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3 years ago

The number of students is six more than 10 times a number of teachers. There are 12 teachers how many students are there?

Mathematics

2 answers:

Cloud [144]3 years ago

8 0

Answer:

126 students

Step-by-step explanation:

students = 10*(teachers) + 6

teachers = 12

students = 10(12) +6

students = 120 + 6

students = 126

ddd [48]3 years ago

5 0

Answer:

126 students

Step-by-step explanation:

Lets x = the number of students and y = the number of teachers

The number of students is six more than 10 times a number of teachers. :

x = 10y + 6 and 12 teachers so y = 12

x = 10(12) + 6

x = 120 + 6

x = 126

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Find an equation for the line that passes through the points (5.-5) and (-4,-2)

ANEK [815]

Answer:

$\large\boxed{y=-\dfrac{1}{3}x-\dfrac{10}{3}\to x+3y=-10}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (5, -5) and (-4, -2).

Substiute:

$m=\dfrac{-2-(-5)}{-4-5}=\dfrac{-2+5}{-9}=\dfrac{3}{-9}=-\dfrac{1}{3}$

Put the value of the slope and the coordinates of the point (5, -5) to the equation of a line:

$-5=-\dfrac{1}{3}(5)+b$

$-5=-\dfrac{5}{3}+b$ add 5/3 to both sides

$-\dfrac{15}{3}+\dfrac{5}{3}=b\\\\-\dfrac{10}{3}=b\to b=-\dfrac{10}{3}$

Finally we have the equation of a line in the slope-intercept form:

$y=-\dfrac{1}{3}x-\dfrac{10}{3}$

Convert to the standard form (Ax + By = C):

$y=-\dfrac{1}{3}x-\dfrac{10}{3}$ multiply both sides by 3

$3y=-x-10$ add x to both sides

$x+3y=-10$

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3 years ago

If point Q(3,-4) is rotated +270° about the origin, what are the coordinates of Q?

erica [24]

Answer:

$Q' =(-4,-3)$

Step-by-step explanation:

Given

$Q = (3,-4)$

Rotation = +270 degrees

Required

Determine the new coordinates of Q (i.e. Q')

When a point (x,y) is rotated +270° about the origin, the new coordinates is: (y,−x)

So:

$Q = (3,-4)$

Where:

$x = 3$ and $y = -4$

Q' will be:

$Q' =(-4,-3)$

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Vadim26 [7]

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ruslelena [56]

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