Why is the longest side of a triangle always opposite the largest angle?

A linear graph is one whose equation is in the form y = mx + b, where m and b are constants. A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants.

To determine if a given graph is linear, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = mx + b.

For example, if the two points on the graph are (2, 3) and (5, 7), then plugging these values into the equation gives us:

y = mx + b

3 = m*2 + b

7 = m*5 + b

Solving this system of equations gives m = 2 and b = -1, so the equation of the line is y = 2x - 1.

A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants. To determine if a given graph is quadratic, calculate the equation of the parabola by finding three points on the graph and plugging them into the equation y = ax^2 + bx + c.

For example, if the points on the graph are (1, 6), (2, 13), and (3, 24), then plugging these values into the equation gives us:

y = ax^2 + bx + c

6 = a*1^2 + b*1 + c

13 = a*2^2 + b*2 + c

24 = a*3^2 + b*3 + c

Solving this system of equations gives a = 4, b = -5, and c = 6, so the equation of the parabola is y = 4x^2 - 5x + 6.

An exponential graph is one whose equation is in the form y = a*b^x, where a and b are constants. To determine if a given graph is exponential, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = a*b^x.

For example, if the two points on the graph are (2, 16) and (3, 24), then plugging these values into the equation gives us:

y = a*b^x

16 = a*b^2

24 = a*b^3

Solving this system of equations gives a = 2 and b = 2, so the equation of the line is y = 2*2^x.

Learn more about graph here:

https://brainly.com/question/14375099

#SPJ4

The difference between log with base 10 and log with base e is that the log with base 10 is called a common logarithmic function and the log with base e is called a Natural Logarithmic Function .

What is Logarithmic Function ?

The logarithm is defined as a power to which a number must be raised in order to get some other values. Log is the most convenient way to express the large numbers.

The Logarithm with base 10 is defined as a power to which the  number must be raised  to get some other number. It can also be  called as the logarithm of base 10, or common logarithm.

The general form of Common  logarithm is written as: [tex]log_{10} (x)[/tex] ;

The Logarithm  with base e is called as Natural Log , where e is an irrational number .

The general form to represent a Natural Log is : [tex]log_{e} (x)[/tex] or [tex]ln(x)[/tex] .

Learn more about Logarithm here

https://brainly.com/question/11630468

#SPJ4

Answer:

Step-by-step explanation:

We have, C(x) = 0.005x3 – 0.02x2 + 30x + 5000

Clearly, the marginal cost, MC (x) = \(\frac{d}{d x}\)C(x)

= \(\frac{d}{d x}\)(0.005x3 – 0.02x2 + 30x + 500)

= 0.005 × 3x2 – 0.02 × 2x + 30 + 0

= 0.015x2 – 0.04x + 30

Now, marginal cost when 3 units arei produced

MC(3)= 0.015(9) – 0.04(3) + 30

= 0135 – 0.12 + 30= 30.015

Answer:

62 candies can fit into each box

Step-by-step explanation:

We know

A small box can hold 94.24 g of candy

Each candy has a mass of 1.52 g

How many candies can fit into each box?​

To find it we take

94.24 divided 1.52 = 62 candies

So, 62 candies can fit into each box

Mario make total $132.1 from the tip of his two customers.

The amount of tip obtained = total bill × percentage of the bill

Put the respective values in equation depending on the customer A or B

Tip from customer A

Tip = 430.50 × 20%

Now find percentage by multiplication and division on Right Hand Side of the equation

Tip = $86.1

Tip from customer B

Tip = 184 × 25%

Again perform multiplication and division on Right Hand Side of the equation

Tip = $46

Total tip earned = 86.1 + 46

Simply add the two numbers on Right Hand Side of the equation to find the total tip earned

Total tip earned = $132.1

Learn more about percentage -

https://brainly.com/question/24877689

#SPJ4

Answer:

320 grams ÷ 27% = 8.3 grams

Step-by-step explanation:

mark brainliest plss

Answer:

Sine                                                                                                                                                                                                                                         AB is perpendicular to sides AE and BC/                                                                                                                                                  

Step-by-step explanation:

The slope is the change in y over the change in x.

Line segment AE has a slope of 3/4

(0,4)(4,7)

The y values are 7 and 4.

The x values are 4 and 0.  

You find the change by subtracting

[tex]\frac{7-4}{4-0}[/tex] = [tex]\frac{3}{4}[/tex]

Line segment BC has the same slope

((3,0)(7,3)

The y values are 3 and 0.

