Let x = marbles Leah has
x - 28 = marbles Dan has
![\frac{1}{3} x= \frac{4}{5} (x - 28)](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B3%7D%20x%3D%20%5Cfrac%7B4%7D%7B5%7D%20%28x%20-%2028%29)
LCD: 15 multiply that on both sides of the equation to eliminate the fractions
5x = 12(x - 28)
5x = 12x - 336
-7x = -336
x = 48
Leah has 48 marbles
Answer:3.677 miles
Step-by-step explanation:
First we have to know that the distance between two consecutive milestone is 1mile, I have attached a diagram representing the problem, point C being the point of the balloon and point A and point B being the points of the consecutive milestones
I labelled the horizontal length between the balloon and the first milestone x and the height of the balloon h
From the diagram, we use the tan rule for right angle triangles to find x and h
Tan22=h/x
Making her the subject of formula
h=xtan22 (1)
Similarly
Tan20=h/(x+1)
h=(x+1)tan20 (2)
Putting (1) and (2) together
We solve for x, and then input our value for in (1) to get the value for h, the solution is in the second picture I sent
Note: tan rule says the tan of an angle is equal to the opposite side of the triangle(side directly facing the angle) divided by the adjacent side of the triangle( side of the triangle the angle is resting on)
Angle of depression from C to B is also angle of elevation from B to C( alternate angle are equal)
Answer:
Correct option is (C).
Step-by-step explanation:
![f(x) = 8 {x}^{2} - 2x + 3](https://tex.z-dn.net/?f=f%28x%29%20%3D%208%20%7Bx%7D%5E%7B2%7D%20%20-%202x%20%2B%203)
![g(x) = 12 {x}^{2} + 4x - 3](https://tex.z-dn.net/?f=g%28x%29%20%3D%2012%20%7Bx%7D%5E%7B2%7D%20%20%2B%204x%20-%203)
Now,
h (x) =f (x) - g (x)
![h(x) = \: 8 {x}^{2} - 2x + 3 - 12 {x}^{2} - 4x + 3](https://tex.z-dn.net/?f=h%28x%29%20%3D%20%5C%3A%208%20%7Bx%7D%5E%7B2%7D%20%20-%202x%20%2B%203%20%20-%2012%20%7Bx%7D%5E%7B2%7D%20%20-%204x%20%2B%203)
![h(x) = - 4 {x}^{2} - 6x + 6](https://tex.z-dn.net/?f=h%28x%29%20%3D%20%20-%204%20%7Bx%7D%5E%7B2%7D%20%20-%206x%20%2B%206)
So, correct option is (C).
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Answer:
14
Step-by-step explanation:
x=35÷2.5 will devide 35 by 2.5 to get x
Answer:
$1,408.21.
Step-by-step explanation:
Since it is compounded annually we could use the formula
A=Pe^rt
We know that the initial amount she deposits is $1200, as stated by the problem. That is our P.
e is well, the e in your calculator which is approximately: 2.7182818284590452353602874713527
r is the rate which is 8%, although you must convert this into a decimal, which would be 0.08 as your r.
Lastly, t is the time, so in this case, 2 years.
And then plug in the values.
A=1200(e)^(0.08)(2)
A=1200(e)^(0.16)
A=1200(1.173510870991810235018611086892)
A=1,408.2130451901722820223333042704
Now since it is a money problem we must put it in the correct format.
A=$1,408.21