the rational roots theorem - state the possible rational zeros for each function (please show work)

f(x)=3x^2+2x-1

Answer:

\(a_n=4n-11\)

Step-by-step explanation:

The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:

\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)

Answer:

10 times as much as 60 equals 600

Step-by-step explanation:

10x60=600

Answer:

10 times as much as 60 is 600

Step-by-step explanation:

60×10=600

Step-by-step explanation:

What is the question exactly?

Answer: cinq minutes

Step-by-step explanation: 1h est egalle à 60minutes. Alors I'll a couru 12km Dan's 60minute. La duration pour 1km sera 60÷12=5 minutes

Answer:

0.666667*​x+​4-​3/​5-​2

HOPE I HELP!!!! :)

Answer:

y=-4/3x-60

Step-by-step explanation:

Answer:

y=-4/3x-60

Step-by-step explanation:

The line intercepts -60 and the slope by using a slope triangle, for y it was from -20 to 20 so 40 units difference, and for x it was -30 to -60 so 30 unit difference. 40/-30 simplified = -4/3

Answer:

6 hours

Step-by-step explanation:

Let both of them plan for  t hours to plant 111 trees n t hours

Melissa  can plants 10 trees in 1 hour

in t hours she can plant 10 t trees

Jane plants 17 tree in 2 hours

in one hour Jane can plant 17/2 trees

in t hours she can plant (17/2)t  trees.

Total trees planted by both of them in t hours in terms of t will be

10t + (17/2)t

= (10t*2 + 17t)/2

= (20t + 17t)/2

= 37t/2

but it is given that they planted 111 trees together

so 37t/2 should be equal to 111

37t/2 = 111

=> 37t = 111*2 = 222

=> t = 222/37 = 6.

Thus, it takes 6 hours for both of them to plant 111 trees together.

(2x - 7) + ( x + 4) = 90°

2x + x - 7 + 4 = 90°

3x - 3 = 90°

3x = 90 + 3

3x = 93

x = 93/3

x = 31°

▪2x - 7

= (2 . 31) - 7

= 62 - 7

= 55°

▪x + 4

= 31 + 4

= 35°

Sanyo  option (b) would be chosen using the elimination-by-aspects decision rule.

In the elimination-by-aspects decision rule, you compare the options based on specific aspects and eliminate those that do not meet a certain cutoff point for each aspect.

Here's how the comparison unfolds based on the given information:

1. Performance: The cutoff point is ranked 1. Sanyo and Sony meet the cutoff, but Pioneer does not.

  Eliminated: Pioneer

2. Price: The cutoff point is ranked 4. Sanyo and Pioneer meet the cutoff, but Sony does not.

  Eliminated: Sony

3. Quality: The cutoff point is ranked 4. All three options (Sanyo, Sony, Pioneer) meet the cutoff.

4. Style: The cutoff point is ranked 3. Sanyo meets the cutoff, but Sony and Pioneer do not.

  Eliminated: Sony and Pioneer

Based on the elimination process, the remaining option is Sanyo. Therefore, (b) Sanyo would be chosen using the elimination-by-aspects decision rule.

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Answer:

true that you pretty but, dont date me bc i have a gf

Step-by-step explanation:

Answer:

true( I'm sowwie if this is wrong):(

We conclude that the model is significant that is test hypothesis are H₀: β₁ = β₂ = β₃ =0 and H₁ : at least one β₁ ≠ 0.

Given that,

A test of interactions should be conducted. the statistix printout of these test's outcomes.

We know that,

Take

Full model is  E(y) = β₀ + β₁x₁ + β₂x₁₂ + β₃x₂+ β₄x₁ x₂ + β₅x₁₂ x₂

Reduced model is F(y) = β₀ + β₁x₁ + β₂x₂ + β₃x₁ x₂

Test hypothesis are

H₀: β₁ = β₂ = β₃ =0

H₁ : at least one β₁ ≠ 0

Test statistic F = 83.05

p-value = 0.000

Since p-value < alpha hence reject H₀

Therefore, we conclude that the model is significant that is test hypothesis are H₀: β₁ = β₂ = β₃ =0 and H₁ : at least one β₁ ≠ 0.

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Complete Question

Interactions Test: run an interactions test. Insert the STATISTIX Printout of the results of this test (4 points). Х Car Data Set.xlsx Linear ...

Answer:

20

Step-by-step explanation:

because you have a 50 % 50% shot of getting either.

Answer:

20

Step-by-step explanation:

Answer:

58 miles/hour

Step-by-step explanation:

Given that the family Christmas gathering has been scheduled at 2:00 p.m.,

and Joshua left the house at 8:00 a.m.

So, the total time available in order to arrive on time to attend the Christmas gathering, t=6 hours

The total distance, Joshua has to travel, d= 348 miles.

As average speed= (total distance)/(total time)

So, the average speed of driving = 348/6=58 miles/hour

Hence, Joshua must drive at an average speed of 58 miles/hour in order to arrive on time.

