Element X is a radioactive isotope such that every 51 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 7500 grams, how long would it be until the mass of the sample reached 6900 grams, to the nearest tenth of a year?

Answer:

Slope of the graph is steeper.

The answer is: [tex]\mathbf{Slope=\frac{1}{3}}[/tex]

Step-by-step explanation:

First we will find slope of the graph.

The formula used to find slope is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

We need to find two points from the graph to find the slope.

Let we take point 1 (-2,1) and point 2 (1,2)

We will have: [tex]x_1=-2, y_1=1, x_2=1, y_2=2[/tex]

Now finding slope of the graph

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{2-1}{1-(-2)} \\Slope=\frac{2-1}{1+2}\\Slope=\frac{1}{3}[/tex]

So, slope of the graph is: [tex]\mathbf{Slope=\frac{1}{3}}[/tex]

Now, we will find slope of Linear function.

It has x-intercept of 1 and y-intercept of -2

x-intercept means y=0

So, the point will be: (1,0)

y-intercept means x=0

So, the point will be: (0,-2)

We will have: [tex]x_1=1, y_1=0, x_2=0, y_2=-2[/tex]

Putting values and finding slope

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-2-0}{0-(1)} \\Slope=\frac{-2-0}{0+1}\\Slope=\frac{-2}{1}\\Slope=-2[/tex]

So, the slope of linear function is: [tex]\mathbf{Slope=-2}[/tex]

Now, we need to find which of the slope is steeper.

The larger the value of slope, more steeper it is:

Now, comparing the slopes:

The slope of the graph is: [tex]\mathbf{Slope=\frac{1}{3}}[/tex]

The slope of linear function is: [tex]\mathbf{Slope=-2}[/tex]

We know that, [tex]\frac{1}{3}>-2[/tex]

So, Slope of the graph is steeper.

The answer is: [tex]\mathbf{Slope=\frac{1}{3}}[/tex]

Answer:

20 miles

Step-by-step explanation:

If Maria has been riding for 2 1/2 hours and Aiden only for 2. That means that the first 4 miles she rode alone was for 1/2 hour. So that is the rate.

1/2 hour for every 4 miles

Maria rode for 2 1/2 hours divided by 1/2 hours is 5. So 5 x 4mi = 20 miles

Answer:

20 miles

because 4 miles= 1/2 hr

9514 1404 393

Answer:

  7x

Step-by-step explanation:

We can factor out x and simplify.

  4x +3x = x(4 +3) = 7x

Answer:

b

Step-by-step explanation:

Answer:

136

Step-by-step explanation:

triangles CAB and CED are similar, their sides are proportional

set up a proportion:

[tex]\frac{51}{144-x}[/tex] = [tex]\frac{3}{x}[/tex]

cross-multiply:  51x = 3(144 - x)

                         51x = 432 - 3x

                         54x = 432

                          x = 8

Plug in:

144 - 8 = 136

Answer:

19/20

Step-by-step explanation:

1/5+3/4

(4+15)/20....take L.C.M

19/20

Answer:

0.95 OR 19/20 OR 95%

Step-by-step explanation:

(1/5)+(3/4)=0.95

HOPE IT HELPS

Answer: M<2=38 m<3=142 m<4=38

Step-by-step explanation:

142+142+38+38=360-Both side

142+38=180- one side

180-142=38

Answers:

========================================================

Explanation:

Angle 1 is given to be 142 degrees. Angle 3 is equal to this measure since vertical angles are congruent. Vertical angles are angles that form when you have an X shape like this. They are opposite angles.

Angles 2 and 4 are the other pair of congruent vertical angles. This means angle 2 = angle 4.

Note how angle 1 and angle 2 form a straight line. These two angles add to 180.

(angle1) + (angle2) = 180

(142) + (angle2) = 180

angle2 = 180-142

angle2 = 38 degrees

angle 4 is also 38 degrees since angles 2 and 4 are a congruent vertical angle pairing.

