Ask question

Ask question

All categories

4 years ago

7

a driver had 18 2/3 gallons of gas in his car before the trip. when he arrived he had only 9 1/2 gallons left. the trip used 9 1

/2 gallons. if the car gets 30 mpg, how many miles was the trip ?

1 answer:

Ksju [112]4 years ago

5 0

Answer:

IT IS YES AND MORE YESES yo tango

Step-by-step explanation:

You might be interested in

Simplify. 4 × (8 + 5) + 9 45 46 61 62

Darya [45]

Answer:

61

Step-by-step explanation:

4 × (8 + 5) + 9

Parentheses first

4 × (13) + 9

Then multiply

52 +9

Then add

61

7 0

3 years ago

I am holding $2 in dimes and quarters. There are 11 total coins in my hand. How many are dimes and how many are quarters?

Ilia_Sergeevich [38]

Answer:

6 quarters and five dimes

Step-by-step explanation:

;)

8 0

3 years ago

Read 2 more answers

do you think theres anyway at all that Fernando and i could ever work it out. i am crazy in love wirh him and wish that he would

nikklg [1K]

Answer:

I do. But keep in mind, sometimes things aren't meant to be. You may not see it now but you could be better off without him.

6 0

3 years ago

Read 2 more answers

PLEASE HELP! Thank you so much, I’m just a little confused.

Whitepunk [10]

The domain is the values of x from the x-axis that 'cover' the given function.

Look at the end points of the graph and the corresponding values of x on the x-axis. These go from - 5 to 4

Thus the domain is x ∈ [- 5, 4 ] ← domain

The square bracket indicates that the values of - 5 and 4 are included in the domain

Whereas (- 5, 4 ) indicates that - 5 and 4 are not included but all values in between are

The range is the values of y from the y-axis that cover the given function

Look at the minimum value and maximum value of the function along the y-axis

The minimum is 0 and the maximum is 5

range is y ∈ [0, 5 ]

To determine the value of y when x = -3

Locate x = - 3 on the x-axis, move up vertically until the line representing the function is met, and read off the corresponding y value to the right on the y-axis

The value of f(x) when x = - 3 is 2

6 0

3 years ago

Read 2 more answers

Y^2+X^2=36 y=-3x+5.

lesya [120]

Answer:

The two solutions in exact form are:

$(\frac{15+\sqrt{335}}{10},\frac{5-3\sqrt{335}}{10})$

and

$(\frac{15-\sqrt{335}}{10},\frac{5+3\sqrt{335}}{10})$ .

If you prefer to look at approximations just put into your calculator:

$(3.3303,-4.9909)$

and

$(-0.3303,5.9909)$ .

Step-by-step explanation:

I guess you are asked to find the solution the given system.

I'm going to use substitution.

This means I'm going to plug the second equation into the first giving me:

$(-3x+5)^2+x^2=36$ I replaced the 1st y with what the 2nd y equaled.

Before we continue solving this I'm going to expand the $(-3x+5)^2$ using the following:

$(a+b)^2=a^2+2ab+b^2$ .

$(-3x+5)^2=(-3x)^2+2(-3x)(5)+(5)^2$

$(-3x+5)^2=9x^2-30x+25$

Let's go back to the equation we had:

$(-3x+5)^2+x^2=36$

After expansion of the squared binomial we have:

$9x^2-30x+25+x^2=36$

Combine like terms (doing the $9x^2+x^2$ part:

$10x^2-30x+25=36$

Subtract 36 on both sides:

$10x^2-30x+25-36=0$

Simplify the 25-36 part:

$10x^2-30x-11=0$

Compare this to $ax^2+bx+c=0$ which is standard form for a quadratic.

We should see the following:

$a=10$

$b=-30$

$c=-11$

The formula that solves this equation for the variable $x$ is:

$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

Plugging in our values for $a,b, \text{ and } c$ give us:

$x=\frac{30 \pm \sqrt{(-30)^2-4(10)(-11)}}{2(10)}$

Simplify the bottom; that is 2(10)=20:

$x=\frac{30 \pm \sqrt{(-30)^2-4(10)(-11)}}{20}$

Put the inside of square root into the calculator; that is put $(-30)^2-4(10)(-11)$ in the calculator:

$x=\frac{30 \pm \sqrt{1340}}{20}$

Side notes before continuation:

Let's see if 1340 has a perfect square.

I know 1340 is divisible by 10 because it ends in 0.

1340=10(134)

134 is even so it is divisible by 2:

1340=10(2)(67)

1340=2(2)(5)(67)

1340=4(5)(67)

1340=4(335)

4 is a perfect square so we can simplify the square root part further:

$\sqrt{1340}=\sqrt{4}\sqrt{335}=2\sqrt{335}$ .

Let's go back to the solution:

$x=\frac{30 \pm \sqrt{1340}}{20}$

$x=\frac{30 \pm 2 \sqrt{335}}{20}$

Now I see all three terms contain a common factor of 2 so I'm going to divide top and bottom by 2:

$x=\frac{\frac{30}{2} \pm \frac{2 \sqrt{335}}{2}}{\frac{20}{2}}$

$x=\frac{15 \pm \sqrt{335}}{10}$

So we have these two x values:

$x=\frac{15+\sqrt{335}}{10} \text{ or } \frac{15-\sqrt{335}}{10}$

Now we just need to find the corresponding y-coordinate for each pair of points.

I'm going to use the easier equation $y=-3x+5$ .

Let's do it for the first x I mentioned:

If $x=\frac{15+\sqrt{335}}{10}$ then

$y=-3(\frac{15+\sqrt{335}}{10})+5$ .

Let's simplify:

Distribute the -3 to the terms on top:

$y=\frac{-45-3\sqrt{335}}{10}+5$

Combine the two terms; I'm going to do this by writing 5 as 50/10:

$y=\frac{-45-3\sqrt{335}+50}{10}$

Combine like terms on top; the -45+50 part:

$y=\frac{5-3\sqrt{335}}{10}$ .

So one solution point is:

$(\frac{15+\sqrt{335}}{10},\frac{5-3\sqrt{335}}{10})$ .

Let's find the other one for the other x that we got.

If $x=\frac{15-\sqrt{335}}{10}$ then

$y=-3(\frac{15-\sqrt{335}}{10})+5$ .

Let's simplify.

Distribute the -3 on top:

$y=\frac{-45+3\sqrt{335}}{10}+5$

I'm going to write 5 as 50/10 so I can combine the terms as one fraction:

$y=\frac{-45+3\sqrt{335}+50}{5}$

Simplify the -45+50 part:

$y=\frac{5+3\sqrt{335}}{10}$ .

So the other point of intersection is:

$(\frac{15-\sqrt{335}}{10},\frac{5+3\sqrt{335}}{10})$ .

The two solutions in exact form are:

$(\frac{15+\sqrt{335}}{10},\frac{5-3\sqrt{335}}{10})$

and

$(\frac{15-\sqrt{335}}{10},\frac{5+3\sqrt{335}}{10})$ .

If you prefer to look at approximations just put into your calculator:

$(3.3303,-4.9909)$

and

$(-0.3303,5.9909)$ .

3 0

3 years ago