The equation of a straight line is given by 3x - 2y - 6 = 0. Find the:
i) Gradient of the line;
ii) Y - intercept

Answer:

p = 3

q = 2

Step-by-step explanation:

they have infinitely many solutions, if they are basically the same equations. in other words, when they can be combined/reduced into a statement of tautology, a statement that is always true, no matter what.

like 15 = 15 or 8x = 8x

now we need to aim for creating the same (or multiples of the same) factors in the original equation 2 as in the original equation 1.

in other words we find the p and q, where we get the same ratios between the factors of squadron 1 and equation 2.

2/(p+q+1) = 3/(p+2q+2) = 7/(4p +4q +1)

p+q+1 = 2/3 × (p+2q+2) = 2/7 × (4p + 4q + 1)

3p + 3q + 3 = 2p + 4q + 4 = 6/7 × (4p+4q+1)

21p + 21q + 21 = 14p + 28q + 28 = 24p + 24q + 6

7p - 7q = 7

p - q = 1

p = 1 + q

14(1+q) + 28q + 28 = 24(1+q) + 24q + 6

14 + 14q + 28q + 28 = 24 + 24q + 24q + 6

42 + 42q = 30 + 48q

12 = 6q

q = 2

p = 1 + 2 = 3

Answer:

break-even point in units = 23,416 units (Approx.)

Step-by-step explanation:

Given:

Initial budget of Php = 8,500,000

Sales price of Php = 600

Variable price of Php = 237

Find:

break-even point in units

Computation:

break-even point in units = Initial budget of Php / [Sales price of Php - Variable price of Php]

break-even point in units = 8,500,000 / [600 - 237]

break-even point in units = 8,500,000 / 363

break-even point in units = 23,415.978

break-even point in units = 23,416 units (Approx.)

Answer:

18

Step-by-step explanation:

4*3 = 12

1/2 * 3 * 4  = 6

Answer:

60

Step-by-step explanation:

To get the value of x;

3x:90

(90/3) = 30

x = 30

To get the value of 2x;

(2×X);

2 × 30

=60

(x-h)²+(y-k)²=r²

(3-h)²+(3-0)²=5²

h²-6h+9+9=25

h²-6h-7=0 —> (h-7)(h+1)=0

h=7 , h=-1

h=7 —> (x-h)²+y²=r² —> (x-7)²+y²=25 —>

x²-14x+49+y²=25 —> x²+y²-14x+24=0

h=–1 —> (x-h)²+y²=r² —> (x+1)²+y²=25 —>

x²+2x+1+y²=25 —> x²+y²+2x–24=0

I hope it helped you ^_^

Answer:

Width = 4.85 feet

Length = 7.85 feet

Step-by-step explanation:

Given:

Perimeter of a rectangle = 25 2/5 ft = 25.4 feet

Length = 3 + Width

Computation:

Assume;

Width = a

So,

Length = 3 + a

Perimeter of a rectangle = 2(l + b)

25.4 = 2[(3 + a) + a]

25.4 = 2[3 + 2a]

25.4 = 6 + 4a

4a = 19.4

a = 4.85

Width = 4.85 feet

Length = 3 + 4.85

Length = 7.85 feet

9514 1404 393

Answer:

  7.5%

Step-by-step explanation:

The tax as a proportion of the selling price is ...

  ₹(860 -800)/₹800 = 60/800 = 0.075 = 7.5%

Step-by-step explanation:

here's the answer to your question

Answer:

( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2

Step-by-step explanation:

x^2 = - 7x - 8

x^2 + 7x + 8 = 0

Here,

a = 1

b = 7

c = 8

D = b^2 - 4ac

= 7^2 - 4 ( 1 ) ( 8 )

= 49 - 32

D = 17

x = - b ± √D / 2a

= - 7 ± √17 / 2 ( 1 )

x = ( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2

Answers:

============================================================

Explanation:

Let's solve the first equation for y

[tex]18 = (x+y)\frac{1}{3}\\\\18*3 = x+y\\\\54 = x+y\\\\x+y = 54\\\\y = 54-x\\\\[/tex]

Then we'll plug this into the second equation and solve for x

[tex]18 = (x-y)*\frac{3}{5}\\\\18 = (x-(y))*\frac{3}{5}\\\\18 = (x-(54-x))*\frac{3}{5}\\\\18 = (x-54+x)*\frac{3}{5}\\\\18 = (2x-54)*\frac{3}{5}\\\\18*5 = 3(2x-54)\\\\90 = 6x-162\\\\6x-162 = 90\\\\6x = 90+162\\\\6x = 252\\\\x = 252/6\\\\x = 42\\\\[/tex]

This is the average airspeed of the plane, in miles per hour (mph). It's the speed without accounting for the wind. If there's no wind at all, then this would be the ground speed of the plane.

Use this value of x to find y

y = 54-x

y = 54-42

y = 12

The average speed of the wind is 12 mph.

Answer:

y = 2x+4

Step-by-step explanation:

slope (m) = 2

point (-1,2)

so,

b = 2-2×(-1) = 4

y = mx+b

or, y = 2x+4

Answer:

6a+17

Step-by-step explanation:

This is an algebra 'expression' where you have to rearrange the question to the correct 'expression'

4a+2a= 6a

8+9= 17

Answer:

= 4a+2a+8+9

=6a+17

Answer:

Step-by-step explanation:

1046 pound

Answer:

1,046

Step-by-step explanation:

because 5 rounds up we raise it to the next whole number

Answer:

arc ≈ 4.2 cm

Step-by-step explanation:

The length of the arc is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{60}{360}[/tex]

     = 2π × 4 × [tex]\frac{1}{6}[/tex]

     = 8π × [tex]\frac{1}{6}[/tex]

    = [tex]\frac{8\pi }{6}[/tex]

    ≈ 4.2 cm ( to the nearest tenth )

Answer:

It would take him 5.9 weeks (rounded). basically almost 6 weeks

Step-by-step explanation:

he makes 6 dollars a week by walking the dog out. he earns 2$ every time he walks the dog out, and he does it 3 times, so 2 x 3 = 6

he makes another 10 dollars a week by babysitting. he earns 2.50$ per hour of babysitting, and he does it for 4 hours per week, so 2.50 x 4 = 10

he makes another 18$ dollars a week by mowing the lawn. he does this once a week. he gets 15$ dollars if he mows, and another 3$ if he pulls weeds. if he does both, he would get 15+3 = 18$ per week by mowing

so add the numbers 6, 10, and 18, and you get 34.

he makes 34 dollars a week

divide the number he wants to make by what he earns in a week to figure out how many weeks it would take.

he wants to get 200$, so the equation is

200 / 34 = 5.88

Its 5.9 rounded or 5.88 weeks exact.

Answer:

6 weeks

Step-by-step explanation:

Job 1:

2 x 3 = 6

$6 per week

Job 2:

2.50 x 4 = 10

$10 per week

Job 3:

15 + 3 = 18

$18 per week

6 + 10 + 18 = 34

$34 per week

200/34 = 5.88

tienees que fijartelos extrreemos

Answer:

A relation is just a set of ordered pairs (x,y) . In formal mathematical language, a function is a relation for which: if (x1,y) and (x2,y) are both in the relation, then x1=x2 . This just says that in a function, you can't have two ordered pairs with the same x -value but different y -values.

Step-by-step explanation:

Answer:

the last one

Step-by-step explanation:

Answer:

equation is 4x-4y= -16

Step-by-step explanation:

b = 4

x = -1

y = 3

so

x/a + y/b = 1

or, -1/a + 3/4 = 1

or, (-4 + 3a) = 4a

or, -4 = 4a - 3a

so, a = -4

now

x/a + y/b = 1

or, x/-4 + y/4 = 1

or, 4x-4y = -16

so

equation : 4x-4y = -16

Answer:

Answer is y=x+4

Step-by-step explanation:

x + y = 32 (1)

3x + 4y = 120 (2)

x = 8; y = 24

Step-by-step explanation:

Total students = 120

Number of groups = 32

If the number of three person groups = x

Number of four person groups = y

write a system of equations that models this situation

x + y = 32 (1)

3x + 4y = 120 (2)

From (1)

x = 32 - y

Substitute x = 32 - y into (2)

3(32 - y) + 4y = 120

96 - 3y + 4y = 120

- 3y + 4y = 120 - 96

y = 24

Substitute y = 24 into (1)

x + y = 32

x + 24 = 32

x = 32 - 24

x = 8

x = 8; y = 24

Answer:

The last answer

Step-by-step explanation:

We can check

For example,

a5=-6×a4

a5=-6×(-216)

a5=1296

Answer:

A & D

First and last

Step-by-step explanation:

Answer: Super Lightweight to Middleweight

Step-by-step explanation: I'm assuming you're talking about boxing weight class. If not, please let me know.

Answer: The answer is C or 13 units

How?: by a method called rise over run

the rise is at the y axis and the run is at x axis

*COUNT VERY CAREFULLY*

if you count right you should get 6 as a rise and  7 for run

6+7= 13

Answer:

B. 10 units

Step-by-step explanation:

Use the pythagorean theorem. (a^2 + b^2 = c^2)

Pretend that PQ is the hypotenuse of a right triangle.

Count the number of units for the supposed legs of the triangle.

The height would be 6 while the base is 8.

6^2 + 8^2 = PQ^2

36 + 64 = PQ^2

100 = PQ^2

PQ = 10

So, the answer is B.

Answer:

20 quarts

Step-by-step explanation:

There are  4 quarts in a gallon

5 gallons * 4 quarts / 1 gallon = 20 quarts

Answer:

20 US quarts

Step-by-step explanation:

there are 4 quarts in a gallon so you have to multiply 5 x 4 to get the total amount of quarts in a gallon.

Hope it helps c:

Answer:

37.68

Step-by-step explanation:

40 -2.32

= 37.68

Answer: is C. 22

Step-by-step explanation:

Answer:

[tex]{ \tt{n _{th} = a + (n - 1)d}} \\ { \tt{n _{57} = 13 + (57 - 1) \times 7}} \\ { \tt{n _{57} = 405}}[/tex]

Answer:

The denominator will be [tex]5\sqrt{3} +5\sqrt{2}[/tex]

Step-by-step explanation:

Answer:

a) 231

b) 52.8

Step-by-step explanation:

210*.10 = 21. 21+210 = 231

48*.10=4.8 4.8+48 =52.8

Answer:

a) 231

b) 52.8

Step-by-step explanation:

a)210x.1=21

210+21=231

b)48x.1=4.8

48+4.8= 52.8

Answer:

x = 78

Step-by-step explanation:

We can find angle y

D + B + y = 180 since the sum of the angles of a triangle are 180

31+47+ y =180

78+y = 180

y = 180 - 78

y = 102

x+y = 180 since they form a straight line

x + 102 = 180

x = 180-102

x = 78

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

we have to find the value of the x°=<GHC

In the triangle BDH,

we know that,

Sum of three angle of a triangle is 180°

According to the question,

But,

<GHC and <BHD forms a straight line

so,

Therefore,

The value of x is 78°