bài 5: rút gọn
(x +1)^2 – (2x + 1)^2

Answer:

Answer is C.

Step-by-step explanation:

[tex] ( {a}^{5} {b}^{2} {c}^{5} )( {ac}^{2} ) [/tex]

form brackets of common terms:

[tex] = ( {a}^{5} .a)( {b}^{2} )( {c}^{5} . {c}^{2} )[/tex]

from law of indices:

[tex]{ \boxed{ \bf{ {x}^{n} \times {x}^{m} = {x}^{(n + m)} }}}[/tex]

therefore:

[tex] = \{ {a}^{(5 + 1)} \} \{ {b}^{2} \} \{ {c}^{(5 + 2)} \} \\ = {a}^{6} {b}^{2} {c}^{7} [/tex]

Answer:

Equation x(6+6)=3(10+x)

x=3.33

Step-by-step explanation:

Form an equation:

x(6+6) The result of 6+6 is multiplied by x, so you would put 6+6 in a bracket (you do what's inside the bracket first in BODMAS) and the x on the outside so you times the result by x.

3(10+x) The number x is added to 10 and the result is multiplied by 3, so the 10+x would go in a bracket with 3 on the outside.

These equal each other, so you would put an equals sign between it to make:

x(6+6)=3(10+x)

Solve to find x:

12x=30+3x You expand the brackets to make this.

9x=30 You would move 3x to the other side by doing the inverse and taking away 3x from 12x.

x=3.33 To get x you would have to do 30 divided by 9 which is 3.33.

Hope this helps :)

The number asked is 8

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, When six is added to six times a number, the result obtained is the same as when the number is added to 10 and the result multiplied by 3.

Let the number be x,

Establishing, the equation,

6x+6 = 3(x+10)

6(x+1) = 3(x+10)

6/3(x+1) = x+10

2(x+1) = x+10

2x+2 = x+10

x = 8

Hence, the required number is 8.

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Answer:

Step-by-step explanation:

y = kx

y = 20

x = 4

20 = k*4           Divide by 4

20/4 = k

k = 5

The equation is y = 5x

Step-by-step explanation:

116/4+28-33

29+28-33

57-33

24

Answer:

Step-by-step explanation:

16 - 8 which will give 8. The 16 is plus, the 8 is minus. They do have different signs.

15 - 7 which gives 8. Same explanation.

108 - 100 = 8 Same method.

Answer:225/8 in square

Step-by-step explanation:

No

the answer is...............

x= 5/3

Answer:

f(2) = 2

Step-by-step explanation:

given:

[tex]f(x) = -2×2-2x+10[/tex]

find:

