The triangles below are similar. Calculate the length of the unknown sides.

The equivalent expressions of [tex]x^3[/tex] are[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]and [tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex], the expressions [tex]\frac{(x^{30}) }{(x^{10})}[/tex] and [tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] are not equivalent to [tex]x^3[/tex].

What are equivalent expressions?

Equivalent expressions are different algebraic expressions that have the same value when evaluated for a particular set of variables.

The equivalent expressions  [tex]x^3[/tex] are:

[tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] : This expression can be simplified as follows:

=[tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex]

= [tex]\frac{(x ^ 8)}{(x ^ 2) }[/tex]

=[tex]x^{8-2}[/tex]

= [tex]x^6[/tex]

[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex] : This expression can be simplified as follows:

=[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]

= [tex]x^{6-3}[/tex]

=[tex]x^3[/tex]

[tex]\frac{(x^{30}) }{(x^{10})}[/tex] : This expression can be simplified as follows:

=[tex]\frac{(x^{30}) }{(x^{10})}[/tex]

=[tex]x^{30-10}[/tex]

=[tex]x^{20}[/tex]

[tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex] : This expression can be simplified as follows:

=[tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex]

=[tex]x^{-3-(-6)}[/tex]

=[tex]x^{-3+6}[/tex]

=[tex]x^{3}[/tex]

Therefore, the equivalent expressions of [tex]x^3[/tex] are[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]and [tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex] , the expressions [tex]\frac{(x^{30}) }{(x^{10})}[/tex] and [tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] are not equivalent to [tex]x^3[/tex].

To know more about equivalent expressions visit:

brainly.com/question/17499155

#SPJ1

The probability that at least 2 of the people in the class share the same birthday is approximately 0.507 or 50.7%.

The probability that at least two people share the same birthday in a class of 23 people can be calculated using the formula for a complement of an event, which states that the probability of an event happening is 1 minus the probability of it not happening.

Therefore, let’s first calculate the probability that no two people share the same birthday in a class of 23 people.

There are 365 days in a year, and if we assume that all the days are equally likely to be birthdays, then the first person can choose any day, and the probability of the second person not having the same birthday is (364/365), and for the third person, it is (363/365), and so on for the other people.

Therefore, the probability of none of them sharing the same birthday is

(364/365) × (363/365) × … × (343/365) which is approximately 0.493.

The probability of at least two people sharing the same birthday is the complement of the probability that none of them share the same birthday.

Therefore, the probability of at least two people sharing the same birthday in a class of 23 people is

1 − 0.493 ⇒ 0.507.

Hence, there is a 50.7% chance that at least two people share the same birthday in a class of 23 people.

To know more about the "complement of an event" in probability: https://brainly.com/question/29508911

#SPJ11

The percentage of observations less than 130 is 97.7%, and the number of observations less than 130 = 879

The question asks about the percentage and number of observations that are less than 130 in a data set that follows a bell-shaped distribution with a mean of 120 and a standard deviation of 5.

a. To find the percentage of observations that are less than 130, we can use the z-score formula:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

Plugging in the given values, we get:
z = (130 - 120) / 5
z = 10 / 5
z = 2

Using a standard normal table or calculator, we can find that the probability of a z-score being less than 2 is approximately 0.9772. This means that approximately 97.7% of the observations are less than 130.

b. To find the number of observations that are less than 130, we can multiply the percentage by the total number of observations:
Number of observations = 0.9772 * 900
Number of observations = 879.48

Rounding to the nearest whole number, we get that approximately 879 observations are less than 130.

Therefore, the answers are:
a. Percentage of observations less than 130 = 97.7%
b. Number of observations less than 130 = 879

To know more about bell-shaped distribution refer here:

https://brainly.com/question/30764739#

#SPJ11

The area of the triangle is given as follows:

22.8 ft².

The area of a triangle of base b and height h is given by half the multiplication of these two dimensions, according to the equation presented as follows:

A = 0.5bh.

From the image given at the end of the answer, the dimensions of the triangle are given as follows:

Hence the area of the triangle is given as follows:

A = 0.5 x 8 x 5.7 = 22.8 ft².

The triangle from which we are going to calculate the area is given by the image presented at the end of the answer.

More can be learned about the area of a triangle at https://brainly.com/question/21735282

#SPJ1

The solution of the system is a = -1, b = 1, c = 0, and d = -3.

To find the cubic function f(x) = ax³ + bx² + cx + d that satisfies the given equations by using a system of equations and solving the system using matrices, we proceed as follows:Equations for the given cubic function:f(-2) = a(-2)³ + b(-2)² + c(-2) + d = -7 ...(1)f(-1) = a(-1)³ + b(-1)² + c(-1) + d = 2 ...(2)f(1) = a(1)³ + b(1)² + c(1) + d = -4 ...(3)f(2) = a(2)³ + b(2)² + c(2) + d = -7 ...(4)The matrix form of the system of equations is given by AX = B, whereA = [(-2)³ (-2)² -2 1; (-1)³ (-1)² -1 1; (1)³ (1)² 1 1; (2)³ (2)² 2 1],X = [a; b; c; d], andB = [-7; 2; -4; -7].The augmented matrix form of the system of equations is given by [A|B] = [(-2)³ (-2)² -2 1 -7; (-1)³ (-1)² -1 1 2; (1)³ (1)² 1 1 -4; (2)³ (2)² 2 1 -7].Performing the row operations, we get the row echelon form of the augmented matrix as follows:[A|B] = [1 0 0 0 -1; 0 1 0 0 1; 0 0 1 0 0; 0 0 0 1 -3].Therefore, the solution of the system is a = -1, b = 1, c = 0, and d = -3.Hence, the cubic function f(x) = ax³ + bx² + cx + d that satisfies the given equations is given by f(x) = -x³ + x² - 3.

Learn more about System of equations

brainly.com/question/12895249

#SPJ11

Answer:

the slope-intercept form of the line which is perpendicular bisector to the segment with endpoints A(5,9), B(7,13) is y = (-1/2)x + 14

Answer:

Step-by-step explanation:

rise is up and run is over.

The first number would be y and the second number would be x

and x is run

y is rise.

Answer:

Step-by-step explanation:

The domain is found by setting the denominator equal to 0 and solving for y. This value of y gives you the values that cause the denominator to go to 0, which is a problem. In this rational expression, there are no real numbers that cause the denominator to go to 0, so the domain is all real numbers.

Mr. Golv's total time to complete the jiu-jitsu drill is 7GG + 2KK seconds, where GG is the time taken for guard passes and KK is the time taken for kimura arm locks.

Mr. Golv's total time to complete the jiu-jitsu drill can be calculated as follows:

Guard passes: 5 x GG = 5GG seconds

Kimura arm locks: 2 x KK = 2KK seconds

Total time: 5GG + 2KK = (5 x GG) + (2 x KK) = 7GG + 2KK seconds

Therefore, the total time required by Mr. Golv to complete the jiu-jitsu drill is 7GG + 2KK seconds.

For example, if GG = 10 and KK = 6, then the total time required by Mr. Golv to complete the jiu-jitsu drill is (5 x 10) + (2 x 6) = 50 + 12 = 62 seconds.

Learn more about total time here:

https://brainly.com/question/29286082

#SPJ4

complete question

How much time will Mr. Golv take to complete his jiu-jitsu drill which includes 5 guard passes and 2 kimura arm locks, where a guard pass takes GG seconds and a kimura arm lock takes KK seconds?

Answer:

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

Step-by-step explanation:

x*x=[tex]x^{2}[/tex]

Answer:

It depends on the values of x and y. If x is positive and y is negative, then option A (x + y) would have a negative value. If y is greater than x, then option B (x - y) would have a negative value. If either x or y (or both) is negative, then option C (x*y) could have a negative value. Option D (x/y) could also have a negative value if x is negative and y is positive, or if both x and y are negative.

Answer:

Step-by-step explanation:

B because it has subtraction

The total area, in square centimeters, of the shaded sections of the below would be 33. 93 cm ²

The area of the shaded sections can be found by finding the area of the two triangular sections that are shaded.

Area of first triangle :

= 1 / 2 x base x height

= 1 / 2 x 5. 3 x 5 . 8

= 15. 37 cm ²

The area of the second triangle is :

= 1 / 2 x 6 . 4 x 5 . 8

= 18. 56 cm ²

The total area of the shaded sections is:

= 15. 37 + 18. 56

= 33. 93 cm ²

Find out more on area at https://brainly.com/question/1297097

#SPJ1

Answer:hello

Step-by-step explanation:

Answer:

x = 6

y = 3√2

Step-by-step explanation:

tan45 = y / (3√2)

y =  (3√2)(tan45) =  3√2

x = (3√2) / cos45  = 6

this is a 45-45-90 isosceles triangle

Answer:

No

Step-by-step explanation:

[tex]\frac{6}{5}=1.2[/tex]

[tex]\frac{4}{3} =1.33[/tex]

[tex]\frac{6}{5} < \frac{4}{3}[/tex]

Hope this helps.

