Answer:
6
a
/x
^8
Step-by-step explanation:
<span>k= Keisha
k + 6=
John</span>
<span>
k + k + 6
= 4k</span>
<span>
2k + 6 ( - 2k)
= 4k ( - 2k)</span>
<span>
6 = 2k</span>
<span>
3 =
k
(Keisha= 3 years old)</span>
<span>
k + 6 = 9
(John = 9 years old)
</span>
3 + 3 + 6 = 4 (3)
<span>
12 = 12
</span><span>So
we made the pawn represent Keisha’s age.
Then we knew that John is 6 years older than Keisha so we represented
his age with a pawn plus 6. This went on 1 side of the equation because it said
that together they equal 4 times Keisha’s age. So on the other side of the
equation we put 4 pawns because we are using each pawn as Keisha’s age. Then we subtracted the pawns from each side
to keep the equation balanced. So we had
that 2 pawns equal 6, which means that each pawn equals 3 so Keisha is 3 years
old. Since John is 6 years older than
Keisha, he must be 9 years old. We
checked our work and substituted 6 in for each pawn and found that 12 equals
12, so our equation is balanced.
</span>
Hope this helps :)
Answer:
-3, 5/2
Step-by-step explanation:
What are the roots of the function y = 4x2 + 2x – 30?
To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.
Factor out the GCF of : 2, so the equation becomes 0 = 2(2x2+x-15)
Next, factor the trinomial completely. The equation becomes: 0=2(x+3)(2x-5)
Use the zero product property and set each factor equal to zero and solve.
x+3=0 2x-5 = 0
x = -3, 5/2
The roots of the function are -3, 5/2.
Hope this helped!
Answer:
In 1979 the amount of transistors in a chip was approximately 27865.
Step-by-step explanation:
Since the number of transistors in 1974 was 5000 per chip and it increases at a rate of 41% per year, the number of transistors in a chip per year can be modelled by the following expression:
chips(t) = 5000*(1.41)^(t - 1974)
Therefore in 1979, we have:
chips(1979) = 5000*(1.41)^(1979 - 1974)
chips(1979) = 5000*(1.41)^5
chips(1979) = 27865.4183
In 1979 the amount of transistors in a chip was approximately 27865.
g(x) = -x² + 10x - 30
the equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here vertex = (5, - 5 ), hence
y = a(x - 5)² - 5
to find a substitute the point on the graph (8, - 14) into the equation
- 14 = 9a - 5 ⇒ 9a = - 9 ⇒ a = - 1
y = - (x - 5)² - 5 = - (x² - 10x + 25) - 5 = - x² + 10x - 30
g(x) = - x² + 10x - 30 ← in standard form