Select the correct answer.
Which graph represents function g?

g(x) = (-x)1/2

The value of x will be 1.17 inches and the maximum volume of the box is 1.6 cubic inches.

Volume is a measurement of three-dimensional space that is occupied. It is frequently numerically quantified using SI-derived units or various imperial or US customary units. The definition of length is linked to the definition of volume.

Given that the rectangular box is made from cardboard the thickness is x.

The length of the box will be,

L = 4.5 - 3x

The width of the box will be,

W = 4 - 2x

The thickness of the box is,

H = x

The volume of the box will be calculated as,

V = ( 4.5 - 3x) ( 4 - 2x ) (x)

V = ( 4.5 - 3x) ( 4 - 2x ) (x)

V = ( 18 - 12x - 9x + 6x² ) x

V = 6x³ -21x² + 18x

For maximum volume differentiate the volume with respect to x and get the value of x,

dV / dx = d / dx (  6x³ -21x² + 18x ) = 0

d / dx (  6x³ -21x² + 18x ) = 0

18x² - 42x + 12 = 0

3x² - 7x + 6 = 0

Solve the above quadratic equation as,

x = [ -b ±√(b² - 4ac) ] / 2a

x = [ -7 ± √ (-7² - 4 x 3 x 6 ) ] / ( 2 x 3 )

x = 1.17

The value of x is 1.17 inches by solving the above quadratic equation. The maximum volume will be calculated as,

V = 6x³ -21x² + 18x

V = 6(1.17)³ -21(1.17)² + 18(1.17)

V = 9.6 - 28.7 + 21.06

V = 1.96 cubic inches

The maximum volume is 1.96 cubic inches and the value of x is 1.17 inches.

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1. f(x) - cubic function -- polynomial , g(x) - linear function

similar

The function f(x) = x³+x²-3x+4 is a polynomial function and g(x) = 2ˣ-4 is an exponential function.

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

y-intercept = 4

x - intercepts = -2.68

Function g(x)

Domain: x > 0

Range: -4 < y < ∞

y - intercept = -4

x - intercepts = none

By comparing the key features above, we can conclude that the common features in both functions are their range

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Answer:

x + x - x = x

explanation:

give us the actual formula lol

Answer:

D

Step-by-step explanation:

when we have the zeroes, we can build the polynomial by multiplying factors that will turn the functional value to 0 at exactly these points.

f(x) = (x - 3)(x + 6)(x - 1)

we don't need to do the full multiplications to see that the constant term of the polynomial is the result of the multiplication of all 3 constant terms of the factors :

-3 × +6 × -1 = +18

and therefore, D is the correct answer (as it is the only answer option with +18 as constant term).

A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.

A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.

Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.

As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.

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the area of the generic rectangle will be x²-2x-15.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and width of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

Area of rectangle is A = a*b

(x + 3)(x - 5) in a generic rectangle

The product will give the area

x²-2x-15

hence the area of the generic rectangle will be x²-2x-15.

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True, is it possible for the results of a study to show a non-zero correlation, even though the correlation for the general population is zero.

When a correlation is statistically significant, it is a significant and strong correlation. Even a very slight association can be statistically significant with a very large sample size.

                   While the correlation for the entire population is zero, it is nevertheless feasible for a sample to have a true, non-zero correlation.

When there is no association in a correlational analysis, what happens?

The variables fluctuate in opposite directions when there is a negative correlation. There is no association between the variables if there is zero correlation.

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The point of the compass located in order to make the arcs is points X and Y.

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc. A circle contains an arc. For instance, a quarter-circle and a semicircle are both examples of arcs. A minor arc is one that is smaller than half of the circle it is a part of, or less than a semicircle, whereas a major arc is one that is more than half of its circle.

Given

The following figure was drawn using a straightedge and a compass.

The point of the compass located in order to make the arcs:

1. points X and Y

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Answer:

-2

Step-by-step explanation:

Given,

g(x) = f(4)

or, 2 - 4x = 3*4 - 2

or, 2 - 4x = 10

or, 2 - 10 = 4x

or, -8 = 4x

or, x = -2

The volume of the rectangular block in this problem is given as follows:

1300 cm³.

The block is a rectangular prism, hence it's volume is given by the multiplication of it's dimensions, as follows:

V = length x width x height.

The dimensions for this block are given as follows:

However, there is a small rectangular block that is removed from the prism, with the dimensions given as follows:

Hence the volume of the rectangular block can be calculated as follows:

V = 16 x 10² - 6 x 5 x 10 = 1300 cm³.

(total volume subtracted by the removed volume from the empty space at the middle).

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Answer:

D.  b + c = 68

    0.08b + 0.15c = 6.00

Step-by-step explanation:

The total cost is $6.00

The total amount of copies is 68

To find the total cost, we multiply the amount of copies by the individual price. So we get

0.08b + 0.15c = 6.00

We add the amount of copies bought to get a total of 68, so we get this equation:

b + 6 = 68

The cubic polynomial with zeros (3,0), (-6,0) and (1,0) is given as follows:

D. x³ + 2x² - 21x + 18.

We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.

The zeros of the polynomial are given as follows:

x = 3, x = -6, x = 1.

Then, applying the Factor Theorem, considering a leading coefficient of 1, the polynomial is given as the product of it's linear factors as follows:

(x - 3)(x + 6)(x - 1)

(x² + 3x - 18)(x - 1)

x³ + 2x² - 21x + 18.

Meaning that option D is correct.

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The remainder of polynomial g(x) divides (x - 3) that is  g(x) / (x - 3) is 0.

What is polynomial?

A polynomial is a mathematical expression made up of variables, constants, and exponents that are combined using addition, subtraction, multiplication, and division operations.

Given: g(x) = 2x^3 + 5x^2 - 28x - 15

(x - 3) is a factor of g(x).

We have to find the remainder of g(x) / (x - 3).

Consider,

                 2x^2 + 11x + 5

         [tex]\sqrt[(x-3)]{2x^3+5x^2 -28x -15}[/tex]

          -    2x^3 -6x^2

____________________________

                      11x^2 - 28x

               -      11x^2 - 33x

____________________________

                               5x - 15

                          -    5x - 15

_______________________________

                                      0

Hence, the remainder of polynomial g(x) divides (x - 3) that is

g(x) / (x - 3) is 0.

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The required solution of the given inequality is given as x > 4, and the answer for the blanks is to Divide both sides by -8 and change the inequality sign.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given inequality,
-8x < 32
Divide both sides by -8
x > 4

The sign of the inequality change because multiplication with the negative value changes the inequality sign and the higher negative value is the least value.

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The significant figure by multiplying 101 with 52 is 5000.

Here given,

101 x 52

Round 101 to 100 and 52 to 50, then multiply together to get 5000.

Significant Figures: 1

Decimals: 0

The significant notation: 5e+3

Therefore the significant notation is 5000.

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The statement "cross-tabulation can only be used for two variables; each variable must have well-defined labels " is false

The cross tabulation is defined as the tool that is used in statistics to categorical data. We can also says that  that present the results of the entire group of respondents

The given statement is "cross-tabulation can only be used for two variables; each variable must have well-defined labels "

The cross tabulation method can be used to represent two or more variables. The cross tabulation table has x axis as one variable and y axis as another variables

The cross tabulation can be used for two or more variables

Therefore, the the given statement is false

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The proposition ststement is: the only prime number that is odd is 2.

The correct answer is an option (d)

In this question we have been given some statements.

we need to identify the proposition statement.

We know that a proposition is a declarative statement. In mathematics proposition gives a clear inference of whether a sentence is true or false. The proposition statement cannot be stated in two ways. The statement must be either correct or incorrect.

a) get me a glass of milkshake.

It is a commanding statement.

b) god bless you!

It is a type of optative statement.

c) what is the time now?

It is a question sentence.

d) the only odd prime number is 2.

It is a false proposition statement.

Therefore, option (d) is a proposition statement.

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The solution to the equation f(x)=g(x) are x=-2 and x=1.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given functions are f(x)=-x+6 and g(x)=-x²-2x+8.

Now, f(x)=g(x)

-x+6=-x²-2x+8

⇒ x²+x-2=0

⇒ x²+2x-x-2=0 (Splitting middle term method)

⇒ x(x+2)-1(x+2)=0

⇒ (x+2)(x-1)=0

⇒ x+2=0 and x-1=0

⇒ x=-2 and x=1

Therefore, the solution for the obtained equation are x=-2 and x=1.

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The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website will be;

⇒ 0.9375

The term probability refers to the likelihood of an event occurring

Given that;

The probability that a visitor is offered a coupon (p) = 50%

Now,

Since, The probability that a visitor is offered a coupon (p) = 50%

Hence, The probability that he gets coupon all 4 days is,

⇒ p (4) = p⁴

⇒ p (4) = (50%)⁴

⇒ p (4) = 0.0625

Hence, By using the complement rule, the probability that he is not offered a coupon at least one day is,

⇒ p' = 1 - 0.0625

⇒ p' = 0.9375

Thus, The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website = 0.9375

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In the given relation, 1 is not a domain.

The domain of a function is the set of all possible inputs for the function. or we can that in an ordered pair, all the values of x are called domain.

All the values that go into a function. The output values are called the range.

The domain of a function is the set of all possible inputs for the function.

If a function f provides a way to successfully produce a single value y using for that purpose a value for x than that chosen x-value is said to belong to the domain of f.

Given that, a function,

{(5, 1), (4, -3), (3, -1)}

We know, a domain is the set of all "x" values.

Therefore, domain of the function are, 5, 4 and 3

But, if we see, 1 is one of the values of y.

Hence, 1 is not a domain.

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According to Euclidean geometry, the geometric system consisting in isosceles triangle has an angle x whose measure is equal to 74°.

In this problem we find a geometric system consisting in a triangle, where two sides are congruent and the measure of an angle equals 74°.

According to Euclidean geometry, a triangle represented by the geometric system, with such features represents an isosceles triangle, that is, a triangle with two congruent sides and two congruent angles between the base side and each of the two congruent sides. Thus:

m ∠ x = 74°

x = 74°

Therefore, the measure of angle x, opposite to the angle whose measure is 74°, must be also equal to 74°.

The measure of angle x associated with the geometric system consisting in an isosceles triangle is equal to 74°.

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Luka will require 24 cups of water to make lemonades as calculated from the data given.

The quantity of sugar which he use is twice the amount of lemon which he us ,

= 2 x 3 = 6

and ,

as we know the amount of water is 4 times as much as lemon juice

Therefore, amount of water

= 4 * 6

= 24

A quantity in a Maths equation is a number or variable plus any algebraic combination of additional quantities. In an equation like x + 6 = 15, four values are represented.

A quantity can be described as the amount of something or how much of it there is. Quantity can also be used to refer to the size of something (its magnitude), whether in terms of numbers, units of measurement, or just relative size.

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The orientation of ABCD is clockwise, as is the orientation of A'B'C'D'. This means the transformation involves a even number of reflections (may be 0).

Does the order of transformations matter in functions?

Order is not important. According to algebra, y=12f (x3). Our four transformations are (1), (3), (2), and (4); all four are in the x direction. When we combine a stretch and a translation in the same direction, the sequence counts.

The orientation of AB is North, and the orientation of A'B' is West, so a rotation of 90° CCW (or equivalent) is involved. We can find the point of intersection of the perpendicular bisectors of AA' and BB' (at (-1, -1)) to determine a suitable center of rotation.

ABCD can be transformed to A'B'C'D' by ...

rotation 90° CCW about the point (-1, -1)

Rotation by 90° can also be accomplished by reflection across a diagonal line. Since we want the orientation to remain unchanged, we need another reflection to put the figure into its final position. A suitable alternate sequence for mapping ABCD to A'B'C'D' is ...

reflection across the line y=x

reflection across the line x=-1

Complete question: A.) Describe a transformation sequence that will transform quadrilateral ABCD into quadrilateral A’B’C’D’.

b.) There is more than one way to transform quadrilateral ABCD into quadrilateral A’B’C’D’. Describe a second sequence of transformations that will accomplish this goal. Explain what tool you used as an aid in identifying a transformation sequence.

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The value of the x would be 9.

Option (A) is correct.

What is a complementary angle?

A complementary angle is an angle that, when added to another angle, forms a right angle (90 degrees). Complementary angles are pairs of angles that add up to 90 degrees.

Angle JKM and angle MKN are complementary angles

so

   (3x + 2) + (6x + 7) = 90

  9x + 9 = 90

  9(x + 1) = 90

     x + 1 = 10

    x = 9

Hence, the value of the x would be 9.

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After solving the equation the value of the x would be 9. Therefore, the correct option is A.

What is a complementary angle?

A complementary angle is a pair of angles that add up to 90 degrees. Complementary angles can be adjacent angles, or angles that share a common vertex and side, or they can be nonadjacent angles that have no common points or sides. Complementary angles are usually referred to by their sum, such as "90-degree angles" or "angles that add up to 90 degrees." Complementary angles can also be called supplementary angles when they add up to 180 degrees.

Angle JKM and angle MKN are complementary angles

so   (3x + 2) + (6x + 7) = 90

 9x + 9 = 90

 9(x + 1) = 90

    x + 1 = 10

   x = 9

Hence, the value of the x would be 9.

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Answer:

80 kg

Step-by-step explanation:

To find the mass of the skater, you can use the formula for centripetal force:

F_centripetal = m * v^2 / r

Where F is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.

Plugging in the values you know, you get:

720 N = m * (15 m/s)^2 / 25 m

Solving for m, you find that the mass of the skater is:

m = 720 N * 25 m / (15 m/s)^2

= 720 N * 25 m / 225 m^2/s^2

= 80 kg

So the mass of the skater is approximately 80 kilograms.

Answer:

2/3 or 0.667

Step-by-step explanation:

5/9 ÷ 5/6

5/9 * 6/5

1/3 * 2/1 (after cancelling off)

= 2/3

Answer:

Solve the equation for [tex]{y}[/tex].

[tex]y=\frac{5x}{2}[/tex]

Choose any value for [tex]{x}[/tex] that is in the domain to plug into the equation.

Choose [tex]{0}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex]{(0,0)}[/tex]

Choose [tex]{1}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex](1,\frac{5}{2})[/tex]

Choose [tex]{2}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex]{(2,5)}[/tex]

These are three possible solutions to the equation.

[tex]{(0,0),}[/tex] [tex](1,\frac{5}{2} )[/tex], [tex]{(2,5)}[/tex]

The given exponential function represents the growth in the function. The percentage of growth (increase) is 1%.

An exponential growth function is a function where the quantity increases slowly and after some time, it increases rapidly.

It is represented by the formula,

y = a(1 + r)ˣ

Here the term 'a' is the initial amount of the quantity, the term 'r' is the rate of increase and the term 'x' is the period.

The given exponential function is y = 10(1.01)ˣ

Here we can write the function as

y = 10(1.01)ˣ

⇒ y = 10(1 + 0.01)ˣ

Since 1.01 > 1, it is an exponential growth function.

So, when comparing with the formula, we get the rate of increase,

r = 0.01

Converting it into fractions, we get 1/100

Then, the percentage rate of increase is 1%.

Therefore, the given exponential function grows with a rate of 1% increase.

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