Find the product of (3a²bc³ )(5a³b4c²)

If two parallel lines have slopes of m(1) and m(2), and if it is known that both lines are perpendicular, then we get m(1) = m(2).

The slope of parallel lines is the same. Since all of the parallel lines are similarly inclined with respect to the positive x-axis, their slopes are also identical. When two parallel lines' slopes are written as m(1), m(2), we get m(1) = m(2).

Equal coefficients for x and y are present in the equations that represent parallel lines. ax + by + c(2) = 0 is the line parallel to ax + by + c(1) = 0. According to observation, the coefficients of x and y in both equations are equivalent.

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Answer:

The lowest comman multiple of 54 and 240 is 6.

Answer:

6

Step-by-step explanation:

Since 54= 2x3x3x3 and 240=2x2x2x2x3x5, the LCM is 2x3=6

The length of FG = (7/18) x 2π(√(28π))/(√140).

Length is a measurement of a distance, size, or quantity. It is usually measured in units such as meters, feet, or miles, but can also refer to an amount of time. Length is a fundamental concept in mathematics and is used for a variety of purposes in the natural and social sciences. In physics, length is related to energy, momentum, and the speed of light. In geometry, length is a measure of the distance between two points on a line or plane. Length also plays an important role in everyday life, from measuring the size of a room to calculating the time it takes to get from one place to another.

Let G be the center of the circle and the radius be ‘r’.

The arc length FG = (140/360) x 2πr = (7/18) x 2πr

Area of sector = (1/2) x r² x θ = 14π

Therefore, r² θ = 28π

Therefore, r² = (28π)/θ

Substituting the value of θ = 140° in the above equation,

r² = (28π)/140

Therefore, radius, r = (√(28π))/(√140)

Therefore, length of FG = (7/18) x 2πr = (7/18) x 2π(√(28π))/(√140)

Hence, the length of FG = (7/18) x 2π(√(28π))/(√140).

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Mile/minute unit rate is represents the faster car.

A common unit of measurement is the mile (mi). It is typically used it to represent the distance among cities, the length of rivers, and the distance between roadways. The letter "mi" stands for the unit mile in writing. Therefore, a marathon race would be roughly 26.3 mile or 26.3 mi in length.

How are miles measured?

Any point on the map that's not a location's name or emblem should be touched and held.

Count the distance between two points.

The total mileage in mile and km is shown at the bottom (km).

You can add several points, as a tip.

Tap Undo to take away the most recent addition you made. Tap More in the top right corner to erase every point. Clear.

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Distance 10(miles) Which unit rate represents the faster car? Time(minutes)

While the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it .

Due to its three sides and three vertices, a triangle is a polygon. One of the fundamental geometric forms, it. Triangle ABC is the designation given to a triangle with vertices A, B, and C. In Euclidean geometry, when the three points are not collinear, a distinct plane and triangle are found. As a polygon, a triangle has three sides and three corners. The places where the three sides converge are referred to as the triangle's corners. Combining three triangle angles yields a result of 180 degrees.

given

While the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it, the interior angles of a triangle always add up to 180°.

By deducting the angle of the target vertex from 180°, one can also determine a triangle's exterior angle. In a triangle with three angles of 30°, 60°, and 90°, the hypotenuse is twice as long as the shorter leg and three times as long as the latter.

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The best explanation is, 2.The result will always be the same because a solution obtained by graphing is always located on a grid line

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Solving a system of linear equations by graphing will result in the same solution as solving by substitution as graphing answer is always found on a grid line, hence the outcome will always be the same.

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Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is a unifying thread of almost all of mathematics and includes everything from solving elementary equations to studying abstractions such as groups, rings, and fields.

In more formal terms, algebra is the study of mathematical structures that consist of a set of elements and one or more operations defined on those elements, satisfying a set of axioms. These structures include groups, rings, fields, and vector spaces. Algebra also includes the study of algorithms for solving equations and constructing new mathematical objects from given ones.

With the use of mathematical expressions, algebra is the area of mathematics that helps to depict situations or problems. We employ integers that have a fixed or definite value in algebra, such as 2, 7, 0.068, etc. In addition to using numbers, algebra also makes use of variables like x, y, and z.

A meaningful mathematical expression is created by combining mathematical operations such as multiplication, division, addition, and subtraction.

Algebraic calculations usually make use of additional signs and symbols.

Less than (>), greater than (>), equal to (=), not equal to (), less than (>), and equal to (>) are all acceptable terms.

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The slope of function f is - 1 and the y-intercept of f is 4.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Let Two points on the function f are (-1, 5) and (0, 4).

Now,

Since, The equation of line passes through the points (-1, 5) and (0, 4).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - 5) / (0 - (-1))

m = - 1 / 1

m = - 1

Thus, The equation of line with slope - 1 is,

⇒ y - 5 = -1 (x - (-1))

⇒ y - 5 = - 1 (x + 1)

⇒ y = - x - 1 + 5

⇒ y = - x + 4

By comparing with the equation of line y = mx + b, we get;

The y-intercept of f = 4

And, The slope = - 1

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Therefore , the solution of the given problem of linear equation is  x's coefficient is -9.9,x's coefficient is 75  and  y's coefficient is 275.

A model of linear regression is one that applies the formula y=mx+b. B is the slope, and m is the y-intercept. Ignoring the fact that while both y and y are distinct components, the previous sentence is frequently referred as a "mathematical formula with two variables." Bivariate linear equations only have two variables. The application domains of linear equations have zero solutions in all cases.

Here,

Given :

=>0.8 (2x + x) + 3(7 - 4.1x) = __x + 21

=>0.8(3x) + 21 - 12.3x = __x + 21

=>2.4x + 21 - 12.3x = __x + 21

=>-9.9x + 21 = __x + 21

=> -9.9

=> 12 1/2 (6x + 22y) = x + y

=> 75x + 275y = x + y

Therefore , the solution of the given problem of linear equation is  x's coefficient is -9.9,x's coefficient is 75  and  y's coefficient is 275.

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Answer: 0.33

Step-by-step explanation:

You get 0.33 repeating

Answer:

1/3

Step-by-step explanation:

0.5 divided by 1.5 can also be written as 1/2 divided by 3/2.

So lets rewrite it like this:

(1/2)/(3/2)

From here there are two ways we can solve this. One is to multiply by the reciprocal:

(1/2) × (2/3)= 2/6

which simplifies to 1/3 as your final answer.

The other method is to "oreja"

you multiply the top most number and the bottom most number together and then the two middle ones like so:

(1/2)/(3/2) -> (1×2)/(2×3)

which is 2/6 once again and simplifies to 1/3 the final answer.

The total surface area of the rectangular prism in square centimeters is c) 160 cm².

The surface area of a cuboid is the total area of all of the faces of a prism.

If, the length (l), width (w), and height (h) of the prism

then, use the formula: surface area (SA)=2lw+2lh+2hw.

here, we have,

The formula for the Surface Area of a rectangular prism is,

A=2(wl + hl + hw)

given that,

Length = 10cm

Width = 5cm

Height = 2cm

Hence:

Area =2× (5 × 10 + 2 × 10 + 2 × 5) cm²

       = 2 × ( 50 + 20 + 10) cm²

       = 2 × (80) cm²

       = 160 cm²

The total surface area of the rectangular prism in square centimeters is 160.

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Answer:  C = - 2

Step-by-step explanation: Subtract 3c from 4c.

Answer:

/_A+/_C

48°+63°=101°

180°-101°=79°

/_ B=79°

Answer:

C. x(x-7)(x+5)

Step-by-step explanation:

Check the picture below.

The value of x is 6 and the length of each diagonals is 41 units.

In the given question, we have to find the value of x and the length of each diagonal.

The given length of rectangle LMNP is:

LN=4x+17...............(1)

MP=8x-7...............(2)

As given the question,

MP = LN

8x-7 = 4x+17

Add 7 on both side. we get

8x = 4x + 24

Subtract 4x on both side, we get

4x = 24

Divide by 4 on both side, we get

x = 6

Now putting the value of x in the value of LN and MP

LN = 4(6) + 17

LN = 24 + 17

LN = 41 units

MP = 8(6) - 7

MP = 48 - 7

MP = 41 units

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The volume of the prism attached in the figure is calculated to be

A. 9/4 cubic cm

The prism is formed by cubes having a dimension of 1/2 of a centimeter

Using this dimension it can be deduced from the figure that the

the width has 2 units = 2 * 1/2 = 1 cm

the length has 3 units = 3 * 1/2 = 1.5 cm

the height has 3 units = 3 * 1/2 = 1.5 cm

volume of a prism is solved by the formula

= length * width * height

= 1.5 * 1 * 1.5

= 9/4 cubic cm

the volume of the prism is 9/4 cubic units

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Answer: 9

6/8 = 9/12

The value of AC and BC are AC = 6.58 and BC = 2.39.

