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3 years ago

Are the lines y = -x - 6 and 3x - 3y = 9 perpendicular? Explain

Mathematics

1 answer:

irakobra [83]3 years ago

4 0

Answer:

the lines are perpendicular

Step-by-step explanation:

if they are perpendicular the products of their gradients would be -1

the gradient of y=-x-6 is -1

the second equation needs to written to conform to y=mx+c

hence, 3x-3y=9

3x-9=3y

y=3x-9/3=x-3.the gradient of this line is 1

1x-1= -1

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On a map where each unit represents one kilometer, two marinas are located at P(4,2) and Q(8,12). If a boat travels in a straigh

Slav-nsk [51]

Answer:

Step-by-step explanation:

draw a right angled triangle with the right angle in the bottom left

label P as the bottome left corner and write its coordinates next to it

do same with Q

the length of the triangle is 4 (8-4 = 4)

the height is 10 (12-2 = 10)

use pythagoras to work out the hypotenuse:

$\sqrt{4^{2}+10^{2}} =2\sqrt{29}$

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3 years ago

Which of the following are possible rational roots of the polynomial function f(x)=5x^2-3x+3

yanalaym [24]

You didn't post any option, but the ration roots theorem states that all possible rational roots of a polynomial come in the form

$\pm\dfrac{p}{q}$

where p divides the constant term and q divides the leading term of the polynomial. So, in your case, p divides 3 (i.e. it is 1 or 3), and q divides 5 (i.e. it is 1 or 5).

So, the possible roots are

$\pm 1,\quad \pm 3,\quad \pm\dfrac{1}{5},\quad \pm\dfrac{3}{5}$

For the record, this parabola has no real roots.

7 0

3 years ago

Read 2 more answers

What is the sum of -19 and the product of 48 ?

IceJOKER [234]

It has to be -912 because i checked on a caculator

5 0

3 years ago

At the coffee shop, two coffees and one latte cost $10.50. Three coffees and two lattes cost $17.00. What is the cost of one cof

EastWind [94]

To solve this problem, we can set two equations.

Let x be the cost of coffee and y be the cost of latte.

Two coffees and one latte: 2x + y = 10.50

y=10.50 - 2x ...(1)

Three coffees and two lattes: 3x + 2y = 17.00...(2)

Put (1) into (2), we have:

3x + 2(10.50-2x) = 17.00

3x + 2(10.50) - 2(2x) = 17.00

3x + 21 - 4x = 17

Put the unknown to one side:

3x -4x = 17 - 21

-x = -4

When there are negative numbers on both sides, we can take the negative signs away:

x= 4

Therefore, cost of one coffee is A. $4.00.

Hope ot helps!

3 0

4 years ago

Which side lengths form a right triangle?

fredd [130]

Answer:

Answer: $\huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{➔}\$ Pythagoras law:h²=p²+b²

needed to apply

4²+8²=12²

80≠144 not a right angled triangle

again

2²+√5²=3²

9=9/

side are a right angled triangle

again

2²+2²=(√8)²

4+4=8

8=8

side are a right angled triangle

4 0

3 years ago