√-100=____ + _____i

a) Simplification of the algebraic expression 5(x³ - x) + 5x²/3 - 12x when x = 3 is; 99

b) Simplification of the algebraic expression 3y + 16 + (y/2) - (20/y) is; 25

a) We are given the algebraic expression;

5(x³ - x) + 5x²/3 - 12x

We want to simplify this when x = 3. Thus, we plug in 3 for x to get;

5(3³ - 3) + 5(3²)/3 - 12(3)

= 5(27 - 3) + (5 * 3) - 36

= 120 + 15 - 36

= 99

b) We are given the algebraic expression;

3y + 16 + (y/2) - (20/y)

We want to simplify this when y = 4. Thus, we plug in 4 for y to get;

3(4) + 16 + (4/2) - (20/4)

= 12 + 16 + 2 - 5

= 25

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The slope of the equation - 3 x+ 8 y = 12 is 0.375.

We are given an equation of the line:

- 3 x+ 8 y = 12

We need to find the slope of the equation.

x intercept:

- 3 x = 12

x = -4

Point 1 = ( - 4 , 0 )

y intercept:

8 y = 12

y = 1.5

Point 2 = ( 0 , 1.5 )

Slope = (y₂ - y₁) / (x₂ - x₁)

Substituting the values, we get that:

m = ( 1.5 - 0 ) / ( 0 - [-4])

m = 1.5 / 4

m = 0.375

Therefore, we get that, the slope of the equation - 3 x+ 8 y = 12 is 0.375.

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Solving the given equation y = x(ab/a - b) for a, we have: a = by/(y - bx).

To solve an equation for a given variable is to make the variable the subject of the formula. To do this, isolate the variable to one side of the equation using appropriate properties of equality.

Given the equation,

y = x(ab/a - b)

Multiply both sides by 1/x

y/x = ab/(a - b)

Multiply both sides by (a - b)

y/x × (a - b) = ab/(a - b) × (a - b)

y(a - b)/x = ab

(ay - by)/x = ab

ay - by = abx

ay - by + by = abx + by

ay = abx + by

ay - abx = abx + by - abx

ay - abx = by

a(y - bx) = by

Divide both sides by (y - bx):

a(y - bx)/(y - bx) = by/(y - bx)   [division property of equality]

a = by/(y - bx)

Thus, solving the given equation y = x(ab/a - b) for a, we have: a = by/(y - bx).

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The maximum income the doctor can get in a day is $1280

Time required for routine office visits = 15 minutes

Time required for physical visits = 45 minutes

Maximum physical visits possible in a day = 10

Maximum routine visits possible in a day = 12

Available hours for appointment = 9 hours or 540 minutes

Cost of routine appointment = $60

Cost of physical appointment = $70

In order to maximize income, she should do maximum possible routine visits as it gives more return in less time and the remaining time can be used to do physical visits, therefore:

No. of routine visits the doctor should do = 12

Time consumed in 12 visits = 12*15 = 180 minutes

Time remaining = 360 minutes

No. of physical visits she should do = 8

Time consumed in 8 physical visits = 8*45 = 360 minutes

Total income the doctor will generate in a day  = 12*60 + 8*70

= 720 + 560 = $1280

Hence, the maximum income of the doctor will be $1280

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Answer: 75%

Step-by-step explanation:

20-5=15 right handed  students

[tex]\displaystyle\\\frac{15}{20}*100\% =\\\\\frac{15*20*5}{20} \%=\\\\15*5\%=\\\\75\%\ -\ percentage\ of\ students\ are\ right\ handed[/tex]

Answer:

===================

From the right triangle we get the sum:

From the exterior angle theorem we get the sum:

Subtract the first equation from the second to get:

Answer:

y = 25

Step-by-step explanation:

Solution 1:

The line X is on, is a supplementary angle.

180-115 is 65

There are two Xs

A triangle adds up to 180

180- 65- 65= 50

50/2= 25

Solution 2:

The line X is on is a supplementary angle.