The x values are 7 a d 3.  

You find the change by subtracting

[tex]\frac{3-0}{7-3}[/tex] = [tex]\frac{3}{4}[/tex]

Since line segments Ae and BC has the same slope.  They are parallel.

Line segments that are perpendicular will have opposite reciprocals slopes.  In this case the slope should be  - [tex]\frac{4}{3}[/tex].

Let's look at line segment AB

(0,4)(3,0)

The y values are 0 and 4.

The x values are 3 and 0.

You find the change by subtracting  

[tex]\frac{0-4}{3-0}[/tex] = [tex]\frac{-4}{3}[/tex]

Since the slopes are opposite reciprocals, side AB is perpendicular to sides AE and BC                                                                                                                                        

There are two steps of solving the equation -3(2x+6)=12.

The steps are given below.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given equation:

-3(2x+6)=12

The first step:

Solving the parenthesis first,

-6x -18 = 12

Adding 18 to both sides,

-6x = 30

Divide by -6,

x = -5

The alternate step:

-3(2x+6)=12

Divide by -3,

2x + 6 = -4

2x = -10

x = -5

Therefore, x = -5 is the solution of the equation.

To learn more about the equation;

https://brainly.com/question/12788590

#SPJ1

Answer:

20

Step-by-step explanation:

110 -70 = 40 40/2= 20

Answer:

[tex] \sf \: x = {20}^{o} [/tex]

Step-by-step explanation:

Let's take the value of y as,

→ y = 90°

(Because, it is a right angle)

Forming the equation,

→ x + y + 70° = 180°

Now the value of x will be,

→ x + y + 70° = 180°

→ x + 90° + 70° = 180°

→ x + 160° = 180°

→ x = 180° - 160°

→ [ x = 20° ]

Hence, the value of x is 20°.

Angles x° and 157° are neighboring because they share a shared vertex and side, preventing them from overlapping,  the sum of any two angles on a straight line equals 180°.

Two lines converge at a common point to form an angle. They are expressed by the sign ° and are measured in degrees. Acute, right, obtuse, and reflex angles are four crucial types. There are 360° in a circle. Two rays (half-lines) combined into an angle have a single terminal. The latter is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms. The vertex of an angle is the point at which all points meet .

given

If two angles' sums are same, they are said to be supplementary.

If two angles' sums are same, they are said to be complimentary.

Each set of opposite angles generated by crossing lines are referred to as vertical angles. The term "adjacent angles" refers to two angles that share a common vertex and side but do not overlap.

Angles x° and 157° are neighboring because they share a shared vertex and side, preventing them from overlapping, and they are supplementary angles because the sum of any two angles on a straight line equals 180°.

To know more about angles visit :-

https://brainly.com/question/28451077

#SPJ4

5. The width of the house. = 30 feet

6. The height of the house. = 22.5 feet

7. The height of the first floor. = 12.5 feet

8. The height of the roof. = 10 feet

9. The width of the door. = 5 feet

10. The height of the door. = 7.5 feet

The actual length of each segment is calculated by counting the units in the scale drawing and multiplying by the scale factor

In the problem, the scale factor is  two and a half feet = 2.5 feet

5. The width of the house

number of units from the drawing = 12 units

actual length = number of units from the drawing * scale factor

actual length = 12 * 2.5 = 30 feet

6. The height of the house

number of units from the drawing = 9 units

actual length = 9 * 2.5 = 22.5 feet

7. The height of the first floor

number of units from the drawing = 5 units

actual length = 5 * 2.5 = 12.5 feet

8. The height of the roof

number of units from the drawing = 4 units

actual length = 4 * 2.5 = 10 feet

9. The width of the door.

number of units from the drawing = 2 units

actual length = 2 * 2.5 = 5 feet

10. The height of the door.

number of units from the drawing = 3 units

actual length = 3 * 2.5 = 7.5 feet

Learn more about scale drawing at:

https://brainly.com/question/12626179

#SPJ1

The 8.4 inches length of g and the 79° and 25° measures of the angles ∠G and ∠E, using the law of sines, indicates that the length of the side  EG = f is about 8,3 inches.

The law of sines states that the ratio of the sine of an interior angle of a triangle to the length of the opposite side to the angle is the same for the three sides and angles in a triangle.

