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3 years ago

12

Which equation can pair with 3x + 4y = 8 to create a consistent and independent system?

1 answer:

Hunter-Best [27]3 years ago

6 0

There isn't any choices given in this problem but I can give you a tip to answer these kinds of problem. When you say independent, it means that the equation cannot be algebraically altered to result to 3x + 4y = 8. So the equation 6x + 8y = 16 is not an independent equation since when you divide each side by 2 it will result to 3x + 4y =8. You get the idea. <span />

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3 years ago

John and Tyrone each go for a morning jog before work. John's jogging pace

hram777 [196]

Answer:

Tyrone's rate is 1 more mile per hour than John's

Step-by-step explanation:

Given

$y = 5x$ --- John number of jog

See attachment of Tyrone's number of jog

Required

Select the true option

From the attached graph, we have:

$(x_1,y_1) = (0,0)$

$(x_2,y_2) = (2,12)$

Calculate the slope (m); i.e. unit rate

$m = \frac{y_2 - y_1}{x_2 -x_1}$

$m = \frac{12 - 0}{2 -0}$

$m = \frac{12}{2}$

$m = 6$

For John, we have:

$y = 5x$

A linear equation is represented as:

$y = mx+ c$

Where m represents the unit rate. So, by comparison;

$m = 5$

$m = 5$ --- John unit rate

$m = 6$ --- Tyrone unit rate

<em>Option B is correct because Tyrone's rate is 1 more mile per hour than John's</em>

<em>i.e. 6 - 5 = 1</em>

5 0

3 years ago

|13x-4|+12 < 56<br> Anybody know this cuz I do

Ronch [10]

Answer:

$\displaystyle x\in \left(-\frac{40}{13},\frac{48}{13}\right)$

Step-by-step explanation:

<u>Inequalities with Absolute Value</u>

We must recall the following rule:

$\text{If }|M|0$

Then:

$-N$

We have the following inequality:

$|13x-4|+12 < 56$

Subtracting 12:

$|13x-4|< 56-12$

$|13x-4|< 44$

Applying the rule:

$-44$

Adding 4:

$-44+4$

Operating:

$-40$

Dividing by 13:

$\displaystyle -\frac{40}{13}$

The solution expressed in interval form is:

$\boxed{\displaystyle x\in \left(-\frac{40}{13},\frac{48}{13}\right)}$

8 0

3 years ago