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3 years ago

What is the equation of a line that is perpendicular to this line and goes through the

Mathematics

1 answer:

-Dominant- [34]3 years ago

5 0

Answer:

x + 3y + 9 = 0

Step-by-step explanation:

y=3x + 2

Coefficient of x = 3

Gradient (m) of line y= 3x + 2 is 3

Since the line passing through point

(3,-4) is perpendicular to line y=3x + 2

hence gradient (m) of the line is -1/3;

And hence it equation is given as;

y - y1 = m(x - x1)

y - (-4) = -1/3(x - 3)

multiplying through by 3;

3 × y + 3 × 4 = 3 × -1/3(x - 3)

3y + 12 = -1(x - 3)

3y + 12 = -x + 3

x + 3y + 12 - 3 = 0

x + 3y + 9 = 0

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What is the slope and y-intercept

natulia [17]

Slope is 5/4 and y-intercept is -4
hope this helps

8 0

2 years ago

The 5th term in a geometric sequence is 40. The 7th term is 10. What is (are) the possible value(s) of the 4th term?

Lena [83]

Answer:

possible values of 4th term is 80 & - 80

Step-by-step explanation:

The general term of a geometric series is given by

$a(n)=ar^{n-1}$

Where a(n) is the nth term, r is the common ratio (a term divided by the term before it) and n is the number of term

Given, 5th term is 40, we can write:

$ar^{5-1}=40\\ar^4=40$

Given, 7th term is 10, we can write:

$ar^{7-1}=10\\ar^6=10$

We can solve for a in the first equation as:

$ar^4=40\\a=\frac{40}{r^4}$

Now we can plug this into a of the 2nd equation:

$ar^6=10\\(\frac{40}{r^4})r^6=10\\40r^2=10\\r^2=\frac{10}{40}\\r^2=\frac{1}{4}\\r=+-\sqrt{\frac{1}{4}} \\r=\frac{1}{2},-\frac{1}{2}$

Let's solve for a:

$a=\frac{40}{r^4}\\a=\frac{40}{(\frac{1}{2})^4}\\a=640$

Now, using the general formula of a term, we know that 4th term is:

4th term = ar^3

Plugging in a = 640 and r = 1/2 and -1/2 respectively, we get 2 possible values of 4th term as:

$ar^3\\1.(640)(\frac{1}{2})^3=80\\2.(640)(-\frac{1}{2})^3=-80$

possible values of 4th term is 80 & - 80

3 0

3 years ago

I WILL AWARD BRAINLIEST!! Find the value of x in each case.

kondor19780726 [428]

Angle D is equal to Angle B because AB and DE are parallel to each other.

AD is a straight line so the (2) 2x angles and 72 degrees need to equal 180.

Setting up the equation you have:

2x + 2x + 72 = 180

Simplify:

4x + 72 = 180

Subtract 72 from each side:

4x = 108

Divide both sides by 4:

x = 108 / 4

x = 27

5 0

3 years ago

For selected years, the national health care expenditure, in billion of dollors can be modelled by H=29.57e^0.0970t, remains acu

Sliva [168]

Answer:

The correct answer is 54.76 years.

Step-by-step explanation:

The national health care expenditure (H) , in billion of dollars is modeled by

H = 29.57 × $e^{0.0970t}$ .

To measure the time before which national health expenditure reach 6000 billion dollars.

Thus putting the value of H = 6000 in the above modeled equation we get,

⇒ 6000 = 29.57 × $e^{0.0970t}$

⇒ $\frac{6000}{29.57}$ = $e^{0.0970t}$

⇒ 202.908 = $e^{0.0970t}$

Taking logarithm with the base of e (㏑) both sides we get,

⇒ ㏑ 202.908 = ㏑ $e^{0.0970t}$

⇒ ㏑ 202.908 = 0.0970 × t

⇒ 0.0970 × t = 5.312

⇒ t = $\frac{5.312}{0.0970}$

⇒ t = 54.76.

Thus the total time required before which national health expenditure reach 6000 billion dollars is 54.76 years.

3 0

3 years ago

PLEASE HELP ME!!!!!!!

Evgesh-ka [11]

Monday $2000 Tuesday $1800 wendsday $ 1440 thursday $5670

8 0

3 years ago