Using the Euclidean algorithm integer integers $x$ and $y$ is: [ (-30 + 37k ), (133 - 164k) ].
Euclidean AlgorithmGiven:
$164x + 37y = 1
First step
Sequence of quotients
4(37) + 16=164
2(16) + 5=37
3(5) + 1=16
4(1) + 1=5
1(1) + 0=1
4 2 3 4 1
1 0 1 2 7 30 37
0 1 4 9 31 133 164
Determinant
(164×30) - (37×133)
=4,920-4,921
= -1
164(-30) + 37(133)
=-4,920+4,921
= 1
Second step
Integer
[(x + bk), (y - ak) ]
Where:
x = -30
y = 133
k=integer
Hence:
[ (-30 + 37k ), (133 - 164k) ]
Therefore using the Euclidean algorithm the integer is: [ (-30 + 37k ), (133 - 164k) ].
Learn more about Eucledian Algorithm here:https://brainly.com/question/24836675
#SPJ1
Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form. (x, y) = (−2, 10) and (x, y) = (4, −8) are points on the line
♪ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ♪
[tex]\textsc{heya!}[/tex]
☑︎ what we need to do:
find the equation of the line☑︎ what we are provided with:
two points on this line[tex]\textsc{solution:}[/tex]
equation: y=-3x+4[tex]\textsc{explanation:}[/tex]
first, these are the points on our line:
• (-2, 10) • (4, -8)
what we need at this moment is the gradient (slope) of the line.
remember, there's a little formula that will help us find the gradient:
[tex]\large\text{$\displaystyle\frac{y_2-y_1}{x_2-x_1}$}[/tex]
our values are:
• (-2, 10) and (4, -8)
after substituting the values into the above formula, we obtain
[tex]\large\text{$\displaystyle\frac{-8-10}{4-(-2)}$}[/tex]
after simplifying, we obtain
[tex]\large\text{$\displaystyle\frac{-18}{4+2}$}[/tex]
simplifying more,
[tex]\large\text{$\displaystyle\frac{-18}{6}$}[/tex]
dividing,
[tex]\large\text{$-3$}[/tex]
but that's only part of our problem. we need to find the equation, and we have the gradient only.
let's use the first point in our equation
• (-2, 10)
[tex]\large\text{$y-y_1=m(x-x_1)$}[/tex]m is the gradient.
this is what we obtain after substituting the values
[tex]\large\text{$y-10=-3(x-(-2)$}[/tex]
simplifying
[tex]\large\text{$y-10=-3(x+2)$}[/tex]
simplifying more
[tex]\large\text{$y-10=-3x-6$}[/tex]
moving 10 to the right side
[tex]\large\text{$y=-3x-6+10$}[/tex]
and finally
[tex]\large\text{$y=-3x+4$}[/tex]
[tex]\textsc{hopefully\:helpful}[/tex]
by: • [tex]\textsc{$d^an_ci^ng$}[/tex]
[tex]\textsc{have\:a\:great\:rest\:of\:your\:day\:ahead!}[/tex]
What is the median of the set of data?
{131, 154, 204, 244, 244, 276, 263, 289, 288, 274, 207}
Enter your answer in the box.
the graph of y = (x) is shown below
Answer:
Step-by-step explanation:
Solution
The question is a bit obscure. The best choice I think, would be A. F(x) could equal something like y = x - 3. When y = 0, x = 3 or put the other way, when x = 3 y= 0.
The points A(4, 3) and B(4, –5) are plotted on the coordinate plane. Rectangle ABCD has a perimeter of 30 units. If points C and D were plotted on the grid shown, what would their coordinates be if point C is below point D? Alt_text C: ( , ) D: ( , )
The possible coordinates of C and D are: C = (11,3) and D = (11,-5) or C = (-3,3) and D = (-3,-5)
How to determine the coordinates of C and D?The given parameters are:
A = (4,3)
B = (4,-5)
Perimeter, P = 30 units
Since points A and B are on the same x-coordinate, then the distance between them is:
AB = 3 - - 5
AB = 8
The perimeter of the rectangle is calculated using:
P = 2 *(AB + CD)
This gives
2 * (8 + CD) = 30
Divide by 2
8 + CD = 15
Subtract 8 from both sides
CD = 7
This means that points C and D are 7 units from points A and B, respectively.
If A = (4,3) and B = (4,-5), then the possible coordinates of C and D are:
C = (11,3) and D = (11,-5) or C = (-3,3) and D = (-3,-5)
Read more about perimeter at:
https://brainly.com/question/24571594
#SPJ1
If P is directly proportional to Q. And Q = 30 when P = 40. Find Q when P = 70
Answer:
Q = 52.5
Step-by-step explanation:
given P is directly proportional to Q then the equation relating them is
P = kQ ← k is the constant of proportion
to find k use the condition Q = 30 when P = 40 , then
40 = 30k ( divide both sides by 30 )
[tex]\frac{40}{30}[/tex] = [tex]\frac{4}{3}[/tex] = k
P = [tex]\frac{4}{3}[/tex] Q ← equation of proportion
when P = 70 , then
70 = [tex]\frac{4}{3}[/tex] Q ( multiply both sides by 3 to clear the fraction )
210 = 4Q ( divide both sides by 4 )
52.5 = Q
Read each item carerur 1. What is the rule of the sequence: 7, 13, 19, 25, 31? A. Add 6 B. Subtract 6 C. Multiply by 2 D. Multiply by 3
Answer:
A.
Step-by-step explanation:
it’s add 6 because, 6 + 7 = 13 and 13 + 6 = 19 and it keeps on continuing this is how I know I am correct.
Answer:
the answer is A) Add 6
Step-by-step explanation:
you add so 7 plus 6 is 13 and 13 plus 6 is 19 and so it continues
hope this helps!!
A. 23.7
B. 11.2
C. 9.5
D. 57.3
E. 30.0
F. 6.0
Answer:
c.9.5
Step-by-step explanation:
im awesome so so very
Find the area of the following figure.
300 cm2
312 cm2
252 cm2
400 cm2
Answer:
312cm2
Step-by-step explanation:
16*12=192
10*6/2=30
30*4=120
192+120=312
Determine the exact value of sin 30° tan 45° + tan 30° sin 60⁰
Answer:
1.
Step-by-step explanation:
1) if sin30=0.5; tan45=1; tan30=1/√3; sin60=√3/2, then
2) 0.5+0.5=1.
What is the quotient?
-3/8 divided -1/4
Answer:
3/2 or 1.5
Step-by-step explanation:
(-3/8) ÷ (-1/4)
Copy dot flip
=(-3/8)* (-4/1)
=12/8
=3/2 or 1.5
Avani misses 5% of the free throws she attempts in a season. How many total free throws did she attempt if she missed 4?
Answer:
She had a total of 80 throws.
Step-by-step explanation:
4x20 (20x5%=100%) = 80, so she had 80 throws.
Find the sum of the first 14 terms of the finite geometric series given as:
0.5+ (-1) +2+...
The sum of the first 14 terms of the finite geometric series 0.5+ (-1) +2+... is -2730.5
How to determine the sum of the series?The series is given as:
0.5+ (-1) +2+...
The above series is a geometric series, with the following parameters:
First term, a = 0.5Common ratio, r = -2Number of terms, n = 14The sum of the first 14 terms is calculated using:
[tex]S_n= a *(1 - r^n) \div (1 - r)[/tex]
So, we have:
[tex]S_{14}= 0.5 *(1 - (-2)^{14}) \div (1 + 2)[/tex]
Evaluate
[tex]S_{14}= -2730.5[/tex]
Hence, the sum of the series is -2730.5
Read more about series at:
https://brainly.com/question/6561461
#SPJ1
Graph the inequality x < - 10/3
Answer:
Picture Below :)
Step-by-step explanation:
*ta da*
- Have a great day -
Books cost $6.95 each. Mary had a $5 bill,a$1 bill.and 3 dimes.How much more money does she need to buy one book?
Answer:
65 cents
Step-by-step explanation:
5 + 1 + .30 = 6.30
6.95 - 6.30 = .65
A couple Invested $6100 in an account some of it went into a savings account paying 3% annual simple interest . The rest was invested in a riskier mini - mall development plan paying 11% annual simple interest . The combined interest earned for the first year was $503 . How much money was invested at each rate ?
Answer:
4387.63
Step-by-step explanation:
Simplify [2 x (10+5)] - 5
Answer:
25
Step-by-step explanation:
[2 x (10+5)] - 5
[2 x (15)] - 5
[30] - 5
25
What is the simplest form of
X^4 y^7/ 3sqrt x^10 y^4
Answer is D
Answer: The answer is Undefined (a/0)
I put a screenshot of how i got that answer
Answer: She's right, it is d
Step-by-step explanation:
h(x) = (x2 − 49)(x + 4)
Answer:
h(x) = x³ + 4x² - 49x - 196
Step-by-step explanation:
h(x) = (x² - 49)(x + 4) <== distribute
h(x) = x²(x) - 49(x) + x²(4) - 49(4)
h(x) = x³ - 49x + 4x² - 196 <== rewrite in standard form (descending degrees)
h(x) = x³ + 4x² - 49x - 196
Hope this helps!
What is 28 percent as a fraction?
Answer:
28 as a fraction would be written as 56/2.
Step-by-step explanation:
The fraction can be written as 7/25.
Explanation:
Given Input Value = 28%
Place the Percentage Value at the top over 100. = 28/100
The given fraction is 28/100.
On reducing the fraction, we get the exact form 28/100. = 7/25
The exact form of the fraction is 7 /25.
Scientists are tracking the population of a specific species of bird. They have determined that the function P(x) = 575 (1.025)x models the number of birds, P(x), after x years. Which of the following is true about the brid?
31. (05.08 MC)
What is the equation for a geometric sequence with a first term of 3 and a second term of -9?
Answer:
[tex]a_n=3(-3)^{n-1}[/tex]
Step-by-step explanation:
Geometric sequence
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termr is the common ratioGiven:
[tex]a_1=3[/tex][tex]a_2=-9[/tex]To find the common ratio r, divide consecutive terms:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{-9}{3}=-3[/tex]
Therefore, the equation is:
[tex]a_n=3(-3)^{n-1}[/tex]
Sarah makes a red hair bow using 21 4/5 inches of ribbon. She makes a purple hair bow using 18 1/4 inches of ribbon.
How much more ribbon is used to make the red hair bow than the purple hair bow?
Answer:
91/20 or 4 11/20
Step-by-step explanation:
First, convert the 2 amounts into improper fractions
Red: 21 4/5 = 114/5
Purple: 18 1/4 = 73/4
Then, using cross multiplication, you can give them the same denominator
Red: 114/5 = 456/20
Purple: 73/4 = 365/20
Then just subtract the numerators and keep the denominator
456/20 - 365/20 = 91/20
So your answer is
91/20 or 4 11/20
A car rental company charges $120 plus $0.37 per mile, m. Which equation represents the total cost, c, of renting a car?
Solve the system of equations 3x - 2y = 8 x-2y = 4
Answer: (2, -1), or x = 2 and y = -1
By graphing:
We can solve by graphing. See attached.
-> The solution is the point of intersection. The lines intersect at (2, -1) which means x is equal to 2 and y is equal to -1.
By substituting:
We can solve this by substituting. It means we will substitute one equation into the other, then solve for the variables.
3x - 2y = 8
x - 2y = 4 -> x = 2y + 4
-
3x - 2y = 8
3(2y + 4) - 2y = 8
6y + 12 - 2y = 8
4y = -4
y = -1
-
x - 2y = 4
x - 2(-1) = 4
x + 2 = 4
x = 2
the perimeter of a rectangle is 84cm if the width of rectanle is 16 cm Find its lenth
Answer:
26 cm
Step-by-step explanation:
Formula for Perimeter
Perimeter = 2(Length + Width)Solving (given Perimeter is 84 cm and width is 16 cm)
84 = 2(Length + 16)42 = Length + 16Length = 42 - 16Length = 26 cmAnswer:
L= 26cm
Step-by-step explanation:
Perimeter= 2(l x w)
Perimeter= 84cm
Width= 16cm
Length=?
84= 2l + 32
2l = 84-32
2l= 52
L= 52/2
L= 26cm
Marci needs to rent a storage. She needs to determine the volume of the storage unit. If the storage unit is 8 feet high, what is the volume of the storage unit
The function y = log(x) is translated 1 unit right and 2 units down. Which is the graph of the translated function?
please help
Answer: [tex]y=\log(x-1)-2[/tex]
Given f(a, b) = 3a2 – 2ab + 5b2 , determine (a) f(-2, 3) and (b) f(x+y, x-y)
Answer:
1) 45
2) 6x^2-4xy+10y^2
Step-by-step explanation:
1) Given f(a, b) = 3a^2 – 2ab + 5b^2 , determine (a) f(-2, 3)
Replace a with (-2) and b with (3):
3(-2)^2-2(-2)(3)+5(3)^2
3(4)-2(-6)+5(9) *Took care of exponents and performed some multiplication in the middle term.
12-12+45 *performed more multiplication
0+45 *additive inverses property applied
45 *performed some addition
2) Given f(a, b) = 3a^2 – 2ab + 5b^2 , determine f(x+y, x-y)
Replace a with (x+y) and b with (x-x-y):
3(x+y)^2-2(x+y)(x-y)+5(x-y)^2
*Explained binomial squares
3(x^2+2xy+y^2)-2(x+y)(x-y)+5(x^2-2xy+y^2)
*Expand product of the sum of two numbers with the difference of said numbers
3(x^2+2xy+y^2)-2(x^2-y^2)+5(x^2-2xy+y^2)
*Distribute
3x^2+6xy+3y^2-2x^2+2y^2+5x^2-10xy+5y^2)
*Combine like terms
6x^2-4xy+10y^2
does anyone know the answer?
Answer: Choice A
40.61 square meters
==========================================================
Explanation:
The area of a full circle is
A = pi*r^2
meaning half of it (aka semicircle) will have this area
A = 0.5*pi*r^2
The diameter of the semicircle is 5.4 meters, which divides in half to get the radius of r = 2.7
The semicircle has an area of...
A = 0.5*pi*r^2
A = 0.5*3.14*(2.7)^2
A = 11.4453
which is approximate since pi = 3.14 is approximate.
Now compute the area of the triangle
area = base*height/2 = 5.4*10.8/2 = 29.16
Then add those sub-areas to get the grand total area.
semicircleArea + triangleArea = 11.4453+29.16 = 40.6053
That rounds to 40.61 which shows why choice A is the answer.
4.1 A bag contains 6 red, 4 green, 2 yellow and 3 blue balls. In each case, give the ratio (in simplest form) of the asked number of balls in the bag.( 4 ) 4.1.1 The number of red balls to the number of green balls.
The number of red balls to the number of green balls is 3 : 2
How to determine the ratio?The distribution of the balls is given as:
6 red, 4 green, 2 yellow and 3 blue balls
The number of red balls to the number of green balls is represented as:
Ratio = Red : Green
So, we have:
Ratio = 6 : 4
Simplify
Ratio = 3 : 2
Hence, the number of red balls to the number of green balls is 3 : 2
Read more about ratios at:
https://brainly.com/question/2328454
#SPJ1