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2 years ago

How do you write 1.5 × 104 in standard form?

1 answer:

5 0

I'm assuming you meant 1.5 × 10⁴. Remember, when we write in standard form, you need to use ^ to denote it's 'to the power of'. So it would be 1.5 × 10^4.

I'm also assuming you meant in decimal form, because that's already in standard form.

However, the answer is 15,000. This is because you lose one zero when multiplying a decimal with one number after it. For each number after the decimal, you take off a zero. Therefore, the end number is 15,000.

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Create a matrix for this system of linear equations, The determinant of the coefficient matrix is

marin [14]

Answer: The determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

Step-by-step explanation: The given system of linear equations is :

$2x+y+3z=13~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+2y=11~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\3x+z=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

We are given to find the determinant of the coefficient matrix and to find the values of x, y and z.

The determinant of the co-efficient matrix is given by

$D=\begin{vmatrix}2 & 1 & 3\\ 1 & 2 & 0\\ 3 & 0 & 1\end{vmatrix}=2(2-0)+1(0-1)+3(0-6)=4-1-18=-15.$

Now, from equations (ii) and (iii), we have

$x+2y=11~~~~~\Rightarrow y=\dfrac{11-x}{2}~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)\\\\\\3x+z=10~~~~~~\Rightarrow z=10-3x~~~~~~~~~~~~~~~~~~~~~~~~~(v)$

Substituting the value of y and z from equations (iv) and (v) in equation (i), we get

$2x+y+3z=13\\\\\Rightarrow 2x+\dfrac{11-x}{2}+3(10-3x)=13\\\\\Rightarrow 4x+11-x+60-18x=26\\\\\Rightarrow -15x+71=26\\\\\Rightarrow -15x=26-71\\\\\Rightarrow -15x=-45\\\\\Rightarrow x=3.$

From equations (iv) and (v), we get

$y=\dfrac{11-3}{2}=4,\\\\z=10-3\times3=1.$

Thus, the determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

3 0

3 years ago

93 27 14 what is next in the sequence?

Assoli18 [71]

Answer:

Step-by-step explanation:

9×3=27

2×7=14

1×4=4

nice logic

6 0

2 years ago

Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3

Ksivusya [100]

Answer:

One solution: 0x + 0.5y = 0

Step-by-step explanation:

9x + 4y = 36

6x + 2.5y = 24

2 * Eq. 1

18x + 8y = 72

-3 * Eq. 2

-18x - 7.5y = -72

Add the multiples of the equations.

0x + 0.5y = 0

Answer: One solution: 0x + 0.5y = 0

4 0

2 years ago

Read 2 more answers

Determine the type of triangle that has side lengths of 45, 45, and 90.

olganol [36]

Answer:

Equilateral triangle

7 0

3 years ago

Read 2 more answers

A cylindrical drinking glass can hold 56.52 cubic inches of

Alborosie

Answer:

The answer is

D. 8 inches

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, a cylinder this time.

Given data

Volume of cylindrical shape v=

56.52 inch³

Diameter of cylindrical glass d= 3

inch

But raduis r =diameter/2=3/2= 1.5

inch

We know that the the expression for the volume of a cylinder is given as

v= πr²h

Substituting our given data to solve for the height h

56.52= 3.14*(1.5)²*h

56.52= 7.065h

h= 56.52/7.065

h= 8 inches

3 0

2 years ago