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2 years ago

2(z+5) +5(z+ 2) = 10(z − 1)

Mathematics

1 answer:

Jlenok [28]2 years ago

4 0

Answer:

z = 10

Step-by-step explanation:

First apply multiplication to inside the parenthesis:

2(z+5) = 2z + 10

5(z+ 2) = 5z + 10

10(z − 1) = 10z - 10 now write the full equation

2z + 10 + 5z + 10 = 10z - 10 add like terms

7z + 20 = 10z - 10 transfer like terms to the same side of the equation

20 + 10 = 10z - 7z

30 = 3z divide both sides by 3

10 = z

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Which math function describes the following situation?

MissTica

This is the concept of inequality;
We are told that the distance a car travels depends on how full gas tank is, this means that the car will travel until the point when gasoline is finished. Thus,
This mean that if the if the distance is given by the function f(x), x will be the gasoline since it is the dependent variable, liters this in other words can be written as (if the tank holds 89 ):

f(x)=distance(gasoline)<89

thus the correct answer will be:

B] Distance (amount of gasoline) < 89

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3 years ago

What are the factors of 3x2 + 10x + 8?

DaniilM [7]

(3x+4) (x+2)
This gives you 3x^2 + 6x + 4x + 8
Which simplifies to 3x^2 + 10x + 8

4 0

3 years ago

Miche found that most helicopters fly at speeds of less than 270 kilometers per hour. Her work is shown below. s > 270 A numb

almond37 [142]

Answer:

The inequality should be s<270.
The number line should be shaded to the left.

Step-by-step explanation:

Miche found that most helicopters fly at speeds of less than 270 kilometers per hour.

If s=speed of the helicopters

Then: s<270

Representing this on a number line:

We have an open circle at 270.

Everything to the left of the circle is shaded.

Since the options are not given, I would list the mistakes made by Miche.

The inequality should be s<270.
The number line should be shaded to the left.

6 0

3 years ago

Which is the equation of a hyperbola centered at the origin with y-intercepts +12 -12, and asymptote y=3x/2

dangina [55]

Answer:

$\frac{y^2}{144}-\frac{x^2}{64}=1$

Step-by-step explanation:

The equation of a hyperbola centered at the origin with vertices on the y-axis is given by: $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$

The vertices of the hyperbola are the y-intercepts (0,12) and (0,-12)

This implies that:

$2a=|12--12|$

$2a=24$

$a=12$

The asymptote equation of a hyperbola is given by:

$y=\pm\frac{a}{b}x$

The given hyperbola has asymptote: $y=\pm\frac{3}{2} x$

By comparison; $\frac{a}{b}=\frac{3}{2}$

$\implies \frac{12}{b}=\frac{12}{8}$

$\implies b=8$

The required equation is:

$\frac{y^2}{12^2}-\frac{x^2}{8^2}=1$

$\frac{y^2}{144}-\frac{x^2}{64}=1$

6 0

3 years ago

Read 2 more answers

How do I do functions

choli [55]

Explanation:

It depends on what you want to do. The topic of functions is easily a semester course in algebra, at least.

A function is a relation that maps an input to a single output. Common representations are ...

list of ordered pairs
table
graph
equation

Functions sometimes take multiple inputs to generate a given output.

Often, one of the first things you're concerned with is whether a given relation is a function. It is not a function if a given input maps to more than one output.

We say a relation passes the vertical line test when a vertical line through its graph cannot intersect the graph in more than one point. Such a relation is a function.

When a function is written in equation form, it is often given a name (usually from the (early) middle of the alphabet. Common function names are f, g, h. Any name can be used.

When a function is defined by an equation, the variables that are inputs to the function are usually listed in parentheses after the function name:

f(x), g(a, b), h(m)

These variables show up in the function definition that follows the equal sign:

f(x) = 3x -4

g(a, b) = (1/2)a·b

h(m) = 1/(m^3 +3) +5

The listed variable is called the "argument" of the function.

This sort of form of an equation is sometimes called "functional form." That is, a dependent variable, such as y, can be defined by ...

y = 3x +4

or the same relation can be written in functional form as ...

f(x) = 3x +4

Sometimes students are confused by this notation, thinking that f(x) means the product of f and x. Yes it looks like that, but no, that's not what it means.

One of the first things we like to do with functions is evaluate them. This means we put a particular value wherever the variable shows up.

If we want to evaluate the above f(x) for x=2, we put 2 (every)where x is:

f(x) = 3·x -4

f(2) = 3·2 -4 = 6 -4 = 2

We can evaluate the function for literals, also.

f(a) = 3a -4

f(x+h) = 3(x+h) -4 = 3x +3h -4 . . . here, h is a variable, not the function name

We can add, subtract, multiply, divide functions, and we can compute functions of functions. The latter is called a "composition", and is signified by a centered circle between the function names.

Add functions: f(x) +h(x) = (3x +4) +(1/(x^3 +3) +5)

also written as (f+h)(x)

Subtract functions: f(x) -h(x) = (3x +4) -(1/(x^3 +3) +5)

also written as (f-h)(x)

Multiply functions: f(x)·h(x) = (3x +4)(1/(x^3 +3) +5)

also written as (f·h)(x) or (fh)(x)

Divide functions: h(x)/f(x) = (1/(x^3 +3) +5)/(3x +4)

also written as (h/f)(x)

Function of a function (composition): f(h(x)) = f(1/(x^3 +3) +5) = 3(1/(x^3 +3) +5) +4

also written as (f∘h)(x) . . . . . the symbol ∘ is called a "ring operator". Sometimes a lower-case 'o' is used in plain text. It is not a period or dot or zero or degree symbol. Note the sequence of names means function f operates on the result of function h.

As with other function evaluations, the inner parentheses are evaluated first, and that result is then used as the argument of the outer function.

Because a function name can stand for an algebraic expression of arbitrary complexity, we often use a function name to talk about the properties of expressions in general.

For example, if we want to reflect the graph of the function y = f(x) over the x-axis, we want to change the sign of every y-value. We can use function notation to write that idea as ...

y = -f(x) . . . . . f(x) reflected over the x-axis

The attached graph shows an example using the above function h(m).

4 0

3 years ago