write an equation in standard form for the line that passes through the points (4,5) and has a slope m= 2/3

Answers

Answer 1

Answer: $standard\ form: \ Ax+By=C\n\nslope\ intercept\ form:\ny=mx+b\nm=(2)/(3)\n\ny=(2)/(3)x+b\ \ \ \ | substitute\ point\ (4,5)\n\n5=(2)/(3)*4+b\n\n5=(8)/(3)+b\ \ \ \ | subtract\ (8)/(3)\n\n5-(8)/(3)=b\n\nb=5-2(2)/(3)=2(1)/(3)\n\ny=(2)/(3)x+2(1)/(3)\ \ \ | subtract\ (2)/(3)x\n\nSolution:\ -(2)/(3)x+y=2(1)/(3)$

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Which pair of angles listed below are adjacent angles?Parallel Lines and Transversals

A.
1 and 2

B.
1 and 3

C.
1 and 4

D.
2 and 3

Answers

Lets look at the question is asking:

They are looking for adjacent angles.

The geometrical definition for adjacent is neighboring.

So with this we can tell that They are looking for neighboring angles.

The adjacent/neighboring angles are

∠1 and∠2 and ∠3 and ∠4.

So since ∠3 and∠4 are not an option, we can make an educated guess that the answer is A.

(I feel slightly confused on this question, so if it wrong I am truly sorry!)

I hope this helped :)

A soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second. Its height above ground in feet is given by:s(t)=-16t^2 +32t
where t is time in seconds.
I am looking for the max height of the ball, as well as when it hits the ground. My major question is this: Do I have to find c before I solve this? (ax^2 +bx+ c) Is that even necessary in this word problem?
Thank you!

Answers

C is the height above the floor when it's kicked . . . zero. Gravitational acceleration reduces its speed to zero in 1 second. Average speed during that time is 1/2 (32+0) = 16 feet per second. At that average speed, it rises 16 feet to its peak. Gravity works exactly the same scenario in reverse after that. Beginning 16 ft high with zero speed, it falls 16 feet in one second, and hits the ground at 32 ft per second.

Evaluate [3(5 + 6) + 2] ÷ 7

Answers

The answer to the problem is 5

The price of oranges went from $.90 per lb to $1.20 per lb in five years. Find the rate of change of the price of oranges.A) $0.30 per pound per year
B) $0.06 per pound per year
C) $0.24 per pound per year
D) $0.18 per pound per year

Answers

Rate is an expression for a change of some unit per unit of time. For this problem, we find the rate of change of the price by a simple equation which is expressed as:

Rate = change in price / change in time
Rate = ($1.20/lb - $0.90/lb) / 5 yrs - 0
Rate = $0.06 per lb per year

Thus, the answer is B.

Identify the numbers that are located below -3.5 on a vertical number line.