Assume that a new lithium isotope, 8Li, is identified. It is a trace isotope, meaning that it exists in a very tiny quantity. How will this discovery affect the atomic mass of lithium?

The missing digits are 0, 4, and 5 in descending order

The complete division operation is

    8 2 0 R 5

6 |4, 9 2 5

 - 4  8

       1 2

  -    1 2

          0  5

From the question, we are to determine the missing digits in the division operation

From the diagram,

The first two digits of the divided were divided by the divisor, this resulted into a quotient of 8 and a remainder of 1.

The divisor is 6

Let the value of the first two digits be x

Thus,

x / 6 = 8 1/6

x/6 = 49 / 6

By comparison,

The first two digits is 49

Therefore,

The dividend of the division operation is 4,925

Now, we can complete the division operation

      8 2 0 R 5

6 |4, 9 2 5

 - 4  8

       1 2

  -    1 2

          0  5

Hence, the missing numbers are 0, 4, and 5

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The cosine function that has an amplitude of 4 and a phase shift of pi over 4 is given by:

f(x) = 4cos(2x - π/4) + 4.

The cosine function is defined as follows, considering it's coefficients:

y = acos(bx - c) + d.

The meaning of the coefficients is given as follows:

In this problem, we want an amplitude of 4, hence coefficient a has a value of:

a = 4.

We also want a phase shift of π/4, hence the coefficient c has a value of:

c = π/4.

Among the given options, the one that gives a cosine function with the desired amplitude and phase shift is:

f(x) = 4cos(2x - π/4) + 4.

Which is the first option.

The options are missing, and are given by the image at the end of the answer.

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The value of the fraction given as - 1 3/4 - (-8 1/3) - (- 4 1/4) will be 10 5/6.

It should be noted that a fraction is simply used to represent the numbers that aren't whole.

Based on the information given, the fraction is illustrated as:

= - 1 3/4 - (-8 1/3) - (- 4 1/4)

Note that (-) × (-) = +

Therefore,

= - 1 3/4 - (-8 1/3) - (- 4 1/4)

= - 1 3/4 + 8 1/3 + 4 1/4

The LCM of the denominator is 12

= - 1 9/12 + 8 4/12 + 4 3/12

= 12 7/12 - 1 9/12

= 10 10/12

= 10 5/6

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The length of metal flashing needed to be purchase is [tex]1\frac{5}{8}[/tex] feet's.

He needs 6 ½ feet of metal flashing to complete a household project.

He has two small pieces measuring 3 1/8 feet and 1 3 / 4 feet.

Therefore, the length of metals for him to purchase can be calculated as follows;

The length he has = 3 1 / 8 + 1 3 / 4

The length he has = 25  /8 + 7 / 4

The length he has =  25 + 14/ 8

The length he has = 39 / 8 feet

Therefore

length required to purchase =  [tex]6\frac{1}{2} - \frac{39}{8}[/tex]

length required to purchase = [tex]\frac{13}{2}-\frac{39}{8}[/tex]

length required to purchase =  [tex]\frac{52-39}{8}[/tex]

length required to purchase = [tex]\frac{13}{8}[/tex] feet

Therefore,

length of metal flashing required to be purchase = [tex]\frac{13}{8}[/tex] feet = [tex]1\frac{5}{8}[/tex] feet

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The weights of meteorite A and meteorite B are 69 tons and 23 tons respectively.

It is given in the question that the weight of meteorite A is 3 times the weight of meteorite B.

Also, the sum of their weights is 92 ​tons.

We have to find the weights of meteorite A and meteorite B.

According to the data given in the question,

Let the weight of meteorite B be x and,

The weight of meteorite A be 3x

Hence, we can write an algebraic equation,

3x + x = 92 tons

4x = 92 tons

x = 92/4 tons

x = 23 tons

Hence, 3x = 3*23 = 69 tons.

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Answer:

A = 0.041138659 Sq. Mi.

