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3 years ago

Select the statement that describes the expression 5 x (8 − 5) ÷ 3.

Mathematics

1 answer:

lys-0071 [83]3 years ago

8 0

Step-by-step explanation:

Substitution: ‘Find the value of 2x + 3 if x = 4.’ In this case the pronumeral is given the value 4.

Solving an equation: ‘Find x if 2x + 3 = 8.’ Here we are seeking the value of the pronumeral that makes the sentence true.

Identity: ‘The statement of the commutative law: a + b = b + a.’ Here a and b can be any real numbers.

Formula: ‘The area of a rectangle is A = lw.‘ Here the values of the pronumerals are connected by the formula.

Equation of a line or curve: ‘The general equation of the straight line is y = mx + c.’

Here m and c are parameters. That is, for a particular straight line, m and c are fixed.

In some languages other than English, one distinguishes between ‘variables’ in functions and ‘unknown quantities’ in equations (‘incógnita’ in Portuguese/Spanish, ‘inconnue’ in French) but this does not completely clarify the situation. The terms such as variable and parameter cannot be precisely defined at this stage and are best left to be introduced later in the development of algebra.

An algebraic expression is an expression involving numbers, parentheses, operation signs and pronumerals that becomes a number when numbers are substituted for the pronumerals. For example 2x + 5 is an expression but +) × is not.

Examples of algebraic expressions are:

3x + 1 and 5(x2 + 3x)

As discussed later in this module the multiplication sign is omitted between letters and between a number and a letter. Thus substituting x = 2 gives

3x + 1 = 3 × 2 + 1 = 7 and 5(x2 + 3x) = 5(22 + 3 × 2) = 30.

In this module, the emphasis is on expressions, and on the connection to the arithmetic that students have already met with whole numbers and fractions. The values of the pronumerals will therefore be restricted to the whole numbers and non-negative fractions.

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I’m confused on this one

Colt1911 [192]

Call M the midpoint. The coordinate of this point is given by....

M=(x1+x2 /2, y1+y2 /2)

So (3,7)=(x1+0 /2, y1+ -5 /2). or

3= x1/2. or x1=6 and

7=y1-5 /2. or 14=y1-5 or y1=19

B is at the point (6,19)

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3 years ago

Number sequences 2, 12, 72, 432, 2592.... is it arithmetic, geometric, or neither?

abruzzese [7]

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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 $x \leq 0$

4 0

3 years ago

If y varies directly as x, and y=8 when x=3, find y when x=15.

Crank

Answer:

y=40

Step-by-step explanation:

The formula for Direct Variation is y=kx or k=y/x. In this case I would use k=y/x. If you're y is 8 and x is 3, this means that K=8/3. Using this, we know that X=15. We have to find a Y value so that the fraction with an x of 15 simplified is 8/3. To do this you would write 8/3 and y/15. Now cross multiply to get 3y=120. Divide by 3 to get y=40. View my attachment for the work!

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kenny6666 [7]

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