What value of x will make the equation below true? x−4.5=9

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:

$155 = 0.2m + 35$

$155-35= 120 = 0.2 m$

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

6 0

3 years ago

Why the systems must have the same solution?system(a)4x-5y=13.....3x+6y=11........system(b) 8x-10y=26.....x-11y=2.........AKA QU

Y_Kistochka [10]

When you add the equations in (a) you get 7x+y=24.

When you subtract the equations in (b) you also get 7x+y=24.

That means to solve both systems you can work with the same equation. However that is not enough. We must have two equivalent equations. We found only one.

Notice however that in the (b) we can take the first equation and divide every term by 2. When we do this we get 4x-5y=13. That’s the first equation in (a).

So both systems can be solved by working with the same two equations. These are 5x-5y=13 and 7x+y=24. And since we have two equations and two unknowns (the number of equations matches the number of variables) there is only one solution — one x and y that would make both systems true — solve both systems.

Basically we showed the systems are equivalent!

3 0

3 years ago

A foot ball field is 120 yard long and 16” wide how many square yard of grass is needed to cover the field

Stells [14]

Answer: 160 yd^2

Step-by-step explanation: (120 yards)*(16 inches)*(1 yard/12 inches) = 160 yd^2

5 0

3 years ago

-4(9n + 9) = -12(4n - 6).

WITCHER [35]

Answer:

n = 9

Step-by-step explanation:

Step 1: Write equation

-4(9n + 9) = -12(4n - 6)

Step 2: Solve for n

Distribute: -36n - 36 = -48n + 72

Add 48n to both sides: 12n - 36 = 72

Add 36 to both sides: 12n = 108

Divide both sides by 12: n = 9

Step 3: Check

Plug in n to verify if it's a solution.

-4(9(9) + 9) = -12(4(9) - 6)

-4(81 + 9) = -12(36 - 6)

-4(90) = -12(30)

-360 = -360

7 0

4 years ago

Measure of angle abc

astra-53 [7]

10x-12 is the answer I believe

3 0

3 years ago

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