what goes in to 18 and 6

Answer:

240

Step-by-step explanation:

25% =1/4

if 1/4 of class is 60, the class have 60x4 students

The polynomials completely factorized have the following expressions;

50). x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

51). x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

52). x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

53). x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

For the polynomial x³ - 3x² - 26x - 12 divisible by x - 6;

(x³ - 3x² - 26x - 12)/(x - 6) = x² + 3x + 2

x² + 3x + 2 = (x + 1)(x + 2)

so;

x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

For the polynomial x³ - 12x² + 12x + 80 divisible by x - 10;

(x³ - 12x² + 12x + 80)/(x - 10) = x² - 2x - 8

x² - 2x - 8 = (x + 2)(x - 4)

so;

x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

For the polynomial x³ - 18x² + 95x + 126 divisible by x - 9;

(x³ - 12x² + 12x + 80)/(x - 9) = x² - 9x + 14

x² - 9x + 14 = (x - 2)(x - 7)

so;

x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

For the polynomial x³ - x² + 21x + 45 divisible by x + 5;

(x³ - x² + 21x + 45)/(x + 5) = x² - 6x + 9

x² - 6x + 9 = (x - 3)(x - 3)

so;

x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

Therefore, by complete factorization the expressions (x - 6)(x + 1)(x + 2), (x - 10)(x + 2)(x - 4), (x - 9)(x - 2)(x - 7), and (x + 5)(x - 3)(x - 3) are the factors of their respective polynomial.

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Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

a) These are the four solutions to the equation z⁴ = 1. We can plot these solutions on an Argand diagram by marking points at (1, 0), (0, 1), (-1, 0), and (0, -1).

b) These are the three solutions to the equation z³ = 8. We can plot these solutions on an Argand diagram by marking points at (2, 0), (-1, √3), and (-1, -√3).

c) These are the three solutions to the equation z³ = i. We can plot these solutions on an Argand diagram by marking points at (1, 0), (-1/2, √3/2), and (-1/2, -√3/2).

a) To find all solutions to the equation z⁴ = 1, we can use De Moivre's theorem:

z⁴ = 1 = cos(0) + i sin(0)

We can rewrite this in polar form as:

z = cos(0/4 + 2kπ/4) + i sin(0/4 + 2kπ/4)

where k = 0, 1, 2, 3.

Simplifying the expression for z, we get:

z = cos(kπ/2) + i sin(kπ/2)

For k = 0, we get z = 1.

For k = 1, we get z = i.

For k = 2, we get z = -1.

For k = 3, we get z = -i.

These are the four solutions to the equation z⁴ = 1. We can plot these solutions on an Argand diagram by marking points at (1, 0), (0, 1), (-1, 0), and (0, -1).

b) To find all solutions to the equation z³ = 8, we can use De Moivre's theorem:

z³ = 8 = 8(cos(0) + i sin(0))

We can rewrite this in polar form as:

z = 2(cos(0/3 + 2kπ/3) + i sin(0/3 + 2kπ/3))

where k = 0, 1, 2.

Simplifying the expression for z, we get:

z = 2(cos(kπ/3) + i sin(kπ/3))

For k = 0, we get z = 2.

For k = 1, we get z = -1 + i√3.

For k = 2, we get z = -1 - i√3.

These are the three solutions to the equation z³ = 8. We can plot these solutions on an Argand diagram by marking points at (2, 0), (-1, √3), and (-1, -√3).

c) To find all solutions to the equation z³ = i, we can use De Moivre's theorem:

z³ = i = cos(π/2) + i sin(π/2)

We can rewrite this in polar form as:

z = (cos(π/6 + 2kπ/3) + i sin(π/6 + 2kπ/3))

where k = 0, 1, 2.

Simplifying the expression for z, we get:

z = cos(kπ/3) + i sin(kπ/3)

For k = 0, we get z = 1.

For k = 1, we get z = (-1 + i√3)/2.

For k = 2, we get z = (-1 - i√3)/2.

These are the three solutions to the equation z³ = i. We can plot these solutions on an Argand diagram by marking points at (1, 0), (-1/2, √3/2), and (-1/2, -√3/2).


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Answer:

(2,16)

Step-by-step explanation:

After checking the information of the table, it is to notice that the table fulfills the behavior of a direct relationship described by the linear equation y = 0.9 · x. #SPJ1

Let be x and y the original investment and the value after applying the change, both in monetary units. A direct relationship is observed by following this model:

y = (1 + r/100) · x     (1)

Where r is change rate, in percentual units.

After checking the information of the table, it is to notice that the table fulfills the behavior of a direct relationship described by the linear equation y = 0.9 · x. #SPJ1

The table of the change in investment with respect to initial investment is missing and is now introduced below:

(x₁, y₁) = (75, 7.5), (x₂, y₂) = (100, 10), (x₃, y₃) = (200, 20), (x₄, y₄) = (300, 30), (x₅, y₅) = (400, 40)

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Answer: Since there are 500 tumblers in each batch, there are a total of:

500 tumblers/batch × 3 batches = 1500 tumblers

To make a set of 3 tumblers with one tumbler of each color, we can choose one tumbler from each batch. There are 500 choices for the tumbler from the red batch, 500 choices for the tumbler from the yellow batch, and 500 choices for the tumbler from the purple batch. Therefore, there are:

500 choices for the first tumbler × 500 choices for the second tumbler × 500 choices for the third tumbler = 500^3 = 125,000,000 possible sets of 3 tumblers.

However, we are interested in the number of sets that can be made from the available tumblers. Each set requires one tumbler from each batch, and since there are 500 tumblers in each batch, we can make:

500 sets/batch = 500 sets/batch × 3 batches = 1500 sets

Therefore, we can make a total of 1500 sets of 3 tumblers from the available tumblers.

Step-by-step explanation:

Answer:

10+8y-9y-12 is equivalent to H.

The truck driver would deliver 105 packages in a 7 hours day

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:

y - 15 = [(60-15)/(4-1)](x - 1)

y = 15x

For a 7 hour day (x = 7):

y = 15(7) = 105

The driver would deliver 105 packages in 7 hours

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7km/ 4km per hour = 1 3/4 hours

3/4 hour = 45 minutes

Total time = 1 hour and 45 minutes.

Answer:

Step-by-step explanation:

Answer:

I believe the answer is D.

P(8/3) is not equal to zero, we can conclude that 8/3 is not a zero of P(x). Therefore, our suspicion was incorrect.

What is quadratic equation and how to solve it ?

A quadratic equation is a second-degree polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

To solve a quadratic equation, there are different methods, such as factoring, completing the square, and using the quadratic formula. The quadratic formula is the most general method and can be used for any quadratic equation.

It states that the solutions to the equation ax^2 + bx + c = 0 are given by the formula

x = (-b ± sqrt(b^2 - 4ac)) / (2a).

We can use this formula to find the roots of the equation by substituting the values of a, b, and c into the formula and simplifying.

To confirm if 8/3 is a zero of the quadratic function P(x) = 3x^2 - 4x - 7, we can substitute 8/3 for x in the equation and check if the resulting expression is equal to zero. If P(8/3) equals zero, then we can confirm that 8/3 is indeed a zero of P(x).

P(8/3) = 3(8/3)^2 - 4(8/3) - 7

= 3(64/9) - 32/3 - 7

= 64/3 - 32/3 - 21/3

= 11/3

Since P(8/3) is not equal to zero, we can conclude that 8/3 is not a zero of P(x). Therefore, our suspicion was incorrect. If we want to find the zeros of P(x), we can use the quadratic formula or factor the equation into (3x + 1)(x - 7) = 0 to get the roots x = -1/3 and x = 7.

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Answer:

x = 27

Step-by-step explanation:

x/9 = 3

Multiply each side by 9

x/9 * 9 = 3*9

x = 27

Answer:

27

Step-by-step explanation:

x/9= 3

Carry over the 9 and make x the subject.

x= 3*9

x= 27

Therefore x is 27.

To check if the answer is correct, replace the x with the value of what it is in brackets. The value of x is 27.

(27)/9= 3

= 27/9

= 3

We got back the 3 so that means the answer is correct

The image coordinates of K′ if the preimage is reflected across y = −7 is (-4, -8)

Based on the given question, we have certain variables that can be utilized for our calculations.

K = (-4, -6)

First, find the equation of the reflection line

The reflection line is y = -7.

This can be expressed as

y = a = -7

The image of the reflection is then calculated as

K' = (x, -(y + 2|a|))

Replace the given or established values in the equation mentioned earlier, resulting in the following expression

K' = (-4, -(-6 + 2 * 7))

Evaluate

K' = (-4, -8)

Hence, the image coordinates of K′ are (-4, -8).

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The transformations that change the domain of a function are given as follows:

The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.

Hence we must look at transformations that change the values of x of the function, which are given as follows:

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The expressions that are completely factored are:

The expressions are considered correct because they have been completely factored, meaning they have been written in the form of "a common factor times another expression". This means that the expression on the right side of the equal sign can be simplified into its simplest form.

For example, in the expression 16a5−20a3=4a3(4a2−5), the 4a3 factor is common to both 16a5 and 20a3, so it can be factored out. The expression then becomes 4a3 times (4a2−5), which is the completely factored form.

Similarly, in the expression 12a3+8a=4(3a3+2a), the factor of 4 is common to both the expressions on the right side, so it can be factored out. This results in the completely factored form of 4 times (3a3+2a).

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Answer:

16a^5−20a^3=4a^3(4a^2−5)

and

24a^4+18=6(4a^4+3)

Step-by-step explanation:

48.50 U.S. dollars = 281 Egyptian pounds

What is a dollar?

The United States dollar (symbol: $; code: USD; often abbreviated US$ or U.S. Dollar to differentiate it from other dollar-denominated currencies; known colloquially as the dollar, U.S. dollar, American dollar, or buck) is the official currency of the United States and numerous other nations. The Coinage Act of 1792 established the United States dollar on equal footing with the Spanish silver dollar, split it into 100 cents, and permitted the minting of coins denominated in dollars and cents. Federal Reserve Notes, generally known as greenbacks owing to their predominately green hue, are the currency of the United States.

Given, 1 U.S. dollar = 5.8 Egyptian pounds

so, 48.50 U.S. dollars = 5.8 x 48.50 = 281.30 Egyptian pounds

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The dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ration.

To determine the amounts of the 70% protein supplement and the 20% protein ratio needed to make a 1900-pound high-grade 55% protein ration, we can set up a system of equations.

Let's assume x represents the pounds of the 70% protein supplement and y represents the pounds of the 20% protein ratio.

The total weight equation is given by:

x + y = 1900

The protein content equation is given by:

(0.70x + 0.20y) / 1900 = 0.55

Simplifying the second equation, we get:

0.70x + 0.20y = 0.55 × 1900

0.70x + 0.20y = 1045

Now, we can solve this system of equations to find the values of x and y.

Rearrange the first equation to solve for x:

x = 1900 - y

Substitute this expression for x in the second equation:

0.70(1900 - y) + 0.20y = 1045

1330 - 0.70y + 0.20y = 1045

1330 - 0.50y = 1045

-0.50y = 1045 - 1330

-0.50y = -285

y = -285 / -0.50

y = 570

Now substitute this value of y back into the first equation to find x:

x + 570 = 1900

x = 1900 - 570

x = 1330

Therefore, the dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ratio.

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Answer:

\(Q(-2,3) \longrightarrow Q'(-1/3, 1/2) \\ \\ R(-3,1) \longrightarrow R'(-1/2, 1/6) \\ \\ T(2,-1) \longrightarrow T'(1/3, -1/6) \\ \\ W(2,4) \longrightarrow W'(1/3, 2/3)\)

Step-by-step explanation:

For a dilation at the origin, multiply each of the coordinates by the scale factor.

\(Q(-2,3) \longrightarrow Q'(-1/3, 1/2) \\ \\ R(-3,1) \longrightarrow R'(-1/2, 1/6) \\ \\ T(2,-1) \longrightarrow T'(1/3, -1/6) \\ \\ W(2,4) \longrightarrow W'(1/3, 2/3)\)

Answer:

19.048%

Step-by-step explanation:

The formula for the increase in cost will be :

[(New cost - Original Cost)÷Original Cost] × 100

So let's substitute values in from the question :

[(50-42)÷42] × 100

[8÷42] × 100

0.19048 × 100

19.048%

Hope this helped and have a good day

Let's use a rule of three to solve this:

This way,

The crew will take 36 hours to repave the road

Answer:

7/15

Step-by-step explanation:

3 + 4 / 3 * 5

7 / 15

Answer:

[See Below]

Step-by-step explanation:

\(Hey~There!\)

_____________________

➜ First we have to turn to into a proper equation:

➜ Now we solve the two parts:

➜ Then we can divide:

_____________________

So your answer would be:

_____________________

\(Hope~this~helps~Mate!\\-Your~Friendly~Answerer,~Shane\) ヅ

The length of BD is 22.

In the given scenario, let's consider the following information.

AD = 8

AE = 6

EC is 12 more than BD.

To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.

From the given information, we know that AD = 8 and AE = 6.

Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.

First, let's find the intercepted arc corresponding to AD:

Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16

Similarly, we can find the intercepted arc corresponding to AE:

Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12

Now, we know that EC is 12 more than BD.

Let's assume the length of BD as x.

BD + 12 = EC

Now, let's consider the intercepted arcs theorem:

Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C

16 - 12 = Angle B - Angle C

4 = Angle B - Angle C.

Since Angle B and Angle C are vertical angles, they are congruent:

Angle B = Angle C.

Therefore, we can say:

4 = Angle B - Angle B

4 = 0

However, we have reached an inconsistency here.

The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.

As a result, we cannot determine the length of BD based on the given information.

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Answer:

40 slices

Step-by-step explanation:

I rounded 38 to 40 and divided by 8

Answer:

second option

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - \(\frac{2}{3}\) and (a, b ) = (1, - 7 ) , then

y - (- 7) = - \(\frac{2}{3}\) (x - 1) , that is

y + 7 = - \(\frac{2}{3}\) (x - 1)

Answer: 6.8622 ; 8.1778

Step-by-step explanation:

Given the data:

2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9

6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9

7 10 7 9 9 9 9

Assume a confidence interval of 95%

Using calculator :

The mean of the distribution (m) = 7.52

Standard deviation (s) = 2.314

Sample size),

Obtaining the t score ;

Degree of freedom (df) = (n-1) = 50 - 1 = 49

t(1-α/2), 49 = t(0.025, 49) = 2.01 ( t distribution table)

Margin of Error :

2.01 * s/√n = 2.01 * 2.314/7.0710678

Margin of Error (E) = 0.6578

Confidence interval:

(Mean - E) ≤μ≤ (mean + E)

(7.52 - 0.6578) ≤μ≤ (7.52 + 0.6578)

6.8622 ≤μ≤ 8.1778

Answer:

1.3

Step-by-step explanation:

It round up

Answer:

1.3

Step-by-step explanation: