Prove that a line parallel to one side of a triangle divides the other two sides proportionally. Be sure to create and name the appropriate geometric figures.

Answer:

234

Step-by-step explanation:

From the given information :

The 4th term, a4

a1 = 3

a2 = 4(a1) + 2

a2 = 4(3) + 2 = 14

a3 = 4(a2) + 2

a3 = 4(14) + 2

a3 = 58

a4 = 4a3 + 2

a4 = 4(58) + 2

a4 = 232 + 2

a4 = 234

Answer:

interesting

Step-by-step explanation:

very interesting

Answer:

4+2/5+3=3/4 slope

Step-by-step explanation:

sssllllooooppppeeee

Answer:

\(h \leq 5\)

Step-by-step explanation:

Time already spent on the train is at least 5 hours

Since the trip to Fairbanks take 10 hours, we have that, the sum of the number of hours left, h and the time already spent will be equal to 10.

\(t+h=10\\$Since the time for which the passenger has been on the train \geq 5\\5+h \leq 10\\h \leq 10-5\\$The inequality that describes in how many more hours, h the train will reach Fairbanks, therefore, is:\\h \leq 5\)

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \stackrel{ 48000+1200 }{\$ 49200}\\ P=\textit{original amount deposited}\dotfill &\$48000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2.6 \end{cases}\)

\(49200 = 48000\left(1+\frac{ ~~ \frac{r}{100} ~~ }{1}\right)^{1\cdot 2.6} \implies \cfrac{49200}{48000}=\left( 1+\cfrac{r}{100} \right)^{2.6} \\\\\\ \cfrac{41}{40}=\left( \cfrac{100+r}{100} \right)^{2.6}\implies \sqrt[2.6]{\cfrac{41}{40}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[2.6]{\cfrac{41}{40}}=100+r\implies 100\sqrt[2.6]{\cfrac{41}{40}}-100=r\implies \stackrel{ \% }{0.95}\approx r\)

Answer:

43.6 has 3 significant figures.

Answer:

I am assuming you mean the smallest decimal so it is 4.125

Step-by-step explanation:

you said quick so

Answer: 4.25

Step-by-step explanation: if you make all of these into a whole number the biggest number comes out to be 20 and its 4.25

Answer:

x = 20

Step-by-step explanation:

We know that the vertically opposite angles are equal.

Accordingly,

41 = 2x + 1

Subtract 1 from both sides.

41 - 1 = 2x

40 = 2x

Divide both sides by 2.

x = 20

Answer: Recall that E ∩ F ∩ G denotes the intersection of the three sets E, F, and G, and the superscript "c" denotes the complement of this set (i.e., everything outside of this intersection).

First, let's find E ∩ F ∩ G:

E ∩ F ∩ G = {24, 29}

Now, let's find the complement of this set:

(E ∩ F ∩ G)c = S - {24, 29}

This means that we take the set S and remove the elements 24 and 29.

So,

(E ∩ F ∩ G)c = {4, 9, 14, 19}

Step-by-step explanation:

Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is essentially what probability means.

The die has 10 faces, with numbers 1 through 10, but we are interested in the number of times it will land on a number less than 10. That means, there are 9 possible outcomes for each roll to be less than 10.

The expected number of times the die will land on a number less than 10 can be calculated by multiplying the probability of getting a number less than 10 on each roll by the total number of rolls.

The probability of getting a number less than 10 on each roll is 9/10, since there are 9 faces with numbers less than 10 out of the total of 10 faces.

Therefore, the expected number of times the die will land on a number less than 10 is:

E = (9/10) x 40 = 36

Therefore, Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.

Learn more about probability on:

https://brainly.com/question/13604758

#SPJ1

☆ 36 times.

— your in college ? im in seventh grade and got this question !

The probability that exactly 2 of the workers interviewed are union members is approximately 0.044.

To solve this problem, we can use the binomial probability formula, which is:

\(P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)\)

where:

n is the sample size (number of workers being interviewed)

k is the number of successes we are interested in (in this case, 2 of the workers being union members)

p is the probability of success (in this case, the probability that a worker is a union member)

(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items (this can be calculated using the formula n! / (k! * (n - k)!))

Plugging in the values, we get:

\(P(X = 2) = (4 choose 2) * (0.96)^2 * (1 - 0.96)^(4 - 2)\)

\(= (6) * (0.96)^2 * (0.04)^2\)

= 0.04403136

Therefore, the probability that exactly 2 of the workers interviewed are union members is approximately 0.044.

To learn more about probability please click on below link.

https://brainly.com/question/30034780

#SPJ1

Answer:

t(2,-2),C(2,-5),z(5,-4),f(5,0)

Step-by-step explanation:

because it reflects across the x-axis the y changes to the opposite.

Answer:

10 times as much

Step-by-step explanation:

90 000 x 10 = 900 000

Required trapizoidal approximation is 174.

What is trapezoidal rule?

The trapezoidal rule is a numerical integration method used to approximate the definite integral of a function over a given interval. It is based on approximating the area under the curve of the function by dividing it into trapezoids and summing up their areas.

To use the trapezoidal rule, you first need to choose an interval [a,b] over which to integrate the function. Then, you divide the interval into a number of subintervals of equal width, typically denoted by h = (b-a)/n, where n is the number of subintervals.

Here,

Using the trapezoidal rule, the approximation of the integral is given by:

\(\int_{-4}^4 f(x),dx \)

\( = \frac{1}{2}[(f(-4)+f(-1))(-1-(-4))+(f(-1)+f(0))(0-(-1)) +(f(0)+f(4))(4-0)] \)

\( = \frac{1}{2}[ (4+18)(-1-(-4)) + (18+36)(0-(-1)) + (36+50)(4-0) ]\)

\(\\ = \frac{1}{2}[22(-3)+54(1)+86(4)] \\ = 174\)

Therefore, the correct answer is 174.

Learn more about trapizoidal rule here,

https://brainly.com/question/30401353

#SPJ1

The length of the side of the square in simplest form is 2sqrt(14).

The area of a square is given by the formula \(A = s^2\), where A is the area and s is the length of a side.

We are given that the area of the square is 56 units, so we can set up the equation:

\(56 = s^2\)

To solve for s, we can take the square root of both sides of the equation:

sqrt(56) = \(sqrt(s^2)\)

We can simplify the square root of 56 by factoring it:

sqrt(56) = sqrt(222*7) = 2sqrt(14)

So, we have:

2sqrt(14) = s

This is an improper fraction because the numerator is larger than the denominator. Therefore, the length of the side of the square in simplest form is 2sqrt(14).

For such more questions on side of a square

https://brainly.com/question/23761891

#SPJ11

The swimming pool can hold a volume of 3.456 cubic meters of water.

The volume of water that the swimming pool can hold can be calculated by multiplying the base area of the pool by its depth. In this case, the base area is given as 192 m² and the depth is 1.8 cm.

However, it is important to note that the depth should be converted to meters before performing the calculation.

To convert 1.8 cm to meters, we divide it by 100 (since there are 100 centimeters in a meter):

Depth = 1.8 cm ÷ 100 = 0.018 m

Now we can calculate the volume of water using the formula:

Volume = Base Area × Depth

Substituting the given values, we get:

Volume = 192 m² × 0.018 m = 3.456 m³

Therefore, the swimming pool can hold a volume of 3.456 cubic meters of water.

In the explanation, we use the formula for calculating the volume of a rectangular prism, which is given by multiplying the base area by the depth. We convert the depth from centimeters to meters and then substitute the given values into the formula to find the volume of water that the swimming pool can hold, which is 3.456 cubic meters.

For more such answers on volume

https://brainly.com/question/463363

#SPJ8

Floyd needs 33 matches to make a rectangle with a length of 20 matches.

To find out how many matches Floyd needs to make a rectangle with a length of 20 matches, we can observe a pattern in the given information.

From the given data, we can see that as the length of the rectangle increases by 4 matches, the number of matches used increases by 8. This means that for every additional 4 matches in length, Floyd requires 8 more matches.

Using this pattern, we can calculate the number of matches needed for a rectangle with a length of 20 matches.

First, we need to determine the number of 4-match increments in the length of 20 matches. We can do this by subtracting the starting length of 3 matches from the target length of 20 matches, which gives us 20 - 3 = 17.

Next, we divide the number of 4-match increments by 4 to determine how many times Floyd needs to add 4 matches. In this case, 17 ÷ 4 = 4 with a remainder of 1.

Since Floyd requires 8 matches for each 4-match increment, we multiply the number of increments by 8, which gives us 4 × 8 = 32 matches.

Finally, we add the remaining matches (1 match in this case) to the total, resulting in 32 + 1 = 33 matches needed to reach a length of 20 matches.

For more such questions on rectangle, click on:

https://brainly.com/question/2607596

#SPJ8

Answer:

0.0

Step-by-step explanation:

To find 0.007 divided by 0.498, we can perform the following calculation:

0.007 / 0.498 ≈ 0.0141

Rounding this to the nearest tenth gives:

0.0141 ≈ 0.0

Therefore, the result, rounded to the nearest tenth, is 0.0.

Answer:

0. 074

Step-by-step explanation:

The result of 14/27 divided by 7 in simplest form is 14/189.

To divide 14/27 by 7, rewrite 7 as a fraction with a denominator of 1:

7 = 7/1

Now, perform the division:

= (14/27) ÷ (7/1)

= (14/27) * (1/7)

To multiply fractions, multiply the numerators and denominators:

= (14/27) * (1/7)

= (14 * 1) / (27 * 7)

= 14/189

Therefore, the result is 14/189.

Learn more about Fraction here:

https://brainly.com/question/10354322

#SPJ6

Answer:

A.    

Step-by-step explanation:

y=mx + b where m is the slope and b is the y-intercept.  So substituting 4/5 for m and 5 for b, you get answer A.

Answer:

- 1

-------

-14

Step-by-step explanation:

y,, - y, (-7) - ( -6 ) - 1

--------- = ---------------- = -------

x,, - x, (-9) - ( 5 ) -14

The answer could be either

C or B

The odd one out in the set is "FOQZ." It deviates from the pattern  by the other sets, where the letters are arranged in Alphabetical order.

The set of letters "BCDEGPTV AJK FOQZ IY" seems to follow a specific pattern. If we examine the letters in each group, we can identify a difference that sets "FOQZ" apart from the others.

In the first group "BCDEGPTV," the letters are arranged in alphabetical order. Similarly, in the second group "AJK," the letters are also in alphabetical order. However, when we look at the third group "FOQZ," the letters do not follow alphabetical order.

Based on this pattern, we can conclude that the odd one out in the set is "FOQZ." It deviates from the pattern followed by the other sets, where the letters are arranged in alphabetical order.

It's worth noting that the pattern could be based on different criteria, such as the position of the letters in the alphabet or some other sequence. Without additional information or context, it is difficult to determine the exact pattern or reason for the deviation.

To know more about  Alphabetical order.

https://brainly.com/question/27870403

#SPJ11

The correct answers are A) 7cm, C) 9cm and D) 12cm

The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.

If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.

Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:

⇒  \(\frac{2cm}{7 feet} = \frac{x cm }{yfeet}\)

where y is the length of the line in real life. Solving for y, we get:

⇒  \(y = \frac{7 feet} {2cm} *x\)  

⇒  \(y = 3.5 x feet\)

If we put x = 2cm (given) then, y = 7 feet

For y = 21 feet, the value of x = 6cm.

Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.

So, the lines on the drawing that are greater than 21 feet in real life are:

A) 7cm, C) 9cm, D) 12cm

Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm

To know more about conversion, visit:
https://brainly.com/question/13016491
#SPJ1

The lines y = 5x + 4 and x + 5y = 2 are neither parallel nor perpendicular.

Two lines are considered parallel if they have the same slope. Two lines are considered perpendicular if the product of their slopes is -1.

In this case, the line y = 5x + 4 has a slope of 5 and the line x + 5y = 2 can be rearranged to get y = -(1/5)x + 2/5, which has a slope of -(1/5). The product of these slopes is not equal to -1, so the lines are not perpendicular. Since the slopes are not equal, the lines are not parallel either.

Learn more about parallel or perpendicular lines on:

https://brainly.com/question/7197064

#SPJ1

The computation shows that the examples of values that will give the exact value of 45 will be:

It should be noted the information is incomplete as the options aren't given and not properly written.

In this case, the examples will be given:

An example of value that will give 45 will be:

= ✓25 × ✓81

= 5 × 9

= 45

The other examples will be 6 × 9 which will give 45 and ✓9 × 15 which will be 45.

Learn more about computations on:

brainly.com/question/4658834

#SPJ1

Answer:

1/2=10

Step-by-step explanation:

it depends upon the area of the triwngle