properties of exponents. the answer is 1/2^12 i need help with the work

Answer:

Option B. M = Log 10000

Step-by-step explanation:

From the question given above, we were told that the intensity (I) is 10000 times that of the reference earthquake (I₀).

Thus, we can obtain the magnitude (M) of the earthquake as follow:

Let the reference earthquake (I₀) = A

Then, the intensity (I) = 10000 × A

M = Log(I/I₀)

M = Log(10000A / A)

M = Log 10000

Thus, option B gives the right answer to the question.

Answer:

[tex]sin\left(90\right)/x=sin\left(25\right)/16[/tex]

x = 37.85

Step-by-step explanation:

9514 1404 393

Answer:

  A = 108.78°

  a = 11 mi

  b = 7 mi

Step-by-step explanation:

The sum of angles in a triangle is 180°, so the third angle is ...

  A = 180° -38.71° -32.51°

  A = 108.78°

__

The remaining sides can be found from the law of sines.

  a/sin(A) = c/sin(C)

  a = sin(A)·c/sin(C) ≈ 0.946762 × 11.163896

  a ≈ 11 mi

  b = sin(B)·11.163896 ≈ 0.625379 × 11.163896

  b ≈ 7 mi

Answer:

Divide 79 by 8

Step-by-step explanation:

79/8

= 9.875

Answer:

x=0,5/2

Step-by-step explanation:

Answer:

40 min

Step-by-step explanation:

his sister can do it twice as fast so the boy does 1 and the sister does 2. he will do 1/3 of the work and it will take 1/3 of the time

Answer:

90 mins

Step-by-step explanation:

1 hour =60 mins

1/2 hour = 60/2=30

so, 60 +30=90

Answer:

$7800

Step-by-step explanation:

1. Principal x interest x rate

So: $7500 + 4% (0.04) x 1 year = $300

2. Interest + Principal

So: $7500 + $300

Mrs Lee had $7800 in the bank.

Answer:

The answer is "21%".

Step-by-step explanation:

[tex]\to 26 + 20 + 29 + 49 = 124\\\\=\frac{26\ \text{brown times}}{124 \ \text{total times}} \\\\= \frac{26}{ 124} \\\\ = 0.209677 \\\\[/tex]

Calculating the percentage:

[tex]= 20.9677 \times 100\\\\=20.9677\% \approx 21\%[/tex]

Answer:

see explanation

Step-by-step explanation:

Using the Sine rule in all 3 questions

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

(2)

[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex] , substitute values

[tex]\frac{45}{sin133}[/tex] = [tex]\frac{c}{sin26}[/tex] ( cross- multiply )

c × sin133°  = 45 × sin26° ( divide both sides by sin133° )

c = [tex]\frac{45sin26}{sin133}[/tex] ≈ 27.0 ( to the nearest tenth )

(4)

[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex] , substitute values

[tex]\frac{19}{sinB}[/tex] = [tex]\frac{30}{sin97}[/tex] ( cross- multiply )

30 sinB = 19 sin97° ( divide both sides by 30 )

sinB = [tex]\frac{19sin97}{30}[/tex] , then

∠ B = [tex]sin^{-1}[/tex] ( [tex]\frac{19sin37}{30}[/tex] ) ≈ 38.9° ( to the nearest tenth )

(6)

[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex], substitute values

[tex]\frac{18}{sin102}[/tex] = [tex]\frac{xAB}{sin45}[/tex] ( cross- multiply )

AB sin102° = 18 sin45° ( divide both sides by sin102° )

AB = [tex]\frac{18sin45}{sin102}[/tex] ≈ 13.0 ( to the nearest tenth )

Answer:

x = -2

Step-by-step explanation:

the line goes through -2 on the x-axis

the line also goes through -3 on the y-axis

Step-by-step explanation:

14.99 - 11.53= 3.46+1.95 =4.41

Answer:

m = 6

c = 0

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + c

Step-by-step explanation:

Step 1: Define

y = 6x

↓ Compare to Slope-Intercept Form

Slope m = 6

y-intercept c = 0

Answer:

[tex]9(7x - 2) = 5(10x - 1) \\ \\ 63x - 18 = 50x - 5 \\ \\ 63x - 50x = - 5 + 18 \\ \\ 13x = - 5 + 18 \\ \\ 13x = 13 \\ \\ x = \frac{13}{13} \\ \\ x = 1[/tex]

Answer:

[tex]9(7x - 2) = 5(10x - 1) \\ 9 \times 7x - 9 \times 2 = 5 \times 10x - 5 \\ 63x - 18 = 50x - 5 \\ 63x - 50x = - 5 + 18 \\ 13x = 13 \\ x = 1 \\ thank \: you[/tex]

Answer:

18 dollars

Step-by-step explanation:

sunglasses = 6 dollars

sandals = 3 * sunglasses

             = 3 * 6 dollars

             = 18 dollars

Answer:

A) U is called an upper triangular matrix because all entries below the principal diagonal element are zeros ( 0 )   since Uij = 0 if i >j  also

L is a lower triangular matrix because all entries above the principal diagonal element are zero ( 0 )

B) sum of two upper triangular matrices = upper triangular matrix.