Answer:

No

Step-by-step explanation:

6/5=4/3

18=20

9≠10

The solution to the system of equations is d = 100 and m = 1/4. Multiplying each term in the second equation by 2 helped us to eliminate the variable d and solve for m.

To solve the system of equations, we can use the elimination method, which involves adding or subtracting the two equations to eliminate one of the variables.

In this case, if we add the two equations as they are, we won't be able to eliminate one of the variables.

Multiply each term in the second equation by 2, we will get:

4d + 200m = 450

4d + 800m = 600

Now, we can subtract the first equation from the second equation to eliminate d:

(4d + 800m) - (4d + 200m) = 600 - 450

600m = 150

m = 1/4

Substituting this value of m back into either of the original equations, we can solve for d:

4d + 200(1/4) = 450

4d + 50 = 450

4d = 400

d = 100

Learn more about system of equations by elimination on:

https://brainly.com/question/13729904

#SPJ1

According to the given information, the measure of the larger acute angle in the 3-4-5 right triangle is approximately 36.87 degrees.

What is 3-4-5 right angle triangle?

A 3-4-5 right triangle is a right triangle where the lengths of the three sides are in the ratio of 3:4:5. In other words, the length of the longest side (the hypotenuse) is 5 times the length of the shortest side, and the length of the remaining side is 4 times the length of the shortest side. This special right triangle has angles of 30 degrees, 60 degrees, and 90 degrees, which are the angles of a 30-60-90 triangle. The sides of a 3-4-5 right triangle can be scaled up or down by any common factor (e.g. 6-8-10, 9-12-15, etc.) and will still form a right triangle with the same angles.

In a 3-4-5 right triangle, the larger acute angle is opposite to the longer leg, which has a length of 4. To find the measure of this angle, we can use the inverse tangent function:

tan(theta) = opposite / adjacent = 3/4

[tex]theta = tan^{-1} (3/4)[/tex]

Using a calculator, we can find that:

theta ≈ 36.87 degrees

Therefore, the measure of the larger acute angle in the 3-4-5 right triangle is approximately 36.87 degrees.

To know more about 3-4-5 right angle triangle visit:

brainly.com/question/25771319

#SPJ1

For the given elementary chemical reaction, the solution to the question is: C = a^2 * (1-t^2/400(1-a))

The question asks about calculating the concentration of C in a chemical reaction. Given that the reaction equation is as follows: A + B → C The rate of reaction can be expressed as: dc/dt = k[A][B] Where, k is the rate constant[A] is the concentration of reactant A in moles/L[B] is the concentration of reactant B in moles/L, c is the concentration of product C in moles/L

The initial concentration of A and B is [A] = a moles/L, [B] = b moles/L Let r be the rate of reaction, i.e. r = dc/dt Thus, using the equation r = k[A][B], we get r = k(a)(b)Now, we can write a differential equation for the concentration of C as follows: dc/dt = r, with initial concentration of C as 0 moles/L∴ dc/dt = kab

Substituting r = k(a)(b) in the equation, we get dc/dt = kabdc/db = kab*dt Differentiating both sides, we get, ln(C) = kab*t + C where C is a constant, ln(C) = ln(a^2) = 2ln(a) = C When a = b, the concentration of C will be maximum at t = (1/k)(ln(a)).

Thus the concentration of C as a function of time (when a = b) is given by C = a^2 * (1-t^2/2)If [C] = a after 20 seconds, then using the equation, we get a = a^2 * (1 - 20^2 * k^2/2)Therefore, 1 = a * (1 - 200k^2) Solving this equation for k, we get, k = ± sqrt[(1-a)/200a^2] For the positive value of k, the concentration of C as a function of time is given by C = a^2 * (1-t^2/400(1-a)).

To know more about elementary chemical reaction, refer here:

https://brainly.com/question/31022212#

#SPJ11

16. The base side y = 10.565 and altitude x = 22.657

17. The hypotenuse c = 49.70 and base y = 46.70.

18. The value of AB = 30√3 and AC = 45

19. The value of AB = 36√3 and BC = 18√3.

In geοmetry, a hypοtenuse is the lοngest side οf a right-angled triangle, the side οppοsite the right angle. The length οf the hypοtenuse can be fοund using the Pythagοrean theοrem, which states that the square οf the length οf the hypοtenuse equals the sum οf the squares οf the lengths οf the οther twο sides.

