Simplify the expression (8y-10x+18)+(6y+12x-2)

Answer:

slope = - \(\frac{7}{5}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, 4 ) and (x₂, y₂ ) = (8, - 3 )

m = \(\frac{-3-4}{8-3}\) = \(\frac{-7}{5}\) = - \(\frac{7}{5}\)

Answer: 1720

Step-by-step explanation:

The constant term in the binomial expansion of [-3x⁷+ (-2/x)]⁴⁸ is ⁴⁸C₆(3)⁶(-2)⁴² = 3.93446261119 × 10²²

Binomial expansion is the expansion of the trerms of a binomial of the form (a + b)ⁿ = ∑ⁿCₓaˣbⁿ⁻ˣ.

Since we want to find the constant term in the binomial expansion of [-3x⁷+ (-2/x)]⁴⁸, comparing [-3x⁷+ (-2/x)]⁴⁸ with the binomial expansion above, we see that

So, we have that

[-3x⁷+ (-2/x)]⁴⁸ =  ∑⁴⁸Cₓ(3x⁷)ˣ(-2/x)⁴⁸⁻ˣ

= ∑⁴⁸Cₓ(3)ˣx⁷ˣ(-2)⁴⁸⁻ˣ (1/x)⁴⁸⁻ˣ

= ∑⁴⁸Cₓ(3)ˣ(-2)⁴⁸⁻ˣx⁷ˣ(x)ˣ ⁻⁴⁸

= ∑⁴⁸Cₓ(3)ˣ(-2)⁴⁸⁻ˣx⁸ˣ⁻⁴⁸

So, the nth term is ⁴⁸Cₓ(3)ˣ(-2)⁴⁸⁻ˣx⁸ˣ⁻⁴⁸  (1)

For the constant term, we have that the power of x is zero.

So, 8x - 48 = 0

8x = 48

x = 48/8

x = 6

So, substituting x = 6 into the nth term, we have

⁴⁸Cₓ(3)ˣ(-2)⁴⁸⁻ˣx⁸ˣ⁻⁴⁸ = ⁴⁸C₆(3)⁶(-2)⁴⁸⁻⁶x⁸ˣ ⁶⁻⁴⁸

= ⁴⁸C₆(3)⁶(-2)⁴²x⁴⁸⁻⁴⁸

= ⁴⁸C₆(3)⁶(-2)⁴²x⁰

= ⁴⁸C₆(3)⁶(-2)⁴²

= 12271512 × 729 × 4.3980465111 × 10¹²

= 3.93446261119 × 10²²

The constant term is ⁴⁸C₆(3)⁶(-2)⁴² = 3.93446261119 × 10²²

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Answer:

\(\Delta s_{T} = 4712.4\,m\)

Step-by-step explanation:

(This exercise is written in Spanish and for this reason the response will be presented in such language).

La distancia recorrida por la mulita tras una vuelta es:

\(\Delta s = 2\pi\cdot (5\,m)\)

\(\Delta s \approx 31.416\,m\)

Ahora, la distancia recorrida total es directamente proporcional a la cantidad de vueltas invertidas. Este indicador se determina por regla de tres simple:

\(\Delta s_{T} = \frac{150}{1}\times (31.416\,m)\)

\(\Delta s_{T} = 4712.4\,m\)

Answer:

63

Step-by-step explanation:

fhj v

If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be \($x=-\frac{2}{3}, x=-\frac{5}{2}$$\).

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.

Area of rectangle = length × breadth

= (3x +2) × (4x +10)

simplifying the above equation, we get

= (3x) × (4x +10) + 2(4x +10)

= 12x² + 30x +8x +20

12x² + 38x + 20 = 0

simplifying the above equation, we get

By using quadratic equation, then

\($x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$\)

simplifying the above equation, we get

\($$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$\)

Separate the solutions, we get

\($$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$\)

The solutions to the quadratic equation are:

\($x=-\frac{2}{3}, x=-\frac{5}{2}$$\)

The complete question is:

Find the area of rectangle with length (3x+2) units and width (4x+10)units.

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x² - 12x + 5 = 0

(x - 6)² - 31 = 0

(x - 6)² = 31

x - 6 = ±√31

x = 6 ± √31

Answer:

p = 2×h + 3

Step-by-step explanation:

for every hour in class she writes 2 pages.

so, the total number of pages written is 2 times the number of hours in class.

and she had already a starting "offset", a head start if you will, of 3 pages.

so, even if she spends 0 hours in class, she has these 3 pages no matter what.

hence the "+ 3" part.

Given:

To find the binomial that is a factor of the polynomial:

By factor theorem,

If f(a) = 0, then the binomial (x - a) is a factor of polynomial f(x).

So, let us check the options one by one.

A) Put x = -7 in the given polynomial.

Since, f(-7)=0

Therefore, (x+7) is a factor.

Thus, the correct option is A.

Answer:

A. AB = AC because of the definition of an isosceles triangle

B. ∠B = ∠C because corresponding parts of congruent triangles are congruent.

D. BM = CM because of the definition of a midpoint

Step-by-step explanation:

A. An isosceles triangle is a triangle with two equal sides, hence:

AB = AC because of the definition of an isosceles triangle. option A is correct.

D. Since Point M is drawn as the midpoint of BC, hence:

BM = CM because of the definition of a midpoint. Option D is correct.

E. Reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself. hence AM ≈ AM because of reflexive property.

AM ≈ AM because of the Symmetric Property is wrong. Option E is wrong.

C) The side - side - side (SSS) triangle congruence theorem states that if all the sides of two triangles are equal, then they are congruent triangles.

Since BM = CM, AM = AM and AB = AC, hence ΔABM = ΔACM because of the SSS triangle congruence criterion

ΔABM = ΔACM because of the SAS triangle congruence criterion is wrong. Option C is wrong.

D. Corresponding parts of congruent triangles are congruent. hence:

∠B = ∠C because corresponding parts of congruent triangles are congruent. Option B is correct

First,

The area of the shape with the points (5,6), (11,3), (11,-3), (4,-3), (5,3), (1,3) is 54 square units.

It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).

We have ordered double pairs of a shape:

(5,6), (11,3), (11,-3), (4,-3), (5,3), (1,3)

First, label all the points in the coordinate plane.

We get a polygon.

To find the area of the shape, we can use the formula:

\(\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|\)

After plugging all the points in the coordinate plane:

We get:

Area of the shape = 54 square units

Thus, the area of the shape with the points (5,6), (11,3), (11,-3), (4,-3), (5,3), (1,3) is 54 square units.

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We have the segment BC, M is the midpoint

M (4,5)=(xm,ym)

B(0.9) =(x1,y1)

C(x,y)=(x2,y2)

We have the next formula

xm=4

x1=0

x2=x

we substitute the values

we isolate x

the for the coordinate y

we have

ym=5

y1=9

y2=y

we substitute the values

then we isolate the y

the coordinate of C is (8,1)

So expressing the given complex solution x = (- 6 ± √(-432))/6 as x = a ± bi we can write that x = -1 ± 2√3i and the values of a and b are -1 and 2√3 respectively.

Given that the standard form of writing a complex solution is,

x = a ± bi, where a and b are the real numbers and i = √(-1)

Given that one of this type of solution is,

x = (- 6 ± √(-432))/6

x = -6/6 ± √(-432)/6, differentiate denominators with each numerator

x = -1 ± √((-1)*144*3)/6

x = -1 ± 12√3i/6

x = -1 ± 2√3i

Comparing with x = a ± bi we get, a = -1 and b = 2√3.

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According to trigonometry, the ground distance covered by the plane is approximately 478.7 feet, rounded to the nearest tenth.

What is trigonometry?

The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations.

The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations.

There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc).

The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.

To draw a diagram of the situation:

\(tan(28°) = opposite / adjacent\\tan(28^{0}) = 250 / x\\x = 250 / tan(28^{0})\\ x= 478.7 ft\)

Therefore, the ground distance covered by the plane is approximately 478.7 feet, rounded to the nearest tenth.

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Your answer is 0.00004650297619

Answer:

hope it helps

stay safe healthy and happy.