What is trigonometric ratio?

The trigonometric functions in mathematics are real functions that relate the angle of a right-angled triangle to the ratios of the lengths of the two sides. All geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many others, use them extensively.

From the given diagram we have to find the value of BC and AC.

First to find the value of AC.

Consider, the trigonometric ratio

    sinθ = [tex]\frac{AC}{AB}[/tex]

sin(70°) = AC / 7

      AC = sin(70°)*7

     AC = 6.58

Now to find the value of BC.

Consider, the trigonometric ratio

cos(70°) = BC / AB

cos(70°) = BC / 7

       BC = cos(70°)*7

       BC = 2.39

Hence, the value of AC and BC are AC = 6.58 and BC = 2.39.

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The domain of the graphed function is:

D: x ≥ 2

For a function y = f(x), we define the domain as the possible inputs, this is, the possible values of x.

To find the domain, we need to look at the horizontal axis, we can see that the minimum is the leftmost value, which is (2, 3), and it is marked with a  colored dot, so the value x = 2 belongs to the domain.

Then, the line extends to the right side, so the domain is the set of all real values larger than x = 2

The domain is:

D: x ≥ 2

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The area of the rug is 1,440 square inches and the sum of partial product is always equal to the area, 1440 square inches.

The area of the rug using the formula:

length x width = area.

The area of the rug is:

32 inches x 45 inches = 1440 square inches.

Refer figure for Erin and Frannie's design. Consider Erin's design

green = 30×5 = 150

red = 2×5 = 10

blue = 2×40 = 80

yellow = 30×40 = 1200

total area = green + red + blue + yellow

= 150 + 10 + 80 + 1200

= 1,440

Now consider Frannie's design

red = 5×1 = 5

blue = 35×1 = 35

green = 5×30 = 150

yellow = 35×30 = 1050

total area = 4red + 2blue + 2green + yellow

= 4×5 + 2×35 + 2×150 + 1050

= 20 + 70 + 300 + 1050

= 1,440

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The roots of the equation √3x²+10x +7√3 = 0 are -7/√3 or -3.

Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The general form of the quadratic equation is:  ax² + bx + c = 0,

where x is an unknown variable and a, b, c are numerical coefficients.

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics.

Given that,

√3x²+10x +7√3 = 0

=> √3x²+3x+7x +7√3 = 0

=> √3(x+√3) +7(x+√3) = 0

=> √3 +7 = 0 or x+√3 = 0

x = -7/√3 or -3 are the two roots of the equation.

Thus, The roots of the equation √3x²+10x +7√3 = 0 are -7/√3 or -3.

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The process of gathering similar phrases and adding them is known as addition of algebraic expressions. To determine the final expression for the above problems, locate, add, and sum the coefficients of similar terms.

3a + 2a - 5b - 3c, 5a + 7b - 6c + b + 2c, and 2c + b.

6c + 2c - 3c. 5a - 3a + 2a + 7b + b.

4a + 3b – 7c.

5a + 7b – 6c, - 3a + b + 2c, 2a - 5b - 3c

+ 5a + 7b - 6c - 3a + b + 2c + 2a - 5b - 3c

4a + 3b – 7c

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Answer:

Step-by-step explanation:

145

Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.

Now, According to the question :

What is Vertical line?

A vertical line is a line, parallel to y-axis and goes straight, up and down, in a coordinate plane. Whereas the horizontal line is parallel to x-axis and goes straight, left and right.

Is a vertical line positive or negative?

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Hence, Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.

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The number after rounding off the given decimal number is

20283.

Rounding means making a number simpler but keeping its value close to what it's original value. The result is less accurate, but easier to use.

Given is the decimal number as -

20282.93

The given number is -

20282.93

20282.9           {3 < 5}

20283              {9 > 5}

Therefore, the number after rounding off the given decimal number is

20283.

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Answer: 3/y

Step-by-step explanation:

Answer:

3/

Step-by-step explanation:

15x/15xy

cancel x on the numerator with x in denominator then divide 15 by 5 to get 3 as numerator and y as denominator.

Based on the values in the table represent a linear function, the common difference of the associated arithmetic sequence is 15.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ = a₁ + (n - 1)d

Where:

Based on the information provided in the given table, we can calculate the common difference by subtracting the first term from the second term as follows;

Common difference, d = a₂ - a₁ = a₃ - a₂

Common difference, d = 23 - 8 = 38 - 23

Common difference, d = 15.

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