Step-by-step explanation:
Let a, b, c be the measures of the interior angles and x, y, z be the measures of the exterior angles of the triangle. Where x and adjacent to a, y is adjacent to b and z is adjacent to c.
By interior angle sum postulate of a triangle:
a + b + c = 180°... (1)
Therefore, by remote interior angle theorem:
x = b + c.... (2)
y = a + c..... (3)
z = a + b.... (4)
Adding equations (2), (3) & (4)
x + y + z = b + c + a + c + a + b
x + y + z = 2a + 2b + 2c
x + y + z = 2(a + b + c)... (5)
From equations (1) & (5)
[tex]x + y + z = 2 \times 180 \degree \\ x + y + z = 360 \degree \\ x + y + z = 4 \times 90\degree \\ x + y + z = 4 \: right \: angles[/tex]
Thus, the sum of exterior angles so formed is equal to four right angles.
Proved.
What symbol u use with this?
Answer:
18-14=4
4 more sandwiches.
0.2(10−5c)=5c− 16 pls help
Answer:
c=3
Step-by-step explanation:
Sara buys 1 pair of jeans for $20 and 5 shirts .The total of her purchase was $55.Witch equation models the scenario? a)1+5=20x b)20+5x=55 c)20-5x=55 d)1x+5=55
Answer:
the answer is b)20+5x=55
The length of a rectangle is four times its width. If the perimeter of the rectangle is 60 yd, find its area.
Answer:
23
Step-by-step explanation:
thgric7cuf j u gif dude jfcrcifcru u fug tu
What’s the sum of 45 and ^
Answer:
45+π ≈ 48.1415926536
Step-by-step explanation:
Maybe you want the sum of 45 and pi:
45+π ≈ 48.1415926536
The sum is irrational, so cannot be expressed exactly, except in the form 45+π.
A student has some $1 and $5 bills in his wallet. He has a total of 19 bills and that are worth $55. how many of each type of bill does he have
Answer:
y= 9 ( 5 dollars bill)
x=10 ( one dollar bill)
Step-by-step explanation:
let x be the one dollar bill and y the 5 dollar bill
x+y=19 ⇒ x=19-y
x+5y=55 ( solve by substitute x=19-y)
19-y+5y=55
4y=55-19
4y=36 ⇒ y=36/4
y= 9 ( 5 dollars bill)
x+y=19
x+9=19
x=19-9
x=10 ( one dollar bill)
check :
x+5y=55
10+5(9)=
10+45 = 55 dollars
Si para una receta de flan para 3 porciones se nesecita un cuarto de litro de leche . ¿ cuanta leche se nesitaria para preparar la receta para 9 personas ?
Answer:
Para preparar la receta de flan para 9 personas se necesita [tex]\frac{3}{4}[/tex] L de leche
Step-by-step explanation:
La regla de tres simple directa se utiliza cuando el problema trata de dos magnitudes directamente proporcionales, es decir, magnitudes que si al multiplicar o dividir una de ellas por un número, la otra queda multiplicada o dividida por ese número. Es decir, cuando una magnitud aumenta la otra también lo hace en la misma proporción, y si la magnitud disminuye la otra disminuirá de igual forma.
Conociendo 3 valores “a”, “b” y “c” y teniendo un valor incógnita que deseamos conocer, la regla de tres simple directa se aplica de la siguiente forma:
a ⇒ b
c ⇒ x
Entonces : [tex]x=\frac{c*b}{a}[/tex]
En este caso se aplica de la siguiente manera: considerando que cada persona recibe una porción, si para preparar la receta para 3 personas se necesita [tex]\frac{1}{4}[/tex] de litros de leche, para preparar la receta para 9 personas cuánta leche se necesita?
3 personas ⇒ [tex]\frac{1}{4}[/tex] L
9 personas ⇒ x
[tex]x=\frac{9 personas*\frac{1}{4} L}{3 personas}[/tex]
x= [tex]\frac{3}{4}[/tex] L
Para preparar la receta de flan para 9 personas se necesita [tex]\frac{3}{4}[/tex] L de leche
I _______ the test when I remembered the correct answer. A. completes B. completing C. had completed D. will complete
Answer:
D
Step-by-step explanation:
Hope this help u
Answer:
c
Step-by-step explanation:
I HAD COMPLETED the test when I REMEMBERED the correct answer.
(remembered is a past tense. Therefore it's more appropriate to use "had completed")
Consider a triangle with vertices at S(-2, -3), A(2, 3), and N(5, -4). Find the length of each side rounding your answer to the nearest tenth and then determine which is the shortest.
The length of side SA is: type your answer...
The length of side AN is: type your answer...
and the length of side NS is: type your answer...
Therefore the shortest side is: type your answer...
CLASS ENDS IN ONE HOUR HELP
We can use the distance formula to solve: √(x2-x1)²+(y2-y1)²
Side SA:
√(2-(-2))²+(3-(-3))²
√4² + 6²
√16 + 36
√52
≈ 7.21
Side AN:
√(5-2)²+(-4-3)²
√3² + -7²
√9 + 49
√58
≈ 7.62
Side NS:
√(-2-5)²+(-3-(-4))²
√-7² + 1²
√49 + 1
√50
≈ 7.07
Therefore, the shortest side is "NS"
Best of Luck!
What's the difference between 9 times a number and 4 in an algebraic expression.
Answer:
9*4 or 9 into 4
Step-by-step explanation:
An airport offers 2 shuttles that run on different schedules. If both shuttles leave the airport at 4.00 pm at what time will they leave the airport together
Answer:
4:18 pm
Step-by-step explanation:
An airport offers 2 shuttles that run on different schedules.If both shuttles leave the airport at 4:00 p.m.,at what time will they next leave theairport together.
Shuttle A leaves every 6 minutes
Shuttle B leaves every 9 minutes
Solution
To solve for when next both shuttles will leave the airport together, find the least common multiples of 6 minutes and 9 minutes
Shuttle A (every 6 minutes) = 6, 12, 18, 24
Shuttle B (every 9 minutes) = 9, 18, 27, 36
The least common multiples of 6 minutes and 9 minutes is 18 minutes
4:00 pm + 18 minutes
= 4:18 pm
The next time both shuttles will leave theairport together is 4:18 pm of the same day
Sam has 106 dollars. And his friend Max has 10 times as many dollars as Sam does. How much does Max have?
Rachel has 24 red candies and Maya has 18 green candies. They want to arrange the candies in such a way that each row contains equal number of candies and also each row should have only red candies or green candies. What is the greatest number of candies that can be arranged in each row?
Answer: 6 candies per row.
Step-by-step explanation:
The restrictions that we have are:
Each row has the same number of candies.
Each row has only one color of candy.
We want to find the largest possible rows.
We have 18 green candies and 24 red candies.
Now, to arrange them in rows of equal numbers, we should find a common factor between 18 and 24. (particularly, we want to find the largest common factor between 18 and 24).
Now, to find common factors we first take the smaller number, and we divide it by different numbers, starting by 2 (we want to divide by small numbers, so the result will be the largest factor)
18/2 = 9.
Now to see if 9 is also a factor of 24, we see if the quotient between 24 and 9 is a whole number.
24/9 = 2.66
This is not a whole number, so 9 is not a common factor.
Now we divide by the next number, 3.
18/3 = 6.
24/6 = 4.
So 6 is a common factor of 18 and 24.
Then each row will have 6 candy.
And we will have:
18/6 = 3 rows of green candy.
24/ = 4 rows of red candy.
Rafiq compares the
expressions 4 X 8 and 8 X 12. He says that 8 is twice
as much as 4, so 4 X 8 must be twice as much as 8 X 12.
Correct his statement, and explain his error.
HELLLPPPPP
Answer:
Hey there!
Rafiq's error was that the other number is also changing. He had 4 x 8 and if he had 8 x 8, that would be twice as much, but he used 8 x 12 instead, and 12 is not 8.
Let me know if this helps :)
The other number that was also changing was Rafiq's mistake if Rafiq compares the expressions 4x8 and 8x12.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that are +, -, ×, and ÷.
It is given that:
Rafiq compares the expressions 4x8 and 8x12
The correct statement is for Rafiq compare the expressions 4 X 8 and 8 X 12
The fact that the other number was also changing was Rafiq's mistake.
