Given the functions f(x) = 4x2 - 1, g(x) = x2 - 8x + 5, and h(x) = -3x2 - 12x + 1, rank them from least to greatest based on their axis of symmetry. (2 points)

The total fee that Ratnam should pay the agency for a journey of 50 kilometers, using a linear equation, is A. x + 10y.

The total fee is a function of summing the fixed charge for the first 40 kilometers and the variable charge for additional kilometers traveled.

In this situation, the variable charge per km represents the slope or the unit rate while the fixed charge for 40 kilometers represents the constant in a linear equation.

Flat charge up to 40 kilometers = Rs. x

Variable charge per kilometer after 40 km = Rs. y

Total distance traveled = 50 kilometers

Total fee paid = Rs. x + (50 - 40)y

= x + 10y

Thus, the correct fee that Ratnam should pay is represented by Option A.

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Answer:

4/

Step-by-step explanation:

gradient=y2-y1/x2-x1

-2-2/-5-2=

-4/-7

=4/

After answering the provided question, we can conclude that The y-intercept in the context of the data represents the predicted test score for a student who did not study at all for the test.

"Scatter plots are graphs that show the relationship between two variables in a data set. Data points are represented by a two-dimensional plane or a Cartesian system. The independent variable or characteristic is represented by the X-axis, while the dependent variable is represented by the Y-axis. These plots are also known as scatter graphs or scatter diagrams."

The y-intercept of the line of fit is approximately 80 based on the scatter plot and line of fit.

The y-intercept in the context of the data represents the predicted test score for a student who did not study at all for the test.

It should be noted that this prediction is based on the linear relationship observed in the sample data and may not be applicable to the entire population. This prediction also assumes that all other factors influencing test performance (such as natural ability, prior knowledge, and test-taking skills) are constant, which may not be the case in real-world situations.

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Answer:

60; a student who studies for 0 hours is predicted to earn 60% on the test

Step-by-step explanation:

Discovering an antiderivative of a function is the process of integration.

Adding or adding up the components to get the whole is a process known as integration. Reducing the functions into their component elements is a reverse differentiation procedure. Utilizing a broad scale, this method is utilised to find the sum.

A function's antiderivative is discovered by integration. It is the definite integration if a function can be integrated and if the integral of that function across the domain is finite with the given bounds. When d/dx(F(x) = f(x), dx = F(x) + C. Indefinite integrals are what these are.

As opposed to differentiation, integration is the opposite. In other words, the integral of 2 can be 2x + 3, 2x + 5, 2x, etc. Because of this, we must include a constant when integrating. The integral of 2 is therefore 2x + c, where c is a constant.

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The method of simplification of the radical trinomial is described below.

Particularly those polynomials that are persistent under the influence of the perpendicular group are referred to as radical polynomials. A rated subalgebra of the circle of all polynomials is the circle of radical polynomials.

Utilize the Product Property to condense a radical phrase.

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The statement that is true is that when p(x) is divided by x-n, the remainder is 7.

This statement can be confirmed by solving the equation

p(x)/x-n = q(x) + 7, where q(x) is the quotient. Solving this equation yields the result that q(x) = 2x - 5. This means that when p(x) is divided by x-n, the remainder is 7 and the quotient is 2x - 5.

This statement can also be verified by using synthetic division. By using synthetic division with 2x2 - 5x + 10 as the dividend and x - n as the divisor, the remainder after the division is 7. This confirms that when p(x) is divided by x-n, the remainder is 7.

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One graph will pass through the origin and the second graph will meet the x-axis at 3, -1.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given two function

For  y=2x²:

Since the value of x = 0, the value of y is 0.

thus this graph will pass through the origin and will only have 1 solution.

For  y = x²-2x-3:

At y = 0

x²-2x-3 = 0

x = 3, -1

Therefore, This graph will pass through the x-axis at 3, -1.

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Since Quadrilateral CDEF is inscribed in Circle A, the value of x is equal to: B. 33.

Since Quadrilateral CDEF is inscribed in Circle A, we can reasonably infer and logically deduce that line segment DF is the chord of Circle A. Mathematically, an equation which can be used to solve for the value of x in this circle is given by:

m∠DEF + m∠DCF = 180°

Substituting the given parameters into the formula above, we have the following;

(3x + 7)° + (2x + 8)° = 180°

3x + 2x + 8 + 7 = 180°

5x + 15 = 180°

5x = 180° - 15

5x = 165

x = 165/5

x = 33.

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The product of radicals is C) x[tex]\sqrt[12]{x^5}[/tex]

What is product of radical form?

