Explain what the constant of proportionality means in the equation y = 5/2 x

The rational inequality f(x) > 0 has the solution x > - 7

A rational inequality is an inequality in the form of a fraction

Given the function f(x) = (x + 7)/(x² - 4x + 3)

To find the value of x for which the function f(x) > 0, we proceed as follows

Given that f(x) > 0

So, this means that

(x + 7)/(x² - 4x + 3) > 0

This implies that

x + 7 > 0

Subtracting 7 from both sides, we have that

x + 7 - 7 > 0 - 7

x + 0 > - 7

x > - 7

So, f(x) > 0 has the solution x > - 7

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Answer:

D

Step-by-step explanation:

Answer:

D. [tex]8a^{9} -4a^{3} +1[/tex]

Step-by-step explanation:

Given [tex]r(x)=x^{3} -2x+1[/tex] and find [tex]r(2a^{3} )[/tex] :

Solve for [tex]r(2a^{3} )[/tex] :

1. [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1[/tex]

2. [tex]r(2a^{3} )=8a^{9} -2(2a^{3})+1[/tex]

3. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]

Answer:

So, if [tex]r(x)=x^{3} -2x+1[/tex], then [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1=8a^{9} -4a^{3}+1[/tex].

Then the answer is D. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]

Answer:

Step-by-step explanation:

If P = 3x² - x + 2 and Q = x² + 5x - 6, then P+ Q =  3x² - x + 2 + x² + 5x - 6 =

4x^2 +4x - 4

D = 16 + 64 = 80

x12 = [tex]\frac{-4+-\sqrt{80} }{8}[/tex]

When X = 5, Y is approximately equal to 27.34.

What is proportion?

The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.

We are given that "Y varies directly as the cube of X", which can be written as:

Y = kX³

where k is a constant of proportionality. We need to find the value of k to solve for Y when X = 5.

Using the values given in the problem, we can write:

7 = k(4³)

Simplifying this equation, we get:

7 = 64k

Dividing both sides by 64, we get:

k = 7/64

Now that we know the value of k, we can solve for Y when X = 5:

Y = (7/64)(5³) = 27.34 (rounded to two decimal places)

Therefore, when X = 5, Y is approximately equal to 27.34.

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Answer:

40 units

Step-by-step explanation:

a = 8

b = 15

To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]8^{2} +15^{2} =x^{2}[/tex]

64 + 225 = c^2

289 = c^2

c = 17

a + b + c = perimeter

8 + 15 + 17 = 40

Answer:

  40 units

Step-by-step explanation:

You want the perimeter of the triangle shown in the graph.

You can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.

The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:

  c² = a² +b²

  c² = 8² +15² = 64 +225 = 289

  c = √289 = 17

The long side of the triangle is 17 units.

The perimeter of the triangle is the sum of the lengths of its sides:

  P = 8 + 15 + 17 = 40

The perimeter is 40 units.

__

Additional comment

A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...

  {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}

You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.

The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)

The correct table should be

Blue yellow

1 5

4 8

7 13

10 17

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

The slope can be calculated as;

m = y2-y1)/x2-x1

m = 13-5)/7-1

m = 8/6

the equation of a line is expressed as,

y-y1 = m (x-x1)

y-5= 4/3 ( x-1)

= 3y - 15= 4x - 4

3y = 4x + 11.

Therefore when x is 10

3y = 40+11

3y = 51

y = 17

therefore the error is that instead of 16 it should be 17

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Answer: 3,45

Step-by-step explanation:

Answer:

3.45

Step-by-step explanation:

Mean is the average of the data set. To find the mean, we need to add all the numbers and divide by the amount of numbers.

{4.2, 3.5, 4.55, 2.75, 2.25}

4.2 + 3.5 + 4.55 + 2.75 + 2.25 = 17.25

17.25/5 = 3.45

Since magnesium has a larger volume than nickel, it will displace more water from an overflow can.

We need to compare their volumes.

