Factorise fully

gcse maths

please help

Answer:

x = 1

Step-by-step explanation:

[tex]\frac{3x-3}{5}[/tex] = [tex]\frac{2x-2}{4}[/tex] ( cross- multiply )

4(3x - 3) = 5(2x - 2) ← distribute parenthesis on both sides

12x - 12 = 10x - 10 ( subtract 10x from both sides )

2x - 12 = - 10 ( add 12 to both sides )

2x = 2 ( divide both sides by 2 )

x = 1

Step-by-step explanation:

16x²y⁵16x²y⁵ is the answer

Answer:

43 1/2

Step-by-step explanation:

answer will be:

original height plus 3 times 8 7/12 inches

3 times 8 7/12 can be done by converting the mixed number to an improper fraction:

[tex]\frac{3}{1}[/tex] · [tex]\frac{103}{12}[/tex] = [tex]\frac{103}{4}[/tex] = 25 3/4

25 3/4 added to 17 3/4 equals 42 6/4 which is 42 + 1 1/2 = 43 1/2

Answer:

number 2 is c, number 3 is c

Answer:

Step-by-step explanation:

.<6 and <3

SOLUTION:  

Interior angles that are non adjacent and lie on

opposite. In the figure, angles <5 and <4 are consecutive interior

angles. sides of the transversal are alternate interior

angles.

<4 and <7

SOLUTION:  

In the figure, angles 1 and 3 are corresponding

angles. Use the Corresponding Angles Postulate:

If two parallel lines are cut by a transversal, then

each pair of corresponding angles is congruent

Answer:

go to https://www.rcboe.org/cms/lib010/GA01903614/Centricity/Domain/1030/Ch.%203.3.pdf

Step-by-step explanation:

i think that will help

Answer:

920 pages

Step-by-step explanation:

Divide 13,789 by 15, you should get 919.27 so just round up so you can hold all the cards.  

Answer:

-44

Step-by-step explanation:

Answer: -44

Step-by-step explanation: same as 36 + 8 and make the answer negative.

Answer:

There would be 10 more Girls.

Answer:

46 boxes of nails

Step-by-step explanation:

She has $187 to spend, the maximum.

187/4 = 46.75

Since she cannot buy 0.75 of a box of nails, she can only buy 46. So she is left with an extra $3 and buys 46 boxes of nails.

Hope this helps, and please mark me the brainliest! :D

Answer:

Step-by-step explanation:

One

The exterior angles of a triangle add up to 360. You know two of them. Therefore you can find w.

125 + 90 + w = 360    Combine like terms on the left

215 + w = 360             Subtract 215 from both sides

w = 360 - 215              Combine

w = 145

Two.

The polygon has 4 exterior angles. They too should add up to 360.

88 + x + 108 + 115 = 360     Combine the left had side

x + 311 = 360                       Subtract 311 from both sides

x = 360 - 311                        Combine

x = 49

What have you learned? You should notice that all polygons have exterior angles that add up to 360

Answer:

the answer is b ok understand

Answer:

16 5c coins

34 10c coins

Step-by-step explanation:

(I prefer to use whole numbers)

5x + 10y = 420

x+y=50

multiply the bottom problem by -5

5x +10y =420

-5x -5y = -250

combine the problems

5y = 170

divide by 5

y = 34

that means x = 16

34 10c coins

16 5c coins

-- Gage Millar, Algebra 1/2 tutor

The number of 5 cent coins are 16 and the number of 10 cent coins are 34.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, a trader has a mixture of 5 c and 10 c coins.

Let the the number of 5 c coins be x and the number of 10 c coins be y.

He has 50 coins in all, with a total value of $4.20.

So, x+y=50 ---------(I)

5x+10y=420 ---------(II)

Multiply equation (I) by 5, we get

5x+5y=250 ---------(III)

Subtract equation (III) from (II), that is

5x+10y-(5x+5y)=420-250

⇒ 5y=170

⇒ y=34

Substitute y=34 in equation (I), we get

x=16

Therefore, the number of 5 cent coins are 16 and the number of 10 cent coins are 34.

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The midpoint of the sides [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex]  are the points that half way between  [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] respectively.

The option that proves [tex]\overline{FB}[/tex] = [tex]\overline{GC}[/tex] is option 3

Reasons:

The given coordinates of the vertices of rectangle ABCD are;

A(0, 0), B(12, 0), C(12, 6), and D(0, 6)

The midpoint of side [tex]\overline{AB}[/tex] = Point F

The midpoint of side [tex]\overline{CD}[/tex] = Point F

The coordinates of point F is given by the midpoint formula, as follows;

[tex]\displaystyle \mathrm{The \ midpoint \ of \ a \ line \ with \ endpoints \ (x_1, \ y_1) \ and \ (x_2, \ y_2) = \mathbf{ \left(\frac{x_1 + x_2}{2}, \ \frac{y_1 + y_2}{2} \right) }}[/tex]

Which gives;

[tex]\displaystyle \mathrm{The \ coordinate \ of \ F \ the \ midpoint \ of \ \overline{AB} = \mathbf{ \left(\frac{0 + 12}{2}, \ \frac{0 + 0}{2} \right)} =(6,\ 0)}[/tex]

[tex]\displaystyle \mathrm{The \ coordinate \ of \ G \ the \ midpoint \ of \ \overline{CD} = \left(\frac{12 + 0}{2}, \ \frac{6 + 6}{2} \right) =(6,\ 6)}[/tex]

[tex]\overline{FB}[/tex] is parallel to the x-axis, therefore;

Similarly, [tex]\overline{GC}[/tex] is parallel to the x-axis, therefore;

Which gives;

The correct option is that proves [tex]\overline{FB}[/tex] = [tex]\overline{GC}[/tex] is option 3.

By the Midpoint Formula, the coordinates of F are (6, 0) and the coordinates of G are (6, 6). Then [tex]\overline{FB}[/tex] = 6, and [tex]\overline{GC}[/tex] = 6. Thus [tex]\overline{FB}[/tex] = [tex]\overline{GC}[/tex]

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Answer:

6,543

Step-by-step explanation:

This is my guess ONLY.

Answer:

Answer is C noumber

Step-by-step explanation:

We know that a combination is a collection of the items where the order doesn't matter. It is a way to calculate the total outcomes of an event where order of the outcomes does not matter. It is denoted by C(n,k) or (n,k) or (n/k).

The formula for the number of combinations of n things taken r at a time is given by :-

C(n,k)=(n/k)=\frac{n!}{k!(n-k)!}C(n,k)=(n/k)=

k!(n−k)!

n!

Hence, C is the right option.

Answer:

the answer is positive.

Step-by-step explanation:

12(-3)(-2)

the 2 negatives cancel out, so you get a positive 6

12(6)

72

positive 72

hope this helped!

mark me brainliest :D

This is karma for doing this to some one else :)

regdcd gvfd vcds xgrcd xre dse dxf crdx vcfx gvf c fcvr fvcrdgbv

Answer:

21

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

f(x)=(x+a)/b

or bf(x)=x+a

let f(x)=y

by=x+a

flip x and y

bx=y+a

or y=bx-a

or f^{-1}(x)=bx-a

also g(x) is inverse of f(x)

bx-a=cx-d

so b=c,a=d

again let g(x)=y

y=cx-d

flip x and y

x=cy-d

cy=x+d

y=(x+d)/c

or g^{-1}(x)=(x+d)/c

also f(x) is inverse of g(x)

so (x+a)/b=(x+d)/c

so a=d,b=c

so in either case a=d,b=c

take b=c=1

a=d=2

f(x)=(x+2)/1=x+2

g(x)=1x-2=x-2

so f(x) and g(x) are two parallel lines f(x) with y- intercept=1 and slope 0

g(x) with y-intercept -2 and slope 0

if we take b=c=2,a=d=3

f(x)=(x+3)/2=x/2+3/2

g(x)=2x-3

here f(x) is of slope 1/2 and y-intercept 3/2

g(x) is of slope 2 and y intercept -3

part 3.

f(f(x))=g((x+a)/b)=c[(x+a)/b]-d=(c/b)(x+a)-d

An inverse function or an anti function exists described as a function, which can change into another function. In other words, if any function “f” carries x to y then, the inverse of “f” will carry y to x.

Part 1: f(x) = (x+2) / 3 and g(x) = 3y-2.

Part 2: g(x) = 3x - 2, the inverse.

Part 3: g(f(x)) = x showing that f(x) and g(x) are mutual inverses.

An inverse function in mathematics exists function which "reverses" the another function.

TASK 1

Part 1

Let y = f(x) = (x + a) / b

x = g(y) = by-a = cy-d,

so c = b and d = a.

Let d = a = 2 and c = b = 3

f(x) = (x+2) / 3 and g(x) = 3y-2.

Part 2

y = f(x) = (x+2) / 3

3y = x+2  

x = 3y-2 = g(y)

so g(x) = 3x - 2, the inverse.

Part 3

g(f(x)) = 3

f(x)-2 = 3(x+2)/3-2 = x+2-2 = x,

so g(f(x)) = x showing that f(x) and g(x) exists mutual inverses.

x       -2  -1        0    1     2

f(x)    0    1/3   2/3   1    4/3

g(x)  -8   -5      -2    1      4

Part 4

The graph is given below.

TASK 2

Part 1

(a) Let a=1, b=2, c=3, d=6: [tex]$\sqrt{x}[/tex]+2+3=6 ; [tex]\sqrt{x}[/tex]-6=-5

(b) Let a=-1, b=2, c=3, d=4

(a) Multiply both sides by

[tex]$\sqrt{x}+6: x-36=-5(\sqrt{x}+6)=-5 \sqrt{x}-30[/tex]

[tex]$ x-36+30=-5 \sqrt{x }[/tex]

[tex]$ x-6=-5 \sqrt{x}$[/tex]

Square both sides:

[tex]$x^{2} -12 x+36=25 x ; x^{2} -37 x+36=0=(x-36)(x-1)$[/tex].

Part 2

(a) So x=36 or 1 (apparently).

Substitute x=36 in the original equation: 6+2+3=6, 11=6 is not true.

So x=36 is an extraneous solution.

substitute x=1: 1+2+3=6 is true, so x=1 exists the actual solution.

(b) [tex]$-\sqrt{x}+2+3=4 ;-\sqrt{x}=-1$[/tex]; multiply both sides by -1: [tex]$\sqrt{x}=1$[/tex]; square both sides: x=1.

Substitute x=1 in the original equation: -1+2+3=4 is true.

So x = 1 is the solution.

Part 3

(a) the act of squaring both sides resulted in creating an extraneous solution [tex]$\left((-5)^{2} =25=5^{2} \right)$[/tex].  

(b) the solution was simpler and there was no ambiguity.

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Answer:

Hence, f −1 (x) = x/3 + 2/3 is the correct answer.

Step-by-step explanation:

Verify (f ∘ f−1) (x) = x

(f ∘ f−1) (x) = f [f −1 (x)]

= f (x/3 + 2/3)

⟹ 3(x/3 + 2/3) – 2

⟹ x + 2 – 2

= x

Hence, f −1 (x) = x/3 + 2/3 is the correct answer.

Step-by-step explanation:

m(gradient) =y2-y1/x2-x1

=8-(-1) /4-5

=8+1/-1

=9/-1

=-9

y-y1=m(x-x1)

y-(-1)=-9(x-5)

y+1=-9x+45

y=9x+45-1

y=9x+44(rule)

Inverse>y+44=9x

y+44/9=9x/9

x=y+44/9

Therefore inverse is y=x+44/9

Answer:

c

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Answer:

ok so you see the equation at the top... you are going to "plug in" the number in the "in" row to get the "out number

Step-by-step explanation:

example

in: 4

-2(-4)+1

8+1

9

so for the out row under -4 you would put 9

-2(-3)+1

6+1

7

so for the out row under 3 you would put 7

Answer:

...

Step-by-step explanation:

Answer:

Using the slope-intercept form, the slope is 4 4 .

Answer: Using the slope-intercept form, the slope is 4 4 .

Explanation: so your answer is 4 4.

Answer:

Option 1:  y = (x - 2)² + 2

Step-by-step explanation:

Given the vertex, (2, 2), of an upward-facing parabola, and using the y-intercept of the graph, (0, 6):

The vertex form of the quadratic equations is:

y = a(x - h)² + k

where:

(h, k) is the vertex.

The sign of a  determines the direction of the graph's opening. The value of a also determines the vertical stretch or shrink of the graph.

Substitute the values of the vertex (2, 2) and the y-intercept, (0, 6) into the  vertex form to solve for the value of the coefficient, a:

y = a(x - h)² + k

6 = a(0 - 2)² + 2

6 = a(-2)² + 2

6 = 4a + 2

Subtract 2 from both sides

6 - 2 = 4a + 2 - 2

4 = 4a

Divide both sides by 4 to solve for a :

[tex]\displaytext\mathsf{\frac{4}{4} \:=\frac{4a}{4}}[/tex]

a = 1

Therefore, given the vertex, (2, 2) and a = 1, the quadratic equation in vertex form is: y = (x - 2)² + 2, thereby matching Option 1.

Step step :

-HayabusaBrainly

Answer: Neither

Step-by-step explanation: Technically the containers hold no water at all as they hold only the bottles in which the water is actually contained. So the answer I suppose is 'Neither'.