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Montano1993 [528]
2 years ago
6

What is the quotient of −42 and −6?

Mathematics
2 answers:
IrinaVladis [17]2 years ago
7 0

The quotient is 7 (not negative as two negative numbers will cancel)

Black_prince [1.1K]2 years ago
4 0

Answer:

7

Step-by-step explanation:

Two negatives cancel out, so you divide just like normal 42÷6 is 7

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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, <em>f</em> and <em>g</em> are inverses, then:

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

So, we can let <em>j</em> be the inverse function of <em>h</em>.

Function <em>h</em> is given by:

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

Find its inverse. Flip variables:

x = 3y - 2

Solve for <em>y. </em>Add:

\displaystyle x + 2 = 3y

Hence:

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

Therefore, <em>a</em> = 1/3 and <em>b</em> = 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
2 years ago
What is the area of a sheet of binder paper? (Binder paper is 8 1/2 inches by 11 inches.)
11Alexandr11 [23.1K]
Area of a rectangle is the product of length times width.  Thus, here we need the product of 8 1/2 inches by 11 inches.

One way of doing this follows:            8.5
                                                         8.5
                                                       ----------         
                                                         93.5 square inches

Rounding up, this comes out to 94 square inches.

Alternatively:     17             187
                         ---- * 11 = ------- = 93.5 square inches; rounded, that's 94.
                           2                 2
3 0
3 years ago
Hi what isthe answer
REY [17]

Answer:

2x^7

Step-by-step explanation:

2x^4 × x^3 =

= 2x^(4+3)

= 2x^7

8 0
3 years ago
Write an addition equation that can help you find 9 - 6. Explain your answer
vfiekz [6]
9 - 6 = 3
so 3 + 6 = 9  which is an addition equation that helps you find the answer. 

6 0
3 years ago
Read 2 more answers
Describe the solution of g(x) shown in the graph.
Ugo [173]

Answer:

All real solutions

Step-by-step explanation:

  • The given graph is a maximum quadratic function.
  • The solution to the graph is where the graph intersects the x-axis.
  • We can see from the graph that, the function intersected the x-axis at two different points, hence its discriminant is greater than zero.
  • Hence the solution of g(x) are two distinct real solutions.
  • The solutions are not whole numbers because the x-intercepts are not exact.
  • The solutions are also not all points that lie on g(x)
  • The first choice is correct.
3 0
3 years ago
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