Lesson 4-1 Solving Systems of Equations by Graphing

Answer:

1)-9x^5 + 7x^2 + 3    2)  -2x2 • (x - 7)      3)  -23v^2 + 7v + 4    4) is just 7x

Answer: A.  the price for a shirt that originally cost s after a 21% discount

Step-by-step explanation:

Step-by-step explanation:

400,200,100,50,25,12.5, ...... 0.78125

Answer:

x < 2

Step-by-step explanation:

3x - 2 < 4

   + 2 | + 2

------------------

    3x < 6

         ↓

(3x) / 3  <  6 / 3

         ↓

       x < 2

9514 1404 393

Answer:

  (x, y) = (1, 1)

Step-by-step explanation:

About Algebra

All of Algebra is based on a few simple rules:

When we solve equations by substitution, we make use of these facts.

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About Substitution

Generally, substitution in equation solving is done for the purpose of eliminating a variable from the equation. That usually means you want to write an expression for one variable in terms of other variables.

Finding the Expression to Substitute

In this set of equations, the variables are x and y. We can substitute for y an expression involving x, or we can substitute for x an expression involving y. These equations are written in such a way that either method works as well as the other.

Let's choose to substitute for y. This means we need an equation of the form ...

  y = <some expression involving x>

The first equation makes it easy to get that. If we add y (to both sides, see rule 3 above), we get ...

  5x -y +y = 4 +y

  5x = 4 + y . . . . . . . . . simplified

Subtracting 4 (from both sides) gets us the form we want.

  5x -4 = 4 -4 + y

  5x -4 = y . . . . . . by rule 4 above, we can use (5x-4) anyplace you see y

Using the Expression to Substitute

Now, we have an expression for y that we can use in the second equation. There, y is multiplied by 4, so we need to be sure to multiply the whole expression by 4:

  -x + 4(5x -4) = 3 . . . . . . substituted for y in the second equation

  -x +20x -16 = 3 . . . . . use the distributive property to eliminate parentheses

  19x -16 = 3 . . . .  . . collect terms

This has a constant (-16) where we don't want it, so we can add 16 (to both sides) to get rid of it.

  19x -16 +16 = 3 +16

  19x = 19 . . . . simplify

Now, we can divide by 19 (to both sides) to get x by itself.

  (19x)/19 = 19/19

  x = 1 . . . . almost done; we still need to find y

Finishing Up

Using the equation for y that we used for substitution, we can find y from our value of x.

  y = 5x -4 = 5×1 -4 = 5-4

  y = 1

So, the solution is x = 1, y = 1, or (x, y) = (1, 1).

_____

Additional comment

In this set of equations, both variables (x and y) appear with coefficients of 1 (actually, -1). This makes it easy to solve for an expression that can be substituted for the variable. In systems of equations that you want to solve by substitution, it usually works well to start by looking for a variable with a coefficient of 1 (or -1). Use that to write the substitution expression as we did here.

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Alternate Solution

If you use a variable with a coefficient other than 1 to write the substitution expression, you end up with fractions. That's OK if you're comfortable with arithmetic using fractions. It generally requires more care.

For example, we could solve the first equation for x:

  x = (4 +y)/5

Substituting that into the second equation gives ...

  -(4 +y)/5 +4y = 3

  -4/5 -y/5 +4y = 3

  (3 4/5)y = 3 4/5 . . . . . add 4/5 (to both sides), collect terms

Now, you get to divide by 3 4/5 to get ...

  y = (3 4/5)/(3 4/5) = 1

Fortunately, in this case, we can see the numerator and denominator are identical, so the division result is 1. If it weren't you'd be faced with dividing mixed numbers--not always a student's first choice of fun math operations.

  x = (4 +1)/5 = 1 . . . . finishing up

Answer:

34.06°

Step-by-step explanation:

25 is the length of the hypotenuse side and 14 is the length of the opposite side.

