Solve the system of linear equations by substitution.

−x−8=−y
9y−12+3x=0

The solution is ( , )

Answer:

P ( X > 1800) = 0.1734

Step-by-step explanation:

Given:-

- The mean, u = 1497

- The standard deviation, s.d = 322

Find:-

P(X>1800)

Solution:-

- We will denote a random variable X that follows a normal distribution for the SAT scores in 2014 with parameters mean (u) and standard deviation (s.d) as follows:

                                  X ~ N ( 1497 , 322 )

- The following probability can be calculated by first computing the Z-score value:

                                 P ( X < x ) = P ( X < Z )

Where,

                                 Z = ( x - u ) / s.d

- P(X > 1800) have the corresponding Z-score value:

                                Z = ( 1800 - 1497 ) / 322

                                Z =  0.941

- Hence, using Z-table:

                               P ( X > 1800) = 1 - P ( Z < 0.9471 )

                               P ( X > 1800) = 1 - 0.8266

                               P ( X > 1800) = 0.1734

The probability that a randomly selected person scored above 1800 on the SAT is approximately 17.36%, after calculating the corresponding z-score and looking up the probability in the Standard Normal Distribution table.

To find P(X>1800), we first need to calculate the z-score for an SAT score of 1800. The z-score is computed as:

z = (X - μ) / σ

Where X is the SAT score, μ is the mean, and σ is the standard deviation. Given μ = 1497 and σ = 322, we have:

z = (1800 - 1497) / 322 = 303 / 322 ≈ 0.941

Once we have the z-score, we can use the Standard Normal Distribution table to find P(Z > 0.941). We find that P(Z > 0.941) ≈ 0.1736. Thus, the probability that a randomly selected college-bound senior has an SAT score above 1800 is approximately 0.1736 or 17.36%.

The sample in the study refers to the 12 children in Mrs. Smith's kindergarten class. A sample is a subset of people selected from a larger group for study purposes. In this research, the data being analyzed only pertains to these selected individuals.

In this study, the sample chosen is the group of 12 children in Mrs. Smith's kindergarten class. This is because the data being collected and scrutinized is related to these particular individuals. In this context, 'sample' refers to the subset of people chosen from a larger group (the population) for research or study purposes. It is the set of individuals on which the study or experiment is conducted. In this case, the larger population could be considered all children in kindergarten, but the sample for the study is specifically the 12 children in Mrs. Smith's class, as the study only includes their sleep patterns.

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The jar has 6+5=11 marbles.

We have to find the probability of the following event:

1.We pick a marble from a jar that has 11 marbles in total, 5 of them are red

2.We pick a marble from a jar that has now 10 marbles in total, 4 of them are red (because in the previous step we picked a red marble and did not put it back in the jar)

The probability of the first event is:

[tex]P_1=\frac{5}{11}[/tex]

The probability of the second event is:

[tex]P_2=\frac{4}{10}=\frac{2}{5}[/tex]

The probability of the both events to happen is:

[tex]P=P_1\cdot P_2=\frac{5}{11}\cdot \frac{2}{5}=\frac{2}{11}=0.1818[/tex]

Answer: 3 ounces of cereals was left in the box.

Step-by-step explanation:

Dan and Carl share a 18-ounce box of cereal. By the end of the week, Dan has eaten 1/6 of the box. This means that the amount of cereals that Dan ate is

1/6 × 18 = 3 ounces of cereals

Also, by the end of the week, Carl has eaten 2/3 of the box of cereal. This means that the amount of cereals that Carl ate is

2/3 × 18 = 12 ounces of cereals

The total amount of cereals that they ate is 12 + 3 = 15 ounces

Therefore, the amount of cereals left in the box is

18 - 15 = 3 ounces

Answer:

Step-by-step explanation:

The total number of permutations of boys and girls on the team are:

¹⁶P₅*¹³P₄

1.

Bob will be one of the fixed boys to be picked. Hence, actually 4 boys are to be picked from 15. The permutations of girls being picked remains the same.

Probability = Permutations with Bob as one of the boys / Total permutations

Probability = (¹⁵P₄*¹³P₄) / (¹⁶P₅*¹³P₄) = ¹⁵P₄ / ¹⁶P₅

Probability = [tex]\frac{15!}{(15-4)!}/\frac{16!}{(16-5)!}[/tex] = 15! / 16! = 1/16

2.

Now, Bob is one of the fixed boys and Jane is one of the fixed girls. Hence, actually 4 boys are to be picked from 15 and 3 girls are to be picked from 12.

Probability = Permutations with bob as one of the boys and jane as one of the girls / Total permutations

Probability = (¹⁵P₄*¹²P₃) / (¹⁶P₅*¹³P₄) = (1/16)*(1/13) = 1/208

3.

Now, the probability that at least Jane or Bob will be picked has been asked. This probability is a combination of three probabilities:

Probability = (Probability that only Bob will be picked) + (Probability that only Jane will be picked) + (Probability that both will be picked)

Probability = 1/16 + 1/13 + 1/208 = 0.123

4.

Total teams possible = ¹⁶P₅*¹³P₄ = 8994585600 teams are possible

Answer:

0.00418

Step-by-step explanation:

The probability of the first one being defected is 3/479, as we have 3 defectives containers in a total of 479 containers.

If the first one is defected and removed, now we have 478 containers, with 2 being defective.

So the probability of the second one being picked being defective, given that the first one was defective, is 2/478 = 1/239 = 0.00418

Answer:

$1272.008264

Step-by-step explanation:

If the mark-up was 21%, then the final price is 121% of the original price.  Simply divide $1,539.13 by 1.21 to get the original price of $1272.008264

The percent markup based on cost is calculated by finding the amount of the markup, dividing it by the original cost and multiplying by 100. In this case, the markup was 21% of the sale price, or $323.12. This correlates to a 26.56% markup based on the original cost ($1,215.91).

The percent markup based on cost can be calculated by first determining the amount of the markup, then dividing the markup by the original cost of the item, and finally multiplying the result by 100 to express it as a percentage. According to the question, the markup is 21% of the $1,539.13 selling price. Therefore, to calculate the markup we multiply $1,539.13 by 0.21 which results in $323.12. This is the amount by which the original price was increased to get the selling price. To calculate the percent markup based on cost, we divide the markup amount ($323.12) by the original cost of the item ($1,215.91) and then multiply by 100. This gives us a percentage markup of approximately 26.56%. So, the percent markup based on cost is 26.56%.

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Final answer:

To find the time it will take for an object to travel a certain distance at a given speed, divide the distance by the speed. The estimated time to travel 4.9 km at a speed of 10 km/h is approximately 0.5 hours. The exact time, considering the speed as 10.1 km/h, is also approximately 0.5 hours.

Explanation:

To find the time it will take for an object to travel a certain distance at a given speed, we can use the formula:

Time (in hours) = Distance (in kilometers) / Speed (in kilometers per hour)

First, let's round the speed to the nearest integer, which is 10 km/h. To estimate the time it will take to travel 4.9 km, we can divide the distance by the estimated speed:

Estimated Time = 4.9 km / 10 km/h ≈ 0.49 hours ≈ 0.5 hours

To find the exact time, we will use the given speed of 10 and one-tenth km/h. We can convert this speed to decimal form, which is 10.1 km/h. Now, we can calculate the exact time:

Exact Time = 4.9 km / 10.1 km/h ≈ 0.485 hours ≈ 0.5 hours

Therefore, it will take approximately 0.5 hours or 30 minutes for the object to travel 4.9 km.

Answer:

A

Step-by-step explanation:

8(2) = 16

17 (2) = 34

34^2 = 16^2 + x^2

1156 = 256 + x^2

1156- 256 = x^2

900 = x^2

square root of 900 = x

x = 30

15(2) = 30

Answer:

A 15a

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2 +b^2 = c^2  where a and b are the legs and c is the hypotenuse

Letting the unknown side be x

(8a)^2 + x^2 = (17a)^2

64a^2 + x^2= 289a^2

Subtracting 64a^2 from each side

64a^2 -64a^2 + x^2= 289a^2-64a^2

x^2 =225a^2

Taking the square root of each side

sqrt(x^2) =sqrt(225a^2)

x = 15a

[tex]\boldsymbol{\mathbf{Answer}}[/tex]

[tex]\boldsymbol{\mathbf{Machine \, A \,will\, take \,6 \,hours\, to \,produce\, 1 \,widget \,on\, its\, own.}}[/tex]

[tex]\boldsymbol{\mathbf{Step-by-step \,explanation:}}[/tex]

Let,

performance rate of machine A is x widget per hour.

performance rate of machine A is y widget per hour.

As given, Machine A and Machine B can produce 1 widget in 3 hours working together.

I.e mathemetically,

[tex]\boldsymbol{x + y=\frac{1}{3}......(1)}[/tex]

lly for second statement, Machine A’s speed were doubled, the two machines could produce 1 widget in 2 hours working together.

i.e mathematically,

[tex]\boldsymbol{2x + y=\frac{1}{2}......(2)}[/tex]

Substact equation (1) in (2)

  [tex]x + y=\frac{1}{3}[/tex]

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

Resultant equation will be,

[tex]-x=\frac{-1}{6}[/tex]

[tex]\boldsymbol{x = \frac{1}{6}}[/tex]

Performance rate of machine A is \frac{1}{6} widget per hour.

what is time Machine A will take to produce 1 widget on its own.

i.e = [tex]\frac{1}{\frac{1}{6}}[/tex]

[tex]\boldsymbol\mathbf{{=\, 6 \,hours.}}[/tex]

The solution is [tex]\$ 6661[/tex]

Explanation:

The initial investment is $4500

The time taken is 10 years.

The rate of interest is 4%

We shall determine the value of A using the formula [tex]A=P(1+r)^t[/tex]

where P is the initial investment,

r is the rate of interest and

t is time

Let us substitute the values [tex]P=4500[/tex] , [tex]t=10[/tex] and [tex]r=4 \%[/tex] in the formula [tex]A=P(1+r)^t[/tex]

Thus, we have,

[tex]A=4500(1+0.04)^{10}[/tex]

Adding the values within the bracket, we have,

[tex]A=4500(1.04)^{10}[/tex]

Simplifying, we get,

[tex]A=4500(1.4802)[/tex]

Multiplying, we have,

[tex]A=6661[/tex]

Thus, the value is $6661

Answer:

p+b[tex]\leq[/tex]30 .......(i)

12.50p+9.50b[tex]\geq[/tex]300 .......(ii)

Step-by-step explanation:

Marcus Hourly Rate at the local pizzeria = $12.50 per hour

Marcus Hourly Rate at the university bookstore = $9.50 per hour

Let the number of hours worked at the local pizzeria=p

Let the number of hours worked at the university bookstore=b

Since he cannot work more than 30 hours per week in order to attend classes, the total of the hours:

p+b[tex]\leq[/tex]30 .......(i)

If he earns $12.50 for p hours at the local pizzeria,

Income from local pizzeria=12.50p

If he earns $9.50 for b hours at the university bookstore,

Income from university bookstore=9.50b

He must make at least $300 per week, therefore his total income must not be less than $300

Total Income=Income from Pizzeria + Income from University bookstore

12.50p+9.50b[tex]\geq[/tex]300 .......(ii)

Therefore the system of inequalities that models this situation is given as:

p+b[tex]\leq[/tex]30 .......(i)

12.50p+9.50b[tex]\geq[/tex]300 .......(ii)

Answer: the third option is the correct answer.

Step-by-step explanation:

The given quadratic equation is expressed as

x² - 10x + 24 = 0

We would apply the method of factorization by finding two numbers such that their sum or difference is -10x and their product is 24x^2. The two numbers are - 6x and - 4x. Therefore,

x² - 6x - 4x + 24 = 0

x(x - 6) - 4(x - 6) = 0

(x - 6)(x - 4) = 0

Therefore, the solutions to the equation are

x = 4 or x = 6

Step-by-step explanation:

Here, given:

The area of the square floor  = 64 sq. ft

Now, as given the floor is in the shape of a square.

Let us assume the side length of the floor = k ft

Area of a square  = (Side) x (Side)

                              = k x k   = 64 sq ft

⇒ k ²  =  64  = (8) ²

⇒ k   = 8 ft

Hence, 64 sq ft   = ( 8 ft) ²

Here, base  = 8 and power = 2, which is greater than 1.

Answer:4. Abstract.

Step-by-step explanation: Abstraction is a term used to describe a departure from reality in the expressions of image in art.

This kind of departure from accurate and actual representation can be slight,can be partial, or complete or total.

Abstract shapes are shapes used in depicting the virtual images of certain objects or people,it usually does not actually display reality or, it only shows the radical altering of the visual realities of different things.

Answer:

a) matched samples.

Step-by-step explanation:

Matched samples (also known as matched pairs, paired samples or dependent samples) are those samples which can be matched in pairs for one set of item and the sample data are not independent of each other. The pairs don’t have to be different people, it could be the same individuals at different time or tested on different activities for example

The completion time data collection method used by the company, which involves each worker using both production methods, is based on matched samples.

The current method used to collect completion time data involves each worker being required to use both production methods. This method is known as matched samples. It involves using the same subjects in two different conditions to measure the difference in outcomes. In this case, the matched samples design is being used to compare the completion times of the workers using both production methods. The design is a test of dependent means, classified as a matched pairs design. This design is useful in situations where the same subject is being tested in two different conditions. The matched pairs design allows for a more accurate comparison of the two conditions, as it eliminates the variability between different subjects.

Answer:

The true statements are 2 and 3.

Step-by-step explanation:

Triangle SRQ undergoes a rigid transformation that results in triangle VUT

So, ΔSRQ ≅ ΔVUT

So, point S will map to point V, point R will map to point U and point Q will map to point T.

According to the previous, We will check the statements:

1) SQ corresponds to VU. Wrong because SQ corresponds to VT

2) ∠R corresponds to ∠U. True

3) UV corresponds to RS. True

4) ∠S corresponds to ∠T.  Wrong because ∠S corresponds to ∠V

5) QS corresponds to RS. Wrong because QS corresponds to TV

So, The true statements are 2 and 3.

2) ∠R corresponds to ∠U

3) UV corresponds to RS.

Answer:

The true statements are 2 and 3.

Step-by-step explanation:

Triangle SRQ undergoes a rigid transformation that results in triangle VUT

So, ΔSRQ ≅ ΔVUT

So, point S will map to point V, point R will map to point U and point Q will map to point T.

According to the previous, We will check the statements:

1) SQ corresponds to VU. Wrong because SQ corresponds to VT

2) ∠R corresponds to ∠U. True

3) UV corresponds to RS. True

4) ∠S corresponds to ∠T.  Wrong because ∠S corresponds to ∠V

5) QS corresponds to RS. Wrong because QS corresponds to TV

So, The true statements are 2 and 3.

2) ∠R corresponds to ∠U

3) UV corresponds to RS.Step-by-step explanation:

The range of the function is [tex]\{-19,-4,16\}[/tex]

Explanation:

The function is [tex]f(n)=5n-4[/tex]

The domain of the function is [tex]\{-3,0,4\}[/tex]

We need to find the range of the function.

The range can be determined by substituting the values of domain in the function.

Thus, the range of the function when the domain is -3 is given by

[tex]f(-3)=5(-3)-4[/tex]

         [tex]=-15-4[/tex]

         [tex]=-19[/tex]

Thus, the range is -19 when [tex]n=-3[/tex]

The range of the function when the domain is 0 is given by

[tex]f(0)=5(0)-4[/tex]

       [tex]=0-4[/tex]

       [tex]=-4[/tex]

Thus, the range is -4 when [tex]n=0[/tex]

The range of the function when the domain is 4 is given by

[tex]f(4)=5(4)-4[/tex]

       [tex]=20-4[/tex]

       [tex]=16[/tex]

Thus, the range is 16 when [tex]n=4[/tex]

Thus, the range of the function is [tex]\{-19,-4,16\}[/tex] when their corresponding domain is [tex]\{-3,0,4\}[/tex]

Arranging the range in order from least to greatest is given by

[tex]\{-19,-4,16\}[/tex]

Hence, the range of the function is [tex]\{-19,-4,16\}[/tex]

Answer:

The answer is 630 students

Step-by-step explanation:

For this case, we have 504 students and the student enrollment has decrease 20%, which mean 504 is the 80% of the total student enrollment of the previous year.

[tex]100 - 20 = 80[/tex]%

This is a direct proportion problem. As shown bellow:

504 -> 80%

x      -> 100%  

For solving this we use the Mathematical Rule of Three, a method of having three numbers to help calculate the unknown.

b  ->  c

x   ->  a

The algorithm for rule of three is the following:

[tex]x = \frac{a * b}{c} \\\\x= \frac{504*100}{80} =\frac{50400}{80}=630\\ \\x=630[/tex]

Answer:

Matched sample design

Step-by-step explanation:

- A matched subject design uses separate experimental groups for each particular treatment, ( A sample of brothers and sisters - genders ).

- But relies upon matching every subject in one group with an equivalent in another. (The differences in ratings between each brother and sister pair were compared. )

- The idea behind this is that it reduces the chances of an influential variable skewing the results by negating it.

The amount paid by Heron for the video game  is $46.64.

Step-by-step explanation:

Here, the marked price of the video game  = $55

The discount percentage on the video game  = 20%

Calculating 20% of the $55, we get:

[tex]\frac{20}{100} \times 55 = 11[/tex]

So, the discount offered on the video game  = $11

Selling Price  = Marked Price  - Discount

                        =$55 - $11 = $44

Now,  the tax percentage on the video game  = 6%

Calculating 6% of the $44, we get:

[tex]\frac{6}{100} \times 44 =2.64[/tex]

So, the tax  on the video game  = $2.64

New Selling Price  = Selling Price  +  Tax

                        =$44 + $2.64  = $46.64

So, the amount paid by Heron for the video game  is $46.64.

Answer:

Step-by-step explanation:

Considering the given triangle KFP, to determine FP, we would apply the sine rule. It is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes

FP/SinK = FK/SinP = KP/SinF

Therefore

FP/Sin 49 = 66/Sin 85

Cross multiplying, it becomes

FPSin85 = 66Sin49

0.996FP = 45 × 0.7547

0.996FP = 33.9615

FP = 33.9615/0.996

FP = 34.1

The fewest number of trucks Lauren should send is D) 4 trucks.

Step-by-step explanation:

Step 1:

The rectangular slab's dimensions are [tex]24 \times 24 \times 1[/tex] feet. Each truck can carry 8 cubic yards of cement.

First, we need to determine the volume of the slabs in yards. 1 foot = 0.333 yards. So 24 feet = [tex]24\times 0.3333[/tex] = 8 yards.

The volume of the slab = [tex]8 \times 8 \times 0.3333[/tex] = 21.3312 cubic yards.

Step 2:

The company sends a surplus of 20% to make sure the job can be completed. So the total cement sent is the required volume and an extra 20%.

The total cement sent = The required cement + 20%.

                                      = 21.3312 + 20% = 25.597 cubic yards.

Step 3:

So to find the number of trucks needed, we divide the cement sent by the load each truck can carry. Each truck can carry 8 cubic yards of cement. So

The number of trucks needed = [tex]\frac{therequiredload}{load per truck} = \frac{25.597}{8} = 3.199625.[/tex]

If 3.199 trucks are needed, it means 4 trucks are needed which is option D.

Answer:

The assumption will depend on the argument that C. Any decrease in per capita sales of cigarettes in Coponia will result mainly from an increase in the number of people who quit smoking entirely.

Step-by-step explanation:

Per capita income or average income measures the average income earned per person in a given area in a specified year. It is calculated by dividing the area's total income by its total population. Per capita income is national income divided by population size.

Tax is a compulsory contribution to state revenue, levied by the government on workers' income and business profits, or added to the cost of some goods, services, and transactions.

Answer:

Step-by-step explanation: they are asking “What is x + 3 + y”. So use Pythagorean’s theorem to get x (it should be 4) and then find y and I think u get square root of 13, then add 4 + 3 + square root 13

Answer: P = Po ( 1 + 0.075)

Step-by-step explanation: let Po = initial population

P = final population.

The increase in population is by 7.5%, which implies that if the initial population Increases by 7.5%, we would have a new (current) population.

Final population = initial population + increament of initial population.

Where increment of initial population = 7.5% of Po = 0.075 Po

P = Po + 0.075Po

P = Po ( 1 + 0.075)

Answer:

C. 160,000

Step-by-step explanation:

Given that the measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300 cm.

Also given that each of the three measurements has an error of at most 1 cm

COnsider the worst case where each dimension is increased by 1 cm

Then we measure the dimensions as 201 , 201 and 301

So volume would be measured as

[tex]201*201*301\\= 12160701[/tex] cubic cm

Actual volume of the box = [tex]200*200*300\\=12000000[/tex] cubic cm

Difference maximum possible = 160701 cubic cm

Out of the five options given option C is nearest to this value

So answer is

C. 160,000

Answer: The answers are stated below

Step-by-step explanation: Attached below is the explaination of the solution.

f + g =4x + 8 Domain - (-∞, ∞)

f - g = 2x + 4 Domain - (-∞, ∞)

(f)(g) = 3x² + 12x + 12 Domain - (-∞, ∞)

f/g = [tex]\frac{3x + 6}{x + 2}[/tex] Domain - [tex](-\infty, -2) \cup (-2, \infty)[/tex]

To solve the problems involving the functions f and g, we start by defining the functions:

Given functions:
[tex]f(x) = 3x + 6[/tex]
[tex]g(x) = x + 2[/tex]

1. Finding f + g, f - g, fg, and f/g:  

f + g:
[tex]f + g = (3x + 6) + (x + 2) = 4x + 8[/tex]  

Domain: All real numbers, [tex](-\infty, \infty)[/tex]

f - g:
[tex]f - g = (3x + 6) - (x + 2) = 2x + 4[/tex]  

Domain: All real numbers, [tex](-\infty, \infty)[/tex]

fg:
[tex]fg = (3x + 6)(x + 2) = 3x^2 + 12x + 12[/tex]  

Domain: All real numbers, [tex](-\infty, \infty)[/tex]

f/g:
[tex]f/g = \frac{3x + 6}{x + 2}[/tex]  

However, g(x) cannot be zero: [tex]g(x) = 0[/tex] for [tex]x = -2[/tex].  

Domain: All real numbers except [tex]x = -2[/tex] , which is [tex](-\infty, -2) \cup (-2, \infty)[/tex]

2. Finding (g ◦ f)(x) and (f ◦ g)(x):  

(g ◦ f)(x):
[tex]g(f(x)) = g(3x + 6) = (3x + 6) + 2 = 3x + 8[/tex]  

(f ◦ g)(x):
[tex]f(g(x)) = f(x + 2) = 3(x + 2) + 6 = 3x + 12[/tex]

3. Completing the square for f(x) = x² - 8x + 2:  

First, take the coefficient of [tex]-8[/tex], halve it to get [tex]-4[/tex], and square it to get [tex]16[/tex].  

Therefore:
[tex]f(x) = (x^{2} - 8x + 16) - 16 + 2 = (x - 4)^{2} - 14[/tex]  

Now in standard form:
[tex]y = (x - 4)² - 14[/tex]

4. Vertex formula for f(x) = x² - 14x:  

Vertex formula: [tex]x = -\frac{b}{2a}[/tex] where [tex]a=1, b=-14[/tex].  

Therefore:
[tex]x = -\frac{-14}{2(1)} = 7[/tex]  

Substituting [tex]x=7[/tex] back to find y:
[tex]f(7) = 7^{2} - 14(7) = 49 - 98 = -49[/tex]  

Standard form:
[tex]f(x) = (x - 7)^{2} - 49[/tex]

5. Vertex for f(x) = 3x² - 10x + 1:  

Vertex x-coordinate:
[tex]x = -\frac{-10}{2(3)} = \frac{10}{6} = \frac{5}{3}[/tex]

Substitute [tex]x=\frac{5}{3}[/tex] back to find y:
[tex]f(\frac{5}{3}) = 3(\frac{5}{3})^{2} - 10(\frac{5}{3}) + 1[/tex]  

Calculate the value:
[tex]3(\frac{25}{9}) - \frac{50}{3} + 1 = \frac{75}{9} - \frac{150}{9} + \frac{9}{9} = -\frac{66}{9} = -\frac{22}{3}[/tex]  

The standard form becomes:
[tex]f(x) = 3(x - \frac{5}{3})^{2} - \frac{22}{3}[/tex]

Answer:

6, 8, 10,

Step-by-step explanation:

you start at zero and go 6 units to the right, then from zero, you go 8 units up; this forms a right triangle with the smaller sides being 6 and 8. Then u can use the Pythagorean theorem to find the bigger side.