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3 years ago

Write the equation of the line that is perpendicular to the line 3x + y = 7 and passes through the point (6, -1).

1 answer:

5 0

Line:
3x+y=7
y=-3x+7

Slope of Perpendicular Line: 1/3x

For the perpendicular line to contain point (6,-1) the y-intercept would be (0,1), thus the equation of the line would be y=1/3x+1

y=1/3x+1

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A recursive rule for a sequence is given. Find the first four terms of the sequence.

tigry1 [53]

Answer:

So...

a0 = -2

a1 = (a0)2 - 4 = 4 - 4 = 0

a2 = (a1)2 - 4 = ((a0)2-4)2 - 4 =...= 02 - 4 = -4

For an+1, you may use the previous term (an) if you have just calculated it, rather than calculating it recursively again

a3 = (-4)2 - 4 = 12

The first four terms in the sequence are -2, 0, -4, 12.

Step-by-step explanation:

This recursive sequence is defined as follows:

a0 = -2 [the first term]

an+1 = an2 - 4 [for all other terms, n≥0; note that you cannot find a0 using this line]

Note that this is not "BASE" for a number base, but it is "SUB" for subscript, indicating the term. Sometimes, sequences are written with the first term being a1 and sometimes sequences are written with the first term being a0. This is because there are situations that make one or the other more convenient (for example, starting with elapsed time t=0 makes sense).

To find the value of later terms, a recursive definition requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, ... which requires that use the value of the first term.

That's why (joke) that the dictionary definition of "recursive" is "see recursive."

4 0

2 years ago

A virus that initially infected four people is spreading at a rate of 15% each week.

Solnce55 [7]

Answer:

"f(x) = 4(1.02)7x; spreads at a rate of approximately 2% daily"

Step-by-step explanation:

Complete Question:

A virus that initially infected four people is spreading at a rate of 15% each week. The following function represents the weekly spread of the virus: f(x) = 4(1.15)x. Rewrite the function to show how quickly the virus spreads each day and calculate this rate as a percentage.

f(x) = 4(1.15)7x; spreads at a rate of approximately 1.5% daily

f(x) = 4(1.02)7x; spreads at a rate of approximately 2% daily

f(x) = 4(1.157)x; spreads at a rate of approximately 2.66% daily

f(x) = 4(1.02)x; spreads at a rate of approximately 0.2% daily

Solution:

The weekly number of people infected would be:

$f(x)=4(1.15)^x$

7 days in a week, so daily number of people infected would be:

$f(x)=4(1+r)^{7x}$

To find daily rate, we set these 2 equations equal and solve for r:

$4(1.15)^x=4(1+r)^{7x}\\1.15^x=(1+r)^{7x}\\1.15^x=((1+r)^7)^x\\1+r=1.02\\r=1-1.02=0.02$

That is 0.02*100 = 2% daily

2nd answer choice is right.

8 0

3 years ago

A park charges $19 for one round of miniature golf and a reduced fee for each additional round played. If Tom paid $34 for 6 rou

iragen [17]

Answer:

Step-by-step explanation:

Given that:

Park charge for one round = $19

Reduced fee for every additional round

Number of rounds played by Tom = 6

Amount paid = $34

Amount left after 1 round :

Amount paid - first round charge

$34 - $19 = $15

Number of rounds left = (6 - 1) = 5

Charge per additional round :

$15 / 5 = $3

3 0

2 years ago

KJ and KL are the legs of the right triangle below. True or False

amm1812

True, because they make up the two line segments make up the right angle

3 0

3 years ago

The surface area for a rectangular prism with a square base is SA=2s^2+4sh. What is the surface area if s=3 and h=5?

Wittaler [7]

The answer is 63. Just plug the answers in for the variables. As my math teacher always says, “just plug and chug!”

3 0

3 years ago

Read 2 more answers