Find the 4 terms in the sequence given [tex]an=n^2+4[/tex]

Answer:

83in²

Step-by-step explanation:

This can also be expressed as;

Area of polygon=Area of ∆ABF +Area of rectangle BCDF + Area 0f ∆DEF

For ∆ABF;

Area of ∆ABO=∆AOF

Area of ∆ABF=2×Area of ∆ABO

Area of ∆ABO=1/2×Length×height

=1×4×7/2=28/2=14in

But area of ∆ABF=2×Area of ∆ABO

Area=2×14in=28in.

Area of rectangle;

Area=length×breadth

Area=5in×8in=40in.

Area of ∆DEF=2×Area of ∆EFG

Area=1/2× base× height

Area=1×2.5×6/2

Area=15/2=7.5in.

But area of ∆EFG=2×7.5in

=15in.

Area of polygon=28in+40in+15in=83in

Answer:

  -3√11

Step-by-step explanation:

If the coefficients of a polynomial are rational, any irrational root will have a conjugate that is also a root.

The root 3√11 is irrational, so its conjugate, -3√11, will also be a root.

__

Additional comments

The conjugate of a root of the form a+√b or a+bi will be the same form with the sign changed: a-√b or a-bi.

The conjugate of 3√11 = 0 +√99 will be 0 -√99 = -3√11.

__

A quadratic with rational coefficients can only have irrational roots of the form a±√b, where 'a' and 'b' may be any rational number.

3 - √11  also be a root of f(x).

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Get the conjugate of any irrational zero if you want rational coefficients.

The conjugate of 3 + √11  is  3 - √11

x = 3 +√ 11

Subtract 3 on both sides

x minus 3 = 3 + √11 - 3

x - 3 = √11

By squaring on both sides

(x - 3)² =√ 11

Now subtract 11 on both sides

(x - 3)² - 11 = 0

To factor use the difference of squares

u² minus v² = (u minus v) (u plus v)

[(x - 3) - 11][(x - 3) + 11] = 0

We get,

(x - 3) - 1 = 0 or (x - 3) + 11 = 0

Solve for x - 3 and x

Add √11 on both sides of first equation and subtract √11 on both sides of second equation

x minus 3 = √11 or x minus 3 = - √11

By adding 3 on both sides

x = 3 + √11 or x = 3 - √11

As a result,

the root of 3 - √11 must likewise be f(x).

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The P(B|A) expressed in the simplest form will be (B) 2/7.

To find the P(B|A) expressed in the simplest form:

Given -

Total possible numbers = 2,3,4,5,6,7,8,9

Let the value of the number be AB.

Therefore, the P(B|A) expressed in the simplest form will be (B) 2/7.

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The complete question is given below:
A locker combination consists of two non-zero digits. The digits in a combination are not repeated and range from 2 through 9.

Event a = a first digit is an odd number

Event b = the second digit is an odd number

If a combination is picked at random with each possible locker combination being equally likely, what is P(B/A) expressed in the simplest form?

A.1/4

B.2/7

C.4/9

D.1/2

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

A mean is also referred to as an arithmetic average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the distance between the means of both classes A and B is given by:

Distance = Mean of class A - Mean of class B

Distance = 12 - 4

Distance = 8.

The mean absolute deviation (MAD) for class A is given by:

MAD A = 1/9[2(9 - 12) + (10 - 12) + (11 - 12) + (12 - 12) + (13 - 12) + (14 - 12) + 2(15 - 12)]

MAD A = 1/9[2(3) + (2) + (1) + 0 + (1) + (2) + (1) + 2(3)]

MAD A = 1/9[6 + 2 + 1 + 1 + 2 + 1 + 6]

MAD A = 1/9 × [18]

MAD A = 18/9

MAD A = 2.

Also, the mean absolute deviation (MAD) for class B is given by:

MAD B = 1/9[2(1 - 4) + (2 - 4) + (3 - 4) + (4 - 4) + (5 - 4) + (6 - 4) + 2(7 - 4)]

MAD B = 1/9[2(3) + 2(2) + (1) + (0) + (1) + (2) + 2(3)]

MAD B = 1/9[6 + 4 + 1 + 0 + 1 + 2 + 6]

MAD B = 1/9 × [18]

MAD B = 18/9

MAD B = 2.

Therefore, distance between the means = four (4) times the MAD.

Distance = Means × MAD

8 = 4 × 2.

In conclusion, we can infer and logically deduce that there is no overlap and the distance between the means of both players A and B is between one (1) times the MAD and five (5) times the MAD.

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By definitions of volume and flow rate, it will take a time of 10 minutes to fill the tank to a height of 50 centimeters.

Herein we find the case of a rectangular tank being filled with water at constant flow are, which is dimensionally speaking, volume by time. We know that dimensions of the tank are described in centimeters, whereas flow rate is described in liters per minute. Please notice that a liter is equal to 1000 cubic centimeters:

t = [(80 cm) · (60 cm) · (50 cm) · (1 L / 1000 cm³)] / (24 L / min)

t = 10 min

By definitions of volume and flow rate, it will take a time of 10 minutes to fill the tank to a height of 50 centimeters.

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a3=9

assuming the pattern is constant, a3 is right in the middle of a1 and a5 so the answer would be right in the middle of 6 and 12. the average of 6 and 12 is 9, so a3=9.

hope this helps!

Answer:

y=2x+12

Step-by-step explanation:

The total amount the recycler pays Olivia is $1000.

The weight of the copper is expressed as a fraction A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below.

There is a need to convert tons to pounds:

1 ton = 2000 pounds

1/8 x 2000 = 250 pounds

The total amount that the recycler pays can be determined by multiplying the total pounds by cost per pound.

Total cost = cost per pound x total pound

250 x $4 = $1000

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The least common multiple of two or more natural numbers is the least common multiple of all of them. This concept has historically been linked to natural numbers, but can be used for negative integers or complex numbers.

We calculate the least common multiple, by simultaneous decomposition, this method consists of extracting the common and non-common prime factors, therefore

L.c.m.(12,15,18)= 2² × 3² × 5 = 180 min

The least common multiple of 12, 15, and 18 is 180.

Convert the minutes to hours, for this we apply the rule of 3:

As the bells all together ring at 6 am, so we add

Answer: The bells are rung together again at 9 in the morning.

Answer:

The frame will be 4 inches in width

Step-by-step explanation:

The length of the outside is 24+2x

The width of the outside is 20+2x

(24+2x)(20+2x) - 20(24) = 416

480 + 40x + 48x + 4x2 - 480 = 416

4x2 + 88x - 416 = 0

x2 + 22x - 104 = 0

(x+26)(x-4) = 0

x = -26 or x=4

The frame will be 4 inches in width

Answer:

x^2

Step-by-step explanation:

So there's very two obvious ones we can elimination immediately, that's f(x) = x, and f(x) = |x|. The reason for this is because we can just look at the first ordered pair of (-2, 4). If it was f(x) = x, then the ordered pair would be (-2, -2), but it isn't. Very similar reasoning for f(x) = |x|, except for this function each ordered pair should have the same magnitude or absolute value. So the f(-2) should output 2, since it's the absolute value, but of course this isn't the case since it's 4.

So let's look at 2^x

[tex]2^{-2} = \frac{1}{2^2} = \frac{1}{4}[/tex]

Since the y value is 4 and not 1/4, this is not the parent function

It should be the second option (x^2), and we can double check

(-2)^2 = 4

(-1)^2 = 1

(0)^2 = 0

(1)^2 = 1

(2)^2 = 4

It outputs the same y-values as the table so this is the parent function

He has thrown 425 free throws if he missed 17

The given parameters are:

Proportion of free throw missed, p = 4%

Number of free throw missed, n = 17

Let the total number of throws be N.

So we have

n = p * N

Substitute the known values in the above equation

17 = 4% * N

Divide both sides by 4%

N = 425

Hence, he has thrown 425 free throws if he missed 17

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(i) The measures of the angles are m ∠ TCM = m ∠ TCQ = m ∠ CMQ = 90°.

(ii) The lengths of sides CM and CQ are 2 cm and 2√2 cm, respectively.

(iii) The angle between the side face and the base is equal to θ = cos⁻¹ (2 / MT) and the angle between the slant edge and the base is θ = cos⁻¹ [2√2 / √(4 + MT²)].

In this problem we have a right pyramid as line segment TC is perpendicular to the base PQRS, which means that any line coplanar with PQRS is perpendicular to line segment TC. i) the measures of the angles are m ∠ TCM = m ∠ TCQ = 90°.

Besides, the base PQRS is a square, which is equivalent to four right triangles with angles 45° - 45° - 90° and each triangle can be divided into two right triangles. Hence, the measure of the angle CMQ is 90°.

ii) The length of the sides can be found by the 45-45-90 theorem, which states that the length of the hypotenuse is √2 times the length of any of the legs:

CQ = (√2 / 2) · PQ

CQ = (√2 / 2) · (4 cm)

CQ = 2√2 cm

CM = (√2 / 2) · (2 √2 cm)

CM = 2 cm

iii)  The angle between the side face, one of them contains the line segment MT and the base can be found by the following inverse trigonometric relation: (value of the pyramid height is missing)

θ = cos⁻¹ (CM / MT)

θ = cos⁻¹ (2 / MT)            (1)

Similarly, the angle between the slant edge and the base is found by Pythagorean theorem and inverse trigonometric relation: (value of the pyramid height is missing)

θ = cos⁻¹ (CQ / TQ)

θ = cos⁻¹ [2√2 / √(QM² + MT²)]

θ = cos⁻¹ [2√2 / √(4 + MT²)]          (2)

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The resulting equation on completing the square is (x+19/2)^2 = 39 + (19/2)^2

Quadratic equation are equations that has a leading degree of 2. Most quadratic equations have 3 terms.

Given the quadratic equation x^2-19x-39 = 0

Add 39 to both sides to have:

x^2 - 19x - 39 + 39 = 0 + 39

x^2 -19x = 39

Complete the square of the resulting

x^2-19x+(19/2)^2 = 39 + (19/2)^2
(x+19/2)^2 = 39 + (19/2)^2

x + 19/2 = ±√39 + (19/2)^2

x = ±√39 + (19/2)^2 - 19/2

Hence the resulting equation on completing the square is (x+19/2)^2 = 39 + (19/2)^2

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∠KJI≅ZJX is the additional information.

What are the AAS congruency criteria?

⇒ AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent

We have been given that

⇒ kJ=ZJ

⇒∠KJI=∠ZJX (vertically opposite angle)

And we require one more angle which can't be on the non-included side

so we have only one angle that can satisfy this  

⇒∠JIK=∠JXZ

⇒ Now we can say that △KJI ≅ △ZJX is congruent with AAS congruency criteria

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When one organism gains a benefit at the expense of a second organism and causes them harm is called:

A. Parasitism

B. Mutualism

C. Commensalism

D. Predation

Answer:

Step-by-step explanation:

a

We know that there are (3 + 1/2) groups, such that each group fill one bus.

2/5 of the students are boys, then the number of groups that we can make only with boys is:

(2/5)*(3 + 1/2) = 6/5 + 1/5 = 7/5 = 5/5 + 2/5 = 1 + 2/5

Then you can make one and a little less than a half of a group, which means that you need 1 and 2/5 of a buss to transport the boys, rounding that to the a whole number, you will need 2 busses to only transport the boys.

The original distance is:

D = (2 + 3/4) miles.

But Mark only covers 2/3 of that distance, then we have:

d = (2/3)*D = (2/3)*(2 + 3/4) miles = (4/3 + 2/4) miles

d = (4/3 + 1/2) miles = (8/6 + 3/6) miles = (1 + 5/6) miles

Mark is at (1 + 5/6) miles of his house.

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Solving the quadratic equation we conclude that:

The height of the rocket is defined by the quadratic equation:

[tex]d = 90t - 5t^2[/tex]

The maximum height is what we get in the vertex of the quadratic equation, such that for this quadratic equation, the vertex is at:

[tex]t = -90/(2*-5) = 9[/tex]

So the maximum height is what we get when we evaluate in t = 9:

[tex]d = 90*9 - 5*9^2 = 45[/tex]

The maximum height is 45ft.

Now we need to solve the equation for the largest value of t:

[tex]d = 90*t - 5t^2 = 0[/tex]

Rewriting it, we get:

[tex]0 = 90*t - 5*t^2\\\\0 = t*(90 - t*5)[/tex]

The maximum solution is what we get when:

0 = 90 - t*5

t = 90/5 = 18

The rocket is 18 seconds in the air.

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Answer:

n = 2

Step-by-step explanation:

cross multiply

-5 times -4 = 20

10n = 20

n = 2

[tex]\bf{Move \ the \ negative \ symbol \ to \ the \ left. }[/tex]

[tex]\boldsymbol{\sf{-\dfrac{10n}{5}=-4 \ \ \longmapsto \ \ [Split] }}[/tex]

[tex]\boldsymbol{\sf{-2n=-4 }}[/tex]

[tex]\bf{Divide \ both \ sides \ by \ -2. }[/tex]

[tex]\boldsymbol{\sf{n=\dfrac{-4}{-2} }}[/tex]

[tex]\bf{Two \ negatives \ make \ a \ positive. }[/tex]

[tex]\boldsymbol{\sf{n=\dfrac{4}{2} \ \ \longmapsto \ \ [Split] }}[/tex]

[tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \underline{n=2}}}}}[/tex]

the equation that represents the new graph is:

g(x) = √(x - 3) - 2

Here we start with the function:

y = f(x) = √x

First, we shift it 2 units down, then the new equation will be:

g(x) = f(x) - 2

Now we apply a horizontal shift, this time we shift the graph 3 units to the left, then the new equation is:

g(x) = f(x - 3) - 2

Now we replace f(x) = √x to get:

g(x) = √(x - 3) - 2

That is the equation that represents the new graph.

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The scale factor of the given dilation transformation is calculated as; 1/2

We know that from transformation that  a dilation is a non - rigid transformation that produces similar figures.

If two lines are similar, then the lines are parallel and parallel lines always have the same slope.

Thus;

Line A has the formula; 2y = x + 8

Writing it in slope intercept form gives us;

y = 0.5x + 4   ------(1)

Thus;

slope of the line A is m = 0.5

y-intercept of the line A is b = 4

Line B has the equation;

y - ¹/₂x = 2

Rearranging in Slope Intercept form gives us;

y = ¹/₂x + 2

Thus;

slope of the line B is m = 0.5

y-intercept of the line B is b = 2

Now, it should be noted that the y-intercept of line A multiplied by the scale factor k must be equal to the y-intercept of line B. Thus;

4k = 2

k = 2/4

k =  ¹/₂

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We have:

√32x + 1 = 9x - 2

<=> √32x - 9x = -2 - 1

<=> (√32 - 9)x = -3

<=> x = -3/(√32 - 9) = (27+12√2)/49

ANSWER: x = (27+12√2)/49

P/s: i'm not pretty sure

Ok done. Thank to me :3

It would be the bottom left graph

Initial production: 1050

so the graph will be started at 1050 which makes top right graph incorrect

Next, the money at the lowest was 250 which makes the top left and bottom right incorrect.

leaving only the bottom right graph to be correct

Answer:

Graph Y

Step-by-step explanation:

Given information:

The initial production cost is when the number of items is zero.

Therefore, the y-intercept of the graph will be (0, 1050).

The lowest production cost is the minimum point of the curve.

Therefore, the vertex of the graph will be (2, 250).

The only graph that satisfies these conditions is graph Y (attached).

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[tex]-16=r^3\implies \sqrt[3]{-16}=\sqrt[3]{r^3}\implies \sqrt[3]{-16}=r\implies \sqrt[3]{-2^4}=r \\\\\\ \sqrt[3]{(-2)^3\cdot 2^1}=r\implies -2\sqrt[3]{2^1}=r\implies -2\sqrt[3]{2}=r[/tex]

There are 20! number of ways for everyone to do this so that at the end of the move, each seat is taken by exactly one person.

People are seated in a 2 by 10 rectangle grid. All 20 persons stand up from their seats and relocate to an orthogonally neighboring one upon the blowing of a whistle.

Now, we have to find the number of possible ways in which each seat is taken up by exactly one person after the move.

As the number of people is 20 and 20 seats are to filled exactly once.

So, the number of ways = 20!

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Answer:

Option C: x = 6

Step-by-step explanation:

Hi There!

7 + 5 (x - 3) = 22

=> 7 + 5x - 15 = 22

=> 5x = 22 - 7 + 15

=> 5x = 30

=> x = 30/5

=> x = 6

x = 6 makes the statement true.

Thank you,

Eddie

Carries two brothers each ate 4 pieces, the rest of carries family ate 14 pieces and there were 14 pieces remaining given that Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces. This can be obtained by multiplying the fractions given with the total number.

From the question it is given that,

Carries family broke a package of graham crackers into 32 pieces.

Therefore total number of pieces will be 32 pieces.

carries two brothers each ate 1/8 of the pieces

This means that out of 32, 1/8 of the pieces were ate by the two brothers.

1/8 of 32 = 1/8 × 32 = 4 pieces

⇒ Carries two brothers each ate 4 pieces

the rest of the family ate 7/16 of the pieces

This means that out of 32, 7/16 of the pieces were ate by the rest of the family

7/16 of 32 = 7/16 × 32 = 14 pieces

⇒ the rest of carries family ate 14 pieces

remaining pieces = 32 - (4 + 14) = 32 - 18 = 14 pieces

⇒ there were 14 pieces remaining

Hence Carries two brothers each ate 4 pieces, the rest of carries family ate 14 pieces and there were 14 pieces remaining given that Carries family broke a package of graham crackers into 32 pieces.

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces.

carries two brothers each ate ____ pieces

the rest of carries family ate ____ pieces

there were ____ pieces remaining

To estimate the volume of the chord of wood, since the wood exists cut into equal lengths and stacked evenly in a rack then we can use a cylinder as a model.

In mathematics, a cylinder exists as a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases exist normally circular (like a circle) and the center of the two bases exists joined by a line segment, which exists named the axis.

A cylinder exists as a closed solid that contains two parallel circular bases joined by a curved surface.

To calculate the volume of the chord of wood, since the wood exists cut into equal lengths and stacked evenly in a rack then we can use a cylinder as a model.

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Answer:

11/24 ths each

Step-by-step explanation:

Add the portions left...then divide by the five of them

3/4 + 5/8 + 11/12  = ?      must find common denominator (24) and convert

(18 + 15+22) / 24 = 55/24  now divide by 5 (which is the same as mult by 1/5)

55/24 * 1/5 = 55/120     now simplify to 11/24

generally, tanA=opposite/adjacent

answer:tanC=36/15=12/5

Answer:

[tex]Tan \space\ \theta =\frac{\boxed{12}}{\boxed5}}[/tex]

Step-by-step explanation:

The tangent (Tan) of an angle is the ratio of the opposite side and the adjacent side, so that:

[tex]\boxed{Tan\space\ \theta = \frac{opposite}{adjacent}}[/tex].

In this case, with respect to angle C:

• opposite = AB =  36 units

• adjacent = CB = 15 units.

Substituting the values into the equation:

[tex]Tan \space\ C = \frac{36}{15}[/tex]

           = [tex]\bf \frac{12}{5}[/tex]   (simplified)