Therefore, you will need to use sine to work out the missing angle.

sinx = opp / hyp

sinx = 14 / 25

x = sin ^ -1 (14 / 25)

= 34.06°

Answer:

The ladder is 10 ft long...

Answer:

i think its c 6-6 so good luck

Answer:

dial it up

2:16

simplify

1:8

now multiply 8 by the number of gigs

2:16

3:24

and so on.....

ring ring

1:9

again multiply the cost by the number of gigs

2:18

3:27

and so on....

Answer:

x = 8

Step-by-step explanation:

Let the number = x

x/6 - 1/3 = x/8

-1/3 = x/8 - x/6

-1/3 = (6x-8x)/48

-1/3 = -2/48x

Divide both sides by -2/48

x = -1/3 ÷ -2/48

= -1/3 × -48/2

= 48/6

= 8

x = 8

The number = 8

Answer:(b) step 1

Step-by-step explanation:

The wrong step in the student's workings is step 1

The equation is given as:

x^2 - 2x - 8 = 0

Expand the equation

x^2 + 2x - 4x - 8 = 0

Factorize the equation

x(x + 2)- 4(x + 2)

Factor out x + 2

(x - 4)(x + 2) = 0

The above means that the factored equation of x^2 - 2x - 8 = 0 is (x - 4)(x + 2) = 0

This means that the step 1 of the student's step is wrong and incorrect

Read more about equations at:

https://brainly.com/question/2972832

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[tex]\displaystyle K_c \approx 0.0424[/tex]

Math

Pre-Algebra

Order of Operations: BPEMDAS

Chemistry

Equilibrium

Step 1: Define

[RxN]   2NO₂ ⇆ N₂O₄

[Equilibrium Rate Law]   [tex]\displaystyle K_c = \frac{[N_2O_4]}{[NO_2]^2}[/tex]

NO₂ = 11.95 M

N₂O₄ = 6.05 M

Step 2: Find K

This value of K tells us that the reactants are favored in the equilibrium reaction (K < 0.1).

Answer:

Write a situation in which positive and negative numbers are used to describe values that have opposite meaning. What does 0 represent in this situation you created?

Step-by-step explanation:

Answer:

-x^3 + 2x^3+ 4x^3 + 3x^2 + 7x^2-x^2-9x + 8x-5-1

Step-by-step explanation:

Here, we want to have an expression of at least ten terms which when simplified would give polynomial

We have the expression as

x^3 - 2x^3+ 4x^3 + 3x^2 + 7x^2-x^2+ 2x^2-9x + 8x-5-1

Answer:

it would be 3 in the first box and 24 in the other

Step-by-step explanation:

because the ratio is 3 years to 24 montsh most of the time the larger number is on the left and the smaller number is on the right and 3 years is more than 24 months 24 months is only two years

Answer:

(500÷1.8)÷60

By dividing 1.8 out of 500, u can know

Answer:

Its either 8x/5 or 5x/8

im not sure sorry.

Answer:

the answer is option : D

Step-by-step explanation:

multiply 9 with the given hrs to find the correct one

Answer:d) g(x)=x^1/3-1.5

Step-by-step explanation:

Answer:

3 and 7

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

Use the elimination method.

15x - 12y = 13

30x + 9y = 4

If you add both equations you will not cancel out any variables, so you need to multiply one of the equations by something. Multiply the first equation by -2 to cancel out the x values.

-2(15x - 12y = 13)

30x + 9y = 4

You should have these two equations now:

-30x + 24y = -26

30x + 9y = 4

Add them together now. You should get this now.

33y = -22

Divide both sides by 33. You should get y = -2/3

Now, substitute the y value into any of the two equations that you started with. Let's substitute the y value for the second equation.

30x + 9 (-2/3) = 4

30x - 6 = 4

30x = 10

30     30   (divide 30 and 10 by 30)

x = 1/3

Answer:

where are the squares?

Step-by-step explanation: