Which system of equations has the same solutions as the system below? `3x-y=7` `2x+3y=12`

Answer:

m = -3/5

Step-by-step explanation:

We have to get to the equation y = mx + b

3x 5y = -15

We subtract 3x from both sides

5y = -3x - 15

Then we divided by 5 into both sides

y = -3/5x - 3

We know our equation is y = mx + b

m = the slope

b = y-intercept

The slope is -3/5

Answer: (a+b)2 = a2 + b2 + 2ab., (a-b)2 = a2 + b2 – 2ab.,a2 – b2 = (a+b) (a-b)

Step-by-step explanation:

Yes, the equation has no real roots.

To solve this equation, we first move the constant terms to the right side and the terms with x to the left side.

3x² - 4√3x = -4

Next, we square both sides of the equation.

(3x² - 4√3x)² = (-4)²

9x⁴ - 24√3x² + 16x = 16

Next, we move the constant terms to the right side of the equation.

9x⁴ - 24√3x² = -16

Next, we factor the left side of the equation.

(3x² - 8√3)(3x² + 8√3) = 0

Finally, we set each factor equal to zero and solve for x.

3x² - 8√3 = 0

3x² + 8√3 = 0

However, these equations have no real solutions, so the original equation has no real roots.

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Step-by-step explanation:

obtuse-larger than 90 degrees

acute-smaller that 90 degrees

right-exactly 90 degrees

The given expression x² is an algebraic expression where x is the base and 2 is the exponent.

Therefore, the answer is x.

In an expression aᵇ, a is the base and b is the exponent. Here the expression aᵇ implies the base a is multiplied b times. For example x² implies x multiplied twice, that is

x² = x × x

Base number is the number which is multiplied to itself and the exponent denotes the number of times it is multiplied to itself. For example

x⁰ = 1

x¹ = x

x² = x×x

x³ = x×x×x

x⁴ = x×x×x×x

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Answer:

63 degrees

Step-by-step explanation:

similar triangles have the same angles.

XYZ is similar to EDF. Therefore the measure of angle Z is the same as angle F. The measure of angle Z is 63, so the measure of angle F is also 63.

Answer:

19 and 13/30

Step-by-step explanation:

First make 2/3 have a common denominator with 23/30

You can do this by multiplying the numerator and denominator of 2/3 to get 20/30

Now add

20/30 + 23/30  = 43/ 30

Simplify this fraction

1 and 13/30

add this to 18

18 + 1 and 13/30 = 19 and 13/30

The two given rectangles are proportional to each other since they have a width-to-length ratio of 2 and the area ratio between them is equal to 9.

Two rectangles are proportional to each other when both have the same length-to-width ratio. The area ratio is defined by the following formula:

r' = (l' · h')/(l · h)      (1)

Where:

l' - Length of the enlarged rectangle.

l - Length of the original rectangle.

h' - Length of the enlarged rectangle.

h - Length of the original rectangle.

Now we determine the length-to-width ratio of each rectangle:

Original rectangle

s = 4/2

s = 2

Enlarge rectangle

s' = 12/6

s' = 2

The two rectangles have the same length-to-width ratio.

The area ratio is:

r' = (12 · 6)/(4 · 2)

r' = 72/8

r' = 9

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Two rectangles are proportional to each other when both have the same length-to-width ratio. The area ratio is defined by the following formula:

r' = (l' · h')/(l · h)      (1)

Now we determine the length-to-width ratio of each rectangle:

Original rectangle

s = 4/2

s = 2

Enlarge rectangle

s' = 12/6

s' = 2

The two rectangles have the same length-to-width ratio.

The area ratio is:

r' = (12 · 6)/(4 · 2)

r' = 72/8

r' = 9

Considering the definition of a line, the equation of the line that passes through the point (5, -5) and has a slope of -1/5 is y= -1/5x -4.

A linear equation o line can be expressed in the form y = mx + b

where

In this case, you know that:

Substituting the value of the slope m and the value of the point in the expression of a line, the value of the ordinate to the origin b can be obtained as follow:

-5= -1/5×5 + b

-5= -1 + b

-5 +1= b

-4= b

Finally, the equation of the line is y= -1/5x -4.