Rafiq had 4 × 8, therefore 8 x 8 would have been twice as much; however, he utilized 8 x 12, even though 12 is not equal to 8.
Thus, the other number was also changing was Rafiq's mistake if Rafiq compares the expressions 4x8 and 8x12.
Learn more about the arithmetic operation here:
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Choose the value for x that solves this equation. 0 = -2x + 6
Answer:
x = 3
Step-by-step explanation:
Hi there !
0 = - 2x + 6
2x = 6
x = 6 : 2
x = 3
Good luck !
Tammy is recording the percentages she earned on each quiz in her math class. Here are her results for the last quizzes. 91, 86, 85, 74, 90, 87,86 Find the range of the data set. PLZ HELP
Answer:
The range is 17
Step-by-step explanation:
91-74 = 17
The range is the highest number subtracted by the lowest number
Answer:
17
Step-by-step explanation:
5. A shipping service uses the weight of a package to determine its postage.
The charge is $3 for the first pound and $2 for each additional pound up to
5 pounds. What are the domain and range of the function?
3,0 <1
5, 1<x<2
f(x) = 7,2 <x<3
9,3 < x < 4
11,4 < x < 5
You put in 3 to you piecewise function and 2 to your X value
PLEASE HELP I HAVE UNTIL TOMORROW
Answer:
The answer is A. 10b = c
Step-by-step explanation:
Well if it's $10 per book and the total cost is C. Then you would multiply the amount of books with the cost per book and have it equal the the total C.
The formula D =3/2 (100 – C) relates D,
the temperature measured on the Delisle
scale, in degrees, and C, the temperature
measured on the Celsius scale, also in
degrees. What is the temperature in
degrees Celsius when the temperature in
degrees Delisle is 78°?
BO
Answer:33
Step-by-step explanation:
3/2 —> 1.5
1.5(100-C) C is 78°
1.5(100-78)
1.5(22)
33
The temperature in degrees Celsius, if the function of the relationship is given as 78 = 3/2(100 - C), is calculated as: C = 48
What is Function?A function is a form of equation that relates one quantity that changes with another.
Given the formula for the function representing the relationship between D and C as, D = 3/2(100 - C), to find the temperature in degrees Celsius when the D = 78, substitute D = 78 into D = 3/2(100 - C).
78 = 3/2(100 - C)
(2)(78) = 3(100 - C)
156 = 3(100 - C)
156/3 = 100 - C
52 = 100 - C
52 - 100 = -C
-48 = -C
C = 48
Learn more about functions on:
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On side of a square measures 9 centimeters. Find the area of the square
Answer:
I think it is 81cm squared
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \: 81 \: {cm}^{2} }}}}}[/tex]
Step-by-step explanation:
Given , length of a square = 9 cm
We know that, all the sides of the square are same.
Finding the area of the square
[tex] \boxed{ \sf{area \: of \: a \: square = {l}^{2} }}[/tex]
[tex] \dashrightarrow{ \sf{ \: area \: of \: a \: square \: = \: {(9 \: cm)}^{2} }}[/tex]
[tex] \dashrightarrow{ \sf{area \: of \: a \: square \: = 9 \: cm \: \times \: 9 \: cm}}[/tex]
[tex] \dashrightarrow{ \sf{area \: of \: a \: square = 81 \: {cm}^{2} }}[/tex]
Hope I helped!
Best regards! :D
I
Is x= -2 a solution to:
a.
7X = -1
b. X* 14 = -28
Answer:
Step-by-step explanation:
-2 x 14 = -28
b is the answer
It's looking for the solved answer, not the simplified expression (no variable in final answer)
Answer:
BC = 144 units
Step-by-step explanation:
BC = BD + DC , substitute values
8x = 4x + 10 + 3x + 8 = 7x + 18 ( subtract 7x from both sides )
x = 18
Thus
BC = 8x = 8 × 18 = 144 units
Does (-6)2 have a value less than zero?
Answer:
yes it does, -6x2= -18
Step-by-step explanation:
The sum of 15 and a number is equal to 85. What is the number
Answer:
The sum of 15 and a number is
85 - 15 = 70
Diagnostic Test
3
What is the value of the expression below when x equals 6?
15 + 12x
A.
72
B.
33
21
D.
87
Answer:
87
Step-by-step explanation:
x=6
15+12(6)
15+72
87
A customer wants you to enlarge a photo to 2 3 4 234 its current height. The photo's current height is 3 1 4 314 inches. What should its enlarged height be, in inches? 6 6 3 16 6316 6 11 16 61116 7 8 15 16
Answer:
The question is not clearly stated, below is the clearly stated question and answer:
A customer wants you to enlarge a photo to 2 3/4 its current height. The photo’s current height is 3 1/4 inches. What should its enlarged height be, in inches?
Answer:
[tex]Enlarged\ height = 8\frac{15}{16}\ inches[/tex]
Step-by-step explanation:
[tex]current\ height\ =\ 3\frac{1}{4} = \frac{13}{4} \\ magnification\ factor = 2\frac{3}{4} = \frac{11}{4} \\Magnification (enlargement)\ =\ (magnification\ factor) \times (current\ height)\\Magnification\ =\ \frac{11}{4} \times \frac{13}{4}\\ Magnification\ =\ \frac{143}{16}[/tex]
Next, we will concert from the improper fraction to a mixed fraction:
when 143 is divided by 16, there will be 8 whole numbers and a remainder of 15, hence, the mixed fraction is:
[tex]\frac{143}{16} = 8\frac{15}{16}[/tex] (Alternatively, a scientific calculator can be used)
Therefore, enlarged height [tex]= 8\frac{15}{16}\ inches[/tex]
The value of a car is $22,000. It loses 13.9% of its value every year. Find the approximate monthly decrease in value. Round your answer to the nearest tenth.
Answer:
.200 because 22,000 % by 7 is 1540 which you divide by 10,000
Step-by-step explanation:
hope this helps
The approximate monthly decrease in value is $255.2
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100.
Given,
Value of the car = $22000
Loss percentage of value per year = 13.9%
Loss percentage of value per month =[tex]\frac{13.9}{12}[/tex] =1.16%
Decrease in value per month = [tex]22000(\frac{1.16}{100})[/tex]= $255.2
Hence, the approximate monthly decrease in value is $255.2
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Chocolate ganache is made from chocolate and cream in a3:2 ratio, respectively. If one batch of ganache requires 240 grams of chocolate, how many grams of cream is required?
Answer:
160 grams
Step-by-step explanation:
Since one batch of ganache needs 240 grams of chocolate, you divide 240 by 3, since the ratio is 3:2.
240÷3x= 80.
Now that you have x, multiply x by 2.
80*2= 160
Adrian creates some paintings every month. The numbers below show how many paintings Adrian has completed each month for the last year. What is the median of the set of data? 4, 5, 2, 1, 0, 3, 2, 4, 3, 2, 7, 5 *
Given :
Number of paintings Adrian created each month for the last year are :
4, 5, 2, 1, 0, 3, 2, 4, 3, 2, 7, 5 .
To Find :
The median of the set of data .
Solution :
To find the median we should arrange the numbers in ascending order .
So , 0, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 7 .
Now , median for odd is the middle term but for even numbers it is the average of middle two terms .
So ,
[tex]Median =\dfrac{3+3}{2}\\\\Median =3[/tex]
Therefore , the median of the set of data is 3 .
Hence , this is the required solution .
What is the 8th term of this geometric sequence?
1, 3, 9, 27,...
Answer:
1*3*3*3*3*3*3=729. For each term you multiply the previous term by three.
Answer:
2187
Step-by-step explanation:
To find the 8th term, we can find and use the explicit formula.
The standard form of the explicit formula for a geometric sequence is:
[tex]x_n=a(r)^{n-1}[/tex]
Where a is the initial term, r is the common ratio, and n is the nth term.
From the sequence, we can see that the first term is 1, and each term is 3 times the previous term. Thus, the common ratio is 3.
Substituting these into our equation, we will have:
[tex]x_n=1(3)^{n-1}\\x_n=(3)^{n-1}[/tex]
So, to find the 8th term, substitute 8 for n:
[tex]x_8=(3)^{8-1}[/tex]
Subtract:
[tex]x_8=(3)^7[/tex]
Evaluate:
[tex]x_8=2187[/tex]
So, the 8th term is 2187.
And we're done!