–2.5x – 7.5 = x + 6.5

The slope intercept form of equation of required line is

[tex]y = \frac{3}{2}x + \frac{1}{2}[/tex]

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

Slope of the line = 1.5

The line passes through (21, 32)

Equation of required line =

[tex]y - 32 = 1.5(x - 21)\\y - 32 = \frac{3}{2}(x - 21)\\2y - 64 = 3x - 63\\2y = 3x - 63 + 64\\2y = 3x + 1\\y = \frac{3}{2}x + \frac{1}{2}[/tex]

Putting x = 1 on the line,

[tex]\frac{3}{2} \times 1 + \frac{1}{2}\\[/tex]

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

(1, 2) is coordinate of another point on the line

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[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-6)}) \implies y -1= \cfrac{1}{2} (x +6) \\\\\\ y-1=\cfrac{1}{2}x+3\implies {\Large \begin{array}{llll} y=\cfrac{1}{2}x+4 \end{array}}[/tex]

The greatest numbers of these rectangles that can be cut from a piece of paper with width 24 and length 60 is 360 which is option D.

Given:

A rectangle with integer side length has perimeter 10.

If the perimeter of rectangle 2(l+b) = 10

l+b = 10/2

l+b = 5.

Two choices:

1. 2 * 3 rectangle of area 6

2. 1 * 4 rectangle of area 4

The piece of paper has area 24×60 = 1440

This can be divided into rectangles with sides 2×3:

= 24/2 * 60/3

= 12*20

= 240

It can be divided into rectangles with sides 1×4:

= 24/1 * 60/4

= 24*15

= 360

Therefore the greatest numbers of these rectangles that can be cut from a piece of paper with width 24 and length 60 is 360 which is option D.

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Answer: n=-6

Step-by-step explanation:

1. Make your equation

n-5=-11

2. Solve for n by adding 5 to both sides

n=-6

Answer:

16

Step-by-step explanation:

1) Break down the question

We are told that the difference between a number a 5 is minus -11

As it is a minus we have to be careful we are using the correct operation required!

2) Figure out the number

As the difference is -11 we would need add 11 to 5 to get the final number

3) Check your answer makes sense

It is always best to double check your answer to make sure that your answer is 100% correct!

To do this we just have to work out way backwards.

As we can see we have to minus 11 from 16 to get to 5 meaning our answer is correct and the number is 16!!!

Hope this helps, have a great day!

Answer:

y = -6x - 50

Step-by-step explanation:

y = mx + b

Since it is perpendicular to y=1/6, the slope is -6. (Opposite reciprocal)

y = -6x + b.

Substitute to get: -2 = 48 + b

b = -50

y = -6x - 50

30 cars of the delivery company use petrol.

According to the question,

We have the following information:

A delivery company has a total of 160 cars and vans.

The number of cars: the number of vans = 3:7

1/8 of the cars use electricity.

25% of the cars use diesel and rest use petrol.

Let's take the number of cars to be 3x and the number of vans to be 7x.

3x+7x = 160

10x = 160

x = 160/10

x = 16

Number of cars = 3*16

Number of cars = 48

Now, cars that use electricity:

1*48/8

6 cars

Cars that use diesel:

25*48/100

12 cars

Cars that use petrol:

Total number of cars-(number of cars that use electricity and diesel)

48-(6+12)

48-18

30 cars

Hence, 30 cars of the delivery company use petrol.

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Using the given information, the volume of the given rectangle is 6/125 cubic units

From the question, we are to determine the volume of the given rectangle.

From the given information,

The dimension of the rectangle is 1/5 by 2/5 by 3/5

To determine the volume of the rectangle, we will determine the product of the length of the sides of the rectangle.

That is,

Volume of the rectangle = 1/5 × 2/5 × 3/5

Volume of the rectangle = 1 ×2×3 / 5×5×5

Volume of the rectangle = 6/125

Hence, the volume is 6/125 cubic units

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Answer:

395 = 790e^(k*78)

Step-by-step explanation:

Dividing by 790 and taking the natural log

ln ( 395/790 ) = ( kx78 )

-0.6931 = 78k

-0.00888 = k  

Now calculate how much is left after 18 hours:

Amount ( 18 )

= 790e^( -0.00888x18 )

Amount = 673.301 kg

As per the given tax percent deduction from Marquis gross pay of $816 , the gross pay is reduced by $174.66.

As given in the question,

Gross pay taken by Marquis is equal to $816

Items withheld from Marquis gross pay are as follow:

1. Federal tax = $92

2. Social security tax = 6.2% of gross pay

6.2% of 816

= (6.2/100) × 816

= $50.592

3. Medicare tax = 1.45% of gross pay

= 1.45% of 816

= (1.45/100) × 816

= $11.832

4. State tax = 22% of federal tax

= 22% of 92

= ( 22 /100) × 92

= $20.24

Total reduced tax amount from Marquis gross pay

= $ ( 92 + 50.592 + 11.832 +20.24 )

= $ 174.664

≈ $174.66

Therefore,  for the given tax percent deduction from Marquis gross pay of $816 , the gross pay is reduced by $174.66.

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Answer:

B. Subset

Step-by-step explanation:

A(n) subset is a member of a set

Answer:

with what

Step-by-step explanation:

lol

where is the picture..................x1000000000000000000

the 30% increase is 1,500 comments made on the website.

A music video website received 5,000 comments on a new song they released.

The next day, the artist performed the song on television and an additional 1,500 comments were made on the website.

As we know,

The percentage increase = [(increase value)/(old value)]x100

Divide the increase by the beginning number and multiply by 100 to determine the percentage increase between two numbers:

Increase value = 1500

old value =5000

Percent of increase = (1500/5000)x100

Percent of increase = 0.3x100

Percent of increase = 30%

30% if the next day, the artist performed.

In mathematics, a percentage is various or a ratio expressed as a fragment of one hundred. it is often denoted the use of the percent sign, "%", despite the fact that the abbreviations "pct.", "pct" and sometimes "laptop" is also used. A percent is a dimensionless wide variety; it has no unit of measurement. The calculation of chances is done and taught in special approaches relying on the stipulations and necessities. in this manner, the same old formulas can be acquired with proportions, which saves them from having to remember them. In so-referred to as intellectual arithmetic.

This unfastened percent calculator computes some of the values related to possibilities, consisting of the sharp distinction between two given values. percentages are essentially fractions where the denominator is 100. to reveal that a number is a percentage, we use the percent image (%) besides the range. as instance, if you purchased seventy-five questions proper out of a hundred on a check (seventy-five/100), you would have scored 75%.

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She can see the horizon till 2.604 meters when the person is standing at a height of 5.76 meters above sea level.

Given that,

If a person can see d kilometers into the distance from her eye level, which is h meters above sea level, then d=3.57 √h. Let's say the person is standing at a height of 5.76 meters above sea level.

We have to find she can see the horizon, but how far.

The SI unit of length is the meter. In addition to meters, length can also be expressed in other units like centimeters, inches, feet, and yards.

So,

d=h

3.57 √h= 5.76 meters

Divide both sides by 3.57

√h= 5.76 meter/ 3.57

√h=1.614

Squaring on both sides.

h=2.604

Therefore, She can see the horizon till 2.604 meters when the person is standing at a height of 5.76 meters above sea level.

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Answer:

x = 4

Step-by-step explanation:

8(x - [tex]\frac{5}{2}[/tex] ) = 3x ← distribute the parenthesis by 8

8x - 20 = 3x ( subtract 3x from both sides )

5x - 20 = 0 ( add 20 to both sides )

5x = 20 ( divide both sides by 5 )

x = 4

Answer:

Step-by-step explanation:

1. Area for triangle. Base* Height/2

Here the base it 13 units and height is 11 units. Apply to the formula:

13*11/2=

71.5 sq units

2. Answer: 71.5 sq units

Step-by-step explanation:

190 = 5

? = 30

30 / 5 = 6

190 x 6 = 1140

answer

Calculate the slopes of the 2 lines and compare them.

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

If they are equal, the lines are parallel. If one slope is the negative reciprocal of the other, the lines are perpendicular. If neither of these conditions are met, the lines are not parallel and are not perpendicular. You have all the information you need. Do the math.

Step-by-step explanation:

hope it helps

Answer:

25 pounds of hamburger meat

Step-by-step explanation:

you need 15 pounds for 60 hamburgers.

We can turn this into a fraction.

15/60

now we need to make the denominator a power of ten.

15/60

=5/20

=25/100

She needs 25 pounds of hamburger meat

The equation that relates the number of triangles in the figure (n) to the perimeter of the figure (P) is P = 5n + 14.

We are given triangles. The triangles are arranged in a certain pattern. We need to find the relationship between the number of triangles and the perimeter of the figure. Let the perimeter of the figure having "n" number of triangles be represented by the variable "P(n)".

P(1) = 24

P(2) = 30

P(3) = 36

There is an increase of 6 units in the perimeter with every addition of a triangle. We can see and continue the pattern. The relationship between the perimeter and the number of triangles is given below.

P(n) = 18 + 6n

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The answer to the given question is true. A chart where the data is arranged in vertical columns is called Column Chart, and this chart is useful for showing data changes over time or illustrating comparisons among items.

What is column chart?

Column chart is a type of chart that compares different object levels over time using a vertical format. It is a chart in which the data is arranged in columns and this is useful for showing data changes over a period of time or for illustrating comparisons among items.

Data that is arranged in columns or rows on a worksheet can be plotted in a column chart. In column charts, categories are typically organized along the horizontal axis and values along the vertical axis. Column charts are useful to show how data changes over time or to show comparisons among items.

Column charts are not useful when there are a lot of categories. Catagories organized along the x-axis, while numbers or numerical values ligned in the y-axis.

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Using Simple Interest formula ,

The rate percent on amount of Rs.300 is 5.5 .

At same rate, R = 5.5 the principle 800 will be Rs1120 in next 7 years .

In first case we have given that ,

principle = Rs.350

time = 4 years

Amount = Rs 1120

simple interest = 1120-350 = Rs.770

let rate of interest be R% .

Using the formul of simple interest

S.I = P×R×t /100

=> 770 = 350×4×R/100

=> R = 5.5 %

In Second case , rate of interest is same as in first case. So,

Amount = Rs. 1120

Principle = Rs. 800

rate of interest (R)= 5.5

Again simple interest formula Used:

Simple Interest = (P × R × T)/100

Simple interest = 1120 - 800 = Rs. 320

Simple Interest = (P × R × T)/100

⇒ 320 = 800×5.5 ×T/100

=> T = 7.27 ~ 7

∴ In the given principle Rs 800 with same rate of interest will be 1120 in 7 next years .

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As per the given data, loan amount is $35,000 with 2% simple interest for the time period of 8 years then monthly payment is equal to

$422.92.

As given in the question,

Loan amount taken from the bank is equal to $35,000

Simple interest rate is 2%

Time period = 8 years

Total interest paid is equal to

= Loan amount × Interest rate × time period

= 35,000 × 2% × 8

= (35,000 × 2 × 8) / 100

= $5600

Total amount to be paid

= Loan amount + Interest amount

= $35,000 + $ 5,600

= $ 40,600

Monthly payment done based on given interest and time period

= $40,600 / ( 8 × 12 )

= $ 40,600 / 96

= $ 422.92

Therefore, for the given data, loan amount is $35,000 with 2% simple interest for the time period of 8 years then monthly payment is equal to $ 422.92.

The complete question is:

Attending the university of Houston main campus ,the bank agrees to give you a loan of $35,000 with 2% simple interest over 8 years. How much will your monthly payments be?

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The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is ;

Pr(C & fewer than 3) = 0.1985

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Here, we are required to find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years.

Let Pr(C) be the number of consumers who believe that cash will be obsolete in the next 20 years.

Therefore, since 39.7% believe so,

Pr(C) = 39.7/100 = 0.397

If 6 consumers are selected randomly, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years will be;

Probability of 2 out 6 to believe so or Probability of 1 out of 6 to believe so.

Pr(2/6) + Pr (1/6)

Therefore the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is;

Pr (fewer than 3) = (2/6) + (1/6)

Pr (fewer than 3) = 3/6

Therefore, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is ;

Pr(C) × Pr (fewer than 3)

i.e 0.397 × (3/6) = 0.1985

Therefore, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is ;

Pr(C & fewer than 3) = 0.1985

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Answer: 12

Step-by-step explanation: multiply it all together then divide it by the product.

Answer:

I don't know I just got the app

Step-by-step explanation:

; /

Answer:

oh no

Step-by-step explanation:

The person at the 300th number will get a t-shirt and a gift card both.

Given, at the grand opening of a sporting goods store, the store is giving a free shirt to every 12th person who attends.

They give a $25 gift card to every 30th person.

We have to find that which person will get both a t-shirt and a gift card.

To find the person who will get both, we have to find the LCM of 12 and 25.

As, the LCM of 12 and 25 is 300

So, the person at the 300th number will get a t-shirt and a gift card both.

Hence, the person at the 300th number will get a t-shirt and a gift card both.

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Answer: B

Step-by-step explanation:

100/9

11.1

11 1/9

Answer:

Step-by-step explanation:

500(108)=54000 i may not be right