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svetoff [14.1K]
2 years ago
13

F (x) = –2x+1 If f (x) = 11 Find the value of x:

Mathematics
1 answer:
a_sh-v [17]2 years ago
8 0

Answer:

Now x is equals to 11

-2(11) + 1 = - 22 + 1 = - 21

The answer is - 21

Thank you and please rate me as brainliest as it will help me to level up

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For integers a, b, and c, consider the linear Diophantine equation ax C by D c: Suppose integers x0 and y0 satisfy the equation;
Dmitrij [34]

Answer:

a.

x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )

b. x = -8 and y = 4

Step-by-step explanation:

This question is incomplete. I will type the complete question below before giving my solution.

For integers a, b, c, consider the linear Diophantine equation

ax+by=c

Suppose integers x0 and yo satisfy the equation; that is,

ax_0+by_0 = c

what other values

x = x_0+h and y=y_0+k

also satisfy ax + by = c? Formulate a conjecture that answers this question.

Devise some numerical examples to ground your exploration. For example, 6(-3) + 15*2 = 12.

Can you find other integers x and y such that 6x + 15y = 12?

How many other pairs of integers x and y can you find ?

Can you find infinitely many other solutions?

From the Extended Euclidean Algorithm, given any integers a and b, integers s and t can be found such that

as+bt=gcd(a,b)

the numbers s and t are not unique, but you only need one pair. Once s and t are found, since we are assuming that gcd(a,b) divides c, there exists an integer k such that gcd(a,b)k = c.

Multiplying as + bt = gcd(a,b) through by k you get

a(sk) + b(tk) = gcd(a,b)k = c

So this gives one solution, with x = sk and y = tk.

Now assuming that ax1 + by1 = c is a solution, and ax + by = c is some other solution. Taking the difference between the two, we get

a(x_1-x) + b(y_1-y)=0

Therefore,

a(x_1-x) = b(y-y_1)

This means that a divides b(y−y1), and therefore a/gcd(a,b) divides y−y1. Hence,

y = y_1+r(\frac{a}{gcd(a, b)})  for some integer r. Substituting into the equation

a(x_1-x)=rb(\frac{a}{gcd(a, b)} )\\gcd(a, b)*a(x_1-x)=rba

or

x = x_1-r(\frac{b}{gcd(a, b)} )

Thus if ax1 + by1 = c is any solution, then all solutions are of the form

x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )

In order to find all integer solutions to 6x + 15y = 12

we first use the Euclidean algorithm to find gcd(15,6); the parenthetical equation is how we will use this equality after we complete the computation.

15 = 6*2+3\\6=3*2+0

Therefore gcd(6,15) = 3. Since 3|12, the equation has integral solutions.

We then find a way of representing 3 as a linear combination of 6 and 15, using the Euclidean algorithm computation and the equalities, we have,

3 = 15-6*2

Because 4 multiplies 3 to give 12, we multiply by 4

12 = 15*4-6*8

So one solution is

x=-8 & y = 4

All other solutions will have the form

x=-8+\frac{15r}{3} = -8+5r\\y=4-\frac{6r}{3} =4-2r

where r ∈ Ζ

Hence by putting r values, we get many (x, y)

3 0
3 years ago
Please help me with the work because i dont understand this.
Alexandra [31]

Answer:

The dimension are 20 ft by 15 ft

Step-by-step explanation:

A = l*w

P = 2(l+w)

we know the area = 300

and the perimeter = 70

300 = lw

70 = 2 (l+w)

divide by 2

70/2 = 2/2 (l+w)

35 = l+w

subtract w

35-w = l+w-w

35 -w =l

substitute this into 300 = lw

300 = (35-w) * w

distribute

300 = 35w - w^2

subtract 300 from each side

0 = -w^2 +35w - 300

divide by -1

0 = w^2 - 35w + 300

factor

0= (w-15) (w-20)

using the zero product property

w-15 = 0   w-20 =0

so w=15, w=20

if w=15   then l=35 -w  l = 35-15   l=20

if w=20  then l=35-w   l= 35-20 = 15


The dimension are 20 ft by 15 ft

7 0
3 years ago
Wat are the two qualifications a graph must follow for it to be proportional
Oksi-84 [34.3K]

The two requirements for a proportional relationship are: The ratio of the two variables maintain the same ratio.

4 0
2 years ago
Simplify (3x+1)^2(4x-2) hurry
Arisa [49]
The answer is going to be 20x-4
4 0
3 years ago
PLZZZZZZZZZ HELP ME THIS IS DUE TODAY
zalisa [80]
Answer:
2, 5, 8, 11, 14
3/2
explanation:
linear functions go up by the same x and same y (f(x))
so while x is going up by 2, y is going up by 3
y/x
the rate of change is 3/2
6 0
3 years ago
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