Answer:

1. b d

2. is c or d

3. a or c

4. b or c

5. c

Step-by-step explanation:

Answer:

It’s 32

Step-by-step explanation:

Answer:

5 guests: 6 slices 10 guests: 3 slices 15 guests : 2 slices

Step-by-step explanation:

So, we have 30 slices of pizza and 5, 10, and 15 slices

So , we need to divide 30 by each of the guests

30÷5=6

30÷10=3

30÷15=2

We can also heck by multiplying teh guests by our answer

5*6=30 ✔️

10*3=30✔️

15*2=30✔️

So, for 5 guests, each oione gets 6 slices

For 10 guests, each guest gets 3 slices

For 15 guests, each guest gets 2 slices

Answer:

y = 5x -3

Step-by-step explanation:

m=5

b=- 3

y = mx + b

y = 5x -3

Answer:

X = 37.6

Step-by-step explanation:

Cos(62°) = X/80

80cos(62°) = X

X = 80cos(62°)

X = 37.6

Answer: yes

Step-by-step explanation:

Answer:

x = 12

y = 8

Step-by-step explanation:

to solve for x you would set up your equation:

4x - 3 = 45

then solve using algebra:

4x - 3 = 45

4x = 48

x = 12

to solve for y set up your equation as:

11y + 6 = 94

TO GET 94: you will need to subtract 41 and 45 from 180 to get 94.

(each triangle equals 180 and we need the 3rd measure)

solve the equation:

11y + 6 = 94

11y = 88

y = 8

Hope this helped!!

Answer:

1. 18 2. 30

Step-by-step explanation:

finding a triangle a=b(base)h(height) 1/2

9 times 4=36/2 =18

the whole thing is 48- the triangle 18=30

Answer:

40 kph

Step-by-step explanation:

I'm not to familiar with km but if it took you 30 minutes to travel 20km you would have to be going 40kph. It's basic math too. If you went 20 kph for 20km it would take you an hour to get there, but since they made it in 30 minutes, you just double the speed.

Answer:

x is equal to 3 and -0.25

Step-by-step explanation:

The answer can be found by factoring the equation and solving for zero:

[tex]8x^2 = 6 + 22x\\4x^2 = 3 + 11x\\4x^2 - 11x - 3 = 0\\4x^2 -12x + x - 3 = 0\\4x(x - 3) + (x - 3) = 0\\(4x + 1)(x - 3) = 0[/tex]

So x is equal 3 and -0.25

Answer:

$1711.5

Step-by-step explanation:

Step one

given data

Principal = $1500

interest rate= 4.5% = 0.045

time = 3 years

Step two:

The compound interest expression is

[tex]A= P(1+r)^t\\\\A=1500(1+0.045)^3\\\\A=1500(1.045)^3\\\\A=1500*1.141\\\\A=1711.5[/tex]

Answer:

4x^6

Step-by-step explanation:

Area of the square pasture = L² where:

L is the

length of one side of the pasture

Given

L = 2x³

Area of the pasture = (2x³)²

Area of the pasture =2x³•2x³

Area of the pasture = 4x^{3+3}

Area of the pasture = 4x^6

Hence the area of the pasture is 4x^6

Answer:

21. is 18 dollars

22. is 75 dollars

Step-by-step explanation:

Answer:

21. $18.00

22. $75.00

Step-by-step explanation:

21. you can first start by seeing that since two pairs of socks are $6, then one pair must be $3. So, by multiplying 6 by 3, you would get 18 which would show that the socks would cost $18.

22. By dividing 15 by 3, you can deduce that an hour of cleaning would yield $5. So, by multiplying that by 15, she would earn $75.

Hope this helped!

Answer:

2

Step-by-step explanation:

9x-7 = 7x-3

9x-7x = 2x

2x -7 = -3

   +7   +7

2x=4

x=2

Answer:

25%

Step-by-step explanation:

Answer:

x=1/6

Step-by-step explanation:

The steps are in the picture below

Answer:

Step-by-step explanation:

here you go mate

step 1

3х + 4 = 9x + 3 ​ equation

step 2

3х + 4 = 9x + 3 ​ simplify

-6x+4=3

step 3

−6x+4=3  subtract 4 from both sides

−6x+4(-4)=3(-4)

-6x=-1

step 4

[tex]\frac{-6x}{-6} =\frac{-1}{-6}[/tex]  divide both sides

answer

x=[tex]\frac{1}{6}[/tex]

Answer:

I didn't receive enough information about this, but I hope this helps?

Step-by-step explanation:

A 50%?

B 50%?

This problem needs more information.  :3

ik i’m late but, 5/4 fabric or 1 1/4 fabric. :)

Answer:

Step-by-step explanation:

K is located at -25

L is located at -15

just move 5 units away from J on both sides

hope this helps <3

Answer:

Step-by-step explanation:

34