Step-by-step explanation:

now I'm guessing that mark's backyard is GIGANTIC

and according to the info the question gave I know his back yard is also a Rectangle, knowing this we can safely say the formula to find the Area of a rectangle: A = LW to break this down it's like saying:

Area = length × width

the question already states that the width was 4/5 of a mile and the length was 1/2 of a mile we would convert the miles to feet

1 mile = 5,280 ft

4/5 × 5,280 = 4,224 ft

so, 4/5 of a mile would be 4,224 ft

similarly, 1/2 of a mile would be 2,640

1/2 × 5,280 = 2,640

GREAT we found our new length and width

length= 2,640 ft

width=4,224 ft

plug it in the formula

A= L×W

A= 2,640 ft · 4,224 ft

A= 1,146,880 sq. ft.

change that into square miles by dividing by 27878000

0.041138659 Square Miles

The x value of 24 makes the equation to be true

The equation is given as

x/2 - 2 = x/4 + 4

Add 2 to all sides of the equation

So, we have

x/2 = x/4 + 6

Subtract x/4 from all sides of the equation

So, we have

x/2 - x/4 = 6

Multiply through by 4

So, we have

2x - x = 24

So, we have

x = 24

Hence, the value of x in the equation is 24

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

x - y = 3

x + y = 27

add them:

2x = 30

x = 15

from x+y=27, we can see that y = 12

Answer:

it is a linear equation

Step-by-step explanation:

Check the picture below.

[tex]\stackrel{\textit{\LARGE Areas}}{ \stackrel{\textit{two triangles}}{2\left[\cfrac{1}{2}(\underset{b}{8})(\underset{h}{6}) \right]}~~ + ~~\stackrel{\textit{three rectangles}}{(14)(6)~~ + ~~(14)(8)~~ + ~~(14)(10)}} \\\\\\ 48~~ + ~~84~~ + ~~112~~ + ~~140\implies \text{\LARGE 384}~cm^2[/tex]

The number of terms of the 2nd A.P if its common difference is given as 4 is 76.

What is common difference?

The difference between consecutive integers in an arithematic sequence is a frequent distinction. Simply subtract the first word from the second term, or the second from the third, or anything similar, to find it. See how we have to add 8 each time to reach the following term? Thus, our common difference is eight.

1st A.P

Let 1st term be a d = 6

Therefore T51 = a + ( 51 - 1 )6

= a + 300

Now 2nd A.P

let the 1st term be a

Therefore for n no. of terms,

lats term,  a + ( n - 1 )4

But according to the question:

 a + ( n - 1 )4 =  a + 300

n - 1 = 300/4

n = 75 + 1

n = 76

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Answer:

1_y=3(0)-5

y=0-5

y=-5

(0,-5)

2_y=3(-1)-5

y=-3-5

y=-8

(-1,-8)

3_y=3(2)-5

y=6-5

y=1

(2,1)

Step-by-step explanation:

different numerators and denominators but are equal to the same value.
-
if you need a specific number answer from a problem, you'd need to attach a picture

The order of the scales from smallest to largest would be,

inch, centimeter, yard, meter

In this question, we have been given a scale drawing of a car is presented in the following three scales.

We need to order the scale drawings from smallest to largest.

We know that,

1 cm = 2.54 inch

and 1 meter = 1.1 yards

We know that the metric conversion,

1 meter = 100 centimeters

And 1 cm = 2.54 inch

So, 1 meter = 254 inches

This means, meter is the largest scale and inch is the smallest scale.

1 yd = 91.44 cm

This means, yard is greater than centimeter.

Therefore, the order of the scales from smallest to largest would be,

inch, centimeter, yard, meter

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Step-by-step explanation:

Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. The correct option is C, -7/25.

What are Trigonometric Identities?

Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. There are several trigonometric identities relating to the side length and angle of a triangle.

Given that the value of tan(x) = -4/3 and x is in quadrant 2.

In order to find the value of cos(2x), we can use the trigonometric identity of cos(2x), therefore, for cos(2x) we can write,

\cos(2x) = \dfrac{1-\tan^2(x)}{1+\tan^2(x)}cos(2x)=

1+tan

2

(x)

1−tan

2

(x)

Since the value of tan(x) is known, substitute the value in the identity,

\begin{gathered}\cos(2x) = \dfrac{1-(-\frac{4}{3})^2}{1+(-\frac{4}{3})^2}\\\\\cos(2x) = \dfrac{1-(\frac{16}{9})}{1+(\frac{16}{9})}\\\\\end{gathered}

cos(2x)=

1+(−

3

4

)

2

1−(−

3

4

)

2

cos(2x)=

1+(

9

16

)

1−(

9

16

)

cos(2x) = (-7/9) × (9/25)

Cancelling 9 from the numerator and the denominator,

cos(2x) = -7/25

Hence, if tanx=-4/3 and x are in quadrant 2 then cos2x=-7/25.

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Step-by-step explanation:

sgshshsbhehdbdbdbsbehebebdbebd

Answer:

16

Explanation:

It states the answer in the question. Unless you meant something else?

Hope this helps!

Have a good day :)

Answer: He shared 16.

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

    There are 14 girls and 19 boys in the chess club.

    Let x be girls and y be boys in the chess club. First, we need to write the system.

    We know there are 33 students in total.

x + y = 33

    We also know there are five more boys than girls in the club.

x + 5 = y

x + y = 33

x + 5 = y

    First, we will solve for y with substitution:

x + y = 33

x + (x + 5) = 33

2x = 28

x = 14

    Now, we will plug in this x-value:

x + y = 33

(14) + y = 33

y = 19

           There are 14 girls and 19 boys in the chess club.

At 1 hour, 3 hours and 6.5 hours she travels 36 miles, 108 miles and 234 miles respectively using the concept of average speed of an object.

As per the question statement, Clare covers a distance of 0 miles, 72 miles, 144 miles and 216 miles in 0 hours, 2 hours, 4 hours and 6 hours respectively.

We are supposed to find out the distance travelled by her in 1 hour, 3 hours and 6.5 hours.

We will use the concept of average speed of an object which is as follows

average speed = total distance divided by the total time taken

average speed = 216/6 = 36 miles per hour

Hence at 1 hour, distance = 1 * 36 = 36 miles

at 3 hours, distance = 3 * 36 =108 miles

at 6.5 hours, distance = 6.5 * 36 = 234 miles

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The solution of the equation 11kx+13kx= 6 is x = 1/(4k)

The given equation is 11kx+13kx = 6

To solve this equation first we have to take x as common and rearrange the equation, so we can group the like terms together

x(11k+13k) = 6

Add the like terms in the equation

x(24k) = 6

Move 24k to the right hand side of the equation

x = 6/(24k)

Here we have to simplify the value of x, for that we have to divide 6 by 24k in the equation

x = 1/(4k)

Hence, the solution of the equation 11kx+13kx= 6 is x = 1/(4k)

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Sebastian has solved the expression wrongly and the correct answer will be 536.

We are given the expression:

(87 × 8) - (4 × 40)

We need to simplify the expression.

For this, we need to follow the rule of PEMDAS.

So, we get that:

696 - 160

= 536

Sebastian has simplified it wrong as he has not followed the rule of PEMDAS and first subtracted 4 from 8.

Therefore, we get that, Sebastian has solved the expression wrongly and the correct answer will be 536.

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Answer:

400 miles

Step-by-step explanation:

Let m be the number of miles.

[tex]85(2) + .30m = 290[/tex]

[tex]170 + .30m = 290[/tex]

[tex].30m = 120[/tex]

[tex] m = 400[/tex]

Answer:

Step-by-step explanation:

The graph starts at 70 and decreases by 5 temp after 15 mins

70

65               o

60                                      o

55                                                            o

50

45

40

35

30

25

20

15

10

5                 i                      i                     i

0   5   10   15   20   25   30   35   40   45   50

                      time

Based on Jaylen's equation and the distance, as well as the time, the missing values are:
                 Distance                               Time minutes

                      2.89                                        24.0

                       3                                             24.9

                     4.34                                          36.0

                       6                                             49.8

The missing values can be found by Jaylen's equation where y is the Time in minutes and x is the distance.

With a time of 24 minutes, the distance is:

24 = 8.3x

x = 24/8.3

= 2.89

With a distance of 3, time would be:

= 8.3x

= 8.3 (3)

= 24.9 minutes

With a time of 36 minutes:

= 36 / 8.3

= 4.34  

With a distance of 6, the time is:

= 6 x 8.3

= 49.8 minutes

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Answer:

A = 1

B = 5

Step-by-step explanation: