I need help please what is the correct answer

for what value of k, the line joining 3x-ky+7=0 is perpendicular to the line joining (4 ,3) and ( 5, -3).

Schach [20]

Answer:

k = 18

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<h2>Given</h2>

3x - ky + 7 = 0

Passing through the points (4, 3) and (5, - 3)

The value of k, if the lines are perpendicular

<h2>Solution</h2>

We know the perpendicular lines have opposite reciprocal slopes, that is the product of their slopes is - 1.

Find the slope of line 1 by converting the equation into slope-intercept from standard form:

Info:

standard form is ⇒ ax + by + c = 0,
slope - intercept form is ⇒ y = mx + b, where m is the slope

3x - ky + 7 = 0
ky = 3x + 7
y = (3/k)x + 7/k

Its slope is 3/k.

Find the slope of line 2, using the slope formula:

m = (y₂ - y₁)/(x₂ - x₁) = (-3 - 3)/(5 - 4) = - 6/1 = - 6

We have both the slopes now. Find their product:

(3/k)*(- 6) = - 1
- 18/k = - 1
k = 18

So when k is 18, the lines are perpendicular.

4 0

1 year ago

Paul is saving for a down payment to buy a house. The account earns 13% interest compound quarterly, and he wants to have $15,00

Tatiana [17]

Answer:

The principal must be = $8991.88

Step-by-step explanation:

Formula for compound interest is:

$A = P(1 + \frac{r}{n})^{nt}$

Where A is the amount after 't' years.

P is the principal amount

n is the number of times interest is compounded each year.

r is the rate of interest.

Here, we are given that:

Amount, A = $15000

Rate of interest = 13 % compounded quarterly i.e. 4 times every year

Number of times, interest is compounded each year, n = 4

Time, t = 4 years.

To find, Principal P = ?

Putting all the given values in the formula to find P.

$15000 = P(1 + \frac{13}{400})^{4\times 4}\\\Rightarrow 15000 = P(1 + 0.0325)^{16}\\\Rightarrow 15000 = P(1.0325)^{16} \\\Rightarrow 15000 = P \times 1.66817253\\\Rightarrow P = \dfrac{15000}{1.66817253}\\\Rightarrow P \approx \$8991.88$

So, the principal must be = $8991.88

4 0

2 years ago

If a circle has a circumference of 81.64 cm, what is the radius?

ipn [44]

Answer:13cm

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

You want to save $5000 to buy a car. You have $1325 in your account right now. You plan to work and save $150 out of each payche

d1i1m1o1n [39]

Answer:

approximately 25 weeks

Step-by-step explanation:

take $ 5000-$ 1325=$3675 this is what is remaining to achieve $5000

if you get $150 in one week what about $3675 is equal to how many weeks

$150=1 week

$3675=??weeks

$3675 × 1 week

$150

Ans =24.5 the same as 25 weeks

3 0

2 years ago

The difference between nineteen and eleven divided by the sum of two and one

igor_vitrenko [27]

Answer:

Step-by-step explanation:

EN 3x=17

4 0

3 years ago