If f(x) = 3x² + 2 and g(x)=x2-9, find (f- g)(x).
OA. 2x² - 7
OB. 2x² +11
OC. 4x²-7
OD. 4x² +11.

The solutions of x + 2 = 2ˣ + 1 are x = 0 and 1.

The answers are given in the attached image.

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

Given:

Two functions,

f(x) = x + 2 and g(x) = 2ˣ + 1.

The graph of the functions on the same coordinate plane is given in the attached image.

The blue line represents the graph f(x) and the green represents g(x).

Then f(x) = g(x)

x + 2 = 2ˣ + 1.

The solution is the x-value of the point of intersection.

That means,

x = 0 and 1

Therefore, the solutions of the f(x) = g(x) are x = 0 and 1.

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To solve a piecewise defined function, you should follow these steps:

1. Understand the definition of the function. A piecewise defined function is a function that is defined differently on different intervals of its domain.

2. Identify the different intervals on which the function is defined. These intervals are usually separated by vertical asymptotes, which are points where the function is undefined.

3. Determine the formula for the function on each interval. This is usually given in the problem statement, but if not, you will need to figure it out from the context.

4. Find the domain and range of each formula. The domain of a function is the set of all input values for which the function is defined, and the range is the set of all output values.

5. Determine any discontinuities in the function. These are points at which the function is defined differently on different intervals, and they will be vertical asymptotes.

6. Sketch the graph of the function by plotting points and connecting them with line segments.

7. If the function is a piecewise continuous function, Analyze it further by finding its limits, derivatives, integrals, or other properties of interest as you would with any other function.

8. Evaluate the function for a given input value, you need to determine which interval the input value belongs to and then use the appropriate formula for that interval to find the output value.

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When graphing polynomials, we can determine the end behavior by the degree of the polynomial and the coefficient of the leading term.

The degree of a polynomial is the highest exponent of the variable found in the equation. The coefficient of the leading term is the number that is multiplied by the variable in the leading term. The end behavior of a polynomial can be determined by examining the sign of the coefficient and the degree of the polynomial.

For example, let's consider the polynomial equation y = x^3 - 2x^2 + 5x + 7. The degree of this polynomial is 3, and the coefficient of the leading term is 1. This means that the end behavior of this polynomial equation will be increasing, since the coefficient and degree are both positive. To confirm this, we can calculate the limit of the polynomial as x approaches positive and negative infinity. As x approaches positive infinity, the limit of y is positive infinity (∞), and as x approaches negative infinity, the limit of y is also positive infinity (∞). This confirms that the end behavior of this polynomial equation is increasing.

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Answer:

Opens up

a =  1

b =  0

c = -6

Step-by-step explanation:

y=x^2-6

This is a parabola that opens upwards (see attached graph).  

I will assume the a, b, and c are the coefficients of a parabolic equation of the form:

y = ax^2 + bx + c

Since y = x^2 - 6, the values are:

a = 1

b = 0

c = -6

the solution of equation  y=x+2 and  y=3x-2 are x= 2 and y=4

y = x+2 ------------ equation 1

y = 3x -2 ------------ equation 2

in the first equation y = x +2

in the second equation y = 3x -2

this mean equation 1 = equation 2

then we can equate the two together to get one of the variable

remember, we have to unknown variables which are x and y, so we need to isolate y to get x

x + 2 = 3x -2

let collect the like terms

x - 3x = -2 -2

let us factorize out x on the right hand side of the equation

x(1 - 3) = -4

x(-2) = -4

-2x = -4

divide both sides by -2

-2x/-2 = -4/-2

x = 2

to find y put x in any of the above equations

let us use equation one

y = 2 + 2

y = 4

complete question

How do you solve, y=x+2 y=3x-2

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Answer: The diagonal and the height of the right triangle form the legs of the triangle, and the unknown length is the hypotenuse. To find the length of the hypotenuse, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

So, if the legs of the right triangle measure 12 inches and 15 inches, the hypotenuse c can be calculated as follows:

c² = a² + b²

c² = 12² + 15²

c² = 144 + 225

c² = 369

Therefore, the length of the hypotenuse c is the square root of 369.

c = √369

c = 19.1 inches

Therefore, the top of the spider web is 19.1 inches long.

Step-by-step explanation:

She spends a total of $ 180 in copayments, $20 for medical visits and $10 for generic prescriptions.

