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1 year ago

Solve the equation: \frac{2}{3}t=\frac{5}{9} (hint: reciprocal)

Mathematics

1 answer:

Aleks04 [339]1 year ago

3 0

Given:

$\frac{2}{3}t=\frac{5}{9}$ $\text{ We know that the reciprocal of }\frac{2}{3}\text{ is }\frac{3}{2}\text{.}$

Multiply both sides by 3/2, we get

$\frac{3}{2}\times\frac{2}{3}t=\frac{3}{2}\times\frac{5}{9}$

Cancel out the common multiples, we get

$t=\frac{1}{2}\times\frac{5}{3}$

$t=\frac{1\times5}{2\times3}$

$t=\frac{5}{6}$

The solution of the given equation is

$t=\frac{5}{6}$

$t=0.8333.$

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Read 2 more answers

The table below represents a linear function in the equation represents a function. table numbers are X: -1,0,1. f(x): -3,0,3. G

Alexxx [7]

A)
SLOPE OF f(x)
To find the slope of f(x) we pick two points on the function and use the slope formula. Each point can be written (x, f(x) ) so we are given three points in the table. These are: (-1, -3) , (0,0) and (1,3). We can also refer to the points as (x,y). We call one of the points $( x_{1} , y_{1} )$ and another $( x_{2} , y_{2} )$ . It doesn't matter which two points we use, we will always get the same slope. I suggest we use (0,0) as one of the points since zeros are easy to work with.

Let's pick as follows:
$( x_{1} , y_{1} )= (0.0)$
$( x_{2} , y_{2} )= (1.3)$

The slope formula is: $m= \frac{y_{2} - y_{1} }{ x_{2}- x_{1} }$
We now substitute the values we got from the points to obtain.
$m= \frac{3-0}{ 1-0 } = \frac{3}{1}=3$

The slope of f(x) = 3

SLOPE OF g(x)
The equation of a line is y=mx+b where m is the slope and b is the y intercept. Since g(x) is given in this form, the number in front of the x is the slope and the number by itself is the y-intercept.

That is, since g(x)=7x+2 the slope is 7 and the y-intercept is 2.

The slope of g(x) = 2

B)
Y-INTERCEPT OF g(x)
From the work in part a we know the y-intercept of g(x) is 2.

Y-INTERCEPT OF f(x)
The y-intercept is the y-coordinate of the point where the line crosses the y-axis. This point will always have an x-coordinate of 0 which is why we need only identify the y-coordinate. Since you are given the point (0,0) which has an x-coordinate of 0 this must be the point where the line crosses the y-axis. Since the point also has a y-coordinate of 0, it's y-intercept is 0

So the function g(x) has the greater y-intercept

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