The polynomial of degree 4,
P(x) has a root of multiplicity 2 at x=3 and roots of multiplicity 1 at x=0 and x = - 4. It goes through the point (5,144). Find a formula for P(x).

The value of x is equal to 8, in the equation 14x -22.

An equation is a mathematical statement consisting of two expressions joined by an equal sign. 

Solution:

The diagonals of the dragon intersect at right angles. This gives a solvable relationship for x.

setting the displayed dimensions correspond to 90° angular dimensions.

14x -22 = 90

You can solve this two-level linear equation in the usual way.

14x = 112. . . . . . Step 1, add the reciprocal of the constant to get just x

x = 112/14 = 8 . . . Step 2, divide by the factor of x

Hence, the value of x is 8. 

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Answer:

  77.5°

Step-by-step explanation:

You want the measures of the angles formed when ray OX bisects the 155° angle AOB.

The angle bisector creates two equal angles, each of which is half the measure of the original angle. The measures of the angles formed are ...

  155°/2 = 77.5°

The boat's displacement is approximately 84,016.8 metric tons.

To convert the boat's top speed from knots to miles per hour, we can use the conversion factor of 1.15078 miles per hour per knot:

26 knots × 1.15078 miles per hour per knot = 29.86 miles per hour (rounded to two decimal places)

Therefore, the boat's top speed is approximately 29.86 miles per hour.

To convert the boat's displacement from tons to metric tons, we can use the conversion factor of 0.907185 metric tons per ton:

93,000 tons × 0.907185 metric tons per ton = 84,016.8 metric tons (rounded to one decimal place)

Therefore, the boat's displacement is approximately 84,016.8 metric tons.

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Answer:

the final answer is 7x + 5xy.

Step-by-step explanation:

3x + 4x = 7x

3xy + 2xy = 5xy

So, the final answer is 7x + 5xy.

Answer:

5xy+7x

Step-by-step explanation:

You see which ones have the same exact variables (x or xy)

Then you add the ones with the same variables together.

3x+4x=7x

3xy+2xy = 5xy

5xy+7x

(Depending on your teacher, they may not have to be in this order)

Liters of 10% solution = 1 liters

Liters of 70% solution = 5 liters

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x +3 = 8 is an equation.

We have,

10% solution = x

70% solution = y

Now,

A 10% antifreeze solution is to be mixed with a 70% antifreeze solution to get 6 liters of a 20% solution.

This means,

We can make two equations.

0.10x + 0.70y = 6 x 0.20

0.10x + 0.70y = 1.2 ______(1)

x + y = 6 ______(2)

Solve for x and y.

From (2),

x = 6 - y

Substituting in (1) we get,

0.10x + 0.70y = 1.2

0.10 (6 - y) + 0.70y = 1.2

0.6 - 0.10y + 0.70y = 1.2

0.6 + 0.60y = 1.2

0.60y = 1.2 - 0.6

0.60y = 0.6

y = 1

And,

x = 6 - y

x = 6 - 1

x = 5

Thus,

10% solution = 1 liter

70% solution = 5 liters

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The value of 10p - 3p/4- 2 +5 for p=10 is 95.5.

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

We have 10p - 3p/4- 2 +5.

Now put the value of p =10 we get

= 10p - 3p/4- 2 +5

= 10(10) - 3(10)/4- 2 +5

= 100 - 30/4 -2 + 5

= 100 -7.5 -2 +5

= 95.5

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One inequality that is equivalent to 3x<1 and 6x<2 is 3x<1/2.

To see why this is true, we can divide both sides of the second inequality by 2, which gives 3x<1/3. However, we want an inequality that is equivalent to both 3x<1 and 6x<2, so we need to find a common solution.

Notice that if 3x<1, then x<1/3. And if 6x<2, then x<1/3 as well (since 1/3 is less than 2/6). Therefore, the intersection of the solutions for these two inequalities is x<1/3.

But we want an inequality in the form of 3x<a, where a is some constant. To find this value, we need to solve for x in the intersection of the two solutions:

x<1/3

Multiplying both sides by 3 gives:

3x<1

So we can choose a=1/2, which gives us the final inequality:

3x<1/2

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The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

What is a polynomial ?

A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) multiplied by coefficients.

where n is a non-negative integer (the degree of the polynomial), x is the variable, and (the coefficients of the polynomial). The highest power of x in the expression is n, and this term is called the leading term. The coefficient of the leading term, a_n, is called the leading coefficient.

To find the other linear factors of the polynomial function f(x) = x³ - 4x² - 3x + 18, we can use long division by dividing the polynomial function by (x + 2).

Here's how the long division would look like:

x³ - 4x² - 3x + 18

       ÷ x + 2

__________________________

x² - 6x - 20

             ÷ x + 2

__________________________

x - 22

       ÷ x + 2

__________________________

-20

here -20 is the remainder.

The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

So, the other linear factors are x - 22.

Therefore, The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

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A quadratic function could represent the data in the table, as the increase rate decreases as x increases, meaning that the function could be approaching it's vertex.

Traditionally, functions are classified as either linear or exponential, as follows:

As there is not a constant neither a multiplicative rate of change for the table, the function is neither linear nor exponential.

Considering that from x = 1 to x = 4 the rate of change is of 4/3, while from x = 16 to x = 25 the rate of change is of 4/9, that is, the increase rate decreases as x increases, the function is classified as a quadratic function.

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The measure of angle ∠ACB is 45 degrees

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

A (-3, 2), B (0, 0), C (2, 3)

The graph is attached

The lines AB and BC are perpendicular lines

This means that

∠B = 90 degrees

Calculate the length AB and BC using

distance = √[(x2 - x1)² + (y2 - y1)²]

So, we have

AB = √[(-3 - 0)² + (2 - 0)²] = √13

BC = √[(0 - 2)² + (0 - 3)²] = √13

The angle C is then calculated as

tan(C) = AB/BC

tan(C) = √13/√13

tan(C) = 1

Take the arctan of both sides

C = 45

Hence, the measure of ∠ACB is 45 degrees

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The volume of the cube  is 444.19 in³

The volume of the rectangular prism is 661.2 ft³

The volume of the triangular prism is 30.04 yd³

The volume of the cylinder is 380.57 km³

Volume of a cube is solved using the formula

= length³

= 7.63³

= 444.19 in³

Volume of a rectangular prism is solved using the formula

= Area of base * height

= 9.5 * 8.7 * 8

= 661.2 ft³

Volume of a triangular prism is solved using the formula

= 1/2 × base × height × length

= 1/2 * 5.84 * 3.08 * 3.34

= 30.04 yd³

Volume of a cylinder is solved using the formula

= π * radius² * height

= π * 3² * 13.46

= 380.57 km³

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Answer:

35 mph

Step-by-step explanation:

5×5=25

60-25=35.

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Answer:

x = -5

Step-by-step explanation:

15 - 2x = -4(x+1) + 9

-4(x+1) can be distributed and simplified to -4x - 4

15 - 2x = -4x - 4 + 9

15 - 2x = -4x +5

-2x + 4x = 5 - 15

2x = -10

x = -5

Answer:

[tex]x=-5[/tex]

Step-by-step explanation:

Given

[tex]15-2x=-4(x+1)+9[/tex]

Simplify the right side by applying the distributive property.

[tex]15-2x=(-4*x)+(-4*1)+9[/tex]

[tex]15-2x=-4x-4+9[/tex]

Add [tex]-4[/tex] and 9.

[tex]15-2x=-4x+5[/tex]

Add [tex]4x[/tex] to both sides of the equation.

[tex]15-2x+4x=5[/tex]

Add [tex]-2x[/tex] and [tex]4x[/tex].

[tex]15+2x=5[/tex]

Subtract [tex]15[/tex] from both sides of the equation.

[tex]2x=-10[/tex]

Divide both sides of the equation by [tex]2[/tex].

[tex]x=-5[/tex]

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In the trigonometry relation the value of θ is 45 degrees and the coterminal angle between 0° < θ < 360° is 315 degrees

Coterminal angles are angles that have the same terminal side in a given circle. They are angles that differ by a multiple of 360 degrees.

In other words, if two angles are coterminal, they have the same trigonometric functions, despite having different degrees.

If sec θ = √2

θ = arc sec (√2)

θ = arc cos (1/√2))

θ = 45 degrees

coterminal of angle 45 degrees between 0° < θ < 360°

360 - 45 = 315.

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The sample distribution of (PM-PB) will not be normal, because w expect fewer than 10 electric cars in both samples.

There are two types of data sets are collected for the research. They are population and sample. Population includes all the elements from the data set. Sample is a part of population.

The company planned to take survey from the employees from both the main office and the branch office.

For this, the company took 100 employees from main office and 50 employees from a branch office.

We expect at least 10 successes and at least 10 failures in both samples, then the sampling distribution of [tex]p_{1 }and p_{2}[/tex] will be approximately normal.[tex]n_{1}p_{1}\ge 10 and n_1(1-p_1)\ge10[/tex]

[tex]n_{2}p_{2}\ge 10 and n_2(1-p_2)\ge10[/tex]

Let [tex]x_{1} and x_2[/tex] denotes the number of persons in the sample.

[tex]x_{1} =100\\n_{2} =50[/tex]

Also given 1.5% of employees at the main office have electric cars and 2% of employees at the branch office have electric cars.

so, [tex]p_{1}=0.015, p_{2}=0.02[/tex]

Combining this values we have,

[tex]n_1p_1=100(0.015)=1.5\le10[/tex] and

[tex]n_1(1-p_1)=100(1-0.015)=98.5 > 10[/tex]

Similarly, [tex]n_2p_2=50(0.02)=1\le10[/tex] and

[tex]n_2(1-p_1)=50(1-0.02)=49\ge10[/tex]

Hence, the sample distribution of PM-PB will not be normal, because w expect fewer than 10 electric cars in both samples.

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If X and Y are independent and identically distributed uniform random variables on (0, 1), then the joint density of

(a) U = X + Y, V = X/Y is u/v² for v > 1 and 0 ≤ u ≤ 1.

(b) U = X, V = X/Y is 1/v for v > 1 and 0 ≤ u ≤ 1.

(c) U = X + Y, V = X/(X+Y) is v/(1+v)² for v > 0 and v/(1+v) ≤ u ≤ 1.

In probability theory, joint density is a mathematical function that describes the probability distribution of two or more random variables. It represents the probability of occurrence of different values of those variables in a particular region of space. In this problem, we have to calculate the joint density of U and V, where U and V are functions of X and Y.

(a) For U = X + Y and V = X/Y, we can find the joint density as follows:

First, we need to find the distribution of U and V separately. Since X and Y are independent and identically distributed uniform random variables on (0, 1), their individual probability density functions are f(x) = 1 for 0 ≤ x ≤ 1.

To find the density of U, we can use the convolution formula, which states that the density of the sum of two independent random variables is the convolution of their individual densities. Thus,

fU(u) = ∫ fX(u - y)fY(y) dy

= ∫ 1 dy

= u for 0 ≤ u ≤ 1.

Next, to find the density of V, we need to transform X and Y using the change of variables formula. Let Z = X/Y, then

fV(v) = fZ(z)|dz/dv|

= fX(vz)/(z²) |z|

= 1/(v²) for v > 1.

Therefore, the joint density of U and V is given by the product of their individual densities:

fUV(u,v) = fU(u) fV(v)

= u/v² for v > 1 and 0 ≤ u ≤ 1.

(b) For U = X and V = X/Y, we can similarly find the joint density as:

fUV(u,v) = fX(u) fV(v)

= 1/v for v > 1 and 0 ≤ u ≤ 1.

(c) For U = X + Y and V = X/(X+Y), we can use the same method as in (a) to find the individual densities of U and V:

fU(u) = u for 0 ≤ u ≤ 1,

fV(v) = v/(1+v)² for v > 0.

Then, the joint density of U and V is given by:

fUV(u,v) = fU(u) fV(v) |du/dx|

= v/(1+v)² for v > 0 and v/(1+v) ≤ u ≤ 1.

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Answer:

That's not math. Please classify your question correctly.

Answer: Since the perimeter of all the rectangles is equal (24 cm), the sum of the length and width of each rectangle must be equal for each rectangle. This is because the perimeter of a rectangle is equal to the sum of its lengths plus the sum of its widths, multiplied by 2.

For example, if the length of one rectangle is "l" cm and its width is "w" cm, then its perimeter would be 2l + 2w = 24 cm.

So, in general, we can write the equation: l + w = P/2, where P is the perimeter of the rectangle (in this case, P = 24 cm).

Therefore, the sum of the length and width of each rectangle is equal and constant, regardless of the individual values of the length and width. This means that as the length of a rectangle increases, its width must decrease by an equal amount to keep the sum constant. And vice versa.

In conclusion, the sum of the length and width of each rectangle is equal, and it is equal to half of the perimeter of the rectangle.

Step-by-step explanation:

Using a system of equations, the number of points given for an arrow in target B is 7.

A system of equations means two or more equations solved at the same time or concurrently.

A system of equations is also described as simultaneous equations since they are solved simultaneously.

                              Target A    Target B   Total Score

Rence shots                3                1                  19

Sunil shots                  2                2                22

Let the points for an arrow into target A = x

Let the points for an arrow into target B = y

3x + y = 19 ... Equation 1

2x + 2y = 22 ... Equation 2

Multiply Equation 1 by 2:

6x + 2y = 38 ... Equation 3

Subtract Equation 2 from Equation 3:

6x + 2y = 38

-

2x + 2y = 22

4x = 16

x = 4

From Equation 1, substitute x = 4:

3x + y = 19

3(4) + y = 19

12 + y = 19

y = 19 -12

y = 7

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1. The height of the cone is, 22.18 mm.

2. The slant height is, 28.14 mm.

3. The ant crawl to get from the base of the cone to the top of the hill is, 28.14 mm.

In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.

The volume of cone V = (1/3)πr²h

Given that,

The volume  = 8792 mm³

1. by using the formula to solve for h,

we get h = (3V)/(πr²).

Plugging in the values given,

we have h = (3(8792 mm³))/(π(20 mm)²) ≈ 22.18 mm.

Therefore, the height of the cone is approximately 22.18 mm.

2. it is known that, from the Pythagoras theorem

s² = h² + r²,

where s is the slant height, h is the height, and r is the radius.

Plugging in the values we found in part 1,

we have s² = (22.18 mm)² + (20 mm)² ≈ 791.88 mm².

Taking the square root of both sides, we get s ≈ 28.14 mm.

Therefore, the slant height is approximately 28.14 mm.

3. To find the distance the ant crawls to get from the base of the cone to the top of the hill, we need to find the length of the slant height.

Using the value we found in part 2,

the length of the slant height is approximately 28.14 mm.

Therefore, that is the distance the ant would crawl to get from the base of the cone to the top of the hill.

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Answer:

To determine the balance in the Allowance for Doubtful Accounts on December 31, we first need to estimate the bad debts based on the credit sales.

Bad debts = 2% of credit sales = 2% * $400,000 = $8,000

The balance in the Allowance for Doubtful Accounts would then be equal to the estimated bad debts, which is $8,000.

Therefore, the Accounts Receivable and the Allowance for Doubtful Accounts would appear on the December 31 balance sheet as follows:

Current Assets:

Accounts receivable $120,000

Less: Allowance for doubtful accounts $8,000

Net accounts receivable $112,000

The number of weekly downloads can be modeled using an exponential function h(x) = 548 × 1.04ˣ.

What is exponential function?

An exponential function is a mathematical function in which the value of the output is proportional to the value of a fixed number (known as the base) raised to the power of the input value. The general form of an exponential function is:

                                      y = abˣ

where a and b are constants, x is the input value, and y is the output value. The constant a controls the vertical scaling of the function, while the constant b controls the rate of growth or decay. If b is greater than 1, the function grows rapidly as x increases. If 0 < b < 1, the function decays as x increases. If b is equal to 1, the function is a linear function.

Exponential functions are widely used in many fields, including finance, biology, physics, and engineering, to model growth and decay processes.

The number of weekly downloads can be modeled using an exponential function.

                             h(x) = 548 * 1.04ˣ

where x is the number of weeks after the release date, h(x) is the estimated number of weekly downloads, and 1.04 is the growth factor (1 + the expected weekly increase of 4%).

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The number of bees that will equal the mass of a single moose is 5 × 10⁶.

Given the data in the question;

To determine the number of bees that will equal the mass of a single moose.

Let the number be represented by x.

Hence;

Number of bees × mass of bee = mass of moose

n × ( 2.5 × 10⁻⁴ ) = 1.25 × 10³

Divide both sides by ( 2.5 × 10⁻⁴ ).

n = ( 1.25 × 10³ ) / ( 2.5 × 10⁻⁴ )

n = 1250 / 0.00025

n = 5,000,000

Therefore, the number of bees is 5,000,000.

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To convert inches to yards, we need to divide by 36, since 36 inches make 1 yard. Therefore, to convert the length of the shed and ramp from inches to yards, we can use the following expressions: (12 + 1) / 36 = 0.3611... yards, (12 / 36) + (1 / 36) = 0.3611... yards, 13 / 36 = 0.3611... yards

An expression in mathematics is a grouping of variables, numbers, and actions that can be evaluated to yield a value. A wide range of mathematical notions, from basic arithmetic computations to intricate algebraic formulas and beyond, are represented by expressions.

These components can be used to combine expressions in a wide range of different ways. For instance, we can construct straightforward arithmetic phrases such as "2 + 3" or "5 * 4" or more intricate algebraic expressions such as "3x2 + 2x + 1" or "sin(x) + cos(x)". In each instance, the expression denotes a mathematical idea that may be tested to provide a certain value.

Expressions play a significant role in mathematics and are utilized in a wide range of fields in science, engineering, and finance. By being aware of how expressions work, we can better understand and solve a wide variety of mathematical problems.

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Answer: D Im doing the quiz

Answer:D:the range is 5, and the IQR is 10.

Step-by-step explanation:

Answer:

15:18

Step-by-step explanation:

So, to say 9 more apples than pears means that 15-9 = 6. Now 3 times of 6 (pears) is 6*3= 18.

Write it in ratio is 15:18!

hope this helped!

To prove that point d is equidistant from the jungle gym and monkey bars, we need to show that the distances from d to both points are equal.

Let's call the distance from d to the jungle gym "x" and the distance from d to the monkey bars "y". We need to show that x = y.

Since angle acd is a right angle, we can use the Pythagorean theorem to relate the distances:

ad^2 + cd^2 = ac^2

We know that ad = bd (since the jungle gym and monkey bars are the same distance from d), so we can write:

bd^2 + cd^2 = ac^2

We also know that c lies on ab, so we can write:

ac = ab - bc

Substituting this into our equation, we get:

bd^2 + cd^2 = ab^2 - 2abbc + bc^2

Since d is on cd, we can write cd = y, and since c is on ab, we can write ab = x + y. Substituting these into our equation, we get:

bd^2 + y^2 = (x + y)^2 - 2xy + x^2

Simplifying, we get:

bd^2 - x^2 = 2xy - y^2

Now, if we can show that bd = x, then we will have proven that y = x and therefore that point d is equidistant from the jungle gym and monkey bars.

To do this, we can use the fact that triangle adb is isosceles (since ad = bd). This means that angle adb is equal to angle bad. We also know that angle acd is a right angle. Therefore, angle adb + angle acd = 90 degrees.

Since angle adb = angle bad, we can write:

2 angle adb + angle acd = 180 degrees

Substituting in the values of our angles, we get:

2 angle adb + 90 degrees = 180 degrees

Solving for angle adb, we get:

angle adb = 45 degrees

Now, we can use the fact that triangle adb is isosceles to write:

angle bad = (180 - 45)/2 = 67.5 degrees

Finally, we can use the law of sines to relate bd and x:

bd/sin(67.5) = x/sin(45)

Simplifying, we get:

bd = x

Therefore, we have shown that point d is equidistant from the jungle gym and monkey bars.

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