If 27³+27³+27³=27x,what is the value of x?

x(t) = [tex]c_1e^1^4^t+c_2e^-^t[/tex]  , y(t) = [tex]2c_1e^1^4^t-c_2e^-^t[/tex]   is the general solution of the sytem of differention eqution dx/dt = 4x+ 5y , dy/dt = 10x + 9y .

given  dx/dt = 4x+ 5y  and dy/dt = 10x + 9y

X'(t) = [tex]\left[\begin{array}{ccc}4&5\\10&9\end{array}\right][/tex]  X

where X = [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]

so A = [tex]\left[\begin{array}{ccc}4&5\\10&9\end{array}\right][/tex]

now we need to find eigen value of the matrix and the corresponding eigen vector.

| A- λI | = 0

so after equation the value to zero

λ = 14 and λ = -1

now for the  λ = 14 corresponding eigen vector = [tex]\left[\begin{array}{ccc}1\\2\\\end{array}\right][/tex]

for λ = -1 corresponding eigen vector =  [tex]\left[\begin{array}{ccc}1\\-1\\\end{array}\right][/tex]

So general equation is given by:

X(t) = [tex]c_1e^1^4^t[/tex]  [tex]\left[\begin{array}{ccc}1\\2\\\end{array}\right][/tex]  +  [tex]c_2e^-^t[/tex]   [tex]\left[\begin{array}{ccc}1\\-1\\\end{array}\right][/tex]

after solving this

x(t) = [tex]c_1e^1^4^t+c_2e^-^t[/tex]

y(t) = [tex]2c_1e^1^4^t-c_2e^-^t[/tex]

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The two side lengths are congruent, and their opposite angles are congruent, and the hypotenuse is the length of either leg times the square root of two, √2.

A 45° 45° 90° triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.

A 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.

properties of 45°-45°-90°:

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Answer: 18

Step-by-step explanation:

Answer: 18.04347826086957

Step-by-step explanation: you could use a calculator too-

Answer:

x = - 2 or x = - 4

Step-by-step explanation:

Via completing the square:

x^2 + 6x + 8  = x^2 + 6x + (6/2)^2 - (6/2)^2 + 8

                     = (x + 3)^2 - 3^2 + 8

                     = (x + 3)^2 - 9 + 8

                     = (x + 3)^2 - 1

Since x^2+6x+8=0,

(x + 3)^2 - 1 = 0

(x + 3)^2 = 1

x + 3 = +- sqrt(1)

x + 3 = +- 1

x + 3 = 1 or x + 3 = -1

x = -2 or x = -4

The degree of the polynomial 7x³ 5x 4x³ 2x² is 3.

The degree of a polynomial is the highest power of x in the polynomial.

In this case, the polynomial is 7x³ 5x 4x³ 2x², and the highest power of x is x³. This means that the degree of this polynomial is 3.

It's important to note that when working with polynomials it's important to pay attention to the signs of the coefficients. In this case, we have 7x³, 5x, 4x³, 2x². The x³ term has the highest degree and it's coefficient is 7, the x term has the second highest degree and it's coefficient is 5, the x³ term has the same degree as the first x³ term, but the coefficient is different, and the x² term has the fourth highest degree and it's coefficient is 2.

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In the expression 52 + 6 + ya,

The terms are the individual parts of the expression that are being added together. The coefficient is the numerical factor that is multiplied by a variable in a term, and the constant is a term that has no variable.

Any expression with variables will either add or delete one or more variables. Any one of a variety of numbers to represent a generic idea. An absolute number is a constant. A constant is a number, whereas a coefficient is a number that is "in front of" a variable.

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The polynomial in terms of its simplest factors is (x + 3)(x − 6)

From the question, we have the following parameters that can be used in our computation:

x2 − 3x − 18.

Rewrite as

x² − 3x − 18

Expand

x² − 3x − 18 = x² − 6x + 3x − 18

Factorize the expression

This gives

x² − 3x − 18 = x(x − 6) + 3(x − 6)

Factor out x - 6

x² − 3x − 18 = (x + 3)(x − 6)

Hence, the expression is (x + 3)(x − 6)

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K must be equal to 0, for the pair of equations to have no solution.

For the pair of equations KX + 3y - K = 0 and 12x + Ky - K = 0 to have no solution, the value of K must be such that the two equations have no common solution.

