Answer:
Step-by-step explanation:
Given
Solving (a): Multiplication sentence
Rewrite of as *
Solve
Hence, the multiplication sentence is:
Solving (b): Rectangular fraction model
In (a) above, the result is 2/5
The fraction model will be represented as thus:
- Draw a rectangle
- Partition in to 5 equal parts (5 represents the denominator)
- Shade 2 of the 5 partitions (2 represents the numerator)
<em>See attachment for model</em>
Y1 is the simplest parabola. Its vertex is at (0,0) and it passes thru (2,4). This is enough info to conclude that y1 = x^2.
y4, the lower red graph, is a bit more of a challenge. We can easily identify its vertex, which is (-4,0), and several points on the grah, such as (2,-3).
Let's try this: assume that the general equation for a parabola is
y-k = a(x-h)^2, where (h,k) is the vertex. Subst. the known values,
-3-(-4) = a(2-0)^2. Then 1 = a(2)^2, or 1 = 4a, or a = 1/4.
The equation of parabola y4 is y+4 = (1/4)x^2
Or you could elim. the fraction and write the eqn as 4y+16=x^2, or
4y = x^2-16, or y = (1/4)x - 4. Take your pick! Hope this helps you find "a" for the other parabolas.
Answer:
A possible solution is 60/2 = 30
Step-by-step explanation:
The given parameters are;
The dividend is a factor of 60
The divisor is a factor of 18
The quotient is a multiple of 3
The dividend is the amount divided
The dividend is the number that is dividing the dividend
The quotient is the result of the division operation
The given numbers to use are 60, 2, 30, and 18
Therefore one possible solution is 60/2 = 30
The dividend = 60 which is a factor of 60 (60 × 1 = 60)
The divisor = 2 which is a factor of 18 (2 × 9 = 18)
The quotient = 30 which is a multiple of 3 (3 × 10 = 30)
Express √3 + i in polar form:
|√3 + i| = √((√3)² + 1²) = √4 = 2
arg(√3 + i) = arctan(1/√3) = π/6
Then
√3 + i = 2 (cos(π/6) + i sin(π/6))
By DeMoivre's theorem,
(√3 + i)³ = (2 (cos(π/6) + i sin(π/6)))³
… = 2³ (cos(3 • π/6) + i sin(3 • π/6))
… = 8 (cos(π/2) + i sin(π/2))
… = 8i
If the weight of the little brother is x, then the weight of Charles is x + 9
The equation that can be used to determine what each one weighs is:
x + (x + 9) = 99.
Let us now solve it.
x + x +9 = 99
2x + 9 = 99
2x = 99 - 9
2x = 90
x = 90/2
x = 45
Little brother's weight is 45 kg.
Charles' weight will be 45 + 9 = 54 kg
Adding these two weights will give 99kg