The condition for the equation (∂U/∂V)T = (∂U/∂P)T = (∂H/∂V)T = 0 to be true is that the system described must be in a state of mechanical, thermal, and chemical equilibrium.

Let's break down the conditions for each partial derivative:

1. (∂U/∂V)T = 0: This condition implies that the internal energy of the system does not change with respect to volume at constant temperature.

It indicates mechanical equilibrium, where the system is in balance and no work is being done on or by the system due to volume changes.

2. (∂U/∂P)T = 0: This condition suggests that the internal energy of the system does not change with respect to pressure at constant temperature.

It indicates thermal equilibrium, where the system is in balance and there is no transfer of energy as heat due to pressure changes.

3. (∂H/∂V)T = 0: This condition implies that the enthalpy of the system does not change with respect to volume at constant temperature.

It also indicates mechanical equilibrium, where the system is in balance and there is no work being done on or by the system due to volume changes.

In summary, the condition (∂U/∂V)T = (∂U/∂P)T = (∂H/∂V)T = 0 is true when the system is in a state of mechanical, thermal, and chemical equilibrium, where there are no changes in internal energy, pressure, and enthalpy with respect to volume at constant temperature.

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The correct inequality is y > 2x + 3, as it accurately represents the region above the line in the graph.The linear inequality represented by the graph is y > 2x + 3.

In the graph, the boundary line is a dashed line with a positive slope of 2, passing through the y-intercept at (0, 3).

This means that the line itself is not included in the solution set. The region above the line represents all the possible solutions to the inequality.

To understand this, consider a point in the shaded region above the line. For any given x-coordinate, the corresponding y-coordinate is greater than the value obtained by substituting that x into the equation 2x + 3.

This means that all the points in the shaded region have y-values greater than 2x + 3, satisfying the inequality y > 2x + 3.

To understand why the other options are not correct, let's analyze them:

y < 2x + 3: This option would represent the region below the line, which contradicts the graph.

y > -2x + 3: This option would have a negative slope, but the graph shows a positive slope. So, it does not match the given graph.

y < -2x + 3: This option would represent the region below the line with a negative slope, which does not match the graph either.

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Answer:

He doesn't have enough plant to feed strawberry 2 more times and tomato 1 more time

Step-by-step explanation:

On sunday , sheldon bought 4 1/2 kg of plant food. He uses 1 2/3 kg on his strawberry plants and used 1/4 kg for his tomato plants. b. Sheldon wants to feed his strawberry plants 2 more times and his tomato plants one more time. He will use the same amounts of plant food as before. How much plant food will be need? Does he have enough left to do so.

Total food bought = 4 1/2 kg

Strawberry feed = 1 2/3 kg

Tomato feed = 1/4 kg

Total food used on Sunday = Strawberry + tomato

= 1 2/3 + 1/4

= 5/3 + 1/4

= (20+3)/12

= 23/12 kg

Total food remaining after Sunday = Total food bought - used food

= 4 1/2kg - 23/12kg

= 9/2 - 23/12

= (54-23)/12

= 31/12 kg

= 2 7/12 kg

Sheldon wants to feed his strawberry plants 2 more times and his tomato plants one more time.

Strawberry = 2 × 1 2/3kg

= 2 × 5/3

= 10/3 kg

Tomato = 1 × 1/4kg

= 1/4 kg

Total food needed to feed strawberry two more times and tomato 1 more time

= 10/3 kg + 1/4 kg

= (40+3)/12

= 43/12 kg

= 3 7/12 kg

He will need 3 7/12 kg of food

He has 2 7/12 kg of food left

Therefore, he doesn't have enough plant to feed strawberry 2 more times and tomato 1 more time

a) The vertex of the problem is given as follows: (220, -583), meaning that the minimum depth reached by the vertex is of 583 after 220 hours.

b) The submarine was submerged for 440.1 hours.

The quadratic function in this problem is defined as follows:

d(t) = 0.012t² - 5.29t.

Which gives the depth of the submarine after t hours.

The coefficients of the equation are given as follows:

a = 0.012, b = -5.29.

Then the t-coordinate of the vertex is given as follows:

t = -b/2a = 5.29/(2(0.012)) = 220.

The minimum depth is then of:

d(220) = 0.012(220)² - 5.29(220) = -583.

This is a concave up parabola, which is the reason why the vertex is a minimum.

The roots of the function are given as follows:

0.012t² - 5.29t = 0

t(0.012t - 5.29) = 0.

Hence:

Meaning that the submarine was submerged for 440.1 hours.

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Answer:

x = 117°

Step-by-step explanation:

The right vertex of the triangle and 101° are a corresponding pair, thus

vertex = 180° - 101° = 79° The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle , thus

x = 38° + 79° = 117°

Answer:

the answer would be 7

Step-by-step explanation:

because you take the 24 stamps and divide them by 3 rows.

Answer:

Each row has 8 stamps.

Step-by-step explanation:

Given that,

→ 24 stamps into 3 equal rows.

Now we have to,

→ find the stamps in each row.

Forming the equation,

→ x = 24 ÷ 3

Then required value of x will be,

→ x = 24 ÷ 3

→ [ x = 8 stamps ]

Hence, each row has 8 stamps.

Answer:

one kilometer is 1000 meters so

3,12×1000=3120

The measure of angle A in triangle ABC is approximately 95.59 degrees. By using the dot product formula and the arccosine function, we can calculate the measure of angle A in triangle ABC.

By calculating the vectors AB and AC, finding their dot product, and determining their magnitudes, we can apply the cosine formula to find the cosine of angle A. Taking the inverse cosine (arccos) of the resulting value gives us the measure of angle A in degrees.

In the given case, angle A is approximately 95.59 degrees. This method allows us to determine the measure of an angle in a three-dimensional triangle using vector calculations and trigonometric functions.

To find the measure of angle A in triangle ABC, we can use the dot product formula:

cos(A) = (AB · AC) / (|AB| * |AC|)

where AB represents the vector from point A to point B and AC represents the vector from point A to point C.

First, let's calculate the vectors AB and AC:

AB = B - A = (5 - 1, -2 - 1, -5 - 7) = (4, -3, -12)

AC = C - A = (-2 - 1, 1 - 1, 3 - 7) = (-3, 0, -4)

Next, we calculate the dot product of AB and AC:

AB · AC = (4 * -3) + (-3 * 0) + (-12 * -4) = -12 + 0 + 48 = 36

Then, we calculate the magnitudes of AB and AC:

|AB| = √(4^2 + (-3)^2 + (-12)^2) = √(16 + 9 + 144) = √169 = 13

|AC| = √((-3)^2 + 0^2 + (-4)^2) = √(9 + 0 + 16) = √25 = 5

Now we can plug these values into the cosine formula:

cos(A) = (36) / (13 * 5) = 36 / 65

To find the measure of angle A, we can use the inverse cosine (arccos) function:

A = arccos(36 / 65) ≈ 95.59 degrees

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Answer:

24 times

Step-by-step explanation:

16 divided by 2/3 is 24

hope this helped!

Answer:

324m^2

Step-by-step explanation:

To find the surface area, you have to find the area of all the sides of the prism. First of all, let's find the measurements of the numbers we already see.

base: 6x16= 96

front: 6x3=18

side: 16x3=48

Now we have these three numbers. Because it says to find the surface area, You can see that each of these numbers has to be doubled because, for the base, there is also a ceiling to it. For the sides, there are two sides. for the front, there is also a back. This is why you have to double all these numbers.

96x2= 192

18x2= 36

48x2= 96

Now add them all

192+36+96=324

hence, the surface area of this prism is...

324m^2

Hope this helps!  '∆'

Answer:

3*16*6=288 m

Step-by-step explanation: Because a rectangular prism has six rectangular faces or sides, its surface area is just the sum of the six faces, and because each face has an identical opposite, you can calculate the surface area with the formula 2 * length * width + 2 * width * height + 2 * height * length. Also, Multiply the area of the rectangular base face times the height. Simply multiply the area of the base times the height. After you multiply the base and height, you'll have the volume of the rectangular prism. State your answer in cubic units.

Hope this helps

Answer:

A = 53°

AB = 23.3

BC = 18.6

Step-by-step explanation:

2. Given,

C = 90°

B = 37°

AC = 14

Required:

A, AB, and BC

Solution:

✔️A = 180 - (90 + 37) (sum of triangle)

A = 53°

✔️Find AB and BC using trigonometric function:

Reference angle = 37°

Opp = 14

Hyp = AB

Adj = BC

To find AB, apply SOH:

Sin 37 = Opp/Hyp

Sin 37 = 14/AB

AB = 14/Sin 37

AB = 23.262962 ≈ 23.3 (nearest tenth)

To find BC, apply TOA:

Tan 37 = Opp/Adj

Tan 37 = 14/BC

BC = 14/Tan 37

BC = 18.5786275 ≈ 18.6 (nearest tenth)

Answer:

Number of chickens = 8

Number of pigs = 16

Step-by-step explanation:

Let the pigs = p

Let the number of chickens = c

Number of heads = 24

p + c = 24 ----------------(I)

p= 24 - c

Number of feet = 80

Chicken has 2 legs and pig has 4 legs

4p + 2c = 80 --------------(II)

Substitute p = 24 - c in equation (II)

4*(24 - c) + 2c = 80

4*24 - 4*c + 2c = 80

96 - 4c + 2c = 80          {Combine like terms}

     96 - 2c = 80        {subtract 96 from both sides}

          -2c = 80 - 96

         -2c = -16          {Divide both sides by (-2)}

           c = -16/-2

          c = 8

Plugin c = 8 in equation (I)

p + 8 = 24

    p = 24 - 8

  p = 16

Answer:

That is wonderful. I love you!

Answer:

Step-by-step explanation:

Y= -6

X=-2

Answer:

Step-by-step explanation:

A = P(1-r)^n

A = 35098(1-2.33%)^13

   = $25 833.18