What is the simplified form of the expression 3 + 8x − 2y − x + 1 + 4y? Enter your answers in the boxes.

Mathematics

2 answers:

mamaluj [8]3 years ago

7 0

Answer:

=7x+2y+4

Step-by-step explanation:

djverab [1.8K]3 years ago

5 0

Answer:

7x+2y+4

Step-by-step explanation:

combine like terms:

8x-x=7x

-2y+4y=2y

3+1=4

so the simplified form of the equation is 7x+2y+4

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What is the total number of different routes that a fire

Pavlova-9 [17]

The total number of different routes that a fire truck can travel the m-distance from F to Z = 4 (Option C).

<h3 /><h3>What is a graph?</h3>

A graph refers to a diagram that shows how a variable varies in relation to one or more other variables, such as a collection of points, lines, line segments, curves, or regions.

Now,

Firstly, refer to the graph attached.

The graph can be used to manually calculate the number of routes that lead from F to Z.
F is four m-distances from Z.
Now, manually calculate the m-distance of the path from F to Z using the 4 boxes that represent it. We discover 6 distinct pathways, each with an m-distance of 4.

Hence, The total number of different routes that a fire truck can travel the m-distance from F to Z = 4 (Option C).

To learn more about graphs, refer to the link: brainly.com/question/4025726

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4 0

1 year ago

Find the exact value of x.

PolarNik [594]

Answer:

$x = 4 \sqrt{3}$

Step-by-step explanation:

$\frac{8}{2} = 4 \\ 4 \times \sqrt{3} = 4 \sqrt{3}$

7 0

3 years ago

[Will mark as brainliest]

Aleks04 [339]

The answer is: $f^{-1} = 4x^2-3,\quad\text{for } x \leq 0$

The inverse of a function $f(x)$ is another function, $f^{-1}(x)$ , with the following property:

$f(f^{-1}(x)) = f^{-1}(f(x)) = x$

In other words, the inverse of a function does exactly "the opposite" of what the original function does, and so if you compute them both in sequence you return to the starting point.

Think for example to a function that doubles the input, $f(x)=2x$ , and one that halves it: $f(x)= \frac{x}{2}$ . Their composition is clearly the identity function $f(x)=x$ , since you consider "twice the half of something", or "half the double of something".

In general, to invert a function $y=f(x)$ , you have to solve the expression for $x$ , writing an expression like $x = g(y)$ . If you manage to do so, then $g$ is the inverse of $f$ .

In your case, you have

$f(x) = y = -\frac{1}{2}\sqrt{x+3}$

Multiply both sides by $-2$ to get

$-2y = \sqrt{x+3}$

Square both sides to get

$4y^2 = x+3$

Finally, subtract 3 from both sides to get

$x = 4y^2 - 3$

Since the name of the variables doesn't really have a meaning, you can say that the inverse function is

$f^{-1}(x) = 4x^2 - 3$

As for the domain of the inverse function, remember what we said ad the beginning: if the original function goes from set A (domain) to set B (codomain), then the inverse function goes from set B (domain) to set A (codomain). This means that the inverse function is defined on an element in B if and only if that element belongs to the range of the original function, i.e. the set of the elements of the codomain $b \in B$ such that there exists $a \in A : f(a)=b$ . So, we need the range of $f(x)$ .

We know that the range of $g(x)=\sqrt{x}$ is $[0,\infty)$ . When you transform it to $g(x)=\sqrt{x+3}$ you simply translate the graph horizontally, so the range doesn't change. But when you multiply the function times $-\frac{1}{2}$ you affect both extrema of the range, turning it into $(-\infty,0]$ , which you can simply write as $x \leq 0$