Translate the following sentence into an equation using n for the unknown number. Then solve for n.
when 15 is decreased by three times a number, the result is 21
a.
15 - 372 = 21
n = -2
b.
312 - 15 = 21
n = -2
C.
31 - 15 = 21
n = 12
d.
15 - 3n2 = 21
n-2

If the function f(x) = 5 + 3x and g(x) = 5 - 9x. The value of f(g(2))  is -34

The given functions are

f(x) = 5 + 3x and g(x) = 5 − 9x.

a. We plug-in 2 in the function g(x) and then the obtained image in the function

f(x)g(2) = 5 − 9 × 2

           = 5 - 18

           = -13

f(g(2)) = f(-13)

        = 5 + 3 × (−13)

        = 5 - 39

        = -34

b. We find the composite function by replacing x in f(x)  by  

g(x) f(g(x)) = 5 + 3g(x)

                = 5 + 3 × (5−9x)

                = 5 + 15 − 27x

f(g(x)) = 20 − 27x

f(g(2)) = 20 − 27 × 2

         = 20 − 54

         = -34

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It is an iterated function also known as hailstone problem and can be solved on iterated steps.

Since then, the 3X + 1 issue has taken many different shapes. It is among the most infamous puzzles that have never been solved. For more than 40 years, prizes have been offered for its resolution, but nobody has totally and properly done so.

The 3x+1 Conjecture states that this function can be iterated through multiple times to eventually produce the value 1 starting from any positive integer n.

Take a positive integer X and divide it by 2 if it is even. If it is odd, multiply it by 3 and add 1 to the result to form the conjecture 3X + 1. The ends operate repeatedly according to the aforementioned criteria, and after a finite number of repetitions, the final end is always 1.

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Answer: 363.49

Step-by-step explanation:

6.75%=.0675

5385*.0675+300=363.4875

round up

$363.49

The name of the condition in which factors f and g are correlated and may not be independent is confounded

What is  Fractional factorial?

In statistics, fractional factorial designs are experimental layouts made up of a carefully selected subset of full factorial design's experimental runs.

In a fractional factorial experiment, confounded factors are those that cannot be varied independently of each other because they are correlated. Confounded factors can affect the interpretation of the results of the experiment, as it may not be clear which factor is responsible for a particular effect. To control for confounded factors, it may be necessary to include them both in the experimental design or to use additional statistical techniques to account for their correlated nature.

Confounded factors are also known as aliased factors.

Hence, Name of the condition in which factors f and g are correlated and may not be independent is confounded

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The missing number in an integer array of 1 to 100 can be found by summing the numbers 1-100 and subtracting the sum of the given array. The difference between the two sums will be the missing number.

To find the missing number, first sum the numbers 1-100 to get the total sum. Then sum the given array and subtract this sum from the total sum. The difference between the two sums will be the missing number. This method works because the total of the array should be equal to the sum of 1-100 if all the numbers are present. By subtracting the sum of the given array from the total sum, any missing numbers will be accounted for in the difference.

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The measure of each side of the isosceles right triangle with hypotnuse 2.5√2 cm is  2.5 cm   .

The Isosceles Right Triangle is a type of right triangle which consists of two equal length legs .

In the right isosceles triangle the measure of the base and the perpendicular is same , So , base = perpendicular

let the side of the isosceles right triangle be = x .

given that the measure of the hypotnuse is = 2.5√2 cm

In a right triangle , By Pythagoras Theorem ,

base + perpendicular = hypotnuse

x² + x² = (2.5√2)²

2x² = 6.25 × 2

2x² = 6.25 × 2

2x² = 12.5

x² = 12.5/2

x² = 6.25 ,

x =  2.5 cm   ,....by taking square root on both the sides .

Therefore , the measure of each side is  2.5 cm  .

The given question is incomplete , the complete question is

What is the measure of each side of the given isosceles right triangle with a hypotenuse that measure 2.5√2 cm ?

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The true statement on dilations are that :

Dilation is the process of increasing an object's size without altering its shape. Depending on the scale factor, the object's size may increase or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's shape doesn't change.

Dilation therefore allows for the same shape as the original shape, but it is a reduction of the original shape and so cannot be the same size.

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Answer:

yes its a polynomial espero te sirva

We will use the concept of Simplification of Equations . The value of p in the given equation is 1.

An Algerbraic equation in algebra is any equation that can be transformed in standard form like the following:

ax+bx+c=0 or ap+bp+cp+d=0 it can be of any form.

