Tom’ cell phone plan ha a monthly fee of $105, which include unlimited free text meage and phone call and 4GB of data. Each extra gigabyte of data, or part thereof, cot $12. A. Find the cot of a month in which Tom ued 7. 1GB of data b. If x repreent the number of gigabyte ued, expre the monthly charge c(x) of thi plan a a piecewie function

The lengths of the unknown sides that are marked with a variable are;

a. x = 24

   y = 10

b. x = 5

When on comparing the corresponding sides of two or more triangles, they are said to be similar if they have some common properties.

To find the lengths of the unknown sides that are marked with a variable, we have;

a. To determine the value of y,

21/ y = 15/ 21

cross multiply to have

15y = 21 * 21

     = 441

y = 441/ 15

  = 29.4

y = 24

ii. To determine the value of x,

25/ (25 + x) = 15/ 21

cross multiply

15(25 + x) = 25 * 21

375 + 15x = 525

15x = 525 - 375

      = 150

x = 150/ 15

 x = 10

b. 5/ 6 = 4.2/ x

6*4.2 = 5x

25.2 = 5x

x = 25.2/ 5

  = 5.04

x = 5.0

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The solution of the expression   12 + [2 - (4 × a²)] ÷ 7 + b with the given values of a and b (using BODMAS) is -1 .

Given,

Equation is :     12 + [2 - (4 × a²)] ÷ 7 + b

Values of a and b are; 5 and 1 respectively

Substitute the values of a and b into the equation

12 + [2 - (4 × 5²)] ÷ 7 + 1

Using BODMAS :

solve the expression that is in the bracket first :

⇒ 12 + [2 - 100] ÷ 7 + 1

⇒ 12 + [-98] ÷ 7 + 1

Solve the division next :

⇒ 12 - 14 + 1

Solve the addition next :

⇒ 13 - 14

Solve the subtraction next :

⇒ -1

Therefore, the solution of the expression with the given values of a and b is - 1

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Sublimation is the straight transition from a solid state of materials to a vapor state upon heating (without becoming liquid).

When a substance changes from one state to another, as as from a solid to a gas, this transition, transformation, or conversion is referred to as sublimation.

Sublimation is the procedure through which a material is converted from its solid to gaseous phase without moving to its liquid form. At a temperature and pressure below the substance's triple point, this process, an endothermic phase transition, takes place. The opposite of this process, in which a gas is transformed straight into a solid state, is desublimation or deposition.

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Answer:

the correct answer would be "the team that installs the new pools" and "the employees who clean and maintain pools" are services provided by this business to its customers, as they are actively performing tasks for the customer related to swimming pools.

O pool cleaning is a service that is provided by this business to its customers.

The correct option is C. The team that installs the new pools.

Business-to-consumer (B2C) refers to the process of selling goods and services directly between an organization and the customers who will ultimately use them. The majority of businesses that sell directly to customers are referred to as B2C businesses.

The correct answer would be "the team that installs the new pools" and "the employees who clean and maintain pools" are services provided by this business to its customers, as they are actively performing tasks for the customer related to swimming pools. Pool cleaning is a service that is provided by this business to its customers.

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Let P and Q represent the intersections of two triangle sides. Consequently, the third side's length is divided in half by the length of the section that connects P and Q.

Vega is attempting to prove that the segment joining the midpoints of two sides of a triangle is equal to half the length of the third side. To do this, she must first identify the two midpoints of any given triangle. Let P and Q be the midpoints of two sides of the triangle. She must then demonstrate that the segment connecting P and Q is equal to half the length of the third side. To do this, Vega must calculate the distance between P and Q and then compare it to the length of the third side. If the two measurements are equal, then Vega will have proven her point. This statement can be rephrased as "the length of the segment connecting P and Q is equal to half the length of the third side."

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19.6x -2.1y + 13 is a simplified form of the 18.4x - 2.1y +9.6 - (-1.2x) + 3.4 equation.

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

Given expression 18.4x - 2.1y +9.6 - (-1.2x) + 3.4

Simplifying using PEMDAS

=> 18.4x - 2.1y +9.6 - (-1.2x) + 3.4

First, we will open the bracket

=> 18.4x - 2.1y +9.6 + 1.2x + 3.4

Calculating the like terms

=> 19.6x -2.1y + 13

Therefore, a simplified form of the given equation is  19.6x -2.1y + 13.

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To simplify a polynomial, we have to do two things:

1) combine like terms, and

2) rearrange the terms so that they're written in descending order of exponent.

In order to combine like terms, we must first determine which terms can be added to or subtracted from one another. The same variable (with the same exponent) is always associated with like expressions. For instance, adding one "x-squared" to two "x-squareds" results in three "x-squareds," but adding one "x-squared" to a "x" is impossible because the two words are unrelated.

An algebraic expression that displays the sum of monomials is called a polynomial. Since "mono" signifies "one" in the prefix, a monomial is a singular element or phrase. 'Poly' is a prefix that means'many. Thus, an expression that has numerous terms is said to be polynomial. The relationships between the terms may be sums or differences.

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The equation 2x + 3y = 16 has infinitely many solutions.

We know that a linear equation in two variables is of the form ax + by + c = 0, where a, b, c are non-zero real numbers.

Here we have been given a linear equation in two variables 2x + 3y = 16

We solve this equation for x,

Consider 2x + 3y = 16

2x + 3y - 3y = 16 - 3y            .........(subtract 3y from each side of equation)

2x/2 = (16 - 3y)/2                   .........(divide each side by 2)

x = (16 - 3y)/2

for any real value of y we can find value of x.

This means, an equation 2x + 3y = 16 has infintely many solutions.

For x = 0,

2(0) + 3y = 16

y = 16/3

y = 5.333

This means, the y-intercept of line 2x + 3y = 16 is (0, 5.333)

For y = 0 ,

2x + 3(0) = 16

x = 16/2

x = 8

This means, the x-intercept of line 2x + 3y = 16 is (8, 0)

The graph of 2x + 3y = 16 is shown below.

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The complete question is:

How many solutions does the equation 2x + 3y = 16 have?.

Answer: 8 yd

Step-by-step explanation:

12 - 4 = 8

u can see that the side below the side x is "side x + 4" so if we substract 12-4 we get 8

Answer:

Zero Angle (0° in Measure), Acute Angle (0 to 90° in Measure), Right Angle (90° in Measure), Obtuse Angle (90 to 180° in Measure), Straight Angle (180° in Measure), Reflex Angle (180 to 360° in Measure), and Complete Angle (360° in Measure)

Step-by-step explanation:

Answer: A. -3

A1. -2

A2. -6

Step-by-step explanation:

The expression -3x^2 - 24x - 36 can be factored into the form (ax + b)(cx + d) by using the technique of grouping or by using the factoring by grouping method.

The factored form of -3x^2 - 24x - 36 is

( -3x - 6)( x + 6)

So the answer is:

A. -3

A1. -2

A2. -6

Answer:

Sandra has 34 classmates.

Step-by-step explanation:

Answer:

The number of students in Sandra's class is 34.

Step-by-step explanation:

Step 1: Let x be the number of students in Sandra's class.

Step 2: We know that Sandra has at least 10 toffees left after giving some toffees away to her classmates. This means that:

x + 10 <= 44

Step 3: We can simplify the inequality in step 2 as:

x <= 44 - 10

x <= 34

Step 4: This means that the number of students in Sandra's class is 34 or fewer.

Step 5: The number of students in her class is the number of toffees Sandra gives away, so we can set up an equation:

x = 44 - 10

Step 6: Solving the equation in step 5 gives:

x = 34

hope it helps you

Step-by-step explanation:

hope it helped you

The equation that is equivalent is

-x/4 + 3/4 = 12

Option D is the correct a nswer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

The equation for Negative one-fourth (x) + three-fourths = 12 is,

(-1/4)x + (3/4) = 12 _____(1)

Now,

-4x + 3/4 = 12

This is not equivalent to (1).

-1(x/4) + 3/4 = 12

This is not equivalent to (1).

-x + 3/4 = 12

This is not equivalent to (1).

1/4 (x + 3) = 12

(1/4)x + 3/4 = 12

This is not equivalent to (1).

-x/4 + 3/4 = 12

This is equivalent to (1).

Thus,

The equation that is equivalent is

-x/4 + 3/4 = 12

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The shortcut method of dividing a polynomial by a linear polynomial by using only the coefficients of the terms of the polynomial is called synthetic division.

Synthetic division is a simplified method of dividing a polynomial by a linear polynomial. It is used to divide a polynomial by a linear polynomial that is of the form x-c, where c is a constant. The synthetic division method is based on dividing the polynomial by the linear polynomial by using the coefficients of the terms of the polynomial.

The quotient and the remainder of the division are obtained by performing a few simple arithmetic operations. It is a quick and efficient way to divide polynomials and is particularly useful when dividing polynomials with large degrees

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Answer:

Domain is  [-1, 3]

Range is [1, 2]

================================

Explanation:

The domain is the set of allowed input values. It's the set of all possible x coordinates of the points shown.

The left-most point is when x = -1, while the right-most point is at x = 3.

We can say [tex]-1 \le \text{x} \le 3[/tex] meaning x is between -1 and 3, including both endpoints.

That compound inequality translates to the interval notation [-1, 3]

Square brackets are used to include the endpoints.

-----------------

The range handles the set of possible y outputs.

The lowest we can go on the graph is y = 1, and the highest is y = 2

Therefore we arrive at [tex]1 \le \text{y} \le 2[/tex] which translates to [1, 2]

So, the mass of a teaspoon of sugar in milligrams is 4200 milligrams.

A teaspoon of sugar has a mass of 4.2 grams. To convert this mass to milligrams, we can use the conversion factor of 1 gram = 1000 milligrams. This means that for every gram, there are 1000 milligrams. To convert a value in grams to milligrams, we simply multiply the value in grams by 1000.

So to convert the mass of 4.2 grams to milligrams, we can use the following calculation:

4.2 grams * 1000 milligrams/gram = 4200 milligrams

Therefore, the mass of a teaspoon of sugar in milligrams is 4200 milligrams. This is because 4.2 grams is equivalent to 4200 milligrams. The conversion factor of 1 gram = 1000 milligrams is used to convert the value of 4.2 grams to 4200 milligrams.

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The y-intercept is (0,9)

The y-intercept of a linear equation in the form of y = mx + b is represented by the constant term, b. In this case, the y-intercept is 9. This means that the line represented by this equation crosses the y-axis at the point (0, 9).

To find the y-intercept, we can substitute x = 0 into the equation, y = 10x + 9 and we get:

y = 10(0) + 9

y = 9

So the y-intercept is (0,9)

A linear equation is an equation that can be written in the form of y = mx + b, where m is the slope (or rate of change) and b is the y-intercept (the point where the line crosses the y-axis).

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answer

Step-by-step explanation:

they two are in a straight line so

it can be added

or, 3x+2+6x-20=180[straight angle]

or, 9x-18=180

or, 9x=180+18

or, 9x=198

or, x=198÷9

or, x=22

the value of x is 22

The range of a number collection in mathematics is the difference between its highest and lowest values.

By dividing the greatest number by the lowest value, the range is computed. The difference between a group of numbers' highest and lowest values is regarded as the range.

Subtract the distribution's lowest number from its greatest number to calculate it. The function's range is the resolution. f(x) is [0,∞] and its domain f(x)=|x-1| is R.

The space between the greatest and smallest data points in a set of numerical information is termed the range. The average of the greatest and smallest data points is intermediate.

The minimum value from the maximum value from the supplied set of observations must always be subtracted in order to establish the range. The range between the maximum and least frequencies is regarded as the range.

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The percentage change in the amount of sugar used is 38.8%

Sugar used the previous week = 42. 5 pounds

Sugar used this week = 26 pounds

Calculating the difference between two amounts of sugar -

Sugar used the previous week - Sugar used this week

= 42.5 - 26

= 16.5 pounds.

To calculate the change in percentage, the differential amount is to be multiplied by 100 to express the result as a percentage, which is required to determine the percent change in the amount of sugar utilised.

Calculating the per cent change -

Differential sugar amount / Sugar used in previous week x 100

= 16.5 / 42.5 x 100

= 38.8%.

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No, an isosceles triangle is not always 90 degrees

Two of a triangle's sides must be the same length for the triangle to be considered isosceles. The third side, which is not equally long as the first two, is referred to as the base. The angle at the vertex opposite to the base is obtuse, acute, or right angle and the angles at the vertex opposite to the base are congruent.

Not all angles in an isosceles triangle are 90 degrees. A triangle with equal-length sides is called an isosceles triangle, although the angles at the vertex opposite the equal sides might be of any degree. The isosceles right triangle, the golden triangle, the faces of bipyramids, and some Catalan solids are all examples of isosceles triangles.

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Answer:

The grand pacer test stated that the percentage of the core would be 50%

SThe range of tep-by-step explanation:

The width of the flag is 640 ft and the length is 1040 ft

To calculate this we can take the width of the flag can be represented as "w" and the length as "l".

From the information given, we know:

l = w + 400 (because the length is 400 ft greater than the width)

2 * (w + l) = 2080 (because the perimeter is 2,080 ft)

We can substitute the first equation into the second equation to get:

2 * (w + w + 400) = 2080

2w + 800 = 2080

2w = 1280

w = 640

Therefore, the width of the flag is 640 ft and the length is 1040 ft (since l = w + 400)

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Answer:5

Step-by-step explanation:

Answer:

+ (5x + 9y = -5)

Step-by-step explanation:

+ (2x + 5y = -9)

+ ( 3x + 4y =  4)

+ (5x + 9y = -5)

Quadratic equation x² + 6 · x - 27 = 0 contains roots x₁ = - 9 and x₂ = 3.

In this question we find the case of a quadratic equation of the form x² + b · x + c = 0, whose roots are x₁ = - 9 and x₂ = 3, respectively. A value of x is a roots when x² + b · x + c = 0. Then, we proceed to find the values of the two coefficients.

First, write the resulting system of linear equations:

- 9 · b + c = - 81

3 · b + c = - 9

Second, use numerical methods to find the values of the coefficients:

(b, c) = (6, - 27)

Third, write the resulting quadratic equation:

x² + 6 · x - 27 = 0

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Answer:4682.830393

Step-by-step explanation: