y^2 + 4 = x. for x the independent variable and the dependent variable. Determine whether the relation is a function.

A graph of this quadratic equation x² + x - 6 = 0 is shown below.

The solutions to the equation x² + x - 6 = 0 are (-3, 0) and (2, 0).

In Mathematics, the graph of a quadratic function always form a parabolic curve or arc because it is u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive one (1) and the value of "a" is greater than zero (0).

Since the leading coefficient (value of a) in the given quadratic function x² + x - 6 = 0 is positive one (1), we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts (-3, 0) and (2, 0). Also, the value of the quadratic function f(x) would be minimum at -6.25.

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The revised Doubtful Debts Provision should be, $4,555.

Now, Using a net debtors value of $91,100 and a provision rate of 5%, use the calculation to get the adjusted Provision for Doubtful Debts (PDD):

Net Debts x Provision Rate equals Adjusted PDD.

The computation would then be:

= $91,100 x 0.05

= $4,555 is the adjusted PDD.

Because of the additional $550 in bad debt and the revised net debtors value of $91,100, the Provision for Doubtful Debts must be raised by ,

= $4,555 - $3,500

= $1,055

Hence, The revised Doubtful Debts Provision should be $4,555.

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Hello!

4 + (6/10) + (7/100)

= 4 + 0.6 + 0.07

= 4.67

[tex]2\cdot20\text{ m}\cdot n+2\cdot20\text{ m}\cdot 5\text{ m}+2\cdot 5\text{ m}\cdot n=1100\text{ m}^2\\40n\text{ m}+200\text{ m}^2+10n\text{ m}=1100\text{ m}^2\\50n\text{ m}=900\text{ m}^2\\n=18\text{ m}[/tex]

Answer:

22 is answer

Step-by-step explanation:

Answer:

лвоалалалоала.сллслала лвлвлвл

The value of x in the triangle is 9, the volume of the cylinder is 1272.3 yd³ and the volume of the sphere is 268.1 mi³.

To solve for the value of x in the triangle, we use ratio:

[tex]\frac{20}{20 + 16}=\frac{45}{45 + 3x + 9}[/tex]

Simplify and solve for x:

20/36 = 45/(3x + 54 )

Cross mulltiply:

20( 3x + 54 ) = 36 × 45

60x + 1080 = 1620

60x = 1620 - 1080

60x = 540

x = 540/60

x = 9

Therefore, the value of x is 9.

Option A) 9 is the correct answer.

Question 2)

Height of ctlinder h = 5 yd

Diameter = 18 yd

Radius = diameter/2 = 18/2 = 9 yd

Volume of cylinder = π × (radius)² × height

Volume = π × 9² × 5

Volume = 1272.3 yd³

Therefore, the volume of the cylinder is 1272.3 yd³.

Option B) 1272.3 yd³ is the correct ansswer.

Question 3)

Radius of the sphere r = 4 mi

Volume = ?

Volume = 4/3 × π × ( radius )³

Volume = 4/3 × π × ( 4 )³

Volume = 268.1 mi³

Therefore, the volume of the sphere is 268.1 mi³.

Option B) 268.1 mi³ is the correct answer.

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The horizontal variance of sales between 2021 and 2022 is 340

By removing the sales figure of 2021 from that of 2022, we are able to arrive at the above figure.

That is Amount of 2022  – Amount of 2021 = Absolute Change.

Figure for 2022 = 3800

Less

Figure for 2021 = 3,460

Variance                340

Excel formula : = Cell no. of amount of 2022 - Cell no of amount of 2021

Note that a negative amount means decrease and positive amount means increase.

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[tex]X'=\varepsilon\setminus X[/tex] where [tex]\varepsilon[/tex] is the universe. It means that [tex]X'[/tex] is everything except the set [tex]X[/tex], and that in shown in the image C.

Answer:

Option C y = -4x + 9

Step-by-step explanation:

            The line l bisects BC. The line l passes through the midpoint of BC.

B(1, 4) ; C(3 , -2)

  [tex]\sf Midpoint \ of \ BC = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

                           [tex]\sf = \left(\dfrac{1+3}{2},\dfrac{4-2}2{}\right)\\\\\\=\left(\dfrac{4}{2},\dfrac{2}{2}\right)\\\\\\=(2 , 1)[/tex]

Line l passes through (2,1) and A(3 , -3),

    [tex]\sf \boxed{Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                [tex]\sf =\dfrac{-3-1}{3-2}\\\\\\=\dfrac{-4}{1}\\\\=-4[/tex]

m = -4

Equation of line in slope intercept form: y =mx +c

Here, m is the slope and c is the y-intercept.

        y = -4x + c

    As the line l is passing through (2,1), substitute the point (2,1) in the above equation and find c.

        1 = -4*2 + c

        1 = -8 +  c

  1 + 8 = c

        c = 9

Equation of the line l:

       y = -4x + 9    

The probability of either events A or B occurring is determined as 0.89.

The probability of either events occurring is calculated by applying the following formula as shown below;

P (A or B ) = P ( A ) + P ( B )

The probability of A is calculated as follows;

P ( A ) = A / total outcome

P ( A ) = ( 20 ) / ( 20 + 12 + 4 )

P ( A ) = ( 20 ) / ( 36 )

P ( A ) = 5/9

The probability of B is calculated as follows;

P ( B ) = B / total outcome

P ( B ) = 12 / 36

P ( B ) = 1/3

The probability of either A or B is calculated as follows;

P (A or B) = 5/9  +  1/3

P (A or B) = 8/9 = 0.89

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The triangle ∆DEF is similar by the SSS similarly to the triangle ∆JKL

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

To know if the triangles DEF and JKL are similar, we check if their sides corresponds in the same ratio, that is;

JK/DE = KL/EF = JL/DF

JK/DE = 9/12 = 3/4

KL/EF = 18/24 = 3/4

JL/DF = 12/16 = 3/4

Therefore, the triangle ∆DEF is similar by the SSS similarly to the triangle ∆JKL

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Answer:

64π

Step-by-step explanation:

To calculate the surface area (S.A) of the circle with a radius (r) of 4 inches and a height (h) of 6 inches, we need to consider both the curved surface area (lateral surface area) and the area of the circular base.

The curved surface area, also known as the lateral surface area, is calculated using the formula:

L.A = 2πrh

Substituting the given values, we have:

L.A = 2π(4)(6)

L.A = 48π square inches

The area of the circular base is calculated using the formula:

A = πr^2

Substituting the given radius, we have:

A = π(4^2)

A = 16π square inches

To find the total surface area (S.A), we need to sum the lateral surface area (L.A) and the area of the circular base (A):

S.A = L.A + A

S.A = 48π + 16π

S.A = 64π square inches

Therefore, the surface area (S.A) of the given circle is 64π square inches.

Answer:

h(t) = 1.75 cos (π/6) + 2.25

Step-by-step explanation:

the amplitude of a regular cos graph is 1 (it alternates between +1 and -1 on the y-axis). that is, amplitude =  (1 - -1)/2 = 2/2 = 1.

this graph has amplitude (4 - 0.5)/2 = 3.5/2 = 1.75.

the graph repeats for every sixth value on the x-axis (time axis).

in the x-axis direction, a cos graph that becomes 6 times larger is cos (π/6). a cos graph that becomes 6 times smaller is cos (6π).

so for our graph, it is cos (π/6).

what about the y-shift?

the graph has already been enlarged 1.75 times parallel to the y-axis.

it crosses the y-axis at 4. so the y-shift is 4 - 1.75 = 2.25.

so our graph is given by h(t) = 1.75 cos (π/6) + 2.25

Answer: got it right

h(t)=1.75, cos(1/3), + 2.25

Step-by-step explanation:

Only Priya's statement is correct based on the expected value. The expected value of X represents the average or mean number of successful free-throws that the player makes. Therefore, it is correct to say that the probability of making a free-throw is 0.80 on average. Hadley's statement about the next set of 2 free-throws is incorrect because the expected value does not tell us exactly how many free-throws the player will make in a given set, but rather what the average or expected number of successful free-throws will be over a series of trials.

Answer:

5.25 feet tall

Step-by-step explanation:

Doug's height / Doug's shadow = Statue's height / Statue's shadow

x / 3.5 = 12 / 8

Cross-multiplying:

8x = 3.5 * 12

8x = 42

Dividing both sides by 8:

x = 42 / 8

x ≈ 5.25

Answer: 70 + 3 + [tex]\frac{9}{100}[/tex]

Step-by-step explanation:

     Firstly, what is expanded form? Expanded form is a sum of a number's digit place values.