C) product of two upper triangular matrices = upper triangular matrix

Step-by-step explanation:

A) U is called an upper triangular matrix because all entries below the principal diagonal element are zeros ( 0 )   since Uij = 0 if i >j  also

L is a lower triangular matrix because all entries above the principal diagonal element are zero ( 0 ) since Lij = 0  if i < j

B) To prove that sum of two upper triangular matrices

attached below

C) Prove or disprove that product of two upper triangular matrices is an upper triangular matrix

attached below

Answer:

(m-6+2root3)(m-6-2root3)

Step-by-step explanation:

m^2 - 12m +36 -12

= (m-6)^2 - 12

= (m-6+2root3)(m-6-2root3)[root 12 = 2root3]

1,4,9,16,25,36,49,........

7th pattern =49.....

Answer:

1, 4, 9, 16, 25, 36, 49…................the 7 the pattern is 49

Answer:

Step-by-step explanation:

Functions are always relations, but not every relation is a function. This passes the vertical line test so it is a function. Since it's not a line, it's not linear. B is your choice.

Answer:

Pencils = 325 ; Pens = 975 ; Markers = 650

Step-by-step explanation:

Let :

Number of Pencils = x

Number of pens = y

Number of markers = z

2 times as many markers as pencils

z = 2x

3 times as many pens as pencils

y = 3x

x + y + z = 1950

Write z and y in terms of x in the equation :

x + 3x + 2x = 1950

6x = 1950

Divide both sides by 6

6x / 6 = 1950 / 6

x = 325

Number of pencils = 325

Pens = 3 * 325 = 975

Markers = 2 * 325 = 650

Pencils = 325 ; Pens = 975 ; Markers = 650

Answer:

2x, a linear pair

Step-by-step explanation:

2/5x/3/4 = 7/4 = 1 3/4

Answer:

The zeros of this function would be: x = 4 and x = 6, assuming that option got caught off while you were taking a picture.

Step-by-step explanation:

When they're asking for the zeros of this type of function, where is forms this kind of U-shape or also known as a quadratic equation, they're asking what the x-value is when y = 0, or when the line of the function touches the x-axis. Notice that it happens when x = 4 and when x = 6.

In short, it's asking what the x-value is of the points of the function when it intersects the x-axis. Hopefully my explanation wasn't too confusing. Good luck on the rest of the quiz!

Answer:

1884

Step-by-step explanation:

1)If you hear the condition "less than four letters" it means that each word can consist of 3,2 or 1 letter. Firstly, consider the easiest situation with the word from one letter. There are 12 letters, so there are 12 words from one letter.

Then the words from two letters. The first letter of such a word can be chosen in 12 means(because 12 letters are available), then the second letter can be chosen in 12 means too. 12*12=144 words with 2 letters. (Multiplying, not adding, because each two words form one combination).

Then for the words from three letters, use the same rule, 12 means for the first letter, 12 means for the second letter, 12 means for the third letter. 12*12*12=1728 words.

Having particular words from 1,2,3 letters add them to get total quantity of words: 12+144+1728=1884words,that is the answer.

Answer:

A square can be defined as a rhombus which is also a rectangle and a parellelogram with four congruent sides and four right angles

I hope this helps

Answer:

Step-by-step explanation:

Begin the solution by squaring both sides of the given equation.  We get:

(3x - 4)^2 = 2x^2 - 2x + 2, or:

9x^2 - 24x + 16 = 2x ^2 - 2x + 2

Combining like terms results in:

7x^2 - 22x + 14 = 0

and the coefficients are a = 7, b = -22, c = 14, so that the discriminant of the quadratic formula, b^2 - 4ac becomes (-22)^2 - 4(7)(14) = 92

According to the quadratic formula, the solutions are

       -b ± √discriminant           -(-22) ± √92             22 ± √92

x = ------------------------------- = ----------------------- = ------------------------

                   2a                                   14                            14

Answer:

(0,-4)

Step-by-step explanation:

The plot for x intercept is at -4,0 and the y intercept is at 0,5

type it in as (0,-4), some require the (#,#) format

Answer:

the square root of 24 is 4.89897948557

Answer:

4.89

Step-by-step explanation:

2root 6........***

Answer:

B. x = 2.77

Step-by-step explanation:

3^x = 21

You first look for a base for 21 that is 3 to the power of something.

21 = 3^2.77

So 3^x = 2^2.77

They have the same base so

x= 2.77

Answer:

The student took the numbers for the factors 5, -4 for the zeros  instead of solving the equation

The zeros are -5, 4

Step-by-step explanation:

x^2 +x - 20=0

What 2 number multiply to -20 and add to 1

5*-4 = -20

5+-4 = 1

(x+5)(x-4) =0

Using the zero product property

x+5 = 0  x-4 =0

x=-5  x=4

Answer:

Solution given:

equation is:

x²+x-20=0

doing middle term factorisation

note:we need to get 1 while subtracting factor of the product of constant and coefficient of x².

