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2 years ago

A straight line passes through A (-2, 0) and B (2,-k). The line is

Mathematics

1 answer:

gtnhenbr [62]2 years ago

3 0

Answer:

Step-by-step explanation:

Let the slope of the first line be m1

Let the slope of the second line be m2

If both lines are perpendicular, then;

m1m2 = -1

Get m1, the slope of the line passing through A (-2, 0) and B (2,-k).

m1 = y2-y1/x2-x1

m1 = -k-0/2-(-2)

m1 = -k/4

Get the slope of the line 3y + 2x = 5

Rewrite the equation;

3y = -2x + 5

y = -2/3 x + 5/3

Hence the slope of the line m2 is -2/3

Since m1m2 = -1, then;

-k/4(-2/3) = -1

2k/12 = -1

k/6 = -1

k = -6

Hence the value of k is -6

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Find the sum of the first 13 terms in the series -5+1+7...+67

valentinak56 [21]

This is an arithmetic series with common difference 6

S13 = (13/2)[2*-5 + (13-1)*6)] = 403

5 0

3 years ago

If the perimeter of a triangle is 45 cm and the ratio of the 3 sides is 2:3:4, find the length of all 3 sides

frozen [14]

Answer:

Below.

Step-by-step explanation:

2 + 3 + 4 = 9 so

the smallest side = 2/9 * 45, the next = 3/9 * 45 and the longest = 4/9 *45.

= 10, 15 and 20 cm.

5 0

3 years ago

The cash drawer of the market contains $227. There are six more $5 bills than $10 bills. The number of $1 bills is two more than

k0ka [10]

Answer:

There are 122 one dollar bills, 11 five dollar bills and 5 ten dollar bills.

Step-by-step explanation:

There are bills of one dollar, five dollars and ten dollars on the cash drawer, therefore the sum of all of them multiplied by their respective values must be equal to the total amount of money on the drawer. We will call the number of one dollar bills, five dollar bills and ten dollar bills, respectively "x","y" and "z", therefore we can create the following expression:

$x + 5*y + 10*z = 227$

We know that there are six more 5 dollar bills than 10 dollar bills and that the number of 1 dollar bills is two more than 24 times the number of 10 dollar bills, therefore:

$y = z + 6\\x = 2 + 24*z$

Applying these values on the first equation, we have:

$2 + 24*z + 5*(z + 6) + 10*z = 227\\2 + 24*z + 5*z + 30 + 10*z = 227\\39*z + 32 = 227\\39*z = 227 - 32\\39*z = 195\\z = \frac{195}{39}\\z = 5$

Applying z to the formulas of y and x, we have:

$y = 5 + 6 = 11\\x = 2 + 24*5 = 122$

There are 122 one dollar bills, 11 five dollar bills and 5 ten dollar bills.

4 0

3 years ago

After the 4th half life how much of the sample is left if the mass is 100g.

vazorg [7]

Answer:

$\huge\boxed{\sf 6.25 \ g}$

Step-by-step explanation:

After every Half life , Half of the mass is left.

After 1st Half life = 100 g / 2 = 50 g

After 2nd Half life = 50 / 2 = 25 g

After 3rd Half life = 25 / 2 = 12.5 g

After 4th Half life = 12.5 / 2 = 6.25 g

$\rule[225]{225}{2}$

Hope this helped!

6 0

2 years ago

Help me plz I don’t understand

puteri [66]

Emma’s statement makes sense and Charles’ doesn’t, bcuz when you say 0.75 it should be 75 tenths, because it’s less than a whole number, but charles said 7 and 5 tenths, if it’s 7 and 5 tenths, it would be 7.5.

3 0

3 years ago