Factorise
4a(3a-b)+2b(3a-b)
​

Answer:

[tex](x +10)^2 + (y+6)^2 = 121[/tex]

Step-by-step explanation:

Given equation :

                        [tex]x^2 + y^2 + 20x +12y + 15 = 0[/tex]

Standard equation of circle :

                                            [tex](x - a)^2 + (y-b)^2 = r^2[/tex]

We will consider the x terms in the equation first to find a.

[tex](x-a)^2 = x^2 - 2ax + a^2[/tex]

-2ax = 20x

a = -20x/2x = -10

a = -10

Next consider the y terms to find b.

[tex](y - b)^2 = y^2 -2by + b^2[/tex]

-2by = 12y

b = -12y /2y = -6

b = -6

[tex](x+10)^2 + (y-6)^2 = x^2 +20x +100 + y^2 +12y + 36[/tex]

                             [tex]=x^2 + y^2 + 20x +12y + 136\\[/tex]

But the given equation constant is 15. So find the difference between 136 and 15 to find the radius : 136 - 15 = 121

Therefore, radius = √121 = 11

Equation in standard form :

                                         [tex](x +10)^2 + (y+6)^2 = 121[/tex]

Answeni ideAA{

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Step-by-step explanation:

i think its C.No;the system has many solución

Answer:

thanks the quark is w wl1pp39iejbs sthe akwyve s akw9u27 2babe

Answer:

A) y=4+x

Step-by-step explanation:

Since the initial amount was 4 gallons, any additional fuel added will be in addition to that.

Answer:

[tex] \frac{2}{4} , \frac{3}{4} \\ 1 \frac{2}{4} \\ 2 \frac{1}{4} [/tex]

Answer:

a=18-3 and b=32÷8

Step-by-step explanation:

the first one

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

Explanation:

We'll involve the nCr combination formula here. This is because order doesn't matter.

There are n = 13 diamonds and we want to select exactly r = 3 of them.

So,

[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{13} C _{3} = \frac{13!}{3!*(13-3)!}\\\\_{13} C _{3} = \frac{13!}{3!*10!}\\\\_{13} C _{3} = \frac{13*12*11*10!}{3!*10!}\\\\_{13} C _{3} = \frac{13*12*11}{3!}\\\\_{13} C _{3} = \frac{13*12*11}{3*2*1}\\\\_{13} C _{3} = \frac{1716}{6}\\\\_{13} C _{3} = 286\\\\[/tex]

There are 286 ways to pick the three diamond cards. Then there are 52-13 = 39 ways to pick the fourth card that is either a spade, club of heart.

So we have 286*39 = 11,154 ways to pick the four cards given the conditions your teacher set.

This is out of 52C4 = 270,725 ways to pick four cards (use the nCr formula above with n = 52 and r = 4).

Divide the two values to get the answer:

(11,154)/(270,725) = 0.04120048019208

that rounds to 0.04 which converts to 4%

So there's roughly a 4% chance of getting exactly 3 diamond cards.

Answer:

4% (four percent)

Answer:

17) just take the root of 100. the text says its square(d).

10m

And checking it gives 10m * 10m = 100m²

18) you need to learn some square numbers to ace this topic. it isn't that complicated, just multiply natural numbers with themselves

like

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

Now we can see that a) sqrt(55) lies between 7 and 8, and that its value is somewhere in between

7 < a < 8

(ignoring the negative solution to the root oc)

try b, c and d yourself. if you struggle, leave a comment.

I got a problem finding exercises 19 to 21, seriously....

22) well...

a * b = 18ft²

6ft * 3ft seems just right. pure guesswork here, seems to be to easy with these numbers.

but we can also write it as a system of two functions

a * b = 18ft²

a = 2b

and then solve it by substituting a in line one with 2b, since a is 2b this is allowed.

2b * b = 18

2 b² = 18

b² = 9

b = 3

(we ignore -3 as a solution bc negative length makes no sense)

plugging that b into line two of the system gives

a = 2 * 3

a = 6

27) rationale can we written as a ratio (a fration)

it almost sounds too simply

rationals are either the root of square numbers, bc they can be solved cleanly, or they got a repeating pattern after the point.

b and c apply to these rules, a and d not

30) lol, I just figured out where the missing exercises are hidden XD

31) just add up the three rectangles (easy part) with the two triangles top and bottom each triangle is just 12m * 16m / 2 (bc it's a triangle, not a rectangle). since you got two triangles you just multiply by two (it's like ignoring the decision. also, the two triangles together would indeed make just a n9ce rectangle).

if you really need the values, leave a comment, but that will not help you in any test.

you can also post your solutions and I'll check them.

32) area of the circle times two

plus area of a rectangle wrapped around the cylinder.

circle are is pi*r² -> pi * (28 in)²

(remember to double for two circles)

rectangle is the circumference of the circle (pi * 28in) times the height of the cylinder

like in 31), feel free two post your results or ask for values if you really struggle to grasp the pattern here.

hope you have a great day and that you understand some more of the topic. you can ace it :)

Answer:

[tex]x = 51^o[/tex]

Step-by-step explanation:

Given

Intersecting lines

Required

Find x

To do this, we make use of:

[tex]x + 23^o + 2x + 4^o = 180^o[/tex] --- angle on a straight line

Collect like terms

[tex]x + 2x = 180^o - 4^o - 23^o[/tex]

[tex]3x = 153^o[/tex]

Divide both sides by 3

[tex]x = 51^o[/tex]

Answer:

the independent variable

Step-by-step explanation:

tome is the independent variable

position is the dependent variable

In the given graph titled "Time vs. Position of Battery Operated Car," the "Time (s)" represents the independent variable.

The independent variable is typically plotted on the x-axis of a graph and represents the variable that is intentionally changed or controlled in an experiment or study.

In this case, the graph shows how the position of the battery-operated car changes over time, with time being the independent variable.

So the time represents the independent variable.

To learn more on Graph click:

https://brainly.com/question/17267403

#SPJ7

Step-by-step explanation:

The answer is A

Answer:

D. 5

Step-by-step explanation:

Applying,

cos∅ = adjacent/Hypotenuse

From the diagram,

Given: ∅ = 45°, adjacent = s, hyptenuse = 5√2

Therefore,

cos45° = s/5√2

make s the subject of the equation

s = cos45°×5√2

s = (1/√2)(5√2)

s = 5

Hence the right answer is D. 5

Answer:

x=22

Step-by-step explanation:

x+14=5x-74 (being corresponding angles and correcponding angles are always equal)

14+74=5x-x

88=4x

88/4=x

22=x

Answer:

I think its Your Values, but try and a get a second opinion

Answer:

First one.

Step-by-step explanation:

0.3/3=0.1 ==> 0.1$ per meter

0.77/7 ==> 0.11$ per meter

The first option is cheaper, therefore better to buy if you agree with "the cheaper. the better".

Answer:

The 4th one

Step-by-step explanation:

The number are times -4

-3 x -4 = 12

-6 x -4 = 24

-9 x -4 = 36

So, the answer is the 4th one

Answer:

30/100×150=

24/5%, that is the answer

Answer:

a and b

no the definitions have opposite results

Step-by-step explanation:

Answer:

no

Step-by-step explanation

3,6,9

Answer:

R and S

Step-by-step explanation:

Given

See attachment for plot

Required

Point on ray PQ

A ray is a line with a starting point, and  extends infinitely in the other direction.

So;

Ray PQ implies that.

P is the starting point, and it extends towards Q direction (however, it is endless).

Towards the direction of Q, we have points R and S.

This implies that R and S are on ray PQ.

Answer:

Is this a line on a graph with point for x,y.

Step-by-step explanation:

-9 is x and 9 is y

Answer:

24

Step-by-step explanation:

use a calculator for these type of problems next time!

the answer to this equation would be 24x

Answer:

The angle is 60°

Step-by-step explanation:

A supplement angle is the angle whose sum is equal to 180°.

The supplement angle = 180° - x

A complement angle is the angle whose sum is equal to 90°.

The complement angle = 90° - x

Given,

supplement angle = 4 × complement angle

(180° - x) = 4 × (90° - x)

180° - x = 360° - 4x

4x - x = 360° - 180°

3x = 180°

x = 60°

The supplement angle = 180° - x

⇒ 180° - 60°

⇒ 120°

The complement angle = 90° - x

⇒ 90° - 60°

⇒ 30°

Answer:

The angle is 60 degrees.

Step-by-step explanation:

Let the angle be x.

Then its supplement = 180-x.

Its complement = 90-x, so we have the equation:

180 - x = 4(90 - x)

180 - x = 360 - 4x

-x + 4x = 360 - 180

3x = 180

x= 60 degrees.

Answer:

Step-by-step explanation:

Angle b and the one that measures 76 are vertical angles. That means that they also have the same exact angle values. Therefore, b = 76 degrees

Answer:

B) $3 per gallon

Step-by-step explanation:

You can see on the graph that for 1 gallon of gasoline, it is $3.

Hope this helped!

Please mark as brainliest!

Answer:

90.6

Step-by-step explanation:

total is 181.2 divided by 2 is 90.6

Answer:

[tex]\sqrt{105}[/tex] is slightly more than 10, so 15 - [tex]\sqrt{105}[/tex] is less than 5.

Step-by-step explanation:

Given expression is (15 - √105).

Since, √105 ≈ Slightly greater than 10 [Since, [tex]\sqrt{100}=10[/tex]]

Therefore, when we subtract the value of [tex]\sqrt{105}[/tex] from 15,

15 - [tex]\sqrt{105}[/tex] = Slightly less than 5

From the given options answer will be,

[tex]\sqrt{105}[/tex] is slightly more than 10, so 15 - [tex]\sqrt{105}[/tex] is less than 5.