The term "simplest radical form" refers to the most basic representation of a number or algebraic expression. It indicates that we should multiply the radicals when they are placed next to one another in this manner. Simply multiplying the radicands and placing the result behind the radical sign is all that is required to multiply two square roots. The square root of the product of the radicands, in other words, is equal to the product of two square roots.

Here the given form is

=> [tex]\sqrt[3]{x^2} \sqrt[4]{x^3}[/tex]

Now use [tex]\sqrt[n]{a}= \sqrt[mn]{a^m}[/tex] to expand the expression then

=> [tex]\sqrt[12]{x^8} .\sqrt[12]{x^9}[/tex]

Now the product of roots with the same index is equal to the root of the product then

=> [tex]\sqrt[12]{x^8x^9}[/tex]

=> [tex]\sqrt[12]{x^{17}}[/tex]

=> x[tex]\sqrt[12]{x^5}[/tex]

Hence the correct option is C) x[tex]\sqrt[12]{x^5}[/tex]

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Answer:

Solutions 1 and 2.

Step-by-step explanation:

The closest correlation coefficient of the scatterplot is 0.8

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

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values increases

This represents a positive linear association.

Because the points appear to be on a straight line, but they are not on a straight line, the r value will most likely be between 0.7 and 0.9

The closest value to this is 0.8

Hence, the r value is 0.8

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Answer: No solution

Step-by-step explanation:

Since we are given what y is, we can plug in y into the first equation.

[tex]3x-2(\frac{3}{2} x-\frac{5}{4} )=8[/tex]                    [distribute]

[tex]3x-3x+\frac{5}{2} =8[/tex]                         [subtract]

[tex]\frac{5}{2}\neq8[/tex]

Since this is false, then the only option is that we have no solution.

Standard form is ax^2 + bx + c. Vertex form is a(x-h)^2 + k, which reveals the vertex and axis of symmetry. Factored form is a(x-r)(x-s), which reveals the roots.

What is quadratic equation?

Factoring, using square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic problem.

Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.

x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Therefore, Standard form is ax^2 + bx + c. Vertex form is a(x-h)^2 + k, which reveals the vertex and axis of symmetry. Factored form is a(x-r)(x-s), which reveals the roots.

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The inequality which represents the possible additional amounts Dan will spend is; c ≤ 17.

As evident in the task content; the possible additional amounts Dan will spend is to be determined from the information given in the task content.

Since it is stated that Dan can spend at most $32 in which case, he has spent $15 already.

Let c be the additional amount Dan would spend.

Therefore the inequality which represents the situation is;

c + 15 ≤ 32

Ultimately, the solution set which represents the possible additional amounts he will spend is;

c ≤ 17.

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Answer:

A and C

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle so first option,

A. m∠4 = m∠1 + m∠2

is correct.

m∠3 and m∠4 are supplementary angles because they make a straight line and their sum is equal 180°, so third option,

C. m∠4 = 180 - m∠3

is also correct.

Answer:1.4

Step-by-step explanation: Because lbs are the same thing as pounds

The number of zeros and nature of zeros for the functions,

g(x) =  8x⁶ - 9x² - 6x⁵        ⇒ 6 Roots and 4 real & 2 imaginary roots

h(x) = -4x² - 3x - 1              ⇒  2 Roots and both are imaginary

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

Functions,

g(x) =  8x⁶ - 9x² - 6x⁵

h(x) = -4x² - 3x - 1

Number of roots and nature of roots = ?

First take,

g(x) =  8x⁶ - 9x² - 6x⁵

8x⁶ - 9x² - 6x⁵  = 0

x² = 0

its two of the zeros are 0, 0

After plotting graph for the given function

It can be say that,

It is intersecting x axis at 3 places

So it will have total 6 roots, 4 real roots and two imaginary roots

h(x) = -4x² - 3x - 1

D  = b² - 4ac

   =  9  - 4 × -4 × -1

   =  9  - 16

D =  -7

D is  negative so it will have 2 roots and nature will be imaginary

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f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

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Complete question:

Of the two methods for area calculation, the preferred method is the second method because the objects around the polygon are smaller, and easier to calculate their area.

There are several ways to calculate the area of a polygon. Two of them were carried out by the two students in the problem:

Of the two methods for the area of a polygon calculation, the preferred method is the second method because the objects around the polygon are smaller and easier to calculate their area.

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Answer:

vertical line x = -3

horizontal line y =  -9

Step-by-step explanation:

Answer:

Tax paid on video game: $4.20

Total price of game w/tax: $64.19

Step-by-step explanation:

7% of 59.99 = 4.20

59.99+4.20=64.19

Part A - The cycle has a total distance travelled of 130 meters.

Part B - The cycle has an acceleration of 0 meters per square second at t = 8 seconds.

In this question we find the case of a graph between time (t), in seconds, and velocity (v), in meters per second, from which we need to determine the total distance travelled (s), in meters, on the cycle and the acceleration (a), in meters per square second, at a given time.

Part A - The total distance travelled is the area below the curve, defined as the sum of the areas of two triangles and rectangle, thus:

s = 0.5 · (6 s) · (10 m / s) + (6 s) · (10 m / s) + 0.5 · (8 s) · (10 m / s)

s = 30 m + 60 m + 40 m

s = 130 m

The total distance traveled by the cycle is 130 meters.

Part B - The acceleration at a given time t is the slope of the curve at point (t, v). In this case, we find that slope can be found by secant line formula:

a = [v(12) - v(6)] / (12 - 6)

a = (0 - 0) / (12 - 6)

a = 0 m / s²

The acceleration of the cycle at t = 8 seconds is equal to 0 meters per square second.

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A system of three linear equations in two variables that satisfies the given situation can be x + y = 5, 2x + y = 5, and x + 2y = 5

To satisfy the given situation for a system of three linear equations, write any linear equation as the first equation. Let's say

x + y = 5

For the second equation, multiply the x term of the first equation by any factor, keeping the y term and the constant unchanged.

2x + y = 5

The last equation could be written using the second equation wherein the constant of the variable x and y are interchanged.

x + 2y = 5

Any two of the equations in this system have exactly one solution, because they have a unique solution when we solve them individually. However, when we try to solve the entire system by using all three equations, we find that the system has no solution.

This can be easily seen by solving the system by substitution, elimination, or graphical method.

It is also possible to use different equations but with the same criteria, the key is that at least one of the equations should be the negation or a multiple of another equation.

The problem seems incomplete/unreadable, it must have been...

"Write a system of three linear equations in two variables so that any two of the equations have exactly one solution, but the entire system of equations has no solution."

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To make a true equation, check your math to make sure that the values on each side of the equals sign are the same.

step1

(a) a +v = b-(v+5)

1+5=6 not equal a+ v=5

To check if a given value is a solution to an equation:

Evaluate the left-hand side expression at the given value to get a number

Evaluate the right-hand side expression at the given value to get a number.

See if the numbers match.

If you add the same number to both sides of an inequality, the inequality remains true.

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Correct question:

What criteria must meet to say that a+v=b-(v+5) is true?

The answer is 2500 - 45W = B

2500 is the total amount

45 is taken out a week, so let w be the variable

B is the total bank balance

So 2500 - 45W = B

I hope this was able to help you :D

The rate of change for the linear is -5 and the initial value  is -1

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph. If the function has more variables, they should all be constants or known variables in order for the function to continue to function as a linear function. We'll go into great detail about what a linear function is in this article, along with its table, graph, formulas, traits, and examples.

The rate of change refers to the slope of the linear function, because the slope is actually a ration between the two variables. So, to find the slope, we use its definition:

m = [tex]y^{2}[/tex]-[tex]y^{1}[/tex]/[tex]x^{2}[/tex]-[tex]x^{1}[/tex]

Now we replace the given points, being C the first point and D the second point:

m= -11-(-1)/2-0= -5

Therefore, the rate of change is -5, where the negative sign refers to a decreasing change, it's a decreasing linear function. In addition, the initial values is where the independent variable is zero, which is given in the point C (0;-1), so the initial condition is y = -1

 Therefore ,The rate of change for the linear is -5 and the initial value  is -1

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The value of sinθ is 15/17.

What are the trigonometric functions?

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

Given:

Cosθ = 8/17

We apply here trignometric functions.

Sinθ = √1 - cos²θ

Sinθ = √1 - (8/17)²

Sinθ = √(289 - 64)289

Sinθ = √225/289

Sinθ = 15/17

Hence, the value of Sinθ is 15/17.

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The scale of the picture is 1 in,: 3 cm, and the length of the Thermos in the picture is 4 inches, which indicates that the actual length of the Thermos is 12 centimeters

A scale factor is a number by which the dimensions of an actual or original image are multiplied to obtain the dimensions of the image.

The dimensions of the image are proportionately smaller or larger than the actual dimensions of the image.

The scale of the drawing is 1 inch is equivalent to 3 centimeters

Therefore, each inch of theThermos flask in the drawing is equivalent to 3 centimeter length of the actual Thermos flask.

The dimensions of the thermos flask in the drawing = 4 inches

Therefore;

Length of the thermos flask in the diagram ÷ Actual length of the thermos flask = 1 in./3 cm

Actual length = Image length × 3 cm/1 in.

Actual length = 4 inches × 3 cm/(1 inch) = 12 cm

The actual length of the thermos flask is 12 centimeters

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Answer:

Step-by-step explanation:

when GDK goes up GD goes down