List 3 values that would make this inequality true. Y-30<43

Mathematics

1 answer:

Anna11 [10]3 years ago

4 0

Answer:

72.999999, 0, -10000234

Step-by-step explanation:

y-30 < 43

y < 73

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Please help!! this is algebra 2

sveta [45]

Answer: The last one bc it the same thing!

Step-by-step explanation: one 5/3 is the exact same as 5/3! and for the last one says -5/3

It would be the last one!

3 0

3 years ago

There are 363 students at Meadowbrook High School. There are 10 more

saveliy_v [14]

First, put each grade in terms of x. Most grades are compared to Sophomores, so I made that x

Freshmen = x + 10
Sophomores = x
Juniors = x + 20
Seniors = (x + 10) + 7 = x + 17

Then, the total number of students = 363, so we’ll make an equation that adds them all up in terms of x to equal 363

(x + 10) + x + (x + 20) + (x + 17) = 363

Combine like terms:
4x + 47 = 363
Subtract 47 from both sides:
4x = 316
Divide both sides by 4:
x = 79

The question was how many seniors there are. Seniors were x + 17, so 79 + 17 = 96

4 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 $x \leq 0$