A 3.5 inch-by-5 inch image is being enlarged by
a scale factor of x. Express the area of the
enlarged image in terms of x.

Answer: 47/4

Step-by-step explanation:

Convert the words into math:

The number = x

( 13 + x ) * 3 = 7 * x - 9

Expand:

39 + 3x = 7x - 9

Subtract 3x from both sides:

38 = 4x - 9

Add 9 to both sides:

47 = 4x

x = 47/4

The quadratic equation that matches the graph is f(x) = (x - 2)² + 4.

The correct option is B.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The graph shows the function.

The graph is given in the attached image.

In the interval, [x = 0, x = 2],

we have a line that passes through the points (0, 8) and (2, 4).

That means, the points satisfies then function.

Let the f(x) = (x - 2)² + 4.

That means,

f(0) = 8

And f(2) = 4

Therefore, the quadratic function is f(x) = (x - 2)² + 4.

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x² - 9x-19=0 is a quadratic equation in x such that the sum of its roots is 9 and the product of its roots is −19.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

If the Sum of zeroes and Product of the zeroes of a quadratic equation is given then the quadratic equation is

x² - sum of the zeroes x + Product of the zeros =0

In the given question sum of its roots is 9 and the product of its roots is −19.

So the equation will be x² - 9x-19=0

Hence,  x² - 9x-19=0 is a quadratic equation in x such that the sum of its roots is 9 and the product of its roots is −19.

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Answer:

i tried to solve it and the solution is : x=3/2 or 1.5 so ig its neither

Solving a system of 3 equations with 3 variables using a scientific calculator can be done by using matrix operations. The method is called Gaussian elimination or Gauss-Jordan elimination. Here is an overview of the steps you can follow:

Write the system of equations in matrix form. For example, if the equations are

a₁x + b₁y + c₁z = d₁

a₂x + b₂y + c₂z = d₂

a₃x + b₃y + c₃z = d₃

the matrix form would be:

| a₁ b₁ c₁ | |x| |d₁|

| a₂ b₂ c₂ | |y| = |d₂|

| a₃ b₃ c₃ | |z| = |d₃|

Enter the matrix of coefficients (on the left side of the equations) into your calculator, usually by using the matrix function or the linear equation solver function.

Enter the constant terms of the equations (on the right side of the equations) into your calculator as a column matrix or vector.

Perform row operations to make the matrix of coefficients into an upper-triangular matrix.

Solve the system by back-substitution using the values of x, y, z in the matrix of coefficients and the matrix of constant terms.

The calculator will give you the solution of the system in terms of x, y, z.

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The figure in which two rays intersect at a single location known as the vertex is referred to as an angle. The symbol "" is used to indicate an angle.

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Therefore , the solution of the given problem of probability comes out be probability of don't get green or purple candy = 0.75 .

Calculating the likelihood that a statement is true or that an event will occur is the focus of the branch of mathematics known as probability theory. Any number from range 0 to 1, where 1 represents certainty and 0 normally represents possibility, may be used to represent chance. The likelihood that a particular event will occur is depicted in a probability diagram.

Here,

Given :

there are 3 green, 2 purple, 4 yellow, 6 red, and 5 orange candies in the skittles.

total candies = 3 + 2 + 4 + 6 +5 =20

To find the probability that you don't get green or purple candy :

So , the probability of green candies is  = 3/20 = 0.15

and  the probability of purple candies is = 2/20 = 1/10 = 0.1

The probability of don't get green or purple candy

=> 0.15 + 0.1

=> 0.25

and 1 - 0.25 = 0.75

Therefore , the solution of the given problem of probability comes out be  probability of don't get green or purple candy = 0.75 .

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The distance between the origin and the point (3, 4) is 5 units.

The distance between the origin (0,0) and a point (x,y) in a two-dimensional coordinate system can be found using the distance formula, which is given by:

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, the point is (3, 4) and the origin is (0, 0)

So, the distance between the origin and the point (3, 4) is:

distance = √((3 - 0)² + (4 - 0)²)

distance = √(3² + 4²)

distance = √(9 + 16)

distance = √(25)

distance = 5

So the distance between the origin (0,0) and the point (3,4) is 5

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As per the Empirical Rule and the properties of a Normal distribution , 99.7% of the data lies within three standard deviation not 100%.

What is Empirical Rule?

According to the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, practically all observed data for a normal distribution will lie within three standard deviations of the mean or average.

In specifically, the empirical rule predicts that 68 percent of observations will fall within the first standard deviation, 95 percent will fall within the first two standard deviations, and 99.7 percent will fall within the first three standard deviations.

Hence, as per the Empirical Rule and the properties of a Normal distribution , 99.7% of the data lies within three standard deviation not 100%.

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The amount of money left for the 5 other employees is 0.75x dollars.

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

Employees = 5

Salary = 25%

If the manager's salary is 25% of the company's salary budget, and the company's salary budget is x dollars, we can represent the manager's salary as 0.25x.

To find the amount of money left for the 5 other employees, we need to subtract the manager's salary from the total salary budget.

We can represent this using the following expression: x - 0.25x

Simplifying this further, we get

x(1-0.25) = 0.75x dollars

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Answer:

Step-by-step explanation:  Hello!

I don't remember all of the postulates to these, but I hope this will help you! Vertical angles are congruent, so both angles SRT and PRQ are congruent.  This also means that line segments PQ and ST are congruent.  You also know that angles Q and S are congruent which is given.  By the ASA Theorem, when two angles and a side are congruent, then the triangles are congruent.

The concept is Inverse function. The answer is, the inverse of a convex differentiable function with a non-zero derivative is strictly concave.

In mathematics, an inverse function is a function used to "cancel" another function.  In other words, if f(x) yields y, then setting y to be the inverse of f yields x.

A convex function is a continuous function whose value at the middle of each interval of its domain does not exceed the arithmetic mean of its values ​​at the ends of the interval.

The convex function has an increasing first derivative, making it appear curved upwards. Conversely, the concave function has a decreasing first derivative, so it curves down.

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Answer:

Step-by-step explanation:

=([tex]\frac{24}{-6}[/tex])([tex]x^{6-3}[/tex])([tex]y^{3-1}[/tex])

=[tex]-4x^{3} y{2}[/tex]

Small popcorn Scenario=Emilio is right.

Medium Popcorn Scenario=Tomas is right.

Large Popcorn Scenario=Tomas is right.

A budget is a spending plan based on income and expenses. In other words, it’s an estimate of how much money you’ll make and spend over a certain period of time, such as a month or year.

1. Small popcorn Scenario.

Rent cost=46

Movie ticket cost + popcorn cost=17

For Tomas : 46+ (17*7)=46+119=$165

For Emilio : 46+(17*9)=46+153=$199

2.Medium Popcorn Scenario

Rent cost=46

Movie ticket cost + popcorn cost=?

For Tomas :46+ (18*7)=46+126=$172

For Emilio : 46+(18*9)=46+162=$208

3. Large Popcorn Scenario

Rent cost=46

Movie ticket cost + popcorn cost=?

For Tomas :46+ (19*7)=46+133=$179

For Emilio : 46+(19*9)=46+171=$217.

Small popcorn Scenario=Emilio is right.

Medium Popcorn Scenario=Tomas is right.

Large Popcorn Scenario=Tomas is right.

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The multiplication formula in maths is given as follows Multiplier × Multiplicand = Product.

The product meaning in maths is a number you get to by multiplying two or more other numbers. For example, if you multiply 3 and 5 together, you get a product of 15.

Multiplication is an important part of maths. Learning and understanding how to find the product in maths is an important basis for developing their skills in maths.

You can help children learn the maths definition of the product by reminding them that it is produced when two or more numbers are multiplied together.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

[tex] \textsf{As per the given figure, observations can be made} [/tex] [tex] \textsf{that : } [/tex]

[tex] \textbf{1.) Two sides of the given triangle are equal.} [/tex]

[tex] \textbf{2.) All the three angles are less than 90° } [/tex]

[tex] \textsf{So, to sum it up, it can be said that the } [/tex][tex] \textsf{triangle is both Isosceles and acute } [/tex][tex] \textsf{angled triangle.} [/tex]

Answer : A.) acute and isosceles, but not equilateral

Answer:

Acute and Isosceles, but not equilateral.

Step-by-step explanation:

First, let us address equilateral. Equilateral triangles assumes by definition that all triangle sides are symmetrical (60° in measurement), and that all side lengths are congruent (the same length). As shown in the picture, it is not a equilateral triangle, as there is only a pair of congruent sides.

Therefore, the given triangle is a isosceles triangle, which by definition calls for having two sides of equal length, and two equal angles.

Next, we are solving for whether or not the triangle angles are obtuse or acute. Acute angles measure less than 90° (The measurement of a right angle). Obtuse angles, on the other hand, measure more than 90°. In this case, all sides are less than 90°, per definition of isosceles triangle.

Therefore, the given triangle is acute.

Your answer is Acute and isosceles, but not equilateral.

The Speed of the train in Miles per hour will be 105 miles per hour.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

A train travels at a constant speed during a portion of its cross-country route the table shows the distance the train traveled over different intervals of time at this speed.

The slope represents the speed of the train. Then we have

m = (157.5 - 131.25) / (1.50 - 1.25)

m = 26.25 / 0.25

m = 105 miles per hour

The Speed of the train in Miles per hour will be 105 miles per hour.

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Answer: What you chose was correct :>

Answer:

Theoretical.

Step-by-step explanation:

120/400 = 30/100 = 3/10

She is correct.

It is the theoretical probability since it is based on calculations alone.

Answer:

170 miles

Step-by-step explanation:

first, for 3 hours they drove 40 mph. this means you have to multiply 40 mph by the 3 hours.

40*3=120

then you have to add the extra 50 miles that they drive north because their speed changed.

120+50=170

For the given figure, the value of upper quartile is 68.

When presented in increasing order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3). As the second quartile, the median is used (Q2).

The distance between the upper and lower quartiles is known as the interquartile range.

The median of a data set's upper half is the upper quartile.

To find this, divide the data set by the median, and then divide the remaining upper half by the median once more, with the higher quartile serving as the median.

Third or higher quartile is another name for the 75th percentile.

The value at which 25% of the answers are above that value and 75% of the answers are below that value is known as the 75th percentile.

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There are three types of polynomials in class 9  there are linear, quadratic, and cubic polynomials.

The words Nominal, which means "terms," and Poly, which means "many," are combined to make the word polynomial.

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).

Linear polynomials are straightforward and simple to solve. Isolate the variable term first, then set the equation's solution equal to zero.

First, rewrite the expression using a quadratic polynomial in the order of decreasing degree. To find the equation's solution, equate the equation and use polynomial factorization.

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The 7 properties of equality are the following,

The properties of equality is used to represent the relation between the two sides of an equation and state that the two sides remain equal even after applying the same arithmetic operation on each side.

1) The Reflexive equality property : As per reflexive property, x = x ; x R

2) The Symmetric equality p : If x = y, then y = x .

3) The Transitive equality property : If x = y and y = z, then x = z.

4) The Addition equality Property :

If x = y, then x+z = y+p.

5) Subtraction equality property :

If x = y, and z = p, then x - z = y- p.

5) The Multiplication equialty Properties :

6) The Division equaility properties : If x = y, and c≠ 0, then x/c = y/c. If x = y, and c = d ≠0, then x/c = y/d.

Consider the example : Assume the expression is 10 + x = 4(x - 2).

Solution: Solution of this using above properties, 10 + x = 4(x - 2)

=> 10 + x = 4x - 8

=> 10 = 3x - 8

=> 18= 3x

=> 6 = x

=> x = 6

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Answer:

  see attached

Step-by-step explanation:

You want the given diagram annotated with an arrow to show the direction of acceleration.

Acceleration is a result of a net force on an object. It is in the direction of that net force.

Here, the forces to the left and right are equal and opposite, so have a sum of zero.

The forces up and down are opposite, but unequal. The downward force is larger, so the direction of the net force is downward. (+5 +(-10) = -5)

The object will be accelerated downward in the direction of the 10 N force.

Answer:

either the mean or the median

For k=6 the system of equations have a no unique solution

So,we have given 2 equations from the question:

kx+2y=5…(1)
3x+y=1 …(2)

First multiply the second equation by 2
We get:
6x+2y=2

Now subtracting (2) from (1), we get:

kx+2y−6x−2y=5−2
(k−6)x=3
x= 3/K-6

​So, here if we put any value in k, then we will get a corresponding value of x but if we put k=6, then we will not get any value of x.

So, for k=6 this equation has no unique solution.

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A circle's arc length can be determined from its radius and central angle using the formula Length of an Arc = r, where is in radians.

Length of an Arc = r, where is in radians, is a formula that may be used to calculate the arc length of a circle given its radius and central angle. A circle's length is equal to (r/180)r, where r is the radius and is the angle. The length of the arc on a circle of radius r intercepted by a central angle is S = r.

Multiply the radius (6 in) by the central angle's measurement in radians to determine the length of the arc. Remember that the angle must be expressed in radians in order to employ the calculation s = r.

Assuming that is measured in radians, the formula for the length s of the arc that is intercepted on a circle with radius r by a central angle is: s = r.

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On solving the provided question, we can say that the equation  [tex]8x^3 - 1[/tex][tex]= (2x- I) (4x^2 + 2x + I)[/tex] so, a = 2 and b = 1

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here the equation is

[tex]8x^3 - 1[/tex]

[tex]= (2x- I) (4x^2 + 2x + I)[/tex]

so, a = 2 and b = 1

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The sum of an irrational number and a rational number can either be rational or irrational.

Depending on the specific numbers involved. There is no general expression for the sum of an irrational number and a rational number being irrational. If the sum of two numbers is irrational, it means that the result cannot be expressed as a simple fraction, and its decimal representation either goes on forever without repeating or repeats after a certain number of digits.

One example of the sum of an irrational number and a rational number being irrational is:

√2 + 1/2 = 1.732 + 0.5 = 2.232 (irrational)

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Not quite, but really close. All you need to do is switch -4/3 and -0.2, because -4/3 is about -1.3, and negative numbers get greater as they get closer to 0