Answer:
(7,5)
Step-by-step explanation:
{2x + 4y = 34
{4y = 27 - x
2x + 27 - x = 34
x=7
4y = 27 - 7
y = 5 so the answer is ( 7,5)
<u>We are given the equation:</u>
(a + b)! = a! + b!
<u>Testing the given equation</u>
In order to test it, we will let: a = 2 and b = 3
So, we can rewrite the equation as:
(2+3)! = 2! + 3!
5! = 2! + 3!
<em>We know that (5! = 120) , (2! = 2) and (3! = 6):</em>
120 = 2 + 6
We can see that LHS ≠ RHS,
So, we can say that the given equation is incorrect
Answer:
Horizontal shift of 4 units to the left.
Vertical translation of 8 units downward.
Step-by-step explanation:
Given the quadratic function, y = (x + 4)² - 8, which represents the horizontal and vertical translations of the parent graph, y = x²:
The vertex form of the quadratic function is y = a(x - h)² + k
Where:
The vertex is (h , k), which is either the <u>minimum</u> (upward facing graph) or <u>maximum</u> (downward-facing graph).
The axis of symmetry occurs at <em>x = h</em>.
<em>a</em> = determines whether the graph opens up or down, and makes the graph wider or narrower.
<em>h</em> = determines how far left or right the parent function is translated.
<em>k</em> = determines how far up or down the parent function is translated.
Going back to your quadratic function,
y = (x + 4)² - 8
- The vertex occrs at (-4, -8)
- a is assumed to have a value of 1.
- Given the value of <em>h</em> = -4, then it means that the graph shifted horizontally by <u>4 units to the left</u>.
- Since k = -8, then it implies that the graph translated vertically at <u>8 units downward</u>.
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F(-1) = 2(-1)^2 + 8(-1)
= 2(1) + (-8)
= -6
Angle between
is
° .
<u>Step-by-step explanation:</u>
We have , two vectors u = <-5, -4>, v = <-4, -3> or ,
We need to find angle between these two vectors . Let's find out:
We know that dot product of two vectors is defined as :
, where x is angle between u & v !
⇒ 
⇒ 
Now , 
⇒ 
⇒
{
}
⇒ 
Now , Modulus of any vector
is
So ,

Putting all these values in equation
we get:
⇒ 
⇒ 
⇒
{
}
⇒
°
Therefore , Angle between
is
° .