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Ilia_Sergeevich [38]
3 years ago
5

Traveling from Atlanta, Georgia to Orlando, Florida is about 550 miles. Jen traveled 338 miles yesterday and the rest today. Whi

ch equation expresses how many miles she drove today?
Mathematics
1 answer:
Alexxx [7]3 years ago
7 0

Answer:

x + 338 = 550

Step-by-step explanation:

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A line joins the point
Harrizon [31]

Intersection of the first two lines:

\begin{cases}5x - 2y + 3 = 0\\4x - 3y + 1 = 0\end{cases}

Multiply the first equation by 4 and the second by 5:

\begin{cases}20x - 8y + 12 = 0\\20x - 15y + 5 = 0\end{cases}

Subtract the two equations:

(20x - 8y + 12)-(20x - 15y + 5)=0 \iff 7y+7=0 \iff y=-1

Plug this value for y in one of the equation, for example the first:

5x - 2\cdot (-1) + 3 = 0\iff 5x+5=0 \iff x=-1

So, the first point of intersection is (-1,-1)

We can find the intersection of the other two lines in the same way: we start with

\begin{cases}x=y\\x=3y+4\end{cases}

Use the fact that x and y are the same to rewrite the second equation as

x=3x+4 \iff 2x=-4 \iff x=-2

And since x and y are the same, the second point is (-2, -2)

So, we're looking for a line passing through (-1,-1) and (-2, -2). We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be y=x

In the attached figure, line 5x - 2y + 3 = 0 is light green, line 4x - 3y + 1 = 0 is dark green, and their intersection is point A.

Simiarly, line x=y is red, line x = 3y + 4 is orange, and their intersection is B.

As you can see, the line connecting A and B is the red line itself.

5 0
3 years ago
Translate into an equation or inequality to solve: Two more than twice the sum of a number and 12 is greater than the difference
tamaranim1 [39]
Let say the number is 0.5
Then, sum of this number will be 0.5+0.5=1
Now two is twice of 1.
Hence, it proved to be correct.
And difference between 5 and 1 is 4 which is less than 12. It also match the question condition.

Answer: The number is 1.
3 0
2 years ago
Find the volume of the rectangular prism below. Answer as a mixed number not a decimal.
dangina [55]

Answer:

242 2/3in^3

Step-by-step explanation:

The formula is l*w*h. So if you multiply all of them you'll get  242 2/3.

4 0
3 years ago
The length of a rectangle is 1.2 × 10-4 kilometer. the width of the rectangle is 6.25 × 10-5 kilometer.what is the area in squar
Serhud [2]
We have 1.2 × 10^(-4)  x 6.25 × 10^(-5 )  = 7,5 x 10^(-9) = 75 x 10^(-10) square kilometers.
3 0
3 years ago
Gustavo and yuki were asked to find an explicit formula for the sequence 19, 0, -19, -38...
KiRa [710]

Answer:

<h2>Neither Gustavo nor Yuki</h2>

Step-by-step explanation:

It's an arithmetic sequence.

0-19=-19\\-19-0=-19\\-38-(-19)=-38+19=-19

The difference is constant.

The explicit formula of an arithmetic sequence:

a_n=a_1+(n-1)d

Substitute:

a_1=19,\ d=-19

a_n=19+(n-1)(-19)             <em>use distributive property</em>

a_n=19-19n+19\\\\a_n=(19+19)-19n\\\\a_n=38-19n

4 0
3 years ago
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