You and a friend have dinner at a restaurant. Your meal costs $15.85 and you leave an 18% tip. Your friend’s meal costs
$14.30 and he leaves a 20% tip. Who left the bigger tip

The presence of such a row tell us about the consistency of the corresponding linear system is inconsistent

What is Linear System?

A linear system is a mathematical model of a system that is based on the usage of a linear operator in systems theory. Linear systems often have considerably simpler features and properties than nonlinear systems.

1. The pivot positions in the first augmented matrix are a11, a22, and a33. Because the last column lacks a pivot, the linear system corresponding to the first augmented matrix is consistent.

2. The pivot positions in the second augmented matrix are a11 and a22. Because the last column lacks a pivot, the linear system corresponding to the second augmented matrix is consistent.

3. The a11, a22, and a34 elements in the third augmented matrix serve as pivot points. Because the last column has a pivot, the linear system corresponding to the third augmented matrix is consistent.

b) 1. The linear system corresponding to the first augmented matrix comprises four equations and three unknowns. The presence of a zero row indicates that one of the four equations is a linear combination of the other three linearly independent equations. As a result, the linear system corresponding to the first augmented matrix is reduced to three equations in three unknowns. The linear system is stable and has a single solution.

2. The linear system that corresponds to the second augmented matrix comprises four equations and three unknowns. The presence of two zero rows indicates that two of the four equations are linear combinations of the other two linearly independent equations. As a result, the linear system corresponding to the second augmented matrix is reduced to two equations with three unknowns. The linear system is consistent and has an endless number of solutions.

3. The linear system that corresponds to the third augmented matrix comprises four equations and three unknowns. One zero row indicates that one of the four equations is a linear combination of the other three linearly independent equations. As a result, the linear system corresponding to the third augmented matrix is transformed into three equations with three unknowns. Because the augmented matrix includes a pivot in the last column, the linear system is inconsistent.

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The presence of such a row tell us about the consistency of the corresponding linear system is inconsistent

What is Linear System?

A linear system is a mathematical model of a system that is based on the usage of a linear operator in systems theory. Linear systems often have considerably simpler features and properties than nonlinear systems.

1. The pivot positions in the first augmented matrix are a11, a22, and a33. Because the last column lacks a pivot, the linear system corresponding to the first augmented matrix is consistent.

2. The pivot positions in the second augmented matrix are a11 and a22. Because the last column lacks a pivot, the linear system corresponding to the second augmented matrix is consistent.

3. The a11, a22, and a34 elements in the third augmented matrix serve as pivot points. Because the last column has a pivot, the linear system corresponding to the third augmented matrix is consistent.

b) 1. The linear system corresponding to the first augmented matrix comprises four equations and three unknowns. The presence of a zero row indicates that one of the four equations is a linear combination of the other three linearly independent equations. As a result, the linear system corresponding to the first augmented matrix is reduced to three equations in three unknowns. The linear system is stable and has a single solution.

2. The linear system that corresponds to the second augmented matrix comprises four equations and three unknowns. The presence of two zero rows indicates that two of the four equations are linear combinations of the other two linearly independent equations. As a result, the linear system corresponding to the second augmented matrix is reduced to two equations with three unknowns. The linear system is consistent and has an endless number of solutions.

3. The linear system that corresponds to the third augmented matrix comprises four equations and three unknowns. One zero row indicates that one of the four equations is a linear combination of the other three linearly independent equations. As a result, the linear system corresponding to the third augmented matrix is transformed into three equations with three unknowns. Because the augmented matrix includes a pivot in the last column, the linear system is inconsistent.

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The required quadratic equation of h(x) is given as h(x) = (x + 1)² + 2. Option C is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The required function that shows the relationship shown in the table can be evaluated just by putting values in the function,
So by putting value in each function this values only satisfied in function,
h(x) = {x + 1}² + 2
As,
h(0) = 3
h(-1) = 2

Thus, the required quadratic equation of h(x) is given as h(x) = (x + 1)² + 2. Option C is correct.

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Answer:

There is only one solution because when you set the two y's to each other you only get one solution.

Step-by-step explanation:

y=x+5

y=-2x-1

x+5 = -2x-1

3x = -6

x = -2

Since we only get one value for x, there is only one solution. Also if you graph the two lines, you will see that there is only one intersection, which is the solution of this systems of equations

Pat travels much by automobile, and she keeps track of how frequently she fills it with gas. The 4 day average is 0.1263157895.

A minimum of four days is four or more; in this case, 4,5 or six. So             (17+6+1) / 190 = 0.1263157895 . 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.

The likelihood that something will happen is known as probability. The number of possible outcomes is divided by the total number of possible outcomes to determine probability. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, as well as as percentages with a range of 0% to 100%.

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A triangle can't have two right angles. If a triangle has two right angles, then the sum of its three angles will be more than the two right angles i.e. more than 180∘ which is impossible​.

A right-angled triangle is one that has three sides, “base” “hypotenuse” and “perpendicular” with the angle between the base and the perpendicular is 90°.

A right-angled triangle is one of the basic shapes in geometry and it forms the foundation for trigonometry.

A right triangle has one angle exactly equal to 90 degrees

The angles other than the right angle must be acute angles, i.e. less than 90 degrees

The side opposite to vertex of 90 degrees is called the hypotenuse of the right triangle and is the longest side of the triangle

A triangle can't have two right angles. If a triangle has two right angles, then the sum of its three angles will be more than the two right angles i.e. more than 180∘ which is impossible​.

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The equation ㏑ 5 + 4 ㏑ x = 2 ㏑5 is equivalent to 4 logx=log 5

Two or more expressions with an Equal sign is called as Equation.

Given equation is ㏑ 5 + 4 ㏑ x = 2 ㏑5

log 5+logx⁴= 2log5

logx⁴=2 log 5 -log5

logx⁴=log5

4 logx=log 5

Hence, the equation ㏑ 5 + 4 ㏑ x = 2 ㏑5 is equivalent to 4 logx=log 5

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The Area of the region bounded by the line "y = 3x - 6" , "y = -2x + 8" and line "x = 5" is 12.1 square units    .

the three lines are given as : "y = 3x - 6" , "y = -2x + 8" and line "x = 5" ;

(i) Solving the first two lines ,

we get ,

⇒ [tex]3x - 6 = -2x + 8[/tex] ;

⇒ 5x = 14 ;

⇒ x = 2.8 ;

putting it in y = 3x - 6 , we get , y = 2.4 ;  

the point is (2.8,2.4) ....equation(1)

(ii) Solving the first and third equation ,

we get ; x = 5 and

⇒ [tex]y = 3 \times 5 - 6[/tex]

⇒ y = 9 ;

So , the point becomes (5,9) ;.....equation(2)

(iii) Solving the second and third equation ,

we get ; x = 5 and

⇒ [tex]y = -2 \times 5 + 8[/tex]

⇒ [tex]y = -2[/tex] ;

So , the point becomes (5,-2) ;....equation(3) ;

From equation (1) , (2) and (3) , we get that the coordinates of the intersection of these three lines forms a triangle ,

the height of the triangle can be calculated as : 5 - 2.8 = 2.2 units ,

The area of triangle is = [tex]\frac{1}{2} \times base \times height[/tex] ;

substituting the values ,

we get ;

Area = [tex]\frac{1}{2} \times 11\times 2.2[/tex] = 12.1 square Units .

Therefore , the required area of the triangle is 12.1 square units .

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The possible values of x ( in hours) will be less than four to achieve gains from trade .

Opportunity cost is what we have to sacrifice to achieve something. It is a very important concept in international trade, as it forms the basic criteria for opening a trade. For trade to take place there should be atleast comparative advantage in the production of a good by each country.

Produced item Germany France

Car 600 hours x hours

Wine 3 hours 4 hours

We have to calculate the value of "x"

Opportunity cost of a car for German worker

= 600/5 = 120 cases of wine

Opportunity cost of a wine for German worker

= 1/120 cars

Similarly, Opportunity cost of a car for Italian worker = 4/x cases of wine

Opportunity cost of wine for Italian worker

= x/4 car

A country has a comparative advantage when it can produce a good with a lower opportunity cost than another. To achieve the gains from trade, when the opportunity cost of a car for Italian worker is greater than german worker

4/x > 120 => x < 4/120 = 1/30 .

or in case of wine, x/4 < 1/120

=> x < 4/120 = 1/30

So, possible value of x is less than 4.

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The scale factor of the dilation is the square root of 17.

A dilation is a transformation in geometry that changes the size of a figure while preserving its shape. In other words, a dilation stretches or shrinks a figure proportionally, but does not change its shape. The dilation is defined by a scale factor, which is the ratio of the length of the image to the length of the original figure. The scale factor can be greater than 1, which means the dilation is an enlargement, or less than 1, which means the dilation is a reduction. The center of dilation is a fixed point, which is used to determine the scale factor and direction of the dilation. Dilations play an important role in many areas of mathematics, including coordinate geometry and metric spaces.

The scale factor of the dilation can be found by comparing the equations of the original line and the image line. The slope of the original line is 1/4, and the slope of the image line is also 1/4. Since the slope is unchanged, the dilation did not affect the slope, and therefore the scale factor is 1 in the x-direction.

To find the scale factor in the y-direction, we can compare the y-intercepts of the original and image lines. The y-intercept of the original line is -1, and the y-intercept of the image line is -5. The difference between the y-intercepts of the original and image lines is 4, which is the change in the y-coordinate of the image relative to the original.

Therefore, the scale factor in the y-direction is 4. Since the scale factor in the x-direction is 1, the overall scale factor is the square root of (1^2 + 4^2) = the square root of 17.

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The three basic inverse trigonometric functions are arcsine (or inverse sine), arccosine (or inverse cosine), and arctangent (or inverse tangent).

Inverse trigonometric functions are the reverse of the trigonometric functions. They are used to solve problems involving angles or lengths in a right triangle. The three basic inverse trigonometric functions are arcsine (or inverse sine), arccosine (or inverse cosine), and arctangent (or inverse tangent). The arcsine of an angle is equal to the sine of its inverse angle; likewise, the arccosine of an angle is equal to the cosine of its inverse angle, and the arctangent of an angle is equal to the tangent of its inverse angle.

The three basic inverse trigonometric functions are arcsine (or inverse sine), arccosine (or inverse cosine), and arctangent (or inverse tangent).

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There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, cosecant, tangent and cotangent.

By using a right-angled triangle as a reference, the trigonometric functions and identities are derived:

sin θ = Opposite Side/Hypotenuse

cos θ = Adjacent Side/Hypotenuse

tan θ = Opposite Side/Adjacent Side

sec θ = Hypotenuse/Adjacent Side

cosec θ = Hypotenuse/Opposite Side

cot θ = Adjacent Side/Opposite Side

Trigonometric Identities are formulas that involve Trigonometric functions.

These identities are true for all values of the variables.

Trigonometric Ratio is known for the relationship between the measurement of the angles and the length of the sides of the right triangle.

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The exact number of triangles is found if the side opposing the given angle is bigger than the other side.

The complete question is,

How can a triangle's solutions be determined—one, two, or none?

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The 30-60-90 triangle is a special type of right triangle, where the three angles measure 30°, 60°, and 90°.

The hypotenuse of the triangle is always twice the length of the shortest side, or the side opposite the 30° angle. The longest side of the triangle, or the side opposite the 90° angle, is always equal to the sum of the other two sides.

The angle opposite of the hypotenuse is the 90° angle. To calculate this we can use the Pythagorean Theorem and the ratios of sides in a 30-60-90 triangle to solve for the length of the side opposite the 90° angle.

The Pythagorean Theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, for a 30-60-90 triangle, we have the equation: a2 + b2 = c2

Since the hypotenuse is c, the side opposite the 90° angle is a, and the side opposite the 30° angle is b, we can rearrange the equation to solve for a:

a = √(c2 - b2)

Since the hypotenuse is twice the length

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We have the table as,

a. The slope is 20.-True

b. The point (0, 500) is on the line.-False

c. The line starts downward from left to right. -False

d. The slope is -200.-False

e. The y-intercept is 50.-True

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b).   It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.

Here the given equation is 10y-200x=500

a) Now rewrite the equation into slope intercept form then,

=> 10y-200x=500

=> 10y=200x+500

=> y = 20x+50.

We know that slope intercept form of the equation is y=mx+b. Where m is slope, Then slope of the given equation is 20.

b)Now put (x,y)=(0,500) in 10y-200x=500 then

=> 10×500-200×0=500

=> 5000≠500

Then the point (0,500) is not on the line.

c)Comparing with y = mx + d, we get,

Slope, m = 20 (Positive which implies the line starts upward from left to right)

d) The equation y=20x+50 ,y-intercept, d = 50 (That means the line passes through the point (0, 50)

e) y intercept is 50.

