Enter the correct answer in the box. Write the sum of √28x^6 + 4√7x^6 in simplest form, if x ≠ 0.

The half-life of Carbon-14 is 5730 years. Suppose a fossil is found with 50% of Carbon-14 as compared to a living sample. How ol

melisa1 [442]

The answer is C. Because it takes 5730 years for half of a sample of carbon-14 atoms to decay. It says that 50% of the carbon atoms have decayed so that means that 5730 years have elapsed for that fossil.

I hope that helps.

4 0

2 years ago

Which equation represents a line that passes through the two points in the table x 1,5 and y 1,6

aleksandrvk [35]

For this case we must find a linear equation of the form:

$y = mx + b$

Where,

m: slope of the line

b: cutting point with vertical axis.

For the slope we have the following equation:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}$

Substituting values we have:

$m = \frac {6-5} {1-1}\\m = \frac {1} {0}$

We observe that the slope of the line is not defined.

Therefore, the line is vertical.

Thus, the equation of the line is given by:

$x = 1$

Answer:

The equation of the line is given by:

$x = 1$

8 0

2 years ago

Read 2 more answers

Which of the following methods can be used to determine if a relation is a function?? Select all that apply.

CaHeK987 [17]

Answer:

B) Write out the relation in an x-y table and check that each x-value corresponds to the only one x - value

8 0

2 years ago

A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. Solve by e

borishaifa [10]

Answer: 31 nickels and 29 dimes

<u>Step-by-step explanation:</u>

Nickels (.05): x

Dimes (.10): y

Value: .05x + .10y = 4.45 → -20(.05x + .10y = 4.45) → -x - 2y = -89

Quantity: x + y = 60 → 1(x + y = 60) → <u> x + y </u> = <u> 60 </u>

-y = -29

y = 29

Next, substitute "29" for "y" into either equation and solve for "x":

x + y = 60

x + 29 = 60

x = 31

5 0

2 years ago

The endpoints of one diagonal of a rhombus are (-7, -2) and (-1, -4). If the coordinates of the 3rd vertex are (-6, -9), what ar

podryga [215]

The coordinates of the 4th vertex of the rhombus are (-2,3)

<h3>How to determine the coordinates of the 4th vertex?</h3>

The diagonals are given as:

(-7, -2) and (-1, -4)

The 3rd vertex is given as: (-6,-9)

Calculate the distance between the vertices of the diagonals and the 3rd vertex using:

$d = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}$

So, we have:

$d_1 = \sqrt{(-7 + 6)^2 + (-2 + 9)^2} =\sqrt{50$

$d_2 = \sqrt{(-1 + 6)^2 + (-4 + 9)^2} =\sqrt{50$

Let the 4th vertex be (x,y)

So, we have:

$d_3 = \sqrt{(-7 - x)^2 + (-2 - y)^2} =\sqrt{50$

$d_4 = \sqrt{(-1 - x)^2 + (-4 - y)^2} =\sqrt{50$

Equate d3 and d4

$\sqrt{(-1 - x)^2 + (-4 - y)^2} = \sqrt{(-7 - x)^2 + (-2 - y)^2}$

Take the square of both sides

$(-1 - x)^2 + (-4 - y)^2 = (-7 - x)^2 + (-2 - y)^2$

Expand

$1 + 2x + x^2 + 16 + 8y + y^2 = 49 + 14x + x^2 + 4 + 4y + y^2$

Evaluate the like terms

1 + 2x + 16 + 8y = 49 + 14x + 4 + 4y

Collect like terms

14x - 2x + 4y - 8y = 1 + 16 - 49 - 4

12x - 4y = -36

Divide through by 4

3x - y = -9

Next, we test the options in the above equation

Point (-8,13) means x = -8 and y = 13

So, we have:

3x - y = -9

3(-8) - 13 = -9

-37 = -9 --- this is false

Point (-2, 3) means x = -2 and y = 3

So, we have:

3x - y = -9

3(-2) - 3 = -9

-9 = -9 --- this is true.

Hence, the coordinates of the 4th vertex are (-2,3)