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Answer:

7y + 4

Step-by-step explanation:

2y+(4+5y)

2y + 4 + 5y

combine y terms:

7y + 4

Probability of getting the sum as 4 when a pair of dice is rolled is 1/12.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

No, probability is aways between 0 to 1.

Find total number of possible outcomes

Here it is given that a pair of dice is rolled

So the event points are

= { (1,1), (1,2), (1,3), (1,4),(1,5),(1,6),(2,1), (2,2), (2,3), (2,4),(2,5),(2,6),(3,1), (3,2), (3,3), (3,4),(3,5),(3,6),(4,1), (4,2), (4,3), (4,4),(4,5),(4,6),(5,1), (5,2), (5,3), (5,4),(5,5),(5,6),(6,1), (6,2), (6,3), (6,4),(6,5),(6,6)}

So the total number of possible outcomes = 36

Let A be the event that of getting a sum of 4

So the event points are (1,3) , (2,2) , (3,1)

So total number of possible outcomes for the event A is 3

Hence the required probability= P(A)= no. of favorable cases to event A/total no of outcomes

=3/36

=1/12

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Answer:

see explanation below

if you have any questions on equation you can send it to me

Step-by-step explanation:

We have various of ways in which we can simplify an equation

for example

simplify: 2x – 4 = 10

soln

2x – 4 = 10

since we are looking for x we need to collect like terms

2x = 10 + 4

2x = 14

Then we will divide both sides by 2 to get x

x = 14/2

x = 7

N.B:- after solving an equation if you want to check the answer just substitute for the value

2x – 4 = 10

2(7) – 4 = 10

14 – 4 = 10

10 = 10

LHS = RHS

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The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

Given that,

We have to find why i squared is equal to negative 1.

We know that,

The imaginary numbers are denoted as i.

We occasionally obtained negative integers in equations when using the radican (square root) symbol to solve them. When they realized this, some would halt and respond, "no actual solution," which is technically accurate. We can further simplify radicals by using the imaginary number I which is the square root of real numbers. We occasionally even manage to get rid of the fictitious element, which provides us with actual solutions.

The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

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The current value of "i" in the complex numbers is √(-1)

The value of I as current is expressed as Amperes

In order to know what "i" is and what its value is, we must first know what kind of number it is.

The current is the flow of electric charge, it is denoted with the letter "I" and its unit of measure is Amperes, it can take any value even complex numbers.

Complex numbers are known as imaginary numbers and can be defined as an extension of the set of real numbers, since in its structure it has a real number followed by an imaginary number denoted with the letter "i".

In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:

√(-1) = i

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Answer:

2x - 7y > 10

8 + x > 5

3 < 5

Step-by-step explanation:

The equations are

Ax + By + C < 0 or Ax + By + C > 0

There is no equal in a linear inequality

The first option 2x + 8 = 10y is an equation, so it is wrong. The other 3 are correct!

Simply said, a z-score, also known as a standard score, informs you of how much a data point deviates from the mean.

It is not possible to determine the z-score for a height of 67 inches without additional information.

The sum of all values divided by the total number of values determines the mean  of a dataset.

A z-score, also known as a standard score, informs you of how much a data point deviates from the mean.

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The mean of the given data set is 29.5.

The term "mean" refers to the arithmetic average of the data set and is derived by dividing the total number of data points in the data set by the total number of data points. It is a data point that represents the average of all the data points in the collection.

Example :

Find the mean of the following data set.

10, 20, 36, 12, 35, 40, 36, 30, 36, 40

Given,

xi = 10, 20, 36, 12, 35, 40, 36, 30, 36, 40

n = 10

Mean = ∑xi/n

= (10 + 20 + 36 + 12 + 35 + 40 + 36 + 30 + 36 + 40)/10

= 295/10

= 29.5

Therefore, the mean of the given data set is 29.5.

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Find the mean of the following data set.

10, 20, 36, 12, 35, 40, 36, 30, 36, 40

Given,

xi = 10, 20, 36, 12, 35, 40, 36, 30, 36, 40

n = 10

Mean = ∑xi/n

= (10 + 20 + 36 + 12 + 35 + 40 + 36 + 30 + 36 + 40)/10

= 295/10

= 29.5

To count 1 in an array, one can use a looping structure to iterate through each element in the array and increment a counter every time the element is equal to 1.

