Answer:
393 more minnows than goldfish
Step-by-step explanation:
add 458 rosy red minnows and 212 white minnows,you get 670.Subtract the 277 goldfish from the 670 minnows and you get 393
Using cosine law,
d^2 = 65^2 + 35^2 - 2(65)(35)cos140
= 8935.5022
d = sqrt(8935.5022)
= 94.5 m
Angle = inverseCos(35sin40 / 94.5) = 76.23 degrees South of East
Answer:
b
Step-by-step explanation:
Using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (4, 1)
d = 
= 
= 
= 
→ b
An equilateral triangle has all side lengths the same, and all angles are 60 degrees. Using this we can split the triangle along its altitude to get two right triangles with a hypotenuse of length 10 and a base of 1/2 of the original length, so 5. Now we can either use the Pythagorean theorem (a^2+b^2=c^2) or the fact that it is a 30 60 90 triangle (angles measure at 30 60 and 90 degrees) Pythagorean theorem is probably easier.
It stated that the squares of the two legs of a right triangle add to the square of the hypotenuse. So a(the altitude)^2+5(the base)^2=10(the hypotenuse)^2
A^2+5^2=10^2
A^2+25=100
A^2=75
A=sqrt(75)
A=5*sqrt(3)
Final answer:
The altitude of an equilateral triangle with side length 10 is 5sqrt(3), or about 8.66
The greatest number of people that they may invite and still stay within their budget is 130 people.
The standard form of a linear equation is given by:
y = mx + b
Where y is a dependent variable, x is an independent variable, m is the slope of the line (the rate of change), b is the y intercept (that is the initial value of y).
Let y represent the budget for x number of people.
Since the reception hall charges a $80 cleanup fee plus $34 per person, hence this can be represented by the function:
y = 34x + 80
They have budgeted $4,500 for their reception. Therefore the greatest number of people can be found from:
4500 = 34x + 80
34x = 4420
x = 130 people
Therefore the greatest number of people that they may invite and still stay within their budget is 130 people.
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