The production of a gold mine decreases by 5% per year.
What is the approximate half-life for the production decline?
Based on this approximate half-life and assuming that the
mine's current annual production is 5000 kilograms, about
what will its production be in 10 years?

Answer:

Step-by-step explanation:

1

y-6 = -2/5(x-(-5)
y - 6 = -2/5(x+5)

y -6 = -2/5 x -2

y = -2/5 x -2 + 6

y = -2/5 x + 4

2

y-6 = 5/2 (x-(-5)

y-6 = 5/2 (x+5)

y - 6 = 5/2 x + 25/2

y = 5/2 x + 25/2 + 6

y = 5/2 x  + (25+12)/2

y = 5/2 x + 37/2

Answers:

A. 79 − 3x = 12x + 19

B. 7 − x = 12/x

C. x^2 + 3 = 10x − 21

The elements of AUB is {6, 7, 8, 9, 11} when A = {6,7,8,11} and B = {7,6,7,9}.

According to the question,

We have the following information:

A = {6,7,8,11} and B = {7,6,7,9}

Now, we know that the elements of AUB means that all the elements which are there in both sets but the elements are not supposed to be repeated.

(Please that AUB can also be found using Venn diagram and questions are asked where the question has to be solved by making Venn diagram and representing all the elements in it.)

So, we have the following expression:

AUB = {6,7,8,9,11}

(Now, note that numbers however repeated in sets are not repeated here.)

Hence, the elements of AUB is {6, 7, 8, 9, 11} when A = {6,7,8,11} and B = {7,6,7,9}.

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Answer: Read explanation

Step-by-step explanation: Observations of setting: Humanoid beings. Earth-like world. A human base to collect information. Forest like setting. Bird-like transportation creatures.

Theme ideas: Man a part of research group enters an avatar of beings to collect information on this world. Research group makes an invasion on these creatures home land.  

Make any corrections if you want! Make it more comfortable to your style!

Answer: Center: (-3, 2). Radius: 4.

Step-by-step explanation:

The x-coordinate of the center of the circle is given by the constant within the parenthesis with variable x. Whatever number makes the equation x + 3 = 0 is the x-coordinate of the center of the circle, which in this case is -3.

The y-coordinate of the center of the circle is given by the constant within the parenthesis with variable y. Whatever number makes the equation y - 2 = 0 is the y-coordinate of the center of the circle, which in this case is -2.

The radius of the circle is the square root of the constant on the other side of the equation. So, r = [tex]\sqrt{16}[/tex] = 4.

The explanation is from the equation of a circle in a graph:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

h and k in this equation stand for the coordinates of the center of the circle, with h being the x-coordinate and k being the y-coordinate. IN your equation, we have:

[tex](x+3)^2 + (y-2)^2 =16[/tex]

Which can also be written as

[tex](x-(-3))^2 + (y-(2))^2=16[/tex]

See the correlation of numbers -3 and 2 with h and k?

Notice also how the equation contains [tex]r^2[/tex], so to find the radius you do [tex]\sqrt{r^2}[/tex].

Answer:

The correct answer is D

Step-by-step explanation:

the negative power shows that on the exponent shows that the value is small and is being simplified.

When ever there is a negative power we increase zeros with respect to the exponent value.

The equation for the value of x will be 11/C.

According to the question,

We have the following equation:

Cx — 4 = 7

Now, we can easily find the value of x from this equation by following the given steps.

We will first add 4 on both sides of the equation:

Cx = 7+4

Adding the two numbers on the right hand side:

Cx = 11

Dividing by C on both sides of the equation:

x = 11/C

(More to know: we can now find the value of x if the value of C is given.)

Hence, the equation for the value of x will be 11/C.

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Answer:

7 * 5 =35 because if you say 5 10 15 20 25 30 35 then that's your answer

Answer:

a) 7:13  b) 5:13

Step-by-step explanation:

There are 7 new books (-> 7:--) theres 5 used books, add the 7 new books and 5 used books together. it said "The ratio for new books to all books?" it must be in that order. with leads you to 7:13

do the same thing for b) using the same steps.

Answer:√53 or 7.28010988928

Step-by-step explanation:

Answer:

[tex]y_1=\boxed{-3}[/tex]

[tex]y_2=\boxed{-8}[/tex]

[tex]y_3=\boxed{-16}[/tex]

[tex]y_4=\boxed{-28.5}[/tex]

Step-by-step explanation:

Given:

Use Euler’s method with h = 0.5 to find approximate values for the solution of the initial value problem:

[tex]y'=y-2x, \;\;y(3)=0[/tex]

at x = 3.5, 4, 4.5, 5.

Therefore:

[tex]f(x,y)=y-2x, \quad x_0=3 \;\;\text{and}\; \;y_0=0[/tex]

Euler's Method

[tex]\boxed{y_{n+1}=y_n+hf(x_n,y_n)}[/tex]

[tex]\begin{aligned}\implies y_1&=y_0+hf(x_0,y_0)\\&=0+(0.5)f(3,0)\\&=0+0.5[0-2(3)]\\&=0+0.5(-6)\\&=-3\end{aligned}[/tex]

[tex]\begin{aligned}\implies y_2&=y_1+hf(x_1,y_1)\\&=-3+(0.5)f(3.5,-3)\\&=-3+0.5[-3-2(3.5)]\\&=-3+0.5(-10)\\&=-3-5\\&=-8\end{aligned}[/tex]

[tex]\begin{aligned}\implies y_3&=y_2+hf(x_2,y_2)\\&=-8+(0.5)f(4,-8)\\&=-8+0.5[-8-2(4)]\\&=-8+0.5(-16)\\&=-8-8\\&=-16\end{aligned}[/tex]

[tex]\begin{aligned}\implies y_4&=y_3+hf(x_3,y_3)\\&=-16+(0.5)f(4.5,-16)\\&=-16+0.5[-16-2(4.5)]\\&=-16+0.5(-25)\\&=-16-12.5\\&=-28.5\end{aligned}[/tex]

[tex]\begin{array}{|c|c|c|}\cline{1-3} \text{Step}\;(n) & x_n&y_n\\\cline{1-3} 0&3&0\\\cline{1-3} 1&3.5&-3\\\cline{1-3} 2&4&-8\\\cline{1-3} 3&4.5&-16\\\cline{1-3} 4&5&-28.5\\\cline{1-3} \end{array}[/tex]

Answer: 16

Step-by-step explanation:

Imagine you had 4 apples and someone gave you 12 more. You would have 16 apples.

Answer: y= 3 times 2 to the power x. Second answer

Step-by-step explanation:

if you plug in 0 for x, y= 3x 1= 3

if you plug in 1 for x y= 3 x 2 = 6

Look at the x values and y values

(0,3) and (1, 6) on the graph. It matches answer number 2. Remember, 2 raised to the power 0 = 1 and 3 times 1 = 3. And 2 raised to the power 1 =2 and 3 times 2 = 6.

Answer:

The limit does not exist

Step-by-step explanation:

This is because the left hand limit is 3,we know this because as the graph approaches from the left side of the Cartesian plan the open dot is on 3

and the right hand limit is 1 because as the graph approaches the X=1 from the right hand side the open dot lands on 1

Since the left hand limit doesn't equal to right hand limit,the overall limit of x=1 doesn't exist.

Answer:

143

Step-by-step explanation:

Answer:

5q + 5q + 5 is equivalent to 10q + 5

Answer:

A.

Step-by-step explanation:

Answer:

this is how to do it. Now find the answer

Step-by-step explanation:

find the common factor for the denominators, which is 30.

then × the numerator by however much you ×tl the denominator by to get 30

The length of each factory worker on average is 25.57 lengths

From the question, we have the following parameters that can be used in our computation:

Total length of the pool = 179 lengths

Number of workers = 7

The length of each on average is calculated as

Average length = Total length of the pool/Number of workers

Substitute the known values in the above equation

So, we have the following equation

Average length = 179/7

Evaluate the quotient

Average length = 25.57

Hence, the average length is 25.57 lengths

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The slope of the line is - 2 with the equation as 2 x + y - 2 = 0

We are given that:

y intercept of the line = 2

Point is (0, 2)

It is parallel to the line 2 x + y = - 5

Slope of line 2 x + y = - 5:

y' = - 2

m = - 2

Slope of parallel lines are equal

m = m'

m' = - 2

Equation of the line:

y - y₁ = m( x - x₁)

y - 2 = - 2( x - 0)

y - 2 = - 2 x

2 x + y - 2 = 0

a) standard form of the equation = 2 x + y - 2 = 0

b) slope of the line = m' = - 2

c) point-slope form = (y - 2) / (x - 0) = - 2

d) Properties of algebra used = cross multiplication and simplification.

Therefore, we get that, the slope of the line is - 2 with the equation as 2 x + y - 2 = 0

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The linear function for the situation is :-

Amount at the end of 3 years = Original investment + original investment*Rate*Time/100

It is given in the question that:-

Investment of George's friend in startup company = $ 500.

Interest percent = 8 %

Time period of investment = 3 years

We have to find the linear function for this situation.

As this interest is on original investment, the interest will be simple.

Hence,

The linear function for the situation will be :-

Amount at the end of 3 years= Original investment + original investment*Rate*Time/100

Amount at the end of 3 years = 500 +  500*8*3/100 = 500 + 120 = $ 620

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Answer:

Step-by-step explanation:

The solution to the equation using graph is x= -0.62 or x = 1.62.

What is equation?

A mathematical equation may be a formula that uses the equals sign to represent the equality of two expressions.

Main Body:

For [tex]-x^{2} +y = 1[/tex]

We make y the subject to obtain

[tex]y = x^{2} +1[/tex]

We can easily graph this function, because we just have to transform the graph [tex]y = x^{2}[/tex] of  by shifting the intercept up to 1.

As for the straight line, -x +y = 2

We find the intercepts as follows,

When y = 0 , x = -2

When x = 0 , y = 2

We plot the points (-2,0)  and (0,2).

We now draw the two graphs on the same graph sheet. The intersection of the two graphs gives the solution to be

x= -0.62 or  x= 1.62

See graph

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Answer:

x = 3

y = -1

Step-by-step explanation:

4x + 10y = 2        Eq. 1

 x  - 10y = 13       Eq. 2

The result of the sum of Eq. 1 and Eq. 2 is:

4x + x = 5x

10y - 10y = 0y = 0

2 + 13 = 15

Then the result is:

5x = 15

x = 15/5

x = 3

From Eq. 2:

x - 10y = 13

3 - 10y = 13

-10y = 13 - 3

-10y = 10

y = 10/-10

y = -1

Check:

From Eq. 1:

4x + 10y = 2

4*3 + 10*-1 = 2

12 - 10 = 2

The solution of the equation is that the value of x = 3 and y = -1.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The equation will be solved as,

4x + 10y = 2        Eq. 1

x  - 10y = 13       Eq. 2

The result of the sum of Eq. 1 and Eq. 2 is:

4x + x = 5x

10y - 10y = 0y = 0

2 + 13 = 15

Then the result is:

5x = 15

x = 15/5

x = 3

From Eq. 2:

x - 10y = 13

3 - 10y = 13

-10y = 13 - 3

-10y = 10

y = 10/-10

y = -1

Therefore, the solution of the equation is that the value of x = 3 and y = -1.

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If you multiply by 12 you will get rid of all your fractions.

In mathematics, a linear equation is one that may be written in the form where the variables are alphabets, and the coefficients are frequently real integers. An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

It is rather simple to locate both intercepts when an equation is stated in this way (x and y).

The given linear equation is

6 - (3/4)x + (1/3) = (1/2)x + 5

In this equation the fractions are
(3/4), (1/3) and (1/2)

Take the LCM of 4, 3, and 2

LCM(4, 3, 2) = 12

So, if we multiply the equation with the number 12  we can eliminate the fractions.

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The final solution is all the values that make (x+5) (x+2) (x−2)=0 true.

x = −5,−2,2

What is factorization?

Factorization, also known as factoring, is the process of breaking down an object (such as a number, a matrix, or a polynomial) into a product of another object, or factors, which when multiplied together yield the original object (such as the number or matrix) in question.

What is inequality?

A relationship between two expressions or values that are not equal to each other is called an inequality.

Here, we have

Factor out the greatest common factor from each group

x²(x+5) - 4(x+5) = 0

Factor the polynomial by factoring out the greatest common factor, (x+5)

(x+5)(x²-4) = 0

Rewrite 4 as 2².

(x+5)(x²-2²) = 0

(x+5)(x+2)(x-2) = 0

Now,

x+5 = 0

x-2 = 0

x+2 = 0

set x+5 =0 then we get

x = -5

set x+2 =0 then we get

x = -2

set x-2 =0 then we get

x = 2

Hence, the final solution is all the values that make (x+5) (x+2) (x−2)=0 true.

x = −5,−2,2

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Answer:

1.) 10: 1, 2, 5, 10.

15: 1, 3, 5, 15,

Answer would be 5.

2.) 18: 1, 2, 3, 6, 9, 18

21: 1, 3, 7, 21

Answer would be 3.

3.) 12: 1, 2, 3, 4, 6, 12.

24: 1, 2, 3, 4, 6, 8, 12, 24.

Answer would be 12.

4.) 8: 1, 2, 4, 8.

20: 1, 2, 4, 5, 10, 20.

Answer would be 4.

5.) 14: 1, 2, 7, 14.

28: 1, 2, 4, 7, 14, 28.

Answer would be 14.

Step-by-step explanation:

Using the listing method, you would first list the common factors of each number, to which that number could be multiplied by. Then, you would search for the greatest common factor.

On solving for [H], we get -

H = (T - Ga)/y

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the following equation -

T = Ga + Hy

We have -

T = Ga + Hy

Solving for [H], we get -

Hy = T - Ga

H = (T - Ga)/y

Therefore, On solving for [H], we get -

H = (T - Ga)/y

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Answer:

20/5 is the slope, or 4.

Step-by-step explanation:

It went up 20 units on the y axis, and over 5 units on the x-axis. So 20/5 is the slope.

-Hope this helped