Every complex number can be written in the form a+bi. For the complex numbers 8-4i, identify the values of a and b

The answer is a) 0 height, b) 25 seconds c) 10,600 feet d) 3 times e) (x+1)(x-3)(x+5).

A projectile is fired vertically upward, and its height s(t) in feet after t seconds is given by the function defined by

s(t) = -16t² + 800t + 600.

To find out

(a) From what height was the projectile fired

Given height functions: s(t) = -16t² + 800t + 600

Now,

[tex]s^{'}(t)[/tex] - -32t+800

(b) Now, to find the time it will attain maximum height,

[tex]s^{'}(t)[/tex] = 0

-32t = -800

t = 25 seconds

(c) The maximum height it will reach

= [tex]-16*(25)^{2} + 800*25+600[/tex]

= -10000+20000+600

= 10,600 feet

(d) Between what two times (in seconds, to the nearest tenth) will it be more than 5000 ft above the ground

By putting x = 3

[tex]P(3) = 4*(3)^{3}-50 * (3)^{2}-8*3+6[/tex]

= 108-90-24+6

= 114-114

= 0

Therefore x = 3 is a zero of P(x)

(e) How long to the nearest tenth of a second will the projectile be in the air

Now, factoring,

[tex]f(x) = x^{3}+3x^{2} -13x-15\\ \\= x^{3}+x^{2} +2x^{2}+2x-15x-15\\ \\ = (x+1)(x^{2} +5x-3x-15)\\\\= (x+1)(x(x+5)-3(x+5))\\\\=(x+1)(x-3)(x+5)[/tex]

Hence the answer is a) 0 height, b) 25 seconds c) 10,600 feet d) 3 times e) (x+1)(x-3)(x+5)

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a. Constant of proportionality is equal to 5.

b. Point (12, 60) represents that 12 pounds of sugar required to make 60 cups of coffee.

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Usually, data that varies over time is represented with a line graph.

Given:

We have the relation between total number of cups of coffee and the total amount of sugar:

Let y represents the number of cups of coffee

and, x represents the amount of sugar

y ∝ x

y = kx

a. 'k' is the constant of proportionality

When  y = 20 , x = 4

20 = k × 4

k = 20/ 4

k = 5

b. From the graph point (12, 60) represents 12 is on the x-axis and y is on the y-axis.

12 represents amount of sugar and 60 represents the number of cups of coffee.

Hence, the Constant of proportionality is equal to 5.

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The angles of the triangle will be 50°, 70°, 60° .

let the 3 angles of a triangle be A, B and C

The first acute angle A is given by = x + 20

The second acute angle B is given by = 2x + 10

The third acute angle C is given by = 4x - 60

Now we know that the sum of the angles of a triangle is 180°

So ,

A + B + C + = 180°

x + 20 + 2x + 10 +  4x - 60 = 180°

7x - 30 = 180°

7x = 210°

x = 30°

So, from the value of x , we can calculate the value of each angle

Therefore, the required angles are :

angle A = (x + 20)° = 30° + 20° = 50°

angle B = (2x + 10)° = 60° + 10° = 70°

angle C = (4x - 60)° = 120° - 60° = 60°

verification : sum of the angles = 50°  + 70° + 60°  = 180°

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Answer:

Step-by-step explanation:

Total number of candidates is:

Probability of a girl to be chosen as prefect:

Answer:

Probability = 15/23

Step-by-step explanation:

Now we have to,

→ find probability that prefect is a girl.

The total members are,

→ 15 girls + 8 boys

→ s = 15 + 8

→ [ s = 23 ]

Then the probability will be,

→ P = 15/s

→ [ P = 15/23 ]

Hence, the answer is 15/23.

The  GCF of 140 and 180 in the question can be expressed as 20.

The concept that will be used in the calculation is the concept of the Prime factorization.

Prime factorization  can be described as the way that can be used to find the prime factors of a number , making sure that the  original number is evenly divisible by these factors.

Prime factorization of 140 and 180 are:

40: (2 × 2 × 5 × 7)

180: (2 × 2 × 3 × 3 × 5)

Then the  common prime factors which are common  that can be associated with 140 and 180 which is the GCF of 140 and 180 is ( 2 × 2 × 5 )= 20.

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Answer:

a₈ = - 1280

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 10 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-20}{10}[/tex] = - 2 , then

a₈ = 10 [tex](-2)^{7}[/tex] = 10 × - 128 = - 1280

The 8th term of geometric sequence is -1280

Step of calculate geometric sequence

This is a geometric sequence. The geometric number sequence is characterized by the presence of a ratio (the ratio between the next term and the previous term). The next term is the product of the previous term with the ratio. Another sequence called arithmetic sequence is characterized by the presence of difference (the difference between the next term and the previous term).

10, -20, 40, ...