16. Given hypotenuse = 25

θ = 25°

Sin θ = opposite/hypotenuse

Sin 25° = y/25

y = Sin 25° × 25

y = 10.565

Given hypotenuse = 25

θ = 25°

Cos θ = adjacent/hypotenuse

Cos 25° = x/25

x = Cos 25° × 25

x = 22.657

17. Given Side = 17

θ = 20°

Sin 20° = 17/c

c = 17/Sin 20°

c = 49.70

Cos θ = adjacent/hypotenuse

Cos 20° = y/49.70

y = Cos 20° × 49.70

y = 46.70

18. Given BC = 15√3

In a 30°−60°−90°  triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3√ times the length of the shorter leg.

Thus, BC = 15√3

AB = 2(15√3)

= 30√3

and

AC = √3(15√3)

= 15 × 3

= 45

Thus, when BC = 15√3, then AB = 30√3 and AC = 45

19. Given AC = 54

In a 30°−60°−90°  triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3√ times the length of the shorter leg.

Thus, BC = x and AC = x√3

54 = x√3

54 = x√3

x = 54/√3

x = 18√3

BC = 18√3

AB = 2x = 2(BC) = 2(18√3)

= 36(√3)

Thus, when AC = 54, then AB = 36√3 and BC = 18√3.

Learn more about hypotenuse

https://brainly.com/question/29407794

#SPJ1

Mark and Lynne have 28 years left on their mortgage. To figure out how old their house is right now, we need to divide the remaining years on the mortgage by 5.

This is because when the mortgage is paid off, their house will be 5 times as old. Therefore, 28 divided by 5 is equal to 5.6 years old. This means that the house is currently 5.6 years old. After 28 years, the house will be 33.6 years old.

Mark and Lynne have a mortgage on their house that still has 28 years remaining on it. To figure out the age of the house currently, we need to do a simple calculation. When the mortgage is paid off, their house will be 5 times as old as it is now. Therefore, if we divide the remaining years on the mortgage by 5, we will get the current age of the house. 28 divided by 5 is equal to 5.6 years old. This means that the house is currently 5.6 years old. In 28 years, when the mortgage is paid off, the house will be 33.6 years old. It is important to pay off the mortgage in a timely manner, as this will save Mark and Lynne a lot of money in the long run.

learn more about remainder here

https://brainly.com/question/30302805

#SPJ4

In some circumstances, it might also be essential to demonstrate congruence using various transformations.

In mathematics, transformations are modifications done to a geometric figure in a coordinate plane, such as a shape, point, or line. Applying various operations or functions on the coordinates of the points that make up the figure will result in these changes. Four fundamental types of transformations exist: Translation: A figure is moved horizontally, vertically, or both while maintaining its size, form, and orientation.

Translation, rotation, and reflection are the three fundamental transformations that can be employed to demonstrate the congruence of two figures.

To demonstrate that Figures 1 and 2 are congruent with one another, the following two transformational sequences could be used:

Figure 1 should be translated to overlap with Figure 2, then rotated.

b. Rotate Figure 1 about a point until it aligns with Figure 2's orientation.

c. Evaluate the two figures side by side to ensure that all related sides and angles match.

Rotation after reflection:

a. Create a mirror image of Figure 1 by reflecting it across a line.

b. Rotate the reflected Figure 1 about a certain point until it aligns with Figure 2's orientation.

c. Evaluate the two figures side by side to ensure that all related sides and angles match.

To ensure that the two figures are congruent, the transformations must be used in a precise order.

In some circumstances, it might also be essential to demonstrate congruence using various transformations.

To know more about transformation visit :-

brainly.com/question/11709244

#SPJ1

Answer:

Given as steps.

Step-by-step explanation:

Step 2: Transitive Property of Equality
Step 3: SSS Congruency Therom
Step 5: If alt. Interior angles are congruent when two lines are cut by a transversal then the lines are parallel
Step 6: Quadrilateral with opposite sides parallel and congruent is a parallelogram


hope it helps.

Based on the principle of Inequality, Attached image is a graph of the inequality for  |x| < 5. The red region is the solution set.

A mathematical statement known as an equation demonstrates the relationship between two or more numbers and variables by utilizing mathematical operations such as addition, subtraction, multiplication, division, exponents, and so forth.

Therefore, An expression that demonstrates a non-equal comparison of numbers and variables is called an inequality. So, the graph that best represents this solution set is a number line with open circles at x = -5 and x = 5 and a shaded region in between, indicating that all values of x within this range satisfy the inequality.

