what two numbers multiply to 24 and add 14

The simplified complex expression of (10 - 6i)/(6 + 5i) is (30 + 14i)/61

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

(10 - 6i)/(6 + 5i)

Using the above as a guide, we have the following:

Start by rationalizing the expression

So, we have the following representation

(10 - 6i)/(6 + 5i) = (10 - 6i)/(6 + 5i) * (6 - 5i)/(6 - 5i)

Evaluate the products of the numerator

This gives

(10 - 6i)/(6 + 5i) = (60 -30 + 50i - 36i)/(6 + 5i) * 1/(6 - 5i)

Evaluate the products of the denominator

This gives

(10 - 6i)/(6 + 5i) = (60 -30 + 50i - 36i)/(30 +25)

Evaluate the like terms

(10 - 6i)/(6 + 5i) = (30 + 14i)/61

So, we have

(10 - 6i)/(6 + 5i) = (30 + 14i)/61

Hence, the solution is (30 + 14i)/61

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Answer: x + 4.8 = 14.3

Step-by-step explanation:

Let x be the initial amount of water that was already in the bucket before the additional 4.8 liters of water was poured in.

Then the total amount of water in the bucket after pouring in the 4.8 liters is the sum of the initial amount x and the amount of water poured in, which is 4.8 liters. This can be represented by the equation:

x + 4.8 = 14.3

We can simplify this equation by solving for x:

x = 14.3 - 4.8

x = 9.5

Therefore, the initial amount of water in the bucket was 9.5 liters, and after pouring in 4.8 liters, the bucket contained a total of 14.3 liters.

Answer:

a

Step-by-step explanation:

1. The equation of the line in graph 1 in slope-intercept form is

y = (2/3)x + 2/3.

2. The equation of the line in graph 2 is

y = (1/3)x + 4/3.

a. To find the equation of the line passing through (3, 4) and (0, 2) (points obtained from the graph) in slope-intercept form, we need to first find the slope of the line.

slope = (y2 - y1) / (x2 - x1)

Substituting the given values, we get:

slope = (2 - 4) / (0 - 3) = -2 / (-3) = 2/3

The point-slope form of the equation of a line passing through a point (x1, y1) with slope m is given by:

y - y1 = m(x - x1)

y - 4 = (2/3)(x - 3)

y = (2/3)x + 2/3

b. points obtained from the graph (-3, 1) and (-6, 0)

slope = (y2 - y1) / (x2 - x1)

slope = (0 - 1) / (-6 - (-3)) = -1 / (-3) = 1/3

y - y1 = m(x - x1)

y - 1 = (1/3)(x - (-3))

y = (1/3)x + 4/3

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Answer:

Step-by-step explanation:

Here is all the solutions:

Answer:

all are 0

thats why you should do y+4=4-7=×-7=×+4=0

Answer:

for #2 do b

Step-by-step explanation:

Break at centre into triangle and rectangle

Area of rectangle

Area of triangle

Total area

Answer:

47x  (square units)

Step-by-step explanation:

The given shape is made up of:

Area of the rectangle

= width × length

= 3x × 14

= 42x

Area of the triangle

= 1/2 × base × height

= 1/2 × (14 - 9) × (5x - 3x)

= 1/2 × 5 × 2x

= 5x

Area of given shape

= area of rectangle + area of triangle

= 42x + 5x

= 47x  (square units)

Answer:

6

Step-by-step explanation:

siri=6x-10

alexa= 50-4x

im making a table which is an easy way to tell or you can guess and check

X       S       A

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

 2     |    2    |42

  3    |   8     |38

   4   |     14   |34

  5    |   20     |30

   6   |     26   |26

10,000 records have 30 predictor variables, each with 5% of the values missing, resulting in 15,000 missing values. The predictive model drops any row with even a single missing value, so 5,000 records would be dropped from the analysis.

1. There are 30 predictor variables.

2. Each variable has 5% of the values missing.

3. 5% of 10,000 records = 500 records.

4. 30 variables x 500 records = 15,000 missing values.

5. 10,000 records - 15,000 missing values = 5,000 records dropped from the analysis.

The data set has 10,000 records and 30 predictor variables. Each variable has 5% of the values missing, so 500 records are missing for each variable. This results in 15,000 missing values spread randomly and independently throughout the data set. The analyst uses a predictive model that drops any row (record) with even a single missing value, so 5,000 records would be dropped from the analysis.

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Answer:

10 cm

Step-by-step explanation:

Volume = length x width x height

360 cm³ = 6 cm x 6 cm x h

Simplifying this expression:

360 cm³ = 36 cm² x h

h = 360 cm³ / 36 cm²

h = 10 cm

Answer:

10

Step-by-step explanation:

length ×width×height =360cm³

6×6=36cm³

360÷36=10

Explanatory variable: The type of pill the men took each day.

Response variable: Whether a subject had a heart attack.

We have been given that :

Participated candidates are 400

Men are divided randomly so we find out explanatory and response  variable.

The explanatory variable is the variable that is manipulated by the researcher. Explanatory Variable also known as the independent or predictor variable, it explains variations in the response variable; in an experimental study, it is manipulated by the researcher.

Response variable: Response Variable is the result of the experiment where the explanatory variable is manipulated. It is a factor whose variation is explained by the other factors. Response Variable is often referred to as the Dependent Variable or the Outcome Variable.

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\( \large \mathfrak{Answer : }\)

The ray opposite to OP is :

Answer:

45 levels

Step-by-step explanation:

60% of 75 is 45 i think

Answer:

2

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Pemdas is the order of operations

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Answer:

16

Step-by-step explanation:

3 x 6 - 12 / 6.

18 - 2

  16

Answer: Could be 0,1,2,3,4,5

Step-by-step explanation: 9-n has to be greater or equal to four. 9 minus 4 is five. So all of the answers must be positive numbers that are less than five.

Answer:

f(50) = 109.44943 feet

Step-by-step explanation:

Modeling

The model of a situation where the skid distance f is measured against the car speed x can be expressed as:

\(f(x) = 0.0425x^2 + 0.07381x - 0.49107\)

Using this equation, we can predict the skid distance for a car that is driving at x=50 mph by substituting in the equation of the model:

\(f(50) = 0.0425*50^2 + 0.07381*50 - 0.49107\)

\(f(50) = 106.25 + 3.6905 - 0.49107\)

f(50) = 109.44943 feet

Answer:

19,000

Step-by-step explanation:

because for 1 year its 19,000 just for that year so it would be 19,000

Answer:

Step-by-step explanation:

The answer is simple

18 - 1 = 17

Answer:

18<b

Step-by-step explanation:

b can repersent any number and you can use any letter in replace of b.

Hope this helps!

Answer:

10 horas.

Step-by-step explanation:

Dado que una muestra de laboratorio contiene 32 bacterias inicialmente, y luego de aplicar una vacuna, se autodestruyen a la mitad cada una hora, para determinar al cabo de cuántas horas no quedará ninguna bacteria se debe realizar el siguiente cálculo:

32 / 2  = 16

16 / 2 = 8

8 / 2 = 4

4 / 2 = 2

2 / 2 = 1

1 / 2 = 0.5

0.5 / 2 = 0.25

0.25 / 2 = 0.125

0.125 / 2 = 0.0625

0.0625 / 2 = 0.03125

Por lo tanto, al cabo de 10 horas no quedará ninguna bacteria.

It  takes for the account to reach $200 is 4 years.

Compound Interest is the interest calculated on the cumulative amount, rather than being calculated on the principal amount only quantity.

Given that aldonia deposits $150 into an account that pays 7.3% annual interest compounded quarterly.

\(A = P(1 +\frac{r}{n})^n^t\)

where:

A = the total account balance after t years

P = the initial deposit $150

r = the annual interest rate =0.073

n = the number of compounding periods per year, which is 4 (quarterly) in this case

t = the number of years the money is in the account

Now let us substitute the values

\(A = 150(1 + \frac{0.073}{4} )^4^t\) is the equation to represent Caldonia's account balance after t years.

Now let us determine the number of  years it will take for the account to reach $200.

\(200 = 150(1 + \frac{0.073}{4} )^4^t\)

200=150(1+0.01825)^4t

\(1.333=1.018^4^t\)

Take log on both sides

log1.333=4tlog(1.018)

0.1248=4t 0.0077

0.1248=0.0309t

Divide both sides by 0.0309

t=4.038

Hence, it takes 4 years to reach account balance of $200

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The optimal clutch size is 1.

a)The survivorship of an offspring, S, decreases with the clutch size, C.

Therefore, the formula is given as:

S = 0.5 - 0.1C

We need to find the optimal clutch size for this bird species.

We can do this by differentiating S with respect to C, and equating the result to zero.

That is:S = 0.5 - 0.1C => dS/dC = -0.1

Equating dS/dC to zero gives:-0.1 = 0 => C = 0

This implies that there is no optimal clutch size for this species.

However, since C represents clutch size, it must be a positive integer.

Therefore, we can choose a clutch size of 1, which will result in the highest survivorship of offspring. Hence, the optimal clutch size is

1.b)The optimal clutch size for a species with a survivorship-clutch size relationship of the form S = a - bC can be obtained by following the same procedure as above.

We can differentiate S with respect to C, and equate the result to zero.

That is:S = a - bC => dS/dC = -b

Equating dS/dC to zero gives:-b = 0 => C = 0

This implies that there is no optimal clutch size for this species. However, since C represents clutch size, it must be a positive integer. Therefore, we can choose a clutch size of 1, which will result in the highest survivorship of offspring. Hence, the optimal clutch size is 1.

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The coordinates of the vertices after a rotation 270° counterclockwise around the origin is

T' = (-8, -4)

U' = (-8, -6)

V' = (-3, -9)

W' = (-3, -7)

The coordinates of T = (4, -8)

The coordinates of U = (6, -8)

The coordinates of V = (9, -3)

The coordinates of W = (7, -3)

The rule of rotating 270 degree clockwise around the origin is

P(x, y) = P'(y, -x)

The coordinates of T' = (-8, -4)

The coordinates of U' = (-8, -6)

The coordinates of V' = (-3, -9)

The coordinates of W' = (-3, -7)

Hence, The coordinates of the vertices after a rotation 270° counterclockwise around the origin is

T' = (-8, -4)

U' = (-8, -6)

V' = (-3, -9)

W' = (-3, -7)

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Therefore, the statement that is true is: "The solution to the equation is x = 0.1."

In mathematics, an equation is a statement that shows the equality between two expressions. It is made up of two sides: the left-hand side (LHS) and the right-hand side (RHS), which are connected by an equal sign (=). An equation indicates that the two expressions on either side of the equal sign have the same value. Equations can take different forms, depending on the types of expressions involved and the operations used.

Here,

However, we can solve the equation ourselves to find the solution and then check the options.

5x − 6 + 7 = 15x (Given equation)

Simplifying the left-hand side of the equation, we get:

5x + 1 = 15x

Subtracting 5x from both sides, we get:

1 = 10x

Dividing both sides by 10, we get:

x = 1/10

Now we can check each option to see which statement is true:

x = 0.1: This is true, as 1/10 is equal to 0.1.

x = -0.1: This is false, as we found that x = 0.1, not x = -0.1.

x = 10: This is false, as we found that x = 0.1, not x = 10.

The equation has no solution: This is false, as we found a solution for x, namely x = 0.1.

The solution to the equation is x = 1: This is false, as we found that x = 0.1, not x = 1.

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Complete question:

The steps to solve equation 5x−6+7=15x are shown. Which statement about the solution is true?

x = 0.1

x = -0.1

x = 10

The equation has no solution

The solution to the equation is x = 1

16. the correct answer is: A) Brand A, 3 cents saved. Each cookie from Brand A saves 3 cents compared to Brand B.

17.  the correct answer is: D) 72mph. Mr. Jones was traveling at a speed of approximately 72 miles per hour.

18. the correct answer is: C) 0.625 meter. Tony has 0.625 meter of ribbon left.

16. To determine which brand is the better deal, we need to calculate the price per cookie for each brand.

Brand A: 24 cookies for $3.98

Price per cookie = $3.98 / 24 = $0.1658 (rounded to four decimal places)

Brand B: 12 cookies for $2.41

Price per cookie = $2.41 / 12 = $0.2008 (rounded to four decimal places)

Comparing the price per cookie, we can see that Brand A offers a lower price per cookie ($0.1658) compared to Brand B ($0.2008). Therefore, Brand A is the better deal in terms of price per cookie.

To calculate the amount saved per cookie, we can subtract the price per cookie of Brand A from the price per cookie of Brand B:

Savings per cookie = Price per cookie of Brand B - Price per cookie of Brand A

Savings per cookie = $0.2008 - $0.1658 = $0.035 (rounded to three decimal places)

Therefore, the correct answer is: A) Brand A, 3 cents saved. Each cookie from Brand A saves 3 cents compared to Brand B.

17. To determine the speed at which Mr. Jones was traveling, we can use the formula:

Speed = Distance / Time

Given:

Time = 23/4 hours

Distance = 198 miles

Substituting the values into the formula:

Speed = 198 miles / (23/4) hours

Speed = 198 miles * (4/23) hours

Speed = 8.6087 miles per hour (rounded to four decimal places)

Therefore, the correct answer is: D) 72mph. Mr. Jones was traveling at a speed of approximately 72 miles per hour.

18. To determine how much ribbon is left after Tony cuts off 0.125 meter, we can subtract that amount from the initial length of 0.75 meter:

Remaining length = 0.75 meter - 0.125 meter

Remaining length = 0.625 meter

Therefore, the correct answer is: C) 0.625 meter. Tony has 0.625 meter of ribbon left.

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Answer:

1. \(\overline {TU}\)

2. Given

3. \(\overline {RT}\)  

4. Side-Side-Side (SSS) rule of congruency

Step-by-step explanation:

The two column proof is presented as follows;

Statement    \({}\)                Reason

1.  \(\overline {RS}\) ≅  \(\overline {TU}\)    \({}\)            Given

2. \(\overline {ST}\) ≅  \(\overline {UR}\)     \({}\)           Given

3. \(\overline {RT}\) ≅  \(\overline {RT}\)     \({}\)           Reflexive property

4. ΔRST ≅ ΔTUR   \({}\)      SSS rule of congruency\({}\)

The Side-Side-Side rule of congruency states that if three sides of one triangle are congruent to three sides of another triangle then both triangles are congruent.    

The perimeter of the new figure is approximately 17.89 inches.

since we are rotating the isosceles right triangle around point a, the new figure will still be an isosceles right triangle with the same length of the long side as the original triangle. however, the vertices of the triangle will have been rearranged by the rotations.

let's start by drawing the original triangle and labeling its sides:

   n

   |

   |     5.66

   |----|-----

   a    a    a

since the long side of the triangle has length 5.66 inches, each of the other sides must have length 5.66/√2 inches, since the triangle is isosceles and right.

now, let's apply the rotations and draw the new triangles:

rotation 1) 90° clockwise around a:

        N

         |

5.66  |

   -----|----

        A    A

         |

        A

rotation 2) 180° clockwise around a:

            n

              |

        -----|----

   5.66   |

             A   A    A

                    I

                   A

rotation 3) 270° clockwise around a:

            n

             |

       -----|----

             |

   5.66   |    A

             A    A    A

              |

in each of the new triangles, we can see that the length of the long side is still 5.66 inches, and each of the other sides has length 5.66/√2 inches. so each new triangle has the same perimeter as the original triangle, which is:

perimeter = 5.66 + 2*(5.66/√2)

         = 5.66 + 2*(5.66/1.414)

         ≈ 17.89 inches

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