Complete the square and then find the center and radius from the circle equation
2 answers:
Answer:
center: (2, -4); radius: 5
Step-by-step explanation:
Group x-terms and y-terms. Add the squares of half the coefficient of the linear term in each group. It can be convenient to subtract the constant, too.
(x^2 -4x) +(y^2 +8y) = 5
(x^2 -4x +4) +(y^2 +8x +16) = 5 + 4 + 16
(x -2)^2 +(y +4)^2 = 5^2
Comparing this to the form of a circle centered at (h, k) with radius r, we can find the center and radius.
(x -h)^2 +(y -k)^2 = r^2
(h, k) = (2, -4) . . . . . the circle center
r = 5 . . . . . . . . . . . . the radius
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Answer:
520 feets
Step-by-step explanation:
The height of the building, h can be obtuined using trigonometry ;
From the attached diagram, opposite side = 300 feets ; height, h = adjacent side
Hence,
Tan θ = opposite / Adjacent
Tan 30° = 300 / height
0.5773502 = 300 / height
Height = 300 / 0.5773502
Height = 519.615
Height = 520 feets
Answer:
The price of rice per gram is 0.006$
Step-by-step explanation:
I. David wants to make 10 servings,
each require 75 g of rice and 5 spice. When ratio is 15:1
If rice : spice = 75 : x
15x = 75
x = 5
=> 5 * 15 : 1 * 5
= 75 : 5
So rice : spice is 75 : 5
II. When 1 serving require 75 : 5
So 10 servings is 10 * 75 : 5 * 10
= 750 : 50
So he must has 750 grams rice and 50 grams spice.
III. He must buy spice and rice which..
a) He has 40 grams spice, he'll buy for 10 grams spice.
b) He has no rice, he'll buy for 750 grams rice.
But the question only ask for price of rice which he spend 4.5$
=
= 0.006$
In 1 gram of rice he spend 0.006$
If 750 grams of rice, he'll spend 750 * 0.006$ = 4.5$ => true
That makes 0.006$ is the right answer.
Hope that help :)
Answer: 0.002718
Step-by-step explanation:
Given : The population mean annual salary for environmental compliance specialists is about $62,000.
i.e.
Sample size : n= 32
Let x be the random variable that represents the annual salary for environmental compliance specialists.
Using formula , the z-value corresponds to x= 59000 will be :
Now, by using the standard normal z-table , the probability that the mean salary of the sample is less than $59,000 :-
Hence, the probability that the mean salary of the sample is less than $59,000= 0.002718