Ash and Bea are engravers. Ash charges a flat fee of $\$1.50$ for the first $21$ letters engraved, and $8$ cents per letter thereafter. Bea charges a flat fee of $\$1.60$ for the first $15$ letters engraved, and $7$ cents per letter thereafter. For what nonzero number of letters will Ash and Bea's engraving prices be the same?

The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the sides of a right-angled triangle relate to one another. Pythagorean triples are another name for the sides of the right triangle. Here, examples help to demonstrate the formula and proof of this theorem.

In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulae.

In order to determine sin a without using the Pythagorean theorem, we will need to have the value of the opposite side and angle. Sin (a) = opposite / hypotenuseHere, the hypotenuse is not given, so we will need to have the value of the opposite side and angle (a) in order to determine sin a without using the Pythagorean theorem.

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required equation is, y=3x-37.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Here, given that,

we have to find,

the equation of a line that passes through the point (7,-16) with slope 3.

we know,

y = mx+c

i.e. -16 = 3*7+c

so, c= -37

hence, required equation is, y=3x-37.

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Answer: 18

Step-by-step explanation:

Answer: 18.04347826086957

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

The examples for each of the quadrant is explained below.

Quadrant in math is defined as one of the four regions or sections of the coordinate system and the quadrants are separated by the x-axis and the y-axis and these axes are perpendicular to each other.

Here we have to know the value that must be placed on each quadrant.

Here the first quadrant has both x and y-coordinates are positive.

The second quadrant has the value of the x-coordinate is negative and the y-coordinate is positive.

The third quadrant has both x and y-coordinates are negative.

The fourth quadrant has the value of the x-coordinate is positive and the y-coordinate is negative.

Therefore, the example for each of them are written as

=> Quadrant I = (1, 1)

=> Quadrant II = (-1, 1)

=> Quadrant III = (-1, -1)

=> Quadrant IV = (1, -1)

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To make the sum X 3x² x 1, you must add -5x³ -2x² -6x -7 to 5x³ 2x² 6x 7.

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three (as terms) is said to be an expression. It is to be noted that, unlike the algebraic equation, an algebraic expression has no sides or equal to sign.

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Based on the table, an equation of the linear relationship in slope-intercept form include the following: A. y = 2x − 8

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Next, we would determine the slope of the data points in this table as follows;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (-6 - (-8))/(1 - 0)

Slope, m = 2/1

Slope, m = 2.

At point (0, -8), an equation of this line can be calculated in slope-intercept form as follows:

Note: The y-intercept is equal to -8.

y = mx + c

y = 2x + (-8)

y = 2x - 8.

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Answer:

A. y = 2x − 8

Step-by-step explanation:

The solution of the inequality is x < 7 and x >= -2.

What is linear inequality?

An inequality is a mathematical statement comparing two values or expressions, usually involving one of the following relational operators: < (less than), > (greater than), <= (less than or equal to), >= (greater than or equal to), or != (not equal to). The solution to inequality is a set of values that make the inequality true.

To solve the inequality -10 < -2x + 4 ≤ 8, we have to solve the inequality twice because of the less than or equal to symbol and greater than or equal to symbol.

First we have to solve -10 < -2x + 4

-2x + 4 > -10

-2x > -14

x < 7

Second, we have to solve -2x + 4 <= 8

-2x + 4 <= 8

-2x <= 4

x >= -2

Hence, the solution of the inequality is x < 7 and x >= -2. This solution is represented by all the values of x that are less than 7 and greater than or equal to -2.

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A line which is confined between two endpoints is known as a line segment. In other words, we can say that a line segment is a portion of a line that is connected by two points.

The length of the line segment does not vary and the distance between them does not change. The units in which a line can be calculated in centimetres, millimetres, meters, inches, or feet.

The difference between a line segment and a line is that the line segment had two endpoints while the line extends indefinitely. When only one side of the line has an endpoint, it is called a ray or a half-open line segment.

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The number of adult tickets purchased is 12.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Let no. of adult = x

No. of children = 28 -x

So, 7. 25 * x + (28 - x) *4. 50  = 159

⇒2.75x +126=159

⇒2.75x =33

⇒x=33/2.75

x=12

Hence, the number of adult tickets purchased is 12.

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In linear equation, 35 feet per minute is the rate of descent per minute.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.        

                         Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

It’s 35 feet per minute. 175 divided by 5 equals 35.

   A submarine descends =  175 ft

                   Time = 5 minutes

         The rate of descent is constant = 175/5

                                             = 35 feet per minute

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The equation that best represents the line on the first graph is

5x + 3y = 3

Option C is the correct answer.

The equation that best represents the line on the second graph is

x - y = -7

Option A is the correct answer.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Pick two coordinates that the line passes through in each graph.