We will first analyze the things that can be found in the three numbers in the sequence. The thing to look for is the first term (a) and also the ratio (r). The first term can also be written as U1, where the 2nd term is U2, and the n-th term is Un.

[tex]a = 10[/tex]

[tex]r=\frac{U2}{U1}[/tex]

[tex]r=\frac{-20}{10}[/tex]

[tex]r=2[/tex]

When the first term (U1) and ratio (r) have been obtained, then we can find the 8th term by substitute it in the formula.

[tex]Un=ar^{n-1}[/tex]

With that formula, let's find the 8th term.

[tex]U8=10(-2)^{8-1}[/tex]

[tex]U8=10(-2)^{7}\\U8=10(-128)\\U8=-1280[/tex]

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Since the first child is a boy, this means we need to find the probability of another boy. This is 1/2 since we assume each gender has the same chance of happening.

Asymptote indicates that as time increases, the number of bacteria approaches 0.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

Once an antibiotic is given, number of bacteria decreases at a rate of 15% /day.

There were about 15,000 bacteria prior to the treatment.

The line y = 0 is an asymptote of the graph.

The y-intercept is 15,000.

The y-intercept represents the number of bacteria when treatment began.

The asymptote indicates that as time increases, the number of bacteria approaches 0.

Hence, asymptote indicates that as time increases, the number of bacteria approaches 0.

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Answer:

3.7miles

Step-by-step explanation:

divide the length value by 1.6

Answer: 3/5

Step-by-step explanation:

              Once such a triangle is chosen, the sine of the angle is equal to the length of the opposite side, divided by the length of the hypotenuse: The other trigonometric functions of the angle can be defined similarly; for example, the tangent is the ratio between the opposite and adjacent sides. As stated, the values and.

Answer:2

Step-by-step explanation:i did it

Answer:

Absolutely correct. you got the answer

Let's solve your system by substitution.

4x−4y=8 and 5x−3y=18

Step: Solve 4x−4y=8 for x:

4x − 4y = 8

4x − 4y + 4y = 8 + 4y (Add 4y to both sides)

4x = 4y + 8

[tex]\frac{4x}{4} = \frac{4y + 8}{4}[/tex]

x = y + 2

Step: Substitute y + 2 for x in 5x − 3y = 18:

5x − 3y = 18

5(y+2) − 3y = 18

2y + 10 = 18  (Simplify both sides of the equation)

2y + 10 + (−10) = 18 + (−10)  (Add -10 to both sides)

2y = 8

y = 4

Step: Substitute 4 for y in x = y + 2:

x = y + 2

x=4+2

x=6  (Simplify both sides of the equation)

Answer:

x = 6 and y =4

The sales tax is $2 and the total cost of the item is $42.

Given:

selling price = $40

rate of sales tax = 5%

sales tax = 40*5%

= 40*5 / 100

= 200/100

= $2

Total cost = 40+2

= $42.

Therefore the sales tax is $2 and the total cost of the item is $42.

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Answer:yes

Step-by-step explanation:

yes

Answer:

25%

Step-by-step explanation:

Answer:

4/6 and 6/9

Put 6 in both the boxes as the both ratios will be equal to 2/3 if 6 is put.

Answer:

[tex] \frac{4}{6} \: and \: \frac{6}{9} [/tex]

The expressions that represent the total weekly wages of Rita is 11r + 32 and of Tina is 11t.

We are given;

Rita and Tina each make $11 an hour working as cashiers at a supermarket.

Last week, Rita worked r hours while Tina worked t hours.

Rita also worked overtime hours during the week, for which she was paid an extra $32 flat wage.

We need to find the expressions that represent the total weekly wages of both Rita and Tina.

Let us form an algebraic expression for both one by one;

For Rita:

Number of hours Rita worked for = r

Cost per hour = $ 11

The amount for overtime Rita earned = $32

So, the equation expressing the total weekly wage for Rita = 11r + 32.

For Tina :

Number of hours Tina worked for = t

Cost per hour = $ 11

So, the equation expressing the total weekly wage for Tina = 11t.

Thus, the expressions that represent the total weekly wages of Rita is 11r + 32 and of Tina is 11t.

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Answer: 4,375 rs

Step-by-step explanation:

25% × 17,500 = 4,375

Answer:

$4375

Step-by-step explanation:

25 percent *17500 =

(25:100)*17500 =

(25*17500):100 =

437500:100 = 4375

Now we have: 25 percent of 17500 = 4375

The equation for the proportional relationship is y = 65x

The animal shelter wants to track its profit for each animal that is

adopted.