This can be accomplished using a while loop, a for loop, or a for-each loop. A while loop would use a variable to track the index of the array, and then use a conditional statement to check if the value at the current index is equal to 1. Then, the loop can increment the counter and the index variable. A for loop can be used in the same manner, but with the index variable declared within the loop.

A for-each loop can be used to iterate through the elements of the array, and a conditional statement can be used to check if the current element is equal to 1 and increment the counter if necessary. Whichever looping structure is used, the result should be the same. The counter will hold the number of 1s present in the array after the loop completes.

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Answer:

m = 12

Step-by-step explanation:

The equation is y=mx +b

Where m is the slope

So, in this case slope is 12

12 is an integer, so my answer is correct!

A set of all rational and irrational numbers is called the real numbers. All real numbers can be plotted on the number line. It is not imaginary number which cannot be quantified. It is denoted by capital Latin letter R.

Rational numbers are number that can be expressed as p/q where p and q are integers and value of q not equal to 0.

For example, -3/4, 5/3, 6/1.

Irrational numbers are not rational numbers but they can be plotted on the number line. It cannot be expressed as a simple ratio.

For example π, √2, -√7.

But √(-7) is an imaginary number.

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The sum of the x and y coordinates of D" is 6

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

D = (-1, -3)

The transformation rule is given as

T(-2,0) R180° about the origin.

Mathematically, this can be represented as

(x, y) = (-x + 2, -y)

So, we have the following representation

D" = (1 + 2, 3)

Evaluate the like terms

D" = (3, 3)

When the coordinates are added, we have

Sum = 3 + 3

Evaluate

Sum = 6

Hence, the sum is 6

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Complete question

A"B"C"D" is the image of ABCD after the composition of transformations

T(-2,0) R180° about the origin.

What is the sum of the x and y coordinates of D" if the coordinate of point D is (-1, -3)?

By Quadratic Formula factors of [tex]a^2+4b^2[/tex] are [tex](a+2bi),(a-2bi)[/tex].

The quadratic formula in elementary algebra is a formula that gives the solution(s) to a quadratic equation. In addition to the quadratic formula, there are various methods for solving quadratic equations, including factoring (direct factoring, grouping, and the AC technique), completing the square, graphing, and others.

The following general quadratic equation is given:

[tex]ax^2+bx+c=0[/tex]

The quadratic formula is:

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}, \frac{-b-\sqrt{b^2-4ac} }{2a}[/tex];

where x stands for an unknown, a, b, and c are constants, and a≠0.

Each of these two answers is also referred to as a quadratic equation root (or zero). These roots, which are clearly stated as [tex]y = ax^2 + bx + c[/tex], are the x-values at which any parabola crosses the x-axis geometrically.

Given;

[tex]y=a^2+4b^2;\\[/tex]

By comparing this with general equation [tex]x=a,a=1,b=0,[/tex][tex]c=4b^2[/tex]

By substituting in the formula;

[tex]x=\frac{-0+\sqrt{(0)^2-4(1)(4b^2)} }{2(1)} =2bi\\(or) x=\frac{-0-\sqrt{(0)^2-4(1)(4b^2)} }{2(1)} =-2bi[/tex]

That gives us;

[tex]y=(a+2bi)(a-2bi)[/tex]

By Quadratic Formula factors of [tex]a^2+4b^2[/tex] are [tex](a+2bi),(a-2bi)[/tex].

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The value of x in the equation -2.25 + 0.4x = -2.8 is -12.625

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

The equation is given as:

-2.25 + 0.4x = -2.8

Collect like terms

0.4x = -2.8 + 2.25

0.4x = -5.05

Collect like terms

x = -5.05 / 0.4

x = -12.625

The value of x is -12.625.

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The solution to the given linear equation, -2.25 + 0.4x = -2.8, is x = -1.375 or x = -1 3/8

From the question, we are to solve the given equation

The given equation is

-2.25 + 0.4x = -2.8

To solve the equation, we will determine the value of the unknown variable.

In the given equation, the unknown variable is x

Solving for x

-2.25 + 0.4x = -2.8

Add 2.25 to both sides of the equation

-2.25 + 2.25 + 0.4x = -2.8 + 2.25

0.4x = -0.55

Divide both sides of the equation by 0.4

0.4x/0.4 = -0.55/0.4

x = -1.375

Convert to a mixed number

x = -1.375 = -1375/1000

x = -11/8

x = -1 3/8

Hence, the solution is -1.375 or  -1 3/8

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Members who have made at least 36 months' worth of contributions overall and six months' worth within the previous 12 months are eligible to apply for a loan through SSS.

One month's worth of salary is equal to the amount of the salary loan. If you have at least 72 months of posted contributions and six months of contributions during the last 12 months, you may also be eligible to apply for a two-month wage loan.

If you have a job, your employer is responsible for keeping your loan payments and monthly contributions current. Additionally, you need to keep up with payments on all of your other loans.

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The segment e g contains the points e and g, and it bisects the triangle d e f into two congruent parts.

The points that segment e g contains are the points e and g.

Segment e g bisects triangle d e f, which means that it cuts the triangle into two equal parts. This means that the two sides d e and e f are congruent, and that the vertex angle d e f is divided into two equal angles, d e g with measure 3 y plus 4, and f e g with measure 5 y minus 10.

This can be expressed using the following formula:

Let d e = x

Then d e g = 3x + 4

f e g = 5x - 10

and d e + e f + f e g = 180°

Substituting the values for d e g and f e g, we get:

3x + 4 + x + 5x - 10 = 180°

9x = 196

x = 21.77

Therefore, the length of the sides d e and e f is 21.77.

Since segment e g bisects the base d f, it divides the base into two equal parts, each of length 10.88. The segment e g also divides the vertex angle d e f into two angles, d e g with measure 3 x + 4 = 67.33, and f e g with measure 5 x - 10 = 108.67.

Therefore, segment e g contains the points e and g, and it bisects the triangle d e f into two congruent parts. The segment also divides the vertex angle d e f into two angles, d e g with measure 67.33, and f e g with measure 108.67.

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The main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.

Solving system can be defined as solution set of a system of equations to the collection of all solutions. Solving the system also means finding all solutions with formulas involving some number of parameters.

There are three methods used to solve systems of equations such as:

Therefore the main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.

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An exponential function with a base greater than 1 will be increasing in nature.

This is because when the base of an exponential function is greater than 1, the exponent is raised to a power greater than 1, and the result will always be greater than the original number. This means that as the value of x increases, so too will the value of the function. To illustrate this, the formula for an exponential function with base b can be written as f(x) = b^x. As x increases, b^x will become larger and larger, resulting in a continually increasing function. For example, if b = 2, then f(x) = 2^x. As x increases, 2^x will increase exponentially, resulting in a function that is always increasing.

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Tori earns more money.

Given data :

Tori : $24/h; 150% OT

Calculate Tori's overtime (OT) pay

Convert OT rate to decimals --> 150% = 1.

Tori's OT wage is 1.5*$24 = $36

Tori worked for 20h OT. (60h-40h = 20h)

(Regular pay X regular hours worked) + (OT wage X OT hours worked)

= ($24 X 40h) + ($36 X 20h)

= $1680

Matias : 5% commission

Convert 5% to decimals --> 0.05

(Jewelry sold) X (commission rate)

= $21000 X 0.05

= $1050

Since $1680 > $1080, Tori earns more.

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Answer:

⭐2 corresponding, congruent angles

⭐1 corresponding, congruent side length that is included between the 2 angles

Example (figures not drawn to scale);

Answer:

To find the area of a circle, we can use the formula A = πr^2, where A is the area of the circle, π is a constant with a value of approximately 3.14, and r is the radius of the circle. To use this formula, we first need to find the radius of the circle. We can do this by dividing the diameter of the circle by 2:

r = Diameter / 2

r = 6 m / 2

r = 3 m

Substituting this value for r into the formula for the area of a circle, we get:

A = πr^2

A = 3.14 * 3^2

A = 3.14 * 9

A = 28.26

Therefore, the area of the circle is 28.26 square meters. Rounded to the nearest whole number, this is equal to 28 square meters.