4- 7f=f- 12j jrk. it ivtivivvitvittivivtvti

Directions: Use substitution to solve the systems of equations. Show your work please.

Len [333]

Hey there!

To use substitution, you substitute one of the equations into the other for one of the variables.

Since thhe first equation is already solved for y, let's substitute that one into the second equation.

Before substitution: x - y = 1

After substitution: x - 2x = 1

See how we replaced the y with 2x? This is because the first equation is y = 2x.

Combine like terms.

-x = 1

Multiply each side by -1 so we get the value of x, not -x.

x = -1

We can now solve for y using the 1st equation, substituting the value for x into it.

Before: y = 2x

After: y = 2(-1)

Multiply the two together.

y = -2

Let's check this in the second equation, so we know we didn't make a mistake somewhere.

Before: x - y = 1

After: (-1) - (-2) = 1

Subtracting a negative is the same as adding a positive, so let's notate it that way to make it easier.

-1 + 2 = 1

Add.

1 = 1

Since both sides are equal, that means we've got the correct solution.

The notation for our answer will be (x, y) since it is a point on a graph.

Your final answer is (-1, -2).

Hope this helps!

7 0

3 years ago

What is the standard form of function f?

Tomtit [17]

Answer:

A = 4; B = -1 ; C = -29

Step-by-step explanation:

y = 4(x + 6) + 5

y = 4x + 24 +5

y = 4x + 29

Standard form: Ax + By = C

4x - y = -29

8 0

3 years ago

Help me please!!!!!!

lara [203]

Answer:

a. $b=2$

b. $b = 2a$

c. $a = \frac{1}{2}b\\$

d. $b = 10$

Step-by-step explanation:

Gradient is just another similar term for slope l, $m$ , and it can be calculated by $m = \frac{y_2 -y_1}{x_2 -x_1}\\$ where $x_n$ and 1 $y_n$ is the $xy$ -coordinates of point $n$

We let $(0,0)$ be point $1$ and $(a,b)$ be point $2$ , we can then write the equation:

$m = \frac{b -0}{a -0}\\ m = \frac{b}{a}$ .

It also says that the points are with a gradient of $2$ so $m = 2$ . We can then write the equation:

$2 = \frac{b}{a}\\$

Finding $b$ If $a = 1$ :

$2 = \frac{b}{a} \\ 2 = \frac{b}{1} \\ 2 = b \\ b = 2$

Writing an expression for $b$ in terms of $a$ .

$2 = \frac{b}{a} \\ \frac{b}{a} = 2 \\ \frac{b}{a} \times a = 2 \times a \\ b = 2a$

Writing an expression for $a$ in terms of $b$

$2 = \frac{b}{a} \\ \frac{b}{a} = 2 \\ \frac{a}{b} = \frac{1}{2} \\ \frac{a}{b} \times b = \frac{1}{2} \times b \\ a = \frac{1}{2}b$

Finding $b$ if $a = 5$

$2 = \frac{b}{a} \\ 2 = \frac{b}{5} \\ \frac{b}{5} = 2 \\ \frac{b}{5} \times 5 = 2 \times 5 \\ b = 10$

4 0

3 years ago

What value of x makes the equation -4x – (-3 − 5x) = -3(2x − 8) true?.

zzz [600]

Answer:

x=3

Step-by-step explanation:

-4x-(-3-5x)=-3(2x-8)

-4x+3+5x=-6x+24

x+3=-6x+24

+6x +6x

7x+3=24

-3 -3

7x=21

/7 /7

x=3

-hope it helps

7 0

3 years ago

For the given set, first calculate the number of subsets for the set, then calculate the

vodomira [7]

Answer:

$\fbox{\begin{minipage}{14em}Number of subsets: 16\\Number of proper subsets: 15\end{minipage}}$

Step-by-step explanation:

Given:

The set A = {5, 13, 17, 20}

Question:

Find the number of subsets of A

Find the number of proper subsets of A

Simple solution by counting:

Subset of A that has 0 element:

{∅} - 1 set

Subset of A that has 1 element:

{5}, {13}, {17}, {20} - 4 sets

Subset of A that has 2 elements:

{5, 13}, {5, 17}, {5, 20}, {13, 17}, {13, 20}, {17, 20} - 6 sets

Subset of A that has 3 elements:

{5, 13, 17}, {5, 13, 20}, {5, 17, 20}, {13, 17, 20} - 4 sets

Subset of A that has 4 elements:

{5, 13, 17, 20} - 1 set

In total, the number of subsets of A: N = 1 + 4 + 6 + 4 + 1 = 16

The number of proper subsets (all of subsets, except subset which is equal to original set A): N = 16 - 1 = 15

Key-point:

The counting method might be used for finding the number of subsets when the original set contains few elements.

The question is that, for a set that contains many elements, how to find out the number of subsets?

The answer is that: there is a fix formula to calculate the total number ( $N$ ) of subsets of a set containing $n$ elements: N = $2^{n}$

With original set A = {5, 13, 17, 20}, there are 4 elements belonged to A.

=> Number of subsets of A: N = $2^{4} = 16$

(same result as using counting method)

Brief proof of formula: N = $2^{n}$

Each element of original set is considered in 2 status: existed or not.

If existed => fill that element in.

If not => leave empty.

For i.e.: empty subset means that all elements are selected as not existed, subset with 1 element means that all elements are selected as not existed, except 1 element, ... and so on.

=> From the point of view of a permutation problem, for each element in original set, there are 2 ways to select: existed or not. There are $n$ elements in total. => There are $2^n}$ ways to select, or in other words, there are $2^{n}$ subsets.

Hope this helps!

:)

8 0

3 years ago

4- 7f=f- 12j jrk. it ivtivivvitvittivivtvti​

4- 7f=f- 12j jrk. it ivtivivvitvittivivtvti