[tex]f(2) [/tex]

~~~~~~~~~~~~

➡️ [tex] f(2) = -2×2-2(2)+10[/tex]

➡️ [tex] f(2) = -2×2 = -4[/tex]

➡️ [tex] f(2) = -4-2×2+10[/tex]

➡️ [tex] f(2) = -4-4+10 [/tex]

➡️ [tex] f(2) = -8 +10 [/tex]

➡️ [tex] f(2) = 2 [/tex]

Answer:

All right

6. 7

7. -40

8. -1/6

9.  1

10. 3/5

11. -7

If you have any questions don't hesitate to ask

Answer:

Solve the following equations, and explain its each step.

6. 6x +3= 5x + 10

Solution given:

6x +3= 5x + 10

Subtracting both side by 5x

6x-5x+3=5x-5x+10

x+3=10

subtracting both side by 3

x+3-3=10-3

x=7

7. 6+ 0.10x = 0.15x+8

Subtracting both side by 0.15x

6+0.10x-0.10x=0.15x-0.10x+8

6=0.05x+8

subtracting both side by 8

6-8=0.05x+8-8

-2=0.05x

dividing both side by 0.05

-2/0.05=x

x=-40

8. 5-4x=6+2x

adding 4 on both side

5-4x-4x=6+2x+4x

5=6+6x

subtracting both side by 6

5-6=6-6+6x

-1=6x

dividing both side by 6

-1/6=6x/6

x=-1/6

9. 9-2x=7x

Solution given

adding 2x on both side

9-2x+2x=7x+2x

9=9x

dividing both side by 9

9/9=9x/9

x=1

10. 2(x-4) + 2x = -6x-2

open bracket

2x-8+2x=-6x-2

solve like terms

4x-8=-6x-2

adding 6 on both side

4x+6x-8=-6x+6x-2

10x-8=-2

adding 8 on both side

10x-8+8=-2+8

10x=6

dividing both side by 10

10x/10=6/10

x=3/5

11. ½x-3=3/2 x+4

Subtracting both side by ½x

½x-½x-3=³/2 x-½ x +4

solve like terms

-3=x+4

Subtracting both side by 4

-3-4=x+4-4

x=-7

Answer:

She makes $2,250/day

Step-by-step explanation:

$75 x 6 = $450 (amount of patients seen)

$450 x 6 = $2,700 (amount of hours she works)

$2,700 - $450 = $2,250 (the cost of the building, reception desk, & insurance)

We are given that the doctor charges $75 for each patient

In each she sees an average of 6 patients so,

Charge each hr = $75(6) = $450

For each hr she receives $450

So, for 6 hrs she receives = $450(6) = $2700

She pays for all the stuff = $200 + $200 + $50 = $450

Profit = Selling Price - Cost Price

Profit = $2700 - $450

Profit = $2250

Answer:

never

Step-by-step explanation:

p->q means if p is true, then q must also be true

but since q is false, p->q is never true

Answer: Never

Explanation:

The notation p -> q refers to a conditional statement.

Conditionals are only false when the first part (p) is true while the second part (q) is false. In other words, the template true --> false ultimately leads to a false statement. Otherwise, the entire thing is true.

In our case, we have something that fits the "true -> false" template, so that's why p -> q is never true when p = true and q = false.

Answer:

I think that some information is missing? what is the slope?

If you are trying to say that there is NO SLOPE then the

answer is " x = 4 "

Step-by-step explanation:

Step-by-step explanation:

the bonus received by each share is 24,000

Answer:

-33/80

Step-by-step explanation:

3/20 - 9/16

(4)(3/20) - (9/16)(5)

12/80 - 45/80

= -33/80

Answer:

18√2

Step-by-step explanation:

2√3 x 3√6

2 x 3 x (√6 x √3)

=> 6√18

=> 6√(3x3x2)

=> 6 x 3√2

=> 18√2

Answer:

<BAC=60°

Step-by-step explanation:

THIS IS THE ANSWER

Answer:

done the first 3

Step-by-step explanation:

5×-3=-15

2×4=8

3×-5=-15

(-15+8)²+-15

(-7)²+-15

-49-15

=-74

(2×-3×-6)²-5(4)

(36)²-20

1296-20

=1276

(-3×4×-5)+3(4)³

60+192

=252

Answers;

1. {(5x + 2y)}^{2} + 3z \\ {(5( - 3) + 2(4))}^{2} + 3( - 5) \\ {( - 15 + 8)}^{2} - 15 \\ {( - 7)}^{2} - 15 \\ 49 - 15 \\ 34 \\ \\ 2. \: 2 {(xz)}^{2} - 5y \\ 2 ({( - 3)( - 5)})^{2} - 5(4) \\ 2 {(15)}^{2} - 20 \\ 2(225) - 20 \\ 450 - 20 \\ 430

Step-by-step explanation:

[tex] \frac{10}{6} \\ \frac{15}{9} \\ \frac{20}{12} [/tex]

