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Veronika [31]
3 years ago
15

I don’t understand how to do this

Mathematics
2 answers:
neonofarm [45]3 years ago
8 0

Answer:

y = 8x + 0

Step-by-step explanation:

y = mx + b

m is slope

slope = change in y / change in x = (24 - 8) / (3 - 1) = 16/2 = 8

so equation is now y = 8x + b

Substitute any coordinate from the table to find b. let's use (1,8)

y = 8x + b

8 = 8(1) + b

0 = b

So equation is y = 8x + 0

il63 [147K]3 years ago
5 0
Answer is ; y= 8x + 0
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the length of a rectangle is 4in more than its width, and its perimeter is 34in find the length and width of the rectangle ​
Anna [14]

Let l and w be, respectively, the length and the width of the rectangle.

If the length is 4 inches more than the width, we have

l = w+4

Moreover, the perimeter of a rectangle is given by

2(l+w)

And we can substitute l=w+4 to get

2(w+4+w)=2(2w+4)=4w+8

We know that the perimeter is 34 inches:

4w+8=34 \iff 4w = 26 \iff w = \dfrac{26}{4}=6.5

Which implies

l=w+4=6.5+4=10.5

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Y - 2 = -4/3 ( x + 6)
Vikentia [17]
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3 years ago
Explain the steps to finding the vertex of g(x) = 3x2 + 12x + 15
RUDIKE [14]

Answer:

The vertex of this parabola, (-2, 3), can be found by completing the square.

Step-by-step explanation:

The goal is to express this parabola in its vertex form:

g(x) = a\, (x - h)^2 + k,

where a, h, and k are constants. Once these three constants were found, it can be concluded that the vertex of this parabola is at (h,\, k).

The vertex form can be expanded to obtain:

\begin{aligned}g(x)&= a\, (x - h)^2 + k \\ &= a\, \left(x^2 - 2\, x\, h + h^2\right) + k = a\, x^2 - 2\, a\, h\, x + \left(a\,h^2 + k\right)\end{aligned}.

Compare that expression with the given equation of this parabola. The constant term, the coefficient for x, and the coefficient for x^2 should all match accordingly. That is:

\left\lbrace\begin{aligned}& a = 3 \\ & -2\,a\, h = 12 \\& a\, h^2 + k = 15\end{aligned}\right..

The first equation implies that a is equal to 3. Hence, replace the "a\!" in the second equation with 3\! to eliminate \! a:

(-2\times 3)\, h = 12.

h = -2.

Similarly, replace the "a" and the "h" in the third equation with 3 and (-2), respectively:

3 \times (-2)^2 + k = 15.

k = 3.

Therefore, g(x) = 3\, x^2 + 12\, x + 15 would be equivalent to g(x) = 3\, (x - (-2))^2 + 3. The vertex of this parabola would thus be:

\begin{aligned}&(-2, \, 3)\\ &\phantom{(}\uparrow \phantom{,\,} \uparrow \phantom{)} \\ &\phantom{(}\; h \phantom{,\,} \;\;k\end{aligned}.

8 0
3 years ago
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