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4 years ago

The system of equations is coincident.What are the missing values?

Mathematics

1 answer:

telo118 [61]4 years ago

7 0

Coincident lines are lines that are the same.

In the beginning of both equations we have '4x' and '8x'.

Note that 8 / 4 = 2.

Multiply the rest of the numbers in the first equation by 2.

5y * 2 = 10y

8 * 2 = 16

So our 2nd line will be:

8x + 10y = 16

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Simplify (39x+54y)+(46x-28y)

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4 years ago

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At a baseball game, a vender sold a combined total of 170 sodas and hot dogs. the number of hot dogs sold was 50 less than the n

Juliette [100K]

Let the number of sodas sold be x and the number of hotdogs sold be y. We can assemble a system of equations from the information given and solve.

x+y=170 (We know that soda + dogs is 170)

x-50=y (We know that dogs is equal to 50 less than sodas)

We can use substitution to solve this system of equations.

x+y=170

Sub in the value of y from the second equation

x+(x-50)=170

2x-50=170

2x=220

x=110

We now know the number of sodas sold was 110. Lets now plug this value into the equation to solve for y.

x+y=170

110+y=170

y=60

So, there were 60 hotdogs sold and 110 sodas sold.

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3 years ago

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nikitadnepr [17]

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6 0

3 years ago

Find the equation for the plane that contains the line x=−1+3t , y=1+2t, z=2+4t and is perpendicular to the plane containing the

Ivan

Let $L$ be the line given by the vector equation

$(-1,1,2) + \lambda(3,2,4) \ , \lambda \in \mathbb{R}$ .

First, we use the director vectors of the lines L1 and L2 to get the

vector equation of the plane containing them, which we denote by $\Pi_1$ . This is,

$\\\\\Pi_1 : (1,-1,5) + \alpha (2,-1,6) + \beta (1,1,-3) \ , \alpha, \beta \in \mathbb{R}\\\\\\$

We observe that $\vec{N} = (2,-1,6)\times(1,1,-3) = (-3,12,3) \ne (0,0,0)$ . Therefore, the vector equation of $\Pi_1$ defines a plane and $\vec{N}$ is a normal vector to $\Pi_1.$

Finally, the vector equation for the wanted plane, which we denote by $\Pi$ , is

$\Pi : (-1,1,2) + r(3,2,4) + s(-3,12,3), r,s \in \mathbb{R} \ .$

Thus, if $s = 0$ , then $L \subset \Pi$ and since $\vec{N}$ is parallel to $\Pi$ , then it is perpendicular to $\Pi_1$ .

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3 years ago

How to solve 2x+12 when x=-14

MariettaO [177]

If x = -14, substitute the x back into the equation.

so now the equation is 2(-14) + 12. multiply the 2 by -14 first to get -28 + 12.
add those two together to get -16. hope this helps!

6 0

3 years ago