Answer:
38/50 or 19/25
Step-by-step explanation:
One way could be that you add all the marbles together to get your total marbles; 12 + 10 + 15 + 13 = 50.
Then you add all the colours expect red; 10 + 15 + 13 = 38.
Which would give me 38/50; which simplifed would be 19/25
Answer: y = 4\5*x
We can get this through slope intercept form.
Slope intercept form is y=mx +b where m is the slope and b is the y intercept.
We plug in 4.5 for the slope and 0 for the y-intercept.
Answer:
a) 3.507
b) 75.48
c) 78.41
Step-by-step explanation:
Problem A
The opposite side of the angle and the hypotenuse are involved in the question. Therefore you will be using the sine.
sin(26) = x / 8 Multiply both sides by 8
8*sin(26) = x Sin(26) = 0.4384
8*0.4384 = x Do the multiplication
3.507 = x
Problem B
The side adjacent and the hypotenuse are used in this problem. The angle is given, so you are working with the cosine.
Cos(58) = adjacent / hypotenuse
Cos(58) = 0.5299
0.5299 = 40/x Multiply both sides by x
0.5299 x = 40 Divide both sides by 0.5299
x = 40 / 0.5299
x = 75.48
Problem C
The opposite side and the adjacent side are involved and the angle is given.
Tan(71) = opposite / adjacent
tan(71) = 2.904
2.904 = x / 27 Multiply both sides by 27
2.904 * 27 = x Combine
x = 78.414
Answer:
A)

B)

Step-by-step explanation:
<em>x</em> and <em>y</em> are differentiable functions of <em>t, </em>and we are given the equation:

First, let's differentiate both sides of the equation with respect to <em>t</em>. So:
![\displaystyle \frac{d}{dt}\left[xy\right]=\frac{d}{dt}[6]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5Bxy%5Cright%5D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B6%5D)
By the Product Rule and rewriting:
![\displaystyle \frac{d}{dt}[x(t)]y+x\frac{d}{dt}[y(t)]=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdt%7D%5Bx%28t%29%5Dy%2Bx%5Cfrac%7Bd%7D%7Bdt%7D%5By%28t%29%5D%3D0)
Therefore:

A)
We want to find dy/dt when <em>x</em> = 4 and dx/dt = 11.
Using our original equation, find <em>y</em> when <em>x</em> = 4:

Therefore:

Solve for dy/dt:

B)
We want to find dx/dt when <em>x</em> = 1 and dy/dt = -9.
Again, using our original equation, find <em>y</em> when <em>x</em> = 1:

Therefore:

Solve for dx/dt:

Answer:
(x + 4)² + (y + 5)² = 73
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 4, - 5), thus
(x - (- 4))² + (y - (- 5))² = r², that is
(x + 4)² + (y + 5)² = r²
The radius is the distance from the centre to a point on the circle.
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 4, - 5) and (x₂, y₂ ) = (4, - 2)
r =
= 
=
=
⇒ r² = 73, thus
(x + 4)² + (y + 5)² = 73 ← equation of circle