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2 years ago

Solve the system of equations

Mathematics

1 answer:

Solnce55 [7]2 years ago

5 0

Hey, there!!

Given that:

y = 3x.........(i)

$y = {x}^{2} + 3x - 16.......(ii)$

Putting the value of y in equation (ii)

${3x}^{} = {x}^{2} + 3x - 16$

${x }^{2} - 16$ =0

$( {x)}^{2} - {4}^{2} = 0$

$(x + 4)(x - 4) = 0$

Therefore,

Either Or

(x+4)=0 (x-4)=0

x= -4 x= 4

so, x= (+ -)4

And if you wanna get value of y, just keep value of x in equation (i).

y= 3x

y= (3×4) or (3×-4)

y= 12 or -12

{As it is the quadratic equation it has two values. }

Hope it helps....

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anygoal [31]

Answer:

It would be the second option

Step-by-step explanation:

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2 years ago

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MariettaO [177]

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2 years ago

In triangle HJK shown above what is the measure of ∠J in degrees

ludmilkaskok [199]

Angles in a triangle adds up to 180

180 - (25.5 +120.2) = 34.3

So, missing angle is 34.3 degrees

Hope this helps!

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2 years ago

Use the discriminant to describe the roots of each equation. Then select the best description.

Marrrta [24]

Let's find the discriminant of x^2+9x+14=0. Here, a=1, b=9 and c=14.

The discriminant is b^2-4ac. Substituting the above numeric values,
9^2-4(1)(14) = 81-56 = 25

The sqrt of 25 is 5. Thus, your polynomial has two unequal, real roots.

Off the point example: If the discriminant were zero, your poly would have two real, equal roots.

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3 years ago

42. Which matrix represents the image of the triangle with vertices at (-2,0), (1,5), and (4,-8) when dilated by a scale factor

jasenka [17]

The second matrix $\left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right]$ represents the triangle dilated by a scale factor of 3.

Step-by-step explanation:

Step 1:

To calculate the scale factor for any dilation, we divide the coordinates after dilation by the same coordinated before dilation.

The coordinates of a vertice are represented in the column of the matrix. Since there are three vertices, there are 2 rows with 3 columns. The order of the matrices is 2 × 3.

Step 2:

If we form a matrix with the vertices (-2,0), (1,5), and (4,-8), we get

$\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right]$

The scale factor is 3, so if we multiply the above matrix with 3 throughout, we will get the matrix that represents the vertices of the triangle after dilation.

Step 3:

The matrix that represents the triangle after dilation is given by

$3\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right] = \left[\begin{array}{ccc}3(-2)&3(1)&3(4)\\3(0)&3(5)&3(-8)\end{array}\right] = \left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right]$

This is the second option.

4 0

2 years ago

Solve the system of equations​

Solve the system of equations