The cost of each animal adoption = $65

Consider the number of animal adoption = x

Consider the total profit from animal adoption = y

From the given the details, we can say that the profit from the animal adoption is directly proportional to the number of animal adoption,

Then the relationship will be

y ∝ x

y = kx

Here the cost of each animal adoption is k = 65

Then the equation will be

y = 65x

Hence, the equation for the proportional relationship is y = 65x

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From the given data , equation which can be formed to get the value of y that is the total amount of flour Otto used in his recipe is given by :

y = x + 5.5

With the constraints x and y where,

 x is any real number ≥ 0,

 y is any real number ≥ 5.5

As given in the question,

Number of cups of wheat flour used by Otto  = 5.5.cups

Number of cups of white flour used by Otto = x cups

Let y represent the total amount of flour used by Otto in the recipe

Required equation  to represent the total amount of flour used by Otto in the recipe is given by :

y = x + 5.5

Where x is any real number which is greater than or equal to 0.

As cups of flour can be in fractions.

And y is any real number which is greater than or equal to 5.5.

As y = x + 5.5, and x ≥0 and cups of flour can be in fractions.

Therefore, from the given data , equation which can be formed to get the value of y that is the total amount of flour Otto used in his recipe is given by :

y = x + 5.5

With the constraints x and y where,

 x is any real number ≥ 0,

 y is any real number ≥ 5.5

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Answer:

it is basic and .........

Student 1 expression is correct 1/4(10 x+8) = -(1/2 x +13)+3(x +5)

Algebra is defined as a generalization of arithmetic in which numbers are represented by letters that are combined according to arithmetic rules. Elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra are some of the sub-branches.

Given that 1/4(10 x+8) and -(1/2 x +13)+3(x +5)

Student 1: 1/4(10 x+8) = -(1/2 x +13)+3(x +5)

Student 2: 1/4(10 x+8) > -(1/2 x +13)+3(x +5)

Student 3: 1/4(10 x+8) < -(1/2 x +13)+3(x +5)

We have to find which student is correct for all values of x

Let us take x =1

Now substitute the x vale in student 1 expression

1/4(10 x+8) = -(1/2 x +13)+3(x +5)

1/4(10 (1)+8) = -(1/2 (1)+13)+3(1 +5)

1/4(18) = (-1/2 -13)+3(6)

18/4 = -1/2 -13 + 18

9/2 = -1/2 + 5

9/2 = (-1+10)/2

9/2 =9/2

So Student 1 expression satisfies

If student 1 expression is correct two are wrong

Therefore Student 1 expression is correct

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The Submarine is 7.74 Km away from its base .

In the question ,

it is given that ,

the distance travelled by Submarine from base in East direction = 4.2 Km

let the distance from base to east direction be denoted by AB ,

that means AB = 4.2 Km

the distance travelled by Submarine from East to North direction = 6.5 Km

let the distance from east to north direction be denoted by BC .

that means BC = 6.5 Km

the given situation form a right triangle ,

So , the distance from submarine to its base is the hypotnuse of the right triangle , that is AC .

So By Pythagoras Theorem ,

AC² = AB² + BC²

Substituting the values , we get

AC² = 4.2² + 6.5²

AC² = 17.64 + 42.25

AC² = 59.89

AC = √59.89

AC = 7.7388

AC = 7.74

Therefore ,  The Submarine is 7.74 Km away from its base .

The given question is incomplete , the complete question is

A Submarine travel 4. 2 km due Eat from it base and then turn and travel due North for 6. 5 km. How far away is the submarine from it base ?

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The common difference of the arithmetic sequence -13, -22, -31, is -9.

An arithmetic sequence is a set of numbers that are ordered and have a common difference between each consecutive term. In the arithmetic sequence 3, 9, 15, 21, 27, for example, the common difference is 6. An arithmetic progression is another name for an arithmetic sequence.

To find a specific term in an arithmetic sequence, we use the nth term formula. Step 1: An = a + (n - 1)d gives the nth term of an arithmetic sequence.

Some arithmetic sequence examples using this expression are:

1, 5, 9, 13, 17, 21, 25, 29, 33, ...

2, 4, 6, 8, 10, 12, 14, 16, 18,...

In this case, the difference will be:

= 2nd term - 1st term

= -22 - (-13)

= -22 + 13

= -9

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The volume in liters a person uses daily is about 90 liters which is equivalent to 23.48 gallons

Information given in the question

everyday a person uses about 90 liters of water at home

6 gallons is about 23 liters

how many liters of water does a person use at home daily = ?

Volume is a three dimensional calculation, the formula depends on the object. how ever the calculation is usually done by area * height or thickness

the unit for volume can liters, gallons, cubic meters, and so on

The question have it that a person uses about 90 liters of water daily converting this quantity in gallon is done by

= 90 liters * 6 gallons / 23 liters

= 90 * 6 / 23

= 23.48 gallons

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At point 1, the carrying capacity is both the area is around 5, and therefore it can very well be said that growth rate in Area A is at a much higher pace than that of Area B. And that can subsequently be verified from the succeding graph.

What is Carrying Capacity?

The quantity of humans, other living species, or crops that a place can support without negatively impacting the environment is termed as carrying capacity.

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