The system process is a strategy for addressing issues that entails first figuring out the price of a single item, than multiplication that value to figure out the needed value. Simply put, the unit technique is employed to extract a single unit quantity from a multiple that is supplied. For example, 40 pens would cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and inverse are equivalent in terms of mathematics, algebra, linear algebra, mathematical, or math and science of matrices or operators.

given

$20 for copay for doctor’s visits

$10 copay for generic prescription

for 5 doctor visits = 20*5 = $100

for 8 prescriptions = 10 * 8 = $80

so total = 100+ 80 = $180

She spends a total of $ 180 in copayments, $20 for medical visits and $10 for generic prescriptions.

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The transformations that result in similar triangles are dilations, rotations, reflections, and translations.

A transformation that conserves the shape, but not necessarily the size, of a figure is called a similarity transformation. Rotation, reflection, and translation are rigid motions, which means they preserve both size and shape, on the other hand, dilation only ensures that the shape is preserved. As the rigid motions are congruence transformations, all congruent figures are also similar.

A similarity transformation is a dilation or a combination of rigid motions and dilations. Two geometric figures are similar if and only if there is a similarity transformation that maps one of the figures onto the other. Similar figures have the same shape but necessarily not the same size.

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Answer: 6

Step-by-step explanation:

Each year it will lose $160. So v=160

As per the unitary method, the number of care is 9 and the number of additional method is 2.

The term unitary in set theory is defined as the way to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Here we have given that the total number of units is 56.

And here we also know that the number of units in each care is 6.

Now, we have to find the total number of care, that can be obtained by dividing the total care by the units in each care,

then it can be written as,

=> 56/6

When we divide the term then we get the quotient as 9 and the remainder as 2.

Therefore, while looking into these we have identified that there are 9 cares and 2 additional units are in the group.

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As per the given ratio, the number of roses is 45 and the number of tulips is 27

The term ratio also known as proportion is defined as an ordered pair of numbers a and b, written a / b where b does not equal 0

Here we have given that the ratio of roses to tulips is 5: 3.

Here we also know that the shop has 72 tulips on Friday morning.

And then let us consider that if the florist uses up half of each type of flower to fill an order, then the ratio of roses to tulips in the shop change is calculated as,

=> 5x + 3x = 72

=> 8x = 72

Then the value of x is calculated as,

=> x = 9

Therefore, the number of roses is

=> 5(9) = 45

And the number of tulips is written as,

=> 3(9) = 27

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I've discovered that using the 3:4:5 triangle is the simplest way to determine for sure if an angle is 90 degrees. According to this rule, a triangle is a right triangle if the diagonal between its two points measures 5, even though one of its sides measures 3 and the other measures 4.

Aim for a measuring ratio of 3:4:5, to create an absolutely square corner. To put it another way, you need a length of three feet on the straight line, four feet on the perpendicular line, and five feet crosswise. You will get a corner that is exactly square if all three measurements are accurate.

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The required area of the shaded region is 141.3  sq. in.

A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius. The square unit, such as m^2, cm^2, etc., is the unit of area. Area of a circle is equal to r2 or d2/4, where = 22/7 or 3.14.

inner radius = 6 in, outer radius= 9 in

are of small circle = πr^2

Area = π(6)^2 = 36π sq. in

Similarly

Area of big circle = πr^2

Area = π(9)^2 = 81π sq. in

So,

Area of shaded region =  81π - 36π

Area of shaded region = 45π

Area of shaded region = 141.3  sq. in

Thus, required area is 141.3  sq. in.

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the explanation of how heart disease progresses over time in part of her presentation would be best suited to a video.

Several different heart disorders are referred to as "heart disease." Coronary artery disease (CAD), which affects the blood flow to the heart, is the most typical kind of heart disease in the United States. A heart attack may result from reduced blood flow.

here,

Chest pain or discomfort, pain in the upper back or neck, heartburn, nausea, vomiting, extreme exhaustion, pain in the upper body, dizziness, and shortness of breath are all symptoms of a heart attack.

Heart palpitations are caused by an arrhythmia (palpitations). Heart failure symptoms include shortness of breath, exhaustion, or swelling of the legs, abdomen, or neck veins.

The three main risk factors for heart disease are excessive blood pressure, high cholesterol, and smoking. Nearly half of Americans (47%) have at least one of these three risks.

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Answer:

d

Step-by-step explanation:

Yes, dilation is a type of transformation that involves multiplying the coordinates of a figure by a scale factor.

This scale factor can be greater than 1, which is an enlargement, or less than 1, which is a reduction. To calculate the coordinates of a dilation, the following formula is used: (x, y) → (kx, ky), where (x, y) are the coordinates of the original point and (kx, ky) are the coordinates of the transformed point. The scale factor, k, is the same for both the x and y coordinates. For example, if the scale factor is 2 and the original coordinates are (2, 4), the new coordinates would be (4, 8). This means that the point (2, 4) has been enlarged to (4, 8).

