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3 years ago

Solve 4(x + 1) = 4x + 4. a. No solution b. 0 c. All real numbers d. 1

Mathematics

1 answer:

cricket20 [7]3 years ago

4 0

Answer:

c. All real numbers

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

4 • (x + 1) - (4x + 4) = 0

Step 2 :

Equation at the end of step 2 :

0 = 0

Step 3 :

Equations which are always true :

3.1 Solve 0 = 0This equation is a tautology (Something which is always true)

Equation is alway true

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A line passes through the points (1, 2) and (3, 1). What is the slope of the line?

Verdich [7]

The slope of the line is represented through the letter m, so

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3 years ago

Change each standard form equation to slope-intercept form!

goldenfox [79]

Hello!

Slope-intercept form is this one: $y=a*x+b$ where a is the slope and b the intercept.

So, for transforming these equations to Slope-Intercept you'll need to rearrange the equations by adding or subtracting the same amounts on both sides of the equation (as a rule of thumb, sums are transformed into subtractions and multiplications into divisions).

<span>1) 3x + y = 12

You should notice that Y and X are on the same side of the equation, so by subtracting 3x on both sides of the equation you'll cancel X on the left side:

</span> $3x+y-3x=12-3x \\ y=12-3x$
<span>
To finish, we rearrange this equation to the form y=a*x+b

</span> $y=-3x+12$
<span>
So, the slope is -3 and the intercept is 12

2) 8=y+5x

</span>You should notice that Y and X are on the same side of the equation, so by subtracting 5x on both sides of the equation you'll cancel X on the right side:

$8-5x=y+5x-5x \\ 8-5x=y$

To finish, we rearrange this equation to the form y=a*x+b

$y=-5x+8$

So, the slope is -5 and the intercept is 8

3) 6x + 3y = -9

You should notice that Y and X are on the same side of the equation, so by subtracting 6x on both sides of the equation you'll cancel X on the left side:

$6x+3y-6x=-9-6x \\ 3y=-9-6x$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by 3 to cancel this number on the left side.

$\frac{3}{3}y= \frac{9}{3}- \frac{6}{3}x \\ y=3-2x$

To finish, we rearrange this equation to the form y=a*x+b

$y=-2x+3$

So, the slope is -2 and the intercept is 3

4) x - 5y = 55

You should notice that Y and X are on the same side of the equation, so by subtracting x on both sides of the equation you'll cancel X on the left side:

$x-5y-x=-55-x \\ -5y=-55-x$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by -5 to cancel this number on the left side.

$\frac{-5}{-5}y= \frac{55}{-5}- \frac{1}{-5}x \\ y=-11+ \frac{1}{5}x$

To finish, we rearrange this equation to the form y=a*x+b

$y=\frac{1}{5}x-11$

So, the slope is 1/5 and the intercept is -11

5) -4x-y=-2
You should notice that Y and X are on the same side of the equation, so by adding 4x on both sides of the equation you'll cancel X on the left side:

$-4x-y+4x=-2+4x \\ -y=2+4x$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by -1 to cancel this number on the left side.

$\frac{-1}{-1} y= \frac{-2}{-1}+ \frac{4}{-1}x \\ y=2-4x$

To finish, we rearrange this equation to the form y=a*x+b

$y=-4x+2$

So, the slope is -4 and the intercept is 2

6) -16 = -4x + 2y

You should notice that Y and X are on the same side of the equation, so by adding 4x on both sides of the equation you'll cancel X on the right side:

$-16+4x=-4x+2y+4x \\ -16+4x=2y$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by 2 to cancel this number on the right side.

$\frac{-16}{2}+ \frac{4}{2} x= \frac{2}{2}y \\ -8+2x=y$

To finish, we rearrange this equation to the form y=a*x+b

$y=2x-8$

So, the slope is 2 and the intercept is -8

I hope that this helps. Have a nice day!

8 0

4 years ago

A farmer has 107 acres on which to plant oats or corn. Each acre of oats requires $18 capital and 2 hours of labor. Each acre of

Lera25 [3.4K]

Answer:

Step-by-step explanation:

the objective is to maximize profit

let x be corn and y be oat

let us begging by formulating the linear program for the problem

The objective function is

111x+47y=P

The constraints are

1. capital

36x+18y=2100------------1

2. labor

6x(8)+2y(8)=2400

48x+16y=2400-------------2

solving 1 and 2 we apply substitution method

36x+18y=2100------1

36x=2100-18y

x=(2100-18y)/36

put x=(2100-18y)/36 in 2 we have

48(2100-18y)/36+16y=2400

(100800-864y)/36+16y=2400

2800-24y+16y=2400

-8y=2400-2800

-8y=-400

8y=400

y=400/8

y=50

to find x put y=50 in 36x+18y=2100------------1

36x+18(50)=2100------------1

36x+900=2100

36x=2100-900

36x=1200

x=1200/36

x=33.33

profit is

111x+47y=P

111(33.33)+47(50)=P

3699.63+2350=P

P=6049.63

$6049.63

the planning comnination is to work on

33.33 acre of corn and 50 acre of oat

8 0

3 years ago

James works in a flower shop. He will put 60 tulips in vases for a wedding. He must use the same number of tulips in each vase.

Lina20 [59]

Answer: a. 1, 3, 5, 15

Step-by-step explanation:

If he needs to put an equal number of tulips in each vase he uses, the number of vases will have to be multiples of 15.

The multiples of 15 are;

1, 3, 5, and 15.

James can therefore put;

1 tulip in 15 vases
3 tulips in 5 vases
5 tulips in 3 vases
15 tulips in 1 vase

5 0

3 years ago

Middle school Math!!!

liraira [26]

<h2>Answers:</h2>

Question 1: The equations share the same slope, but different y-intercepts.

Question 2: Option B (y = 2x + 1)

<h2>Explanations:</h2><h3>For Question 1:</h3>

Both equations are written in slope intercept form.

$y = mx+b\\\\\text{m - slope}\\\text{b - y-intercept}$

The equations we have are:

$\left \{ {{y=2x} \atop {y=2x-7}} \right.$

Both equations share the same slope of 2. However, they have different y-intercepts.

y = 2x can be written as y = 2x + 0.

Usually if you only have the slope in your equation then the y-intercept is the origin, or (0, 0).

The second equation's y-intercept is -7. It takes 'b's place.

<h3>For Question 2: </h3>

We are given a graph and we need to find a equation.

According to the graph, the line passes at (0, 1). 1 is the y - intercept.

Since y = 2x + 1 is the only option with 1 as the y - intercept, it should be the correct answer.

I'll do the slope as well to verify our answer.

I will use the points (-1, -1) and (1, 3).

$m=\frac{3-(-1)}{1-(-1)}=\frac{4}{2} =\boxed{2}$

The correct answer should be $y = 2x+1$ .

Hope this helps you.

6 0

3 years ago