2. What are the domain and range for the exponential parent function,
where b is a positive real number not equal to 1 and a > 0?

On solving the provided question, we can say that - the linear equation

y=mx+b = [tex]y=6.4(82)+1900= > y=524.8+1900= > y=2424.8[/tex]

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

y=mx+b

x=gallons of fuel

y=total weight of plane including fuel

m=slope=6.4

b=weight of plane, no fuel....a constant to be calc'd

[tex]y=mx+b\\2245.6=6.4(54)+b\\2245.6=345.6+b\\ b=1900\\ y=6.4x+1900\\ y=6.4x+1900\\ y=6.4(82)+1900\\ y=524.8+1900\\ y=2424.8[/tex]

82gallons fuel is 2424.80 lbs

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The function f(x) = -x-3.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given function:

f(x)+3f(-x) = 2x+6.

Let the function is an even function.

So, f(-x) = f(x)

To solve for f(x):

Substituting the property of an even function,

f(x) - 3f(x) = 2x + 6

-2f(x) = 2x + 6

f(x) = -x-3

Therefore, f(x) = -x-3 is the function.

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The sum of the solutions of the equation 4x(x - 3) = 23 is 3.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, An equation 4x(x - 3) = 23.

Now, Distributing the terms in the LHS we have,

4x² - 12x = 23.

4x² - 12x - 23 = 0.

By applying Sridhar acharya's formula we have,

[tex]x_{1,\:2}=\frac{-\left(-12\right)\pm \sqrt{\left(-12\right)^2-4\cdot \:4\left(-23\right)}}{2\cdot \:4}[/tex].

[tex]x=\frac{3+4\sqrt{2}}{2},\:x=\frac{3-4\sqrt{2}}{2}[/tex].

Therefore, The sum of the solutions of the equation is,

x + x = (3 + 4√2)/2 + (3 - 4√2)/2.

= (3 + 4√2 + 3 - 4√2)/2.

= 6/2.

= 3.

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The number of positive 10 digit numbers that can be made using seven ones and three zeros is; 28

We want to find the number of positive 10 digit numbers that can be made using seven ones and three zeros.

Now, the leftmost position digit cannot be 0 and as such it is 1, due to the fact that there are no other possibilities.

The rightmost position therefore must be 0 in order to fill the need for an even number.

Thus, we have 8 remaining positions that we need to fill with six ones and two zeros using an arbitrary manner.

This means that we can place two digits of zero among 8 positions by using combination formula as;

⁸C₂ = 8!/(2! * 6*)

= 28 different ways

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Answer:

Step-by-step explanation:

6

Answer:

x = -5

y = 2

Step-by-step explanation:

1)  -5x-4y = 17

2) 3x-4y = -23

subtract equation 2 from equation 1:

-8x + 0 = 40

-8x = 40

x = -5

substitute x = -5 into equation 1 and solve for y:

-5(-5) - 4y = 17

-4y = -8

y = 2

test answers by substituting x and y values into eqation 2:

3(-5) - 4(2) = -23   Answers are correct!

If Raj was getting a 5% commission, he would make 24000 * 5% = $<<240005.01=1200>>1200 on $24,000 of sales.

If he is now getting a 6.5% commission, he will make 24000 * 6.5% = $<<240006.5.01=1560>>1560 on $24,000 of sales.

Thus, Raj will make 1560 - 1200 = $<<1560-1200=360>>360 more on $24,000 of sales with his new commission rate of 6.5% than he did with his old commission rate of 5%.

Therefore, $52.25 is the answer to the inquiry about what percentage of a person's income is withheld each week for federal income tax.

A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

Here,

The Federal Insurance Contribution Act is the American legislative framework in use here, and it contains the criteria and guidelines that are utilized to determine payroll taxes on an employee's paychecks. The social security and Medicare programs are funded through taxation, which is paid by both employers and employees.

The amount of federal income tax deducted from the weekly cheque is:

6.2% from Social Security plus 1.45% from Medicare.

= 7.5 percent of the weekly gross salary.

The amount of federal income tax withheld each week from Beverly Hibbs's $683.00 weekly salary is:

= 0.0765 × 683

= $52.25

Therefore, $52.25 is the answer to the inquiry about what proportion of a person's income is withheld each week for federal income tax.

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The graph of an inequality in two variables is the set of points that represents all solutions to the inequality.

