Why does the following equation have no solutions?
5-4x-7-10x=-8x-4-6x-10

The greatest common factor amongst the three factors is 3x² as it has a degree of 2 and a coefficient greater than 1.

Sums of terms of the form k-x^n, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Here,

The polynomial=12x⁴+27x³+6x²

On simplifying,

=3x²(4x²+9x+2)

With a degree of 2 and a coefficient larger than 1, 3x² has the highest common factor of the three components.

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The APR for this loan is equal to 468%.

In Mathematics, APR is an abbreviation for annual percentage rate and it can be defined as a measure of an amount of money based on a yearly rate of interest, which a borrower must pay on a loan or credit card.

Mathematically, the annual percentage rate (APR) of a loan can be calculated by using this formula:

APR = [((simple interest/principal)/n) × 365] × 100

Where:

n represents the number of days.

Note: n is equal to 14 days (2 weeks).

Next, we would determine the FC for this loan as follows;

FC = $295 - $250

FC = $45.

For the two-week period, we have;

Interest = 45/250

Interest = 0.18.

Therefore, the annual percentage rate (APR) of this loan is given by;

APR = 0.18 × 52/2

APR = 468%.

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It takes 1 second  for the ball to reach its highest point.

Acceleration of gravity is the acceleration by which earth pulls

objects towards itself. Acceleration is the rate of change of speed.

Given,

The initial velocity of the ball = 16 feet/second

The initial height of the ball = 10 feet

The ball will first travel upward with an initial velocity of 16 feet/second

and the ball will reach a height of x feet from the point of release. After

that the ball will travel a total downward distance of (10+16) = 26 feet.

At highest point, velocity=0.

Applying, v = u + at

                0 = 16 + (-16)t

                t = 16/16

                t = 1 second

Hence, the ball will take 1 second to reach the highest point.

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Answer:

  3 solutions

Step-by-step explanation:

You want to know the number of solutions (zeros) of the cubic function ...

  f(x) = -x³ -32x² +12x +40

Any 3rd-degree polynomial function has 3 zeros. (This is the fundamental theorem of algebra.)

Descartes' rule of signs says the one sign change in the coefficients (--++) means there is one positive real root. On its face, this means there will be 0 or 2 negative real roots.

The value of f(0) is positive (40), and the value of f(-1) is negative (-3), so there must be two negative real roots. (F(x) is positive for very large negative x, so there must be two x-intercepts for x < 0.)

A graph shows the roots to be irrational. The three real roots are approximately ...

__

Additional comment

The "steps" are to find the degree of the polynomial. It is 3, so there are 3 zeros. It is not complicated.

What is more complicated is finding their values. The checks we described above can tell whether there are 1 or 3 real roots. (An odd-degree polynomial always has at least 1 real root.) A graph is helpful for finding whether the roots are real or complex, rational or irrational.

Here, any rational roots must be integer divisors of the constant term, 40. We know the root between 0 and -1 is irrational, so all of them are.

The above root values were obtained by Newton's Method iteration, starting from the approximate values shown on the graph.

Answer:

f(3)=25

Step-by-step explanation:

f(3)=11(3)-8

f(3)=33-8

f(3)=25

Answer:

f(3)=25

Step-by-step explanation:

substitute 3 into the equation for x.

f(3)=11(3)-8

11×3=33 so,

33-8=25

f(3)=25

The number of dollars that should be bought and sold to have the profit of $10 is 8.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the buying and selling rates of U.S. dollar ($) in a day are - Rs 115.25 and Rs 116.5 respectively. Let the dollars bought be illustrated as x.

This will be:

116.5x - 115.25x = 10

1.25x = 10

Divide

x = 10 / 1.25

x = 8

The number is 8.

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The polygons from the figure given below that are similar are Polygon B and Polygon C .

In the question ,

it is given that there are three polygons ,

we have to check which polygons are similar ,

to find the similarity we compare the length of all the polygons .

Let us first check for  Polygon A and Polygon B ,

105/120 = 7/8

80/90 = 8/9.

and  105/120 ≠ 80/90 ,

So , Sides are not in proportion for Polygons A and B.

Hence , the Polygons A and B are not Similar.

Let us check for Polygon A and C .

105/100 = 21/20

80/75 = 16/15.

and 105/100 ≠ 80/75

So , sides are not in proportion for Polygons A and C.

Hence , the Polygons A and C are Non Similar.

Now  for Polygon B and C .

120/100 = 6/5.

90/75 = 6/5.

and  120/100 = 90/75 = 6/5

So , Sides are in proportion for Polygons B and C .

Hence , the Polygons B and Polygon C are Similar.

Therefore , the Polygon B and Polygon C are similar .

The given question is incomplete , the complete question is

Which pairs of rectangles are similar polygons ? select similar or not similar for each pair of rectangles from the figure given below .

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Answer:

3(n+4)=18

Step-by-step explanation:

Answer:3(n+4)=18

Step-by-step explanation:

The sum of 4 and a number is 4+n

Three times the sum of 4 and a number is 3(4+n)

is means equal sign

3(n+4)=18

Answer:

black and white striped bass

Answer:

81

Step-by-step explanation:

Area is multiplying all side

9 x 9 = 81

Answer:f - 1 ( x ) to show the final answer. Verify if f−1(x)=x2+1 f - 1 ( x ) = x 2 + 1 is the inverse of f(x)=2x−2 f ( x ) = 2 x - 2 .

plug in -10 for x in -x^2

-1(-10)^2 =

10^2 = 100

Answer:

x = you sold

y = friend sold

---

x + y = 58

x = y + 14

---

put the system of linear equations into the standard form:

---

x + y = 58

x - y = 14

x= you sold 36

y= friend sold 22

Step-by-step explanation:

1/3x+3/4+2/3x-1/4-2/3x=0.66666...x+0.5

Answer: No, they are not inverses of one another.

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

Explanation:

There are at least 3 methods we can use to prove the functions aren't inverses of each other.

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

Method 1

Let's say we plugged x = 0 into f(x).

[tex]f(\text{x}) = 2\text{x}+1\\\\f(0) = 2*0+1\\\\f(0) = 1\\\\[/tex]

The input x = 0 leads to the output y = 1.

Then let's treat y = 1 as the input of the g(x) function, so we'll plug x = 1 into here.

[tex]g(\text{x}) = -2\text{x}-1\\\\g(1) = -2*1-1\\\\g(1) = -3\\\\[/tex]

If g(x) was the inverse of f(x), then the g(1) output value should be 0 to get us back where we started. However, we get an output of -3 instead.

This is sufficient evidence to conclude that f(x) and g(x) are not inverses of each other. We only need one counter-example to disprove this claim.

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

Method 2

Recall that if f(x) and g(x) are inverses of each other, then we have the following two properties

The left hand side of each equation involves the concept of "function composition".

Let's see what f(g(x)) is equal to in this case.

[tex]f(\text{x}) = 2\text{x}+1\\\\f(g(\text{x})) = 2(g(\text{x}))+1\\\\f(g(\text{x})) = 2(-2\text{x}-1)+1\\\\f(g(\text{x})) = -4\text{x}-2+1\\\\f(g(\text{x})) = -4\text{x}-1\\\\[/tex]

We do not get an output of simply x only, so this is another way to see how we don't have inverses.

Through similar steps, you should find that [tex]g(f(\text{x})) = -4\text{x}-3[/tex] which is further confirmation that f(x) and g(x) are not inverses of each other.

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

Method 3

Let's ignore g(x) for now. We'll start with f(x) and find the inverse of it.

The process involves this basic outline:

So,

[tex]f(\text{x}) = 2\text{x}+1\\\\\text{y} = 2\text{x}+1\\\\\text{x} = 2\text{y}+1\\\\\text{x}-1 = 2\text{y}\\\\\text{y} = \frac{\text{x}-1}{2}\\\\f^{-1}(x) = \frac{\text{x}-1}{2}\\\\[/tex]

Unfortunately we do not end up with -2x-1 as the actual inverse.

So if [tex]g(\text{x}) = \frac{\text{x}-1}{2}[/tex] was the case, then f(x) and g(x) would be inverses of each other.

Through similar steps, the inverse of [tex]g(\text{x}) = -2\text{x}-1\\\\[/tex] is [tex]g^{-1}(\text{x}) = -\frac{\text{x}+1}{2}\\\\[/tex]

Answer: Yes, it is linear expression

Step-by-step explanation:

The equation is y=mx + b

Here we have 7x, which we have the slope

We don't see the y-intercept, so it is 0

Answer:

Step-by-step explanation:

Aub, probability, set theory and discrete math?

For the given right triangle the measure of the remaining angles are 2.9° and 87.1° and the remaining sides are 5.9 cm and 116.85 cm respectively.

The trigonometric ratios are defined for a right angled triangle.

The example of these ratios are sin, cos, tan, cosec, sec and cot.

The trigonometric ratios are useful in determining the heights and distances of the large objects.

Given that,

In a right triangle tan(P) = 0.051

And, hypotenuse = 117 cm.

The given data can be shown in the diagram as follows,

From the diagram it can be written as,

tan(P) = 0.051

=> P = 2.9°

Then, ∠Q = 180° - (90° + 2.9°)

                = 87.1°

Now, Sin(P) = p/117

        => Sin(2.9°) = p/117

        => p = 117 × Sin(2.9°)

                = 5.9

Similarly, Cos(P) = q/117

            => Cos(2.9°) = q/117

             => q = 117 × Cos(2.9°)

                      = 116.85

Hence, the measure of the remaining angles are 2.9° and 87.1° and the remaining sides are 5.9 cm and 116.85 cm respectively.

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The function h(x) is the result of two rigid transformations, reflecting the function f(x) about the x-axis and translating it vertically 7 units down.