Mathematically, the law of sines can be presented as follows;

[tex]\dfrac{a}{sin(A)} = \dfrac{b}{sin(B)} =\dfrac{c}{sin(C)}[/tex]

Where;

a, b, and c are the length of each of the sides of the triangle, and ∠A, ∠B, and ∠C are the measure of each of the interior angles of the triangle.

The details of the triangle ΔEFG, specifying the side g as the side opposite the angle ∠G, and the side f as the side opposite the ∠F we get;

The length of EF = g = 8.4 inches

Length of EG = f

The angle sum property of a triangle indicates that we get;

∠E + ∠F + ∠G = 180°

∠F = 180° - (∠E  + ∠G)

∠F = 180° - (25°  + 79°) = 76°

According to the law of sines, we get;

8.4/(sin(79°) = f/(sin(76°))

f = (sin(76°)) × 8.4/(sin(79°) ≈ 8.3

Learn more on the law of sines here: https://brainly.com/question/16555495

#SPJ1

Answer: 8 feet

Step-by-step explanation:

you take 33-25 to get the sum of 8. so the squid is 8 feet longer than the shark.

No, a triangle with side length 4 units, 8 units , and 12 units does not exist.

As given in the question,

Let us consider the triangle be ABC,

Side length of the triangle are given as follow:

AB = 4units

BC = 8units

CA = 12units

Triangle inequality for the given triangle ABC is given by:

AB + BC > CA

AB + CA > BC

CA + BC > AB

To check whether the given side length forms a triangle apply triangle inequality we get,

AB + BC

= ( 4 + 8 )units

= 12 units

= CA

Here triangle fails.

Therefore, the given side length does not forms a triangle.

Learn more about triangle here

brainly.com/question/2773823

#SPJ4

A particle takes 5 × 10^7 sec of time to travel a distance of 9.0 × 10^12 meters at a rate of 1.8 × 10^5 meters.

What is speed?

Speed indicates how quickly something or someone is moving. If one knows how far something has travelled and how long it took to get there, then one can calculate its average speed.

The particle travels at a rate of 1.8 × 10^5 m.

The particle travels a distance of 9.0 × 10^12 m.

Let the time taken for the particle to travel be x.

The formula for calculating the distance traveled by the particle is -

distance = rate × time

time = distance/rate

Plugging in the values in the equation -

x = 9.0 × 10^12/1.8 × 10^5

x = 9.0/1.8 × (10^12-5)

x = 5 × 10^7 sec

Therefore, the time taken by the particle to travel is 5 × 10^7 sec.

To learn more about speed from the given link

https://brainly.com/question/4931057

#SPJ4

Answer:

see explanation

Step-by-step explanation:

A

∠ UVX and ∠ WXV are alternate angles and are congruent , then

∠ UVX = ∠ WXV = 15°

∠ WVU = ∠ WVX + ∠ UVX = 24° + 15° = 39°

B

opposite sides of a parallelogram are congruent , then

UV = XW = 36

C

consecutive angles are supplementary , sum to 180° , then

∠ XUV + ∠ WVU = 180° , so

∠ XUV + 39° = 180° ( subtract 39° from both sides )

∠ XUV = 141°

D

diagonals bisect each other , so

YW = UY = 10

The original price of the pair of shoes is $62.5.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Original price = 100%

Offer price = $50

Offer = 20%

Now,

80% = 50

Multiply 100/80 on both sides.

100% = 100/80 x 50

100% = $62.5

Thus,

The original price is $62.5.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ1

The solution to the equations is

The value of first x = € 160

The value of second y = € 120

The value of third z = € 140

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first , second and third be represented as x , y , and z

The total amount to be distributed = € 420

So , x + y + z = € 420   be equation (1)

Now , first has €40 more than the second

So , x = y + 40   be equation (2)

And , third has half of what they have between the first two

So , z = ( 1/2 ) ( x + y )   be equation (3)

Substituting the value of x in the equation (3) , we get

z = ( 1/2 ) ( 2y + 40 )

z = y + 20   be equation (4)

Substituting the value of z and x in equation (1) , we get

( y + 40 ) + y + ( y + 20 ) = 420

On simplifying the equation , we get

3y + 60 = 420

Subtracting 60 on both sides of the equation , we get

3y = 360

Divide by 3 on both sides of the equation , we get

y = € 120

Therefore , the value of x = € 160

The value of z = € 140

Hence , the solution to the equation is € 160 + € 120 + € 140 = € 420

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

Quantitative variable are - 2,3,5,7 and Qualitative are 1, 4 ,6

1. Marital status of nurses in a hospital-qualitative

2. Time it takes to run a marathon-quantitative

3. Weights of lobsters in a tank in a restaurant- quantitative

4. Colors of automobiles in a shopping center parking lot- qualitative

5. Ounces of ice cream in a large milkshake- quantitative

6. Capacity of the NFL football stadiums -qualitative

7. Ages of people living in a personal care home- quantitative

Qualitative variables are categorized or labelled to belong to a certain category or group.

There are two types of qualitative variables, Categorical and ordinal.

Categorical variable are those variables that are labelled in non-numeric or numeric form, where the numbers have no value. The order also does not matters. For example, the number on the jerseys of football players. It is not necessary that the player number 1 is actually the best player.

learn more about of variable here

https://brainly.com/question/17344045

#SPJ4

On solving the provided question, we can say that - by the prime factors we have x^2 + 1 +2x = X= -1, -1

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

here we have the equation,

[tex]x^2 + 1 + 2x\\[/tex]

(x+1)(x+1)

x = -1, -1

To know more about prime factor visit:

https://brainly.com/question/29775157

#SPJ1

The probability that the annual cost will be 5 of the mean is 0.0912.

A method used by risk managers to predict upcoming events, like accidental and commercial losses. In order to determine a probability distribution that can be applied to forecast future losses, this procedure involves reviewing historical loss data.

X = Annual cost of medical care for dogs.

X~ Normal (μ = 200, σ = 60)

Sample size n = 16

We know that the sample mean Xbar has a normal distribution with mean = μ and sd = σ/√n

Xbar ~ Normal (μ’ = 200, σ’ = 60/√16 = 15)

Required probability -

P[Average cost of medical care for 16 sampled dogs is > 220]

= P[Xbar > 220]

= P[(Xbar-μ’)/σ’ > (220-200)/15]

= P[Z > 1.3333], Z is a standard normal variable.

= 1 - P[Z < 1.3333]

= 1 - 0.9087, from standard normal table.

= 0.0912

To know more about probability visit:

brainly.com/question/11234923

#SPJ4

The complete question is:

A veterinary association claims that the annual cost of medical care for dogs averages $200 with a standard deviation of $60, and for cats averages $240 with a standard deviation of $70. Assume the costs follow a normal distribution. What is the probability the average annual cost of medical care for 16 randomly chosen dogs is greater than $220.

the slope of the given straight line will be -3

What is the slope of line?

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.

We know that formula two find the slope of the line joining two points which is

Slope is = y2-y1/x2-x1

=9-0/0-3

=-3

Hence the slope of the given straight line will be -3

Learn more about Slope, by the following link

https://brainly.com/question/3493733

#SPJ1

Function Notation: another way of representing the relation between two variables, y is denoted as f(x) and x remains.

x is the input and f(x) is the output

This question is essentially asking what is the output of the function when the input is equal to 5.

[tex]f(5) = (5)^2-2(5)[/tex]

[tex]f(5) = 25-10[/tex]

[tex]f(5) = 15[/tex]

m = the unknown value

4m = four times that unknown value

4m = 4/3

m = (4/3)*(1/4)

m = 4/12

m = 1/3

Therefore, we multiply 4 with 1/3 to end up with 4/3.

Answer:

Step-by-step explanation:

7(9w)7(9w) = 11

(7 ×7)(9×9)(w×w) = 11

49 ×81 w² = 11

3969w² = 11

[tex]\frac{3969w^{2} }{3969}[/tex] =  [tex]\frac{11}{3969}[/tex]

w²   =  [tex]\frac{11}{3969}[/tex]

[tex]\sqrt{w^{2} }[/tex]   =   [tex]\sqrt{11/3969}[/tex]

w = ± [tex]\frac{\sqrt{11} }{63}[/tex]

Because the solution contains a square root the answer contains both a negative and a positive solution.  

When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent.

Equivalent ratios are two ratios with the same value. By multiplying or dividing the two amounts by the same number, you can determine the equivalent ratio. Finding equivalent fractions follows the same procedure.

The ratio formula can be used to represent a ratio as a fraction. The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.

To know more about ratios visit:-

brainly.com/question/13419413

#SPJ1

Answer: domain(-oo,oo). range= f(x) >-5

Step-by-step explanation:

Answer:

[tex]w^{2}[/tex]

Step-by-step explanation: