Solve: 4x-19-x<br> what is the value if X? pls explain if u can

Automobile license plates in Massachusetts usually consist of three digits followed by three letters. The first digit is never z

Serga [27]

Answer:

1,58,18,400

Step-by-step explanation:

1st digit can have the values 1-9 (9 distinct values)

2nd digit can have the values 0-9 (10 distinct values)

3rd digit can have the values 0-9 (10 distinct values)

1st letter can have the value A-Z (26 distinct values)

2nd letter can have the value A-Z (26 distinct values)

3rd letter can have the value A-Z (26 distinct values)

Total number of different plates possible = 9*10*10*26*26*26

=1,58,18,400

3 0

2 years ago

Complete the following statement: f(3)=_____

Lesechka [4]

Using this equation, f(3) = 23.

In order to find the value of f(3), we need to take the f(x) equation and put 3 everywhere we see x. Then we follow the order of operations to solve. So, let's start with the original.

f(x) = 2x^2 + 5sqrt(x - 2)

Now place 3 in for each x.

f(3) = 2(3)^2 + 5sqrt(3 - 2)

Now square the 3.

f(3) = 2(9) + 5 sqrt(3 - 2)

Do the subtraction inside of the parenthesis.

f(3) = 2(9) + 5sqrt(1)

Take the square root

f(3) = 2(9) + 5(1)

Multiply.

f(3) = 18 + 5

And add.

f(3) = 23

4 0

3 years ago

5. If position of object x = 3 sinΘ – 7 cosΘ then motion of object is bounded between position.

lesya692 [45]

9514 1404 393

Answer:

±√58 ≈ ±7.616

Step-by-step explanation:

The linear combination of sine and cosine functions will have an amplitude that is the root of the sum of the squares of the individual amplitudes.

|x| = √(3² +7²) = √58

The motion is bounded between positions ±√58.

_____

Here's a way to get to the relation used above.

The sine of the sum of angles is given by ...

sin(θ+c) = sin(θ)cos(c) +cos(θ)sin(c)

If this is multiplied by some amplitude A, then we have ...

A·sin(θ+c) = A·sin(θ)cos(c) +A·cos(θ)sin(c)

Comparing this to the given expression, we find ...

A·cos(c) = 3 and A·sin(c) = -7

We know that sin²+cos² = 1, so the sum of the squares of these values is ...

(A·cos(c))² +(A·sin(c))² = A²(cos(c)² +sin(c)²) = A²(1) = A²

That is, A² = (3)² +(-7)² = 9+49 = 58. This tells us the position function can be written as ...

x = A·sin(θ +c) . . . . for some angle c

x = (√58)sin(θ +c)

This has the bounds ±√58.

3 0

2 years ago

How do I simplify the following to "a+bi" form: (1+2i)^3

damaskus [11]

Answer:

Expand it.

(1+2i)^3 is equal to (1+2i)(1+2i)(1+2i).

Multiply everything out (being sure to multiply <em>every</em> term. (1+2i) * (1+2i) = 1+2i+2i+4i^2.

i is the square root of negative one, so i^2 is just -1. 1+2i+2i-4 is what you get from the first two, so now simplify that:

1-4 + 2i+2i = (-3+4i) and now multiply that by (1+2i):

(-3+4i) * (1+2i) = -3 - 6i +4i +8i^2.

Simplify again, and the answer is: -11-2i

Step-by-step explanation:

I hope this helps - really my only tip is don't spend time thinking about what i is, that just hurts your brain. Just remember that i^2 is equal to negative one, and treat it like regular multiplication and you will be fine.

7 0

1 year ago

Find the dimensions of a rectangle with area 343 m2 whose perimeter is as small as possible.

raketka [301]

I hope this helps you

Area=length.width

343=l.w

7.7.7=l.w

l=49

w=7

Perimeter=2 (49+7)

Perimeter=2.56

Perimeter=112

3 0

3 years ago

Solve: 4x-19-x what is the value if X? pls explain if u can