First graph:

(0, 1) and (-3, 6)

m = (6 - 1)/ (-3 - 0) = 5/-3 = -5/3

(0, 1) = (x, y)

1 = (-5/3)0 + c

c = 1

Now,

y = (-5/3)x + 1

3y = -5x + 3

5x + 3y = 3

Second graph:

(0, 7) and (-5, 2)

m = (2 - 7) / (-5 - 0) = -5/-5 = 1

(0, 7) = (x, y)

7 = 1 x 0 + c

c = 7
y = x + 7

x - y = -7

Thus,

The equation of the first graph is 5x + 3y = 3.

The equation of the second graph is x - y = -7.

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Yes, polynomial Y^4+4Y^2+5 has zeroes. Its zeroes can be found by factoring or using the quadratic formula: Y = -2 +/- sqrt(4-5) / 2 = -1 +/- sqrt(-1) / 2 = -1 +/- i/2.

[tex]Y^4+4Y^2+5[/tex]

=[tex](Y^2+1)²-3[/tex]

=([tex]\sqrt{Y^2+1-sqrt3}[/tex])([tex]\sqrt{Y^2+1+sqrt3}[/tex])

=(Y+ sqrt3)(Y-sqrt3)(Y+1)(Y-1)

=(Y+ sqrt3)(Y-sqrt3)(Y²-1)

=(Y+ sqrt3)(Y-sqrt3)(Y-1)(Y+1)

=0

Therefore the zeroes are Y=-√3, Y=1, Y=√3, Y=-1

Polynomial Y^4+4Y^2+5 is a fourth degree polynomial equation and can be solved by factoring or using the quadratic formula. To solve this equation by factoring, we need to use the difference of squares method. First, we rewrite the equation as (Y^2+1)²-3. Then we factor out the square of the binomial (Y^2+1): (Y^2+1-sqrt3)(Y^2+1+sqrt3). Next, we expand the first binomial to get (Y+ sqrt3)(Y-sqrt3)(Y+1)(Y-1). Then, we factor out the second binomial from the first two terms to get (Y+ sqrt3)(Y-sqrt3)(Y²-1). Finally, we expand the last binomial to get (Y+ sqrt3)(Y-sqrt3)(Y-1)(Y+1). This results in a product of zero, which means the equation has zeroes. The zeroes are Y=-√3, Y=1, Y=√3, and Y=-1.

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Therefore , the solution of the given problem of linear equation comes out to be x= -6 , y = 45 and z =60.

The algebraic equation y=mx+b stands in for a linear equation. The slope is m, and B is the y-intercept. The last phrase referred to a "simple formula with two elements" where both y and x are variables. Bivariate linear equations are calculations involving two variables. Here are a few examples: The outcomes are 2x - 3 = 0; 2y = 8; m + 1 = 0; x/2 = 3; x + y = 2; and 3x - y + z = 3. If the answer to a mathematical equation is in the form y=mx+b, where m denotes the slope and b the y-intercept, the equation is said to be linear.

Here,

Given :

According to parallelogram laws

adjacent side sum is 180 degree

=> 4y + 3x-18 = 180

=> 4y+3x = 162

and

2x+12+3z = 180

=> 2x + 3z = 168

and

=> 3x+3z = 162

=> x + z =54

=> z = 54-x

So,

2x + 3(54-x) = 168

=> 162 - 3x+2x =168

=> -x = 6

or x =-6

and

z = 60

and

y = 162 - 3x /4

=> y= 162 +18 /4

=> y =180/4

=> y = 45

Therefore , the solution of the given problem of linear equation comes out to be x= -6 , y = 45 and z =60.

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The six-foot long ladder is 3√5 feet high up the wall having 3 feet distance from bottom of the ladder.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the ladder is the hypotenuse, and the wall and the ground make up the other two sides.

The ladder is 6 feet long, and the bottom of the ladder is 3 feet away from the wall, so the triangle is a 3-4-5 right triangle, which means the wall is 3 feet high.

So, if we square the length of the ladder (6^2 = 36)

The length of the base (3^2 = 9),

and add them together, then take the square root of that, we get the height of the wall.

sqrt(36+9) = sqrt(45) = 3*sqrt(5)

so the ladder is 3√5 feet high up the wall.

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To do Maths fast follow the steps:

Mathematical subjects include quantities and their changes, forms and the spaces in which they are contained, formulae and associated structures, and numbers.

The scientific study of numbers, forms, and their meanings is known as mathematics. The majority of individuals use maths every day to measure and count. Geometry, algebra, and calculus are all forms of mathematics; nonetheless, they are typically referred to as single.

There are many ways to solve math problems, but a three-step technique is a streamlined approach that may assist anybody in solving even the most challenging issue.

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Answer:

6 tubes of lip balm

Step-by-step explanation:

We can start solving this problem by isolating the variable x.

Given the equation 1.5x + 2.5y = 9, and we know that y = 0 (because we're not buying any bottles of hand sanitizer), we can substitute this into the equation:

1.5x + 2.5(0) = 9

Simplifying this, we get:

1.5x = 9

To solve for x, we can divide both sides of the equation by 1.5:

x = 9/1.5

x = 6

So we can buy 6 tubes of lip balm if we do not buy any bottles of hand sanitizer

Solving for X in a Right Triangle

Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees. Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X

Answer:

a：20 km

b：384

Step-by-step explanation:

a：

[tex] \frac{2.5}{ 8} = \frac{1}{x} [/tex]

[tex]x = 20[/tex]

b：

[tex] \frac{2.5}{8} = \frac{120}{y} [/tex]

[tex]y = 384[/tex]

Answer:

There would be 312 acres of old tree growth for 0.4% of the forest. There would be 31.2 acres of old tree growth for 0.04%. I wasn't sure if you meant 0.4 or 0.04.

The numerical coefficient in 3xy is 3.

In algebraic expressions, terms are made up of coefficients and variables. A coefficient is a numerical value that multiplies a variable or a set of variables. In the term 3xy, the numerical coefficient is the number that appears in front of the variable (x and y) and it's 3 in this case.

It is used to indicate the degree of the term or the number of times the variable is present in the term. In this case, it is indicating that the variable x and y are present three times in the term.

It's important to note that if there is no coefficient before the variable, it is assumed to be 1. It's also noteworthy that the coefficient can be a whole number, a fraction, or even a variable, but in this case it is a whole number. Understanding the concept of coefficient is very important in understanding algebraic equations and expressions.

The numerical coefficient in 3xy is 3.

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In 7/25 households, electricity is used for heating. By multiplying by 20,000. You'll receive 3,360. In light of this, the 2000 census indicates that 3,360 out of 12,000 houses use electricity for heating.

Because we've already done it 7 out of every 25 residences are heated by electricity, according to the 2000 U.S. census.At this rate, we must determine how many residences in a 12000-person neighbourhood would be heated by electricity.Let x be the number of homes in a neighbourhood that would be heated by electricity.There being a direct variation

The result is that , A neighbourhood of 12000 people with 3360 dwellings that use electricity for heating. In 7/25 households, electricity is used for heating. By multiplying by 20,000. You'll receive 3,360. According to the 2000 Census, 3,360 dwellings out of 12,000 are heated by electricity.

[tex]$\frac{7}{25}=\frac{x}{12000}$[/tex]

[tex]$x={7 \times 12000}/{25}$$x=3360$[/tex]

As a result, 3360 households out of the 12000 in the community use electricity for heating.

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Answer: $120

Step-by-step explanation:

So you find 1/3 of 180, basically, you multiply them which is 60.

So if he has a third of the money, he has $60, but he needs 180. So we subtract $180 (how much money he needs) from $60 (the money he has). Which is 120 dollars, so the boy needs $120.

Or 2/3 more.

Each video game = $19 and each DVD = $ 32

An equation is a mathematical statement that represent that two expressions are equal. An equation can be formed by one or more variables along with numerical terms.

let, x denotes the cost of each video games.

y denotes the cost of each DVD

Katie bought 2 games and 3 DVD and total spent $134.

the equation can be written as 2x + 3y = $134 .......equation 1

Emily bought 1 less video game than Katie that means she bought 1 game.

 and    2 more DVD than Katie that means 5 DVD bought by Emily.

total spent of Emily = $179

The equation will be x + 5y = $179...... equation 2

in order to solve the two equations by addition method

we multiply by 2 to the second equation.

2x + 10y = 358

the first equation 2x +3y = 134

                             2x + 10y = 358

                            -       -          -

                    by subtracting we get,

                         - 7y = -224

                         y = 32

from the 2nd equation we get x = -5×32 + 179

                                       x = 19

each video game cost $ 19 and each DVD cost $ 32

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The displacement of the pizza delivery driver for the full journey is therefore 6.08 miles.

The pizza delivery driver's displacement for the entire trip is the total distance and direction that she travels from the restaurant to her last delivery and back.

To find her displacement, we can use the Pythagorean theorem to find the total distance from the start to the endpoint.

The displacement is the distance between the start and end point and the direction of the trip. Here we can see that she traveled 4 miles north, 6 miles east, and 5 miles south,

To find the displacement we will use the Pythagorean theorem (ax2 + bx2 = cx2)

where c is the displacement and a and b are the east-west and north-south distances respectively.

so, a = 6 miles (east-west)

b = (4 miles - 5 miles) = -1 miles (north-south)

so, c = √(ax2 + bx2)

c = √(6x2 + (-1)x2)

c = √(36 + 1)

c = √(37)

c = 6.08 miles

So the pizza delivery driver's displacement for the entire trip is 6.08 miles.

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The domain of a function is the set of all input values (x-values) for which the function produces a valid output (y-value). In this case, the function f(x) = (x+2)(x+6) is defined for all real numbers, so the domain is all real numbers.

What do a function example's range and domain mean?

A straightforward function, such as f(x) = x2, can have a domain (what goes in) of just the counting numbers 1, 2, 3, etc., and a range (what comes out) of the set 1, 4, 9, etc. Another function, g(x) = x2, may have an integer domain of..., -3, -2, -1, 0... 1, 2, 3, and its range is..., 1, 4, 9,...

The range of a function is the set of all possible output values (y-values) produced by the function. The function f(x) = (x+2)(x+6) is a polynomial, and all polynomials of the form (ax^2 + bx + c) with real coefficients (a,b,c) have range is all real numbers. The range of the function f(x) = (x+2)(x+6) is also all real numbers.

So the answer is

The domain is all real numbers, and the range is all

real numbers.

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Therefore , the solution of the given problem of equation comes out to be  each diagonal measures 8.4 units in length..

An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.

Here,

Given: 16x + 2 = 36x - 6

8 = 20x

x = 8/20,

simplifying to 2/5, or 0.4

You would set the two equations equal to one another and find x because a rectangle's diagonals are congruent.

Re-enter the value of x into a single of the equations.

=>16(0.4) + 2

=>6.4 + 2

=>8.4

To make sure, confirm with the other diagonal.

=>36(0.4) - 6

=>14.4 - 6

=>8.4

Each diagonal measures 8.4 units in length..

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The complete question is "To find the diagonal  x value by the given equation  16x + 2 = 36x - 6 "

The correct statement regarding the comparison of the linear functions f(x) and the graphed function is given as follows:

A. The function ƒ(x) = 4x + 2 has a greater rate of change than the graphed function.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The function f(x) is given as follows:

f(x) = 4x + 2.

The parameters are given as follows:

For the function g(x), we have that:

Hence the correct option is given by option a, as the function f(x) has a greater rate of change, of 4, compared to the graphed function, of 2.

The graphed function is given by the image presented at the end of the answer.

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Answer: To find the area of the pre-image and the image, you can use the coordinates of the vertices of the shapes to calculate the lengths of the sides and use the formula for the area of a triangle:

Area = (base * height)/2

For the pre-image, the coordinates are X(3,18) Y(18,18) and Z(18,9). The base of the triangle is the distance between X and Z, which is 18 - 3 = 15. The height of the triangle is the distance between Y and Z, which is 18 - 9 = 9. The area of the pre-image is therefore:

Area = (15 * 9)/2 = 67.5

For the image, the coordinates are X’(1,6) Y’(6,6) Z’ (6,3). The base of the triangle is the distance between X’ and Z’, which is 6 - 1 = 5. The height of the triangle is the distance between Y’ and Z’, which is 6 - 3 = 3. The area of the image is therefore:

Area = (5 * 3)/2 = 7.5

The relationship between the two areas is that the area of the image is smaller than the area of the pre-image. This is because the image has been scaled down in size relative to the pre-image. The amount by which the image has been scaled down can be calculated by dividing the area of the image by the area of the pre-image:

Scale factor = area of image / area of pre-image = 7.5 / 67.5 = 0.11

This means that the image has been scaled down by a factor of 0.11 relative to the pre-image.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to know the areas and their relationship of the preimage with coordinates X(3,18), Y(18,18), and Z(18,9), and the image with coordinates X’(1,6), Y’(6,6), Z’ (6,3).

When you plot the points on a graph, you see they define right triangles. Each has sides aligned with the x- and y-axes, so it is easy to find their dimensions by counting grid squares or subtracting coordinates.

The preimage triangle is 18-3 = 15 units in the x-direction, and 18-9 = 9 units in the y-direction.

The image triangle is 6-1 = 5 units in the x-direction, and 6-3 = 3 units in the y-direction.

We notice that both the coordinates and the dimensions of the image triangle are 1/3 those of the preimage triangle.

The area of each triangle is given by the formula ...

  A = 1/2bh

Using the dimensions we found above, the areas are ...

  preimage area: 1/2(15)(9) = 135/2 = 67.5 . . . . square units

  image area: 1/2(5)(3) = 15/2 = 7.5 . . . . square units

We have observed that the image dimensions are 1/3 those of the preimage. The image area is 7.5/67.5 = 1/9 of that of the preimage. This value is the square of the scale factor of the dimensions,

A verbal expression for the given algebraic expression are as follows:

10. The product of a and b

11. Four times the sum of x and seven

12. Twice the value of x

13. The cube of m

14. The difference between x and six

15. Eight hundred twelve

16. The value of y

17. The average of x and y

18. Three times x minus four

19. Five times the difference of a and b

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