Solve the following problem using the substitution method. Please make sure to show all of your work.

6x - 3y = 1
y = -2x - 5

Decay constant: the ratio of the number of radioactive atoms in a population to the rate at which they are vanishing due to radioactive decay. The rate of change is determined by the equation dN/dt = N, where is the decay constant, assuming N is the size of a population of radioactive atoms at a particular time t and dN is the amount by which the population declines in time dt.

When this equation is integrated, N = N0et is obtained, where N0 is the starting population size of radioactive atoms at time t = 0. This demonstrates that the rate of population decay is dependent on the decay constant and is exponential.

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The decay constant: the ratio of the number of radioactive atoms in a population to the rate at which they are vanishing due to radioactive decay.

The rate of change is determined by the equation dN/dt = N,

where is the decay constant, assuming N is the size of a population of radioactive atoms at a particular time t and dN is the amount by which the population declines in time dt.

When this equation is integrated, N = N0et is obtained, where N0 is the starting population size of radioactive atoms at time t = 0. This demonstrates that the rate of population decay is dependent on the decay constant and is exponential.

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Answer:

(2,2)

Step-by-step explanation:

The middle point of (-4,8) and (8,-4) is (2,2)

The value of x would be -3/2.

What is the linear equation in one variable?

A linear equation in one variable is an equation in which the highest power of the variable is 1. A linear equation in one variable can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. The graph of a linear equation in one variable is a straight line.

6 + 3/(x + 1) = 0

3/x+1 = -6

3 = -6(x + 1)

3 = -6x - 6

-6x= 9

x = -9/6

x = -3/2

Hence, the value of x would be -3/2.

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Answer:

Nine hundred thirty-eight one hundred twenty thousandths.

-Hope this helps!

Therefore , the solution of the given problem rate of interest comes out to be he get commission of 4.9%.

Simple interest is calculated by dividing the principal by the borrowing cost, the remaining time, and other elements. The simple return formula in marketing is principal + interest plus hours. Utilizing this method is the simplest way to calculate interest. As a percentage of the principle sum is the most frequent way to calculate income. For instance, he will only pay his portion of the 100% cost if he borrows $100 from a friend and agrees to pay the loan back with 5% interest.. You have to pay interest on money you borrow, and you have to charge interest on money you lend.

Here,

Given :

Gross pay = $680

Sales = $13,600

To find the what rate of commission he get on sale:

=> 680/13800 * 100

=> 0.049 * 100

=> 4.9%

Thus , he get commission of 4.9%

Therefore , the solution of the given problem of interest comes out to be

he get commission of 4.9%.

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Answer:

The other leg is 19.6cm

Step-by-step explanation:

Use Pythagorean Theorem to set up an equation and solve.

The Pythagorean Thm is:

leg^2 + leg^2= hypotenuse^2

Let's fill in what we know:

4^2 + leg^2 = 20^2

(let's use a variable)

4^2 + b^2 = 20^2

simplify

16 + b^2 = 400

subtract 16

b^2 = 384

squareroot both sides.

b = sqrt384

use a calculator to find the squareroot.

b = 19.5959179

round to the nearest tenth.

b = 19.6

don't forget units!

The other leg is 19.6cm

Answer:

A bar graph with x-axis labeled from 0 to 10, and y-axis labeled from 0 to 4, with 4x-2 marked with a solid line.

Answer:

--------------------------

We know that:

Therefore the given expression is simplified as:

Answer:

b) 4i√7

Step-by-step explanation:

Given problem,

→ 2√-28

Let's solve the given problem,

→ 2√-28

→ 2√(-1) × √(28)

→ 2i × √(4) × √(7)

→ 2i × 2 × √7

→ 4i√7

Hence, option (b) is correct.

The equation of the line in the slope-intercept form will be y = 5x + 5.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

A line passes through the points (0, 5) and (1, 10). Then the equation of the line is given as,

(y - 5) = [(10 - 5) / (1 - 0)] (x - 0)

y - 5 = 5x

y = 5x + 5

The equation of the line in the slope-intercept form will be y = 5x + 5.

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Note that Tiana's work is wrong.  Tiana made a mistake going from Step 2 to Step 3. Tiana should have subtracted 2 from 21 before adding. The order of operations says to add and subtract from left to right. The rule in operation here is known as PEMDAS. Note that when corrected and evaluated, the expression results in 27. (Option B)

The order of operations is a rule that specifies the right sequence of actions to be taken while evaluating a mathematical equation. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Using the order of operations (PEMDAS), the expression 21 - 2 + 60 ÷ 15*2  would be evaluated as follows:

Parentheses -  None

Exponents - None

Multiplication and Division (from left to right) - 60 + 15 = 4

Addition and Subtraction (from left to right) - 21 - 2 + 4*2 = 19 + 8 = 27

So the correct result is 27.

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Full Question:

See attached Image.

The value of 1/8 = 0.125 and 3/6 = 0.5.

To simplify an expression, you can use algebraic rules such as combining like terms, using the distributive property, and applying the order of operations (PEMDAS). Additionally, you can use properties of exponents, logarithms, and trigonometric functions to simplify expressions that involve those operations.

For example, you can simplify the expression 2x + 3x by combining the like terms 2x and 3x to get 5x. Another example, you can simplify the expression (3x + 2)(4x - 1) by using the distributive property to get 12x^2 + x - 8.

According to question:-

To simplify 1/8 * 3/6, you can first convert the fractions to have a common denominator. In this case, the least common multiple of 8 and 6 is 24. So you can convert 1/8 to 3/24 and 3/6 to 12/24.

Then, you can multiply the numerators and denominators separately:

(1/8) * (3/6) = (3/24) * (12/24) = 3/24 * 12/24 = 3/24 * 1 = 3/24

So the simplified form of the expression is 3/24.

As a side note, if you want to further simplify, you can divide the numerator and denominator by their greatest common divisor, which is 1 in this case, then you will get 3/24 equals to 1/8.

Hence, the value of 1/8 = 0.125 and 3/6 = 0.5.

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On solving the provided question we cans ay that the value of the function will be x(x−2)=0 => x=0,2

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The given functions are -

f(x)=x^2, g(x)=2^x

Find the value for -

fog(x)= gof(x)....equation 1

f(g(x)={g(x)}^2

First find solution for function f(g(x) -

⇒ f(g(x)={2^x}^2=2^2x

Now find solution for function g(f(x)) -

g(f(x))=2^f(x)

⇒g(f(x))=2^x^2

Now, substitute the values in equation 1 -

gof(x)=fog(x)

2^x^2=2^2x

⇒x^2=2x

x^2−2x=0

Therefore, the solution set is obtained as x=0,2.

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Answer: 2

Step-by-step explanation: The value x in f(x) is a value on the x-axis that we input into the function. F(x) is a value on the y-axis. F(2) means we are inputting the value of 2 on the x-axis and looking for the corresponding point on the y-axis. If we look at the graph at x=2, we can see that the graph is above when y=2. This means that (2,2) is a point that satisfies f(x).

Depth is the result of form having the illusion of the third dimension.

Even while the human brain perceives many flat pictures, such as those in movies and photographs, as being two dimensional, nothing actually exists without all three dimensions (2D). This is due to the fact that everything physically existing is made of atoms, which are imperceptible to the human sight yet include all three spatial dimensions. Human eyes have the capacity to perceive "depth" or three dimensions. The three spatial dimensions of the world may be perceived by someone who possesses depth perception. Each human eye's visual brain first interprets the three spatial dimensions as 2D pictures. Contrarily, stereoscopic vision, which is unique to humans, alters the image seen by the two eyes.

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Answer:

4x>= 10

Step-by-step explanation:

i believe thats the answer

Answer:

Step-by-step explanation:

[tex]\mathrm{Slope=\cfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\mathrm{\left(x_1,\:y_1\right)=\left(-5,\:7\right)}[/tex]

[tex]\mathrm{\left(x_2,\:y_2\right)=\left(0,\:4.5\right)}[/tex]

[tex]\mathrm{m=\cfrac{4.5-7}{0-\left(-5\right)}}[/tex]

[tex]\mathrm{m=-\cfrac{2.5}{5}}[/tex]

[tex]\mathrm{m=-0.5}[/tex]

-Hope this helps!

3⁵ means, multiply 5 factors of 3.

Answer:

10

Step-by-step explanation:

Answer:

Equivalent expression:

= 15

Step-by-step explanation:

Distributive proprty:

(10-7)5 = 10*5 + 10*-7

= 50 - 35

= 15

Evaluate:

(10-7)5 = 3*5

= 15

Answer:

C. 1/4 (-x + 2)

Step-by-step explanation:

-1/4x + 1/2

1/4 (-x + 2)

The bricks having same cost per brick are 1500 bricks for $1,110, 35 bricks for $25.90 and 230 bricks for $170.20. The solution has been obtained using the unitary method.

What is a unitary method?

The value of a single unit is calculated in the unitary approach before the value of the necessary number of units is determined. In order to obtain value of a single unit from a given multiple, the unitary technique is used, to put it simply.

We know that Cost per brick = number of bricks / price of bricks

Therefore, using this, we get

1500/$1110 = $1.35

1300 / $845 = $1.54

230 / $170.20 = $1.35

100 / $75 = $1.33

35 / $25.90 = $1.35

Hence, the bricks having same cost per brick are 1500 bricks for $1,110, 35 bricks for $25.90 and 230 bricks for $170.20.

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Question: The prices for different types and amounts of building bricks are given. Select the options that have the same cost per brick.

1500 bricks for $1,110.00

1300 bricks for $845.00

230 bricks for $170.20

100 bricks for $75.00

35 bricks for $25.90

Answer:

To calculate the amount Sophia needs to invest to reach a certain value in a specific time, given an interest rate compounded monthly, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment

P = the initial principal or investment amount

r = the annual interest rate (expressed as a decimal)

n = the number of times the interest is compounded per year

t = the number of years the investment is held

Since the interest is compounded monthly, we need to divide the annual rate by 12 to find the monthly rate. So:

r/12 = 0.034/12 = 0.002833

Now we can plug in the values into the formula:

A = P(1 + 0.002833)^(12*14)

A = P(1.002833)^(168)

We know that A = $1,450 and we want to find P (the initial principal or investment amount).

So we can rearrange the equation to find P:

P = A/(1.002833)^(168)

Solving for P, we get:

P ≈ $973.99

So Sophia would need to invest around $973.99 to reach $1,450 in 14 years with an annual interest rate of 3.4% compounded monthly.

Step-by-step explanation:

The missing length x is equal to the square root of 10 units.

A triangle is a three sided polygon with 3 angles and three sides it is one of the most basic and fundamental safe in geometry and is used in many different areas of methane science triangle are also after use in architecture art in other areas of the design triangle come in many different form such as equatorial isosceles and scalene and can be classified by their angles side or both.

The formula for finding the area of a triangle is A = 1/2(base × height). In this case, the base and height are both x, so A = 1/2(x2). Plugging in the given area of 5, we have 1/2(x2) = 5 and solve for x to get x = √(10). So the missing length x is equal to the square root of 10 units.

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Answer:

18x - 9 = 72

3(6x - 3) = 72

x = 4.5

Step-by-step explanation:

Given equation:

[tex]\dfrac{3}{5}\left(30x-15\right)=72[/tex]

Separate the fraction:

[tex]\implies 3 \cdot \dfrac{1}{5}\left(30x-15\right)=72[/tex]

Multiply the terms inside the parentheses by 1/5:

[tex]\implies 3\left(\dfrac{1}{5}\cdot30x-\dfrac{1}{5}\cdot 15\right)=72[/tex]

[tex]\implies 3\left(6x-3\right)=72[/tex]

Expand the brackets:

[tex]\implies 3\cdot6x-3\cdot3=72[/tex]

[tex]\implies 18x-9=72[/tex]

Add 9 to both sides of the equation:

[tex]\implies 18x-9+9=72+9[/tex]

[tex]\implies 18x=81[/tex]

Divide both sides pf the equation by 18:

[tex]\implies \dfrac{18x}{18}=\dfrac{81}{18}[/tex]

[tex]\implies x = 4.5[/tex]

Therefore, the three equations that have the same value as the given equation are:

The angles are 90 degree and 30 degree and side PQ=6.93 and PN=8 units.

Three sides and three angles make up a triangle. A triangle's total angles are always 180 degrees. A triangle's exterior angles are always a sum of 360 degrees. The total of the parallel interior and exterior angles is additional.

Since, it is a right angle triangle, we can use Pythagoras theorem.

Sum of all angles is 180 degree in a triangle.

hence,

60+x+90=180

x=30 degrees.

cos 60=base/hypotenuse

1/2=4/Hypotenuse

Hypotenuse=2*4=8 units

Hypotenuse=PN=8 units.

now,

sin 60=perpendicular/hypotenuse

[tex]\sqrt{3}/2=PQ/8[/tex]

PQ=6.93 units

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Answer:

y=(-10x+9)/11

Step-by-step explanation:

10x+11y=9

11y=9-10x

y=(9-10x)/11

y=(-10x+9)/11

Answer:

9.38

I believe this is the answer

The net worth of the surf shop would be $572,922.

Option (B) is correct.

What is the net worth?

Net worth is a financial metric that represents the value of an individual or a company, and it is calculated by taking the total assets and subtracting the total liabilities.

To calculate this, you would add up all of the assets (property value, long term investments, cash, savings account, owned inventory, and owned equipment) and subtract all of the liabilities (building mortgage, other debt, small business loan, and long term liabilities).

In this case, the assets total:

$130,284 (property value) + $106,987 (long term investments) + $208,634 (cash) + $172,839 (savings account) + $38,671 (owned inventory) + $38,291 (owned equipment) = $731,109

And the liabilities total:

$78,280 (building mortgage) + $21,987 (other debt) + $28,950 (small business loan) + $48,970 (long term liabilities) = $178,187

So,

$731,109 (assets) - $178,187 (liabilities) = $572,922 (net worth)

hence, The net worth of the surf shop would be $572,922.

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The typical oil to vinegar ratio is three parts oil to one part vinegar/acid, though this ratio might change depending on the vinegar/acid you use.

One part vinegar to three parts oil is the general ratio for vinaigrettes. I learned this general principle from French culinary school, which results in a somewhat acidic dressing that goes well on salads. This implies that if you start with a cup of vinegar, you would need one cup of oil.

The typical oil to vinegar ratio is three parts oil to one part vinegar or acid, however this ratio might change based on the vinegar or acid you choose and your preferences. Less oil is required the less acidic the vinegar or acid.

Salad dressing mixing involves a physical alteration. Shaking the bottle creates a transient emulsion and suspension since the dressing's constituents are layered and immiscible.

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There are 48, 64, 96 and 144 quarts of milk for 3,4,6 and 9 crates shipped.

Coordinate pair means the two numerical pair bounded by a parenthesis but separated by comma. The first numerical term denotes the X coordinate and the 2nd numerical term indicate Y coordinate. The coordinate pair is used to locate a point on the cartesian plane.

A dairy farm ships crates of milk to food store. There are 48 quarts of milk for every 3 crates shipped.

for every 3 crates shipped there are 48 quarts of milk.

for 4 crates shipped there will be milk quarts = (48 × 4) / 3

                                                            = 64 quarts

for 6 crates shipped milk quarts = (6 × 48) / 3 = 96 quarts milk

for 9 crates shipped number of milk quarts = (9×48)/ 3 = 144

if ship crates are denoted by X axis and milk quarts is denoted by Y axis

then the coordinate pairs will be (3, 48), (4, 64), (6, 96) and (9, 144)

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