]2[/tex] pounds.
What is the value of y in the solution to the following system of equations?
2x + y = -4
5x + 3y = -6
Answers
y= -32
Step-by-step explanation:
step 1: from the first equation you will make X the subject of formula, the equation then becomes;
X= 4-y
2
step 2: substitute X in the second equation, the equation then becomes 5 * [4-y] + 3y = -6
[ 2]
step 3: find the LCM and then cross multiply; 20-5y+6y = -6
2
20+y = -12
y= -12-20
y= -32
Which ordered pair is a solution of the equation?
(I will mark you brainliest if correct)
Answers
Answer:
Step-by-step explanation:
d
Find a.
Round to the nearest tenth:
2 cm
с
150
1050
a =
= [? ]cm
Answers
Answer:
a = 1.8 cm
Step-by-step explanation:
Here. we want to find the value of a
To do this, we are going to use the sine rule
it states that the ratio of a side and the sine of the angle that faces the side is a constant for all the sides of a triangle
From the diagram, we have that;
The angle facing a is;
180-15-105 = 60
So, we have that
a/sin 60 = 2/sin 105
a = 2sin 60/sin 105
a = 1.794 cm
Simplify the problem in the picture
Answers
Answer:
[tex]\frac{n^{10} }{27m^{5} }[/tex]
Step-by-step explanation:
2) 2.25 is 62.5% of what number?
Answers
Answer:
250
Step-by-step explanation:
250 ÷ 400 = 0.625 = 0.625 × 100/100 = (0.625 × 100)/100 = 62.5/100 = 62.5% Answer: Percentage of 62.5% of what number = 250?
The required number whose 62.5% is 2.25 is given as 3.6.
Given that,
To determine the number whose 62.5% is 2.25.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Given that,
Let the number be x,
According to the condition,
62.5% of x = 2.25
0.625x = 2.25
x = 2.25/0.625
x = 3.6
Thus, the required number whose 62.5% is 2.25 is given as 3.6.
Learn more about simplification here:
https://brainly.com/question/1369388
#SPJ2
20 points. A triangle has an exterior angle with a measure of 120°. Can you determine the measures of the interior angles?
The answer is no, I just need an explanation why, thank you :)
Answers
Answer:
Step-by-step explanation:
it is no because there is only 1 angel that u have
two lines that are tangent to p
Answers
Answer:
QR
SR
Step-by-step explanation:
QR and SR are tangent to the circle with center P
PLZ HELP ME
6÷2(1+2)=?????
Answers
9
6/2x3
3x3
9
Hope I helped
What decimal is equivalent to 4/15
Answers
Answer:
0.2667 is the decimal for this
Answer:
0.2bar6
Step-by-step explanation:
The decimal form of 4/15 is 0.2bar6. Divide the numerator by the denominator. 4/15= 0.2666...= 0.2bar(6) In the United States, the repeating decimal is represented with a bar above the repeating decimal.
What is -7x3 =
Need answers asap!
Answers
Answer:
it is -21
Step-by-step explanation:
make it braintliest please
Answer:
-7×3 = -21Step-by-step explanation:
I hope it helps ❤❤What mistake did Brianna make? On Line 1, Brianna should have subtracted 3 instead of adding -3. On Line 1, Brianna violated the addition property of equality. On Line 3, Brianna should have divided by 0.1 instead of subtracting 0.1. On Line 3, Brianna violated the addition property of equality.
Answers
Question:
Brianna solved a two-step equation, but she made a mistake along the way.
[tex]0.1x + 3 = 1.7[/tex]
Line 1 : [tex](-3) + 0.1x + 3 = 1.7 + (-3)[/tex]
Line 2 : [tex]0.1x = -1.3[/tex]
Line 3 : [tex](-0.1) + 0.1x = -1.3 + (-0.1)[/tex]
Line 4: [tex]x = -1.4[/tex]
Answer:
On Line 3, Brianna should have divided by 0.1 instead of subtracting 0.1.
Step-by-step explanation:
Required
Where did she make a mistake?
To do this, we simply analyse her workings one step at a time
Equation: [tex]0.1x + 3 = 1.7[/tex]
Line 1 : [tex](-3) + 0.1x + 3 = 1.7 + (-3)[/tex]
This is correct because she subtracted 0.3 from both sides
Line 2 : [tex]0.1x = -1.3[/tex]
This is also correct because she performed the arithmetic correctly
Line 3 : [tex](-0.1) + 0.1x = -1.3 + (-0.1)[/tex]
This is incorrect.
Division by 0.1 is expected not subtraction
Answer:
It's C
Step-by-step explanation:
a factory can make 2,402 baseballs in 1 hour how many baseballs can the factory make in 5 hours
Answers
Answer:
The factory can make 12,010 baseballs in 5 hours.
Step-by-step explanation:
We have to multiply 2,402 * 5 to find the answer.
5 * 2,402 = 12,010
Hope this helps!
Please mark as brainliest.
x=basketball in 5 hours
2,402=1 hours
which means x=5 hours
Multiply the terms:
2,402x5=12010
x=12010
Hiya! I need help please! Thanks I really appreciate it!
(2 screenshots included)
Answers
Answer:
8. the line the vertical
9. y=3/4x-10
Step-by-step explanation:
For number nine, you must find b with the information given if you were to use slope intercept form.
4= 3/4(-8)+b
4= -6+b
-10=6
Now, just plug this number back into the equation.
y= 3/4x-10
Hector took out a small loan of $900 for 18 months (remember to turn this into
years). The simple interest rate on the loan was 10.5%. How much will he pay in
interest on the loan?
Answers
Answer:
$141.75
Step-by-step explanation:
(900)(-105) (13/12) or 1.5
HELp please!!!!!!!!!!!!!!!!!!!!!!11
Answers
Answer:
it’s 15x+30y-220
Step-by-step explanation:
Because you distribute and then you add the like terms
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
Make a 4-by-4 logic grid on your own paper. Use it to help solve the logic
puzzle and answer the question.
Kim, Maia, Nia, and Shelley play left wing, center, right wing, and defense on
the hockey team, though not necessarily in that order.
When Kim gets the puck, she usually passes it to the left wing or the right
wing.
Nia and Shelley are too small to play defense.
Maia and Shelley both shoot from the left, so the coach wont let them play
right wing.
The defense player and Kim are best friends.
Who plays left wing?
O A. Shelley
O B. Kim
OC. Nia
OD. Maia
Answers
Answer:
Shelly
Step-by-step explanation:
The price per night of a hotel room is $ 250.00 plus $15 per person staying in the room. Which function rule would be used to determine the price of a hotel room, p (x) given the number of people, x, staying in the room.
Answers
The equation is 250+15x is that's what your asking
What is the following quotient?
Answers
2
3
√
3
−
3
√
18 is the answer
Answer: A edge 2021
Step-by-step explanation:
i neeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhheeeeeeeeeeeeeeeeeeeeelllllllllllllllllppppppppppp
If 3x−y=12, what is the value of 8x/2y?
A) 212
B) 44
C) 82
D) The value cannot be determined from the information given.
Answers
Answer:
3x-12=y
which equals to
1/y=1/(3x-12)
Now,multiply both sides by x
x/y=x/(3x-12)
8x/2y=4x/y=4x/(3x-12)
Step-by-step explanation:
''.''
Find the equation of the line
that passes through the points
(4, 7) and (-2, 6)
Answers
y
=
1
6
x
+
19
3
←
equation in slope-intercept form
Step-by-step explanation:
Answer:
y = -x/6 + 19/3
Step-by-step explanation:
[tex](y - 7)( - 2 - 4) = (x - 4)(6 - 7) \\ - 6y + 42 = 4 - x \\ x - 6y = - 38 \\ or \\ y = (38 - x) \div 6[/tex]
PLEASE HELP FAST!! ❤️
for 15 points
Answers
Answer:
2/3?
Step-by-step explanation:
I'm not sure
The current temperature is 30°C. Over the next eight hours the temperature decreases and then increases, returning back to 30°C. if the temperature initially decrease by 13°C, how much did it subsequently increase?
Answers
Answer:
13°C
Step-by-step explanation:
The number of hours that the temperature fluctuates is irrelevant to the problem.
This problem is asking how many degrees did the temperature increase in order to go back to 30°C after being decreased by 13°C.
Find the new temperature after it decreased:
30°C - 13°C = 17°CIf the temperature after decreasing is 17°C, it needs the same amount it was decreased by to go back to 30°C.
Therefore, the temperature subsequently increased by 13°C to go back to 30°C after being decreased by 13°C.
which is the correct graph for the equation?
Answers
Answer:
From the given graph, we can easily determine that graph A contains the y-intercept b = 3.
Thus, option A is the correct option.
The graph of the equation is also attached below.
Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
m is the slopeb is the y-interceptGiven the function
2x+5y=15
converting the equation into the slope-intercept form
5y = -2x + 15
divide both sides by 5
y = -2/5x + 3
Thus,
The slope of the line is: m = -2/5
The y-intercept of the line: b = 3
In other words, the ordered pair (0, 3) represents the y-intercept.
From the given graph, we can easily determine that graph A contains the y-intercept b = 3.
Thus, option A is the correct option.
The graph of the equation is also attached below.
Thissss answerrrrrrrrrrrrrrrrrrr
Answers
Pleaseeeee help asap anyone
Answers
Answer:
73
Step-by-step explanation:
17+90+C=180 since it is a straight angle and yeah.
17+90=107+c=180
180-107=73
Help plz I’m giving a lot of points
And no nonsense answers plz
Answers
Answer:
it is a positive number because she was rising if she had been going down then the number would have become negative.
Step-by-step explanation:
however, if she was going down the number would become negative.
What are the solutions to 7x^2 + 10x -3 = x^2 + 3x?
Answers
Answer:
x=(1)/(3),-(3)/(2)
Step-by-step explanation:
Answer:
(- 3/2, 1/3)
Step-by-step explanation:
7x^2+10x-3=x^2+3x
7x^2+10x-3-x^2-3x=0
6x^2+7x-3=0
6x^2+9x-2x-3=0
3x x (2x+3)-(2x+3)=0
(2x+3)x(3x-1)=0
2x+3=0
3x-1=0
x1=- 3/2
x2= 1/3
