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1 year ago

What is the value of x in this equation: 4x + 5 = 3x + 4? Solve the equation using the algebra tiles.

Mathematics

2 answers:

Yuri [45]1 year ago

6 0

Answer:

x=-1

Step-by-step explanation:

4x+5=3x+4

subtract 3x from both sides of the equation

4x+5=3x+4

-3x -3x

x+5=4

subtract 5 from both sides of the equation

x+5=4

-5 -5

x=-1

Snowcat [4.5K]1 year ago

4 0

Answer:

x = -1

Step-by-step explanation:

4x + 5 = 3x + 4

-5 -5

4x = 3x -1

-3x = -3x

1x = -1

x = -1

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Write three numerical expressions that are equivalent to (0.0004) . (0.005)

yKpoI14uk [10]

The three equivalent numerical expressions are:

$(0.0004) . (0.005) = (\frac{4}{10000}).(\frac{5}{1000})$

$(0.0004) . (0.005)= (\frac{1}{2500}).(\frac{1}{200})$

$(0.0004) . (0.005) = (4 \times 10^{-4}).(5 \times 10^{-3})$

Solution:

We have to write three numerical expressions that are equivalent to (0.0004) . (0.005)

Given expression is:

(0.0004) . (0.005)

First numerical expression:

We know that 0.0004 can be written in fraction as:

$0.0004 = \frac{0.0004 \times 10000}{10000} = \frac{4}{10000}$

Similarly,

$0.005 = \frac{0.005 \times 1000}{1000} = \frac{5}{1000}$

Therefore,

$(0.0004) . (0.005) = (\frac{4}{10000}).(\frac{5}{1000})$

Second numerical expression:

The first numerical expression can be simplified to get second numerical expression

$(\frac{4}{10000}).(\frac{5}{1000}) = (\frac{1}{2500}).(\frac{1}{200})$

Third numerical expression:

The given expression can be expressed in scientific notation:

Steps for converting to scientific notation:

Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.

Count how many places you moved the decimal point. This number is b.

If you moved the decimal to the left b is positive.

If you moved the decimal to the right b is negative.

If you did not need to move the decimal b = 0.

Write your scientific notation number as a x 10^b and read it as "a times 10 to the power of b."

Remove trailing 0's only if they were originally to the left of the decimal point.

$0.0004 = 4 \times 10^{-4}\\\\0.005 = 5 \times 10^{-3}$

Therefore, third equivalent numerical expression is:

$(0.0004) . (0.005) = (4 \times 10^{-4}).(5 \times 10^{-3})$

8 0

1 year ago

Determine whether each of the following functions is a solution of Laplace's equation uxx + uyy = 0. (Select all that apply.) u

Naddika [18.5K]

Answer with Step-by-step explanation:

We are given that Laplace's equation

$u_{xx}+u_{yy}=0$

We have to determine given function is solution of given laplace's equation.

If a function is solution of given Laplace's equation then it satisfy the solution.

1. $u=e^{-x}cosy-e^{-y}cosx$

Differentiate w.r.t x

Then, we get

$u_x=-e^{-x}cosy+e^{-y}sinx$

Again differentiate w.r.t x

$u_{xx}=e^{-x}cosy+e^{-y}cosx$

Now differentiate u w.r.t y

$u_y=-e^{-x}siny+e^{-y}cosx$

Again differentiate w.r.t y

$u_{yy}=-e^{-x}cosy-e^{-y}cosx$

Substitute the values in given Laplace's equation

$e^{-x}cosy+e^{-y}cosx-e^{-x}cosy-e^{-y}cosx=0$

Hence, given function is a solution of given Laplace's equation.

2. $u=sinx coshy+cosx sinhy$

Differentiate w.r.t x

$u_x=cosx coshy-sinx sinhy$

Again differentiate w.r.t x

$u_{xx}=-sin x coshy-cosxsinhy$

Now, differentiate u w.r.t y

$u_y=sinx sinhy+cosx coshy$

Again differentiate w.r.t y

$u_{yy}=sinx coshy+cosx sinhy$

Substitute the values then we get

$-sinx coshy-cosxsinhy+sinxcoshy+cosx sinhy=0$

Hence, given function is a solution of given Laplace's equation.

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1 year ago

The school librarian recorded the types of books students checked out on a typical day. Suppose there are 605 students enrolled

dimulka [17.4K]

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2 years ago

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Does this table represent a function? Why or why not?

Nutka1998 [239]

Answer:

C.No because two of the y values are the same

Step-by-step explanation:

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2 years ago

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A teacher needs 70 lengths of string cut to 40cm each. If balls of string are 10 m long, how many balls will be needed.

Genrish500 [490]

Answer:

Step-by-step explanation:

A ball is 10 meters. Since 100 centimeters are in a meter, each ball has 100*10 = 1000 centimeters.

The teacher needs 70 strings each 40 centimeters. The total amount they need is 70*40 = 2800 centimeters.

Since a ball has 1000 centimeters, 2800 centimeters will need 3 balls for a total of 3000 centimeters.

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2 years ago