> multiply the second equation by 2 and add it to the first equation.
2(-6x - 7y = -10)
-12x -14y = -20
8x + 14y = 4
-12x - 14y = -20
--------------------
- 4x + 0 = - 16
x = -16/-4
x = 4
> use x = 4 in either equation to find y
8(4) + 14y = 4
32 + 14y = 4
14y = 4 - 32
14y = -28
y = -28/14
y = -2
Answer:
Step-by-step explanation:
Given the simultaneous equation 2p - 3q = 4 and 3p + 2q = 9, to get the value of p and q we will use elimination method.
2p - 3q = 4 ...................... 1 * 3
3p + 2q = 9 ..................... 2 * 2
Multiplying equation 1 by 3 and 3 by 2:
6p - 9q = 12
6p + 4q = 18
Subtracting both equation
-9q-4q = 12-18
-13q = -6
q = -6/-13
q = 6/13
Substituting q = 6/13 into equation 2
2p - 3(6/13) = 4
2p - 18/13 = 4
2p = 4+18/13
2p = (52+18)/13
2p = 70/13
p = 70/26
p = 35/13
<em>Hence p = 35/13 and q = 6/13</em>
<em></em>
<em>b) </em>If if 223ₓ = 87 find x
Using the number base system and converting 223ₓ to base 2 will give us;
223ₓ = 2*x² + 2*x¹ + 3*x⁰
223ₓ = 2x²+2x+3
Substituting back into the equation, 2x²+2x+3 = 87
2x²+2x+3-87 = 0
2x²+2x-84 = 0
x²+x-42 = 0
On factorizing:
(x²+6x)-(7x-42) = 0
x(x+6)-7(x+6) = 0
(x+6)(x-7) = 0
x+6 = 0 and x-7 = 0
x = -6 and 7
<em>Hence the value of x is 7 (neglecting the negative value)</em>
Im not sure but CBA i think it has to do with some bank
Answer:
1.25(-xsquare - 8x + 16)
Step-by-step explanation:
pls give me brainliest
I'm not sure but I think so
Answer:
(5,-6)
Step-by-step explanation:
ONE WAY:
If
, then
.
Let's simplify that.
Distribute with
:

Combine the end like terms
:

Use
identity for
:

Combine like terms
and
:

We are given
.
So we have that
.
The vertex happens at
.
Compare
to
to determine
.



Let's plug it in.




So the
coordinate is 5.
Let's find the corresponding
coordinate by evaluating our expression named
at
:




So the ordered pair of the vertex is (5,-6).
ANOTHER WAY:
The vertex form of a quadratic is
where the vertex is
.
Let's put
into this form.
We are given
.
We will need to complete the square.
I like to use the identity
.
So If you add something in, you will have to take it out (and vice versa).





So we have in vertex form
is:
.
The vertex is (3,-6).
So if we are dealing with the function
.
This means we are going to move the vertex of
right 2 units to figure out the vertex of
which puts us at (3+2,-6)=(5,-6).
The
coordinate was not effected here because we were only moving horizontally not up/down.