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4 years ago

−3(x + 3) = −3(x + 1) − 5

Mathematics

1 answer:

g100num [7]4 years ago

4 0

Expand:

-3x - 9 = -3x - 3 - 5

Simplify:

-3x - 9 = -3x - 8

Add 3x to both sides:

-9 = -8

THERE IS NO VALUE FOR X THAT MAKES THIS EQUATION TRUE

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23+52+34+61+300=470 52/470=11.06%

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3 years ago

Read 2 more answers

Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))

sergejj [24]

Answer:

$\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}$

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:

$\displaystyle f(g(x)) = g(f(x)) = x$

So, we can let j be the inverse function of h.

Function h is given by:

$\displaystyle h(x) = y = 3x-2$

Find its inverse. Flip variables:

$x = 3y - 2$

Solve for y. Add:

$\displaystyle x + 2 = 3y$

Hence:

$\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}$

Therefore, a = 1/3 and b = 2/3.

We can verify our solution:

$\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}$

And:

$\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}$

3 0

3 years ago

If the length of AC equals 18, what is the length of the midsection DE

Free_Kalibri [48]

Answer:

The length of the midsegment is 9 ⇒ (B)

Step-by-step explanation:

In a triangle,

The midsegment is the segment which joining the midpoints of two opposite sides of it

The length of the midsegment is half the length of the third side in the triangle which opposite to it

Let us use this rule to solve our question

In Δ AC

∵ DE is the midsegment of it

∵ DE is opposite to the side AC

∴ The length of DE = 1/2 the length of AC

∵ The length of AC = 18

∴ The length of DE = 1/2 × 18

∴ The length of DE = 9

∴ The length of the midsegment is 9

The correct answer is B

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Answer:

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Answer:

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