Which expression is not equivelent to 8+(n-4)

Which linear equation has a slope of 3 and a y-intercept of -2?

natka813 [3]

Slope-intercept form: y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

You know:

m = 3

b = -2 So substitute/plug it into the equation

y = mx + b

y = 3x + (-2)

y = 3x - 2 Your answer is the 2nd option

7 0

3 years ago

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Find n. Perimeter = 86 in.

LuckyWell [14K]

O_o Whhhhaaaaat?? How does that make sense.

7 0

3 years ago

The smaller of two consecutive even integers is two more than half of the greater. find the two integers.

lana [24]

Greetings and Happy Holidays!

Let x represent the smaller, even integer.
Let (x+2) represent the larger, even integer.

We can create an algebraic equation to solve for the numbers:
$x=\frac{(x+2)}{2}+2$

Simplify:
$x=\frac{1}{2}x+1+2$

$x=\frac{1}{2}x+3$

Add $\frac{-1}{2}x$ to both sides:
$(x)+(\frac{-1}{2}x)=(\frac{1}{2}x+3)+(\frac{-1}{2}x)$

$(\frac{1}{2}x)=3$

Divide both sides by $\frac{1}{2}x$
$\frac{\frac{1}{2}x}{ \frac{1}{2}}=\frac{3}{\frac{1}{2}}$

$x=\frac{3}{1}(2)$

$x=\frac{6}{1}$

The Answer Is:
$\boxed{x=6}$
and
$x+2=6$
$\boxed{x=8}$

The two consecutive even integers are 6 and 8.

I hope this helped!
-Benjamin

8 0

3 years ago

Determine if a triangle with the following vertices is a right triangle explain how you arrived at your answer a(-3,5) b(1,4)c(-

soldier1979 [14.2K]

Step-by-step explanation:

5 0

3 years ago

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If the parent function f(x) = x^2 is fatter translated 11 units to the left, then translated 5 units down, write the resulting f

nikklg [1K]

The quadratic function given by:

$f(x)=a(x-h)^2+k, \ \ \ a\neq 0$

is in vertex form. The graph of $f$ is a parabola whose axis is the vertical line $x=h$ and whose vertex is the point $(h, k)$ . So:

To translate the graph of a function to the right, left, upward or downward we have:

$For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)$

By knowing this things, we can solve our problem as follows:

FIRST.

Translating 11 units to the left:

$g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2$

Then translating 5 units down:

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x+11)^2-5$

Since the new function is fatter, the factor we need to multiply the term $(x+11)^2$ must be less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.

Therefore, the right answer is b. f(x) = 1/2(x + 11)^2 - 5

SECOND.

Translating 8 units to the right:

$g(x)=f(x-8) \\ \\ \therefore g(x)=(x-8)^2$

Then translating 1 unit down:

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x-8)^2-1$

As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.

Therefore, the right answer is a. g(x) = 1/3(x - 8)^2 - 1

7 0

3 years ago