MATHEMATICS HIGH SCHOOL

Item 4What is the expanded form of this number?

570.086


(5×100)+(7×10)+(8×110)+(6×1100)

(5×100)+(7×10)+(8×1100)+(6×1100)

(5×100)+(7×10)+(8×1100)+(6×11,000)

(5×100)+(7×10)+(8×110)+(6×11,000)

Answers

Answer 1
Answer:

Answer:

10, 100. 70,700

Step-by-step explanation:

cuz qauntom of 11 77 divided by 11

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Test yourself 215) if f''(x)=6x+6 and there is a stationary point at (0,3), find the equation of the curve

Answers

Ok, so dy/dx=0 at the point (0,3) that is where x=0 and y=3.

\int { 6x+6dx } \n \n =\frac { 6{ x }^( 2 ) }{ 2 } +6x+C\n \n =3{ x }^( 2 )+6x+C

\n \n \therefore \quad { f }^( ' )\left( x \right) =3{ x }^( 2 )+6x+C

Now, f'(x)=0 when x=0.

Therefore:

0=C\n \n \therefore \quad { f }^( ' )\left( x \right) =3{ x }^( 2 )+6x

Now:

\int { 3{ x }^( 2 ) } +6xdx\n \n =\frac { 3{ x }^( 3 ) }{ 3 } +\frac { 6x^( 2 ) }{ 2 } +C

={ x }^( 3 )+3{ x }^( 2 )+C\n \n \therefore \quad f\left( x \right) ={ x }^( 3 )+3{ x }^( 2 )+C

But when x=0, y=3, therefore:

3=C\n \n \therefore \quad f\left( x \right) ={ x }^( 3 )+3{ x }^( 2 )+3
f''(x)=6x+6\nf'(x)=\int 6x+6\, dx\nf'(x)=3x^2+6x+C\n\n0=3\cdot0^2+6\cdot0+C\n0=C\nf'(x)=3x^2+6x\n\nf(x)=\int 3x^2+6x\, dx\nf(x)=x^3+3x^2+C\n\n3=0^3+3\cdot0^2+C\n3=C\n\n\boxed{f(x)=x^3+3x^2+3}

What times what equals 12 but still equals 11? the equation is 5n to the 2nd power + 19+12

Answers

OKay first you have to combine your like terms 19+12=31 then you have to divide by 5n squared which would be 6.2

Solve 7(z +2) - 3z =44

Answers

7(z +2) - 3z =44
Distribute the 7. Distributive property: a(b+c) = ab + ac

7z + 14 - 3z = 44
Simplify like terms.

4z + 14 = 44
Subtract 14 to both sides

4z = 30
Divide by 4 on both sides.


z = 7.5
distribute 7: 
7z+14-3z=44
4z+14=44
4z=30
z=15/2

Sharon is decreasing the size of a diagram of a leaf that is 30 centimeters long by 10 centimeters wide, if the reduced diagram is 4 centimeters wide how long will it be?

Answers

Answer:

12 cm


Step-by-step explanation:

This is a proportionality/similarity problem.

10 cm turned to 4 cm. So by how much has it decreased? In other words, 10 multiplied by WHAT is 4?

10*x=4\nx=(4)/(10)\nx=0.4

0.4 is also known as the scale factor from the large diagram to the small diagram.

So how much would 30 cm become? It would be 30 multiplied by the scale factor, which is 0.4.

30*0.4=12

Hence, the length of the reduced diagram would be 12 cm.
x-length\n\nFrom\ proportion:\n\n(30)/(10)=(x)/(4)\n\n10x=120\ \ \ \ \ \ |:10\n\nx=12\n\nIt\ will\ be\ 12\ cm\ long

If a + b = 28 and a - b = 10, then b =?

Answers

Answer:

b=9

Step-by-step explanation:

A number increased by four is the same as 19 minus 2 times the number

Answers

From the information given, 4 added to the unknown number is equal to 2 times the unknown number when it is subtracted from 19.

Let the number be x

x + 4 = 19 - 2 (x)

We now expand and simplify the equation by placing unknown on one side and the known on the other side

x + 4 = 19 - 2x

x + 2x  = 19 - 4

       3x = 15

         x = 15 /3

          x = 5
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