Solve the following:-
[tex]\sf a-2 = -5[/tex]

The base value of a numeral system can be founded by counting the number of unique digits or symbols used in the system.

The base value of a numeral system can be determined by counting the number of unique digits or symbols used in the system. For example, in the base 10 numeral system, which is commonly used in everyday life, the base value is 10 because it uses the digits 0 through 9. In the base 2 numeral system, which is also known as binary, the base value is 2 because it only uses the digits 0 and 1.

Another way to find the base value is to look at the exponent of the highest power of the base in the numeral system. For example, in the number 42 in base 10, the highest power of 10 is 10¹, which is 10. Therefore, the base value is 10. Similarly, in the number 1010 in binary, the highest power of 2 is 2³, which is 8. Therefore, the base value is 2.

It's important to note that when working with different numeral systems, it is essential to know the base value in order to understand the value of the number being represented.

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The value of the given expression, 5 3/5 + 7 1/10 - 2 2/3, is 10 1/3

From the question, we are to simplify the given expression.

The given expression is

5 3/5 + 7 1/10 - 2 2/3

To solve the given expression, we would convert each of the fractions to an improper fraction

Convert the fractions to improper fractions

28/5 + 71/10 - 8/3

Find the LCM of the denominators

LCM of the denominators = 30

Thus,

(168 + 213 - 80) / 30

301/30

10 1/3

Hence, the simplified form of the expression 10 1/3

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When a number is four greater than its quotient and 6 plus 8 is 18, the number is 18.

You can multiply, divide, add, or take something away in mathematics. An expression is put together as follows: Expression, numeric value, and math operator A mathematical expression is composed of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Contrasting phrases and expressions is possible. An algebraic expression is any mathematical statement that has variables, numbers, and an arithmetic operation. As an illustration, the phrase 4m + 5 consists of the terms 4m and 5, as well as the given equation's variable m, all of which are separated by the arithmetic sign +.

given

A number's n/6 quotient and six (n/6) + 5 five greater than the quotient

(n/6) + 5 = 8

(n/6) + 3 (n/6)

= 18

When a number is four greater than its quotient and 6 plus 8 is 18, the number is 18.

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The finance charge on a $6,500 loan with an interest rate of 9.5% compounded monthly over 36 months is $208.21.

The finance charge on a $6,500 loan with an interest rate of 9.5% compounded monthly over 36 months can be calculated using the formula:

Finance Charge = Principal Amount * Interest Rate * Number of Months

Finance Charge = $6,500 * 9.5% * 36

Finance Charge = $208.21

Therefore, the finance charge on a $6,500 loan with an interest rate of 9.5% compounded monthly over 36 months is $208.21.

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Answer:

s+7

Step-by-step explanation:

The solution to the equation is x = -2.

A system of linear equations can be solved graphically, by substitution, elimination, and by the use of matrices.

The system of equations is given as:

y = x² + 10x + 11

y = x² + x − 7

Equate both equations and we get,

⇒ x² + 10x + 11 = x² + x - 7

Subtract x² from both sides

⇒ 10x + 11 = x - 7

Collect like terms

⇒ 10x - x = -11 - 7

Evaluate the difference and we get

⇒ 9x = -18

Divide both sides by 9

∴x = -2

Hence, the solution to the equation is x = -2.

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When 60 of your favorite songs are purchased from a website for $0.97 apiece, the total cost comes to $58.80.

The unit technique is a method of problem-solving where you first calculate the value of a single unit, then multiply that value to get the answer. Simply expressed, a single unit value is extracted from a specified multiple using the unit method. For instance, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and reciprocal are equivalent. (Linear Algebra, Mathematical Analysis, Mathematics of Matrix or Operators)

given

This straightforward real-world issue can be resolved by by multiplying the number of tracks by the $0.98 per song price.

60 x 0.98 = $ 58.80

When 60 of your favorite songs are purchased from a website for $0.97 apiece, the total cost comes to $58.80.

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The value of x in the given 45-45-90 triangle is 9.89.

The given triangle is a right-angled triangle which can be solved using the Pythagoras theorem. The Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the square of the base and the square of the perpendicular. This theorem can be applied to all right-angled triangles.

In the given triangle, we have been told that the length of both legs is 7. Now, after applying the theorem -

= 7²+7² = H²

= 49 + 49 = H²

= 98 = H²

= √98 = H

= 9.89 = H

Hence, this is the value of x.

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Answer:

12b+3=-2b-4

14b=-7

b=-1/2

Confirm?