20*1=20=2*5*2*1

we get 1 while subtracting 5-2*2=5-4

now substitute value 5-4 at coefficient of x

we get

x²+(5-4)x-20=0

now

distribute

x²+5x-4x-20=0

taking common from each two term

x(x+5)-4(x+5)=0

again taking common (x+5) and keeping remaining at another bracket

(x+5)(x-4)=0

either

x+5=0

x=-5

or

x-4=0

x=4

Error is:

x= 4 not -4

x=-5 not 5.

Answer:

the ratio of lengths of the two rods, Aluminum to Invar is 11.27

Step-by-step explanation:

coefficient of linear expansion of aluminum, [tex]\alpha _{Al} = 23 \times 10^{-6} /K[/tex]

Coefficient of linear expansion of Invar, [tex]\alpha _{Iv} = 1.2 \times 10^{-6}/K[/tex]

Linear thermal expansion is given as;

[tex]\Delta L = L_0 \times \alpha\times \Delta T\\\\where;\\\\L_0 \ is \ the \ original \ length \ of \ the \ metal\\\\\Delta L \ is \ the \ increase \ in \ length[/tex]

The increase in length of Invar is given as;

[tex]\Delta L_{Iv} = L_0_{Iv} \times \alpha _{Iv}\times \Delta T_{Iv}[/tex]

The increase in length of the Aluminum;

[tex]\Delta L_{ Al} = L_0_{Al} \times \alpha _{Al} \times \Delta T_{Al}\\\\from \ the\ given \ question, \ the \ relationship \ between \ the \ rods \ is \ given \ as\\\\ L_0_{Al} \times \alpha _{Al} \times \frac{1}{3} \Delta T_{Iv}= 2( L_0_{Iv} \times \alpha _{Iv} \times \Delta T_{Iv})\\\\ L_0_{Al} \times \alpha _{Al} \times \Delta T_{Iv}= 6( L_0_{Iv} \times \alpha _{Iv} \times \Delta T_{Iv})\\\\ L_0_{Al} \times \alpha _{Al} \times \Delta T_{Iv} = 6L_0_{Iv} \times 6\alpha _{Iv} \times 6 \Delta T_{Iv}\\\\[/tex]

[tex]\frac{L_0_{Al}}{6L_0_{Iv} } = \frac{6\alpha _{Iv} \ \times \ 6 \Delta T_{Iv}}{\alpha _{Al} \ \times \ \Delta T_{Iv}} \\\\\frac{L_0_{Al}}{6L_0_{Iv} } = \frac{6\alpha _{Iv} \ \times \ 6}{\alpha _{Al} \ } \\\\\frac{L_0_{Al}}{L_0_{Iv} } = 6^3(\frac{\alpha _{Iv} }{\alpha _{Al} } )\\\\\frac{L_0_{Al}}{L_0_{Iv} } = 6^3(\frac{1.2 \times 10^{-6} }{23\times 10^{-6} } )\\\\\frac{L_0_{Al}}{L_0_{Iv} } = 6^3(\frac{1.2}{23} )\\\\\frac{L_0_{Al}}{L_0_{Iv} } = \frac{259.2}{23} \\\\\frac{L_0_{Al}}{L_0_{Iv} } = 11.27[/tex]

Therefore, the ratio of lengths of the two rods, Aluminum to Invar is 11.27

The ratio of the lengths of the two rods which is length of aluminum to length of Invar rod is; 11.27

Formula for linear thermal expansion is;

ΔL = L × α × ΔT

Where;

ΔL is change in original length

L is original length

α is coefficient of linear expansion

ΔT is change in temperature

We are told that increase in length of aluminum rod is twice the increase in length of an Invar rod with only a third of the temperature increase.

Thus;

ΔL = 2ΔL

ΔT for the aluminum rod = ⅓ΔT for the Invar rod.

Thus, we have;

L_al × α_al × ⅓ΔT = 2L_in × 2α_in × 2ΔT

ΔT will cancel out to give;

⅓(L_al × α_al) = 2L_in × 2α_in × 2

Multiply both sides by 3 to get;

(L_al × α_al) = 6L_in × 6α_in × 6

From online tables, the linear coefficient of expansion of aluminum is 23 × 10^(-6) C¯¹

While the coefficient of thermal expansion for Invar rod is 1.2 × 10^(-6) K¯¹

Thus;

L_al × 23 × 10^(-6) = 6L_in × (6 × 1.2 × 10^(-6)) × 6

L_al/L_in = (6 × 6 × 1.2 × 10^(-6) × 6)/(23 × 10^(-6))

L_al/L_in = 11.27

Read more on coefficient of linear expansion at; https://brainly.com/question/6985348