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Lelechka [254]
3 years ago
6

4. which ordered pair is a solution of the equation y=5x?

Mathematics
2 answers:
igor_vitrenko [27]3 years ago
7 0
Plug the ordered pairs into the equation. The first number represents x, the second number y. The answer is D. -10=5(-2)
andrezito [222]3 years ago
3 0

Answer:

The answer is d. (-2,-10)

Step-by-step explanation:

In order to determine which ordered pair is a solution of the equation, we have to understand that if we replace the variables into values, the equality must remain. The first value of the ordered pair represents the "x" variable and the second value represents the "y" variable.

So, for every option:

a)

x=-2\\y=10\\\\y=5*x\\10=5*(-2)\\10=-10

There is NOT equality

b)

x=-5\\y=25\\\\y=5*x\\25=5*(-5)\\25=-25

There is NOT equality

c)

x=-3\\y=15\\\\y=5*x\\15=5*(-3)\\15=-15

There is NOT equality

d)

x=-2\\y=-10\\\\y=5*x\\-10=5*(-2)\\-10=-10

There is equality

Finally, the only ordered pair that fulfill the equality is (-2,-10)

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Answer:

\displaystyle f(x)=-\frac{1}{2}(x+1)^2+6

Step-by-step explanation:

We want to write the equation for a quadratic function in vertex form with vertex at (-1, 6) that passes through the point (-3, 4).

Vertex form is given by:

\displaystyle f(x)=a(x-h)^2+k

Where (<em>h, k</em>) is the vertex and <em>a</em> is the leading coefficient.

Since our vertex is at (-1, 6), <em>h</em> = -1 and <em>k</em> = 6. Substitute:

f(x)=a(x-(-1))^2+(6)

Simplify:

f(x)=a(x+1)^2+6

Next, since the quadratic passes through the point (-3, 4), f(x) = 4 when <em>x</em> = -3. Substitute:

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Solve for <em>a</em>. Simplify:

-2=a(-2)^2

Hence:

\displaystyle -2=4a\Rightarrow a=-\frac{1}{2}

Therefore, our function in vertex form is:

\displaystyle f(x)=-\frac{1}{2}(x+1)^2+6

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