In this problem we must determine the difference between the quadratic functions f(x) = x² and h(x) = - x² - 7, we can infer the change necessary to derive h(x) by means of rigid transformations, that is, transformations applied on a function such that the features of the functions are conserved.

All the rigid transformations required to transform f(x) into h(x) are listed below:

Now we proceed to plot the two functions. From the graph we noticed that h(x) is the result of reflecting f(x) about the x-axis and translating 7 units in the -y direction.

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The distance between the point (-3,7) and the line y=1/3x-2 is  11.0 units

Distance shows how long it is between a point and another

We can do this by drawing a segment that is perpendicular to the line

the given equation is 1/3x-2

The slope here is 1/3 That is slope =3

From the equation of slope=intercept form = y=mx+c

put m=3 to have

y=3x+c

From the given coordinates (-3,7)

7=3(-3)+c

7+9=c

c=16

This implies that y=3x+16

Find the line where the equation intersect  the line

⇒3x+16=1/3x-2

Rearrange the equation

8x/3=-18

Make x the subject. x=6.75

Recall that y=1/3(6.75)-2

y=2.25

The second coordinates are (6.75,2.25) and first (-3,7)

The distance is given by

d=[tex]\sqrt({X_{2}-X_{1})^{2} +(Y_{2}-Y_{1} )^{2} }[/tex]

d= √(6.75+3)²+(2.25-7)²

d=√9.75²+(-4.75)²

d=√95.0625+22.5625

d=√117.625

d=10.8455059817

Therefore the distance is 11 units

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The water levels in reservoirs A and B, which initially had 34 million gallon and 38 million gallon water, respectively, will be equal after 13.3 months.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. No, a mathematical equation cannot be solved since it lacks the "equal to" sign $(=)$, but it can be simplified. Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Here,

Let the number of months be x.

34-0.8x=38-1.1x

1.1x-0.8x=38-34

0.3x=4

x=40/3

x=13.33 months

After 13.3 months, The reservoir A and reservoir B will have same amount  of water when initially they have 34 million gallon water and 38 million gallon water respectively.

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Answer:

  (a)  The value 550 represents the initial balance in the account, which means the account started with $550.

Step-by-step explanation:

You want the meaning of 550 in the simple interest expression 687.5 = 550(1 + 0.05t).

The formula for computing the amount A of an account earning simple interest at annual rate r on its initial balance P for t years is ...

  A = P(1 +rt)

Comparing this formula to the given equation, we see ...

  687.5 = 550(1 +0.05t)

The initial balance (starting amount) was 550.

To find the gas unit used in baking of cookies, we plug the values into the given equation: g = t, g = 12. Thus, the gas unit used is 12.

Organic gas usage or production is measured in "gas units." It is frequently employed to estimate the price of natural gas for a predetermined time period, such as a month or a year.

British thermal units (BTUs), a measure of the energy content of natural gas, are the industry standard for quantifying this fuel. One BTU is the amount of heat necessary to raise the temperature of one pound of water by one degree Fahrenheit.

To compute the gas unit for a given time period, the total amount of natural gas used or generated is first converted into BTUs.

How to solve?

To find the gas unit used, we plug the values into the given equation:

g = t, g = 12. Thus, the gas unit used is 12.

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Answer:

  3)  260 ft

Step-by-step explanation:

You want the perimeter of a rectangle 55 ft by 75 ft.

The equation for the perimeter of a rectangle is ...

  P = 2(L +W)

For the given rectangle, the perimeter is ...

  P = 2(75 ft +55 ft) = 2(130 ft) = 260 ft

Maya needs 260 feet of fencing to put fence around her rectangular yard.

He might use the equation y = (3/2) x to determine how much flour he required for the cake.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, etc.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.

According to our question-

Accordingly, we require 2.3 cups of sugar for every cup of flour.

It also means that you need 3 1/2 cups of flour for every cup of sugar.

Therefore, if x cups of sugar and y cups of flour, respectively, are used:

y = (3/2) x.

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In polynomial, x - 2 is not a factor f(x) [By factor theorem]

What is Polynomials ?

Sums of terms with the pattern kxn—where k is any positive integer and n is an arbitrary number—are known as polynomials.

                    For instance, the polynomial 3x+2x-5. a description of polynomials. In this video, basic terms like terms, degrees, standard form, monomial, binomial, and trinomial are covered.

p(x) = 4x^3 + 10x^2 - 6x - 20  

put x = -2 in equation

p(x) = 4 * (-2)³ + 10 * ( -2)² - 6 * -2 - 20

       = 4 *  -8 + 10 * 4 + 12 - 20

        = -32 + 40 + 12 - 20

        = 52 - 52

        = - 2

p(x) ≠ 0

Which is not equal to zero

x - 2 is not a factor f(x) [By factor theorem]

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Answer: 1/2 * 6 = 3

Step-by-step explanation: