Basically, you have to find the line through (-3, 1) that is perpendicular to the line 6x + y = 9 and then find where the two lines intersect. Dropping a perpendicular from the point to the line is the shortest distance from the point to the line.
6x + y = 9
y = -6x + 9
slope is -6
perpendicular would have slope 1/6
(y - 1) = (1/6) (x + 3)
y - 1 = (1/6) x + (1/2)
multiplying both sides by 6
6y - 6 = x + 3
x - 6y = -9
Where do these two lines intersect?
From above we know given equation is y = -6x + 9
Plugging into other equation
x - 6(-6x + 9) = -9
x + 36x - 54 = -9
37 x = 45
x = 45/37
y = -6(45/37) + 9
y = -270/37 + (333/37)
y = 63/37
point is (45/37, 63/37)
Answer:
B
Step-by-step explanation:
You just need to find the volumes of both container and soap and divide them. So;
Volume of Soap = 15cm * 8cm * 6cm = 720 cm^3
Volume of Container = 165cm * 40cm * 96cm = 633600 cm^3
Dividing them gives = 633600 cm^3 / 720 cm^3 = 880
Answer is B.
Answer: 770 voters in his district.
Step-by-step explanation:
- Population is the largest group of individuals carrying some specific similar characteristics.
- A sample is a subset of population that is used to represents the entire population.
Given : A state representative wants to know how voters in his district feel about enacting a statewide smoking ban in all enclosed public places, including bars and restaurants, as well as several other current statewide issues.
So the population here is : Voters in His districts .
He mails a questionnaire addressing these issues to an SRS (simple random sample) of 770 voters in his district. Of the 770 questionnaires mailed, 147 were returned.
Thus , the sample is : <u>770 voters in his district</u>.
Basically 770 voters is a subset of the entire population voters in his district.
Answer:
Step-by-step explanation:
The vertical motion of the object is defined by using the height function h(t) such that :
h(t) = -16t² + vt + s , where t is the time instant , v is the initial velocity and s is the initial height of the object.
Now, the height of the bridge = 200 feet
So it would be the initial height ⇒ s = 200
Initially the speed is 0 because the body is in rest at time instant 0 sec.
Hence, the resultant equation is : h(t) = -16t² + 200
And the graph is attached below :