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The price of one pound of apples is represented in the equation by the number 4.3 by the price in dollars of x pounds of apples, where x is pounds.

A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14.

given

y = 4.3x

the price in dollars of x pounds of apples, where x is pounds.

The price of one pound of apples is represented in the equation by the number 4.3.

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The probability of 45 heads in 100 tosses of a coin given the probability of heads is 50% is 7.1%.

The binomial probability formula is used to calculate the probability of getting a certain number of heads (or success) in a certain number of coin tosses (or trials) when the probability of getting a head (or success) in each individual coin toss is known. The formula is:

P(x) = (n choose x) * (pˣ) * (1-p)^(n-x)

Where,

P(x) is the probability of getting x heads (or success) in n coin tosses (or trials)

n is the number of coin tosses

x is the number of heads (or success)

p is the probability of getting a head (or success) in a single coin toss

1-p is the probability of getting a tail (or failure) in a single coin toss

(n choose x) is the binomial coefficient, which is the number of ways to choose x heads (or success) from n coin tosses (or trials)

In this case, the probability of getting 45 heads in 100 tosses of a coin with a probability of heads of 50% can be calculated using the formula: (100 choose 45) * (0.5⁴⁵) * (0.5⁵⁵) which is approximately 0.071, or 7.1%.

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(x+5)(x - 1) is a factor of p(x) = x² - 4x - 5

We can see that by applying polynomial long division or by applying synthetic division, both of these methods will give the same result.

x² - 4x - 5 = (x + 5)(x - 1)q(x) + r(x)

where q(x) and r(x) are the quotient and remainder of the polynomial division respectively. Since r(x) = 0, it means (x + 5)(x - 1) is a factor of p(x) = x² - 4x - 5.

A "pair of 3" is not a commonly used term.

A set of 3 numbers can be called a triplet, or a set of 3 items can be called "a set of three".

Please let me know if you want me to clarify about something else.

By solving the given expression when x=12 we get a = 11-12b

what is an algebraic expression ?

Algebraic expression can be defined as the combination of  constants , variables and operators.

Algebraic expressions are the concept of expressing numbers using letters or alphabets without specifying their real values. The basics of algebra taught us a way to specific an unknown value the usage of letters which includes x, y, z, and many others. those letters are called here as variables. An algebraic expression may be a combination of each variables and constants. Any value this is positioned before and increased through a variable is a coefficient.

Given,

expression ,

x = (1+a) / (1-b )

By putting x =12

we get,

12 = (1+a) / (1-b)

12 * (1-b) = 1+a

12- 12b =1+a

a = 12-12b-1

a = 11 - 12b

Hence , By solving the given expression we get a = 11-12b

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Therefore , the solution of the given problem of unitary method comes out to be  A.$10.5 total cost and $ 0.12 .

By first multiply the value with one unit by the number of units needed, one can use the unit method to solve a problem. Simply put, the unit function is used to distinguish a single entity unit from a given many. 40 needles may be purchased for 400 rupees, or the price of one pen. There may be a standard method for figuring this out. only one nation. Everything has a unique quality. Algebra, its dialectic and inversion, and matrix logic are all analogous concepts.

Here,

Given:

A) Estimate :

70 * 1.25

80*1.25

=> 80 + 20 = 100

and

100/30 = 3.33

thus, approx 4 gallons of gas felicia needs

=> 4 * 3.5 = 14

thus, $14 total cost

Exact :

=> 70 * 1.25 = 87.5 miles

=> 87.5/30 = 2.92 gallons

thus, approx 3 gallons of gas felicia needs

=> 3*3.5 =10.5

thus, $10.5 total cost

B)

=> per cost / miles

=> 3.5 / 30 = 0.116

=>$ 0.12

Therefore , the solution of the given problem of unitary method comes out to be  A.$10.5 total cost and $ 0.12 .

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

Explanation:

The weight of A is 2/3 that of B. This flips to saying "the weight of B is 3/2 that of A". Because 3/2 = 1.5, we can then have this equation

B = 1.5A

The statement "C is 75% the weight of D" leads to the equation

C = 0.75D

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

The sum of A and B is triple that of the sum of C and D, giving us this equation:

A+B = 3(C+D)

Plug in the previous two equations we found in the previous section. Afterward, solve for the variable "A".

A+B = 3(C+D)

A+1.5A = 3(0.75D+D)

2.5A = 3(1.75D)

A = 3(1.75D)/2.5

A = 2.1D

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

Let's revisit the first equation we set up, and then apply substitution like so:

B = 1.5A

B = 1.5*2.1D

B = 3.15D

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

There's a lot of equations to keep track of. The key equations are these:

A = 2.1D

B = 3.15D

C = 0.75D

The one common factor of all these equations is the variable "D". This will be useful when setting up the ratio A:B:C:D

We'll go from the ratio

A:B:C:D

to

2.1D:3.15D:0.75D:1D

afterward we can divide all four parts by the GCF variable D, to arrive at

2.1:3.15:0.75:1

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

This last section will focus on converting each part of that ratio into integers. This is done by multiplying all four parts by 100 (as shown in the 2nd step).

Then we divide all parts by the GCF 5 to get the final reduced ratio.

2.1:3.15:0.75:1

100*2.1:100*3.15:100*0.75:100*1

210:315:75:100

5*42:5*63:5*15:5*20

42:63:15:20

Acres of land needed by the developer to build a community center that will use up 9/25 of the property is 15.66 acres, option C.

The size of land required to build a community center is calculated as follows:

First plot size = 24.6 acres

Field size = 18.9 acres

The local developer purchases both (24.6 + 18.9) acres to have a total of 43.5 acres.

The amount needed to build a community center is 9/25

Therefore 43.5 x 9/25 = 15.66 acres

9/25 of a 43.5 acres purchased by local developer will require only 15.66 acres.

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The number of maths books sold is 70 and the number of history books sold is 210.

Let no of maths book sold be x.

According to the question, the number of history books sold is three times the number of maths books sold.

Therefore the number of history books sold is 3x.

Given: Total books sold = 280

So, x + 3x = 280

Solving the equation, we get:

4x = 280

x = [tex]\frac{280}{4}[/tex]

x = 70 (Number of maths books sold)

3x = 3 × 70 = 210 (Number of history books sold)

Thus the number of maths books sold is 70 and the number of history books sold is 210.

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sqrt( A / pi ) =r is the solution for r and r is called as radius in the formula  A=πr^2

A large part of the field of operations research is the use of statistical equations to solve problems in business or military operations.

Music, linguistics, and philosophy all use mathematical models (for example, intensively in analytic philosophy).

A model is, for example, the method for the area of a circle, πr2.

Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.

Α= pi r^2

Divide each side by pi

A / pi = r^2

Take the square root of each side

sqrt( A / pi ) = sqrt(r^2)

sqrt( A / pi ) =r

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Answer:

2.44444

but rounded to 2.4 (tens place)

Step-by-step explanation:

hope this helps!:)

Answer:

2x² + x + 3

Step-by-step explanation:

2x² + x + 3

2x² + (5/2)x + 3

By solving the given expression we get this simplified expression 12x³ - 7x²y - 8xy² + 3y³.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

To simplify the expression (3x² - 4xy + y²)(4x + 3y), we can use the distributive property of multiplication to expand the expression as follows:

(3x² - 4xy + y²)(4x + 3y) = 3x²(4x) - 4xy(4x) + y²(4x) + 3x²(3y) - 4xy(3y) + y²(3y)

Simplifying each term, we get:

12x³ - 16x²y + 4xy² + 9x²y - 12xy² + 3y³

Combining like terms, we get:

12x³ - 7x²y - 8xy² + 3y³

Therefore, the simplified expression is 12x³ - 7x²y - 8xy² + 3y³.

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The geometric series which diverges is shown in the option number c as the absolute value of the common ratio of this series 4 is ∑∞n=1 (2/3)(-4)ⁿ⁻¹

The next term in a geometric sequence is produced by multiplying the previous term by the same number across the whole series.

It can be given as,

a+ar+ar²+ar³+...

Here,

is the sequence's (a) initial term, and (r) stands for common ratio.

It should therefore be a series as geometric series diverge.

|r|>1

the first choice is,

3/5+3/10+3/20+3/40+ ...

The common ratio in this case is,

r = (3/10)/(3/5)

r= 1/2

The average ratio is below one. Option an is therefore incorrect.

second option given as,

-10+4-8/4+18/25- ...

Here, the common ratio is,

r = (4/-10)/(-2/5)

r= -2/5

The usual ratio for the second choice is (-2/5), which is below one. This alternative is also incorrect.

The common ratio in option number c is equal to -4. The common ratio's exact value is,

|r|=|-4|

|r|= 4

This common ratio has a greater absolute value than one. This is the best choice as a result.

The absolute value of this series' common ratio, or option number c, represents the geometric series that diverges.

∑∞n=1 (2/3)(-4)ⁿ⁻¹

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