A line has a slope of 3/8 and includes the points (–6,d) and (10,10). What is the value of d?

Answer:

  8196.83

Step-by-step explanation:

You want the quantity after 6 weeks of a value initially 5500 and growing at a continuous rate of 0.95% per day.

Where r is the growth rate in some time period, the value after t periods is ...

  value = initial value × e^(rt)

Here we have an initial value of 5500, a growth rate of 0.95% = 0.0095, and a time period of 1 day. We want the value after 6 weeks, or 6·7 = 42 days.

That value is ...

  value = 5500·e^(0.0095·42) = 5500·e^0.399 ≈ 8196.83

After 6 weeks, the quantity is 8196.83.

The value of quantity grows to 8196.83 at exponential rate.

What is exponential rate?

Exponential growth may be a method that will increase amount over time. It happens once the instant rate of modification (that is, the derivative) of a amount with relevancy time is proportional to the amount itself.

Main body:

Continuous growth

Where r is the growth rate in some time period, the value after t periods is  value = initial value × [tex]e^{rt}[/tex]

Here we have an initial value of 5500, a growth rate of 0.95% = 0.0095, and a time period of 1 day. We want the value after 6 weeks, or 6·7 = 42 days.

That value is ...

 value = 5500·e^([tex]e^{0.0095*42}[/tex]) = 5500·[tex]e^{0.399}[/tex] ≈ 8196.83

After 6 weeks, the quantity is 8196.83.

Therefore the value of quantity grows to 8196.83

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The product is greater than 1 < 8.4375

Given:

In the question:

Product the following question:

1/2 x 4[tex]\frac{1}{2}[/tex] x [tex]1\frac{1}{4}[/tex] x 3

Now, According to the question;

1/2 x 4[tex]\frac{1}{2}[/tex] x [tex]1\frac{1}{4}[/tex] x 3

Solve the mixed fraction:

1/2 x 9/2 x 5/4 x 3

Write as a single fraction:

(9 x 5 x 3) / (2 x 2 x4)

Calculate the product or quotient:

= 135/ 16

= 8.4375

Hence, The product is greater than 1 < 8.4375

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The sum of the first 'n' terms can be expressed as [tex]S_n=\frac{n}{2}[2+(n-1)][/tex]

and the last term will be [tex]t_n = 1+(n-1)[/tex], where a is the first term of A.P. and 'd' is a common difference.

What is an arithmetic progression?

An arithmetic progression or arithmetic sequence is a number sequence in which the difference between consecutive terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15.. is an arithmetic progression with a common difference of 2.

The first 'n' terms will be 1, 2, 3, 4, 5, 6, ...., n

The above sequence is an A.P. because it has a constant common difference of '1' between each consecutive number.

So a = 1, d = 1

By using the standard formula, we get

       [tex]S_n=\frac{n}{2}[2a+(n-1)d]\\\\S_n=\frac{n}{2}[2+(n-1)][/tex]

and for the last term

       [tex]t_n=a+(n-1)d\\\\t_n=1+(n-1)[/tex]

Hence, the sum of the first 'n' terms can be expressed as[tex]S_n=\frac{n}{2}[2+(n-1)][/tex]

and the last term will be [tex]t_n = 1+(n-1)[/tex], where a is the first term of A.P. and 'd' is a common difference.

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The factors of the equation x²-4x+2=0 by using quadratic formula is x=3.414 and 0.585.

Given that,

The quadratic equation is x²-4x+2=0

We have to find the factor by using quadratic formula.

The word "quadratic," which meaning square, is derived from the word "quad." A quadratic equation is a "equation of degree 2," to put it another way.
A quadratic equation is a second-degree algebraic equation in x. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, x's coefficients are a and b, and c is just a constant.

x=[tex]\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]

Take the equation,

x²-4x+2=0

Here,

a=1, b=-4 and c=2

Substitute the values in the formula.

x=[tex]\frac{-(-4)\pm\sqrt{(-4)^{2}-4(1)(2) } }{2(1)}[/tex]

x=[tex]\frac{4\pm\sqrt{16-8 } }{2}[/tex]

x=[tex]\frac{4\pm\sqrt{8 } }{2}[/tex]

x=[tex]\frac{4\pm\sqrt{4 \times 2 } }{2}[/tex]

x=[tex]\frac{4\pm2\sqrt{2 } }{2}[/tex]

x=2±√2

x=2+√2    or    x=2-√2

x=3.414     or     x=0.585

Therefore, The factors of the equation x²-4x+2=0 by using quadratic formula is x=3.414 and 0.585.

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Answer:

Step-by-step explanation:

3x+4y=38

The distance from the base to the summit of the mountain is 3600 meters

The speed when going from base to summit = 45 meter / minute

The time taken for going from base to summit  = x minutes

The speed when descents from top to bottom = 60 meter / minute

The time taken for descents from top to bottom = x - 20 minutes

The speed = Distance / Time

The Distance = Speed × Time

Here in both case the distance is same

Then

45x = 60(x-20)

Solve the equation

45x = 60x - 1200

60x - 45x = 1200

15x = 1200

x = 1200/15

x = 80 minutes

Then the distance = 45x

= 45×80

= 3600 meters

Hence, the distance from the base to the summit of the mountain is 3600 meters

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In order to make profit of 1,200,000, the company should publish 180 copies of magazine.

The formula for the profit is given by:

Profit = revenues - total cost.

Meanwhile, the total cost consists of fixed cost and variable cost.

Total cost = fixed cost + price per unit x number of units sold

Parameters given in the problem:

Fixed cost = 600,000

variable cost = 50,000 per unit

selling price = 60,000 per copy

profit = 1,200,000

Let q be the number of copies sold, then:

Revenues = 60,000 q

Total cost = 600,000 + 50,000 q

Profit = 60,000 q - (600,000 + 50,000 q)

1,200,000 = 60,000 q - (600,000 + 50,000 q)

10,000 q = 1,800,000

q = 1,800,000 / 10,000 = 180

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The equation for the line given on the graph is y = 30x , the correct option is (c) .

In the question ,

it is given that

the cable length varies directly with the amount of time it passes .

let the cable length that is wound on the spool be " y " , and

let the time it passes be " x " .

since they vary directly , it can be denoted by

y ∝ x

So , the equation is , y [tex]=[/tex] k*x

from the graph we see that when x = 1 , the value of y is 30 .

On substituting x = 1 and y = 30 in the equation y = k*x

we get ,

30 = k*1

So , k = 30 .

Substituting k = 30 , we get

the equation as y = 30x .

Therefore , The equation for the line given on the graph is y = 30x .

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Answer:

The answer is 12 hours

Step-by-step explanation:

Jenny would have to work 12 hours to make $156

234/18 = 13

156/13 = 12

If the counterpart likes to have a video call with him 5 pm on Friday London time, it will be 2 am on Saturday in Melbourne.

Given in ques,

When it is 5 pm in Melbourne, he found out that its 8 am in London.

The time difference is of 9 hours with Melbourne's time being ahead.

So, when its 5 pm on Friday in London, Melbourne's time will be ahead by 9 hours which would be 2 am on Saturday.

Hence, it would be 2 am in the morning on Saturday in Melbourne when its 5 pm in the evening on Friday in London.

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Answer:

111

Step-by-step explanation:

1 is squared of the right one so ya

The only true statement is line segment ED intersects line segment AB.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

From the given diagram and going through the options we can surely conclude that line segment ED intersects line segment AB.

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The linear function that represents the total cost per week is y = 4x + 250

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. The y-intercept and slope are represented by c and m respectively.

The equation can be represented in the form of y = mx + c

Data;

The equation to represent the amount spent weekly is y = 4x + 250

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Answer:

y = - x - 13

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x - 4 ← is in slope- intercept form

with slope m = 1

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{1}[/tex] = - 1 , then

y = - x + c ← is the partial equation of line q

to find c substitute (- 10, - 3 ) into the partial equation

- 3 = 10 + c ⇒ c = - 3 - 10 = - 13

y = - x - 13 ← equation of line q

The rate of increase in the value of the baseball card per year is 0.42.

The value of a baseball card in dollars has been found to be 0.42y + 068, where y is the number of years since it was released. We need to find out by how much the value of the baseball card is increasing per year. Let the value of the baseball card be denoted by the variable "V".

V = 0.42y + 068

The value of the baseball card when it has been x years since it was released is : V1 = 0.42x + 068. The value of the baseball card when it has been (x + 1) years since it was released is : V2 = 0.42(x + 1) + 068.

The increase in the value of the baseball card per year is the difference in the values in any two consecutive years.

I = V2 - V1 = [0.42(x + 1) + 068] - [0.42x + 068] = 0.42

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Answer:

The percent being represented by the shaded area is [tex]175\%[/tex]

Step-by-step explanation:

The percent being represented by the shaded area can be calculated as follows

The first step is to evaluate the left square

Since each square represents one whole, and since the left square is all shaded in of [tex]4[/tex] then the percent being represented by the shaded area in the left square is

[tex]1=\frac{4}{4}=\frac{100}{100}=100\%[/tex]

The percent being represented by the shaded area in the first or the left square is [tex]100\%[/tex]

The second step is to evaluate the right square

Since the right or the second square is [tex]3[/tex] shaded in of [tex]4[/tex], then the fraction being represented by the shaded area in the second square is

[tex]\frac{3}{4}[/tex]

