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3 years ago

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A given line has the equation 3x-5y=20 . Which of the following equations represents the line perpendicular to the given line an

d passes through the point (-6,4) ?

1 answer:

AlladinOne [14]3 years ago

8 0

Answer:

y= -5/3 x - 6

Step-by-step explanation:

3x-5y=20

-5y=20-3x

y= (3/5)x - 5

3/5 is the slope

a perpendicular line's slope is the opposite reciprocal

-5/3 = m

y-y1=m(x-x1)

(-6, 4) = (x1, y1)

plug in the values

y-4= -(5/3) (x+6)

y-4= -5/3 x - 10

y= -5/3 x - 6

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y=748(1+.03)^10

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2 years ago

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ludmilkaskok [199]

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3 years ago

PLEASE HELP ASAAP 25 PTS + BRAINLIEST TO RIGHT/BEST ANSWER

Nutka1998 [239]

Let i = sqrt(-1) which is the conventional notation to set up an imaginary number

The idea is to break up the radicand, aka stuff under the square root, to simplify

sqrt(-8) = sqrt(-1*4*2)

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<h3>Answer is choice A</h3>

5 0

3 years ago

HELP: I need help on multiple questions for a quiz before tomorrow night. If all is answered, you will get 40+ points and marked

Vinil7 [7]

Answer:

1. $33,000

2. $6077.53

3.

a) 2.72 seconds

b) 0.96 seconds

4. 189 square meters

5.

a) Average Rate of Change = 4 pounds per week, or -4

b) 160 pounds (after 5 weeks)

6.

Independent Variables = p, A, and H

Dependent Variable = T

141 beats per minute (rounded to nearest whole number)

Step-by-step explanation:

1.

The value of a tractor V(t) decreases over time, t. Its value is given by:

$V(t)=55000-5500t$

To find value of tractor after 4 years, we would need to substitute "4" into t and calculate. It is shown below:

$V(t)=55000-5500t\\V(4)=55000-5500(4)\\V(4) =33000$

The value of the tractor after 4 years is <u>$33,000</u>

<u></u>

2.

The value of investment that is growing each year, is given by:

$f(n)=5000(1.05)^{n}$

Where

5000 is the initial investment (deposit)

1.05 means a 5% growth rate per year

n is the time in years

We want the investment's value after 4 years, so n would be 4. Substituting we get our answer:

$f(n)=5000(1.05)^{n}\\f(4)=5000(1.05)^{4}\\f(4)=6077.53$

To the nearest cent, the value of the investment would be:

<u>$6077.53</u>

<u></u>

3,

The time it takes of pendulum to make one swing is given by the formula:

$T(L)=2\pi \sqrt{\frac{L}{32}}$

Where L is the length of the pendulum in feet

a)

If L = 6ft, the time it will take is:

$T(6)=2\pi \sqrt{\frac{6}{32}}\\T(6)=2.72$

About <u>2.72 seconds</u>

<u></u>

b)

Now, the length is 9 inches, we convert it to feet first:

9/12 = 0.75 feet

So, the time it will take:

$T(0.75)=2\pi \sqrt{\frac{0.75}{32}}\\T(0.75)=0.96$

So, it will take about <u>0.96 seconds</u>

<u></u>

4.

The area of weed after t days can be modeled by:

$A(t)=0.006 \pi t^2$

Where t is number of days

Now, we want to find area after 100 days, so let t = 100, we get:

$A(t)=0.006 \pi t^2\\A(100)=0.006 \pi (100)^2\\A(100)=188.5$

Rounded to nearest sq. m, we have the area to be:

<u>189 square meters</u>

<u></u>

5.

a)

The avg. rate of change is basically how much the program is advertising that someone can loose in a week. It says "4 pounds per week". Since decrease, we give the value of "4" and negative sign So:

<u>Average Rate of Change = 4 pounds per week, or -4</u>

<u></u>

b)

Initial weight is 180 pounds, we know 4 pounds is decreased every week when going through the program course. So, after 5 weeks,

5 * 4 = 20 pounds will be less

So, he will be:

180 - 20 = <u>160 pounds (after 5 weeks)</u>

6.

The Karvonen formula is given as:

$T=p(220-A)+H(1-p)$

Where

T is target heart rate (in bpm)

p is the percent intensity (expressed as decimal)

A is the age (in yrs)

H is the resting heart rate (in bpm)

We need to identity the independent and dependent variables. Now, lets that a simple example:

y = 2x

Here,

x is the independent variable

y is dependent on x, so y in dependent

Similarly, if you look at the formula, you can see:

p, A, and H are all independent

T depends on them

So,

p, A, H are independent variables

T is the dependent variable

<u>Independent Variables = p, A, and H</u>

<u>Dependent Variable = T</u>

<u></u>

We are given

A = 35

H = 60

p = 65% = 65/100 = 0.65

Now, we want T, lets substitute and find:

$T=0.65(220-35)+60(1-0.65)\\T=141.25$

<u>The target heart rate should be: 141 beats per minute (rounded to nearest whole number)</u>

<em><u /></em>

<em><u /></em>

3 0

3 years ago

Can a math god help me out?

Taya2010 [7]

Answer:

$f(1)=70$

$f(n)=f(n-1)+6$

Step-by-step explanation:

One is given the following function:

$f(n)=64+6n$

One is asked to evaluate the function for $(f(1))$ , substitute $(1)$ in place of $(n)$ , and simplify to evaluate:

$f(1)=64+6(1)$

$f(1)=64+6$

$f(1)=70$

A recursive formula is another method used to represent the formula of a sequence such that each term is expressed as a function of the last term in the sequence. In this case, one is asked to find the recursive formula of an arithmetic sequence: that is, a sequence of numbers where the difference between any two consecutive terms is constant. The following general formula is used to represent the recursive formula of an arithmetic sequence:

$a_n=a_(_n_-_1_)+d$

Where ( $a_n$ ) is the evaluator term ( $a_(_n_-_1_)$ ) represents the term before the evaluator term, and (d) represents the common difference (the result attained from subtracting two consecutive terms). In this case (and in the case for most arithmetic sequences), the common difference can be found in the standard formula of the function. It is the coefficient of the variable (n) or the input variable. Substitute this into the recursive formula, then rewrite the recursive formula such that it suits the needs of the given problem,

$a_n=a_(_n_-_1_)+d$

$a_n=a_(_n_-_1_)+6$

$f(n)=f(n-1)+6$

3 0

3 years ago