180-115 is 65

180- 65 - 90 (right angle)= 25

The first five terms of a geometric sequence in which the second term is 6 and fourth term is 54 are 2, 6, 18, 54, 162. Thus, the correct option is option D.

A Geometric progression may be defined as a series of terms in which the ratio between each succeeding term and the preceding term of the series is constant.

It is given that the second term of the series is 6 and the fourth term is 54.

The first five terms of geometric sequence are given by a, ar, ar², ar³ and ar⁴.

Thus, ar = 6                                                            ......(1)

ar³ = 54                                                                  ......(2)

Divide equation (2) by (1)

ar³/ar = 54/6

r² = 9

=> r = 3

Putting value of r in equation (1)

ar = 6

=> a×3 = 6

=>a = 2

Now, substituting the values of a and r the terms of Geometric progression are given by:

a = 2, ar = 6, ar² = 18, ar³ = 54 and ar⁴ = 162.

Thus, the first five terms of Geometric sequence are given by 2, 6, 18, 54, 162.

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Answer:

$29.05

Step-by-step explanation:

First, you have to multiply $19.95 by 2 since he bought 2 shirts that were the same price. 19.95 times 2 is a total of $39.90. It says that he saved $9.10 on both shirts so, in order to see the original price of the shirts, you would have to multiply $9.10 times 2 which is $18.20. Now you need to add 39.90 to 18.20 which is $58.10. You just need to divide that by 2 which will give you $29.05.  Each shirt's orignial price was $29.05

Hope that helps you out :D

Answer: where's the pic?

2x+6-4x-1=13

2x+5=13

2x=8

x=4

Answer:

b=5

Step-by-step explanation:

Here,

b + 13 = 18

or, b = 18 - 13

or, b = 5

Hence, b=5

Answer:

B = 5/b, b  0

Step-by-step explanation:

Bb+13=18

Subtract 13 from both sides.

Bb=18−13

Subtract 13 from 18 to get 5.

Bb=5

The equation is in standard form.

bB=5

Divide both sides by b.

b

bB

​

=

b

5

​

Dividing by b undoes the multiplication by b.

B=

b

5

​

Number Form

C.) 38.107

___________________________________________________

The solution is simple. "Thirty-eight" is just 38, remaining on the left side of the decimal. Meanwhile, "one hundred seven thousandths" is 107, however on the right side of the decimal. Now you know this, put the two parts together and you have your number form; 38.107, aka. Option C.

___________________________________________________

Hope this helps! If so, lmk! Thanks and good luck!

Using distance formula, distance between two points is √61 unit

Let's us consider an example first -

What is the the distance between A and B

Let A = (3,2) and B (9,7)

Given A (3,2) and B( 9,7) are the two points on a plane

We have find to distance between A and B

Put the distance formula in two points as we know -

Distance= d√(x^2-x^1)^2 + (y^2-y^1) ^2

Here X1= 3

         X2 =9

         Y1=2

         Y2=7

Thus putting all these value x and y formula

d= √(9-3)^2+(7-2)^2

d=√(6^2+5^2)

d=√(36+25)

d=√61 unit

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Answer:

x = 5

Step-by-step explanation:

Given:

[tex]2 \frac{2}{7}:(0.6x)=\dfrac{4}{21}:0.25[/tex]

Convert the mixed number into an improper fraction by multiplying the whole number with the denominator of the fraction, adding it to the numerator of the fraction, and placing it all over the denominator of the fraction:

[tex]\implies 2\frac{2}{7}=\dfrac{2 \times 7+2}{7}=\dfrac{16}{7}[/tex]

Therefore:

[tex]\implies \dfrac{16}{7}:(0.6x)=\dfrac{4}{21}:0.25[/tex]

[tex]\implies \dfrac{\frac{16}{7}}{0.6x}=\dfrac{\frac{4}{21}}{0.25}[/tex]

Cross multiply:

[tex]\implies \dfrac{16}{7} \times 0.25 = \dfrac{4}{21} \times 0.6x[/tex]

[tex]\implies \dfrac{16\times 0.25}{7} = \dfrac{4\times 0.6x}{21}[/tex]

[tex]\implies \dfrac{4}{7} = \dfrac{2.4x}{21}[/tex]

Cross multiply again:

[tex]\implies 4 \times 21=2.4x \times 7[/tex]

[tex]\implies 84=16.8x[/tex]

Divide both sides by 16.8:

[tex]\implies \dfrac{84}{16.8}=\dfrac{16.8x}{16.8}[/tex]

[tex]\implies 5=x[/tex]

[tex]\implies x=5[/tex]

Answer:

The value of x is 5.

Step-by-step explanation:

Let's solve for the value of x,

→ 2 2/7 : (0.6x) = 4/21 : 0.25

→ 16/7 : (0.6x) = 4/21 : 0.25

→ (16/7) × 0.25 = (4/21) × 0.6x

→ 4/7 = (2.4x)/21

→ 2.4x × 7 = 4 × 21

→ 16.8x = 84

→ x = 84/16.8

→ [ x = 5 ]

Hence, the value of x is 5.

1:5:1 or 3:2 is the proportional relationship.

In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant. Two sequences are inversely proportional if corresponding elements have a constant product, also called the coefficient of proportionality.

Given Data

If considering that a month has 4 weeks approx, then Laura's hair grows( 0.25 inches×4)= 1 inch in a month.

Whereas the horse's mane grows 1.5 inches in a month.

Thus the proportional relation or ratio between growth of Horse's mane and Laura's hair for the same amount of time period is 1.5:1 or 3:2

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The average speed in meters per second is 10.4 m/s.

Average speed is the total distance travelled per time. Average speed can be determined by dividing total distance by

Average speed = total distance / total time

The first step is to convert kilometer to meter: 1000 meter = 1 kilometer

The second step is to convert hours to seconds:

1 hour = 60 minutes

1 minute = 60 seconds

1 hour = 60 x 60 seconds

1 hour = 3,600 seconds

Multiply the average speed by 1000 meters and divide by 3,600 seconds.

37.6 x (1,000 / 3,600)  = 10.44 m / s

10.4 m/s (1 d.p)

In order to round off to one decimal place, if the hundredth figure is less than 5, there is no change in the tenth digit. Digits that are less than the tenth digit are removed.

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Answer:

3x² + x

Step-by-step explanation:

collect the like terms first:

2x² + x² - 4x + 5x + 1 - 1

3x² + x

Answer:

the last answer. 3x to the second power + x

Step-by-step explanation:

Answer:

y = -4x -4

Step-by-step explanation:

we need to get two points to calculate the gradient

points chosen are (-2,3) and (-3,7)

Gradient = change in y coordinates/ change in X coordinates

G = (7-3)/(-3- -2)

= 4/-1

= -4

to write the equation in slope -intercept form we need one known point (-2,3) and one unknown point (X,y) and the gradient.

G = ∆y/∆x

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

-4 = (y-3)/ (X+2)

we now cross multiply

-4(X + 2) = y - 3

-4x -8 = y-3

-4x -8+4 = y

y = -4x -4

If the sum of three lengths of a fence ranges from 45 to 60 inches and  two side lengths are 9 and 18 inches, If the length of the third side is x inches, then the compound inequality to show the possible length of the third side is 18≤x≤33

Given,

The range of sum of three lengths = 45 to 60 inches

Length of other two side = 9 and 18 inches

Length of third side = x

Sum of three lengths = 9+18+x

= 27+x

The range of sum of three lengths is 45 to 60

then,

45≤27+x≤60

Subtract 27 from each part

18≤x≤33

Hence, if the sum of three lengths of a fence ranges from 45 to 60 inches and  two side lengths are 9 and 18 inches, If the length of the third side is x inches, then the compound inequality to show the possible length of the third side is 18≤x≤33

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Answer:

B

Step-by-step explanation:

This is because 18 is less than or equal to x which is less than or equal to 33. Your welcome

Answer:

Step-by-step explanation:

x=4 is a vertical line.

horizontal line through (-6,5): y=5

y=6 is a horizontal line.

vertical line through (-6,5): x=-6

The equation of line parallel to y = -( 1/3 )x + 4 and passing through the point P ( 6 , 5 ) is y = -( 1/3 )x + 7

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = -( 1/3 )x + 4

Let the first point be P ( 6 , 5 )

Slope m = -1/3

The parallel lines have the same slope , so the point-slope form of the equation of a line to find the equation of the line passing through P(6,5) with slope -1/3 is

y - 5 = ( -1/3 ) ( x - 6 )

Adding 5 on both sides , we get

y = ( -1/3 )x + 2 + 5

y = -( 1/3 )x + 7

Hence , the equation of line is y = -( 1/3 )x + 7

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The complete question is attached below :

What is the equation of the line that is parallel to the line y = -1/3x + 4 and passes through the point (6, 5)?

A) y = -1/3x + 3

B) y= -1/3x + 7

C) y= 3x - 13

D) y= 3x + 5

50 students of the 200 students in the school would favor a new dress code.

We will use simple cross multiplication here

For first case

no. of students surveyed = 20

no. of student agreed for a new dress code = 5

This gives us 5/20

For second case

no. of students surveyed = 200

no. of student agreed for a new dress code = x

This gives us x/200

Lets us cross multiply

5/20 = x/200

20x = 200×5

x = (200×5)/20

x = 50

Given an equation between two fractions or rational expressions in mathematics, particularly in primary arithmetic and elementary algebra, one might cross-multiply the equation to make it simpler or get the value of a variable.

The technique can be used to remember which things to multiply together by drawing lines that resemble the outline of a heart. It is also sometimes called as "cross your heart" technique.

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These measurements are not identical due to confounding;

When the effects of two or more explanatory variables on a response variable cannot be distinguished from one another, confounding occurs in an experiment.

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The two equivalent expressions for the area of the cafeteria are:

a. x = 6² + 7² feet

b. 36 + 49 = x feet.

Given the length of the cafeteria is 7² ft and

the width of the cafeteria is 6² ft.

Area = length × width

let the area be 'x'.

x = 6² × 7²

According to the law of exponents.

x = 36 × 49

x = 1764 ft

hence we get the area as 1764 ft of the cafeteria.

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Answer:

27

Step-by-step explanation:

Say the youngest sibling is a. Anna would be a+1, and the oldest would be a+2. If the sum of all of them are 81, then 3a+3 = 81. minus three on both sides, and you get 78. So 3a = 78/3 = 26. if the youngest is 26, then Anna will be a + 1 so 27.

The age of Anna where she is the middle of three siblings is 27 years.

Given data:

Let's represent Anna's age as "x." Since Anna is the middle sibling, the ages of her siblings would be x - 1 and x + 1, since they are consecutive integers.

According to the information given, the sum of their ages is 8181:

x + (x - 1) + (x + 1) = 81

Now, combine like terms:

3x = 81

Divide both sides by 3:

On simplifying the equation:

x = 81/3

x = 27

Hence, Anna's age is 27 years.

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The complete question is attached below:

Anna is the middle of three siblings whose ages are consecutive integers. If the sum of their ages is 81, find Anna's age.

The average (division) change of the price of one share per one day is $7.896

The given parameters are

Total = $39.48

Number of days =  5 days

The average (division) change of the price of one share per one day is calculated as

Average = Total/Number of days

So, we have

Average = $39.48/5

Evaluate the quotient

Average = $7.896

Hence, the average (division) change of the price of one share per one day is $7.896

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A pair of shoes gives us 48 different outfits.

What is a linear equation?

We will employ the basic counting principle, which states that if one task can be completed in method A and another in way B, then both tasks may be completed in way A*B.

If mom buys 1 shirt, then total shirts(A) = 6+1 =7, total pants(B) = 2 and total shoes (C) = 3

By basic counting principle, number of outfits = A*B*C = 7*2*3 = 42 outfits possible

and

If mom buys 1 pair of shoes, then total shirts(A) = 6, total pants(B) = 2 and total shoes (C) = 3+1 = 4

By basic counting principle, number of outfits = A*B*C = 6*2*4 = 48 outfits possible

hence, buying a pair of shoes gives us 48 different outfits.

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