Answer:

12, 15, 24

Step-by-step explanation:

Let 1st # = x

Let 2nd # = x+3

Let 3rd # = 2x

Your equation is: x + (x+3) + 2x = 51

Add up all the x: x + x +3 +2x =51

Subtract 3 from both sides: 4x + 3 - 3 = 51 - 3

Divide 4 from both sides: 4x / 4 = 48 / 4

Your 1st number is x = 12

For the 2nd # it is 3 more than x so 12 + 3 = 15

For the 3rd # it is 2 times x so 2(12) = 24

Check your answers by adding up the numbers you solved: 12 + 15 +24 = 51

Does it equal to 51 as stated in the question? Yes, answers check out.

Answer:

2.56

Step-by-step explanation:

unit price = 8/3.12

                = 2.56

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

1. Approach

The most logical steps to solve the given equation are to distribute and simplify the left side of the equation. Then use inverse operations to bring all of the terms to the left side of the equation. After doing so, one can factor the equation again, then use the zero-product property to solve it.

2. Simplify

Distribute the terms on the left side, multiply everything in the first parenthesis by everything in the second,

[tex](x+1)(x-11)=-36[/tex]

[tex](x)(x)+(1)(x)+(-11)(x)+(1)(-11)=-36[/tex]

Simplify this expression by performing the multiplication and then combining like terms,

[tex](x)(x)+(1)(x)+(-11)(x)+(1)(-11)=-36[/tex]

[tex]x^2+x-11x-11=-36[/tex]

[tex]x^2-10x-11=-36[/tex]

Inverse operations,

[tex]x^2-10x-11=-36[/tex]

[tex]x^2-10x+25=0[/tex]

3. Factor and solve,

Now that has the simplified version of the equation, one should factor it. Rewrite the quadratic expression as a product of two linear expressions,

[tex]x^2-10x+25=0[/tex]

[tex](x-5)^2=0[/tex]

Use the zero product property to solve this expression. The zero product property states that any number times zero equals zero. Since ([tex](x-5)^2[/tex]) is just ([tex]x-5[/tex]) multiplied by itself, thus, when solving, one can ignore the square part of the equation:

[tex](x-5)^2=0[/tex]

[tex]x-5=0[/tex]

Inverse operations,

[tex]x-5=0[/tex]

[tex]x=5[/tex]

Answer:

they would each get 6 and there would be 2 left over

Step-by-step explanation:

3x6=18

20-18=2

=2 leftovers

Answer:

Each of the friends will get 6 with 2 small prizes remaing

Step-by-step explanation:

20 ÷ 6 = 18 remainder of 2

Ignore the 2 because you cannot split 2 evenly from 3 people.

So each friend gets 6, while there is a 2 remainder

To check our work just do 6 × 3 = 18 and 20 - 18 = 2

So, in conclusion, each friend get 6 while there are 2 small prizes left

Answer:

(5;3)

Step-by-step explanation:

Give your answer both.

The distance between the points (5, 0) and (0, 3) is approximately 5.83095 units.

To find the distance between two points, we can use the distance formula:

Distance = √[tex]((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]

Given the points (5, 0) and (0, 3), we have:

[tex]x_1 = 5, y_1 = 0\\\\x_2 = 0, y_2 = 3[/tex]

Substituting these values into the formula:

Distance = √[tex]((0 - 5)^2 + (3 - 0)^2)[/tex]

Distance = √[tex]((-5)^2 + (3)^2)[/tex]

Distance = √(25 + 9)

Distance = √34

The exact distance between the points is √34, which is approximately 5.83095 when rounded to five decimal places.

So, the distance between the points is approximately 5.83095 units.

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Hi ;-)

Equation 1°

[tex]2(x+1)=-8x+8(x-2)\\\\2x+2=-8x+8x-16\\\\2x+8x-8x=-16-2\\\\2x=-18 \ \ /:2\\\\\huge\boxed{x=-9}[/tex]

Equation 2°

[tex]4(7+2x)=-2(x+4)+4x\\\\28+8x=-2x-8+4x\\\\8x+2x-4x=-8-28\\\\6x=-36 \ \ /:6\\\\\huge\boxed{x=-6}[/tex]