solve the following simultaneous equations and leave your answer in decimal form

3x-y=4
2x^2+y^2+xy=6

The age of the sample of the carbon material is 19042 years.

We have to note that the half life of the sample has to do with the time that it takes for us to have only half of the original amount of the isotopes that are in the sample to be present.

Using the formula;

0.693/[tex]t{\frac{1}{2} }[/tex] = 2.303/t log (No/N)

[tex]t{\frac{1}{2} }[/tex] = Half life of the sample

t = time taken

No = Number of atoms initially present

N = Number of atoms at time t

Then;

0.693/5730 = 2.303/t log (No/0.1No)

0.693/5730 = 2.303/t  * 1

1.21 * 10^-4 = 2.303/t

t = 2.303/1.21 * 10^-4

t = 19042 years

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The difference in income between the richest and poorest Citi zen I

called the wealth gap.

The unequal distribution of money and assets among the people is known as the wealth gap or wealth inequality. For instance, in 2014, the wealthiest 1% of Americans controlled 40% of the country's wealth, while the lowest 80% owned just 7%. It goes without saying that the wealth gap reinforces inequality, especially along racial and class lines.

The wealth gap, or economic or wealth inequality, is the solution. It is often quantified using many indicators, including consumption, income, and asset wealth.

Indices, such as the Gini coefficient, are used to represent the gap's size. National wealth discrepancies vary greatly across several nations. According to the global wealth gap, the richest 1% of the world's population would own two-thirds of the world's wealth by 2030.

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Note that the answer to the above expression is c = 19.35 or x = -32.35. This is resolved using the  Quadratic Formula.

Given

(13+c) * c = 620

⇒ 13c + c² = 620

⇒ c² + 13c -620 = 0 .......................1

We now have a quadratic equation above which we shall solve as follows:

For the above expression   (1)

a = 1, b = 13 and c = -620

that is

1c² + 13c + (-620) =0

Applying the Quadratic Formula = [tex]$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$[/tex]

Rather than say c =  we say x to avoid confusion

[tex]$x = \frac{-13 \pm \sqrt{13^2 - 4(1)(-620)}}{2(1)}$[/tex]

[tex]$x = \frac{-13 \pm \sqrt{169 + 2480}}{2}$[/tex]

[tex]$x = \frac{-13 \pm \sqrt{2649}}{2}$[/tex]

Therefore

x (or c as you would recall) = (-13 + 51.7)/2 or -13 - 51.7)/2

Thus, c = 19.35 or x = -32.35.

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The length of the line segment separating two places is the measure of distance between them. Calculating the length of the line segment that connects the two points in the provided coordinates will tell you the distance between them.

The length of the section of a line connecting any two places represents their distance. Only one line connects the two places, and it passes through both.

The length of the line segment that connects the two places may therefore be used to compute the distance between them. The distance between A and B, for instance, is 10 cm if A and B are two points and [Math Processing Error] cm.

The length of the line segment connecting two places serves as the measure of their distance (but this CANNOT be the length of the curve joining them). You should be aware that a distance between two points is always positive.

The Complete Question is distance.

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Answer:

For 1st triangle value of BC side =9CM

For 2nd triangle value of  EF side =6FT

For 3rd triangle  value of CE side=13.03YD

Using Pythagorean theorem which gives the formula of deriving Hypotenuse in an equilateral triangle.

Formula

c²= a² + b²

using this formula

AB= 12CM

BC=xCM

AC=15CM

AC²= AB² + BC²

BC²= AC²-AB²

x²CM= 225CM - 144CM

X²= 81CM

X=9 CM

Similarly  

EF²= GE² - GF²

x²FT= 100FT - 64FT

x²= 36 FT

x= 6FT

For the last

CE²  YD=  CD² YD + CE² YD

x² YD= 49 YD + 121 YD

x² YD= 170 YD

x YD= 13.03 YD

Step-by-step explanation:

Answer:

Answer: Option 4
The only one where m∠C = m∠D

Step-by-step explanation:

If you rotate the triangle on the right enough to align them then you will see that with the given information the third choice is the correct one.

Even without that process if m∠A = m∠E and m∠B = m∠F then for the two triangles to be similar, ∠C, the remaining angle of ABC and ∠D the remaining angle of DEF must be equal

So ∠C = ∠D is a must for the two triangles to be similar

Only the fourth option has this as one of the entries

The corresponding sides and angles are m∠C = m∠D

Similar figures are zoomed in or zoomed-out (or just no zoom) version of each other. They are scaled versions of each other, and by scale, we mean that each of their dimension(like height, width, etc linear quantities) are constant multiple of their similar figure.

Even without that process if m∠A = m∠E and m∠B = m∠F then for the two triangles to be similar, ∠C, the remaining angle of ABC,

Also, ∠D the remaining angle of DEF must be equal

Therefore, ∠C = ∠D is a must for the two triangles to be similar

Hence,  m∠C = m∠D

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answer is in the photo. lmk if you want the solution steps.

Answer:

1) x = 4, 2) x = 9, 3) x = 9

Step-by-step explanation:

Since you give no other context my guy I am assuming this is a similar triangles kind of thing. Comparing the triangles you can create what is known as a scale factor, (Ex: 10/2 = 5) and then multiple/divide by this scale factor to get the unknown number (Ex: 20/5 = 4)

Repeat with all three triangles

Answer:

[tex]m\angle1=2^\circ\\m\angle2=88^\circ[/tex]

Step-by-step explanation:

As both angles are complementary, meaning they add up to 90°, we can simply solve for x using this sum and find each individual angle measure:

[tex]m\angle1+m\angle2=90^\circ\\(x-9)^\circ+(8x)^\circ=90^\circ\\x-9+8x=90\\9x-9=90\\9x=99\\x=11\\\\m\angle1=(x-9)^\circ=(11-9)^\circ=2^\circ\\m\angle2=(8x)^\circ=(8\cdot11)^\circ=88^\circ[/tex]

Answer:The arrow diagram represents a relation between two sets of data, but it does not provide enough information to determine whether it is a function or not. A function is a relation in which each element of the first set (the domain) is related to exactly one element of the second set (the range). In order to determine if the relation shown in the arrow diagram is a function, we need to know if each element in the domain corresponds to only one element in the range. From the arrow diagram we can not determine that.

As we have a set of ordered pairs (27,39), (31,27), (60,130), (45,67) and (123,180) and there is no repetition of the x-values (domain) or y-values (range) in the ordered pairs, we can say that the relation shown in the arrow diagram is a function.

Step-by-step explanation:

The new current in the circuit is 2.0 amps, which is 1/4th of the original current of 8.0 amps

The relationship between current, resistance, and voltage in an electrical circuit is governed by Ohm's Law, which states that current (I) is equal to voltage (V) divided by resistance (R).

This relationship is represented by the equation I = V/R.

If we know the current and the resistance in a circuit, we can use Ohm's Law to calculate the voltage. For example, if a circuit has a current of 8.0 amps and a resistance of R, then the voltage in the circuit is V = IR = 8.0R.

Now, let's consider the situation where the resistance in the circuit is increased by a factor of 4. If the original resistance was R, then the new resistance is 4*R. Therefore, the new resistance is 4 times greater than the original resistance.

Since Ohm's Law states that current is inversely proportional to resistance, when the resistance is increased by a factor of 4, the current will decrease by a factor of 1/4.

To find the new current, we can use the equation I = V/R, and knowing that V = IR = 8.0R. Then, we can solve for I:

I = V/R = 8.0R / (4R) = 8.0/4 = 2.0 amps

Thus, the new current in the circuit is 2.0 amps, which is 1/4th of the original current of 8.0 amps.

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There are 20 pink flowers in Mr. Elliot's garden.

We can start by using the information provided to figure out how many flowers are not red or purple. We know that 1/8 of the flowers are red, and 1/4 of them are purple, so:

(1/8) * 128 flowers = 16 red flowers

(1/4) * 128 flowers = 32 purple flowers

So, 16 + 32 = 48 flowers are red or purple.

This means that 128 - 48 = 80 flowers are not red or purple.

Then we know that 1/4 of the remaining flowers are pink, so:

(1/4) * 80 flowers = 20 pink flowers

So, there are 20 pink flowers in Mr. Elliot's garden.

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The  expression can be used to find the total cot of the meal with the gratuity is 1.18P

A gratuity is an amount of money that customers typically give to specific service sector employees, including those in the hotel industry, in addition to the service's base charge for the work they have completed.

A party of 8 had a bill of p.

A restaurant charges an automatic gratuity of 18% on tables with more than 6 people.

Since there are 8 people so, gratuity will be applied on the bill

Since bill is of amount p

So, gratuity of 18 % of p =  18% of  P  

                                          = 18/100 ×P

                                         = 0.18P

Now the total bill after adding gratuity : P+0.18P= 1.18P

Hence the total cost of the meal with the gratuity is $1.18p.

Therefore the  expression can be used to find the total cost of the meal with the gratuity is 1.18P

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391 children swam at the public pool that day and 667 - 391 = 276 adults swam.

What is algebraic equation ?

An algebraic equation or polynomial equation is an equation of the form P=0 where P is a polynomial with coefficients in some field, often the field of the rational numbers.

Let's call the number of children that swam "x". The number of adults that swam would then be 667 - x.

The total revenue from the children was 1.75x and the total revenue from the adults was 2.25(667 - x).

set up an equation to represent the total revenue from both groups of swimmers

1.75x + 2.25(667 - x) = 1312.25

Expanding the second term on the left-hand side:

1.75x + 1507.75 - 2.25x = 1312.25

Combining like terms:

-0.5x + 1507.75 = 1312.25

Solving for x:

-0.5x = -195.5

x = 391

So, 391 children swam at the public pool that day and 667 - 391 = 276 adults swam.

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199 children and 468 adults swam at the public pool that day.

Let x be the number of children and y be the number of adults. Then we have the following two equations:

x + y = 667 (the total number of people)

1.75x + 2.25y = 1312.25 (the total amount of money collected)

We can substitute the first equation into the second to eliminate x:

1.75x + 2.25y = 1312.25

1.75(667 - y) + 2.25y = 1312.25

1175 - 1.75y + 2.25y = 1312.25

1175 = 1312.25 - 1.75y + 2.25y

1175 = 1312.25 - 1.75y + 2.25y

1175 = 1312.25 - 4y/2 + 9y/4

1175 = 1312.25 - (4/2)y + (9/4)y

1175 = 1312.25 - (6/4)y + (9/4)y

1175 = 1312.25 - (15/4)y

1175 + (15/4)y = 1312.25 + (15/4)y

15/4y = 137.25

y = 468

So there were 468 adults and 667 - 468 = 199 children.

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$ 240,437.74 - the balance of her fund on her 17th birthday.

His daughter turned 10 years old. Her reward was 5000.

subsequently, she began getting monthly interest compounded at a rate of 15%

She would thus have 5000 (the deposit from her birthday) + 15% = 5750 in her account at the end of the first month.

The amount would have been 5750 + 15% = 6612.50 at the conclusion of the second month.

She would have 6612.50 + 15% + 5000 (quarterly deposit) at the conclusion of the third month, which equals 12,604.38.

When she becomes 17 years old, if you keep doing these calculations, she will have a fun

$1,832,087,983.19

Only 145,000, including the 5,000 deposit made on her father's 17th birthday, would have been made by her father.

I would be grateful if someone could let me know where I can earn 15% compounded monthly.

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Answer:14

40 skittles times the percent of red40 * 0.35 = 14We then take that then subtract that from the total.40 - 14 = 2626 skittles were red.0.35 is equivalent to 35%Leave a thanks or a brainliest if this helped.

a) The probability of event occur is  [tex]\frac{1}{5}[/tex].

b) The probability of event not occur is  [tex]\frac{4}{5}[/tex].

What is probability?

The likelihood of an event happening is gauged by probability. It is difficult to provide a complete prediction for many events. We can only anticipate the likelihood of an event occurring by using it. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

Here The ratio of the odds of an event occurring are 1:4.

Then probability of that the event will occur is ,

=>P(event will occur = [tex]\frac{1}{4+1}[/tex] = [tex]\frac{1}{5}[/tex]

Now the probability of that event not will occur is ,

=> P(event will not occur) = 1 -[tex]\frac{1}{5}[/tex] = [tex]\frac{5-1}{5}[/tex] = [tex]\frac{4}{5}[/tex]

Hence the answers are a) [tex]\frac{1}{5}[/tex] and b) [tex]\frac{4}{5}[/tex].

