What is an equation of the line that passes through the points (-2,7) and (-8,4)

By solving the linear equations we get the final values of x = 4 & y = 4.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order  term are included.

We have,

               2x + 7y = -20           ----------(i)

                x - 3y = 16               ----------(ii)

By multiplying equation (ii) with 2 we get,

               2x + 7y = -20 ---------(III)

               2x - 6y = 32 -----------(IV)

taking subtraction of equations (III) and (IV), we get

               y = 4

by putting value of y in equation (ii) we get,

               x = 4

Hence by solving the linear equations we get the values of x = 4 & y = 4.  

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The domain and the range of a function have the concepts given as follows:

The domain of a function or of a relation is the set that contains all possible input values. Hence, among possible representations, we have that:

The range of a function or of a relation is the set that contains all possible output values. Hence, among possible representations, we have that:

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The dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .

Let length be l and width be b of garden .

According to question ,

l + 2b = 1040

Area of garden = l * b

Substituting value of l in formula for area ,

Area = ( 1040 - 2b ) * b = 1040b - 2[tex]b^{2}[/tex]

Taking derivative of Area wrt. b and putting it equal to 0 ,

1040 - 4b = 0

b = 1040 / 4

b = 260 feet

Therefore , l = 1040 - 520 = 520 feet .

Maximum Area = 260 * 520 = 135200 [tex]feet^{2}[/tex] .

Hence , the dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .

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Answer:-454/539

Step-by-step explanation:32.34(s+1)=5.1

                                            32.34s+32.34=5.1

                                            32.34s=5.1-32.34

                                            32.34s=-27.24

                                            s=-454/539

Answer:

x^3 + 64 + 11x - 20bxy - 80by

(if I am wrong, apologies)

Answer:

x^2+4x-5

Step-by-step explanation:

x^3+8x^2+11x-20/x+4=x^2+4x-5

The value of the function g(x) when x = -2 is 6

The definition of the function is given as

g(x)=x to the power of 2 minus x

Rewrite the above function properly

So, we have the following representation

g(x) = x² - x

To find the function g(-2), we set the value of x in the equation g(x) = x² - x to -2

This is represented by

Calculate g(x), when x = -2

Substitute -2 for x in the equation g(x) = x² - x

So, we have the following equation

g(-2) = (-2)² - (-2)

Evaluate the exponents

This gives

g(-2) = 4 - (-2)

Evaluate the sum

g(-2) = 6

Hence, the value of the function is 6

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The number of kilometers in 5 square gigameters is  5. 0 × 10^18

Proportion can be described as an expression or equation in which two ratios are made equal to each other.

It is also known as the mathematical comparison between two numbers or elements.

From the information given, we have;

1 gigameter = 1.0×10^6 kilometers

But,

5 square gigameters = 5. 1.0×10^6 . 1.0×10^6

Add the powers

5 square gigameters = 5..0×10^12

If 1 gigameter = 1.0×10^6 kilometers

Then 5. 1.0×10^12 gigameter = x

cross multiply

x = 5.0×10^12 ×  1.0×10^6

x = 5. 0 × 10^18 kilometers

Hence, the value is 5. 0 × 10^18 kilometers

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Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.

The ratio of an object's mass to its volume is its density. Grams per cubic centimeter, or g/cm³, are frequently used to measure density. Keep in mind that a volume is measured in cubic centimeters, not gram (the same volume as 1 milliliter). More particles will make a box denser than fewer particles in the same box. Despite the fact that the SI unit of density is kg/m³, we instead use g/cm³ for solids, g/ml for liquids, and g/L for gases out of convenience. The relationship between a substance's mass and the volume it occupies is known as its density.

Given,

Volume = 2.5 cm³

Mass = 10 g

For density:

Mass ÷ volume

10 ÷ 2.5

4

Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.

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Answer: False

Step-by-step explanation:The potential energy will decrease and the kinetic will increase

The person can make 60 trips.

