The length of a rectangle is 3 cm longer than its width.
If the perimeter of the rectangle is 50 cm, find its length and width.

The probability that the mean of a sample of 78 computers would differ from the population mean by less than 0.4 months is:

P (μ-0.4 <x<μ +0.4) = P (-0.39<x<0.39) = 0.3035

By simply dividing the favourable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favourable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Moreover, the proportion of positive outcomes cannot be negative.

Here we have,

μ = 83,0 = 9, n = 78

Since sample size is large so we can assume normal distribution using CLT.

The z-score for x= μ-0.4 is

z=(μ-0.4-μ)/o/√n

=-0.4/9/√78

= -0.39

The z-score for x= μ +0.4 is

z=(μ+0.4-μ)/σ/√n

= 0.4/9/√78

= 0.39

The probability that the mean of a sample of 78 computers would differ from the population mean by less than 0.4 months is:

P (μ-0.4 <x<μ +0.4) = P (-0.39<x<0.39) = 0.3035.

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The correct answer is A′(−3, −2), B′(5, −2), C′(1, 2). The coordinates of the original triangle ABC are (1, -2), (9, -2), and (5, 2). Therefore, the coordinates of the image are A′(−3, −2), B′(5, −2), C′(1, 2).

Coordinates are used to describe a point in space or on a map. They are usually written as two numbers, which represent the position of the point on an x-axis and a y-axis. Coordinates can be used in a variety of ways, such as to describe the location of a specific object or to identify the boundaries of an area.

Triangle ABC is an example of a transformation in which the shape is shifted without changing its size or orientation. When a shape is translated, it is moved from one place to another without changing its size or orientation. In this case, the triangle is being translated 4 units down.

To calculate the new coordinates of the triangle, we need to subtract 4 from the y-coordinate of each of the vertices. The original coordinates of the triangle are (1, −2), (9, −2), and (5, 2). After subtracting 4 from each of the y-coordinates, the new coordinates of the triangle are (1, −6), (9, −6), and (5, −2). This means that the new coordinates of the triangle are A′(−3, −2), B′(5, −2), and C′(1, 2).

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The cοrrect answer is A′(−3, −2), B′(5, −2), C′(1, 2). The cοοrdinates οf the οriginal triangle ABC are (1, -2), (9, -2), and (5, 2). Therefοre, the cοοrdinates οf the image are A′(−3, −2), B′(5, −2), C′(1, 2).

Cοοrdinates are used tο describe a pοint in space οr οn a map. They are usually written as twο numbers, which represent the pοsitiοn οf the pοint οn an x-axis and a y-axis. Cοοrdinates can be used in a variety οf ways, such as tο describe the lοcatiοn οf a specific οbject οr tο identify the bοundaries οf an area.

Triangle ABC is an example οf a transfοrmatiοn in which the shape is shifted withοut changing its size οr οrientatiοn. When a shape is translated, it is mοved frοm οne place tο anοther withοut changing its size οr οrientatiοn. In this case, the triangle is being translated 4 units dοwn.

Tο calculate the new cοοrdinates οf the triangle, we need tο subtract 4 frοm the y-cοοrdinate οf each οf the vertices. The οriginal cοοrdinates οf the triangle are (1, −2), (9, −2), and (5, 2). After subtracting 4 frοm each οf the y-cοοrdinates, the new cοοrdinates οf the triangle are (1, −6), (9, −6), and (5, −2). This means that the new cοοrdinates οf the triangle are A′(−3, −2), B′(5, −2), and C′(1, 2).

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Using the graphs, Olivia is correct if she used one of those two approaches. Michael and Angelica both use the wrong strategies.

An organised-representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.

The development of a research question is followed by the ongoing observational collection of data. The data is then organised, distilled, categorises, and visually represented.

Information and data have different purposes: Data is an unadorned truth; information is the meaning that can be inferred from data.

Challenge 1

Olivia may have, for example, translated 10 units to the right after reflecting over the x axis.

Let's use point C to apply this series of steps.

C = (-2,-4) (-2,-4)

After reversing the x axis, C' becomes (-2,4); the y coordinate changes sign, and C" becomes (8,4) after moving to the right by 10 units. The x coordinate is then increased by 10.

The graphic shows that point C (-2, -4) shifts to C"(8,4). The other four points I'll let you investigate.

Olivia may have also tried shifting 10 units to the right before reflecting across the x axis. The sequence here is irrelevant. Order does important, though, for several other combinations of transformations.

Challenge 2

The point (x,y) will become after reflection across the y axis (-x,y). Here, the sign is reversed, and only the x coordinate changes. The y coordinate remains constant.

With the y axis reflection, a point like C (-2, -4) becomes C'(2, -4). By moving up 8 units, we get at C"(2,4) by adding 8 to the y coordinate, but this is not what the graphic displays. Thus, Angelica's approach is flawed.

The last four points should also contain other contradictions, as well.

Challenge 3

Even Michael's approach is flawed. Instead of using an x axis reflection, he completely relies on translations to change ABCDE into A"B"C"D"E".

Quick inspection suggests that Michael might be right. Yet, if you examine much more closely, you'll notice that things aren't exactly in line.

This time, we'll choose point D rather than point C.

D can be found at (-6, -2). To reach D' if we move up 8 units, we must add 8 to the y coordinate (-6,6). Then, to move 10 units to the right, add 10 to the x coordinate. And brings us to D" (4,6).

The diagram, however, reveals that D" is actually at (4,2)

Let you examine the other points, please. The only points that should go to the right places are C and E; the remaining points should not. Once more, Michael's failure to apply an x axis reflection is to blame. His A"B"C"D"E" figure is reversed from how it should have been.

To sum up, the strategies mentioned in problem 1 are the proper ones to use in order to make ABCDE go to A"B"C"D"E. Olivia is correct if she used one of those two approaches. Michael and Angelica both use the wrong strategies.

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i. The down payment is $11,000    

ii. The mortgage (loan) was for $99,000.      

iii. The current monthly payment is $471.15.  

iv. Total interest is $169,334.00.

The down payment is the initial payment made when purchasing a home, typically expressed as a percentage of the total purchase price.

In the given problem, the mortgage (loan) is the amount of money borrowed to purchase the home, which is equal to the purchase price of the home minus the down payment.

Here we have

Problem 1:

10 years ago you bought a home for $110,000, paying 10% as a down payment, and financing the rest at 9% interest for 30 years.  

The down payment was 10% of the purchase price of the home

=> Down payment = 10% of $110,000

= [10/100] × $110,000 = $11,000

∴ You will be paid $11,000 as your down payment.

Amount borrowed = the purchase price of the home - Down payment

=> Amount borrowed = $110,000 - $11,000 = $99,000

∴ Your mortgage (loan) was for $99,000.    

To calculate the current monthly payment, use the formula for the monthly payment of a fixed-rate mortgage:

P = (A / D) x (r / 12)

Where:

A = amount borrowed

D = discount factor, i.e calculated as (1 - (1 + r / 12)⁻ⁿ)  

r = monthly interest rate,      

n = total number of payments,  

=> P = ($99,000 /124.4) x 0.0075 = $471.15  

∴ The current monthly payment is $471.15.  

The formula for total interest = (P x n) - A  

=> Total interest = ($471.15 x 360) - $99,000 = $169,334.00              

∴ You will pay a total of $169,334.00 in interest over the life of the loan.    

Therefore,

i. The down payment is $11,000    

ii. The mortgage (loan) was for $99,000.      

iii. The current monthly payment is $471.15.  

iv. Total interest is $169,334.00.      

Problem 2

This year, you check your loan balance. You see that you still have $88,536 left to pay on your loan. Your house is now valued at $150,000.

i. Amount paid off = Original loan amount - Current loan balance

Original loan amount = $99,000

Current loan balance = $88,536

Amount paid off = $99,000 - $88,536

Amount paid off = $10,464

∴ you have paid off $10,464 of the loan.

ii. Total paid = Monthly payment x Number of payments

P = ($99,000 / 207.483) x 0.0075

P ≈ $471.15

The number of payments is the number of months since you took out the loan. Since the loan was taken out 10 years ago, or 120 months ago, the number of payments is 120.

Total paid = $471.15 x 120

Total paid = $56,538

∴ you have paid $56,538 to the loan company so far.

iii. To determine how much interest you have paid so far, we need to subtract the amount paid off from the total amount paid:

Interest paid = Total paid - Amount paid off

Interest paid = $56,538 - $10,464

Interest paid = $46,074

∴ you have paid $46,074 in interest so far.

iv. Equity = Current value of the home - Current loan balance

Equity = $150,000 - $88,536

Equity = $61,464

∴ you have $61,464 of equity in your home.

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The total number of cards sold for Mother's Day is 290 cards.

What is the proportions?

Proportion is a mathematical concept that expresses the equality of two ratios. Two ratios are said to be proportional if they have the same relative size or relationship.

Let x be the total number of cards sold for Mother's Day. We know that one salesman sold 29 cards, which is 10% of the total number of cards sold. Using this information, we can set up the following proportion:

(10/100) * x = 29

Simplifying, we get:

x = 290

Hence, the total number of cards sold for Mother's Day is 290 cards.

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It is true that graphs exponential functions either increase or decrease for all x-values.

An exponential function is defined as follows:

y = ab^x.

In which:

An exponential function can either increase or decrease depending on the values of a and b, however the behavior is uniform, meaning that it is true that graphs exponential functions either increase or decrease for all x-values.

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The cost of apples when the number of apples bought is n can be found using the function:

    C(n) = 0.9n

What is a function?

A mathematical statement or rule that establishes the link between an independent variable and a dependent variable is called a function. Relationships called functions provide an output for each input. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Often, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.

Assuming the question is the one given below.

Given a function C which gives the cost of buying the n apples in dollars.

The first expression given is:

1) C(5) = 4.50

The input of the function is 5 and the output is 4.50.

This means that when the number of apples is 5 the total cost is $4.50.

Let us assume the general equation of the function as below:

C(n) = kn

When n = 5

C(5) = 5k = 4.50

k = 4.50/5 = 0.9

Hence the function is C(n) = 0.9n

2) We found the function as C(n) = 0.9n

 C(2) means the cost when the number of apples is 2.

C(2) = 0.9 * 2 = $1.8

Therefore the cost of apples when the number of apples bought is n can be found using the function:

    C(n) = 0.9n

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None of the statements (1) to (6) are true about the equation [tex]x^2-6x+2=0[/tex].

Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd polynomial formula in a variable. a 0. It has at least 1 solution since it is a 2nd polynomial equation, which is guaranteed by the algebraic theorem. The solution might be simple or difficult.

None of the statements (1) to (6) are true about the equation. [tex]x^2-6x+2=0[/tex].

Reason why:

(1) The coefficient of the [tex]x^2[/tex] term is positive, so the graph of the quadratic equation is a parabola that opens upward. Therefore, it does not have a minimum value, but instead has a minimum point.

(2) The coordinates of the minimum point can be found using the formula x = -b/2a, which gives x = 6/2 = 3. Substituting x = 3 into the equation gives y = 2, so the minimum point is (3, 2).

(3) The point (7,-3) is not on the graph of the equation.

(4) The solutions to the equation are given by the quadratic formula x = [tex][6\± \sqrt{(6^2 - 4(1)(2))]}/2 = [6\± \sqrt{(28)]}/2 = 3\± \sqrt{7}[/tex]. So, statement (4) is partially correct, but the value of -3 is incorrect.

(5) Statement (5) is correct, as the solutions to the equation are x = [tex]3\±\sqrt7}[/tex].

(6) The graph of the quadratic equation has a minimum value, not a maximum value.

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Complete question is: Which of the following statements are true about the equation below?

x^2-6x+2=0

( 1 ) The graph of the quadratic equation has a minimum value.

( 2 ) The extreme value is at the point (3,-7).

( 3 ) The extreme value is at the point (7,-3).

( 4 ) The solutions are x = -3 + or - the square root of 7 .

( 5 ) The solutions arex = 3 + or - the square root of 7.

( 6 ) The graph of the quadratic equation has a maximum value.

By answering the above question, we may state that Therefore, all possible values of x that satisfy the inequality [tex]x^3[/tex] - 8 ≥ 1 are x ≥ 2.08.

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Hence, inequity results from imbalance. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and inequality are not the same. Use the not equal symbol most frequently when two values are not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two sides until just the variables are left, many straightforward inequalities may be solved. Nonetheless, a variety of factors support inequality: Both sides' negative values are split or added. Exchange the left and the right.

[tex]x^3[/tex] - 8 ≥ 1

[tex]x^3[/tex] ≥ 9

Taking the cube root of both sides, we get:

x ≥ ∛9

Since ∛9 ≈ 2.08, the solution to the inequality is:

x ≥ 2.08

Therefore, all possible values of x that satisfy the inequality [tex]x^3[/tex] - 8 ≥ 1 are x ≥ 2.08.

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Answer: 48

Step-by-step explanation: 9p p=4 9*4=36 +18 = 48

The exponential growth equation is P ( t ) = 332 ( 1.0059 )^t , where t is the number of years and P ( t ) is the population after 2020

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the initial population be represented as x₀

Now , the value of x₀ = 332 million

And , the exponential growth rate r = 0.59 %

where the population of the U.S. at time/ years after 2020 is of the form equation P( t ) = aekt

On simplifying , we get

The population of the U.S. at a time P ( t ) = 332 ( 1 + 0.59% )^t

Now , the value of P ( t ) is

The population of the U.S. at a time P ( t ) = 332 ( 1 + 0.0059 )^t

The population of the U.S. at a time P ( t ) = 332 ( 1.0059 )^t

where the growth factor k = 1.0059

Hence , the exponential growth equation is P ( t ) = 332 ( 1.0059 )^t

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The normal distribution is N(151, 7), the z-score for verbal and quantitative reasoning are 1.29 and 0.52 respectively.

(a) The shorthand for the normal distribution of the Verbal Reasoning section is N(151, 7), where 151 is the mean score and 7 is the standard deviation. The shorthand for the normal distribution of the Quantitative Reasoning section is N(153, 7.67), where 153 is the mean score and 7.67 is the standard deviation.

(b) Sophia’s Z-score on the Verbal Reasoning section is (160-151)/7 = 1.29. Her Z-score on the Quantitative Reasoning section is (157-153)/7.67 = 0.52.

(c) The Z-scores represent how many standard deviations above or below the mean Sophia’s scores are. A Z-score of 1.29 on the Verbal Reasoning section means Sophia’s score is 1.29 standard deviations above the mean score of all test takers. A Z-score of 0.52 on the Quantitative Reasoning section means Sophia’s score is 0.52 standard deviations above the mean score of all test takers.

(d) Sophia did better on the Verbal Reasoning section because her Z-score is higher for that section.

(e) To find the percentile scores, we use the standard normal distribution table. Sophia’s percentile score on the Verbal Reasoning section is the percentage of test takers who scored lower than her. Using the Z-score of 1.29 and the table, we find that her percentile score is approximately 90.7%. Her percentile score on the Quantitative Reasoning section is the percentage of test takers who scored lower than her. Using the Z-score of 0.52 and the table, we find that her percentile score is approximately 69.4%.

(f) To find the percentage of test takers who did better than Sophia on each section, we can use the standard normal distribution table again. For the Verbal Reasoning section, we need to find the area to the right of Sophia’s Z-score of 1.29. Using the table, we find that this area is approximately 9.3%. Therefore, approximately 9.3% of test takers did better than Sophia on the Verbal Reasoning section. For the Quantitative Reasoning section, we need to find the area to the right of Sophia’s Z-score of 0.52. Using the table, we find that this area is approximately 30.4%. Therefore, approximately 30.4% of test takers did better than Sophia on the Quantitative Reasoning section.

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Answer:

Number 2 and number 1

Step-by-step explanation:

youre all good

Answer:its a

Step-by-step explanation:you did it wrong

One example of a quantity in the life sciences that is modeled by a function of time is the population size of a species.

This can be modeled using a differential equation, where the rate of change of the population size is proportional to the current population size.

If we knew the values of the derivative of this function (i.e., the first derivative), we would be able to make inferences about the growth or decline of the population.

A positive derivative value would indicate that the population is growing, while a negative derivative value would indicate that the population is declining. The magnitude of the derivative would also give us information about the rate of growth or decline of the population. If the derivative is large, the population is changing quickly, while a small derivative indicates slower change.

If we had information about the second derivative of the function (i.e., the rate of change of the derivative), we would be able to make further inferences about the behavior of the population.

A positive second derivative value would indicate that the population is accelerating in its growth, while a negative second derivative value would indicate that the population is decelerating in its growth. This information could be useful in predicting future trends in population size and in making decisions about conservation efforts or resource management.

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The measure of ∠M and ∠N = 76

An isosceles triangle is a triangle that has two sides of equal length and two equal angles opposite those sides.

Given:- ∠NLM = 28°

The given triangle is an isosceles triangle as sides LM and LN are equal.

Therefore ,∠LMN and ∠LNM will be equal.

Let us assume ∠M as x

Therefore,

∠LMN = ∠LNM = x

Sum of all angles of a triangle =180°

Therefore,

∠NLM + ∠LNM + ∠LMN = 180°

28 + x + x = 180

28 + 2x = 180

2x = 180 – 28

2x = 152

x = 152/2

x = 76

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The lateral limits of the function g(x) at x = 4 are given as follows:

[tex]\lim_{x \rightarrow 4^-} g(x) = -4, \lim_{x \rightarrow 4^+} g(x) = 2[/tex]

To obtain lateral limits, we need to take the limit of a function as it approaches a point from the left-hand side and the right-hand side separately.

If the two limits are equal, then this is the limit of the function, while if the lateral limits are different, then the limit of the function does not exist for the value of x.

On a coordinate plane, a curve starts at closed circle (4, negative 4), curves up to (3, negative 3), and curves down to (negative 1, negative 8), and then curves up through (negative 3, 4), hence the lateral limit to the left of x = 4, where x is less than 4, is given as follows:

[tex]\lim_{x \rightarrow 4^-} g(x) = -4[/tex]

A curve starts at open circle (4, 2) and curves up through (8, 5), hence the lateral limit to the right of x = 4, where x is greater than 4, is given as follows:

[tex]\lim_{x \rightarrow 4^+} g(x) = 2[/tex]

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In order to create a 28-pound blend that he can sell for $1.45 per pound, the grocer should combine approximately 17.73 pounds of the less costly coffee and 10.27 pounds of the more expensive coffee.

Let's designate the quantity of the less expensive coffee X and the more expensive coffee Y. Since we are aware that the grocer wishes to combine 28 pounds altogether, we can write:

x + y = 28

The total profit from selling the mixture would be: 28($1.45) = $40.60 because we also know that he intends to sell it for $1.45 per pound.

The costs and quantities of the two varieties of coffee can be used to create a new equation.

0.9x + 2.4y = $40.60

With two variables in each equation, we now have two equations that we can solve by substitution or elimination. Use of substitution

28 + y = x - 0.9x + 2.4y = 40.60

0.9x + 2.4(28 - x) = $40.60

0.9x + 67.2 - 2.4x = $40.60\s-1.5x = -$26.60\sx = 17.73

We can apply the first equation to determine y now that we know x: x + y = 28.

17.73 + y = 28 \sy = 10.27

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The height c of the flagpole c is 5.5 metres.

The triangles formed by the two flags are similar.  

Two triangles are said to be similar when they have two corresponding angles congruent and the sides proportional.

The distance between flag a is 12 metres.

The distance form the flag c to s is 10 metres.

The height of the flagpole a  is 12.1 metres.

Therefore, let's find the height of the pole c.

Hence, using proportion,

12.1 / c = 22 / 10

cross multiply

121 = 22c

divide both sides by 22

c = 121 / 22

c = 5.5

Therefore,

height of the flagpole c = 5.5 metres

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John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. $75 = $15p + A

What is the total of the cost?

Whole cost is the sum of all expenditures made to generate a certain level of production; when this total cost is divided by the amount produced, average or unit cost is discovered.

Let the number of people on John's family plan be represented by p.

According to the problem, the family plan cost is $68, and there is an additional cost of $15 for each person on the plan. Therefore, the total cost C of the plan with p people is:

C = $68 + $15p

We know that John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. Therefore, we can write:

$143 = C + A

where A represents any additional charges.

Substituting C into this equation, we get:

$143 = ($68 + $15p) + A

Simplifying, we can write:

$75 = $15p + A

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These figures have curved surfaces, not flat faces. A cylinder is similar to a prism, but its two bases are circles, not polygons. Also, the sides of a cylinder are curved, not flat. A cone has one circular base and a vertex that is not on the base.

When a cone and cylinder have the same height and radius the cone will fit inside the cylinder. The volume of the cone will be one-third that of the cylinder. If the radius or height are different, then there is no relationship between them.

The analysis of the distances and angles viewed by Felix are presented as follows;

2. The angle formed is a right angle

3. Please find the drawing of the scenario created with MS Word

4. The distance obtained using Pythagorean Theorem is about 438.53 miles

5. The distance the person travels is about 437.86 miles

6. The central angle Felix is viewing from his altitude is about 6.34°

The Pythagorean Theorem states that the square of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the legs of the right triangle.

2. The angle formed by a tangent to a spherical surface, such as the Earth's approximately spherical surface and the radius of the sphere is a right angle.

Therefore;

3. The possible elevation of Felix above the Earth's surface, obtained from a similar question is; 24.214 miles

Therefore;

The legs of the right triangle are the radius of the Earth and the distance from Felix's to the point on the horizon.

The hypotenuse sum of Felix's altitude and the radius of the Earth

Please find attached the drawing of the scenario created with MS Word

4. Pythagorean Theorem indicates that the distance from Felix to the image on the horizon, d, can be obtained as follows;

d = √((3,959 + 24.214)² - 3,959²) ≈ 438.53

The distance from Felix to the image on the horizon is about 438.53 miles

5. The distance the person has to travel can be found as follows;

The surface of the Earth is assumed to be flat

The distance to the horizon from Felix is about 438.53 miles

The distance, l, the person on the ground has to travel is therefore;

l = √(438.53² - 24.214²) ≈ 437.86

6. The central angle, θ, of the Earth that Felix is viewing, with an arc length of 437.86 miles can be found using the formula for finding the arc length of a sector of a circle as follows;

θ/360 × 2 × π × 3,959 ≈ 437.86

θ ≈ 437.86 × 360/(3,959 × 2 × π) ≈ 6.34°

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Answer:

Yes

Step-by-step explanation:

We just need to (0,6) in the equation to see if it gives a true answer or not!

y = -x + 6

6 = 0 + 6

6 = 6

So, (0,6) is a solution to the equation y = -x + 6

The limit of f(x) as x approaches -6 from the positive side is 6.

When x gets closer to 2 on the positive side, we can see that the function seems to be heading towards a value of -8. As a result, f(x) has a limit of -8 as x approaches 2 from the positive side.

The function seems to be heading towards a value of 6 when x approaches 2 from the negative side. Hence, when x gets closer to 2 from the negative side, the limit of f(x) is 6.

The function seems to be getting closer to a value of 6 when x approaches -6 from the positive side. Hence, as x gets closer to -6 on the positive side, the limit of f(x) is equal to 6.

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The third side of the triangle is 8  

Pythagoras' theorem is a fundamental principle in geometry that describes the relationship between the sides of a right triangle.

It states that: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Here we have

A right-angled triangle

From the figure

The sides of the triangle are 7 and √15  

As we know from Pythagoras' theorem

=> Hypotenuse² = side² + side²    

Substitute the above values in the condition

=> Hypotenuse² = (7)² + (√15)²    

=> Hypotenuse² = 49 + 15

=> Hypotenuse² = 64

=> Hypotenuse = 8  

Therefore,

The third side of the triangle is 8  

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Complete Question is given picture

The triangles are classified as:

4. Acute 5. Obtuse 6. Obtuse 7. Acute 8. Obtuse 9. Acute 10. Obtuse

To classify a triangle as right, obtuse, or acute, we need to apply the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

If the square of the hypotenuse is greater than the sum of the squares of the other two sides, then the triangle is obtuse. If the square of the hypotenuse is less than the sum of the squares of the other two sides, then the triangle is acute.

4. To check if this is a right triangle, we need to find if 9² is equal to 4² + 6², which is not true, so the triangle is acute.

5. To check if this is a right triangle, we need to find if 16² is equal to 10² + 12², which is not true, so the triangle is obtuse.

6. To check if this is a right triangle, we need to find if (8√6)² is equal to 8² + 16², which is not true, so the triangle is obtuse.

7. To check if this is a right triangle, we need to find if 29² is equal to 20² + 21², which is true, so the triangle is acute.

8. To check if this is a right triangle, we need to find if √73² is equal to 3² + 8², which is not true, so the triangle is obtuse.

9. To check if this is a right triangle, we need to find if 12² is equal to 8² + 10², which is true, so the triangle is acute.

10. To check if this is a right triangle, we need to find if (3√34)² is equal to 9² + 15², which is not true, so the triangle is obtuse.

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Answer:

Step-by-step explanation 0.4 0.8 5 7 10, 10