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Answer:

(- 6, 0 )

Step-by-step explanation:

x - 4y = - 6 → (1)

2x - 12y = - 12 → (2)

multiplying (1) by - 2 and adding to (2) will eliminate x

- 2x + 8y = 12 → (3)

add (2) and (3) term by term to eliminate x

(2x - 2x) + (- 12y + 8y) = - 12 + 12

0 - 4y = 0

- 4y = 0 , then

y = 0

substitute y = 0 into either of the 2 equations and solve for x

substituting into (1)

x - 4(0) = - 6

x - 0 = - 6

x = - 6

solution is (- 6, 0 )

Answer:

x = -6

y = 0

Step-by-step explanation:

For the first equation, x - 4y = -6, we can move -4y to isolate x. Then, the equation will be: x = -6 + 4y. Now, we can use that x to solve for the second equation, 2x - 12y = -12. Let's plug in x from the first equation down to the second one:

2(-6 + 4y) - 12y = -12

Let's solve:

-12 + 8y - 12y = -12

-4y = 0

y = 0

Now that we have y, we can solve for x. Let's plug in y = 0 for the first problem: x-4(0) = -6

x = -6

First step to solve system of equations using elimination method is to equate the coefficient of the variable you want to eliminate first in opposite sign and add both the equations.

As given in the question,

Let us consider two system of equations :

ax + by = c ___(1)

bx + ay = c ___(2)

First step to solve the system of equation by elimination method is :

To eliminate variable x:

Equate the coefficient of x by multiplying 'b' by (1) and '-a' by (2) we get,

abx + b²y = cb  __(3)

-abx - a²y = -ac __(4)

Now in second step you can add equation (3) and (4) and eliminate x-term.

Therefore, the first step while solving system of equation using elimination method is to equate the coefficient of eliminated term in opposite sign.

The above question is incomplete , the complete question is:

What is the first step in solving a system of equations by elimination method?.

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The equation, y = mx + b, is the slope-intercept form of a straight line.

Here, x and y are the coordinates of the points, m is the gradient, and b is the intercept of the y-axis.

y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept.

The value of b is equal to y when x = 0, and m shows how steep the line is. The slope of the line is also called the gradient.

To find the equation of the straight line, we use the slope-intercept form, y = mx + b, where m is the slope of the line, b is the y-intercept of the line.

We can find the equation of a line in the form of y = mx + b, if the coordinates of points forming the line are known to us.

Thus, The equation, y = mx + b, is the slope-intercept form of a straight line.

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In a factorial design study, (B) the interaction effect is often viewed as the most important influence.

In statistics, a full factorial experiment is one in which all potential combinations of the levels across all of the factors are taken into account by the experimental units.

A full factorial experiment has two or more factors with discrete possible values or "levels" in its design.

A fully crossed design is another name for a full factorial design.

The interaction effect in a factorial design study is typically regarded as the most significant effect.

Using such an experiment, the researcher can examine how each element affects the response variable as well as how different factors interact with one another.

Therefore, in a factorial design study, (B) the interaction effect is often viewed as the most important influence.

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to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{ -4 }{ 4 } \implies \text{\LARGE - 1}[/tex]

Answer:

75

Step-by-step explanation:

First, we solve

y - 16= 4

y = 20

Now we put 20 in for y and solve 3(y+5)

3(20+5)

3(25)

75

So, the answer is 75.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{y - 16 = 4 \rightarrow 3(y + 5)}\\\\\text{FIRST: Let us solve for the first equation}\\\mathsf{y - 16 = 4}\\\textbf{ADD 16 to BOTH SIDES}\\\mathsf{y - 16 + 16 = 4 + 16}\\\textbf{SIMPLIFY it}\\\mathsf{y = 4 + 16}}\\\mathsf{y = 20}\\\\\text{SECOND: Let us plug the value of y into our second equation}\\\mathsf{3(y + 5)}\\\mathsf{= 3(25 + 5)}}\\\mathsf{= 3(25) + 3(5)}\\\mathsf{= 75 + 15}}\\\mathsf{= 90}\\\\\huge\text{Therefore, your answer should be:}[/tex]

[tex]{\mathsf{y = 25 \ when\ we\ found\ \ the\ y-value\ we\ got \ 90 \ for \ the \ answer\ for the \ 2^{nd} \ equation}}}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

x-intercept: (2,0)

y-intercept: (0,-4/3)

vertical asymptote: x = -3

Step-by-step explanation:

To find the x-intercepts, we can set f(x) to 0, which is y=0:

2x-4/x+3 = 0

2x-4 = 0

2x = 4

x = 2

To find the y-intercepts, we can set x to 0:

2(0)-4/(0)+3 = y

y = -4/3

To find the vertical asymptote, we can set the denominator equal to 0:

x+3 = 0

x = -3

To graph a two step inequality solution boundary line is dashed for > and < and solid for ≤ and ≥.

These steps will be used to graphically solve a set of linear inequalities:

1. Find y's inequality solution.

2. Represent the inequality as a linear equation and, depending on the inequality sign, graph the line as either a solid line or a dashed line.

a. Draw the line as a dashed line if the inequality symbol is missing an equals sign ( or >).

b. Draw the line as a solid line if the inequality sign contains an equals sign (or ).

3. Darken the area when the inequality is satisfied.

4. For every disparity, repeat steps 1 through -3.

5. The region where all of the inequalities intersect will be the solution set.

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Alison spends $48 less on the five t-shirts. Typically, the rate is expressed as a percentage.

Typically, the rate is expressed as a percentage. Multiply the rate by the starting cost to determine the discount. Subtract the discount from the original price to obtain the sale price.

Therefore, a sale price of $70 will be achieved with a 30% discount on a $100 list price. The phrase can also mean simply the price at which anything sells. For instance, if a piece of art sells for $10 million, that price set a record.

Typically, the rate is expressed as a percentage. Multiply the rate by the starting cost to determine the discount. Subtract the discount from the original price to obtain the sale price.  

40% * 16 = 4.0 * 16 = 64 - 16 = 48 = $48.

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No, a star does not have 5 angles.

A star is a two-dimensional shape that is made up of multiple straight lines. Each straight line must meet at a point, known as a vertex, which forms an angle.

The number of angles in a star depends on the number of points or vertices it has. A five-pointed star, for example, has five angles, each of which is equal to 36 degrees.

However, stars can have any number of vertices, meaning the angles may vary depending on the star.

A star is a two-dimensional shape that has a symmetrical arrangement of points. The points can vary in number, but typically a star has five or more points.

Each point corresponds to a corner of the star, but since a star does not have any sides, it is not possible for it to have five angles. Instead, the corners of the star form vertices, but no angles.

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Answer:

Let the two numbers be x and y

Given ,

[tex]x + y = 95 \: \: ...(1)[/tex]

Also ,

[tex]y = x + 15 \: \: ...(2)[/tex]

Substiting equation 2 in equation 1 ,

[tex]x + x + 15 = 95 \\ \dashrightarrow \: 2x + 15 = 95 \\ \dashrightarrow \: 2x = 95 - 15 \\ \dashrightarrow \: 2x = 80 \\ \: \: \: \: dividing \: both \: sides \: by \: 2 \: \\ \dashrightarrow \: \cancel\frac{2x}{2} = \cancel\frac{80}{2} \\ \\ \dashrightarrow \: \: \boxed{ x = 40}[/tex]

Now , y = x + 15

therefore ,

[tex] y = 40 + 15 \\ \dashrightarrow \boxed{ y = 55 } [/tex]

Hence ,

the two numbers are 40 and 55 .

hope helpful! :)

The triangle with the given sides is a right triangle and therefore with acute angular measures.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².

Given here: The sides of a triangle here as 24,10,26

Now we know that the hypotenuse is the greatest side of a triangle.

and thus the hypotenuse is the side 26

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given, the length of sides of a triangle are 10, 24 and 26.

We have to find whether the given triangle is the right triangle.

By pythagoras theorem,

a²+b²=c²

Substituting the values

10²+24²=26²

By further calculation

100 + 576 = 676

LHS = RHS

Therefore, the given triangle is a right triangle and a right angle triangle is a acute triangle.

Hence, The triangle with the given sides is a right triangle and therefore with acute angular measures.

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The zeros of polynomial 4x² - 1 are x = 1/2 and x = -1/2

Let us assume that given polynomial be p(x) = 4x² - 1

We know that from the definition of zeros , the zeros of a polynomial are nothing but the values of the variable of the polynomial that makes the polynomial value equal to 0.

To find the zeros of polynomial p(x), we need to equate p(x) to zero then solve it for x.

⇒ p(x) = 0

⇒ 4x² - 1 = 0

⇒ 4x² = 1

⇒ x² = 1/4

⇒ x = ±(1/2)

Thus x = 1/2 and x = -1/2 are zeros of given polynomial.

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The complete question is:

What are the zeros of the polynomial 4x² - 1 ?.