Let us say that A indicates the major sea Islands and B indicates the major lakes. Taking both the cases as events, we will use multiplication principle. Based on the information, the event A occurs in m ways and the event B will occur in n ways. So, the two events will occur in m×n ways.

Thus, A × B = 5 × 12

Performing multiplication on Right Hand Side of the equation to find the number of trips

Total number of trips = 60

Hence, there are 60 trips that could be made.

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Brian has  £63 Initially, by using the ratio and proportion method.

What are Ratio and Proportion?

In this section, the terms ratio and percentage are defined. Both ideas play a significant role in mathematics. Numerous examples where the notion of the ratio is highlighted may be found in daily life, such as the rate of speed (distance/time) or price (rupees/meter) of a substance.

An equation known as proportion shows that the two ratios presented are equal to one another. For instance, the time it takes a train to go 100 kilometers per hour is equal to the time it needs to travel 500 kilometers in five hours. Example: 100 km/hr = 500 km/5 hour. The division technique of comparing two amounts can be quite effective in some circumstances. We can argue that a ratio is a comparison or condensed form of two quantities of the same type. We may determine how many times one quantity is equal to another using this relationship. The ratio may be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects. A ratio is indicated by the symbol ":".

In the question, It is given that:

The ratio of money in Brian's wallet to Colin's wallet one day was 7:2.

Let 7x denotes the amount in Brian's wallet and 2x denote the amount in  Colin's wallet on that day.

we know that:

Brian spent £39 that day.

Amount left in Brian's wallet = 7x- 39

Brian now had £4 less than Colin.

⇒ 2x -4= 7x- 39

⇒  7x-2x=4+39

⇒  5x=35

⇒  x=7   [Divide both sides by 5 ]

So , The initial amount in Brian's wallet  = 7(7)= £49

The initial amount in Colin's wallet = 2(7)= £14

The amount they had together =  £49+£14 = £63

So, They had £63 altogether initially.

Therefore, Brian has  £63 Initially.

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Answer: £14

Answer:

Step-by-step explanation:

1. Put the variable as numbers in the computation. m=6 and n=6

SO:

6+6*6

2. Compute using Pemdas( Parentheses, exponets,multiplication, division, addition, subtraction)! Or order of operations!

6+36= 42

Answer: 42

The required expression for the fenced region is lw = 650.

Given that,
A homeowner wants to fence in a rectangular space in her yard along one side of her house for her dogs. the total area she can fence in is 650 square feet.

The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.

Here,
Let the length of the area be l and the width of the area be w,
The total area she can fence in is 650 square feet.
lw = 650

Thus, the required expression for the fenced region is lw = 650.

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The rate of the passenger train is 60mph.

We know that,

Speed = Distance / Time

Time = Distance / Speed

s = speed of passenger train

speed of freight train = (s - 20)

T = 240 / s

T = 160 / (s-20)

240 / s = 160 / (s-20)

240(s - 20)/s(s - 20) = 160s/s(s - 20)

240(s - 20)/s(s - 20) - 160s/s(s - 20) = 0

240(s - 20) - 160s = 0s(s - 20)

240s - 4800 - 160s = 0

80s - 4800 = 0

80s = 4800

Hence the speed of the freight train is 40mph, while the speed of the passenger train is 60mph.

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Answer:

Im gonna assume its counter clockwise (excuse the bad drawing)

Step-by-step explanation:

The vertices of triangle F'G'H' after a rotation of 180° about (-3, -6) are F'(0, 10), G'(5, 6) and H'(2, 4).

Rotations are transformations that turn a shape around a fixed point. To rotate a shape we need: a centre of rotation. an angle of rotation (given in degrees) a direction of rotation – either clockwise or anti-clockwise.

Given that, triangle FGH has vertices F(-3, 4), G(2, 0), and H(-1, -2).