Step-by-step explanation:

f(2) = 4(2) - 2

= 8 - 2

= 6

g(f(2)) = g(6)

g(6) = 5(6) - 3

= 30 - 3

= 27

g(f(2)) = 27

Answer:

Step-by-step explanation:

Answer:

\(r=4.38\)

Step-by-step explanation:

Step 1: Arrange the equation so that you are calculating rate (divide both sides by t)

\(\frac{d}{t} = \frac{rt}{t}\)

\(t\) cancels out on the right side.

Step 2: Substitute in the numerals

\(r=\frac{d}{t}\)

\(r=\frac{5.7}{1.3}\)

Step 3: Divide

\(r=4.38\) \(mph\)

There's your answer!

Hope this helps you!

a. The graph represents a proportional relationship.

b. The graph does not represent a proportional relationship.

c. The graph does not represent a proportional relationship.

d. The graph represents a proportional relationship.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable exists.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero presented as follows:

y = kx.

Hence graphs a and d represent proportional relationship, as they have intercepts at the origin.

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Answer:

A. cd4

Step-by-step explanation:

The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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Step-by-step explanation:

green = surface area

volume = 9/5 × 2/3

= 18/15

= 6/5 = 1.2 or 1 1/5

On factoring the polynomial 6z² + 6z the values for length and width are obtained as 6z and z + 1.

What is a polynomial?

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

We can factor the polynomial 6z² + 6z by taking out the greatest common factor, which is 6z -

6z² + 6z = 6z(z + 1)

This means that the area of the wall is equal to 6z(z + 1) square meters. Since the area of a rectangle is given by the product of its length and width, we can write -

6z(z + 1) = length × width

Therefore, the possible expressions for the length and width of the wall are -

length = 6z

width = z + 1

or

length = z + 1

width = 6z

Both of these expressions give a product of 6z(z + 1), which is equal to the area of the wall.

We can switch the roles of length and width, so there are two possible expressions for the dimensions of the wall.

Therefore, the length is 6z and width is z + 1.

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Answer:

7.447 × 10(to the power of 6.)

Step-by-step explanation:

Answer:

7.447 × 106

Step-by-step explanation:

ye

Answer:

n(t) = 11e^0.019t

Step-by-step explanation:

The estimated population in 2010 = 11,000,000 = initial population

The growth rate = 1.9% per year = 1.9/100 =

The exponential growth model follows the general form :

n(t) = ae^rt

a = Initial population ; r = growth rate ; t = period

Hence, we have ;

n(t) = 11e^0.019t in millions

Answer:

  a) x = 1 ± (3/7)√7

  b) (-∞, -5) ∪ [-2, 5) ∪ [6, ∞)

Step-by-step explanation:

You want solutions to the relations ...

We like to solve these in the form f(x) = 0. It helps avoid extraneous solutions.

  \(7+\dfrac{1}{x} -\dfrac{1}{x-2}=0\\\\\\\dfrac{7x+1}{x}-\dfrac{1}{x-2}=0\\\\\\\dfrac{(7x+1)(x-2)-x}{x(x-2)}=0\\\\\\ \dfrac{7x^2-14x-2}{x(x-2)}=0\)

The roots of the numerator quadratic are found by ...

  x² -2x -2/7 = 0 . . . . . divide by 7

  x² -2x +1 -9/7 = 0 . . . . add and subtract 1

  (x -1)² = 9/7 . . . . . . . . . . write as a square, add 9/7

  x -1 = ±√(9·7/49) = ±(3/7)√7 . . . . take the square root

  x = 1 ± (3/7)√7

Rational inequalities are best solved by identifying the roots of numerator and denominator. These tell you where the function changes sign. The end behavior of the rational function tells you what the signs are changing from.

  \(\dfrac{x^2-4x-12}{x^2-25}\ge 0\\\\\\\dfrac{(x+2)(x-6)}{(x+5)(x-5)}\ge0\)

This has a horizontal asymptote at y=1 for |x|→∞. It has vertical asymptotes at x=±5.

The sign changes occur at x ∈ {-5, -2, 5, 6}. The rational expression is positive (approaching +1) for x < -5 and for x > 6. It is negative in the adjacent intervals, so positive again for -2 < x < 5.

The inequality is satisfied for ...