Bank service charges are automatically deducted from the bank account, why are these recorded in the cash payments journal

Determine the point that lies on the equation y = -5x - 3.

scZoUnD [109]

Answer:

(4, -23)

Step-by-step explanation:

We are given;

The equation, y = -5x -3

We are needed to determine the point that lies on the equation;

We need to know that for a point to be lying on the equation it must satisfy the equation.
This means when we use the value of x in the equation we should get the exact value of y of the given point;

Therefore, in this case;

Point (4, -23)

Replacing x = 4 in the equation;

y = -5(4) - 3

= -23

Therefore, the point lies on the equation as the point satisfies the equation

Thus, the required point is (4, -23)

8 0

2 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 $x \leq 0$

4 0

2 years ago

On the coordinate plane below, Point P, is located at (2,-3) and point Q is located at (-4,4). Find the distance between points,

marishachu [46]

Answer:

approximately 9.2195

Step-by-step explanation:

We can use Pythagorean theorem

one leg is 7 and the other leg is 6

square them

49 and 36

add

85

square root

approximately 9.2195

4 0

2 years ago

using approximations to 1 significant figure, estimate the value of 9.94² × 29.7 you must show your working

zvonat [6]

Answer:

2934.5

Step-by-step explanation:

2934.46692 Rounded to 1 Sig Fig is 2934.5

4 0

3 years ago

Three consecutive odd intergers have a sum of 27. find the integers

Misha Larkins [42]

Solve for x:
x + (x + 2) + (x + 4) = 27
3x + 6 = 27
3x = 27 - 6
3x = 21
3x / 3 = 21 / 3
x = 7
The integers:
x + (x + 2) + (x + 4) = 27
7 + (7 + 2) + (7 + 4) = 27
7 + 9 + 11 = 27
27 = 27

The integers are 7, 9 , 11

6 0

2 years ago