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2 years ago

Give the function 12x-16y=-48 determine the x-and y intercepts of the graph

1 answer:

8 0

For the x-int, replace y with 0
for the y-int, replace x with 0

x-int:
12x-16(0)=-48
12x=-48
x=-4

y-int:
12(0)-16y=-48
-16y=-48
y=3

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What is the answer to:<br> -4(2x+2) <-40

mars1129 [50]

Answer: x > 6

Step-by-step explanation: -4(2x+2) < -40

-8x - 8 < -40

+8 +8

-8x < 48

/-8x /-8x

x > 6 *The less than sign got flipped to a greater than sign because we divided by a negative.

5 0

1 year ago

What is an equation of the line that passes through the point (2,−6) and is parallel to the line x-2y=8

lana [24]

Answer:

$y=\frac{1}{2}x-7$ , or x-2y=14

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through the point (2, -6) and is parallel to the line x-2y=8

First, we need to find the slope of x-2y=8, since parallel lines have the same slopes

We can convert the equation from standard form (ax+by=c) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept), in order to help us find the slope of the line

Start by subtracting x from both sides

-2y=-x+8

Divide both sides by -2

y= $\frac{1}{2}x$ -4

The slope of the line x-2y=8 is 1/2

It's also the slope of the line parallel to it.

Since we know the slope of the line, we can plug it into the equation for slope intercept form:

$y=\frac{1}{2}x+b$

Now we need to find b.

As the equation of the line passes through (2, -6), we can use it to help solve for b

Substitute -6 as y and 2 as x:

$-6=\frac{1}{2}(2)+b$

Multiply

-6=1+b

Subtract 1 from both sides

-7=b

Substitute -7 as b into the equation:

$y=\frac{1}{2}x-7$

The equation can be left as that, or you can convert it into standard form if you wish.

In that case, you will need to move 1/2x to the other side:

$-\frac{1}{2}x+y=-7$

A rule about the coefficients a, b, and c in standard form is that a (coefficient in front of x) CANNOT be negative, and every coefficient must be an integer (a whole number, not a fraction or decimal).

So multiply both sides by -2 in order to clear the fraction, as well as change the sign of a

x-2y=14

Hope this helps!

8 0

2 years ago

In a certain region, about 6% of a city's population moves to the surrounding suburbs each year, and about 4% of the suburban po

Sedbober [7]

Answer:

City @ 2017 = 8,920,800

Suburbs @ 2017 = 1, 897, 200

Step-by-step explanation:

Solution:

- Let p_c be the population in the city ( in a given year ) and p_s is the population in the suburbs ( in a given year ) . The first sentence tell us that populations p_c' and p_s' for next year would be:

0.94*p_c + 0.04*p_s = p_c'

0.06*p_c + 0.96*p_s = p_s'

- Assuming 6% moved while remaining 94% remained settled at the time of migrations.

- The matrix representation is as follows:

$\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}p_c\\p_s\end{array}\right] = \left[\begin{array}{c}p_c'\\p_s'\end{array}\right]$

- In the sequence for where x_k denotes population of kth year and x_k+1 denotes population of x_k+1 year. We have:

$\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_k = x_k_+_1$

- Let x_o be the populations defined given as 10,000,000 and 800,000 respectively for city and suburbs. We will have a population x_1 as a vector for year 2016 as follows:

$\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o = x_1$

- To get the population in year 2017 we will multiply the migration matrix to the population vector x_1 in 2016 to obtain x_2.

$x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o$

- Where,

$x_o = \left[\begin{array}{c}10,000,000\\800,000\end{array}\right]$

- The population in 2017 x_2 would be:

$x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}10,000,000\\800,000\end{array}\right] \\\\\\x_2 = \left[\begin{array}{c}8,920,800\\1,879,200\end{array}\right]$