The third step is to convert [tex]\frac{3}{4}[/tex] into the percent form by the following equation

[tex]\frac{3}{4}=\frac{x}{100}[/tex]

Where [tex]x[/tex] is the percent value for the second square

Multiply both side by [tex]100[/tex] to isolate [tex]x[/tex]

[tex]\frac{3}{4}\times 100=\frac{x}{100}\times 100[/tex]

Simplify the equation

[tex]\frac{300}{4}=x[/tex]

Simplify the left side of the equation

[tex]75=x[/tex]

Since the value of [tex]x[/tex] is [tex]75[/tex], then the percent being represented by the shaded area in the second square is [tex]75\%[/tex]

The fourth step is to calculate the total percent being represented by the all shaded area

Since the total percent is the sum of the percent for the first square and the percent for the second square, then it follows

[tex]\text{Total percent}=100\%+75\%[/tex]

Simplify the equation

[tex]\text{Total percent}=175\%[/tex]

Hence the percent being represented by the shaded are is [tex]175\%[/tex]

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We move all terms to the left:

Multiply

We add all the numbers and all the variables.

We move all terms containing x to the left hand side, all other terms to the right hand side

Answer:

42 games

Step-by-step explanation:

she lost 6 and won 6 so if she played 84 games she will win 42 and lose 42

The required height of the cliff is  5√3/(√3)-1.

The angle of depression is defined as the If a human looks down at an object, then the angle of depression of that human is the angle between the horizontal line of sight and the object.

we have, angle of depression to top of pole = 45°

that of to foot of pole = 60°

Height of pole is 5 meter.

Then distance between tower is = 5+x/√3        ∴  tan(theta)=P/B

and, tan(45) = x/5+x/√3 = √3x/5+x   =1               ∴  tan(45) =1

5+x =√3x

X = 5/(√3)-1

Now height of cliff = 5+5/(√3)-1 = 5√3/(√3)-1 meter

Thus, the height of cliff is  5√3/(√3)-1.

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With the help of probability we can conclude our answer.

acc to our question-

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The car can go 28.5 miles in 1 gallon of gas.

According to the question,

We have the following information:

Mamadou’s car used [tex]2\frac{2}{3}[/tex] gallons to travel 76 miles.

Now, we can easily find the distance covered by car in one gallon of gas but we will first convert the gas given from mixed fraction.

8/3 gallons of gas = 76 miles

Now, the distance covered in 1 gallon of gas can be found by dividing 76 by 8/3.

1 gallon of gas = 76/(8/3)

1 gallon of gas = 57/2 miles

1 gallon of gas = [tex]28\frac{1}{2}[/tex] miles or 28.5 miles

Hence, the car can go 28.5 miles in 1 gallon of gas.

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Answer:

2.8

Step-by-step explanation:

mean = 54+45+76+33+76= 284

284÷5=56.8

median ,to find median you first arrange the numbers in an accending order

33,45,54,76,76 then you find the middle number which is 54

56.8-54=2.8

Answer:

2.8 marks

Step-by-step explanation:

33, 45, 54, 76, 76

mean score = (54 + 45 + 76 + 33 + 76) ÷ 5

= 56.8

median score = (5 + 1) ÷ 2

= 3rd place

= 54

diff between mean and median score = 56.8 - 54

= 2.8

Answer:

4 over 81

use a calculator then simplify

The length of side RQ in triangle PQR is 7.5.

Given,

ΔJKL ≈ ΔPQR

Therefore, sides are in same ratio to each other i.e.

[tex]\frac{QP}{JK}=\frac{RP}{JL}=\frac{RQ}{LK}[/tex]

[tex]\frac{25}{5} =\frac{22.5}{4.5}= \frac{t}{1.5}[/tex]

Therefore,

5 = t/1.5

t = 5*1.5

t = 7.5

Hence, length of RQ is 7.5.

Correct question,

Triangle JKL is similar to triangle PQR, find t. The sides of JKL measures

sJL = 4.5 sLK = 1.5 sJK = 5. The sides of PQR measures sQP = 25 sRP = 22.5 and sRQ = t. Find the length of RQ.

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Answer:

x = 2

Step-by-step explanation:

calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 8 ) and (x₂, y₂ ) = (2, - 4 )

m = [tex]\frac{-4-(-8)}{2-2}[/tex] = [tex]\frac{-4+8}{0}[/tex] = [tex]\frac{4}{0}[/tex]

since division by zero is undefined then the slope is undefined

a line with undefined slope is a vertical line parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (2, - 8 ) and (2, - 4 ) with x- coordinates 2 , then

x = 2 ← equation of line

Answer:

v=-14

Step-by-step explanation:

Subtract 5 from both sides

5+v=-9

-5 -5

v=-14