Distribute to write an equivalent expression. 2n * (n ^ 2 + 3n + 4)

Answer:

Distributitive Property

Step-by-step explanation:

The correct justification for the first step in solving the provided equation is that the first step should be distributive Property

Property of equality says that by performing any mathematical operation, of both sides of a expression does not change the original value of the equation.

The equation given in the problem is,

[tex]3(x - 4) + 1 = 12x[/tex]

To solve the above equation, we need to open the brackets of the equation. To do this, we need to use the distributive property of the equality.

This can be done by multiplying the number 3 inside the bracket (x-4). This operation simplify the equation, to solve it further. Therefore,

[tex]3x - 3\times4 + 1 = 12x\\3x - 12 + 1 = 12x[/tex]

Hence, the correct justification for the first step in solving the provided equation is that the first step should be distributive Property.

Learn more about the property of equality here;

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Answer:

840

Step-by-step explanation:

b x h = 42 x 20

Answer:

10

Step-by-step explanation:

According to the Pythagorean theorem

x²=6²+8²=100

x=√100

x=10

Answer:

12/15

Step-by-step explanation:

If the probability of drawing a read marble is 3/15

Then that would just make the probability of NOT drawing a red marble 12/5

The percentage shows that number of people that were surveyed is 866.

Let the number of people surveyed be x.

Therefore, from the question given and the percentage, the calculation goes thus:

82% × x = 710

0.82x = 710

x = 710/0.82

x = 866

The number of people surveyed is 866.

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Answer:

Step-by-step explanation:

This is called a 'System of equations'.

Say that you have these two expressions, and the unknown is "b".

5b = y

4b+2 = y

Now we can solve two ways; graph it or solve it.

Solving it, we can see that they both equal y, so:

5b=4b+2

move 4b to the left side by subtraction:

(5b-4b) =2

b = 2

let's see what y equals when b = 2

5 * 2 = y

10 = y

Graphing it we see they intersect, or solve at

(2,10) or b=2, y=10

Hope this helps!

Answer:

The vertex form would be  y =  (x+2)^2

The factored form would be y = (x-2)(x-2)

The standard form would be y = x^2-4x+4

Step-by-step explanation:

To find this, you know that the vertex is 2 left from the center, so you have h = -2, and k = 0 since it isnt shifted up. The graph isn't shifted up either, so a=1.

The vertex form would be:  y = a(x-h)^2+k

                                                 =  (x+2)^2

The factored form would be y = (x-2)(x-2)

The standard form would be y = x^2-4x+4

Your welcome, and comment if you have any questions! :D

Answer:

weight not defined

Step-by-step explanation:

The cost of 20⅕ oranges is rs 300 ,what is the cost of a kg oranges?

HOW ARE WE SUPPOSE TO KNOW THE WEIGHT IF ONLY THE PRICE IS GIVEN

Answer:

Formula for area is length times width

So 2x × x = 2x^2

E. G.

2×2×2=8

And can also be written as 2^3

Meaning 2×2×2

So in this instance x × x=x^2

In front of the length x imagine a 1

So 2×1=2

Therefore 2x^2

Answer:

Area = 2x²

Step-by-step explanation:

Area = L x W

L = 2x

W=x

 x*2 =2x

x*x =x²

 Area = 2x²

Answer:

450 milage

Step-by-step explanation:

45 multiple 10

450 milage

[tex]sin3( \alpha ) = 3 \sin( \alpha ) - 4 { \sin^{3} ( \alpha ) }[/tex]

[tex]2( 3 \sin( \ \frac{\pi}{18} ) - 4 { \sin^{3} ( \ \frac{\pi}{18} ) })[/tex]

[tex]2(sin3( \ \frac{\pi}{18} ))[/tex]

[tex]2( \sin( \frac{\pi}{6} ) )[/tex]

[tex]2 \times \frac{1}{2 } = 1[/tex]

Answer:

D) 140

Step-by-step explanation:

That should be your answer

Answer:

x = 50

y= 40

Step-by-step explanation:

Step-by-step explanation:

[tex]\sf\green{x = 45° (diagonals \: \: of \: \: rectangle \: \: bisect \: \: eachother)}

\sf\green{y = 45° (diagonals \: \: of \: \: rectangle \: \: bisect \: \: eachother)}[/tex]

Answer:

x = 10

Step-by-step explanation:

61 - 21 = 40
40 / 4 = 10
x = 10

Answer:

The answer is 11/35, Hope this helps!

Stay safe, and have a very nice rest of the day!

Answer:

1   1   5

6÷5=6

Step-by-step explanation:

we divide them and keep the quotient as decimals.

=) 4÷3 = 1.33

=) 9÷4 = 2.25

Answer:

£40000

Step-by-step explanation:

→ Set up an equation

x × 0.6 = 24000

→ Divide both sides by 0.6

x = 24000 ÷ 0.6 = 40000

Answer:

[tex]3(x - \frac{ - 7 + \sqrt{73} }{6} )(x - \frac{ - 7 - \sqrt{73} }{6} )[/tex]

Step-by-step explanation:

Here is your answer ☝

Answer:

a. 28

b. 18

Step-by-step explanation:

a. 35% = .35 so .35 * 80 = 28

b. 3/4 = .75 because 3 divided by 4 = .75 so .75 * 24 = 18

Answer:

x=Sin-1(0.470584)

x=28.1°

Step-by-step explanation:

Sin90°/17 =Sin x°/8

0.058823 = Sin x°/8

8(0.058823)=Sin x°

x°=Sin-1(0.470584)

x=28.1°

The total amount of the initial deposit of Natalie account when she opened the account is $225.

Simple interest is the amount charged on the principal amount with a fixed rate of interest for a time period. Simple interest calculated only on the principal amount.

The formula for the simple interest can be given as,

[tex]I=\dfrac{Prt}{100}[/tex]

Here, (I) is the interest amount earned on the principal amount of (P) with the rate of (r) in the time period of (t).

Natalie opened a bank account that earns 2. 5% simple interest.

Natalie's account earned $180 over the period of 10 years. The interest amount she earned is,

[tex]I=\dfrac{Prt}{100}\\I=\dfrac{180\times2.5\times10}{100}\\I=45[/tex]

The interest amount she earned is $45 and the initial amount was $180. Thus, the total amount,

[tex]A=P+I\\A=180+45\\A=225[/tex]

Thus, the total amount of the initial deposit of Natalie account when she opened the account is $225.

Learn more about the simple interest here;

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Answer:

440$

Step-by-step explanation:

55 x 4=220

50 x 4=200

440$

I hope this is correct if not im sorry

Answer:

$ 205

Step-by-step explanation:

55+50x

x= number of hours minus the first hour (3)

so 55+50(3) = $205

Answer:

the doctors should be taken as the actual height because it was measured not estimated.

Answer:

f(x)=-4x-1

Step-by-step explanation:

f(x)=ax+b

a=-4/slope

b=-1/y-intercept

f(x)=-4x-1

By hit and trial of each option and also by graph, solutions to f(x) = 3ˣ and  g(x)=2x-1 will be 0 and 1.

given functions are,

[tex]f(x) = 3^x\\\\g(x) = 2x+1[/tex]

let us put x=0

f(0) = 1

g(0) = 1

f(0)=g(0)=1

so 0 will be a solution.

let us put x=1

f(1)= 3

g(1) = 3

f(1)=g(1)=3

so 1 will be also a solution

let us put x=2

f(2) = 9

g(2) = 5

f(2)≠g(2)

so 2 will not be solution.

x=-2 and x=-1 clearly will not be solution because,

g(-2) = negative value but f(x) cannot be negative, being an exponential function.

Any function in form f(x)= pˣ, where p≥1, is called an exponential function.

therefore, solutions to f(x) = g(x) will be 0 and 1.

to get more about exponential function refer to:

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Answer:

[tex]y=24[/tex]

Step-by-step explanation:

Given:

[tex]y=kx[/tex]

Substitute:

[tex]\left \{ {{y=12} \atop {x=2}} \right.[/tex] into [tex]y=kx[/tex]

[tex]12=k\times2[/tex]

Swap the sides:

[tex]k\times2=12[/tex]

Divide both sides of the equation by the coefficient of variable:

[tex]k=\frac{12}{2}[/tex]

Cross out the common factor:

[tex]k=6[/tex]

Find the equation of the function:

[tex]y=6x[/tex]

Substitute:

[tex]y=6\times4[/tex]

Calculate the product or quotient:

[tex]y=24[/tex]