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3 years ago

Determine the ordered pair that satisfies the equation, 6x - 3y = 5.

Mathematics

2 answers:

Sonja [21]3 years ago

7 0

Answer:

Option d

Step-by-step explanation:

Given is a linear equation in x and y as

$6x-3y =5$

To check whether a point satisfies the equation, let us substitute and check whether the equation holds good

a) $6(9)-3(16/3) = 38 \neq 5$

b) $6(6)-3(-3) \neq 5$

c) $6(1)-3(-11/3) = 17\neq 5$

d) $6(-2)-3(-17/3) = -12+17 =5$

Since last point satisfies the equation, option d is the answer.

Kazeer [188]3 years ago

3 0

Given the equation $6x-3y=5.$

Check all options:

A. $\left(9,\dfrac{16}{3}\right)$ , this means that $x=9, y=\dfrac{16}{3}.$ Substitute these numbers into the left side of the equation equation:

$6\cdot 9-3\cdot \dfrac{16}{3}=54-16=38\neq 5.$

This option is false.

B. $\left(6,-3\right)$ , this means that $x=6, y=-3.$ Substitute these numbers into the left side of the equation equation:

$6\cdot 6-3\cdot (-3)=36+9=45\neq 5.$

This option is false.

C. $\left(1,-\dfrac{11}{3}\right)$ , this means that $x=1, y=-\dfrac{11}{3}.$ Substitute these numbers into the left side of the equation equation:

$6\cdot 1-3\cdot \left(-\dfrac{11}{3}\right)=6+11=17\neq 5.$

This option is false.

D. $\left(-2,-\dfrac{17}{3}\right)$ , this means that $x=-2, y=-\dfrac{17}{3}.$ Substitute these numbers into the left side of the equation equation:

$6\cdot (-2)-3\cdot \left(-\dfrac{17}{3}\right)=-12+17=5.$

This option is true.

Answer: correct choice is D.

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If you rent a car for one day and drive 225 miles, the cost is $80. If you drive 350 miles in one day, the cost is $105. Let cm)

kolezko [41]

Answer:

a) $(x_1 = 225, y_1 = 80) , (x_2 = 350, y_2 = 105)$

And we want to find a function:

$C (m) = b_1 m + b_0$

We can find the slope with this formula:

$b_1= \frac{105-80}{350-225}= \frac{25}{125}=0.2$

And then we can use the point $(x_1 = 225, y_1 = 80)$ to find the intercept $b_o$ and we got:

$80 = 0.2*225 +b_0$

$b_0 = 80-45 = 35$

So then the linear function is given by:

$C(m) = 0.2 m + 35$

b) For this case we have that m = 475 so we can replace into the function to find the cost like this:

$C(m =475) = 0.2*475 + 35 = 130$

And for the other case we have a cost of 155 and we want to find the number of miles associated so we can do this:

$155 = 0.2m + 35$

$155-35= 120 = 0.2 m$

$m= \frac{120}{0.2}= 600 mi$

Step-by-step explanation:

For this case we can define the following notation:

m= represent the miles travelled

C= represent the cost

Part a

For this case we have the following two points given:

$(x_1 = 225, y_1 = 80) , (x_2 = 350, y_2 = 105)$

And we want to find a function:

$C (m) = b_1 m + b_0$

We can find the slope with this formula:

$b_1= \frac{105-80}{350-225}= \frac{25}{125}=0.2$

And then we can use the point $(x_1 = 225, y_1 = 80)$ to find the intercept $b_o$ and we got:

$80 = 0.2*225 +b_0$

$b_0 = 80-45 = 35$

So then the linear function is given by:

$C(m) = 0.2 m + 35$

Part b

For this case we have that m = 475 so we can replace into the function to find the cost like this:

$C(m =475) = 0.2*475 + 35 = 130$

And for the other case we have a cost of 155 and we want to find the number of miles associated so we can do this:

$155 = 0.2m + 35$

$155-35= 120 = 0.2 m$

$m= \frac{120}{0.2}= 600 mi$

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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