-2(-1/2)-4 =-3

12(-1/2)+3=-3

the formula for a circular diameter is 2r ( 2 times radius)

so 2*1=2

If A(0, 3) and B(2,6) be the two points then the equation of the line is y = 1.5x + 3.

A line is a straight, thickness-free, one-dimensional object in geometry that extends indefinitely in both directions.

An object that extends without end in both directions is referred to as a line. Arrowheads are typically used to depict it to demonstrate how it never ends. A line segment is an area within a line that has two end points. Half of a line with one end point makes up a ray. Angle is formed by two rays that have the same terminal point.

Let A(0, 3) this point is the y-intercept of the line B(2,6)

The equation of the line into slope intercept form is equal to y = mx + b

where, m is the slope

b is the y-coordinate of the y-intercept = 3

Find the slope of the line m

The formula to calculate the slope between two points is equal to [tex]$m=\frac{y_ 2-y_ 1}{x _2-x _1}$[/tex]

substitute the values

m = (6 - 3)/(2 - 0)

simplifying the equation, we get

m = 3/2

m = 1.5

The equation of the line is y = 1.5x + 3.

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The average daily cost of Aaron of driving his car to work is $5.1169.

Average cost is calculated by dividing the total cost by the total output quantity.

Miles for a round trip for 1 day = 10.5 miles

Since it is round trip, total miles for 1 day = 10.5 × 2 = 21 miles

Miles for a round trip for 22 days = 21 × 22 = 462 miles

Gallons for 15 miles = 1 gallon

Gallons for 1 mile = 1/15 gallons

Gallons for 462 miles = 30.8 gallons

Cost per gallon = $1.09

Cost for 30.8 gallons = 30.8 × 1.09 = $33.572

Payment for car parking = $79

Total cost per month = $33.572 + $79 = $112.572

Average daily cost = $112.572 / 22 = $5.1169

Hence the average cost per day is $5.1169.

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Answer:

-27+17r

Step-by-step explanation:

[tex]3 + 4(r - 6) = 3(2 + 2r) + 7r \\ 3 + 4r - 24 = 6 + 6r + 7r \\ 3 - 6 - 24 + 4r + 6r + 7r \\ - 27 + 17r[/tex]

Answer:

  2.5 or 3.5

Step-by-step explanation:

You have an x-cm square and a rectangle ℓ cm by 3 cm. Together, they have a total perimeter of 32 cm. You want the length ℓ and the area S in terms of x, and you want to know the values of x that make the area be 30.25 cm².

The length of the wire is 32 cm. This is the sum of the perimeters of the square and the rectangle.

  P = 4s +2(l+w)

  32 = 4x + 2(ℓ +3) . . . . . . . . substitute given values

Solving the equation for ℓ, we have ...

  16 = 2x +ℓ +3 . . . . . . . . . divide by 2

  ℓ = 13 -2x . . . . . . . . . . . subtract 3+2x

The total area of the two figures is the sum of the area of the square and that of the rectangle:

  S = x² +3ℓ

  S = x² +3(13 -2x) . . . . . . substitute for ℓ

  S = x² -6x +39 . . . . . . . simplify

For an area of 30.25 cm, we require ...

  30.25 = x² -6x +39

  -8.75 = x² -6x . . . . . . . . . . subtract 39

  0.25 = x² -6x +9 . . . . . . . complete the square

  ±0.5 = x -3 . . . . . . . . . . . . take the square root

  x = 3 ± 0.5 = {2.5, 3.5}

The total area is 30.25 cm² for x = 2.5 or x = 3.5.

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Answer: No, x^2 and 2x are not like terms. Like terms are terms that have the same variable raised to the same exponent. In this case, x^2 and 2x have the same variable, but they are raised to different exponents, so they are not like terms.

Terms can be added or subtracted together, but terms that are not like terms cannot be combined.

For example:

5x^2 and 2x^2 are like terms, so they can be added together (5x^2 + 2x^2 = 7x^2)

5x and 2x are like terms, so they can be added together (5x + 2x = 7x)

On the other hand:

5x^2 and 2x are not like terms, so they cannot be added together.

Step-by-step explanation:

The amount of interest that Rafa earns in one year, given the amount in the savings account and the interest is $ 238. 65 .

The amount earned by Rafa in one year can be found by the formula :

= Amount in savings account x Interest per year

Amount in savings account = $ 6, 450

Interest per year = 3. 7 %

The amount earned by Rafa for the year is therefore :

= 6, 450 x 3. 7 %

= $ 238. 65

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The solutions to both sets of simultaneous equations by graphical method are; No solution

There are three main ways to solve simultaneous linear equations and they are;

1) Elimination method

2) Substitution method

3) Graphical Method

In this question, we are using the graphical method where the solution will be the coordinate of the point of intersection.

1) The 2 simultaneous linear equations are;

y = ¹/₂x + 1

-2x + 4y = 4

The graph of these 2 equations is as attached.

From the first graph attached, we see that both lines overlap each other and as such don't have any point of intersection which tells us there is no solution to the simultaneous linear equations

2) The 2 simultaneous linear equations are;

y = -x - 3

y + x = 2

The graph of these 2 equations is as attached.

From the second graph attached, we see that both lines don't intersect each other and as such don't have any point of intersection which tells us there is no solution to the simultaneous linear equations

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Answer:

c=9.20

Step-by-step explanation:

SOH CAH TOA

Use cos because it deals with the adjacent angle and the hypotenuse, which is all that we have here.

cos (61 degrees) = c/19

plug in cos(61) degrees into your calculator to get .484

.484 = c/19

Multiply both sides by 19 to isolate c by itself.

9.20 = c

The fraction is evaluated to give -114/10

A fraction can be defined as the part of a whole variable, number or element.

There are some number of types of fractions, they include;

From the information, we have that;

12/3+3/4÷(−1/3)−1/2

These are a mixed of proper fractions and improper fractions

Now, expand the bracket, we have

12/3 + 3/4 ÷ -1/3 -1/2

Find the lowest common multiple

48 + 9 /12 ÷ -2 - 3 /6

Add or subtract the values

57/12  ÷ -5/6

Multiply by taking the inverse

57/12 × 6/-5

114/-10

Hence, the value is 114/-10

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Answer:

He will get 16 bottles if he buys 2 packs and he will need 4 more to get 20.

Step-by-step explanation:

He buys 2 packs of 8 2x8=16 if he wants all 20 he will need to get 3 packs 3x8=24. 20-16=4 he will need 2.5 packs to get the amount he wants. 2.5x8=20

The pair in the solution of the equation -2x + 3y = 6 is (0,2).

The set of all values that, when substituted for unknowns, make an equation true is known as the solution.

A specific location on the graph is the solution of a linear equation in two variables, where ax+by = c, meaning that when the x-coordinate is multiplied by a and the y-coordinate is multiplied by b, the sum of these two values equals c. There are essentially an endless number of solutions to a linear equation with two variables.

Now in the question,

To find the pair of solutions of the equation -2x + 3y = 6, we satisfy all the pairs one by one in the given equation

1. Putting the value of (x, y) as (-3,4) in the equation we get-

-2*-3 +3*4 = 6 ⇒ 18 = 6

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

2. Putting the value of (x, y) as (3,-4) in the equation we get-

-2*3 + 3*-4 = 6 ⇒ -18 = 6

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

3. Putting the value of (x, y) as (0,2) in the equation we get-

-2*0 + 3*2 = 6 ⇒ 6 = 6

Therefore LHS = RHS

Hence it is the solution to the equation.

4. Putting the value of (x, y) as (3,0) in the equation we get-

-2*3 + 3*0 = 6 ⇒ -6 =6

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

Thus (0,2) is the solution of the equation.

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a straight line perpendicular to the y-axis, which means that the range is a set of one value  {y|y =4}

What is the domain and range?

Domain and Range.  The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The domain of x=4 is (−∞,∞) and range is {y|y=4} .

(−∞,∞)

{x|x ∈ R}

y=4

is a straight line perpendicular to the y-axis, which means that the range is a set of one value  {y|y =4}

Set-Builder Notation:{y|y =4}.

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The end behavior of the graph of f(x) = x^5 + 8x^4 + 16x^3 is that it increases without bound as x approaches positive and negative infinity.

The end behavior of the graph of f(x) = x^5 + 8x^4 + 16x^3 can be determined by examining the degree and leading coefficient of the polynomial. The degree of the polynomial is 5, which indicates that the graph increases without bound as x approaches positive and negative infinity. The leading coefficient of the polynomial is 1, which indicates that the graph increases as x approaches positive and negative infinity.

To illustrate this, let's consider the value of f(x) for increasingly large values of x. For x = 10, f(x) = 10^5 + 8(10^4) + 16(10^3) = 1,000,000 + 80,000 + 160,000 = 1,240,000. As x continues to increase, the value of f(x) continues to increase without bound as the terms of the polynomial become increasingly larger.

Similarly, for x = -10, f(x) = (-10)^5 + 8((-10)^4) + 16((-10)^3) = -1,000,000 + 80,000 - 160,000 = -980,000. As x continues to decrease, the value of f(x) continues to decrease without bound as the terms of the polynomial become increasingly larger.

Thus, the end behavior of the graph of f(x) = x^5 + 8x^4 + 16x^3 is that it increases without bound as x approaches positive and negative infinity.

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The formula for the slope (also known as the "rise over run" or "gradient") of a line when given the coordinates of two points is:

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of the two points, and m is the slope of the line.

Note that the coordinates must be in a Cartesian coordinate system, and the points must be distinct, otherwise, the denominator (x2 - x1) will be zero and the division by zero is not defined.

For example, if you have two points (2, 4) and (6, 8), you can use the slope formula to find the slope of the line:

m = (8-4) / (6-2) = 4/4 = 1

The slope of the line is 1

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Answer:

8 × 3 = 24

3 × 8 = 24

Step-by-step explanation:

if she should arrange the chairs in 8 rows that will mean she set 3 chairs per row.

if she then changed the arrangement by arranging the chairs in 3 rows that means she set 8 chairs per row.

in the first paragraph that I wrote, here is how I got it.

24÷8 = 3

8 × 3 = 24

in the second paragraph I wrote, here is how I got it.

24 ÷ 3 = 8

3 × 8 = 24

Therefore your answer will be.

8 × 3 = 24

3 × 8 = 24

The inequality to determine the number of children's table build by Dan on Tuesday is given by x ≤ 5.

As given in the question,

Let us consider 'x' represents the number of children's table build by Dan.

Minimum production times in hour to build the children table is 2 hours.

Children table build by Dan is on Tuesday

Total number of hours Dan works on Tuesday = 10 hours

The required inequality to represent the given condition is :

2x ≤ 10

⇒ x ≤ 10 /2

⇒ x ≤ 5

Therefore, the required inequality to represents the number of children table build by Dan on Tuesday is equal to x ≤ 5 .

Dan builds furniture. The table shows his minimum production times.

Furniture                        Minimum Production Times (hour)

Child’s table                         2

Bench                                   1

Dining table                         4

China cabinet                       7

Dan builds children’s tables on Tuesday. He works 10 hours. Write and solve an inequality to determine how many children’s tables Dan can build that day.

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If Lori made a fraction of 3/4 of a sketch, she spent 9 minutes sketching.

A portion of something is called a fraction. When the numerator and denominator are divided, a number is represented mathematically as a quotient. In a simple fraction, both are integers. A complex fraction contains a fraction in either the numerator or denominator. In a proper fraction, the numerator is smaller than the denominator.

Given the equation

m = 12s,

where

m is the number of minutes, and

s is the number of sketches.

Lori made 3/4 of a sketch i.e.

m = 12(3/4)

m = 9 mins

Thus, If Lori made 3/4 of a sketch, she spent 9 minutes sketching.

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Full question:-

Lori works as a cartoonist for a teen magazine. The time she spends sketching is given by the equation m = 12s, where m is the number of minutes and s is the number of sketches.

If Lori made 3/4 of a sketch, she spent ____ minutes sketching.

One of the triangles' base length, b, is 3 cm. Thus, the correct answer is A.

Two congruent triangles and a rectangle were formed from the trapezoid. The two triangles are 12 cm in height. The rectangle is 12 cm in height, 14 cm in width and the base side is 20 cm. It's worth noting that a congruent triangle has the same three sides and three angles.

The triangle's base length may be calculated as follows:

The sides of the triangle may be calculated using the area of the trapezoid:

Where:

Hence:

We know that the height of the triangles is 12 cm and the area of the trapezoid is 204 cm². The area of the rectangle is also given as 14 cm x 12 cm = 168 cm². This information may be used to construct the equation:

Solving for b, we get:

Therefore, the base length of the triangle is 3 cm, and the correct answer is A.

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Answer:

A

Step-by-step explanation:

a

Based on the graphs of the functions f(x) = 2x + 1, and g(x) = 2(x + 3) + 1, a statement which correctly compares the graphs include the following: A. The graph of g is the graph of f translated 3 units left.

In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image of a function.

On the other hand, a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Mathematically, a horizontal translation to the left is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

Translating the graph of function f, we have:

g(x) = f(x + N)

g(x) = 2(x + 3) + 1

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