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

So, (x, y) → (x+3, y+6)

F(-3, 4) → (-3+3, 4+6) → F'(0, 10)

G(2, 0) → (2+3, 0+6) → G'(5, 6)

H(-1, -2) → (-1+3, -2+6) → H'(2, 4)

Therefore, the vertices of triangle F'G'H' after a rotation of 180° about (-3, -6) are F'(0, 10), G'(5, 6) and H'(2, 4).

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The value of 'm' in the absolute value equation is 3

A linear equation can be described as an equation having the highest power of the variable as 1.

It is also referred to as a one-degree equation.

Example;

x + 1 = 4

Absolute value of a number can be defined as the value of that number irrespective of its direction to zero on the number line.

The value must take a positive sign.

The symbol used to represent the absolute value of a number is '| '

We have the equation;

|m-2|-1=4

Let's take the absolute value

m + 2 - 1 = 4

Now, collect like terms, we get;

m = 4 - 1

Add or subtract like terms

m = 3

Hence, the value is 3

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Answer:

Step-by-step explanation:

5.40/12= 0.45

6.72/16=0.42

Answer:

The 16 pack

Step-by-step explanation:

Pack 1: $5.40 for 12

Pack 2: $6.72 for 16

Therefore the 16 pack is the better buy because you purchase an extra 4 sodas for $0.03 less.

Answer:

3 ¹/₃ years

Step-by-step explanation:

Simple Interest Formula

I = Prt

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\sf \implies 500=3000 \times 0.05 \times t[/tex]

[tex]\sf \implies 500=150t[/tex]

[tex]\sf \implies t=\dfrac{500}{150}[/tex]

[tex]\implies \sf t=3\frac{1}{3}[/tex]

Therefore, the money must be left in the account for 3 ¹/₃ years for the account to earn $500 interest.

After 10 days, the expected number of shoppers at the shopping mall is 163.

It is given that the number of shoppers increases daily by 5% from the number of shoppers the previous day.

As we can see that the increase in the number of shoppers is going to change every day, and the above case is compounded daily.

The formula of compound increase is

Amount = Base X (1 + r/n)ⁿˣ

where,

Base = original amount

r = rate of change

n = no. of times the change occurs in the time period

t = time

Here,

Base = 100

r = 5/100

n = 1, since it changes once every day

x = 10

Therefore we get

100 X (1 + 5/100)¹⁰

= 100 X 1.05¹⁰

162.88

Since the number of people cannot be in decimal,

the expected number of people is 163

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The number of  boys and girls in a class of 150 students is 90 and 60 respectively.

RATIO:

Comparing two quantities of the same units and determining the ratio tells us how much of one quantity is in the other.

i.e., it shows how many times a number contains another.

Total number of students = 150

ratio of boys to girls = 3 : 2

B:G = 3 : 2

now

3x + 2x = 150

5x = 150

x = 30

the number of boys = 3x = 3 X 30 = 90 boys.

the number of girls = 2x = 2 X 30 = 60 girls.

The number of  boys and girls in a class of 150 students is 90 and 60 respectively.

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The percent decrease in the travel time after getting a new job is 36%.

Percentage is defined as part of a whole expressed in hundredths or out of 100. It is usually written with the symbol "%".

First, determine the decrease in travel time after getting a new job by subtracting the new travel time of 30.72 minutes from the initial travel time of 48 minutes.

decrease in time = 48 - 30.72

decrease in time = 17.28

Then, determine the percent decrease by dividing the decrease in time of 17.28 minutes by the initial travel time of 48 minutes and multiply by 100.

percent decrease = (17.28 / 48) x 100

percent decrease = 36%

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a) A mathematical equation that represents the total cost, t, for a adult tickets and c child tickets is t = $5a + $3c.

b)No, she cannot buy 2 adult tickets and 7 child tickets.

Mathematical equations are relationships between two expressions that are equal on both sides of the equal to sign. An equation is, for instance, 3y = 16.

Given,

Maymont Middle School is selling tickets for the winter musical. Adult tickets cost $5 each and child tickets cost $3 each.

a) Mathematical equation:

represents the total cost, t, for a adult tickets and c child tickets

t = $5a + $3c

A mathematical equation that represents the total cost, t, for a adult tickets and c child tickets is t = $5a + $3c.

b) Ciera has $28.

a = 2 c = 7

Equating values in equation,

= $5(2) + $3(7)

= $10 + $27

= $37

No, she cannot buy 2 adult tickets and 7 child tickets.

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Answer:

23.29 ft

Step-by-step explanation:

The given scenario can be modelled as a right triangle, where the angle between the ground and the ladder is 76°, the side opposite the angle is the height the ladder reaches up the wall, and the hypotenuse is the ladder.

To find how high up the wall the ladder reaches, use the sine trigonometric ratio:

[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]

where:

The angle of elevation is 76°, so θ = 76°.

Let x be the height the ladder reaches up the wall, so O = x.

H is the length of the ladder, so H = 24.

Substitute the given values into the sine ratio and round the answer to the nearest hundredth:

[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]

[tex]\sin(76^{\circ})= \dfrac{x}{24}[/tex]

[tex]\sin(76^{\circ})\cdot 24= \dfrac{x}{24}\cdot 24[/tex]

[tex]24 \sin(76^{\circ})= x[/tex]

[tex]x=24 \sin(76^{\circ})[/tex]

[tex]x=23.28709743...[/tex]

[tex]x=23.29\; \sf ft\;(nearest\;hundredth)[/tex]

Therefore, the ladder reaches 23.29 ft up the wall, rounded to the nearest hundredth.

About [0.7479, 0.8091] of medical malpractice cases are abandoned or dismissed, according to the estimate with a 95% confidence level.

A confidence interval is a method for estimating a population parameter, such as the population proportion, at a given level of confidence, using the sample statistic, such as the sample proportion, and the confidence coefficient, such as the critical value.

arbitrary sample size, n = 1228

number of those who were dropped or dismissed, x = 856

The sample percentage of later discarded or dropped, p = 956 / 1228 ≅ 0.7785

Level of confidence = 0.99

Level of significance α = 0.01

The population proportion's 99% confidence interval estimate is calculated as follows:

p ± [tex]z_{a/2}[/tex] * [tex]\sqrt\frac{p (1 - p)}{n}[/tex]

Using the Excel function or the z-distribution table for calculation

[tex]z_{a/2} = z_{0.01/2} = z_{0.005}[/tex]

=NORMSINV(0.05)

[tex]z_{0.01/2}[/tex] ≅ ±2.58

The interval's computation is as follows:

0.7785 ± 2.58 * [tex]\sqrt\frac{0.7785 (1 - 0.7785)}{1228}[/tex]

= 0.7785 ± 2.58 * 0.0118

= = 0.7785 ± 0.0306

(0.7479, 0.8091)

As a result, the estimate of the proportion of medical malpractice claims that are withdrawn or dismissed at a 99 percent confidence interval is roughly [0.7479, 0.8091].

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Answer:

Your first option is correct but your second is wrong

Step-by-step explanation:

In option b-

when an employee receives 10% additional for each of the following weeks:

10% of 200=  10/100 x200= 20

it means he will get $20 in extra in every week

so it will be- 220,240,260

The plane which is parallel to the line WXT is UVZW

two segments parallel to VU is ST and WX

two segments skew to XY is UT

two segments skew to VZ is YU and TX

Lines that are always the same distance apart in a plane are said to be parallel. Lines that are parallel never cross. Lines that cross at a straight angle (90 degrees) are said to be perpendicular.

Given : The quadrilateral prism

Parallel lines means lines which does not interact and run parallel meaning they have equal distance between them.

The plane which is parallel to the line WXT is UVZW

two segments parallel to VU is ST and WX

two segments skew to XY is UT

two segments skew to VZ is YU and TX

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