the value of r is 4/5 times the value of t where r is greater than 0

The solution to the system of equations is: D. (-4, -7).

To solve the system of equations, y = (3/2)x - 1 and y = 3x + 5, you can set the two equations equal to each other and solve for one of the variables. For example, setting the two equations equal to each other:

(3/2)x - 1 = 3x + 5

Then you can solve for x by isolating it on one side of the equation:

(3/2)x - 3x = 5 + 1

-5x/2 = 6

x = -4

Now that you know the value of x, you can substitute it back into one of the equations to find the value of y:

y = (3/2)(-4) - 1 = -6 - 1 = -7

So the solution to the system of equations is x = -4, y = -7.

The solution is: (-4, -7).

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Answer:

Just giving my first answer.I don't know the answer.If I knew I'd tell you

The solution to the given recurrence relation is (c): ak = (3^k + 1) + 2^k + 1

The solution of the given recurrence relation can be found by substitution. We can substitute the given formula for ak into the equation for a_(k+1) and see if the two are equal. If they are equal, then we have the solution.

Starting with the equation for ak:

a_k = 2a_(k-1) + 3^k

Substituting the formula for ak-1:

a_k = 2(2a_(k-2) + 3^{k-1}) + 3^k

Expanding the right side:

a_k = 4 a_(k-2) + 2 * 3^{k-1} + 3^k

Continuing this process, we can see that the solution is:

a_k = 2^(k) a₀ + (2^{k-1} + 2^{k-2} + ... + 2^1) * 3^{k-1} + 3^k

Since the series 2^k-1 + 2^{k-1} + ... + 2^1 = 2^k - 1, we have:

a_k = 2^(k) a₀ + (2^k - 1) * 3^{k-1} + 3^k

Substituting the initial value a₀ = 5:

a_k = 2^(k) * 5 + (2^k - 1) * 3^{k-1} + 3^k

Simplifying:

a_k = 2^{k} (5 + 3^{k -1}) - 3^{k-1}(1 + 3)

a_k =  2^{k} (5 + 3^{k -1}) - 4* 3^{k-1}

a_k = 5* 2^{k} + 3^{k -1}( 2^{k}  - 4)

So, the solution to the given recurrence relation is (c):

ak = (3^k + 1) + 2^k + 1

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The linear inequality in two variables is  3x + 6y ≤ 9 . Option B

Linear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another

Inequalities are math expressions or statements that use the inequalities "less than or equal to", "greater than or equal to", "less than", "greater than", and "not equal to".

Linear expressions are math statements or expressions whose expressions of a degree 1 (Highest exponent).

Variables are mathematical symbol or term that represents the unknown values.

In the problem, the question asks for a linear inequality in two variables. As you can see, all of the choices are linear expressions. The only option that uses one of the inequality symbols and has two unknown variables is the third option. So, it's the option B.

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After solving, the height of the cylinder is 6 meters.

The surface area of a cylinder is 24π m².

The distance around the base of the cylinder is 3π meter.

The diameter of a base of the cylinder is 4 meter.

Now the radius of the cylinder = diameter/2

The radius of the cylinder = 4/2

The radius of the cylinder = 2 meter.

The formula of surface area of cylinder:

S = 2πrh

From the question:

2πrh = 24π

Now putting the value of r

2π × 2 × h = 24π

4πh = 24π

Divide by 4π on both side, we get

h = 6

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The complete question is:

The surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meter and the diameter of a base of the cylinder is 4 meter. What is the height of the cylinder? Enter your answer, in a simplified fraction, in the box.

Volume of solid is 343 cubic yards.

Volume is defined as the amount of space occupied by an object within the boundaries in the three dimensional space.

A base of a solid whose height is 7 yards is shown.

Let us consider the solid as cube.

Volume of cube = [tex]a^{3}[/tex] cubic units.

Here side, a =7 yards.

Volume ,V= [tex]7^{3}[/tex] = 343 cubic yards.

Hence, Volume of solid is 343 cubic yards.

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Alright, so they want you to find the probability of landing on 4 or 2.

There are 8 numbers total so that will be our denominator x/8

There are two outcomes we are finding the probability, that gives us 2/8

We must simplify the fraction into its lowest form.

2/8=1/4

Your answer would be 1/4

Step-by-step explanation:

0.3333333333.... = 1/3

0.2222222222... = 1/3 / 3 × 2 = 2/9

so, we now know all the involved fractions.

(1/3 - 1)² - sqrt(1 - 3/2/2) + 2/9

(-2/3)² - sqrt (1 - 3/4) + 2/9

4/9 - sqrt(1/4) + 2/9

6/9 - 1/2

2/3 - 1/2

to calculate that we need to bring both fractions to the same denominator (6).

2/2 × 2/3 - 3/3 × 1/2 = 4/6 - 3/6 = 1/6

so, the complete result is 1/6.

Unconstrained population growth equation solved by separation of variables. P = Ce^(Kt). Corrected function found using initial and 5 hour population data. After 10 hours, population is 16,333,333.33.

What is integral ?

An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration.

(a) Solution by separation of variables:

P' = KP

dp/dt = KP => dP/P = K dt

∫(dP/P) = ∫K dt => ln|P| = Kt + C, where C is the integration constant.

P = Ce^(Kt)

(b) Initial population is 3M and after 5 hours the population is 7M.

Using the formula from (a), we have:

Ce^(K5) = 7M => Ce^(K5) = 7*10^6

3M = Ce^(K0) => 310^6 = C

Therefore, the exact function describing the population growth is:

P = 3*10^6 * e^(Kt)

(c) After 10 hours, the population will be:

P = 310^6 * e^(K10)

(d) The population after 10 hours should be exactly 49/3.

Checking with the formula from (c), we have:

P = 310^6 * e^(K10) = 49/3 * 10^6 = 49,000,000 / 3 = 16,333,333.33

Unconstrained population growth equation solved by separation of variables. P = Ce^(Kt). Corrected function found using initial and 5 hour population data. After 10 hours, population is 16,333,333.33.

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Answer:

240000000

Step-by-step explanation:

2.4x100000000=240000000

(π/180) x (180) x (7) = (π) x (7) = 21π cm.

The length of the semicircular arc of a circle can be found using the formula:

arc length = (π/180) x (arc degree measure) x (circle's diameter)

If the diameter of the circle is 7cm, then the length of the semicircular arc would be:

(π/180) x (180) x (7) = (π) x (7) = 21π cm.

Answer:11cm

Step-by-step explanation:

Diameter of the circle= 7cm

so, radius of the circle= 7/2= 3.5 cm

for getting length of the semicircular arc= sircumference of circle / 2

circumference of the circle = 2pi r

lenght of the semicircular arc= 2pi r/2

                                             =pi r

                                              = {22/7}*

                                              =11cm

The equation of the line perpendicular to the line 2x + 5y + 5 = 0 is 5x - 2y + 1 = 0.

As per the given data the given equation is 2x + 5y + 5 = 0

Here we have to determine the equation of the line perpendicular to the line 2x + 5y + 5 = 0

Firstly write the equation in y = mx + c format.

2x + 5y + 5 = 0

5y = -2x - 5

y = [tex]$\frac{-2}{5}[/tex]x - 1

[tex]m_{1}=\frac{-2}{5}[/tex]

Condition for two perpendicular lines.

[tex]m_{1} \times m_{2}[/tex] = -1

[tex]$\frac{-2}{5} m_{2} = -1[/tex]

[tex]$m_{2} = \frac{5}{2}[/tex]

Now substitute the slope value in the equation y = mx + c

We get:

y = [tex]$(\frac{5}{2} )[/tex]x + c

2y = 5x + 2c

2y - 5x = 2c

Since the line passes through (-1, -2)

Hence:

2(-2) - 5(-1) = 2c

-4 + 5 = 2c

2c = 1

c = [tex]$\frac{1}{2}[/tex]

Now substitute the value of c in 2y - 5x = 2c

2y - 5x = 2[tex]$(\frac{1}{2} )[/tex]

2y - 5x = 1

(0r)

5x - 2y + 1 = 0

Therefore the equation is 5x - 2y + 1 = 0.

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The time that the ferries will leave together next, given the time they leave the jetty would be 12 : 15 pm

The ferries leave at intervals of 8 minutes, 12minutes, and 15 minutes. To find  the time when they will all leave at the same time again, you need to find the lowest common multiple of 8, 12 and 15 as this would show the next time the ferries would be lined up together again.

The lowest common multiple of 8, 12 and 15 is 120 which in minutes is 2 hours.

The next time both ferries would leave together is:

= 10 : 15 + 2 hours

= 12 : 15 pm

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z=122/17

Step-by-step explanation:

1) Distribuez: 278=34z+34

2) Soustrayez 34 des deux côtés: 244=34z

3) diviser les deux par 34 puis simplifier: le résultat est z= 122/17

Answer:

reason 1: Given

reason 2: Property of Cross Multiplication

reason 3: Vertical Angles are Congruent.

reason 4: SAS

Answer:

(x-4)2=16

Step-by-step explanation:

Answer:

0.6 divided by 78 is 0.00769230769

or if you meant

78 divided by 0.6 it is 360

Step-by-step explanation:

The area of R is ln(4) - ln(√2) and the value of k is √2.

a) To find the area of the region R, we need to find its definite integral with respect to x. Using substitution, we can write the integral as follows:

Let u = [tex]x^{2}[/tex] + 2, du/dx = 2x, dx = du/2x

Area of R = ∫[0,√6] x/([tex]x^{2}[/tex] + 2) dx = ∫[2,8] (1/2) du/u = (1/2) ln(u) evaluated from 2 to 8 = (1/2) ln(8) - (1/2) ln(2) = ln(4) - ln(√2)

b) The line x = k divides the region R into two regions of equal area if the definite integral of R with respect to x from 0 to k is equal to the definite integral of R with respect to x from k to √6.

Letting k = x in the definite integral, we have:

∫[0,k] x/( [tex]x^{2}[/tex]  + 2) dx = ∫[k,√6] x/( [tex]x^{2}[/tex]  + 2) dx

(1/2) ln([tex]k^{2}[/tex] + 2) - (1/2) ln(2) = (1/2) ln(6 - [tex]k^{2}[/tex] ) - (1/2) ln(2)

Solving for k, we get:

ln( [tex]k^{2}[/tex]  + 2) = ln(6 - [tex]k^{2}[/tex] )

[tex]k^{2}[/tex] + 2 = 6 - [tex]k^{2}[/tex]

2 [tex]k^{2}[/tex]  = 4

k = ±√2

Since k must be in the first quadrant, k = √2.

So, the line x = √2 divides the region R into two regions of equal area.

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Answer:  the answer is $442.80

Answer:

442.80

Step-by-step explanation:

You would first multiply 15 by 36 to get a product of 540. Then you would subtract $540 by $37.80 and $59.40 to get a difference of 442.80

15x36 =540
540 - 37.80 - 59.40 = $442.80

The number of blocks needed to make the 9th figure in the pattern is 24.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Dionne builds a pattern that is represented by the equation b = 2f + 6, where f is the figure number of the pattern and b is the number of blocks in each figure.

For the first figure, number of blocks = (2 × 1) + 6 = 8

For the 2nd figure, number of blocks = (2 × 2) + 6 = 10

This will go on.

For the 9th figure, number of blocks =  (2 × 9) + 6 = 24

Hence there will be 24 blocks in the 9th figure.

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Answer:

x = 2

Step-by-step explanation:

3x + 5 = 11

Let x = 1. Let's substitute the value of x into the equation to check if it's correct.

3(1) + 5 = 3 + 5

            = 8

8 ≠ 11

x is not 1.

---

Let x = 3. Let's substitute the value of x into the equation to check if it's correct.

3(3) + 5 = 9 + 5

            = 14

14 ≠ 11

x is not 3.

---

Let x = 2. Let's substitute the value of x into the equation to check if it's correct.

3(2) + 5 = 6 + 5

            = 11

11 = 11 so you can see that the value of 2 for x satisfies the equation!

x = 2.

---

Answer:

The width of the base is 120ft. The length of the base is 60ft less than three times the width [1][2], so the length of the base is 180ft. Therefore, the dimensions of the base are 120ft x 180ft.

Based on the information we can infer that 25 km is equivalent to 7.5 cm on the map.

To find the relationship between centimeters and kilometers on the map we must take into account the following information:

3cm = 10km

According to the above, we must make a rule of three to find the equivalence of kilometers. Below is the procedure:

According to the above, 7.5 centimeters would represent the 25 kilometers distance on the map.

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The correct grouping of the trinomial "-10x² + 13x + 3" is option 4, (-10x² + 0x) + (13x + 3).

To find the correct grouping, we need to factor out the greatest common factor from the first two terms, -10x² + 13x.

