Write $a^4 - 3a^2 + 9$ as a product of two monic quadratics with integer coefficients.

The set of -values that are appropriate in the given situation is known as the practical domain. Solution: F (x) = 2 x is the function's formula.

You are not accounting for or measuring any rainfall that occurred prior to the storm's onset, thus there is a total of 0 inches of precipitation at that time. Six and a half hours are spent in the storm.

Example :

Miami, Florida, experiences heavy rainfall due to a powerful hurricane. A 2 inch per hour downpour is occurring. In 6 and a half hours, the storm is over. The total amount of rain that has fallen throughout time should be modeled mathematically. The function is plotted. For this situation, identify the practical domain. The set of -values that are appropriate in the given situation is known as the practical domain.

Solution: Since there was no rain measured or included before the storm began, the function is as follows:

f(x)= 2x

There was 0 inches of rain at the moment the storm began. Six and a half hours are spent in the storm. f(6.5) = 2(6.5) = 13 inches of rain had been recorded at 6.5 hours, or so. It follows in words what the domain and range are:

Domain :

All real numbers between and including 0 and 6.5 hours.

Range :

All real numbers between and including 0 and 1.3 inches.

Domain and range can be expressed more easily with the help of some helpful notation, such as the following:

Domain { x∈R,0≤ x ≤ 6.5} [0,6.5]

Range { x∈R,0≤ x ≤ 6.13 [0,13].

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If the body of insect has length of 5m, then in microscope of a scale factor of 60, it will become 300 millimetres

Scale factor is a multiplying entity that falls between (0, infinity). Depending on the scale factor, an original figure may be increased or decreased.

Imagine that you have two circles that are visually identical. Even though both circles are described as identical, this does not guarantee equality. Their radii might differ. The one figure would be the scaled version of the other one.

Scale factors and the ideas of ratio and proportion go hand in hand. In ratio and proportion, we multiply or divide a given quantity to create a new one.

If the scale factor is 60

Then body length of insect under the microscope is

5 ×  60

= 300 millimetres

Thus, If the body of insect has length of 5m, then in microscope of a scale factor of 60, it will become 300 millimetres

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Both coaches will charge $440 after 3 hours of coaching.

To find when the two coaches will charge the same amount, we need to set up the equation with help Compound Interest Formula:-

Where:-

Cost of Coach A = Cost of Coach B

200 + 80x = 230 + 70x

where x is the number of hours of coaching.

To solve for x, we can subtract 200 from both sides and 230 from both sides:

80x = 30 + 70x

10x = 30

x = 3

So, the two coaches will charge the same amount after 3 hours of coaching.

To find out how much it will cost, we can substitute 3 for x in the equation for either coach:

Cost of Coach A = 200 + 80x = 200 + 803 = $440

Cost of Coach B = 230 + 70x = 230 + 703 = $440

Therefore, both coaches will charge $440 after 3 hours of coaching.

It's important to note that this calculation assumes that the cost of the coaches is based solely on the hourly rate and initial fee, and does not take into account any other factors such as discounts, taxes, or additional services offered by the coaches.

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The transformation will map ΔABC onto image ΔA'B'C' is, a reflection in the line y = x. So Option C is correct

In mathematics, the triangle is a type of polygon which has three sides and three vertices. the sum of all the interior angles of the triangle is 180°

If anyone of the triangle is 90° then it is called as right angle triangle

Given that,

Two triangles,

First,   ΔABC

Whose coordinates are A(1,3), B(1, 6), C(4, 6)

Second,  ΔA'B'C'

Whose coordinates are A'(3, 1), B'(6, 1), C'(6, 4)

There is only one transformation is  possible,

Which is a reflection in the line  y = x

Because,  the distance of the points will be equal from the line y = x

In comparison of corresponding points

Hence, the transformation is a reflection in the line y = x

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The slope and y-intercept of y=-9 is 0 and (0,-9).

Linear equations can be written in the form y=mx+b, where:y is a y coordinate on the line m is the slope of the line.A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Change y=9 in the slope-intercept form: y=mx+c, where m is the slope of the line and c is the y-intercept, y=0(x)+(-9),

Comparing the equation y=0(x)+9 with the equation y=mx+c, we get that m=0. It is a horizontal line. The slope = 0.

The line cuts the y-axis at the point (0,-9), The y-intercept is at the point  (0,-9)

Hence, the slope and y intercept is 0 and (0,-9).

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The length from the point the ladder touche the wall from the ground 13 feet approximately to the nearest whole number derived using the Pythagoras rule

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

We shall represent the length of the from the wall where the ladder touches the wall to the ground with the letter x, such that by Pythagoras rule we evaluate for the hypotenuse as follows;

14² = x² + 5²

196 = x² - 25

x² = 196 - 25 {subtract 25 from both sides}

x² = 171

x = √171 {take square root of both sides}

x = 13.08

Therefore, the ladder is 13 feet approximately to the nearest whole number from the ground to where it touches the wall using the Pythagoras rule

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Answer: I think it’s m= 262

Step-by-step explanation:

Answer:

m = 262

Step-by-step explanation:

Now we have to,

→ find the required value of m.

The equation is,

→ -3m = -786

Then the value of m will be,

→ -3m = -786

→ m = (-786)/(-3)

→ m = 786/3

→ [ m = 262 ]

Hence, the value of m is 262.

B = 3 + S

Where:

In this equation, B stands for Brooke's number of dresses and S stands for Sarah's number of dresses. The equation states that Brooke's number of dresses is three more than Sarah's number of dresses, so if we know how many dresses Sarah has, we can calculate how many dresses Brooke owns.

The equation B = 3 + S shows that Brooke has three more dresses than Sarah. Knowing Sarah's number of dresses allows us to calculate Brooke's number of dresses by adding three.

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The inverse of the logarithmic function f(x) = log9x is f^-1(x) = 9^x.

The inverse of a function is a new function that "undoes" the original function. For a logarithmic function, such as f(x) = log9x, the inverse is an exponential function.

To find the inverse of f(x) = log9x, you can follow these steps:

Switch the roles of x and y in the original function to make y the subject of the formula.

log9x = y

Replace the logarithm function with its inverse function, the exponential function.

9^y = x

Switch x and y back to their original roles in the equation.

x = 9^y

It's worth noting that for this logarithmic function, the domain of the function is x > 0 and the range is y > 0, and the inverse function will have its domain as y > 0 and range as x > 0. Also, the base of the logarithm 9, is a positive real number, different than 1, this ensures that the logarithm function is defined for all x > 0, for b = 1 it would not be defined for x = 1.

So the inverse of the logarithmic function f(x) = log9x is f^-1(x) = 9^x

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The functions could represent g(x) is C. g(x) = f(x - 5)

Using the general equation as Witten which can be used to find the y intercept of the line

g(x) = f(x) + b

The g(x) has intercept of y=-2,

Then the  y-intercept of f(x) is at y=3

If we find the difference between both y-intercepts, we have

Recall that the y-intercept is the point where the graph intersects the y-axis

( -2 -3) = -5

This implies that the intercept of the line is -5

Then b=-5

Hence, g(x) = f(x - 5) is correct option for the function

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There are different methods to solve a system of equations, but some common ones that are typically taught in 8th grade are graphing, substitution and elimination.

Graphing: This method involves plotting each equation on a coordinate plane and then finding the point of intersection, which represents the solution of the system.

Substitution: This method involves solving one equation for one of the variables and then substituting that expression into the other equation. This will give you an equation with only one variable, which you can then solve.

Elimination: This method involves adding or subtracting the equations in such a way that one of the variables is eliminated. This will give you an equation with only one variable, which you can then solve.

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Answer:14

Step-by-step explanation: This question is asked oddly but I believe it's still 14

3.5 x 4 = 14

Answer: 26/3

Step-by-step explanation:

[tex]f(x) = 2x - \frac{4}{3} \\f(5) = 2(5) - \frac{4}{3} \\f(5) = 10 - \frac{4}{3} \\f(5) = \frac{30}{3} - \frac{4}{3} \\f(5) = \frac{26}{3}[/tex]

In this question we need to evaluate the function f(x) = (2x-4)/3 for the question to be solved with perfect answer.

Evaluating a function means:

Replaces or substitutes each variable with the specified number or expression.

Now, according to question we have to replace x with number 5 so we can get the desired solution.

First evaluate by replacing and substituting the function for variable x with number 5 which is x=5. Hence by replacing the given number gives us the following equation

f (5) = (2*5-4)/3

Now, simplifying

f (5) = (10-4)/3

f (5) = (6)/3

f (5) = 2

Hence, the correct answer for this is 2.

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The slope of the line y = -5x is -5

The slope of a line is a measure of its steepness or incline. It is calculated as the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. Mathematically, it is represented as "m" in the equation y = mx + b, where "m" is the slope, "x" and "y" are the coordinates of a point on the line, and "b" is the y-intercept.

According to the question,

The slope of a line in the equation y = mx + b, where m is the slope of the line and b is the y-intercept, is the coefficient of x.

In the equation y = -5x, the slope of the line is -5.

The slope of a line represents the steepness or the "slant" of the line. It is the ratio of the change in y to the change in x. In the equation y = -5x, the slope of the line is negative, which means that the line is slanting downwards as we move from left to right on the graph. The absolute value of the slope gives the steepness of the line, in this case, the line is steep because the absolute value of -5 is 5.

A negative slope indicates that the line is decreasing and for every 1 unit increase in the x-axis, the y-value will decrease by 5 units. Conversely, for every 1 unit decrease in the x-axis, the y-value will increase by 5 units.

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The statement "In the statement ~(M ⊃ X)~) governs the simple statement M" is false

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

In the statement ~(M ⊃ X)~) governs the simple statement M.

In logic and binary, the negation of an implication (M ⊃ X) is written as ~(M ⊃ X), which is read as "not (M implies X)".

This statement does not govern or control the simple statement M. The simple statement M can be true or false independently of the negation of the implication.

In other words, the truth value of ~(M ⊃ X)is dependent on the truth values of both M and X, not just M.

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Answer:

4. [tex]4^{x}[/tex] - [tex]2x^{2}[/tex] + 5x - 19

5. -[tex]4x^{3}[/tex] + [tex]x^{2}[/tex] - x - 5

Step-by-step explanation:

Find f - g

4. f(x) = 4^x - 7 and g(x) = 2x^2 - 5x + 12

f(x) - g(x) = 4^x - 7 - (2x^2 - 5x + 12)

distribute the -1 to 2x^2 - 5x + 12

4^x - 7 - 2x^2 + 5x - 12

combine like terms

4^x - 2x^2 + 5x - 19

5. f(x) = 3x - 8 and g(x) = 4x^3 - x^2 + 4x - 3

f(x) - g(x) = 3x - 8 - (4x^3 - x^2 + 4x - 3)

distribute the -1 to 4x^3 - x^2 + 4x - 3

3x - 8 - 4x^3 + x^2 - 4x + 3

combine like terms

-4x^3 + x^2 - x - 5

The owner should use a significance level of 0.10 to minimize the chance of firing the quarterback when he has improved.

The owner should use a significance level of 0.10, not 0.01 when evaluating the quarterback's performance. The significance level is the probability of making a type I error, which is rejecting the null hypothesis when it is true. A lower significance level (e.g. 0.01) means that the owner is setting more stringent criteria for accepting the null hypothesis, and therefore is more likely to reject it and potentially fire the quarterback, even if he has improved.

On the other hand, a higher significance level (e.g. 0.10) means that the owner is setting less stringent criteria, and therefore is less likely to reject the null hypothesis and fire the quarterback if he has improved. In this case, the owner wants to minimize the chance of firing the quarterback when he has improved, so it is better to use a higher significance level of 0.10.

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The number of 5ths in the fraction, 6/10 are 3, or there are 3 1/5s in 6/10

A fraction is a representation of a part of a whole. A fraction consists of a number (the numerator) known as the dividend, being divided by another number, (the denominator), also known as the divisor, arranged one over the other.

The expression of a fifth is 1/5

The number of fifths in 6/10 can be obtained by dividing 6/10 by 1/5 as follows;

6/10 ÷ 1/5 = 3

The number of fifths in 6/10 are 3 fifths

The number of fifths in 6/10 can also be obtained by simplifying the fraction, 6/10 as follows;

6/10 = (2 × 3)/(2 × 5) = (2/2) × (3/5)

2/2 = 1, therefore;

6/10 = 1 × 3/5 = 3/5

3/5 = 3 × 1/5

Therefore;

6/10 = 3/5 = 3 × 1/5

6/10 = 3 × 1/5

3 × 1/5 = 6/10

There are three 1/5s (fifths) in 6/10

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Answer:

10

Step-by-step explanation:

hi

The proof that ∠FCB≅∠DCE is shown below

Given that AECF is a rhombus, opposite angles of the rhombus are congruent.

This is represented as

∠EAF = ∠ECF

Also, given that EB ≅ FD, we can conclude that:

∠EBF = ∠DFC

This is by the definition of congruent segments having equal corresponding angles

Add the angles

∠CEB + ∠EBF = ∠CEB + ∠DFC = 180°

Recall that

Since ∠CEB = ∠AEF

So, we have:

∠AEF + ∠EBF = ∠AEF + ∠DFC = 180°

Hence, ∠FCB=∠DCE.

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We need to remove the decimal and multiply and divide by 10, resulting in 0.4/1 x 10/10 = 4/104/10. This can be further reduced to 2/5, so 0.4 as a fraction is 4/10 or 2/5.

A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word "fraction" which means 'to break'. The Egyptians, being the earliest civilization to study fractions, used fractions to resolve their mathematical problems, which included the division of food, supplies, and the absence of a bullion currency.

In Ancient Rome, fractions were only written using words to describe a part of the whole. In India, the fractions were first written with one number above another (numerator and denominator), but without a line. It was the Arabs only, who added the line which is used to separate the numerator and the denominator.

First, we need to remove the decimal.

For that, we multiply and divide by 10 as there is only one digit after the decimal.

We get, 0.4/1 x 10/10 = 4/10

4/10 can further be reduced to 2/5

Hence, we can say that 0.4 as a fraction is 4/10 or 2/5.

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To find the missing length of a triangle using sine it is essential to know at least one side's length

One needs to know the lengths of at least one side and one angle of the triangle in order to use the sine function to get the missing length. In a right triangle, the sine function describes the relationship between the hypotenuse's length and the side length that is opposite the angle.

There are certain steps as to how the sine function determines a triangle's missing length. These steps are -

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В саду росте 500 дерев, з яких 24% є яблуні, що дає 120 яблунь. Груші становлять 115% кількості яблунь, тобто 135 груш. Вишні становлять 5/6 кількості груш, тобто 112,5 вишні. Решта дерев - сливи становлять 500 - 120 - 135 - 112.5 = 142.5 сливових дерев.

[tex]\it \dfrac{24}{100}\cdot500=24\cdot5=120\ apples\ trees\\ \\ \\ \dfrac{115}{100}\cdot120=\dfrac{115\cdot12}{10}=\dfrac{1380}{10}=138\ \ pears\ trees\\ \\ \\ \dfrac{5}{6}\cdot138=\dfrac{5\cdot138}{5}=\dfrac{690}{6}=115\ cherries\ trees\\ \\ \\ 500-(120+138+115)=500-373=127\ plums\ trees[/tex]

Answer:

Every triangle has interior angles that add up tp 180°

Step-by-step explanation:

Complex numbers are those expressed as a+ib, where a, b are real numbers and I is a fictitious number called a "iota." I is equal to (-1).

A complex equation is one that needs complex numbers to be solved. Complex numbers are those that have both real and fictitious components. It is spelled out as follows: Both the letters A and B in the previous equation stand for numerical values. 4+3i is an example of a complicated number.

Complex issue solving is a set of self-regulated psychological processes and activities that are used to achieve ill-defined goals that cannot be accomplished through typical behaviors. Numerous strategies and creative knowledge combinations are needed.

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The base is 5 and the exponential is 2. This can be written in expanded form as 5 multiplied by 5, which is equal to 25. In standard form, this can be written as 52, which is shorthand for the same calculation.

Base: 5

Exponent: 2

Expanded form: 5 x 5

Standard form: 52

An exponential expression is a mathematical expression that uses the operation of exponentiation. In this expression, one number, known as the base, is raised to the power of another number called the exponent. To write an exponential expression, choose a number between 0 and 10 for the base and another number between 0 and 10, different from the base, for the exponent. Then, write the exponential expression in expanded form and standard form. For example, if the base is 5 and the exponent is 2, then the expression can be written in expanded form as 5 multiplied by 5, which is equal to 25. In standard form, this can be written as 52, which is shorthand for the same calculation. This expression can be used to represent any number or calculation that can be written in exponential form.

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The requried area of the actual room is given as 264 foot².

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
As given in the question,
1/2 inch = 1 foot
1 inch = 2 foot

Now,
A rectangular room measures 6 inches by 11 inches on the drawing.
= 6 inch × 11 inch
= 6 (2 foot) × 11 (2 foot)
= 12 × 22 foot²
= 264 foot²

Thus, the requried area of the actual room is given as 264 foot².

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The ordered pair that is a solution to all system inequalities is the linear inequality's solution, and the linear inequality's graph is the system's solution graph.

Shade the half-plane that satisfies the inequality and graph one line at a time in the same coordinate plane.

The system does not have a solution when two inequalities have parallel lines and the shaded areas do not overlap (i.e., the opposite areas are shaded). As a result, neither of the inequalities can be proven true at any given coordinate point.

Solution to a System of Linear Equations To determine whether a point is a solution to a system, we will either look for the point of intersection of two lines on a graph or look for the point's algebraic location on both lines.

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