A rectangular box has a square base. The combined length of a side of the square base, and the height is 20 in. Let x be the length of a side of the base of the box.

a. Write a polynomial function in factored form modeling the volume V of the box.

b. What is the maximum possible volume of the box?

c. Explain how you found the maximum possible volume.

The solution to a system of linear equations is the ordered pair (or pairs) that satisfies all equations in the system.

What ordered pair is a solution to the system of linear equations?

An equation is said to linear when it is in ax+ by = c form where a , b and c are real numbers . System of linear equation consist of a set of two or more equation with same variables. such as ,

a₁ x + b₁ y = c₁

a₂ x + b₂ y = c₂

A solution to a linear system is an ordered pair (x ,y) that solves both the equations .

To check that an ordered pair is a solution ,we have to substitute the corresponding values of our variables (x ,y) into our equations and see if they satisfy both the equations.

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After differentiation of function with respect to y, the value of y'(1) is 0.225.

In the given question we have to find the value of derivative of y at 1.

The given function is [tex]\frac{x^2}{36}+\frac{y^2}{64}=1[/tex]

To find the derivative of y at 1 we have to firstly derivate the given function with respect to y.

Now writing the given function in the y form

[tex]\frac{x^2}{36}+\frac{y^2}{64}=1[/tex]

Subtract x^2/36 on both side, we get

[tex]\frac{y^2}{64}=1-\frac{x^2}{36}[/tex]

Multiply by 64 on both side, we get

[tex]y^2=64-64\times\frac{x^2}{36}[/tex]

[tex]y^2=64-\frac{16x^2}{9}[/tex]

Differentiating with respect to y on both side

[tex]2y\frac{dy}{dx}=0-\frac{16\times2x}{9}[/tex]

[tex]2y\frac{dy}{dx}=\frac{32x}{9}[/tex]

Simplifying

dy/dx = 16x/9y

We can write dy/dx as y' so

y' = 16x/9y

We have to find the value of y'(1).

Since the y is the function of x so we put x=1 and we know y(1)=7.89, so

y'(1) = 16*1/9*7.89

y'(1) = 16/71.01

y'(1) = 0.225

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The distance between the two cities, Ottawa and Toronto, as determined by Greg and Max is 280.37 miles.

What is a Speedometer?

What is Distance?

How is Distance Calculated?

The distance between two locations can be calculated using the formula,
d = s x t,------ (1)

where [tex]d[/tex] is the distance travelled, [tex]s[/tex] is the average speed, and [tex]t[/tex] is the total time.

In the given question, it is given that Greg and Max travel from Ottawa to Toronto with an average speed of 40 mph and 30 mph for the return trip.

So, [tex]s_{1}=40 mph[/tex] and [tex]s_{2}=35mph[/tex].

The total travelling time for the round trip, T = 15h  ------(2)

Let the distance from Ottawa to Toronto be x.

From (1), we get that, the formula for the time taken is,

[tex]t=\frac{d}{s}[/tex]

So, the time taken to travel from Ottawa to Toronto,

[tex]t_{1} =\frac{d}{s_{1} } \\\implies t_{1} =\frac{x}{40}[/tex]      ------- (3)

And, the time taken for the return trip (back from Toronto to Ottawa),

[tex]t_{2} =\frac{d}{s_{2} } \\\implies t_{2} =\frac{x}{35}[/tex]      --------(4)

Here, the total time travelled from the round trip is equal to the sum of the time taken to travel from Ottawa to Toronto and back from Toronto to Ottawa.