The boundary line that separates the coordinate plane into two halves by a linear inequality represents the solutions to the inequality in one half. For > and, the border line is solid, and for and, it is dashed.

To determine the equation governing the inequality line, enter your slope and a point into the formula y = mx + B, where "m" denotes the slope, "x, y" denotes a point on the line, and "b" is the y-intercept. By inserting (0, 0), you get 0 = 0 + b, which equals 0.

When you rewrite the equation, you get y = x/2. The linear inequality x - 5 > 3x - 10 is an illustration. Due to the greater than symbol being utilised in this inequality, the LHS is clearly greater than the RHS.

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Answer:

54°

Step-by-step explanation:

Angles corresponding in parallel lines are the same

Therefore ,As a result, y = 5x + 35 is the equation that gives the answer to the given algebra issue.

Algebra is used to analyze mathematical symbols, and logic is used to manipulate those symbols. The PEMDAS rule stands for the following operations: parenthesis, exponent, multiplication, division, addition, and subtraction. This rule is applied to solve the equation properly and accurately.

Here,

In this case, the equation for y in terms of x will be as follows:

y = 5(x + 7)

If you make the equation simpler, you get

y = 5(x + 7)

y = 5x + 35

y will have the linear equation y = 5x + 35 in terms of x.

Therefore , As a result, y = 5x + 35 is the equation that gives the answer to the given algebraic issue.

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Prime numbers of the form p and p+2, where p is a prime number, are known as twin prime numbers.

A twin prime is a prime number that is either 2 less or 2 more than another prime number. For example, the number 3 and 5 are twin primes, because they are both prime and the number 5 is 2 more than 3. Similarly, the number 5 and 7 are also twin primes, because they are both prime and the number 7 is 2 more than 5.

Therefore, Twin primes are considered as interesting numbers in number theory because of their relative rarity, rare in nature and because they are the building blocks for certain types of primes such as Sophie Germain primes and safe primes.

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When Nancy wanted to find the volume of a cuboid, the volume is 352cm³.

Word problem simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Since Nancy wanted to find the volume of a cubiod she measured the length of the cubiod as 11 cm and width as 8cm and the height as 4cm.

The volume will be:

= Length × Width × Height

= 11cm × 8cm × 4cm

= 352cm³

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Complete question

Nancy wanted to find the volume of a cubiod she measured the length of the cubiod as 11 cm and width as 8cm and the height as 4cm. Find the. volume

Answer:

Step-by-step explanation:

sin40°=[tex]\frac{AC}{12}[/tex]
⇒AC=sin40°×12

⇒AC=7.713≈7.7
cos40°=[tex]\frac{AB}{12}[/tex]
⇒AB=cos40°×12

⇒AB=9.192≈9.2

as A=90°,B=40°

from A+B+C=180°

we can write C=180°-90°-40°

⇒C=50°

Answer:

(-∞, 1] or {x|x<=1}

Step-by-step explanation:

Answer:

Based on the given equation, the function g is an exponential function with base 2. The y-intercept of the function g is at (0, 4).

The graph of function f is not described, so it is not possible to accurately compare the two functions. In order to accurately compare the two functions, it would be helpful to have more information about the graph of function f, such as the vertex and any other points that the graph passes through.

An equation may have more than one solution.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. A condition on a variable is an equation when it ensures that two expressions in the variable have the same value. The variable's value for which the equation holds true is referred to as the equation's solution. If the LHS and RHS are switched, an equation doesn't change. The solution is discovered after isolating the variable for which the value must be determined. Depending on the kind of equation we are dealing with, we can solve it. There are various types of equations, including linear, quadratic, rational, and radical ones.

Steps to solve a linear equation:

1. If necessary, remove the parentheses and use the distributive property.

2. By merging like terms, make both sides of the equation simpler.

3. The LCD (least common denominator) of all the fractions should be multiplied by both sides of the equation if there are any fractions.

4. If the equation contains decimals, multiply both sides by the lowest power of 10 to make the result a whole number.

5. Using the addition and subtraction properties of equality, move the constant terms to the other side of the equation and the variable terms to the other.

6. Using the equality properties of multiplication or division, set the variable's coefficient to 1.

7. Get the answer by isolating the variable.

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Answer:

x=-1 and y=4

Step-by-step explanation:

When you draw a graph you will see point of intersection which is solution

By altering schedules without giving adequate notice, terminating employees without giving adequate notice, and making false claims about its products, company x is not adhering to best practises.

These include bar codes, ISBNs, ASCII codes, postal codes, and bank account numbers; many of these contemporary codes use a checking mechanism, also known as a check digit. The ISBN system, now used uniformly on all new books, is one illustration of this.

Adopting sensible company procedures and policies with reference to apparently contentious issues is referred to as practicing business ethics. Corporate governance, market manipulation, bribery, racism, social duty, and fiduciary responsibilities are a few of the topics that come up in an ethical discussion.

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Answer:

The first one is right...

Step-by-step explanation:

The angle m∠D of the triangle is 78 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The ΔKDT and ΔKPQ are isosceles triangle.

Isosceles triangle is a triangle that has two sides and angles equal to each other.

Therefore,

∠D + ∠T + ∠k = 180

∠D  = 6x + 6

∠T = 6x + 6

∠K = 2x

Therefore,

6x + 6 + 6x + 6 + 2x = 180

14x + 12  = 180

14x = 180 - 12

14x = 168

divide both side by 14

x = 168 / 14

x = 12

Therefore,

m∠D = 6x + 6 = 6(12) + 6 = 72 + 6 = 78 degrees.

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Answer:

1/12

Step-by-step explanation:

3/4 - 2/3 = 9/12 - 8/12 = 1/12

Answer:

The answer is 1/12 good luck with the rest

The average speed in laps per minute of Ryan is 2.5 laps per minute

From the question, we have the following parameters that can be used in our computation:

The above can be expressed as

(x, y) = (1, 5) and (3, 10)

The average speed in laps per minute can be calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Rewrite as

Average speed = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (1, 5) and (3, 10)

Substitute the known values in the above equation

So, we have the following equation

Average speed = (10 - 5)/(3 - 1)

Evaluate

Average speed = 2.5

Hence, the average speed is 2.5

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In math, a pattern is defined as a sequence of repeating objects, shapes or numbers. We can relate a pattern to any type of event or object.

A pattern has a rule that identifies the items that are part of the pattern and those that are not. A pattern in mathematics is a series of recurring figures, shapes, or numbers.

Any kind of event or thing can be connected to a pattern. A pattern has a rule that identifies the items that are part of the pattern and those that are not. A specific set of rules must be taken into account in order to create a full pattern.

We must first comprehend the nature of the sequence and the distinction between the two successive numbers provided in the pattern in order to apply these rules. 

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On solving the provided question, we can say that - he re the slope value is using the formula y/x = k => [tex]k = 2/3[/tex]

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

Use the point (3, 2) and divide y by x using the formula y/x = k.

[tex]k = 2/3[/tex]

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Using the Algebraic tile method we get x=2 solution for equation model

The algebra tile method is a method of solving equations by using visual models, such as tiles with different values on them, to represent the unknowns and constants in the equation. It is often used to help students understand the process of solving equations and to see how the operations of addition and subtraction correspond to the process of combining or separating algebraic expressions.

In the question, we have 3 kinds of tile

Equation will be :

⇒ 3x - 1 - 1 = 1 + 1 + 1 + 1

⇒ 3x - 2 = 4

⇒ 3x = 6

⇒ x = 2

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Choices that is equivalent to the expression √5. √20 is 5.2

In mathematics, the word "equivalent" designates two quantities, numbers, or meanings that are the same. A bar across an equivalent sign or Equivalent Sign shall be used to indicate the equivalence of two such quantities. Additionally, it denotes the logical equivalent of two values or a group of quantities.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

x= (5)^1/2*(20)^1/2

x= (5)^1/2*(2.2.5)^1/2

x=5.2

So B is the correct option.

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Answer:100

Step-by-step explanation:

Answer:

[tex] \sf \: b) \: 45[/tex]

Step-by-step explanation:

The values given are,

→ u = 7

→ d = 10

→ e = 3.2

Now the expression is,

→ 15(d - u)

Evaluating the expression,

→ 15(d - u)

→ 15(10 - 7)

→ 15 × 3

→ 45

Hence, option (b) is correct.

Answer:45

Step-by-step explanation:

15(10-7)

15(3)

multiply and get 45

Answer:

Discrete

Step-by-step explanation:

Discrete means it has ends, and continuous means it continues on forever.