We can use the formula:

Density = mass / volume

To solve for volume, we rearrange the formula:

Volume = mass / density

For nickel:

Volume = 130g / 8.90 g/cm³ = 14.61 cm³

For magnesium:

Volume = 60g / 1.78 g/cm³ = 33.71 cm³

Therefore, Since magnesium has a larger volume than nickel, it will displace more water from an overflow can.

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Answer: 1809.6

Step-by-step explanation: I got to be honest is looked up the cone calculator and I tried 3 three and they all go me 1809.6 (rounded)

Answer: To find two complex numbers that add up to c = -11 + 3i, we can set up the following system of equations:

a + b = -11

ai + bi = 3i

Solving for a and b, we can multiply the first equation by i and subtract it from the second equation multiplied by -1 to eliminate b:

ai + bi = 3i

-ai - bi = 11i

0 + 10bi = 14i

Simplifying, we get b = 1.4. Substituting this into the first equation gives:

a + 1.4 = -11

a = -12.4

So the two complex numbers that add up to c are -12.4 + 1.4i and 1.4i.

To find the value of iº, we need to evaluate i raised to the power of 90 degrees (or pi/2 radians) using Euler's formula:

e^(iθ) = cos(θ) + i sin(θ)

So we have:

iº = i^(90°) = e^(iπ/2) = cos(π/2) + i sin(π/2) = 0 + i(1) = i

Therefore, iº = i.

Step-by-step explanation:

Answer:

Step-by-step explanation:

just add the two numbers up 576x1 1/2= 864

The interpretation of the Chicago white sox data is shown below

The record 53-28 for the Chicago White Sox in the 2021 season means that they won 53 games and lost 28 games in the home games they played during the season.

This record indicates that the White Sox were a strong team at home, winning more games than they lost.

It also suggests that they had a good advantage playing in their home stadium, as winning a high percentage of home games is generally seen as a positive factor in sports.

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The transformation that maps ΔABC to ΔA°B°C° is: a reflection across the x-axis

There are different methods of transformation such as:

Dilation

Reflection

Translation

Rotation

We are given the coordinates as:

A(-3, 4)

B(5, 2)

C(-6, 1)

A°(-3, -4)

B°(5, -2)

C°(-6, -1)

We want to find the transformation that maps ΔABC to ΔA°B°C°. Thus, from transformation rules, this is:

(x, y) → (x, -y) which is a reflection across the x-axis

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The calculated value of the percent of decrease from 8 to 6 is 25%.

To find the percent of decrease from 8 to 6, we need to find the difference between the two numbers and express it as a percentage of the original number (8).

The difference between 8 and 6 is 8 - 6 = 2.

To express this difference as a percentage of 8, we can use the formula:

percent decrease = (difference / original number) x 100%

Substituting the values we get:

percent decrease = (2 / 8) x 100% = 0.25 x 100% = 25%

Therefore, the percent of decrease from 8 to 6 is 25%.

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Therefore, the maximum height the ball will attain is 221.875 feet.

We are given the equation for the height of a projectile as a function of time:

[tex]h(t) = -16t^2 + v0t + h0[/tex]

where v0 is the initial velocity, h0 is the initial height, and t is the time. We are also given that a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 120 feet per second. Therefore, we can plug in the values of v0 and h0 into the equation:

[tex]h(t) = -16t^2 + 120t + 2[/tex]

To find the maximum height, we need to find the vertex of this parabola. The x-coordinate of the vertex is given by:

[tex]t = -b/2a[/tex]

where a = -16 and b = 120. Substituting these values, we get:

[tex]t = -120/(2(-16)) = 3.75 seconds[/tex]

To find the corresponding maximum height, we can plug this value of t back into the equation:

[tex]h(3.75) = -16(3.75)^2 + 120(3.75) + 2 = 221.875 feet[/tex]

Therefore, the maximum height the ball will attain is 221.875 feet.

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We can use the trigonometric identities to find the exact values of the expressions.

First, we can find cos(alpha) and cos(beta) using the Pythagorean identity:

cos(alpha) = sqrt(1 - sin^2(alpha)) = sqrt(1 - (24/25)^2) = 7/25

cos(beta) = -sqrt(1 - sin^2(beta)) = -sqrt(1 - (15/17)^2) = -8/17 (since beta is in quadrant II, where cosine is negative)

Next, we can use the sum formulas for sine and cosine to find sin(alpha + beta) and cos(alpha + beta):

sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta) = (24/25)(-8/17) + (7/25)(15/17) = -117/425

cos(alpha + beta) = cos(alpha)cos(beta) - sin(alpha)sin(beta) = (7/25)(-8/17) - (24/25)(15/17) = -24/85

Finally, we can use the quotient identity for tangent to find tan(alpha + beta):

tan(alpha + beta) = sin(alpha + beta) / cos(alpha + beta) = (-117/425) / (-24/85) = 39/85

Therefore, cos(alpha + beta) sin(alpha + beta) = (-24/85)(-117/425) = 936/7225, and tan(alpha + beta) = 39/85.

The approximate distance from the origin to the point (-2, -7, -4) is 8.3 units.

In three-dimensional space, the distance formula is used to calculate the distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in a three-dimensional coordinate system.

The formula is given by:

d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Here we have

The point (-2, -7, -4)

We need to find the distance between the origin to the point

Let (x₁, y₁, z₁) = (-2, -7, -4) and (x₂, y₂, z₂) = (0, 0, 0)

Using the distance formula,

d = √ [(x₂ - x₁)² + (y₂ - y₁)²+ (z₂ - z₁)² ]

d = √ [(0 - (-2))² + (0 - (-7))²+ (0 - (-4))² ]

d = √ [(2)² + (7)²+ (4)² ]

d = √ [4 + 49 + 16 ]

d = √69 = 8.3066

d = 8.3

Therefore,

The approximate distance from the origin to the point (-2, -7, -4) is 8.3 units.

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With the help of the given graph, we know that Juan has read 10 books by day 12.

In mathematics, a graph is a collection of points, called vertices or nodes, that are connected by lines or arcs, called edges. Graphs are used to model and study a wide range of phenomena in various fields such as computer science, mathematics, physics, social sciences, and more.

Graphs can be represented visually, with nodes represented as dots or circles, and edges represented as lines or arrows connecting the nodes. The placement of the nodes and edges in the graph can convey additional information about the relationships between the objects being modeled. For example, a graph could be used to model a social network, with the nodes representing individuals and the edges representing connections between them.

Graphs can also be used to study various properties and relationships between objects, such as connectivity, distance, and shortest paths. They can be classified based on various characteristics, such as whether they are directed or undirected, weighted or unweighted, and connected or disconnected.

Create a graph by placing a series of bars on graph paper.

So, for path:

The curve line: y = kx + 5 which passes (4, 10)

10 = 4k + 5, k = 5/4

For Juan:

His reading rate same as Patti's.

Curve line: y = ax + b

a = 5/4

He has not read any book before 4th day.

So, when x = 4, y = 0.

0 = 4a + 5, 4 * 5/4 + b

b = -5

y = 5/4 * -5 (x > 4)

When x = 12, y = 5/4 * 12 - 5 = 15 - 5 = 1

Juan has read 10 books by day 12.

Therefore, with the help of the given graph, we know that Juan has read 10 books by day 12.

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Answe: The distance of light bulb can be calculated using equation of parabola. The parabola is a plane curve which is U-shaped.

Step-by-step explanation:

The option that is true about the equations for these two lines iis that they represent the same lines.

The trick to questions like this is to get both equations into the slope-intercept form.  That is done for our first equation (y = 3x + 5).  However, for the second, some rearranging must be done:

5y – 25 = 15x; 5y = 15x + 25; y = 3x + 5

Note: Not only do these equations have the same slope (3), they are totally the same; therefore, they represent the same equation.

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Two lines are described by the equations:

y = 3x + 5 and 5y – 25 = 15x

Which of the following is true about the equations for these two lines?They represent perpendicular lines.

None of the other answers

They represent non-perpendicular, intersecting lines.

They represent the same lines.

They represent parallel lines.

Using the long division method, the division operation (x³ − 8x² + 2) ÷ (x − 3) gives x² - 5x - 15 + (-43)/(x -3). The correct option is the first option

x2−5x+15−43x−3

x squared minus 5 x plus 15 minus fraction numerator 43 over denominator x minus 3 end denominator end fraction

From the question, we are to determine the quotient and the remainder of the given division operation

From the given information,

The given division operation is

(x³ − 8x² + 2) ÷ (x − 3)

The division operation can be carried out as follows:

                  x² - 5x - 15

x - 3 |  x³ − 8x² + 2              

          x³ - 3x²            

                -5x² + 0x

                -5x² + 15x          

                         -15x + 2

                         -15x + 45    

                                  - 43

From above, we can see that the quotient of the operation is x² - 5x - 15 and the remainder is -43

Hence, we can write that

(x³ − 8x² + 2) ÷ (x − 3) = x² - 5x - 15 + (-43)/(x -3)

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The answer is X + 5 = 10

X = 5

Answer:

380 weight

Step-by-step explanation:

please brilliant answer me

Answer:

$357

Step-by-step explanation:

Hours = h

Oil changes = o

Money = m

m = 8.5h + 3o

Now we can substitute:

m = 8.5(36) + 3(17)

m = 306 + 51

m = 357

The matrix that represents the system of equations shown below

4x + 5y = 12

6x-2y = 15 is option B which is Matrix C.

The matrix that represents the system of equations shown below is:

C

[4 5 | 12]

[6 -2 | 15]

Here, we have two equations with two variables x and y. We can represent this system in matrix form by taking the coefficients of x and y and placing them in the left matrix, and the constants on the right-hand side in the right matrix. This gives us:

[4 5 | 12]

[6 -2 | 15]

Therefore, the correct answer is option C

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The requried quantity of drug that remains in the body, in the long run, is 220 mg.

Let's denote the amount of drug in the body just before taking the nth tablet by [tex]D_n[/tex]. We know that [tex]D_0 = 0[/tex](since the patient hasn't taken any tablets yet) and that 5% of the drug is present in the body just before taking a tablet remains in the body. Therefore, we can write:

[tex]D_1 = 110\\D_2 = 0.95 * D_1 + 110 = 203.5\\D_3 = 0.95 * D_2 + 110 = 292.225\\D_4 = 0.95 * D_3 + 110 = 376.81375[/tex]

We can see that the formula for [tex]D_n[/tex] is:

[tex]D_n = 110 * (1 - 0.05)^n + 110 * (1 - (1 - 0.05)^n) / 0.05[/tex]

Simplifying this formula, we get:

[tex]D_n = 220 * (1 - 0.95^n)[/tex]

Now, we want to find the amount of drug that remains in the body in the long run. This means we want to find the limit of [tex]D_n[/tex]  as n goes to infinity. Using the formula above, we can see that:

[tex]lim_ {n- > oo} D_n = lim_ {n- > oo} 220 * (1 - 0.95^n) = 220[/tex]

Therefore, the quantity of drug that remains in the body, in the long run, is 220 mg.

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Answer: a.     c(n) = 15 + 0.75(n - 10)

b.   15 + 0.75(n - 10) = 2.50(n - 10)=

Simplifying and solving for n, we get:

n = 50

c.  n > 50

Step-by-step explanation:

a. The cost c of the credit union account in terms of the number of checks written n can be expressed as:

c(n) = 15 + 0.75(n - 10)

The first term, 15, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.

The cost c of the bank account in terms of the number of checks written n can be expressed as:

c(n) = 2.50(n - 10)

The first term, 0, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.

b. We want to find the number of checks for which the bank account is more expensive than the credit union account. Let x be the number of checks that makes the cost of the two accounts equal. Then we have:

15 + 0.75(n - 10) = 2.50(n - 10)

Simplifying and solving for n, we get:

n = 50

So if the number of checks written in a month is greater than 50, the bank account will be more expensive than the credit union account.

c. The solution to the inequality is:

n > 50

This means that the number of checks written in a month must be greater than 50 for the bank account to be more expensive than the credit union account.

Answer:

Step-by-step explanation:

2.1 so a