First we need to find the gradient of K
which is y1-y2/x1-x2
(-1,3) and (5,-2)
so it becomes 3-(-2)/-1-5
m=-5/6
when two lines are perpendicular their gradients multiply to make -1
that means the gradient of L has to be 6/5
we can substitute the point on L (5,-2) and the gradient of 6/5 into y=mx+c
-2 = (6/5) x 5 + c
c = -8
the equation of line L is y= 6x/5 -8
Answer:
x = 4
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define Equation</u>
7(2x - 5) = 21
<u>Step 2: Solve for </u><em><u>x</u></em>
- Distribute 7: 2x - 5 = 3
- Isolate <em>x</em> term: 2x = 8
- Isolate <em>x</em>: x = 4
<u>Step 3: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: 7(2(4) - 5) = 21
- Multiply: 7(8 - 5) = 21
- Subtract: 7(3) = 21
- Multiply: 21 = 21
Here we see that 21 does indeed equal 21.
∴ x = 4 is the solution to the equation.
Answer:
See Below.
Step-by-step explanation:
We are given that:

By vertical angles:

Hence, by substitution:

Then by Angle-Angle Similarity:

The price of less expensive equipment is $1575.
Step-by-step explanation:
Let,
Price of one equipment = x
Price of other equipment = y
According to given statement;
x+y=4000 Eqn 1
x = y+850 Eqn 2
Putting Eqn 2 in Eqn 1

Dividing both sides by 2;

Putting y=1575 in Eqn 2;

The price of less expensive equipment is $1575.
Keywords: linear equation, substitution method
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