Hence the correct answer  is

a. The slope is 20.-True

b. The point (0, 500) is on the line.-False

c. The line starts downward from left to right. -False

d. The slope is -200.-False

e. The y-intercept is 50.-True

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The percentage of winners driving a chevrolet won with an average speed of at least 140 miles per hour is 81.25%

Percentage represent a fraction of a hundred.

To convert a fraction into percent, first, find the equivalent fraction with 100 as its denominator.

Example:

3/5 = 60/100 = 60%

We can also convert it into percent by multiplying it by 100%

3/5 = 3/5 x 100% = 60%

In the given problem, the total number of chevrolet won is 16.  Three of then have average speed less than 140 miles per hour.

Therefore,

Number of chevrolet with an average speed ≥ 140 mph = 16 - 3 = 13

Its percentage = 13/16 x 100 % = 81.25%

The table in your question is missing, most likely it was like in the attached picture.

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Answer:

SQ=115/4 =28.75

Step-by-step explanation:

108/27 = 115/SQ

108*SQ=27*115

108*SQ=3105

SQ=3105/108

SQ=115/4 =28.75

The range best describes how much these bowling scores varied.

What is the median of a data set ?

The median of a data set is the value that falls in the middle, indicating that 50% of the data points have values that are lower or equal to the median and 50% of the data points have values that are higher or equal to the median. When working with a small data collection, you must first count the number of data points (n) and organize them in ascending order.

The difference between the highest and lowest values for a given data collection is the range in statistics. As an illustration, if the data set contains 2, 5, 8, 10, 3, the range will be 10 - 2 = 8. So, another way to describe range is as the difference between the highest and lowest observation.

Given data set:

112, 123, 136, 145, 159

Range = 159 - 112 = 47

The range best describes how much these bowling scores varied.

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The machine is working correctly and filling cans with a mean of 128 ounces.

The Central Limit Theorem states that the distribution of the sample means will be approximately normal, regardless of the underlying distribution of the population, as long as the sample size is large enough.

With a random sample of 40 cans, we can use the Central Limit Theorem to assume that the sample mean of paint cans is approximately normally distributed with a mean of 128 ounces and a standard deviation of 0.2/[tex]\sqrt{40}[/tex].

We can then use this information to perform a hypothesis test to determine if the sample mean of 127.9 ounces is significantly different from the population mean of 128 ounces.

The null hypothesis is that the machine is working correctly and filling cans with a mean of 128 ounces, and the alternative hypothesis is that the machine is not working correctly and filling cans with a mean different from 128 ounces.

We can use a significance level of 0.05 for this test and calculate the z-score using the formula (sample mean - population mean)/(standard deviation of sample mean).

If the calculated z-score is greater than the critical value of z (from a standard normal table) at the significance level 0.05, we reject the null hypothesis and conclude that the machine is not working correctly and filling cans with a mean different from 128 ounces.

However, based on the sample mean of 127.9 and the population mean of 128, we can see that the sample mean is 0.1 ounce below the population mean which is not a significant difference. Therefore, we fail to reject the null hypothesis and conclude that the machine is working correctly and filling cans with a mean of 128 ounces.

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The required fraction of the first 100 pizzas were not pepperoni, cheese, or sausage are 77/100, 7/10, 83/100 respectively.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

23/100 were pepperoni,

fraction of the first 100 pizzas were not pepperoni

1 - 23/100

= 77/100

And

3/10 were cheese.

fraction of the first 100 pizzas were not cheese.

1 - 3/10

= 7/10

Another 17/100 were sausage.

fraction of the first 100 pizzas were not sausage.

1 - 17/100

83/100

Thus,required fraction of the first 100 pizzas were not pepperoni, cheese, or sausage are 77/100, 7/10, 83/100 respectively.

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The length of AC is 32. The measurement of ∠EBA = 57°.

What is a diagonal?

The diagonal is the line that runs through the center of the figure from one corner of the square or rectangle to the opposite corner. Any square with two diagonals that are the same length.

Given that AE = 4x+8 and BE=5x+6, ∠EBA=57°.

The diagonals of a rectangle equal and bisect each other.

Therefore,

AE = BE

4x+8 = 5x+6

5x -4x = 8 -6

x = 2

Putting x=2 in AC = 2AE :

AC = 2[4×2+8]

AC = 32

The diagonals of the rectangle bisect each angle.

The diagonal is a bisector to the rectangle.

∠EBA =∠ECB = 57°

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The most calories are expended per hour while running. Swimming, walking, and stationary bicycling are also great possibilities. HIIT workouts are excellent for calorie burning as well.

When it comes to calorie burn per hour, running comes out on top. Other great options include stationary cycling, walking, and swimming. Calorie burning is also excellent with HIIT exercises.

Circulatory endurance refers to your body's capacity to maintain itself throughout activities like running, jogging, swimming, cycling, and anything else that requires your cardiovascular system (lungs, heart, and blood vessels) to exert itself for an extended length of time.

Regular exercise can help kids and teenagers lose weight, develop strong bones and muscles, enhance cardiorespiratory fitness, lessen the symptoms of anxiety and depression, and lower their chance of contracting diseases like heart disease.

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The statement is true about the given equation 3(2-k)= -3k+2 as, follows:

"The equation has no solution".

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question, as follows:

3(2 - k)= -3k + 2

Apply the distributive property of multiplication,

3 × 2 - 3 × k = -3k + 2

6 - 3k = -3k + 2

6 - 2 = 3k - 3k

4 = 0

This is not true, so the equation has no solution.

Hence, the correct answer would be an option (A).

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BOTH the triangles share the side [tex]\overline {\text{AC}}[/tex], EQUAL pairs of congruent side. The given congruent angles are included angles, so ΔABC is CONGRUENT to ΔCDA by SAS Congruency rule.

Three corresponding parts must be equal in order to demonstrate the congruence of two triangles.

The first two postulates—Side-Angle-Side (SAS) and Side-Side-Side (SSS)—concentrate primarily on the side aspects, whereas the following lesson discusses two other postulates that do the opposite. The Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) postulates describe these relationships.

The two triangles are congruent if we can prove that two sides and the included angle of one triangle are congruent with two sides and the included angle of another triangle.

The Side Angle Side Postulate, or SAS, is the theory behind this. The Side-Angle-Side Postulate also allows us to demonstrate that triangle ABC and triangle EDC are congruent.

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The probability that a randomly chosen family with two or more children has children of the same gender is 1/2

To find the probability that a randomly chosen family with two or more children has children of the same gender, we can use the following information:

The probability of having a boy is 1/2 and the probability of having a girl is 1/2

The number of children is 2 or more

The sample space is all possible families with two or more children.

We can use the formula of conditional probability:

P(A|B) = P(A and B) / P(B)

Where A is the event of having children of the same gender, and B is the event of having two or more children.

We can use the formula of conditional probability to find the probability of having children of the same gender given that they have two or more children.

P(A and B) = P(A) * P(B|A)

Where P(A) is the probability of having children of the same gender, which is 1/2.

P(B|A) is the probability of having two or more children given that they have children of the same gender, which can be found using the formula of conditional probability as well.

P(B|A) = 1 - P(not B|A)

Where P(not B|A) is the probability of having less than two children given that they have children of the same gender.

Given that the family has children of the same gender, the probability of having less than two children is 0, because if the family has children of the same gender, it implies that the family has at least two children.

So, P(B|A) = 1- 0 = 1

Now we can substitute these values to the first equation:

P(A|B) = P(A) * P(B|A) / P(B) = (1/2) * 1 / P(B)

The only thing left to find is P(B) which is the probability of having two or more children. We don't have the exact number, but we know that the number of children is 2 or more, so P(B) is greater than 0.

We can say that P(A and B) = P(A) * P(B|A) = (1/2) * 1 = 1/2

Thus, the probability that a randomly chosen family with two or more children has children of the same gender is 1/2.

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No equation can represent a linear combination of the system since it has no solution. This means that the equations are not linearly independent, and therefore the system cannot be represented by a linear combination.

A system of equations is said to be linearly dependent if one equation can be derived from the other. In this case, the second equation is simply a multiple of the first equation, meaning that it is not linearly independent. This means that the system cannot be represented by a linear combination, since the equations are not linearly independent.  

A linear combination is defined as a combination of two or more linear equations, where each equation contains a different variable. The coefficients of the variables in each equation must be different in order for the linear combination to exist. Since the system of equations does not have any coefficients that are different from each other, the system does not have a linear combination.  

Therefore, no equation can represent a linear combination of the system since the system has no solution.

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The system of equations below has no solution. which equation could represent a linear combination of the system?

 2x + 3y = 4

4x + 6y = 8

The general way to write factored form of the given quadratic equation is given by f (x) = A ( x - u ) ( x - r ).

As given in the question,

Let us consider the standard quadratic equation as :

ax² + bx + c = 0

To represent general way of factored form take example :

Example : 2x² + 14x + 24 = 0

Split the middle term :

4x + 3x = 7x

(4x)(3x) = 12x²

⇒2(x² + 7x + 12 )= 0

⇒ x² + 4x + 3x + 12 = 0

⇒x( x + 4 ) + 3 ( x+ 4 ) = 0

⇒ ( x + 3 )(x + 4 ) = 0

Factored form of the quadratic equation is : f (x) = A ( x - u ) ( x - r ).

Therefore, in standard way the factored form of the quadratic equation is equal to f (x) = A ( x - u ) ( x - r ).

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The triangle with sides 12 cm 16 cm and 18 cm is not a right triangle.

What is right traingle ?

A right triangle consists of two legs and a hypotenuse. The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle. There are a couple of special types of right triangles, like the 45°-45° right triangles and the 30°-60° right triangle.

Let sides of triangles are a , b , c,

Have given ,

a = 12 , b = 16 and c = 18

We know that condition for a right triangle ,

[tex]a^{2} + b^{2} = c^{2}[/tex]

∵ [tex]12^{2} + 16^{2} = 18^{2}[/tex]

144 + 256 = 324

400 ≠  324 , that's equation is not right ,

So , The triangle with sides 12 cm 16 cm and 18 cm is not a right triangle.

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The area of the parallelogram, that have a base length of 22 and one-half feet, and a height of 19 and one-fourth feet is 433 and one-eight square feet. The correct option is therefore;

Four hundred thirty-three and one-eighth ft²

A parallelogram is a quadrilateral that has a pair of opposite sides that are parallel. The area of a parallelogram, A, of base length, b, and height, h can be presented as ; A = b·h

The base length of the parallelogram = 22 1/2 feet

Height of the parallelogram = 19 1/4 feet

Area of a parallelogram = Base length × Height

Therefore; The area of the parallelogram = 22 1/2 × 19 1/4 = 433 1/8

The area of the parallelogram = 433 1/8 square feet

The third option is correct;

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Answer:

[tex]x=\sqrt{31}[/tex]

Step-by-step explanation:

We can use the Pythagorean theorem to evaluate x.

The formula for the Pythagorean theorem is

[tex]a^2+b^2=c^2[/tex]

Lets look at the bottom triangle.

We are given both legs of the triangle. We can evaluate the hypotenuse.

[tex]3^2+3^2=c^2\\9+9=c^2\\18=c^2\\\sqrt{18} =c\\3\sqrt{2} =c[/tex]

Lets look at the top triangle.

Notice the hypotenuse in the bottom triangle is the same length as one of the legs in the triangle on the top.

We are given 1 leg and the hypotenuse. We can evaluate the missing leg.

[tex]x^2+(3\sqrt{2})^2=7^2\\x^2+3^2\sqrt{2} ^2=7^2\\x^2+9\sqrt{2} ^2=7^2\\x^2*+9*2=7^2\\x^2+18=7^2\\x^2+18=49\\x^2=49-18\\x^2=31\\x=\sqrt{31}[/tex]

21.5°C was the temperature of Louisiana in the morning. This can be solved using the concept of equations.

The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.

Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.

Let, the temperatures in Louisiana = x

the temperatures in North Dakota = y

y = x  - 10

or, x - y = 10 ....... (i)

By the afternoon, the temperature in Louisiana increased by 2°C. So, temperature of Louisiana in afternoon: (x + 2)

(x +2) + y = 35

or, x + y = 33 ........ (ii)

now, solving this two equations we get

2x = 43

or, x = 21.5°C

Thus, 21.5°C was the temperature of Louisiana in the morning.

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