With a 0 and a, b, and c are known numbers, x is an unknown value, and a. The equation is linear, not quadratic, if a = 0 and b 0. The coefficients of the equation, denoted by the numbers a, b, and c, are the quadratic coefficient, linear coefficient, and constant or free term, respectively.

The roots or zeros of the expression on the left-hand side of the equation are the values of x that fulfill the equation. There can only be only solution to an Algebraic equation.

6p=2(5-2p) is the given equation

Divide by 2 on both LHS and RHS of the equation

6p/2 = 2(5-2p)/2

⇒3p=5-2p

⇒5p=5

∴p=1

We will use the concept of Simplification of Equations . The value of p in the given equation is 1.

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Answer:

Step-by-step explanation:

To find the area of the base of the box, we need to determine the length, breadth, and height of the box. We can set up a system of equations to represent the given information:

breadth = 2/3 * length

height = 1/3 * length

volume = length * breadth * height

Substituting the second equation into the third equation, we get:

volume = length * breadth * (1/3 * length)

      = length^2 * (2/3) * (1/3)

      = (2/9) * length^2

      = 48

      = 2^4 * 3

Solving for length, we find that length = 6. Plugging this value back into the first equation, we find that breadth = 4.

Therefore, the area of the base of the box is length * breadth = 6 * 4 = 24 square meters.

Answer:

3/7

Step-by-step explanation:

[tex]g(-2)=\log_{2}(1)-4=-4 \\ \\ g(5)=\log_{2}(8)-4=-1 \\ \\ \frac{g(5)-g(-2)}{5-(-2)}=\frac{-1-(-4)}{5-(-2)}=\frac{3}{7}[/tex]

The base of a solid, three-dimensional, or shaped item. What the thing "rests" on is the base. Polygons, forms, and solids all employ base.

Any pyramid's surface area can be calculated by multiplying the base's surface area by the lateral faces' surface areas.

Pyramid's slant height and the square base's side length.

Thus, base area of the square pyramid is length x width.

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The equation that has similar equation with the one given is D. 3/2p - 5 + 9/4p = 7 - 5/4p

We are given the equation;

-16p + 37 = 49 - 21p

We are supposed to identify the equation that has similar solution with the equation given;

The solution for the equation given is;

-16p + 37 = 49 - 21p

Combining the like terms;

-16p + 21p = 49 - 37

5p = 12

  p = 2.4

Solution for the choices given;

A.  -14 + 6p = -9 - 6p

    6p + 6p = -9 +14

     12p = 5

        p= 0.417

B. -55 + 12p = 5p + 16

   12p - 5p = 16 + 55

      7p = 71

        p = 10.14

C. 2 + 1.25p = 3.75p + 10

   1.25p - 3.75p = 10 - 2

            -2.5p = 8

               p = -3.2

D.  3/2p - 5 + 9/4p = 7 - 5/4p

    3/2p +5/4p +9/4p = 7 + 5

              5p =12

                    p = 2.4

Therefore, the equation that has similar equation with the one given is D. 3/2p - 5 + 9/4p = 7 - 5/4p

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The commission the employee earns as a percentage of the total cost of the gym membership is 19%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

In this case, the gym keeps $42 and the employee who sold it gets $8.

The commission the employee earns as a percentage of the total cost of the gym membership will be:

= 8 / 42 × 100

= 19%

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Given a system of two equations in two variables, solve using the substitution method.

Word problems that require us to write systems of linear equations have two unknown quantities and two different ways to relate them.

This means we need to write two linear equations, and each contains the two unknowns as variables. The Understanding linear relationships lesson details how to translate verbal descriptions into equations.

After we write the equations, we can solve the system using our preferred method(s) for solving systems of linear equations covered in the Solving systems of linear equations lesson.

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Answer:

4

Step-by-step explanation:

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 4 is 2, because 2 x 2 = 4. The square root of 9 is 3, because 3 x 3 = 9.

The square root of 16 is 4, because 4 x 4 = 16. Therefore, the value of the square root of 16 is 4.

(i) 0 is the remainder when x³ + 3x² + 3x + 1 is divided by (x +1)

(ii) 27/8 is the remainder when x³ + 3x² + 3x + 1 is divided by (x - 1/2)

(iii) 1 is the remainder when x³ + 3x² + 3x + 1 is divided by x

(iv) -π³ + 3π² - 3π + 1 is the remainder when x³ + 3x² + 3x + 1 is divided by (x + π)

(v) -27/8 is the remainder when x³ + 3x² + 3x + 1 is divided by (5 + 2x)

The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remaining is the name for this amount.

Let a be any real number and let p(x) be any polynomial with degree greater than or equal to one.

Now, if a polynomial p(x) is divided by (x - a) then the remainder is p(a).

Assume, p(x) = x³ + 3x² + 3x + 1

Now,

(i) The root of x + 1 = 0 is -1

or, p(-1) = (-1)³ + 3(-1)² + 3(-1) + 1

or, p(-1) = -1 + 3 - 3 + 1

or, p(-1) = 0

Hence by the remainder theorem, 0 is the remainder when, x³ + 3x² + 3x + 1 is divided by x + 1. We can also say that x + 1 is a factor of x³ + 3x² + 3x + 1.

(ii) The root of x - (1/2) = 0 is 1/2.

or, p(1/2) = (1/2)³ + 3(1/2)² + 3(1/2) + 1

or, p(1/2) = 1/8 + 3/4 + 3/2 + 1

or, p(1/2) = (1 + 6 + 12 + 8)/8

or, p(1/2) = 27/8

Hence by the remainder theorem, 27 / 8 is the remainder when x³ + 3x² + 3x + 1 is divided by x.

(iii) The root of x = 0 is 0

or, p(0) = (0)³ + 3(0)² + 3(0) +1

or, p(0) = 0 + 0 + 0 + 1

or, p(0) = 1

Hence by the remainder theorem, 1 is the remainder when  x³ + 3x² + 3x + 1 is divided by x.

(iv) The root of x + π = 0 is - π

or, p(-π) = (-π)³ + 3(π)² - 3π + 1

or, p(-π) = -π³ + 3π² - 3π + 1

Hence by the remainder theorem, (-π)³ + 3(π)² - 3π + 1 is the remainder when x³ + 3x² + 3x + 1 is divided by x + π.

(v) Now, the root of 5 + 2x = 0 is -5/2

or, p(-5/2) = [(-5/2)³ + 3(-5/2)² + 3(-5/2) + 1]

or, p(-5/2) = [(-125/8) + (75/4) + (-15/2) + 1]

or, p(-5/2) = (-125 + 150 - 60 + 8) / 8

or, p(-5/2) = (-185 + 158) / 8

or, p(-5/2) = -27/8

Hence by remainder theorem, -27/8 is the remainder when x³ + 3x² + 3x + 1 is divided by 5 + 2x.

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The complete question is as follows:

Find the remainder when x³ + 3x² + 3x + 1 is divided by

i) x + 1    ii) x - (1/2)    iii) x    iv) x + π    v) 5 + 2x

Answer:

3

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Scalar projection}\\\\Scalar projection $=\dfrac{u \cdot v}{|u|}$\\\\where:\\ \phantom{ww}$\bullet$ $u$ is the vector being projected onto.\\\end{minipage}}[/tex]

Given:

Calculate the magnitude of vector u:

[tex]\implies |u|=\sqrt{(0)^2+(-1)^2}=1[/tex]

The scalar projection is the magnitude of the vector projection.

Therefore, the magnitude of the projection of vector v onto vector u is:

[tex]\implies \dfrac{u \cdot v}{|u|}=\dfrac{\langle0, -1\rangle \cdot \langle-5, -3\rangle}{1}=\dfrac{0 +3}{1}=\dfrac{3}{1}=3[/tex]

The roots of a quadratic equation can be found by analyzing the shape of the parabola formed by the equation's graph. The number of roots is determined by the number of x-intercepts.

To find the nature of the roots of a quadratic equation using a graph, you can plot the graph of the equation and analyze the shape of the graph. The graph of a quadratic equation is a parabola which opens upward or downward depending on the sign of the coefficient of the x² term. If the coefficient is a positive number, the parabola opens upward and if the coefficient is a negative number, the parabola opens downward. The roots of the equation are the x-intercepts of the graph, and there may be zero, one, or two roots. If the graph intersects the x-axis at two distinct points, the equation has two real, distinct roots. If the graph touches the x-axis at one point, the equation has one real root. If the graph does not intersect the x-axis, the equation has no real roots.

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Answer:

Step-by-step explanation:

The standard acceleration due to gravity (or standard acceleration of free fall), sometimes abbreviated as standard gravity, usually denoted by ɡ0 or ɡn, is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is defined by standard as 9.80665 m/s2 (about 32.17405 ft/s2).

The slope of the given equation y = 10 - 4x is equal to -4.

As given in the question,

Given equation is equal to y = 10 - 4x

Standard form in slope intercept form for the equation  is given by :

y = mx  + c

'm' is representing the slope of the given equation

'c' is representing the value of the  y-intercept of the given equation.

Now after simplifying the given equation in the standard form we get,

y = 10 - 4x

⇒ y = -4x + 10 __(1)

Compare equation (1) with the standard form of slope intercept form we get,

Slope of the equation is equal to m = -2.

Therefore, the slope of the given equation y = 10 - 4x is given by m = -4.

The given question is incomplete , the complete question is:

What is the slope of the equation y = 10 - 4x ?

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Solution of the equation using substitution method is given by following steps:

1. Get the value of one variable in the other variable form using one equation.

2. Substitute the value of that variable in the second equation and get the value of both the variables.

Let us consider the system of equation to explain the solution of substitution method:

x + y = 0   __(1)

2x + 3y = 6  ___(2)

Get the value of y in the x form and substitute the value of y in equation (2) we get,

y = -x

2x + 3(-x) = 6

⇒2x - 3x = 6

⇒ -x = 6

⇒ x = -6

Now substitute the value of x in equation (1) we get,

y = -( -6)

⇒ y = 6

Therefore, the solution of the equation using substitution method is given by following way:

1. Get the value of one variable in the other variable form using one equation.

2. Substitute the value of that variable in the second equation and get the value of both the variables.

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The gradient of the line whose equation is x = -4 is: undefined.

The graph of an vertical line is a line that cuts the x-axis at (a, 0), of which has an undefined slope because it has a change in y but has no change in x. That is, the run of the line is zero. This means the gradient of a vertical line is undefined.

The equation of a vertical line is given as x = a, where a is the point that the line intersects the x-axis at.

Given the equation, x = -4, it means the line is a vertical line.

Therefore, since the gradient of vertical lines are undefined, the gradient of x = -4 is also determined to be undefined.

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The median x˜ is the data value separating the upper half of a data set from the lower half.

Arrange data values from lowest to highest value

The median is the data value in the middle of the set

If there are 2 data values in the middle the median is the mean of those 2 values.

Median Example

For the data set 1, 1, 2, 5, 6, 6, 9 the median is 5.

For the data set 1, 1, 2, 6, 6, 9 the median is 4. Take the mean of 2 and 6 or, (2+6)/2 = 4.

Median Formula

Ordering a data set x1 ≤ x2 ≤ x3 ≤ ... ≤ xn from lowest to highest value, the median x˜ is the data point separating the upper half of the data values from the lower half.

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Answer: Part A: 994 feet higher thanks to absolute value.

Part B: -86 feet.

Step-by-step explanation: math

As per the concept of linear equation, the college student took 13 courses of 3 credit hours.

An equation in math is defined as a mathematical statement with an 'equal to' symbol between two expressions that have equal values

Here we have given that college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses

And we need to find number of students in each category.

While we looking into the given question, we have given the values like the following,

Here the total credits = 59

And the total courses = 18

Then let us consider the number of 3 credit hour courses is referred as x and the number of 4 credit hour courses referred as y

Then based on the given statement, we have written the equation as

=> x + y = 18 ----------------------------(1)

=> 3x+4y=59   --------------------------(2)

Here we have to eliminate y to find the number of 3 credit hour courses, by multiplying Equation 1 by 4

Then we get,

=> 4x + 4y = 72

Then we have to subtract Equation 2 from Equation 3

Then we get,

=> x = 13

Therefore, the resulting value is 13.

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So, the length of triangle side a in centimeters is 6.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

We can use the fact that the ratio of corresponding sides in similar figures is constant to solve this problem.

Since the two triangles are similar, we know that the ratio of their sides is constant. Letting x represent the length of side a in centimeters, we have

(a/3) = (8/4)

We can solve this equation by multiplying both sides by 3 to get

a = (8/4) * 3

= 6

Therefore, the length of side a in centimeters is 6.

The answer is therefore 6.

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Since the two triangles are similar, we know that the ratio of their sides is constant. Letting x represent the length of side a in centimeters, we have

(a/3) = (8/4)

We can solve this equation by multiplying both sides by 3 to get

a = (8/4) * 3

= 6

Therefore, the length of side a in centimeters is 6.

The answer is therefore 6.

There are four terms in the expression –2p³ – 3p² + 4p + 7. The first term is –2p³, the second term is –3p², the third term is 4p, and the fourth and final term is 7.

Terms in math are individual components of equations or expressions, which can consist of constants, variables, and operators. A term can also be a single number or variable, or several numbers or variables multiplied together. Terms are separated by addition or subtraction operators. Terms can also be used to describe an algebraic expression such as the sum of two terms, or the product of two terms.

The expression can be written as –2p³ – 3p² + 4p + 7 = 0. This expression is a polynomial equation with degree three, meaning the largest exponent of the variables is 3.

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