math hw for tonight
help solve this problem! Thank you!
ap cal bc

The quadratic polynomial with integer as coefficients that has four real roots including these conjugates is a² + b² - 2ab - 20a - 20b + 88 ≥ 0

One possible quartic polynomial with integer coefficients that has four real roots, including the conjugates 5+√3 and 5-√3, is:

(x - 5 - √3)(x - 5 + √3)(x - a)(x - b)

where a and b are the remaining two roots.

Expanding the first two factors using the difference of squares formula, we get:

(x - 5)² - 3

Expanding the last two factors, we get:

x² - (a + b)x + ab

Putting it all together, the quartic polynomial is:

a² + b² - 2ab - 20a - 20b + 88 ≥ 0

To ensure that a and b are also real, we can use the fact that the discriminant of a quadratic equation ax² + bx + c = 0 with real coefficients is b² - 4ac ≥ 0. Applying this to the quadratic factor in the above polynomial, we get:

(a + b)² - 4ab ≥ 0

Expanding and simplifying, we get:

a² + b² - 2ab - 20a - 20b + 88 ≥ 0

To simplify the problem, we can set a = b, since the polynomial is symmetric with respect to the roots. Then, the inequality becomes:

2a² - 40a + 88 ≥ 0

Dividing by 2 and factoring, we get:

(a - 10)² - 12 ≥ 0

This inequality is always true for real values of a, so we can choose any real value for a and set b = a to obtain a quartic polynomial with integer coefficients that has four real roots, including the conjugates 5+√3 and 5-√3.

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The length of m∠WYX is equal to 12π units.

In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:

Area of sector = θπr²/360

Where:

By substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = θπr²/360

16π = θ(π/360) × 8²

Central angle, θ = 0.5π

m∠WYX = 2π - m∠WX

m∠WYX = 2π - 0.5π

m∠WYX = 1.5π

Length of m∠WYX = (1.5π)/2π × 2πr

Length of m∠WYX = (1.5π)/2π × 2π(8)

Length of m∠WYX = 12π units.

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The missing length is 4 in.

The volume of a rectangular prism is 32 in³.

We have,

Since the two faces of the blocks are squares.

The face that has the missing length can be considered as a square face.

i.e

The front and back faces are squares.

So,

The missing length is 4 in.

Now,

The volume of a rectangular prism.

= length x width x height

= 4 x 2 x 4

= 32 in³

Thus,

The missing length is 4 in.

The volume of a rectangular prism is 32 in³.

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The evaluated speed of P is 54.5 m s¯¹, under the condition that two forces F₁ and F₂ act on a particle P. The force F₁ is given by F₁ = (-i + 2j) N and F₂ acts in the direction of the vector (i + j).

To evaluate the speed of particle P when t = 3 seconds, we can apply the equations of motion formulas to calculate the velocity if the acceleration and initial velocity values are already given.
The formula can be derived :
v = u + at
Here,
v =  final velocity of the particle,
u = initial velocity of the particle,
a = acceleration acting on the particle
t = time taken.
It is known to us that the acceleration of P is (3i + 9j) ms² and at time t = 0, the velocity of P is (31 -22j) m s¯¹. We can evaluate the initial velocity u by taking the magnitude of (31 -22j) that is
√(31² + (-22)²)
= 39.051 m s¯¹.
Now we can staging all values into the formula
v = u + at
v = 39.051 + (3i + 9j) × 3
v = 39.051 + (9i + 27j)
v = (39.051 + 9)i + (27)j
v = 48.051i + 27j
Then, when t = 3 seconds, the speed of particle P is √(48.051² + 27²)
= 54.5 m s¯¹.
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2 nickels and 1 dime

4 nickels and 2 dimes

6 nickels and 3 dimes

8 nickels and 4 dimes

10 nickels and 5 dimes

If teacher has total "52 cards", and teacher gives each student "1 card" until all 52 cards are distributed, then number of students which got exactly 9 cards are (b) 4 students.

There are 6 students and 52 cards. The teacher gives each student one card until all 52 cards are given out in game. We want to know how many students receive exactly 9 cards.

To solve the problem, we divide the total number of cards (52) by the number of students (6) to find the average number of cards per student.

⇒ 52 cards / 6 students = 8.67 cards per student;

Since we can't give a student a fraction of a card, we need to round down to 8 cards,

If we give each student 8 cards, that will total of 8 cards × 6 students = 48 cards. which leaves 4 cards left over that we can't give out evenly.

This means that four-students will receive 9 cards each and two students will receive 8 cards each.

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

A teacher gives 6 students some cards to play a game, She has 52 cards in total, The teacher gives each 1 card until all 52 cards are given.

How many students gets exactly 9 cards?

(a) 2

(b) 4

(c) 5

(d) 6.

Answer:

Kenyon could make a total of 7 bouquets.

Step-by-step explanation:

To find the greatest number of bouquets we need to find GCF.

We need to find GCF for 21 and 28.

The factors of 21 are: 1,3,7, and 21.

The factors of 28 are: 1,2,4,7,14, and 28

1 and 7 are the common factors between 21 and 28.

From the factors, the greatest common factor is 7.

You can use functions to complete the table as follow:

x   f(g(x))

4      2

10     4

20    6

34    8

52   10

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

We have:

f(x) = √(x+1)

g(x) = 2x - 5

When x = 4:

f(g(x)) = f(g(4))

f(g(4)) = f(2*4 - 5)

f(g(4)) = f(3)

f(g(4)) = √(3+1)      [Remember f(x) = √(x+1)]

f(g(4)) =  2

When x = 10:

f(g(10)) = f(2*10 - 5)

f(g(10)) = f(15)

f(g(10)) = √(15+1)

f(g(10)) = 4

When x = 20:

f(g(20)) = f(2*20 - 5)

f(g(20)) = f(35)

f(g(20)) = √(35+1)

f(g(20)) = 6

When x = 34:

f(g(34)) = f(2*34 - 5)

f(g(34)) = f(63)

f(g(34)) = √(63+1)

f(g(34)) = 8

When x = 52:

f(g(34)) = f(2*52 - 5)

f(g(34)) = f(99)

f(g(34)) = √(99+1)

f(g(34)) = 10

Thus, fill the values into the table to complete it.

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Answer:

The height of the kite is 63.40 feet.

Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.

Let h represent the height of the kite. Hence, using trigonometric ratios:

sin(30) = h / 95

h = 47.5 feet

Therefore the height of the kite is 63.40 feet.

The ground distance of the plane is 170,138.5 ft.

The ground distance of the plane is calculated by applying trigonometry ratio as shown below;

SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The height attained by the plane is the opposite side, while the ground distance is the adjacent side

tan (10) = 30,000 ft/d

d = 30,000 ft/tan(10)

d = 170,138.5 ft

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Answer:

40, 2

Step-by-step explanation:

x = number 1

y = number 2

x = 15y + 10

x + y = 42

we use the first in the second equation and get

15y + 10 + y = 42

16y = 32

y = 32/16 = 2

x + y = 42

x + 2 = 42

x = 40

Answer:

Step-by-step explanation: The answer is 4 all u do is add 2 to 2

Answer: 2+2=4

Step-by-step explanation: The sum of two and two results in a value of four in a quantitative analysis.

The volume of the solid is 1922.7 in³.

The volume of a solid can be found by adding the volume of the shapes that make the solid. In this case:

Volume of solid = volume of hemisphere + volume of cylinder

Volume =  2/3πr³ + πr²h

where r = 12/2 = 6 in

height of cylinder (h) = 13 - 6 = 7 in

Volume =  (2/3 * π * 6³) + (π * 6² * 13)

Volume =  1922.7 in³

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As per the unitary method, each piece is 3.25 meters long by dividing the total length of the ribbon by the number of pieces.

Larry has cut a ribbon into 8 equal pieces. The total length of the ribbon is 26 m. We need to find out the length of each piece of the ribbon.

To do this, we can use the unitary method. We know that the ribbon is divided into 8 equal pieces, so each piece is 1/8th of the total length of the ribbon.

Therefore, we can find the length of each piece by dividing the total length of the ribbon by 8:

Length of each piece = Total length of ribbon / Number of pieces

Length of each piece = 26 m / 8

Length of each piece = 3.25 m

So, each piece of the ribbon is 3.25 meters long.

We used the unitary method by finding the value of one unit (1/8th of the ribbon) and then using it to calculate the value of other units (the length of each piece).

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The outputs for industries X and Y will be 31 million and 43.2 million, respectively  supposedly the final demand changes to 20 for X and 30 for Y.

We will  start with industry X.

The final demand for X hade an increment from 14 million to 20 million with  an increase of 6 million, hence the final output of X must also increase by 6 million to make up for demand.

Users    Final    Producers

Demand     X          Y

X          14         7

Y           6        18

Total     20        25

The table tells us that for every additional million of final demand for X, the producers in industry X need to produce 0.5 million of output.

So the new total output for industry X is 28 + 3 = 31 million.

For  industry Y

The same scenario occurred for Industry Y which had final output of 12 in order to meet the demand increment.

So the new total output for industry Y is 36 + 7.2 = 43.2 million.

In conclusion, the outputs for industries X and Y will be 31 million and 43.2 million, respectively, if the final demand changes to 20 for X and 30 for Y.

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Yes, data provide convincing evident that contest has increased participation.

We have,

H₀: p = 0.12

Hₐ: p > 0.12

So, z = (p' - p)/ (√pq/n)

z = 1/6 - 0.2/ √(0.12 x 0.88) /210

z= 2.08

The test is right tailed.

So, P value = P( z> 2.08) = 0.0188

and, P- value < α, Reject H₀

Yes, data provide convincing evident that contest has increased participation.

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The sales after 5 months is 36,000 units (since f(t) is given in thousands of units).

The given function f(t) represents the sales of a gaming product in thousands of units after t months. To find the sales after 5 months, we need to substitute t = 5 in the function f(t) and evaluate the expression. f(5) = 5(5) + 11

= 25 + 11

= 36

Therefore, the sales of the gaming product after 5 months is 36 thousand units. This means that the company has sold 36 thousand units of the gaming product within the first 5 months since the launch of the product. It also indicates that the sales are increasing by 5 thousand units every month.

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-- The given question is incomplete, the complete question is

"Let f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11. Find the sales after 5 months."

The triangles are similar, and the scale factor is given as follows: k = 0.8.

Similar triangles are triangles that share these two features listed as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of the missing angle is given as follows:

x + 114 + 24 = 180

x + 138 = 180

x = 42º.

Which is equals to the measure on the second triangle, hence they are similar.

The scale factor is given as follows:

k = 16/20 = 36/45 = 0.8.

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The total number of cups of grapes and raisins include the following: 5/6 cups of grapes and raisins.

In Mathematics and Geometry, a fraction is a numerical quantity (number or numeral) that is typically expressed as a quotient (ratio) or not expressed as a whole number. This ultimately implies that, a fraction simply refers to a part of a whole number.

Based on the information provided above, the total number of cups of grapes and raisins can be calculated as follows;

Fraction = 1/2 + 2/3

Fraction = (3 + 2)/6

Fraction = 5/6 cups of grapes and raisins.

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The length of each garden side is 4 ft.

Given that, Paola has 48 ft² of mulch, she wants to make three square vegetable gardens of equal sizes, we need to find the length of each garden side.

Let s be the length of the side of the gardens,

Since, she need 3 gardens,

So,

3 × side² = 48

3s² = 48

s² = 16

s = 4

Hence, the length of each garden side is 4 ft.

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The domain can be written as follows:

R - {x = n*12pi or m*4pi | n, m ∈ Z}

where pi = 3.14 and R is the set of real numbers.

Here we want to find the domain of the function:

y = tan(x/8)

The tangent is the quotient between the cosine and the sine, then we will get:

sin(x/8)/cos(x/8)

The problems of the tangent are all the values that make the denominator equal to zero, then we need to remove these.

The zeros are:

cos(x/8) = 0

We know that cos(pi/2) = cos(3pi/2)  = 0

Then:

x/8 = pi/2

x = 4pi

x/8 = 3pi/2

x = 12pi

So the domain is the set of all real numbers except the ones in the next set:

{x = n*12pi or m*4pi | n, m ∈ Z}

Where Z is the set of integers.

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The probability which is selected randomly from a lot of people living alone in the area in the 25-34 age range will be; 0.1487

Since the total digit of individuals living independently in the area = 31.6

The digit of individuals living in the area who fall within the 25 - 34 age range is 4.7

The probability formula will be

P = required outcome / Total possible outcomes

From the information provided above the given data is:

P(range 25 - 34) = 4.7 / 31.6

= 0.1487

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Answer: Option C.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.

Given that the diameter of the container is 24 ft, the radius (r) would be half of that, which is 12 ft.

The depth of the container (h) is given as 4 ft.

Plugging in these values into the formula, we get:

V = π(12^2)(4)

V = 3.14(144)(4)

V = 1808.6 cubic feet (rounded to the nearest tenth)

So, the storage container can hold approximately 1808.6 cubic feet of wood, rounded to the nearest tenth.

Step-by-step explanation:

Answer:

√50

Step-by-step explanation:

To solve, use distance formula.

√(9-4)^2 + (2-(-7))^2=

√5^2+5^2=

√50

-1.2, earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X

Given that two machines, X and Y, produce earbuds

Let X represent the diameter of an earbud produced by machine X, and

let Y represent the diameter of an earbud produced by machine Y. X has a mean of 14 mm with a standard deviation of 0.6 mm

Y has a mean of 15.2 mm with a standard deviation of 0.2 mm.

The mean of the difference, D = X - Y, can be calculated as:

mean(D) = mean(X) - mean(Y)

= 14 - 15.2

= -1.2

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The measure of inverse of sinθ is c/√ (c² - a²)..

The measure of inverse of sinθ is calculated by applying trigonometry identities for right triangles.

Mathematically, the trig identities are represented using the following method;

SOH CAN TOA

SOH is for sine θ

CAH is fof cos θ

TOA is for tan θ

From the diagram we need find the value of the opposite side;

b = √ (c² - a²)

Sin θ = b/c

The inverse of b/c = c/b

1/sinθ = c/b = c/√ (c² - a²).

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Answer:

Step-by-step explanation:

A full revolution on a circle/radians is 2[tex]\pi[/tex], so keep adding or subtracting 2[tex]\pi[/tex] til you get a base angle, that's when the sign changes.  Then decide which quadrant your in.

For this one the equivalent of 2[tex]\pi[/tex] is [tex]6\pi /3[/tex]

-29[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= -23[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= -17[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= -11[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= -5[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= 1[tex]\pi[/tex]/3            sign changed it's equavalent to [tex]\pi /3[/tex]  Which is in the first quadrant.   See unit circle.

-5[tex]\pi[/tex]/6 + [tex]12\pi /6[/tex]

=[tex]7\pi /6[/tex]              third quadrant,  i count quadrants by know [tex]\pi[/tex]/6 is 30°, so every 30° line is 1/6 of the unit circle.  when i count 7 of them that's in the 3rd quadrant.  Don't forget to count the axis's

2[tex]\pi[/tex]/3 is in the 2nd quadrant.  Count my pi/3's which is 60°

45[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7

= 31[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7

=17[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7

=3[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7

= -11[tex]\pi[/tex]/7      1/7th's is not your typical unit circle angle

This one i think of logically.  this is -1 4pi/7  

1 pi going backwards is 180

keep going backards 4/7 is bigger than 1/2 so it's in the 1st quadrant