This can be done by equating the two equations and solving for K.

KX + 3y - K = 0

12x + Ky - K = 0

Subtracting equation (1) from equation (2)

11x + 3y = 0

Divide both sides by 3

x + y = 0

Therefore, K must be equal to 0, for the pair of equations to have no solution.

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The height of the pole anchored to a cable is 6.17 meters.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, The anchor cable is forming an angle of 51° angle with the ground attached to a pole and the distance between them is 5 meters.

So, We need height or the opposite side length with an adjacent length of 5 meters.

We know, tan = opposite/adjacent.

tan51° = opposite/5.

opposite = tan51°×5.

opposite = 1.235×5.

opposite = 6.17 meters.

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To calculate seed number, divide the total number of inches available for crop by the in-row crop spacing. For example, 120 inches divided by one inch per pea seed equals 120 pea seeds.

In botany, a seed is an undeveloped plant embryo and food reserve encased in a protective outer covering. In a broader sense, "seed" refers to anything that can be sown, such as seed and husk or tuber.

Seeds are formed when a ripened ovule is fertilised by pollen-derived sperm, resulting in a zygote. The embryo develops from the zygote within a seed, forming a seed coat around the ovule and growing to a certain size within the mother plant before growth stops.

The formation of seeds is a stage in the reproduction of seed plants (spermatophytes). Other plants, such as ferns, mosses, and liverworts, lack seeds and must reproduce exclusively through water.

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well, maybe Pam has been eating the wrong chips or something, but if she's correct, that can only happen if both equations are exactly equal, are they?

[tex]\boxed{\cfrac{x}{16}=4}\implies x=(16)(4)\implies \cfrac{x}{4}=16 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x}{4}=16\implies x=(4)(16)\implies \boxed{\cfrac{x}{16}=4}\qquad \begin{array}{llll} \textit{yeap, Pam is correct}\\ \textit{she's Da Bomb} \end{array}[/tex]

The total cost of an item that sells for $12 is $12.96

From the question, we have the following parameters that can be used in our computation:

Selling price = $12

Sales tax = 8%

The total cost of an item that sells for $12 is then calculated as

Total cost = Selling price * (1 + Sales tax)

Substitute the known values in the above equation, so, we have the following representation

Total cost = 12 * (1 + 8%)

Evaluate

Total cost = 12.96

Hence, the total cost is $12.96

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Step-by-step explanation:

(8 + 2)/(6 - p)= -10

10/6 - p = -10

-60 + 10p = 10

10p= 70

p= 7

The statements that are always true regarding the diagram are:

i. m∠5 + m∠6 =180°

ii. m∠2 + m∠3 = m∠6

iii. m∠2 + m∠3 + m∠5 = 180°

A triangle is a 2 dimensional plane figure which is formed by three straight lines and has three interior angles. It has both interior and exterior angles. Some examples of a triangle are; isosceles, equilateral, scalene, right angled etc.

The interior angles of a triangle are the measure of the three internal angles of the triangle, while exterior angles are external to the interior angles of the triangle.

Note that; the exterior angle of a triangle is equal to the sum of the two adjacent interior angles.

Therefore considering the given diagram, the required statements that are always true regarding the diagram are:

i. m∠5 + m∠6 =180°

ii. m∠2 + m∠3 = m∠6

iii. m∠2 + m∠3 + m∠5 = 180°

A sketch of the diagram is herewith attached to this answer for clarity.

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[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{3}}} \implies \cfrac{-2 +2}{2} \implies \cfrac{ 0 }{ 2 } \implies \text{\LARGE 0}[/tex]

Answer:

slope = 0

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, - 2 ) and (x₂, y₂ ) = (5, - 2 )

m = [tex]\frac{-2-(-2)}{5-3}[/tex] = [tex]\frac{-2+2}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0

In triangle abc, i the circumcenter bc i equal to 72cm d i equal to 15cm then the radiu of the circumcircle is 39

A chord is the line segment joining two points of the circumference of a circle as shown in the image attached.

If the chord is passing through the center of the circle then it will become diameter which means the diameter is the longest possible chord inside a circle.

A chord is always within the circumference because it is inside the circle.

Whats the definition of a circumference?

a line that goes around or encloses a circle. : the outer boundary of a figure or area. 3. : the distance around something. the circumference of the earth at the equator.

since ABC is an equilateral triangle

therefore SD bisects BC

BD= BC/2

BD= 36

IN Triangle ABC

since angle BDS = 90 degree

Therefore

BS = 39

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The factory can make 744 quarts of ice cream per day.

To find out how many quarts of ice cream could be made in 48 hours, we can use the principle of proportionality. Since the factory makes 310 quarts of ice cream in 10 hours, we can set up a proportion:

310 quarts / 10 hours = x quarts / 48 hours

To solve for x, we can cross multiply:

310 quarts * 48 hours = 10 hours * x quarts

x = (310 quarts * 48 hours) / 10 hours = 1480 quarts

So the factory could make 1480 quarts of ice cream in 48 hours.

To find the rate per day, we need to divide the number of quarts made per hour by the number of hours in a day. Since there are 24 hours in a day, we can calculate the rate per day as:

rate per day = (310 quarts / 10 hours) * 24 hours = (31 quarts/hour) * 24 hours = 744 quarts/day

So the factory can make 744 quarts of ice cream per day.

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The response to the given domain range questions is [go f oh]. (9) = 5(18^2 - 1 )

Domain and range. A function's authorised range of values is known as its domain. The x values in a function like f make up this set (x). A function's range is the collection of values that it can take as input. When we enter an x value, the function outputs this set of values.

f(x) = x^5 – 1, g(x) = 5x^2, and h(x) = 2x

[g o f o h](9)=g(f(h(9))

Let's find h(9) first

h(x)= 2x

h(9)= 2(9) =18

Now plug in 18 for h(9)

[g o f o h](9)=g(f(h(9)) = g(f(18))

now we find f(18)

f(x) = x^5 – 1, f(18)= 18^5 -1

Now we plug in 18^5 -1 for f(18)

[g o f o h](9)=g(f(h(9)) = g(18^5 -1)

Plug it in g(x)

g(x)= 5x^2

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On solving the provided question, we can say that - the value of the cube root is 19683 =  27

In mathematics, y3 = x since the cube root of a number x equals a number y. Each non-zero real integer has precisely one real cube root, one set of complex conjugate cube roots, and three different complex cube roots. When a number is multiplied three times, the result is the cube root of that number. Three cube roots, the final cube root, is the symbol for the cube root. The opposite of cubing an integer is finding the cube root of that number. Prime factorization is a fairly straightforward technique that may be used to get a number's cube root. The sign stands for a cube root.

here,

we have f(27)

cube will be [tex]( 27 )^3[/tex] = 19683

and f(-343) = -7

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Kaj bought 3 bananas and 5 apples.

From these three pieces of information, we can set up the following two equations:

We can substitute the third equation into the first equation and get:

y+2 + y = 8

So we know that y = 3

Now we can substitute this value into the second equation and get:

x + 0.5(3) = 8

So we know that x = 5

So Kaj bought 3 bananas and 5 apples.

And also we can substitute y = 3 into the third equation and get:

x = y + 2

So we know that x = 5

So Kaj bought 3 bananas and 5 apples.

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Following is the graph of two given equations.

The mapping of functions of two variables onto a Cartesian coordinate system, which is made up of a horizontal x-axis, or abscissa, and a vertical y-axis, or ordinate, is done analytically through the use of graphs. The intersection of each axis, which is a real number line, at its zero point is known as the origin.

On solving the two equations,

2x-3y=-6                              ....(1)

7x-3y=9                               .....(2)

Firstly we will find common points by elimination -

The common points are - (3,4)

Then We can find all the values of equation (1)

2x-3y=-6                          

x    0      3    -3

y    2      4     0

7x-3y=9

x    0      3    10

y   -3      4    20.33

The respective graph is attached below

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Area of quadrilateral is 24 units and it is known as parallelogram.

A point in the plane is one-to-one connected to an ordered pair of real numbers (x, y) using point plotting. The 2-dimensional Cartesian coordinate system is as a result obtained.

A parallelogram results from plotting the four points.

the lower side is between (-6,-3) and (-2,-3)

0 to 3 is at the top (4,3)

As a result, the base length is 4 because the distance

between (-6,-3) and (-2,-3) = 4

the separation between (0,3) and (4,3)

The sides are the lines that connect (0,3) to (-6,-3)

along with (4,3) to (-2,-3).

Vertical height ranges from -3 to 3 or 6.

The parallelogram's area is given by base*height = 4(6) = 24.

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The rate exists water being poured into the cup when the water level is 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].

To determine the derivative of a composite function in differential calculus, apply the chain rule formula. If y = f(g(x)), then according to the chain rule, the instantaneous rates of change of the functions f and g with respect to x produce the instantaneous rate of change of f with respect to x.

A composition of functions, such as the composition of the functions f and g, f(g(x)), can be used to determine the derivative using the chain rule.

Let us set up the following variables:

R, Radius of conical cup (cm) = 30 cm

H, Height of the conical cup (cm) = 10 cm

Our aim is to find dV/dt when h = 9 and we are given dh/dt = 2

By similar triangles we have

r : h = R : H

r/h = 30/10

⇒ r = 3h

The volume of a cone is 1/3π r²h, So:

V = 1/3π r²h

simplifying the equation, we get

= 1/3π (3h²)h

= 1/3π 9h²h

= 3π h³

Differentiating wrt h we get:

dV/dh = 9π h²

Applying the chain rule we have:

dV/dt = (dV/dh)(dh/dt)

= 9π h² × 2

= 18π h²

If h = 9 then

[tex]$\left[\frac{d V}{d t}\right]_{h=9}=18 \pi\left(9^2\right)=1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].

Therefore, the rate exists water being poured into the cup when the water level 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].

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The length of the straw is 3.74 inches.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

In rectangular box,

Length (l) = 2 inches

Width (w) = 1 inches

Height (h) = 3 inches

Here, The straw is said to fit into the box diagonally from the bottom.

So, the length (s) of the straw is calculated as:

⇒ s = √ l² + w² + h²

⇒ s = √ 2² + 1² + 3²

⇒ s = √ 4 + 1 + 9

⇒ s = √ 14

⇒ s = 3.74 inches

Thus, The length of straw = 3.74 inches

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The length of the straw will be 3.7416  inches long in radical form.

If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula : X²=l²+b²+h²

Here,

As per the question the length of the straw is equal to length of the diagonal of Rectangular box.

l= 3 inch , b= 2 inch , h= 1 inch

Let us consider the length of the straw be 'x'.

As, Diagonal of Cuboid is,

X²=14

X=√14

i.e. X=3.7416

We get, X= 3.7416 (in radical form)

Hence, the length of the straw will be  5.91607 inches.

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Answer:

absolute deviation means distance between each data value and the mean of the data set.

Step-by-step explanation:

(MAD)

or

(Average)

x² + 14x + 49, this is a perfect square trinomial, which is expressed as

(x + 7)².

Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."

An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.

A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.

Given that,

x² + 14x + 49

(x)² + 2(7x) + 49

= (x)² + 2(x)(7) + 7²

This is similar to a² + 2ab + b² = (a + b)²

so, we can write:

= (x + 7)²

= (x +7) (x + 7)

so, this is a perfect square trinomial.

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The solution of given triangle is 32°.

Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, and a scalene triangle is one in which none of its sides are equal.

Given,

∠BAC=52°

since, ΔBAC is isosceles triangle hence opposite angle will be equal.

∠BAC+∠ABC+∠ACB=180°

2∠BCA=180°-52°

∠BCA=128/2

∠BCA=64°

also,

∠BCA+∠DCA=180°

∠ACD=180°-64°

∠ACD=116°

since,

ΔACD is isosceles triangle, hence opposite angle is equal

∠ACD+∠CAD∠ADC=180°

2∠CAD=180°-116°

∠CAD=64/2

∠CAD=32°

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the main three types of trigonometry are ,

1- sine angle (sin Q)

2- cosine angle (cos Q)

3- tangent angle (tan Q)

all the other types of trigonometry are related to these three types only.

sine angle

we can find out the sine angle by taking perpendicular of the triangle divided by hypotenuse of the triangle. sine angle is a acute angle.

cosine angle

we can find out the cosine angle by taking base of the triangle divided by hypotenuse of the triangle. cosine angle is a acute angle.

tangent angle

we can find out the sine angle by taking perpendicular of the triangle divided by base of the triangle.

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