     For example, the expanded form of 814 is 800 + 10 + 4.

To find the expanded form of 73.09, we will do the same as the example provided above. However, we have a decimal. This means we will use a fraction. This 9 is in the hundredth place, so we will use the fraction  [tex]\frac{9}{100}[/tex].

73.09 = 70 + 3 + [tex]\frac{9}{100}[/tex]

Answer:

23

Step-by-step explanation:

An integer is a whole number that can be positive, negative, or zero, without any fractional or decimal parts.

The given expressions for three consecutive integers are:

Give that twice the first number is 20 more than the second:

[tex]2x = (x + 1) + 20[/tex]

Solve this equation for x:

[tex]\begin{aligned}2x &= (x + 1) + 20\\2x&=x+1+20\\2x&=x+21\\2x-x&=x+21-x\\x&=21\end{aligned}[/tex]

The expression for the largest integer is (x + 2).

Therefore, to find the largest number, substitute the found value of x into this expression:

[tex]\begin{aligned}\sf Largest\;number&=(x+2)\\&=21+2\\&=23\end{aligned}[/tex]

Therefore, the largest number is 23.

Answer:

Therefore, if Derrick wants to spend a maximum of $50 and he intends to buy a maximum of 8 tacos, then the general admission option is the cheapest. If he intends to buy 9 or more tacos, then the VIP option is the cheapest.

Step-by-step explanation:

To determine how many tacos Derrick must buy for each pricing option to be the cheapest, we can set up separate equations for each pricing option based on the total cost. Let's assume Derrick wants to spend a maximum of $50 on admission and tacos.

For the general admission option:

Total cost = 15 + 4x, where x is the number of tacos

We want to find the value of x that makes the total cost the same or less than $50:

15 + 4x ≤ 50

4x ≤ 35

x ≤ 8.75

For the VIP option:

Total cost = 36 + 1.5x, where x is the number of tacos

We want to find the value of x that makes the total cost the same or less than $50:

36 + 1.5x ≤ 50

1.5x ≤ 14

x ≤ 9.33

The elements in the range that correspond to the elements 0 and 3 are y = 2 and y = 4 and the equations are solved.

Given data ,

To find the elements in the range that correspond to the elements 0 and 3 of the domain, we need to solve the equation 3y - 2x = 6 for the corresponding values of y when x = 0 and x = 3.

When x = 0:

Substituting x = 0 into the equation 3y - 2x = 6, we get:

3y - 2(0) = 6

3y = 6

y = 2

So, when x = 0, the corresponding value of y is 2.

When x = 3:

Substituting x = 3 into the equation 3y - 2x = 6, we get:

3y - 2(3) = 6

3y - 6 = 6

3y = 12

y = 4

So, when x = 3, the corresponding value of y is 4.

Hence , the elements in the range that correspond to the elements 0 and 3 of the domain are y = 2 and y = 4, respectively.

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The numeric values for this problem are given as follows:

The function in this problem is a piecewise function, meaning that it has different definitions based on the input x of the function.

For x between -2 and 2, the function is defined as follows:

g(x) = -(x - 1)² + 2.

Hence the numeric value at x = -1 is given as follows:

g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2.

For x at x = 2 and greater, the function is given as follows:

g(x) = 0.5x - 1.

Hence the numeric values at x = 2 and x = 3 are given as follows:

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The estimate for the number of females in marketing is given as follows:

225 females.

A bar graph shows the output considering a given input. In the context of this problem, the inputs are the prices, and for each input there are two outputs, which are the number of male employees and the number of females employees in each department.

For this problem, the second input is the number of male employees and the number of females employees in the marketing departments.

Hence the number of employees is given as follows:

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Each friend drank a total of 3 beverages during their visit to the beach.

To find the number of beverages each friend drank, let's assume the number of drinks they brought and consumed this year is represented by 'x'.

From the given information, we can set up the following equations:

Last year:

5x + 2 = Total number of drinks (equation 1)

This year:

3x + 8 = Total number of drinks (equation 2)

Since the total number of drinks should be the same in both years, we can set equation 1 equal to equation 2:

5x + 2 = 3x + 8

Now, let's solve this equation to find the value of 'x':

5x - 3x = 8 - 2

2x = 6

x = 3

So, each friend drank 3 canned drinks both last year and this year.

Therefore, each friend drank 3 beverages.

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Answer:

Step-by-step explanation:

Answer: Therefore, the correct factorization by grouping is (a - 2)(6a - 5).

Step-by-step explanation:

To factor 6a² - 12a - 5a + 10 by grouping, we can group the terms in pairs:

6a² - 12a - 5a + 10

Taking common factors from the first two terms and the last two terms separately:

6a(a - 2) - 5(a - 2)

Now, we can see that (a - 2) is common in both terms, so we can factor it out:

(a - 2)(6a - 5)

Hello!

6a² - 12a - 5a + 10

= 6a² - 17a + 10

= 6a² - 5a - 12a + 10

= (6a² - 5a) + (-12a + 10)

= a(6a - 5) - 2(6a - 5)

= (6a - 5)(a - 2)

Answer:

(a)2030

Step-by-step explanation:

I'm assuming the 100 at the end of the question is a typo.
In 2040, the son's age can be written as [tex]\frac{x}{3}[/tex], where x equals the age of his father. In 2050, the son's age can be written as [tex]\frac{x-10}{2}[/tex] (as ten years is added between 2040 and 2050). When equated to each other--> [tex]\frac{x-10}{2}[/tex] = [tex]\frac{x}{3}[/tex], we can first simplify by multiplying both sides to reach the least common denomination 6, giving us 3(x-10)=2x --->3x-30=2x--->x=30 is the dad's age. The son's age in 2040, 30/3, is equal to 10 years, meaning he was born in the year 2030 (a).

The image of the figure  after dilation is attached and the new dimensions are

A'B' = C'D' = 6 units

A'D' = B'C' = 2 units

To find the new dimensions after dilation, we need to know the dimension of the preimage.

Examining the attached figure, assuming each do represent 1 unit we have that

AB = CD = 18 units

AD = BC  6 units

Using the scale factor of 1/3 results to

A'B' = C'D' = 18 * 1/3 = 6 units

A'D' = B'C' =  6 * 1/3 = 2 units

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The simplified form of (5m² - 3)² is 25m⁴ - 30m² + 9.

Given is an expression (5m² - 3)², we need to simplify the expression,

To multiply the expression (5m² - 3)², we can use the formula for squaring a binomial:

(a - b)² = a² - 2ab + b²

In this case, a = 5m² and b = 3.

Substituting these values into the formula, we get:

(5m² - 3)² = (5m²)² - 2(5m²)(3) + (3)²

= 25m⁴ - 30m² + 9

Therefore, the simplified form of (5m² - 3)² is 25m⁴ - 30m² + 9.

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The equation m(x) = (x-3)(x+5) is written in intercept form.

The equation m(x) = (x-3)(x+5) represents a quadratic function.

Analysing the equation.

Standard form of a quadratic equation is written as:

f(x) = ax^2 + bx + c, where a, b, and c are constants.

Intercept form of a quadratic equation is written as:

f(x) = a(x-p)(x-q), where a, p, and q are constants representing the x-intercepts.

Vertex form of a quadratic equation is written as:

f(x) = a(x-h)^2 + k, where a, h, and k are constants representing the vertex coordinates.

The factors (x-3) and (x+5) represent the x-intercepts of the quadratic function.

Therefore, the equation m(x) = (x-3)(x+5) is written in intercept form.

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De acuerdo con la información, el tipo de estudio de caso descrito es estudios de caso mixtos debido a que son aquellos que combinan características cualitativas y cuantitativas.

Los estudios de caso mixtos se caracterizan por combinar características cualitativas y cuantitativas en la recopilación y análisis de datos. Estos estudios buscan obtener una comprensión más completa y profunda del fenómeno estudiado.

ENGLISH VERSION

According to the information, the type of case study described is mixed case studies because they are those that combine qualitative and quantitative characteristics.

The mixed case studies are characterized by combining qualitative and quantitative characteristics in the compilation and analysis of data. These studies seek to obtain a more complete and profound understanding of the phenomenon studied.

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