A mistake was made in the steps shown to simplify the expression. Which step includes the mistake?

deff fn [24]

The slope and intercept form is the form of the straight line equation that includes the value of the slope of the line

Neither
║
Neither
⊥
║
Neither
Neither
Neither

Reason:

The slope and intercept form is the form y = m·x + c

Where;

m = The slope

Two equations are parallel if their slopes are equal

Two equations are perpendicular if the relationship between their slopes, m₁, and m₂ are; $m_1 = -\dfrac{1}{m_2}$

1. The given equations are in the slope and intercept form

$\ y = 3 \cdot x + 1$

The slope, m₁ = 3

$y = \dfrac{1}{3} \cdot x + 1$

The slope, m₂ = $\dfrac{1}{3}$

Therefore, the equations are neither parallel or perpendicular

Neither

2. y = 5·x - 3

10·x - 2·y = 7

The second equation can be rewritten in the slope and intercept form as follows;

$y = 5 \cdot x -\dfrac{7}{2}$

Therefore, the two equations are parallel

║

3. The given equations are;

-2·x - 4·y = -8

-2·x + 4·y = -8

The given equations in slope and intercept form are;

$y = 2 -\dfrac{1}{2} \cdot x$

Slope, m₁ = $-\dfrac{1}{2}$

$y = \dfrac{1}{2} \cdot x - 2$

Slope, m₂ = $\dfrac{1}{2}$

The slopes

Therefore, m₁ ≠ m₂

$m_1 \neq -\dfrac{1}{m_2}$

The lines are Neither parallel nor perpendicular

Neither

4. The given equations are;

2·y - x = 2

$y = \dfrac{1}{2} \cdot x +1$

m₁ = $\dfrac{1}{2}$

y = -2·x + 4

m₂ = -2

Therefore;

$m_1 \neq -\dfrac{1}{m_2}$

Therefore, the lines are perpendicular

⊥

5. The given equations are;

4·y = 3·x + 12

-3·x + 4·y = 2

Which gives;

First equation, $y = \dfrac{3}{4} \cdot x + 3$

Second equation, $y = \dfrac{3}{4} \cdot x + \dfrac{1}{2}$

Therefore, m₁ = m₂, the lines are parallel

║

6. The given equations are;

8·x - 4·y = 16

Which gives; y = 2·x - 4

5·y - 10 = 3, therefore, y = $\dfrac{13}{5}$

Therefore, the two equations are neither parallel nor perpendicular

Neither

7. The equations are;

2·x + 6·y = -3

Which gives $y = -\dfrac{1}{3} \cdot x - \dfrac{1}{2}$

12·y = 4·x + 20

Which gives

$y = \dfrac{1}{3} \cdot x + \dfrac{5}{3}$

m₁ ≠ m₂

$m_1 \neq -\dfrac{1}{m_2}$

Neither

8. 2·x - 5·y = -3

Which gives; $y = \dfrac{2}{5} \cdot x +\dfrac{3}{5}$

5·x + 27 = 6

$x = -\dfrac{21}{5}$

Therefore, the slopes are not equal, or perpendicular, the correct option is Neither

Learn more here:

brainly.com/question/16732089

6 0

3 years ago

On the first part of her trip Natalie rode her bike 16 miles and on the second part of the trip she rode her bike 42 miles. Her

-BARSIC- [3]

Answer:

14 mph ( average speed during the second part of the trip )

Step-by-step explanation:

Let´s call "x" the average speed during the first part then

t = 5 hours

t = t₁ + t₂ t₁ and t₂ times during part 1 and 2 respectively

l = t*v ( distance is speed by time ) t = l/v

First part

t₁ = 16/x and t₂ = 42 / ( x + 6)

Then

t = 5 = 16/x + 42 /(x + 6)

5 = [ 16 * ( x + 6 ) + 42 * x ] / x* ( x + 6 )

5 *x * ( x + 6 ) = 16*x + 96 + 42 x

5*x² + 30*x - 58*x - 96 = 0

5*x² - 28*x - 96 = 0

We obtained a second degree equation, we will solve for x and dismiss any negative root since negative time has not sense

x₁,₂ = [28 ± √ (28)² + 1920 ] / 10

x₁,₂ = ( 28 ± √2704 )/ 10

x₁ = 28 - 52 /10 we dismiss that root

x₂ = 80/10

x₂ = 8 mph average speed during the first part, and the average speed in the second part was 6 more miles than in the firsst part. then the average spedd dring the scond part was 8 + 6 = 14 mph

6 0

3 years ago

if it takes 10 men 10 days to dig a hole how long will it take 5 men to dig a hole that's half as big

Nataly [62]

Answer:

10 days

Step-by-step explanation:

It will take 10 men 5 days to dig a hole half as big.

It will take 5 men 10 days to dig a hole half as big.

( Remember, the less people, the more time it will take. )

8 0

2 years ago

Read 2 more answers

48 is 9 less than 3 times a number. What is the number?

Kamila [148]

19 x 3 = 57 57 - 9 = 48 Your answer is 19.

4 0

3 years ago

Read 2 more answers

Determine the greatest intergral value of K for which 2x^2 - Kx +2 =0 will have non-real roots ...Use quadratic inequalities to

Mrac [35]

Answer:

Greatest integral value of K = 3.

Step-by-step explanation:

The nature of the roots of a quadratic equation is determined by the sign of the discriminant, b^2 - 4ac. For non-real roots this is negative.

2x^2 - kx + 9 = 0

The discriminant = (-k)^2 - 4*2*2 , so:

k^2 - 16 < 0 for non-real roots.

k^2 < 16

k < √16

k < 4

So the answer is 3.

The greatest integral value is 8.

6 0

3 years ago