T = t_1 + t_2------(5)

Substituting the values of (2), (3), and (4) in (5), we get

15 = x/40 + x/35
--> 15 = 0.0535x

Simplifying,

x = 15/0.0535
--> x = 280.37 miles

Therefore, the distance between the two cities as determined by Greg and Max is equal to 280.37 miles.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6629\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A=6629\left(1+\frac{0.1}{1}\right)^{1\cdot 4} \implies A \approx 9705.52~\hfill \underset{earned~interest}{\stackrel{9705.52~~ - ~~6629}{\approx\text{\LARGE 3076.52 }}}[/tex]

Answer:

Area = 1/2 * base * height

Area = 1/2 * 155 * 175

Area = 13,563.75

The graph is a function with the domain {-6 < x < 0} and the range {0 ≤ y ≤ 5}.as stated

The term "range" refers to every potential value in a graph's output.

The result of range is seen in the y coordinate, and the range of potential values is given here.

0 ≤ y ≤ 5

The term "domain" refers to every conceivable value in a graph's input.

The x coordinate is the input, and the extent of potential values is

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The length of the side a = 9.43 cm and b = 12.04 cm

Consider the first triangle

The hypotenuse of the triangle = a

The base of the triangle = 5 cm

The length of the vertical side = 8 cm

Apply the Pythagorean theorem here

[tex]a= \sqrt{8^2+5^2}[/tex]

Find the square of the terms

a = [tex]\sqrt{64+25}[/tex]

a = [tex]\sqrt{89}[/tex]

a = 9.43 cm

Consider the second triangle

The hypotenuse of the triangle = 17 cm

The base of the triangle = 12 cm

The length of vertical side = y cm

Apply the Pythagorean theorem

b = [tex]\sqrt{17^2-12^2}[/tex]

b = [tex]\sqrt{289-144}[/tex]

b = [tex]\sqrt{145}[/tex]

b = 12.04 cm

Hence, the length of the side a = 9.43 cm and b = 12.04 cm

The complete question is

Work out the lengths of sides a and b give your answer to the 1st decimal

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Answer:

D or C

Step-by-step explanation:

the area of the original square garden is 80 square meters.

Let the side of the original square be a. We are given that the area of the new garden was (a - x)(a + x) = a² - x² = 64.

We want to find the area of the original square, so the value of a².

(1) The area of the new garden was 80 percent of the area of the original square garden --> 64 = 0.8a² --> a² = 80. Sufficient.

(2) x = 4 --> a² - 4² = 64 --> a² = 80. Sufficient.

the area is the quantity that expresses the quantity of a location on the aircraft or on a curved surface. The place of an aircraft region or plane vicinity refers back to the location of a form or planar lamina, at the same time as floor area refers to the place of an open surface or the boundary of a 3-dimensional object. location may be understood as the quantity of fabric with a given thickness that might be vital to style a model of the form, or the amount of paint necessary to cowl the surface with an unmarried coat. it's by far the two-dimensional analog of the duration of a curve (a one-dimensional idea) or the volume of a strong (a three-dimensional concept).

place plays a vital position in current mathematics. further to its apparent importance in geometry and calculus, the place is associated with the definition of determinants in linear algebra and is a simple asset of surfaces in differential geometry. In analysis, the vicinity of a subset of the plane has defined the use of the Lebesgue measure, though no longer every subset is measurable. In the trendy, region in better mathematics is visible as a unique case of quantity for two-dimensional regions.

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[tex]\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=\stackrel{width}{base}\\ h=height\\[-0.5em] \hrulefill\\ A=247\\ b=19 \end{cases}\implies 247=\cfrac{1}{2}(19)h \\\\\\ 494=19h\implies \cfrac{494}{19}=h\implies 26=h[/tex]

[tex]\boldsymbol{\sf{Your\:exersice \to \dfrac{1}{x+9}+\dfrac{1}{5}=\dfrac{1}{4} }}[/tex]

Variable x cannot be equal to −9 as division by zero is undefined. Multiply both sides of the equation by 20(x+9), the lowest common denominator of x+9,5,4.

[tex]\boldsymbol{\sf{20+20(x+9)\times\left(\dfrac{1}{5}\right)=5(x+9) }}[/tex]

Multiply 5 and 1/5 to get 4.

[tex]\boldsymbol{\sf{20+4(x+9)=5(x+9)}}[/tex]

Use the distributive property to multiply 4 by x+9.

[tex]\boldsymbol{\sf{20+4x+36=5(x+9)}}[/tex]

Add 20 and 36 to get 56.

[tex]\boldsymbol{\sf{56+4x=5(x+9)}}[/tex]

Use the distributive property to multiply 5 by x+9.

[tex]\boldsymbol{\sf{56+4x=5x+45}}[/tex]

Subtract 5x on both sides.

[tex]\boldsymbol{\sf{56+4x-5x=45}}[/tex]

Combine 4x and −5x to get −x.

[tex]\boldsymbol{\sf{56-x=45}}[/tex]

Subtract 56 from both sides.

[tex]\boldsymbol{\sf{-x=45-56}}[/tex]

Subtract 56 from 45 to get −11.

[tex]\boldsymbol{\sf{-x=-11}}[/tex]

Multiply both sides by −1.

[tex]\boldsymbol{\sf{x=11}}[/tex]

The sine and cosine functions with the ordered pairs A(1,4) and B(0,-4) are given as follows:

Both the sine and the cosine functions have similar definitions, given as follows:

The meaning of the coefficients of the functions are presented as follows:

The functions vary between -4 and 4, hence the amplitude is given as follows:

a = 4.

This is the standard oscillation for a trigonometric function with amplitude 4, between -4 and 4, hence the vertical shift is of:

d = 0.

The difference between the x-coordinates of the maximum and the minimum value is half the period, hence the period is of 2 x 1 = 2, and the coefficient b is:

2π/b = 2

b = π.

The cosine function has no phase shift, it just is inverted, as it should assume a value of 4 at x = 0, hence the definition is:

g(x) = -4cos(πx).

The sine function has a phase shift, as it should assume a value of -4 at -π/2, not π/2, hence it is shifted shift π/2 units, hence the definition is:

f(x) = 4sin(π(x + π/2)).

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SSS should be used to show that the triangles are congruent.

What is the congruent triangle?

Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them. Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.

From the given images of the triangles, it is clear that the the legs of the triangles are equal to each other.

If two legs of two triangles are equal, then the bases are equal to each other.

Thus to prove that the triangles are congruent to each other, apply SSS  postulate.

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The probability of first tile is less than 15, is 70% and the second tile is even or greater than 25, is 60%.

In the given question we have to find the probability of first tile is less than 15 and the second tile is even or greater than 25.

Tiles numbered 1 through 20 are placed in a box.

Tiles numbered 11 through 30 are placed in a second box.

One tile is randomly drawn from each box.

Now finding the probability of first tile is less than 15.

Since in first box tile is numbered as 1 to 20.

So the outcomes of less than 15 = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

So favourable outcome = 14

Total number of tile = 20

So the probability = 14/20 = 70%

Now finding the probability of second tile is even or greater than 25.

Since in second box tile is numbered as 11 to 30.

So the outcomes of even or greater than 25 = 12, 14, 16, 18, 20, 22, 24, 26, 27, 28, 29, 30

So favourable outcome = 12

Total number of tile = 20

So the probability = 12/20 = 60%

Hence, the probability of first tile is less than 15, is 70% and the second tile is even or greater than 25, is 60%.

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The right question

"Tiles numbered 1 through 20 are placed in a box. Tiles numbered 11 through 30 are placed in a second box. One tile is randomly drawn from each box. Find each probability. The first tile is less than 15 and the second tile is even or greater than 25."

Answer:

m∠X=75.75

Step-by-step explanation:

A triangle's angles combine to 180 degrees. Subtract 62.45+41.8 from 180.

The measure of the exterior angle of the triangle is given by ∠A = 104.25°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ΔXYZ

Let the measure of the exterior angle be m∠A

Now , the measures of the angles of the triangle are

The measure of angle ∠Y = 62.45°

The measure of angle ∠Z = 41.8°

The measure of angle ∠X = m∠X

Now , for a triangle , the sum of the interior angles = 180°

So ,

m∠X + m∠Y + m∠Z = 180°

Substituting the values in the equation , we get

m∠X + 62.45° + 41.8° = 180°

Subtracting 104.25 on both sides of the equation , we get

m∠X = 75.75°

Now , the measure of angle exterior to m∠X be ∠A = 180° - m∠X

The measure of m∠A = 180° - 75.75°

The measure of m∠A = 104.25°

Therefore , the measure of ∠A = 104.25°

Hence , the exterior angle of the triangle is ∠A = 104.25°

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Answer:

Step-by-step explanation:

Between 9 and 10.

Why?

Because sq of 9 is 81 and sq of 10 is 100 which gives us the gesture that sq.rt of 84 is between 9&10.  

Hence, Two integers are 9 and 10.

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Step-by-step explanation:

you take the specific number (males prefer cycling = 0.22) and the fitting total.

note there are 2 possibilities for that total :

all males

all people preferring cycling

the way it was phrased I would say the reference is all males.

the conditional relative frequency is then

0.22 / 0.54 = 0.407407407... ≈ 0.41

but if the meaning would be rather about how many of all people preferring cycling are male, then we would have

0.22 / 0.37 = 0.594594595... ≈ 0.59

both results are in your answer options.

I think the intended result is 0.41, because I understand the problem that way :

find the conditional relative frequency that a student athlete surveyed prefers cycling, given that the student is male.

the other should be phrased like

find the conditional relative frequency that a student athlete surveyed is male, given that the student prefers cycling.

The solution for this system of equations. 12x+ 15y = 34 -6x+ 5y = 3

is (x,y) =(2/3, 8/5)

Given a system of equations,

12x + 15y = 34  ------(1)

-6x + 5y = 3 ------(2),

To solve this we use the elimination method

In the elimination method, you either add or subtract the equations to get an equation in one variable.

Equation (1) + 2 × Equation (2),

We get,

(12x+15y=34)+(-12x+10y=6)

⇒ 15y+10y=34+6

⇒ 25y=40

⇒ y=40/25

⇒ y=8/5

From equation (2),

⇒  -6x+5(y)=6

⇒  -6x+5(8/5)=6

⇒  -6x+8=6

⇒  -6x=-2

⇒ x=2/3

Hence the solution for this system of equations. 12x 15y = 34 -6x 5y = 3

is (x,y =(2/3, 8/5)

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The like terms in the expression are -8x^2,-10x,14 and -6. The like terms are 14 and -6

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms. For example, in the expression 5x + y, the two terms are 5x and y.

In the expression 14-8x^2-6-10x, there are 4 terms in it: 14, -8x^2, - 6, - 10x.

out of the four terms only two are alike because of they are both constant. This like terms are -6 and 14.

10x and -8x^2 are unlike terms because x^2 is a different term from 10x.

Therefore the like terms are -6 and 14

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Answer: C: 62

Step-by-step explanation: -7 + -12 = -19

-19 + 81 = 62

The equation of the polynomial equation P(x) = (x + 3)²(x - 5)²

The given parameters are

The sum of multiplicities of the polynomial equation must be equal to the degree.

This means that the multiplicity of the zero 5 is 2

The equation of the polynomial is then calculated as

P(x) = (x - zero)^multiplicity

So, we have

P(x) = (x - (-3))² * (x - 5)²

This gives

P(x) = (x + 3)²(x - 5)²

Hence, the equation is P(x) = (x + 3)²(x - 5)²

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Possible question

Form a polynomial with real coefficients having the given degree and zeros.

Degree​ 4; ​

Zeros: -3 and 5 with multiplicity 2

The slope between points (17,8) and (17,24) is (B) undefined.

We know that the slope of a line passing through two points (a,b) and (c,d) is given by,

m = (d-b)/(c-a)

So here given points are (17,8) and (17,24)

Then, a=17, b=8, c=17, d=24

Now the slope between these two points is given by,

m = (24-8)/(17-17) = 16/0

So the slope value does not exist or infinity.

Hence the slope between the points (17,8) and (17,24) is Infinity or undefined.

Thus, the correct option is (B).

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1/16 is the ratio of a blue and unbarred parrot as offspring

Dihybrid cross is a cross between two individuals with two observed traits that are controlled by two distinct genes. The idea of a dihybrid cross came from Gregor Mendel when he observed pea plants that were either yellow or green and either round or wrinkled. Crossing of two heterozygous individuals will result in predictable ratios for both genotype and phenotype in the offspring. The expected phenotypic ratio of crossing heterozygous parents would be  Deviations from these expected ratios may indicate that the two traits are linked or that one or both traits has a non-Mendelian mode of inheritance.

When two heterozygous parents for color (Gg) and barring (Bb) are crossed, each parent's genotype is GgBb. Each parent produces four gametes, such as GB, Gb, gB, and gb. As a result, the total number of offspring will be 16, as each parent produces four gametes. Nine will be G B_, three will be G bb, three will be ggB_, and one will be ggbb.

Therefore, 1/16 is the ratio of a blue and unbarred parrot as offspring

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Step-by-step explanation:

55/12

hope this helps:)

Answer:

I think 28.6

Step-by-step explanation:

Coordinate of circumcenter of the given triangle = (3, 2)

What is circumcenter of a triangle?

Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.

Let the coordinate of circumcenter be (x , y)

Distance of Circumcenter from (4,2) =

[tex]\sqrt{(x - 4)^2 + (y-2)^2[/tex]

Distance of Circumcenter from (3, 3) =

[tex]\sqrt{(x - 3)^2 + (y-3)^2[/tex]

Distance of Circumcenter from (2,2) =

[tex]\sqrt{(x - 2)^2 + (y-2)^2[/tex]

By the problem,

[tex]\sqrt{(x - 2)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 2)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 4x + 4 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\6x - 4x +6y -4y = 18-8\\2x +2y = 10\\x+ y = 5\\[/tex]..... (1)

Again,

[tex]\sqrt{(x - 4)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 4)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 8x + 16 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\8x - 6x +4y -6y = 20-18\\2x -2y = 2\\x- y = 1\\[/tex]...... (2)

Adding (1) and (2)

[tex]2x = 6\\x = \frac{6}{2}\\x = 3[/tex]

Putting the value of x in (1),

3 + y = 5

y = 5 - 3

y  = 2

Coordinate of circumcenter = (3, 2)

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The possible heights of the parallelogram are 2/3 and 3

So, the correct option is A and C

The given expression:

area of a parallelogram, A = 12 square unit

a side of the parallelogram,  = 18 units

another side of the parallelogram = 6 units

let,

the height of the parallelogram, h

The area of a parallelogram is given as;

Area = base (b) x height (h)

height (h) = Area/base(b)

From the given sides, the possible heights of the parallelogram are calculated as follows;

if the base, b = 18 units

height(h) =  12/18

              = 2/3

Also, if the base, b = 6 units

height(h) =  12/6

              = 2

Therefore, the possible heights of the parallelogram are 2/3 and 2

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Answer:

SAS, ASA, SSS, ASA, Yes

Step-by-step explanation:

The distance Manatee will swim in 5 hours is 25 miles.

Distance can be defined as the length between two points.

To calculate the distance manatee can swim in 16 hours, we use the equation below

Make y₂ the subject of the equation

Where:

Substitute these values into equation 2

Hence, manatee can swim a distance of 25 miles.

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Complete question: A manatee can swim an average of 10 miles every 2 hours how far can it swim in 5 hours. Assume the distance y in miles is proportional to the number of hours x the manatee swam.