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stealth61 [152]
2 years ago
6

Find the ratio a:b, if 2a−b/6 = b/3

Mathematics
1 answer:
evablogger [386]2 years ago
6 0

If 2a−b/6 = b/3, then ratio a:b = 3 : 2

<h3><u>Solution:</u></h3>

Given that 2a−b/6 = b/3

We have to find the ratio of a:b

In mathematics, a ratio indicates how many times one number contains another

A ratio between two or more quantities is a way of measuring their sizes compared to each other

let us first solve the given expression

\frac{2a -b}{6} = \frac{b}{3}

On cross multiplication we get,

6a - 3b = 6b

6a = 6b + 3b

6a = 9b

a = \frac{9b}{6}\\\\\frac{a}{b} = \frac{3}{2}

To convert a fraction to a ratio, first write down the numerator, or top number. Second, write a colon. Thirdly, write down the denominator, or bottom number

Therefore ratio a:b = 3 : 2

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How do you interpret a decimals meaning as a ratio as a ratio<br> How do you interpret 0.003
agasfer [191]
The 3 is in the one-thousandths place.
You can call this number "zero point zero zero three."
Since the 3 is in the thousandths place, this number can also be called "three thousandths."
Use the name of the number to find the ratio.
"three thousandths" means 3 out of 1000.
The ratio is 3:1000 or 3/1000.
4 0
3 years ago
Gary just started a new job as a nurse. he is given a starting salary of $58,550 per year. he is also told that his salary will
IRINA_888 [86]

Firts we need to find the rate of change, or in other words, the slope of the line.

Question 1:

a)

For this we can take two points in the form (years, salary). Then we can define as year 0 the year when Gary starts to work. In this year the salary is $58,550. The first point is (0, $58,550)

The next point we can take is at the year 10, when the salary of Gary will be $71,950. The second point is (10, $71,950)

b) Now that we have the two points, we can use the slope formula to get the rate of change. The slope formula is, for two points A and B:

\begin{gathered} \begin{cases}A(x_a,y_a) \\ B(x_b,y_b)\end{cases} \\ m=\frac{y_a-y_b}{x_a-x_b} \end{gathered}

In this case, we can call the points A(0, $58,550) and B(10, $71,950). Using the formula:

m=\frac{58,550-71,950}{0-10}=\frac{-13400}{-10}=1340

c) "The rate of change in Gary's salary is $1340 per year."

Question 2:

a) The slope intercept form of a line is:

y-y_1=m(x_{}-x_1)

Where:

y is the output of the function.

x is the input of the function. (we provide the function with a value for x and the function give us a value of y)

m is the slope of the line. We calculate it in question 1.

x1 is the x coordinate of a point we choose.

y1 is the y-coordinate of the same point of x1.

In this case, we know:

m = 1340;

And we can take the point (0, $58,550), thus:

x1 = 0

y1 = 58,550

b) Now we need to use all this values and use the slope-intercept form:

y-58,550=1340(x-0)

And solve to get:

y=1340x+58,550

Question 3:

a) Now we have a equation for the salary, we can use this to find the salary in 13 years. We just need to replace x = 13 in the equation:

\begin{gathered} \begin{cases}y=1340x+58,550 \\ x=13\end{cases} \\ y=1340\cdot13+58,550 \\ y=75,970 \end{gathered}

B) The salary of Gary in 13 years will be $75,970.

6 0
1 year ago
Which system of linear inequalities is represented by the graph?
masha68 [24]
For the red line, we have:
 
gradient (m) = 1/3
y-intercept = 3

Equation of straight line is given by y=mx+c, where m is the gradient and c is where the line intercept the y-axis

So we have, y= \frac{1}{3}x+3

The shaded part is above the line, hence the first inequality is
y \geq \frac{1}{3}x+3

The black line, we have
gradient, (m) = 3
y-intercept = -2

y=mx+c
y=3x-2, rearranging gives
3x-y=2

The shaded region is to the right of the line, hence the inequality is
3x-y\ \textgreater \ 2

Note: The first option should be the correct answer but the inequality sign for <span>y > 1/3x + 3 should be </span>\geq 



6 0
3 years ago
Read 2 more answers
Y=2x-15 y=5x what the x equals
daser333 [38]

Answer:

16y=13x

Step-by-step explanation:

this honestly doesn't make sense but this is as much as i could simplify

7 0
3 years ago
In the diagram below, the circle has a radius of 25 inches. the area of the unshaded is 500pi in^2Determine and state the degree
Dmitriy789 [7]
72^{\circ}

1) In this question, we are going to make use of the formula for the area of that sector, to find the central angle.

2) So, let's write it out an expression involving the area of a circle, the unshaded area, and the shaded one and then plug into that the given data:

\begin{gathered} A=\frac{\alpha}{360^{\circ}}\times\pi r^2 \\ A_{Unshaded}+A_{shaded}=A_{Circle} \\ 500\pi+\frac{\alpha}{360}\times\pi r^2=\pi r^2 \\  \\ 500\pi+\frac{α}{360}\pi25^2=25^2\pi \\  \\ 500\pi+\frac{125\piα}{72}=625\pi \\  \\ 500\pi +\frac{125\pi α}{72}-500\pi =625\pi -500\pi  \\  \\ \frac{125\pi α}{72}=125\pi  \\  \\ \frac{72\times \:125\pi α}{72}=72\times \:125\pi  \\  \\ \frac{125\pi α}{125\pi }=\frac{9000\pi }{125\pi } \\  \\ α=72^{\circ} \\  \\  \end{gathered}

Thus, the centra angle of that shaded area is 72º

6 0
1 year ago
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