What is 2/3 ÷ 1/2 ? A.3/4 B.4/3 C.1/3 D.1/4

The sum of 11 and the product of 2 and a number r

andrew-mc [135]

Algebraically that would be expressed as 2r + 11

The product of 2 and r is 2r.

The sum of 2r and 11 is 2r + 11

5 0

4 years ago

Write a system of equations and solve. Three times the first number minus two times the second number equals -7. The second numb

Fynjy0 [20]

Answer:

-1 and 2

Step-by-step explanation:

Let the numbers be x and y

Three times the first number minus two times the second number equals -7:

3x - 2y = -7

The second number equals one less than negative three times the first number:

y = -3x - 1

Substitute y in the first equation and solve for x:

3x - 2(-3x - 1) = -7
3x + 6x + 2 = -7
9x = -9
x = -1

Find the value of y:

y = -3(-1) - 1
y = 3 - 1
y = 2

The numbers are -1 and 2

8 0

3 years ago

The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the o

Korvikt [17]

Answer:

a) $k = 0.000124$

b) According to these data, the Shroud of Turin has around 760 years.

Step-by-step explanation:

The amount of carbon-14 is modeled by the following equation:

$C(t) = C_{0}e^{-kt}$

In which $C_{0}$ is the initial amount and k is the rate of decrease.

(a) Find the value of the constant k in the differential equation.

Half-life of 5595 years.

So $C(5595) = 0.5C_{0}$

$C(t) = C_{0}e^{-kt}$

$0.5C_{0} = C_{0}e^{-5595k}$

$e^{-5595k} = 0.5$

Applying ln to both sides

$-5595k = -0.69$

$k = 0.000124$

b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained about 91 percent of the amount of carbon-14 contained in freshly made cloth of the same material. How old is the Shroud of Turin, according to these data?

This is t when $C(t) = 0.91C_{0}$

$C(t) = C_{0}e^{-kt}$

$0.91C_{0} = C_{0}e^{-0.000124t}$

$e^{-0.000124t} = 0.91$

Applying ln to both sides

$-0.000124t = -0.094$

$t = 760.57$

According to these data, the Shroud of Turin has around 760 years.

8 0

4 years ago

What is the volume of the pyramid?

Deffense [45]

Given,

base=6 ft

height=5 ft

Now,

volume of pyramid=1/3×B×h(where B is base area)

=1/3×(6×6)×5

=1/3×36×5

=60 ft cubed

6 0

3 years ago

HELP ME PLEASE WHAT IS THE ANSWER TO THESE QUESTIONS

sergejj [24]

Answer:

question 3.3 Answer: Angle 3

question 3.4 Answer: ABD and DBC are complementary angles

question 3.5 Answer: x is 7 degrees (first answer option)

Step-by-step explanation:

First question:

Recall that suplementary angles are those whose addition gives 180 degrees. Therefore the supplementary angle to angle 8 is angle 3.

Second question:

Recall that complementary angles are those angles which added give 90 degrees. Therefore, the only correct answer for this question is the third one: ABD and DBC are complementary angles.

Third question:

Notice that the two angles added should render 90 degrees, therefore, their expression should as well add to 90 degrees. Such can be written in equation form as:

( 6 x - 20 ) + (4 x + 40 ) = 90

combining like terms and later solving for x we get:

6 x + 4 x - 20 + 40 = 90

10 x + 20 = 90

10 x = 90 - 20

10 x = 70

x = 7

Therefore x is 7 degrees

5 0

3 years ago