All categories

3 years ago

I need to know how to do Solving Systems of Equations by Elimination

1 answer:

6 0

The point of elimination is to have one variable so example

3x + 2y = 4

7X + 3y = 5

1) Try to find a way to have one variable

7(3x + 2y = 4) ----> 21x + 14y = 28

-3(7x+ 3y = 5) -----> -21x -9y = -15

2) add

0 + 5y = 13

3) solve for the last variable

5y = 13
y = 13/5 = 2 3/5 = 2.8

4) Subsitute the variable to get the other one

3x + 2(2.8) = 4

3x + 5.6 = 4

3x = -1.6

x = 0.533333333 (continue)

The intersection would be 0.53 with a line above the 3 and 2.8. (0.5333 , 2.8)

Hope you understand!!

You might be interested in

Determine the relationship between the two triangles and whether or not they can be

xz_007 [3.2K]

The photo wont load uhhhhh

5 0

3 years ago

Read 2 more answers

A small town has 2000 inhabitants. At 8 AM, 160 people have heard a rumor. By noon half the town has heard it. At what time will

QveST [7]

Answer:

3:36 PM

Step-by-step explanation:

Let fraction (y) of the people that heard the rumor , the differential equation that is satisfied by the by y is,

$\frac{dy}{dt} = ky(1-y)$

Solving the differential equation,

$y(t) = \frac{y_{o}}{[y_{o} + (1 + y_{o})e^{-kt}]}$

The total number of inhabitants of the town = 2000

The number of people that heard the rumor = 160

At 8 AM, let t = 0,

$y(0) = \frac{160}{2000}$

= 0.08

By noon, half of the town as heard the rumor.

Then,

$y(4) = \frac{1}{2}$

Therefore,

$\frac{1}{2} = \frac{0.08}{[0.08 + (1 - 0.08)e^{-4k}]}$

$\frac{0.08}{[0.08 + 0.92e^{-4k}]} = \frac{1}{2}$

$0.08 + 0.92e^{-4k} = 0.16$

$0.92e^{-4k} = 0.16 - 0.08$

$0.92e^{-4k} = 0.08$

$e^{-4k} = \frac {0.08}{0.92}$

$k = - \frac{1}{4} In(\frac {0.08}{0.92})$

k ≈ 0.06106

Calculating time, t when y(t) = 90%

⇒ y(t) = 0.9

$\frac{0.08}{[0.08 + 0.92e^{-0.06106t}]} =0.9$

$0.08 + 0.92e^{-0.06106t} = \frac {0.9}{0.08}$

$0.08 + 0.92e^{-0.06106t} = 0.089$

$0.92e^{-0.06106t} = 0.089 - 0.08$

$0.92e^{-0.06106t} = 0.0089$

$t = - \frac{1}{0.06106}In (\frac{0.0089}{0.92})$

t = 7.59 hours

⇒ 7 hours 36 minutes

From 8 A.M. plus 7 hours 36 minutes = 3:36 PM

At 3:36 PM will 90% of the population have heard the rumor

7 0

3 years ago

For what values of the variable x is the expression square root of 7x+14+ square root of 7-x a real number?

I am Lyosha [343]

Answer:

√(7·x + 14) + √(7 - x)

7·x + 14 ≥ 0 --> x ≥ -2

7 - x ≥ 0 --> x ≤ 7

x ∈ [-2 ; 7]

4 0

3 years ago

Find a and b, if the points P(6,0) and Q(3,2) lie on the graph of ax + by =12

Musya8 [376]

The given equation is:
ax + by = 12
We are given that the two points (6,0) and (3,2) belong to this line. This means that these two points satisfy the equation of the line.
Therefore, to get the value of a and b, we will substitute with the given points in the equation and solve the resulting equations for a and b as follows:

For the point (6,0):
ax + by = 12
a(6) + b(0) = 12
6a = 12
a = 12/6 = 2

For point (3,2):
ax + by = 12
(2)(3) + b(2) = 12
6 + 2b = 12
2b = 12-6 = 6
b = 3

Based on the above calculations:
a = 2 and b = 3, therefore, the equation is:
2x + 3y = 12

6 0

3 years ago

If the greatest value of n is 8, which inequality best shows all the possible values of n? (5 points) n < 8 n ≤ 8 n > 8 n

hjlf

Answer:

Step-by-step explanation:

"the greatest value of n is 8" is signified by n ≤ 8.

This is a set, and also an inequality.

4 0

3 years ago