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Y_Kistochka [10]
3 years ago
6

Solve −3(7n+3)<6n. Write the solution using set-builder notation.

Mathematics
1 answer:
Darya [45]3 years ago
6 0
-1/3 is less than n.

you distribute and solve for n.
You might be interested in
(a) Derive an equation of the line passing through the points A(0, 545) and B(4, 726). (Let t be the independent variable and y
a_sh-v [17]

Answer:

The equation of the line is y=45.25t+545

Step-by-step explanation:

The general for of a line is:

y=mt+n       (1)

where:

m is the slope of the line and m is the intercept with the axis of the dependent variable, y in this case.

In order to obtain the value of the slope (m) we can use the corresponding slope formula:

m=\frac{y_{2}-y_1 }{t_2-t_1}         (2)

where t_1, t_2, y_1 and y_2 are the corresponding coordinates of the given points. In this case:

t_1=0\\t_2=4\\y_1=545\\y_2=726\\

Substituting these values in equation (2) we obtain:

m=\frac{726-545}{4-0}=\frac{181}{4}=45.25\\m=45.25

Hence, the line equation is now:

y=45.25t+n     (3)

Now to obtain the value of n you can follow two options:

  1. You can substitute one of your points, A or B, in equation (3). In this way, you will obtain an equation where the variable is n

Note that for this question, it is easier to select point A because of having the independent variable equals to zero t=0. Hence, substituting point A in equation (3):

45.25*0+n=545\\n=545

Therefore, the line equation is: y=45.25t+545

The second option to find n is to think of the meaning of the <em>intercept</em>. The <em>intercept </em>of a line is defined as the point in which the line crosses the axis of the dependent variable, which also means that the value of the independent variable for this point is zero. From this, we could have automatically said that n is equal to 545.

See the attachment for a plot of the line.

7 0
3 years ago
The length of a rectangle is 1 units more than the width. The area of the rectangle is 56 units. What is the width, in units, of
pishuonlain [190]

Answer:

7

Step-by-step explanation:

56=8*7\\8-7=1The width is smaller, so it is 7.

8 0
3 years ago
M&lt;5=? what’s it equal
WINSTONCH [101]

Answer:

<8

Step-by-step explanation:

They are the same angle degree.

5 0
3 years ago
What is the y value of the solution to the system of equations shown below y = 22 - 6 y = 50 – 21​
zhannawk [14.2K]

Answer:

22-6y= 29

-6y=29-22

-6y=7

y=-7/6

3 0
2 years ago
Carly lives in Scottsdale, AZ and plans to go visit downtown Glendale, AZ. The map with a scale of 2 cm for every 4 km shows the
AleksandrR [38]
Comparing map distance to real distance we get 2cm/4km. That means 1cm = 2km.

So the map distance is half the real distance (well, technically not as one is in cm and the other in km but it’s enough to think this way) and a real distance of 10km must mean a map distance of half that (again ignoring the units) so we get 5cm.
5 0
3 years ago
Read 2 more answers
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