The greatest common factor of -10x² and 13x is -x². So, we can factor out -x² and get:

-x² * (10 - 13/x) + 3 = (-x² * 10) + (13/x - x²) + 3 = (-10x² + 7x) + (6x + 3)

Therefore, choice 3 is the correct grouping of the trinomial -10x² + 13x + 3.

A trinomial is a mathematical expression consisting of three terms. It is a polynomial of degree three and has the general form ax³ + bx² + cx + d, where a, b, c, and d are constants and x is a variable.

Complete Question:

'which of the answer choices is a correct grouping of the following trinomial? −10x² 13x 3

1. (-10x² + 5x) - (6x + 3)

2.(-10x² + 2x) +(15x + 3)

3.(-10x² + 7x) +(20x + 3)

4.(-10x² + 0x) +(13x + 3)

5.(-10x² + 0x) - (x + 3)

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The maximum number of major ideas that can be included in a specific purpose statement depends on several factors, but it is generally recommended that the statement include one to three major ideas. This helps the speaker to focus their ideas and organize their content in a way that effectively communicates their message to the audience

A specific purpose statement is a statement that defines the main objective or goal of a speech or presentation. It serves as a guide for the speaker, helping them to focus their ideas and organize their content in a way that effectively communicates their message to the audience.

The number of major ideas that can be included in a specific purpose statement depends on several factors, including the length of the speech or presentation, the complexity of the topic, and the speaker's ability to effectively communicate their message.

In general, it is recommended that a specific purpose statement include only one to three major ideas. This allows the speaker to focus their attention on a limited number of key points and ensures that the audience is not overwhelmed with too much information. Additionally, having a limited number of major ideas makes it easier for the speaker to organize their content and for the audience to understand and retain the information.

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A specific purpose statement should include one or two major ideas that are focused and directly relevant to the topic at hand.

Including too many ideas can make the statement confusing and difficult for the audience to understand, so it's important to be selective about which ideas to include.

The goal is to create a specific purpose statement that is clear, concise, and easy for the audience to understand, while effectively conveying the key ideas of the communication.

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The arc length covered by the central angle equal to 72° is 12.56°

Arc length is the distance between two points along a section of a curve.

Given that, a circle with radius 10 units and a central angle equals 72°, we need to find the arc length covered by the central angle = 72°

We know that,

Arc length = 2π × radius × (θ / 360°), where θ is the central angle

Arc length = 2 × 3.14 × 10 × 72°/360°

= 12.56°

Hence, the arc length covered by the central angle equal 72° is 12.56°

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Max's next step after swinging arcs on either side of the segment is to place the compass on the other endpoint and swing another arc that intersects the previous arcs.

After swinging arcs on either side of the segment, Max's next step is to place the compass on the other endpoint of the segment.

He needs to make sure the compass width remains the same as before.

Then, he swings another arc that intersects the previous arcs.

The point where the new arc intersects the segment is the midpoint of the segment.

By connecting this point with the endpoints of the segment, Max will have successfully bisected the segment.

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The required triangles that are similar by angle-angle similarity are,

(1)    ΔCDE ≅ ΔGFE    (2)  ΔLQP ≅ ΔLMN     (3)  ΔSTE ≅ ΔCWH

(4) Triangles are not similar.   (5)  Triangles are not similar.

(6) ΔPXQ ≅ ΔZXY

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,

(1)

Consider ΔCDE and ΔGFE

∠C = ∠G   [alternate interior angle of parallel lines]

∠CED = ∠GEF   [opposite angles]

There, for ΔCDE ≅ ΔGFE bu AA postulate.

Similarly,

(2)  ΔLQP ≅ ΔLMN

(3)  ΔSTE ≅ ΔCWH

(4) Triangles are not similar.

(5)  Triangles are not similar.

(6) ΔPXQ ≅ ΔZXY

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The expression after multiplying the factors in the form is -573.21.

The provided expression is (-√36)(-√22)(-√415).

We have to multiply the factor and express in the radical form.

Let us solve this step by step and one by one,

(-√36) = -6

Now, for -√22,

-√22 = -4.69

Now, for -√415,

-√415 = -20.37

Now, we have to simply multiply these three values and that will be the radical form,

So,

(-√36)(-√22)(-√415) = -6 x -4.69 x -20.37

(-√36)(-√22)(-√415) = -573.21

So, the expression after simplification is -573.21.

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