3x+5y= 8
2х - 5y = 22

Solve system of equations

Answer:

Step-by-step explanation:

122121

A quadratic polynomial does not cross the x axis at any point since it has no zeros.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

x^2 - 2x +  5 when compared with the standard form of the quadratic equation, a = 1, b=- 2, c=5

Value of the discriminant =b^2 - 4 ac                                    

= (-2)2 - 4(1) (5)= 4 - 20                                    

= - 15

The value of the discriminant is negative i.e less than zero.

Hence, the quadratic equation x^2 - 2x +  5 has no real zeroes.

Since a quadratic polynomial may only have two real roots, the number of times the graph will cross the x-axis at most is two, and at least zero when there are no roots in the equation.

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We can tell if a number is rational or irrational by Venn Diagram

Both irrational and rational numbers are exact, yet they have different properties. Any number that can be expressed as P/Q, where P and Q are both integers and Q is more than zero, is considered to be reasonable. Simple fractions, however, cannot be used to express an irrational number. An illustration of a rational number is 2⅔ 3, while an irrational number is √2.

All integers, fractions, and repeating decimals are included in the concept of a rational number. We may represent every rational number as p/q, where p and q are integer numbers.

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(A) (x+4)(x-1)=0 is the proper factors form of the given equation x²+3x-4=0.

A factor is a number that completely divides another number.

To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

So, we have the equation:

x²+ 3x - 4 = 0

By dividing the center term, this quadratic equation can be reduced to its simplest form.

The result of dividing the middle word is:

x² + 4x - x - 4 = 0

One way to spell it is as:

x (x + 4) - 1 (x + 4) = 0

Now, we obtain:

(x + 4) (x - 1) = 0

Therefore, (A) (x+4)(x-1)=0 is the proper factors form of the given equation x²+3x-4=0.

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Correct question:

Which of the following is the correct factored form of the given equation x2+ 3x - 4 = 0?

(A) (x +4) (x - 1) = 0

(B) (x - 4) (x - 1) = 0

(C) (x - 4) (x +1)= 0

The solution for given question of algebra are 10, -42, -38 for question 1st, 2nd and 3rd.

There are several sub-branches of algebra, including commutative algebra, abstract algebra, linear algebra, and elementary algebra.

x + 6/x + 3 = 4/7

7x + 42 = 4x + 12

7x - 4x = 42-12

3x = 30

x = 10

2/x+8 = 3/x+9

2x - 18 = 3x + 24

x = -42

x+2/6 = x-4/7

7x+14 = 6x-24

x = -38

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Answer:

x = 2

Step-by-step explanation:

If you look at the equation:

(x + 2) = 4

We just need to solve for x.

To solve for x, we can subtract the total by the addend, to get the variables value.

4 - 2 = 2

Therefore, the value of x is 2.

The equation indicates that the given equation's constant variable is 8.

In other words, you may claim that y directly depends on x or that y is directly proportional to x. The continuity equation or the constant variable variation in this function is m (or k). a direct variation's product of two variables or the result of two variables in such an inverse variation K is the constant of variation in the direct variation equations.

"X fluctuates directly as Y" denotes that as y rises, x also rises by the same amount. In other words, the ratio between y and x is constant and is:

                            x = k × y                

where k is the constant of variation.

Here,

it is given that y varies as  x,

if y=24 and x=3,

therefore,

y = kx

24 = 3k

∴ k = 8

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The cost of a carpet of the same quality, measuring 5m by 3m is $129.

We can use the unitary method to solve this problem. The unitary method is a technique used for solving a problem by first finding the value of a single unit, and finding the necessary value by multiplying the single unit value.

In this question, it is given that a carpet measuring 4m × 2.5m costs $86. That means the 10m² area of carpet costs $86 if we divide 10 by both the cost and area of the carpet we will find that, 1 m² area of carpet will cost $8.6. So the cost of a carpet of 5m × 3m will be the area of the carpet multiplied by the cost of the carpet per 1 m² i.e, 15m² of carpet will cost $8.6 × 15 which is equal to $129.

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Therefore , the solution of the given problem of triangle comes out to be  ΔA"B"C "≅ ΔABC is congruent.

The fact that a triangle has sides or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with vertices A, B, & C is Triangle ABC. A singular planes and triangle are obtained in Euclidean geometry when the vertices are not collinear. Any triangle that has three sides and three corners is a polygon.

Here,

Triangle A'B'C' is created by reflecting triangle ABC across the y-axis.

Afterward, it was dilated by a ratio of 1/3 to create triangle A "B"C".

Find the right answer for the triangles ABC and A"B"C."

So,

We are aware that reflection undergoes a rigorous transformation, meaning the shape and size of the original object do not change.

As a result, after reflection, figures always match their pictures.

"ABC," "A'B'C," etc (i)

The process of dilation is flexible. Although the size is changed, the shape is still the same.

Figures after dilatation therefore always resemble their photographs.

ΔA'B'C' ≅ ΔA "B"C" ... (ii)

With I and (ii), we obtain

ΔA"B"C "≅ ΔABC

Similar triangles include ABC and ABC.

As a result, choice A is the right one.

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For the given principal and two different rate of interest for the 15 years of time period the cost of four points is given by  $26786.2.

As given in the question,

Principal amount 'P' = $128,000

Time 't' = 15 years

Rate of interest 'r' = 5.5%

                             = 0.055

Total amount 'A' received is given by the formula :

A = P ( 1 + r/100 )^n

  = 128,000 ( 1 + 5.5 / 100 )^15

  = $285756.99

Now when the rate of interest is changed to

Rate of interest 'r' = 4.81%

                             = 0.0481

Total amount 'A' received is given by the formula :

A = P ( 1 + r/100 )^n

  = 128,000 ( 1 + 4.81 / 100 )^15

  = $258970.79

Now, the cost of four points is given by:

= $( 285756.99 - 258970.79 )

= $ 26786.2

Therefore, for the given principal amount with two different rate of interest for the time period of 15 years the cost of four points is equal to  $26786.2.

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The distance between the stake from the pole is 6.25 ft.

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that a utility pole is 5 ft high. An 8 ft cable is stretched from the top of the pole to a stake in the ground.

The distance will be calculated as,

B² =  H² - P²

B = √(8² - 6²)

B = √ ( 64 - 36 )

B = √39

B = 6.25 ft

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Taking into account, the number of successful throws into different shapes, Mollie is just as likely to hit a triangle as a circle. i.e option C.

A probability is a numerical representation of the possibility 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.

Probability is an important method for comprehending and making judgments regarding uncertain occurrences in many disciplines, including statistics, finance, and science. It aids in quantifying and forecasting the probability of specific events, enabling us to make better educated choices and comprehend the degree of risk involved with various activities. In summary, probability is a key idea in decision-making and risk management because it is a potent instrument for comprehending and managing uncertainty.

Since, the number of throws of darts by Mollie is same for both the circle and triangle, there is equal likelyhood to hit the triangle as a circle. Which is the required true statement.

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On solving the provided question, we can say that the spherical balloon's initial radius is 7 cm.; the final radius is 14 cm. ratio =  (7/14) ^2 = 1:4

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle.

The spherical balloon's initial radius is 7 cm.

The final radius is 14 cm.

ratio =

(7/14) ^2 = 1:4

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Answer:

you can use compass to make straight line

Therefore , the solution of the given problem of function comes out to be  f(g(x)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)

Each x value in the domain has one but only one y value range, according to the rule of a function. Definition. If there is only one and only one value of x such that f(x) = y, then the function is one-to-one

Here,

Given : f(x) =X² - 8x+16/2 + 2x

g(x) =(6x)/(x-4)

To find the f(g(x)) :

=> f(g(x)) = f(6x/(x-4))

=>  f(6x/(x-4)) =  (6x/(x-4) )^2 - 8((6x)/(x-4)) +16/2 + 2(6x)/(x-4)

=>  f(6x/(x-4)) = 36[tex]x^{2}[/tex]/ ( [tex]x^{2}[/tex]+ 16 - 8x) - 36[tex]x^{2}[/tex]/(x+4) +8

=> f(6x/(x-4)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)

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

f(g(x)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)

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Answer:

+ - × ÷

Step-by-step explanation:

addition, subtraction, multiplication and division

Answer:

Translate(1.3, -1)

Scale Factor: 2/3

Step-by-step explanation:

First, perform a dilation about the origin. This will make the original shape smaller.

From the given diagram, we can see that R'S' is 10 units long. RS is 15 units long. Using this information, we can create this ratio.

[tex]\frac{10}{15}[/tex]

This means that Triangle R'S'T' is 2/3 of Triangle RST. Construct lines from the origin (the center of dilation) to each point on the original triangle. Then, find two thirds of that line. The new point will be the new y-coordinate.

The new coordinates will (approx.) be:

R = (-2, 4.7)

S = (-2, -5.3)

Only two coordinates are necessary to perform this translation. As per the graph, this triangle must shift approximately 1.3 units up and 1 unit to the left. Thus, the final translation is:

Translate(1.3, -1)

Scale Factor: 2/3

"20" is the Pythagorean triplet of 12 and 16.

A set of three integers that can be the lengths of the sides of a right triangle is called a Pythagorean triple, it also defines the positive integers a,b, and c such that a right triangle exists with legs a,b, and hypotenuse c.

By the Pythagorean theorem, this is equivalent to finding positive integers a, b, and c satisfying  a²+b²=c²

The simplest Pythagorean triple is the set “3,4,5.”

Now, substitute the values in the above equation:

=) x² = 12² + 16²

=) x² = 144 + 256

=) x² = 400

=) x = √(400)

=) x = 20.

Therefore, (12,16,20) is a Pythagorean triplet.

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The y-intercept of the quadratic function f(x) = (x - 8)(x + 3) is (0, -24).

The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula y = f(x) is crucial when graphing the function. An intercept can be one of two different forms for a function. The x-intercept and the y-intercept are what they are. A function's intercept is the location on the axis where the function's graph crosses it.

This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).

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To complete the table, we can simply multiply the number of calories by 0.239 to find the equivalent amount of Joules.

The equation relates Joules to calories as j = 0.239c, where c stands for calories and j stands for joules. For example, 1 calorie is equal to 0.239 Joules, 2 calories is equal to 0.478 Joules, and so on.

Joules (j)              Calories (c)

0.239c                  1

0.478c                  2

0.717c                  3

0.956c                  4

1.195c                  5

1.434c                      6

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The inverse of a function is a function that "undoes" the original function. If f is a function and x is an element in the domain of f, then the inverse of f is denoted as f^-1(x) and is defined as the element in the domain of f such that f(f^-1(x)) = x.

The symbol "φ" (phi) is not a commonly used notation for any function. It is a Greek letter and can be used in different fields such as physics, mathematics, and engineering to represent different things depending on the context.

It is important to note that not all functions have inverses. A function has an inverse only if it is a bijective function, which is a function that is both injective and surjective, meaning that it maps every element of the domain to a unique element in the range and vice-versa.

So to find the inverse of a function, you have to first make sure that the function is bijective. If so, you can find the inverse function by switching the positions of x and y, then replacing y with f^-1(x) or x with f^-1(y) and solving for the new x or y.

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1

To find an unknown number we can use properties of equality.

Algebraic Method

Another word to describe an unknown number is "variable". For the equation, I will call this variable x. Any variable can be used, but x is the most common.

We can write an equation to describe the situation. The statement says that the product of 15 and x is 15. This means that 15 * x = 15. Now we can use algebra to solve this equation.

To find x, divide both sides by 15.

Identity Property of Multiplication

Additionally, if you know all the properties of equality, you can answer this question without doing any math. One of the properties of equality is the identity property of multiplication. The identity property states:

This means that any number multiplied by 1 is itself. So, since the factor and product are equal, the other factor must be 1. If you plug 15 in for a, you can see how this property applies to this situation.

Explanation:

The confidence interval spans from 440 to 472. This is a width of 472-440 = 32 units. It divides in half to get 32/2 = 16. We can think of this as the "radius" of the confidence interval, and it represents the margin of error. It's the distance from the center to either endpoint of the interval.

Side note: use the midpoint formula to determine the center.

On sectional charts, the graticules are the lines that separate each 30 minutes of latitude and each 30 minutes of longitude. One tick mark equals one minute of latitude or longitude. Moving northward increases latitude while moving westward increases longitude. The coordinates of the Garrison (Pvt) airport are 47° 40' 00" N and 101° 26' 00" W.

Direction is characterised as the course that something follows, the route that must be taken to get to a particular location, the direction in which something is beginning to take shape, or the direction you are facing. When you turn right instead of left, that is an illustration of direction.

Identifying whether a direction is clockwise or anticlockwise is a straightforward method for resolving direction problems. If we turn right, the direction will be entirely clockwise. Therefore, when starting from the correct point at North, every right movement will lead in the clockwise directions of East, South, and West.

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The like terms in 3x (3 - 2y) and 2 (xy + x²) are -6xy and 2xy.

Like terms are terms which have the same variables and exponents. In this case, the like terms are -6xy and 2xy because they both have the same variable (xy) and exponents (1). In algebra, like terms can be added or subtracted to simplify an expression.  Like terms are terms which have the same variables and exponents.

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The perimeter of the parallelogram with the given vertices is 33.

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.

Given that:

A = (3, 6)

B = (-5, 6)

C= (6 , -1)

D = (-2, -1)

The length of side is given by the formula:

[tex]L = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Substitute the values in the formula to find the sides of the parallelogram.

[tex]AB= \sqrt{(-5 -3)^2 + (6-6)^2} = 8\\ \\BC = \sqrt{(6+5)^2 + (-1 - 6)^2} = 13\\\\CD= \sqrt{(-2+6)^2 + (-1 +1)^2} = 4\\\\\DA= \sqrt{(3+2)^2 + (6+1)^2} = 8[/tex]

The perimeter is obtained by adding all the sides of the given two-dimensional shape.

P = 8+13+4+8

P = 33

Hence the perimeter of the parallelogram is 33.

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Answer:

Step-by-step explanation:

so

120 = 2x

x = 120 : 2

x = 60

120 = 2 x 60

120 = 120

The Construction is shown below.

Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Given:

a) Steps for perpendicular line:

b) Perpendicular Bisector for triangle

So, if we extend the bisector they can meet inside, at center and outside the triangle.

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Answer:

[tex]y=\frac{9}{10}x-\frac{7}{5}[/tex]

Step-by-step explanation:

Using the points [tex](-4,-5)[/tex] and [tex](6,4)[/tex], the slope is [tex]m=\frac{-5-4}{-4-6}=\frac{9}{10}[/tex].

Using point-slope form:

[tex]y+5=\frac{9}{10}(x+4) \\ \\ y+5=\frac{9}{10}x+\frac{18}{5} \\ \\ y=\frac{9}{10}x-\frac{7}{5}[/tex]