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3 years ago

Write each decimal as a fraction or mixed number in simplest form.

Mathematics

2 answers:

Andrews [41]3 years ago

7 0

Answer:

x = $\frac{325}{999}$

Step-by-step explanation:

Step-by-step explanation:

0.325325325...

1000x = 325.325...

- x - 0.325..

999x = 325

x = 325/999

x = $\frac{325}{999}$

Gnesinka [82]3 years ago

5 0

Answer:

Answer:

$0.{ \bar{325}} = \frac{325}{999 } \\$

Step-by-step explanation:

$1000x = { \boxed{325.325}} \\ - x = { \boxed{0.325325}}$

if we subtract:

$= 999x = 324.999675$

divide by 999:

$x = \frac{324.999675}{999} \\$

round off mumerator to zero decimal place:

$x = \frac{325}{999}$

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Find the gradient of the line segement between the points (0,-6) and (2,-16)

yulyashka [42]

answer = 5

Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m. Generally, a line's steepness is measured by the absolute value of its slope, m. The larger the value is, the steeper the line. Given m, it is possible to determine the direction of the line that m describes based on its sign and value:

A line is increasing, and goes upwards from left to right when m > 0

A line is decreasing, and goes downwards from left to right when m < 0

A line has a constant slope, and is horizontal when m = 0

A vertical line has an undefined slope, since it would result in a fraction with 0 as the denominator. Refer to the equation provided below.

Slope is essentially change in height over change in horizontal distance, and is often referred to as "rise over run." It has applications in gradients in geography as well as civil engineering, such as the building of roads. In the case of a road the "rise" is the change in altitude, while the "run" is the difference in distance between two fixed points, as long as the distance for the measurement is not large enough that the earth's curvature should be considered as a factor. The slope is represented mathematically as:

m =

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7 0

3 years ago

HELPPPPPPPPP i have the most trouble with math what’s the answer??

lakkis [162]

Answer:

Second Option

$\frac{5\sqrt{11} +5\sqrt{3}}{8}$

Step-by-step explanation:

To simplify the expression you must multiply the numerator and the denominator of the fraction by the conjugate of the denominator.

If you have an expression of the form

$a -b$ then its conjugate will be $a + b.$

The result of that multiplication will be

$a ^ 2 -b ^ 2$

Therefore we have the expression

$\frac{5}{\sqrt{11} -\sqrt{3}}$

By multiplying by the conjugate of the denominator we have

$\frac{5}{\sqrt{11} -\sqrt{3}}*\frac{\sqrt{11} +\sqrt{3}}{\sqrt{11} +\sqrt{3}}\\\\\\\frac{5(\sqrt{11} +\sqrt{3})}{(\sqrt{11})^2 -(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11} +5\sqrt{3}}{11 -3}\\\\\\\frac{5\sqrt{11} +5\sqrt{3}}{8}$

6 0

3 years ago

Can you help me please I’ll give brainliest

kolezko [41]

The answer is B I hope it’s right

5 0

3 years ago

which expressions are equivalent to the first one? I don't understand how to determine that so please explain. Thanks!

coldgirl [10]

9514 1404 393

Answer:

(a) -(x+7)/y

(b) (x+7)/-y

Step-by-step explanation:

There are several ways you can show expressions are equivalent. Perhaps the easiest and best is to put them in the same form. For an expression such as this, I prefer the form of answer (a), where the minus sign is factored out and the numerator and denominator have positive coefficients.

The given expression with -1 factored out is ...

$\dfrac{-x-7}{y}=\dfrac{1(x+7)}{y}=\boxed{-\dfrac{x+7}{y}} \quad\text{matches A}$

Likewise, the expression of (b) with the minus sign factored out is ...

$\dfrac{x+7}{-y}=\boxed{-\dfrac{x+7}{y}}$

On the other hand, simplifying expression (c) gives something different.

$\dfrac{-x-7}{-y}=\dfrac{-(x+7)}{-(y)}=\dfrac{x+7}{y} \qquad\text{opposite the given expression}$

Another way you can write the expression is term-by-term with the terms in alpha-numeric sequence (so they're more easily compared).

Given: (-x-7)/y = (-x/y) +(-7/y)

(a) -(x+7)/y = (-x/y) +(-7/y)

(b) (x+7)/(-y) = (-x/y) +(-7/y)

Of course, you need to know the use of the distributive property and the rules of signs.

a(b+c) = ab +ac

-a/b = a/(-b) = -(a/b)

-a/(-b) = a/b

Summary: The given expression matches (a) and (b).

_____

Additional comments

Sometimes, when I'm really stuck trying to see if two expressions are equal, I subtract one from the other. If the difference is zero, then I know they are the same. Looking at (b), we could compute ...

$\left(\dfrac{-x-7}{y}\right)-\left(\dfrac{x+7}{-y}\right)=\dfrac{-y(-x-7)-y(x+7)}{-y^2}\\\\=\dfrac{xy+7y-xy-7y}{-y^2}=\dfrac{0}{-y^2}=0$

Yet another way to check is to substitute numbers for the variables. It is a good idea to use (at least) one more set of numbers than there are variables, just to make sure you didn't accidentally find a solution where the expressions happen to be equal. We can use (x, y) = (1, 2), (2, 3), and (3, 5) for example.

The given expression evaluates to (-1-7)/2 = -4, (-2-7)/3 = -3, and (-3-7)/5 = -2.

(a) evaluates to -(1+7)/2 = -4, -(2+7)/3 = -3, -(3+7)/5 = -2, same as given

(b) evaluates to (1+7)/-2 = -4, (2+7)/-3 = -3, (3+7)/-5 = -2, same as given

3 0

3 years ago

let f(x)= p+ 8/x-q. the line x=4 is a vertical asymptote to the graph of f. what is the value of q and p, if the y intercept is

svlad2 [7]

Answer:

The value of q and p is 4 and -24 respectively.

Step-by-step explanation:

Being $f(x)=\frac{p+8}{x-q}$ , the line x=4 is a vertical asymptote to the graph of f(x). The line r is an asymptote of a function if the graph of the function is infinitely close to the line r. That is, an asymptote is a line to which a function approaches indefinitely, without ever touching it.

Being a rational function that which can be expressed as the quotient of two polynomials, a vertical asymptote occurs when the denominator is 0, that is, where the function is not defined. In this case:

x - q= 0

Solving:

x= q

Being the line x=4 the vertical asymptote, then

4=q

Then the function f (x) is:

$f(x)=y=\frac{p+8}{x-4}$

The y intercept is (0,4). This is, x= 0 and y=4. Replacing:

$4=\frac{p+8}{0-4}$

Solving:

$4=\frac{p+8}{-4}$

4*(-4)= p+8

-16= p+8

-16 - 8= p

-24= p

The value of q and p is 4 and -24 respectively.

7 0

3 years ago

Write each decimal as a fraction or mixed number in simplest form.​

Write each decimal as a fraction or mixed number in simplest form.