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Setler79 [48]
3 years ago
9

3. Find a solution to the following system of equations. -3x + 3y = -9 -3x + y = 7

Mathematics
1 answer:
Alex Ar [27]3 years ago
3 0

Answer:

x = 5

y = 2

Step-by-step explanation:

-3x + 3y = -9

3y = 3x - 9

Equation 1. <em><u>y = x - 3</u></em>

-3x + y = 7

Equation 2. <u><em>y = 3x + 7</em></u>

So, put number 1 equation to number 2's y :

x - 3 = 3x + 7

x -3x = 7 + 3

-2x = 10

2x = 10

x = 10/2

x = 5

And, put x, which is 5 , to the any equation to figure out the y.

This time, I'll use equation number 1.

y = 5 - 3

y = 2

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Find the slope of the line through<br> (-11,8),(-11, -17)
Rom4ik [11]

Answer:

Undefined or Infinity

Step-by-step explanation:

(x1,y1)=(-11,8)

(x2,y2)=(-11,-17)

Slope = (y2-y1)/(x2-x1)

= (-17-8)/(-11-(-11))

= -25/0

= Undefined

5 0
3 years ago
A mountain climber found that the relationship between his altitude and the surrounding air
sukhopar [10]

Answer:- 1/100 degrees Fahrenheit

Step-by-step explanation:

The directions say decreasing so it has to be negative, and the slope is showing how much it is decreasing every meter. y=mx+b. The mx is the slope which is where the answer is located.

5 0
2 years ago
find the smallest number of terms of the AP "-54,-52.5,-51,-49.5" ....that must be taken for the sum of the terms to be positive
wel

The smallest number of terms of the AP that will make the sum of terms positive is 73.

Since we need to know the number for the sum of terms, we find the sum of terms of the AP

<h3>Sum of terms of an AP</h3>

The sum of terms of an AP is given by S = n/2[2a + (n - 1)d] where

  • n = number of terms,
  • a = first term and
  • d = common difference

Since we have the AP "-54,-52.5,-51,-49.5" ....", the first term, a = -54 and the second term, a₂ = -52.5.

The common difference, d = a₂ - a

= -52.5 - (-54)

= -52.5 + 54

= 1.5

<h3>Number of terms for the Sum of terms to be positive</h3>

Since we require the sum of terms , S to be positive for a given number of terms, n.

So, S ≥ 0

n/2[2a + (n - 1)d] ≥ 0

So, substituting the values of the variables into the equation, we have

n/2[2(-54) + (n - 1) × 1.5] ≥ 0

n/2[-108 + 1.5n - 1.5] ≥ 0

n/2[1.5n - 109.5] ≥ 0

n[1.5n - 109.5] ≥ 0

So, n ≥ 0 or 1.5n - 109.5 ≥ 0

n ≥ 0 or 1.5n ≥ 109.5

n ≥ 0 or n ≥ 109.5/1.5

n ≥ 0 or n ≥ 73

Since n > 0, the minimum value of n is 73.

So, the smallest number of terms of the AP that will make the sum of terms positive is 73.

Learn more about sum of terms of an AP here:

brainly.com/question/24579279

#SPJ1

4 0
2 years ago
One less than half a number is 12. What is the number
olga_2 [115]
To find this, turn the word question into an equation.
"One less than" means - 1, which is 1 being subtracted from something.
"half a number" means 1/2x, since 1/2 is half and x is unknown.
"is 12" means = 12, which is something equals 12.
Putting this in order would be 1/2x, then - 1, then = 12.
As an equation, this is 1/2x - 1 = 12.
So the equation is 1/2x - 1 = 12

Now you must find the number by solving this equation.
1/2x - 1 = 12
First, add 1 to both sides.
12 + 1 = 13
1/2x = 13
Now multiply both sides by 2.
This way, x will be isolated since 1/2x • 2 = 1x, and 1x = x.
13 • 2 = 26
x = 26
The number is 26.
6 0
3 years ago
Is 0.25 rational or irrational
love history [14]
0.25 is rational because it is a terminating (means 'its stops') fraction.
3 0
3 years ago
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