All categories

3 years ago

Drag the point on the coordinate plane to the solution of the system of equations shown below: y=-2x-1 y = x + 2

Mathematics

1 answer:

Sveta_85 [38]3 years ago

3 0

Answer:

(1,-1)

Step-by-step explanation:

-2x-1 = x+2

-3x = 3

x = -1

substitute

y = (-1) + 2

y = 1

point: (1,-1)

You might be interested in

The sum of 4 consecutive even integers is -12. find the largest integer.

Ipatiy [6.2K]

Answer:

The largest even integer is 0

Step-by-step explanation:

Given as :

The sum of four consecutive even number = - 12

Let The first even number = 2 x

The second even number = (2 x + 2)

The third even number = (2 x + 4)

The fourth even number = (2 x + 6)

<u>According to question</u>

sum of four consecutive even number = - 12

Or, 2 x + (2 x + 2) + (2 x + 4) + (2 x + 6) = - 12

Or, (2 x + 2 x + 2 x + 2 x) + (2 + 4 + 6) = - 12

Or, 8 x + 12 = - 12

Or, 8 x = - 12 - 12

Or, 8 x = - 24

∴ x = $\frac{- 24}{8}$

i.e x = - 3

now, putting the value of x

The first even number = 2 × - 3 = - 6

The second even number = (2 × - 3 + 2) = - 6 + 2 = - 4

The third even number = (2 × - 3 + 4) = - 6 + 4 = - 2

The fourth even number = (2 × - 3 + 6) = - 6 + 6 = 0

So, The largest even integer = 0

Hence, The largest even integer is 0 Answer

6 0

3 years ago

6/(x+1)-5/2=6/(3x+3)

jolli1 [7]

If you would like to calculate 6/(x+1)-5/2=6/(3x+3), you can do this using the following steps:

6/(x+1)-5/2=6/(3x+3)
6/(x+1)-5/2=6/(3(x+1)) /*(x+1)
6 - 5/2 * (x+1) = 6/3
6 - 2 = 5/2 * (x+1)
4 = 5/2 * (x+1) /*2/5
4 * 2/5 = x + 1
8/5 - 1 = x
x = 8/5 - 5/5 = 3/5

The correct result would be 3/5.

6 0

3 years ago

How do you find a vector that is orthogonal to 5i + 12j ?

Rashid [163]

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{a}{b}\\\\
slope=\cfrac{a}{{{ b}}}\qquad negative\implies -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\
-------------------------------\\\\$

$\bf \boxed{5i+12j}\implies 
\begin{array}{rllll}
\ \textless \ 5&,&12\ \textgreater \ \\
x&&y
\end{array}\quad slope=\cfrac{y}{x}\implies \cfrac{12}{5}
\\\\\\
slope=\cfrac{12}{{{ 5}}}\qquad negative\implies -\cfrac{12}{{{ 5}}}\qquad reciprocal\implies - \cfrac{{{ 5}}}{12}
\\\\\\
\ \textless \ 12, -5\ \textgreater \ \ or\ \ \textless \ -12,5\ \textgreater \ \implies \boxed{12i-5j\ or\ -12i+5j}$

if we were to place <5, 12> in standard position, so it'd be originating from 0,0, then the rise is 12 and the run is 5.

so any other vector that has a negative reciprocal slope to it, will then be perpendicular or "orthogonal" to it.

so... for example a parallel to <-12, 5> is say hmmm < -144, 60>, if you simplify that fraction, you'd end up with <-12, 5>, since all we did was multiply both coordinates by 12.

or using a unit vector for those above, then

$\bf \textit{unit vector}\qquad \cfrac{\ \textless \ a,b\ \textgreater \ }{||\ \textless \ a,b\ \textgreater \ ||}\implies \cfrac{\ \textless \ a,b\ \textgreater \ }{\sqrt{a^2+b^2}}\implies \cfrac{a}{\sqrt{a^2+b^2}},\cfrac{b}{\sqrt{a^2+b^2}}
\\\\\\
\cfrac{12,-5}{\sqrt{12^2+5^2}}\implies \cfrac{12,-5}{13}\implies \boxed{\cfrac{12}{13}\ ,\ \cfrac{-5}{13}}
\\\\\\
\cfrac{-12,5}{\sqrt{12^2+5^2}}\implies \cfrac{-12,5}{13}\implies \boxed{\cfrac{-12}{13}\ ,\ \cfrac{5}{13}}$

4 0

3 years ago

Find the pattern and use it to list the next two terms in the sequence.

lidiya [134]

Answer:

Step-by-step explanation:

a₁ = -3 = (-1)¹×3

a₂ = 6 = (-1)²×2×3

a₃ = -28 = (-1)³×2²×7

a₄ = 72 = (-1)⁴×2³×3²

a₅ = -360 = (-1)⁵×2³×3²×5

a₆ = 2160 = (-1)⁶×2⁴×3³×5

That's as far as I got. I can predict that a₇ is a multiple of -32 and a₈ is a multiple of 64, but I don't see the pattern with the other factors.

8 0

3 years ago

In 25 minutes li can run 10 .find the constant of proportionality

liq [111]

The constant of proportionality is 2.5

6 0

3 years ago

Drag the point on the coordinate plane to the solution of the system of equations shown below: y=-2x-1 y = x + 2​

Drag the point on the coordinate plane to the solution of the system of equations shown below: y=-2x-1 y = x + 2