Find more on equation at:

https://brainly.com/question/2972832

#SPJ1

With the applicatiοn οf Distributive Prοperty οf Multiplicatiοn, the fοllοwing equatiοn 3 (x + 2) + 5 can be written as

3*x + 3*2 + 5

The distributive prοperty οf multiplicatiοn is a mathematical rule that states that the prοduct οf a number and a sum can be οbtained by adding the prοducts οf the number and each term in the sum. In οther wοrds, a(b+c) = ab + ac. This prοperty can be used tο simplify expressiοns by breaking them dοwn intο smaller parts.

It is an impοrtant cοncept in algebra and is οften used tο sοlve equatiοns and simplify expressiοns. The distributive prοperty can alsο be applied tο variables and expοnents, and is a fundamental principle in the study οf algebraic structures such as rings and fields.

With the applicatiοn οf Distributive Prοperty οf Multiplicatiοn, the fοllοwing equatiοn 3 (x + 2) + 5 can be written as

3*x + 3*2 + 5

further simplified will give 3x + 6 + 5 = 3x + 11

To learn more about Distributive Property of Multiplication

https://brainly.com/question/2807928

#SPJ1

Answer:347

Step-by-step explanation:=

347 ⇔ 347 R 0

8328 divided by 24

=

347 with a remainder of 0

Step-by-step explanation:

I do not believe you are given enough info to prove they are congruent....you only have ONE angle and one side that are equal ....you need another side or another angle to prove congruency....

I've added an illustration to show how the two triangles would not be congruent without changing the  info given in the pic

.

Let's use algebra to solve this problem. Let x be the number of 30-minute lessons that the teacher gave last week, and let y be the number of 60-minute lessons. We know that the teacher gave a total of 9 lessons, so we can write:

x + y = 9

We also know that the total time spent on lessons was 7 hours, which we can convert to minutes:

30x + 60y = 420

Now we have two equations with two unknowns, which we can solve using substitution or elimination. Let's use substitution:

x + y = 9 -> y = 9 - x

30x + 60y = 420 -> 30x + 60(9 - x) = 420

Simplifying and solving for x:

30x + 540 - 60x = 420

-30x = -120

x = 4

Therefore, the teacher gave 4 30-minute lessons last week. To find the number of 60-minute lessons, we can substitute x = 4 into either equation:

x + y = 9 -> y = 9 - x -> y = 9 - 4 -> y = 5

So the teacher gave 5 60-minute lessons last week.

Probability 0.919

The probability that the pooled sample variance, S2p, is less than 6.9157 is given by:

P(S2p < 6.9157) = P(S2p - S20 < 6.9157 - S20)

where S20 = ((n1-1)S21 + (n2-1)S22)/(n1+n2-2)



Here, n1 = 10 and n2 = 11. The individual sample variances S21 and S22 are both equal to 4, since both X and Y are samples from N(μ, 4).


Therefore, S20 = ((10-1)4 + (11-1)4)/(10+11-2) = 4.


Hence, P(S2p < 6.9157) = P(S2p - 4 < 6.9157 - 4) = P(S2p - 4 < 2.9157)


The probability can be computed using a chi-square cumulative distribution table. We obtain:

P(S2p - 4 < 2.9157) = 0.919.

Learn more about probability

brainly.com/question/30034780

#SPJ4

The Probability P(Sp² ​<6.9157) is 0.6672.

To solve this problem, we need to first recognize that the statistic Sp² follows a chi-squared distribution with 10+11-2 = 19 degrees of freedom, where:

Sp² = [(nX-1)*SX² + (nY-1)*SY²]/(nX+nY-2)

Here, nX = 10, nY = 11, SX² is the sample variance of X and SY² is the sample variance of Y.

Since X and Y are both normally distributed, we know that the sample variances SX² and SY² follow chi-squared distributions with 9 and 10 degrees of freedom, respectively, and scaled by the common variance sigma² = 4.

So we have:

SX² ~ chi-squared(9)*4 = chi-squared(36)

SY² ~ chi-squared(10)*4 = chi-squared(40)

Now we can use the fact that the sum of two independent chi-squared random variables with k1 and k2 degrees of freedom follows a chi-squared distribution with k1+k2 degrees of freedom.

Therefore, Sp² = [(nX-1)*SX² + (nY-1)*SY²]/(nX+nY-2) follows a chi-squared distribution with 9+10 = 19 degrees of freedom and scale parameter 4/(nX+nY-2) = 4/19.

To find P(Sp² < 6.9157), we can use a chi-squared distribution table or calculator. Using a chi-squared calculator, we find:

P(Sp² < 6.9157) = 0.6672

Therefore, the probability that Sp² is less than 6.9157 is 0.6672.

Learn more about probability at https://brainly.com/question/13796819

#SPJ11