Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<u>Step 2: Solve for </u><em><u>x</u></em>
- Factor:
- [Division Property of Equality] Divide a + b on both sides:
Answer:
(c-a, 0)
Step-by-step explanation:
The horizontal space between (c, b) and P is the same as the space between (a, b) and O.
Coordinates are written (x, y), where x is for horizontal space.
P is on the x-axis, making the y-coordinate 0.
(a+c, 0) would be to the right of the entire parallelogram.
(c, 0) would be directly below (c, b).
(a-c, 0) would be to the left of the entire parallelogram and in the other quadrant.
Answer:
units
Step-by-step explanation:
Given
Shape: Kite WXYZ
W (-3, 3), X (2, 3),
Y (4, -4), Z (-3, -2)
Required
Determine perimeter of the kite
First, we need to determine lengths of sides WX, XY, YZ and ZW using distance formula;
For WX:
For XY:
For YZ:
For ZW:
The Perimeter (P) is as follows:
units
Answer:
The answer is option B
Step-by-step explanation:
To find cos 45° we must first find the adjacent and the hypotenuse
Let the adjacent be x
Let the hypotenuse be h
To find the adjacent we use tan
tan ∅ = opposite / adjacent
From the question
the opposite is 9
So we have
tan 45 = 9 / x
x tan 45 = 9
but tan 45 = 1
x = 9
Since we have the adjacent we use Pythagoras theorem to find the hypotenuse
That's
h² = 9² + 9²
h² = 81 + 81
h² = 162
h = √162
h = 9√2
Now use the formula for cosine
cos∅ = adjacent / hypotenuse
The adjacent is 9
The hypotenuse is 9√2
So we have
cos 45 = 9/9√2
We have the final answer as
<h3 /><h3>cos 45 = 1 / √2</h3>
Hope this helps you
Answer:
Vertex → (2, 4)
Step-by-step explanation:
Quadratic equation has been given as,
y = -x² + 4x
We rewrite this equation in the form of a function as,
f(x) = - x² + 4x
By comparing this equation with the standard quadratic equation,
y = ax² + bx + c
a = -1 and b = 4
Vertex of the parabola represented by this equation is given by
x coordinate =
= 2
y-coordinate = f(2)
= - (2)² + 4(2)
= -4 + 8
= 4
Therefore, vertex of the given function is (2, 4)