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Answer:

The half-life of the substance is of 1600 years.

Step-by-step explanation:

Amount of the substance:

The amount of the substance after t years is given by the following equation:

[tex]C(t) = A(0.999567)^t[/tex]

In which A is the initial amount.

Find the half-life:

This is t for which [tex]C(t) = 0.5A[/tex], that is, the amount is half the initial amount. So

[tex]C(t) = A(0.999567)^t[/tex]

[tex]0.5A = A(0.999567)^t[/tex]

[tex](0.999567)^t = 0.5[/tex]

[tex]\log{(0.999567)^t} = \log{0.5}[/tex]

[tex]t\log{0.999567} = \log{0.5}[/tex]

[tex]t = \frac{\log{0.5}}{\log{0.999567}}[/tex]

[tex]t = 1600[/tex]

The half-life of the substance is of 1600 years.

Answer:

x = 7

S.A.S

Step-by-step explanation:

2x + 14 = 4x

2x = 14

x = 7

Answer:

y = 2

Step-by-step explanation:

Using the sine ratio and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{\sqrt{2} }{y}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

y = ([tex]\sqrt{2}[/tex] )² = 2

Answer:

24.25 feet

Step-by-step explanation:

Answer:

Part A: x = y+45

Part B: 40 125-45 = 80, 80÷2 = 40

Part C: Yes, because 80+45 adds up to 125.

Hope this helps! :)

Answer:

The answer is D

Step-by-step explanation:

This is because it cant be 13 or any smaller, and if the shorter side is 13 than it can't be any less than double itself, so it's D

Answer:

-9

Step-by-step explanation:

Find the common ratio by dividing one of the numbers in the sequence by the previous number:

117/-13

= -9

So, the common ratio is -9.

Answer:

144 = arc DF

Step-by-step explanation:

Inscribed Angle = 1/2 Intercepted Arc

72 = 1/2  arc DF

Multiply by 2

2*72 = arc DF

144 = arc DF

Answer:

16

Step-by-step explanation:

the greatest common factor of 16 and 48 is 16

Factors for 16: 1, 2, 4, 8, and 16.

Factors for 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Answer:

[tex]\frac{47}{2} \to 6[/tex]

[tex]\frac{60}{12} \to 5[/tex]

[tex]\frac{40}{10} \to 4[/tex]

[tex]\frac{56}{8} \to 7[/tex]

[tex]\frac{64}{8} \to 8[/tex]

Step-by-step explanation:

Given

See attachment

Required

Complete the blanks

To do this, we simply carry out the division operation.

So, we have:

[tex]\frac{47}{2} \to 6[/tex]

[tex]\frac{60}{12} \to 5[/tex]

[tex]\frac{40}{10} \to 4[/tex]

[tex]\frac{56}{8} \to 7[/tex]

[tex]\frac{64}{8} \to 8[/tex]

The rates of the given equivalent unit rates are properly matched as follows:

42/7 = 6

60/12 = 5

40/10 = 4

56/8 = 7

64/8 = 8

To find the unit rate, the numerator is divided by the denominator such that the denominator is reduced to 1.

Thus, let's find the unit rates that matches with the equivalent rates given (see attachment below).

Divide the numerators by the denominators such that the value of the denominators are reduced to 1.

Learn more about unit rate on:

https://brainly.com/question/18296886

Answer:

8/35 cubic inches

Step-by-step explanation:

Volume is length x width x height. To find the answer, we must multiply all values together. 2/3 times 3/5 ix 6/15. Let's simplify this before multiplying further. 6/15 can also be written as 2/5. 2/5 times 4/7 is 8/35 which cannot be simplified. 8/35 is the final answer.

Answer:

Expression

Step-by-step explanation:

Given expression :

4a+3b-6cx9

So this is expression not equation because equation consist zero on the righ side

Example: ax+b=0 (This is equation )

And

ax+b (This is expression)

Answer:

75.06239187

Step-by-step explanation:

1/2bh= Area of a Triangle

6^2+b^2=8.5^2 because we are missing a side we need to use the pythagorean theorem.

36+b^2=72.25

b^2=36.25

b=6.02

6.02+19= base

25.02

Now area

1/2bh

1/2 (25.02*6)

25.02*6= 150.1247

150.1247/2= 75.06239187 is Area

The above decimals before area are rounded.

Answer:

The slope is 2 and the y intercept is 6

Step-by-step explanation:

y = 2x+6

This is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 2 and the y intercept is 6

Answer:

2

Step-by-step explanation:

slope intercept form is

y = mx + b

m is the slope and b is the y-intercept

y = 2x + 6

m = 2

Slope is 2

Answer:

The mapping statements (-3,7) -> (-9,10) and (1, -5)-> (-5, -2) describe the same translation.

Step-by-step explanation:

In a translation, we have that:

(x,y) -> (x+a,y+b)

In which a and b are how much the values change.

(6.-9) -> (0,1)

x subtracted by 6, y added by 10. So, the translation rule is:

(x,y) -> (x - 6, y + 10).

(-3,7) -> (-9,10)

x subtracted by 6, y added by 3. So

(x,y) -> (x - 6, y + 3).

(1, -5)-> (-5, -2)

x subtracted by 6, y added by 3. So

(x,y) -> (x - 6, y + 3)

Same rule as the above, so the mapping statements (-3,7) -> (-9,10) and (1, -5)-> (-5, -2) describe the same translation.

(2, 4) -> (-4,1)

x subtracted by 6, y subtracted by 3. So

(x,y) -> (x - 6, y - 3)

Answer:

(C).

[tex]height = \sqrt{ {29}^{2} - {21}^{2} } \\ = \sqrt{400} \\ = 20 \: units[/tex]

Answer:

See below.

Step-by-step explanation:

sin(71) = x/23

x = sin(71) * 23

x = 21.75

Answer:

21.75 (2 digit after decimal)

Step-by-step explanation:

Sin theta = perpendicular/hypotenuse

sin 71=x/23

23 sin 71=x

x=21.747

Answer:

I think it's option B ...

Answer:

A.) F(x)=1/x-5

Step-by-step explanation:

Answer:

x =6

Step-by-step explanation:

The angles are alternate interior angles and alternate interior angles are equal

7x = x+36

Subtract x from each side

7x -x = x+36-x

6x = 36

Divide by 6

6x/6 = 36/6

x = 6

Answer:

centre = (0, 0 ), radius = 5

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 25 ← is in this form

with centre = (0, 0 ) and r = [tex]\sqrt{25}[/tex] = 5

Answer:

B

Step-by-step explanation:

It should be B

Answer:

ratio is 1/2

Step-by-step explanation:

r=8/16 =1/2

Answer:

1/2

Step-by-step explanation:

16 * 1/2 = 8

8 * 1/2 = 4

4 * 1/2 = 2

Hope this helps!

f(-3)=g(-4) 123456789012345

Answer:

20

Step-by-step explanation:

Answer:

option 2

in the first equation y is greater than so it would be shaded above the line and in the second equation y is less than so it would be shaded below the line

Step-by-step explanation:

Answer:

y = 9x + (-7) should be the answer

Answer:

$2.498

Step-by-step explanation: