solve by completing the square
-x^2=5x-14

Answer:

Step-by-step explanation:

so

120 = 2x

x = 120 : 2

x = 60

120 = 2 x 60

120 = 120

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

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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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:

pls give me the brainliest

the answer is in the attached document

Answer:

1 13/15

You need to turn the mixed number into an improper fraction to multiply.

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.

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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The best explanation of Irrational Numbers is that , the numbers  that cannot be expressed as a ratio of integers are called as Irrational Numbers .

What are Irrational Numbers ?

The Irrational numbers are the real numbers that cannot be represented in the form of a ratio ([tex]\frac{p}{q}[/tex]) . In other words, the real numbers that are not rational numbers are called as irrational numbers.

For Example : [tex]\pi[/tex] is an irrational number as   [tex]\pi =3.1415925...[/tex] The decimal value in the expansion never stops at any point.

Some Property of Irrational Numbers are :

(i) The Irrational numbers consist of only non-terminating and non-recurring decimals.

(ii) The Irrational Numbers  are real numbers only.

(iii) The Addition, subtraction, multiplication, and division of any two irrational numbers may or may not be a rational number.

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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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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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mean of the sampling distribution of the difference in sample proportions is 0.36.

The best method for the random sampling will be to write the students' names on paper and pick them out of a hat, as each student will have an equal chance of being chosen.

22% of the population of eastern grey squirrels weigh more than 0.5 kg.

36% of the population of western grey squirrels weigh more than 0.5 kg.

Eastern grey squirrel sample size is 60.

There were 120 western grey squirrels in the sample.

Required:

The difference in sample proportions' mean of the sampling distribution (eastern minus western)

The difference of the mean yields the mean of the difference.

Mean = p1 - p2 is the sampling distribution's average for the difference in the sampling proportion from two populations.

Where;

p1 = 22% of the eastern grey squirrel, which equals 0.22.

p2 = 36% of the western grey squirrel, which equals 0.36.

Therefore;

p1 - p2 = 0.22 - 0.36 is the mean.

The right answer is (E) 0.22 - 0.36.

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Answer:

x = 2,187

Step-by-step explanation:

27×27×27+27×27×27+27×27×27 =27x

19,683+19,683+19,683 =27x

59,049 = 27x

divide both sides by the coefficient of x ( 27 )

59,049 / 27 = 27x / 27

x = 2,187

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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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 formula to find the side of a geometric shape depends on the shape itself. Few details like area or perimeter of a shape or surface area or volume of a solid with few other parameters should be known.

Few examples :

For a square, the formula to find the side (s) is:

s = √(A)

where A is the area of the square.

For a rectangle, the formula to find the length (l) and width (w) are:

l = A/w and w = A/l

where A is the area of the rectangle.

For a triangle, the formula to find the base (b) and height (h) are:

A = (b*h)/2

where A is the area of the triangle.

For a cube, the formula to find the side (s) is:

V = s^3

where V is the volume of the cube.

Keep in mind that these are a few examples of formulas that can be used to find the side of a geometric shape. Depending on the specific problem, different formulas may be required.

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Answer:

72.38

Step-by-step explanation:

When converting from mm to cm divide the length value by 10

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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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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"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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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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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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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]

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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Answer:

+ - × ÷

Step-by-step explanation:

addition, subtraction, multiplication and division

Answer:

Mason can make 20 sandwiches.

Step-by-step explanation:

Answer:

Step-by-step explanation:

122121

Answer:

you can use compass to make straight line

The number of different lottery tickets that can be chosen in a 5/43 lottery is 8,145,060.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

The number of different lottery tickets that can be chosen in a 5/43 lottery is 8,145,060. This can be calculated using the combination formula, which is:

[tex]nCr = n / (r(n-r))[/tex]

where n is the total number of options (43) and r is the number of choices (5).

so, [tex]43C5 = 43 / (5(43-5)) = 8,145,060.[/tex]

Lottery tickets that can be chosen in a 5/43 lottery is 8,145,060.

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