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3 years ago

If −15 + 3x = −7 + 5x, then 6x =_____?

Mathematics

2 answers:

Nadya [2.5K]3 years ago

8 0

Answer:

$- 15 + 3x = - 7 + 5x \\ 3x - 5x = - 7 + 15 \\ - 2x = + 8 \\ - x = 4 \\ x = - 4 \\ therefore = \\ 6x = 6 \times ( - 4) \\ 6x = - 24 \\ i \: hope \: this \: was \: helpful$

vazorg [7]3 years ago

4 0

Answer:

-15+3x=-7+5x

-15+7=5x-3x

-8=2x

-8/2=x

-4=x

6x=6*-4

=-24

Step-by-step explanation:

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Let f(x) = tan(x) - 2/x. Let g(x) = x^2 + 8. What is f(x)*g(y)?

Tema [17]

Answer:

$f(x)\times g(y)=y^2tan(x)+8tan(x)-\frac{2y^2}{x}-\frac{16}{x}$

Step-by-step explanation:

We are given that

$f(x)=tan(x)-\frac{2}{x}$

$g(x)=x^2+8$

We have to find $f(x)\times g(y)$

To find the value of $f(x)\times g(y)$ we will multiply f(x) by g(y)

$g(y)=y^2+8$

Now,

$f(x)\times g(y)=(tanx-\frac{2}{x})(y^2+8)$

$f(x)\times g(y)=tan(x)(y^2+8)-\frac{2}{x}(y^2+8)$

$f(x)\times g(y)=y^2tan(x)+8tan(x)-\frac{2y^2}{x}-\frac{16}{x}$

Hence,

$f(x)\times g(y)=y^2tan(x)+8tan(x)-\frac{2y^2}{x}-\frac{16}{x}$

5 0

3 years ago

PLEASE HELP 100 POINTS!!!!!!

horrorfan [7]

Answer:

A) See attached for graph.

B) (-3, 0) (0, 0) (18, 0)

C) (-3, 0) ∪ [3, 18)

Step-by-step explanation:

Piecewise functions have <u>multiple pieces</u> of curves/lines where each piece corresponds to its definition over an <u>interval</u>.

Given piecewise function:

$g(x)=\begin{cases}x^3-9x \quad \quad \quad \quad \quad \textsf{if }x < 3\\-\log_4(x-2)+2 \quad \textsf{if }x\geq 3\end{cases}$

Therefore, the function has two definitions:

$g(x)=x^3-9x \quad \textsf{when x is less than 3}$

$g(x)=-\log_4(x-2)+2 \quad \textsf{when x is more than or equal to 3}$

When <u>graphing</u> piecewise functions:

Use an open circle where the value of x is <u>not included</u> in the interval.
Use a closed circle where the value of x is <u>included</u> in the interval.
Use an arrow to show that the function <u>continues indefinitely</u>.

<u>First piece of function</u>

Substitute the endpoint of the interval into the corresponding function:

$\implies g(3)=(3)^3-9(3)=0 \implies (3,0)$

Place an open circle at point (3, 0).

Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.

<u>Second piece of function</u>

Substitute the endpoint of the interval into the corresponding function:

$\implies g(3)=-\log_4(3-2)+2=2 \implies (3,2)$

Place an closed circle at point (3, 2).

Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attached for graph.

The x-intercepts are where the curve crosses the x-axis, so when y = 0.

Set the <u>first piece</u> of the function to zero and solve for x:

$\begin{aligned}g(x) & = 0\\\implies x^3-9x & = 0\\x(x^2-9) & = 0\\\\\implies x^2-9 & = 0 \quad \quad \quad \implies x=0\\x^2 & = 9\\\ x & = \pm 3\end{aligned}$

Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.

Set the <u>second piece</u> to zero and solve for x:

$\begin{aligned}\implies g(x) & =0\\-\log_4(x-2)+2 & =0\\\log_4(x-2) & =2\end{aligned}$

$\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b$

$\begin{aligned}\implies 4^2&=x-2\\x & = 16+2\\x & = 18 \end{aligned}$

Therefore, the x-intercept for the second piece is (18, 0).

So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).

From the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.

Interval notation: (-3, 0) ∪ [3, 18)

Learn more about piecewise functions here:

brainly.com/question/11562909

3 0

2 years ago

Please help

Montano1993 [528]

Answer:

M = 2x² - (ax/3) + by

B = - 3x²y + (xy³/3) - cy

Step-by-step explanation:

Equation 1 is

2x² - (1/3)ax + by - M = 0

M = 2x² - (ax/3) + by

Equation 2

3x²y - (1/3)xy³ + cy + B = 0

B = - 3x²y + (xy³/3) - cy

Hope this Helps!!!

7 0

3 years ago