Unit 6 similar triangles homework 5 parallel lines and proportional parts

Answer:

Since triangle ABC is similar to triangle FGH, their angle measures are proportional. We can use the ratios of their angle measures to find the missing angle measures.

Let's call the missing angle measures x, y, z, and w, where x is m∠F, y is m∠G, z is m∠H, and w is m∠C.

From the given information, we have:

m∠A / m∠F = 22 / x

m∠B / m∠G = 75 / y

Since m∠A + m∠B + m∠C = 180 degrees, we can write:

w = 180 - (m∠A + m∠B)

m∠H / m∠C = z / w

Now we can use the ratios to find the missing angle measures:

x = 22 / (22 / x) = 22

y = 75 / (75 / y) = 75

z = m∠H / (m∠H / z) = m∠H

w = 180 - (22 + 75) = 83

So, the missing angle measures are:

m∠F = 22 degrees

m∠G = 75 degrees

m∠H = m∠H (unknown)

m∠C = 83 degrees

The probability of drawing the red 5 is an example of the event shown in option E R'. E' = 1-Pr(R)-1-Pr(E)

Probability in mathematics is the process of finding chances of an event to happen.

Given that, a deck of card have,

Red cards = 1,2,3

Blue cards =1,2,3,4,5,6

Pr(R) =  Drawing a red card = 3/9 = 1/3

Pr(B) = Drawing a blue card = 6/9 = 2/3

Pr(E) = Drawing an even card = 4/9

Pr(O) = Drawing an odd number card = 5/9

Probability of drawing the red 5 = P(red 5) = 1/9

From the options, we have :-

(A) R or O = Pr(R) + Pr(O)  = 1/3 + 1/9 = 8/9 ≠ 1/9

(B) B and O = Pr(B) × Pr(O) =  2/3 × 5/9 = 10/21 ≠ 1/9

(D) R and O = Pr(R) + Pr(O) = 1/3 × 5/9 = 5/27 ≠ 1/9

(E) R'. E' = 1-Pr(R)-1-Pr(E) = 1-1/3 =2/3- 1-4/9 =5/9

= 2/3-5/9

= 1/9

Hence, the probability of drawing the red 5 is an example of the event shown in option E R'. E' = 1-Pr(R)-1-Pr(E)

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Answer:

Step-by-step explanation:

[tex]25-(2x-9)^{2}[/tex]=[tex](25-2x+9)(25+2x-9)=(34-2x)(16+2x)=4(17-x)(8+x)[/tex]

A function that represents exponential growth include the following: C) y = 3(1.5)^x.

Mathematically, an equation which can be used to model an exponential growth rate is given by this mathematical expression:

A(t) = P(1 + r)^{t}

Where:

Based on the exponential functions provided above, we can reasonably infer and logically deduce that the required exponential growth rate function is given by;

y = 3(1.5)^x

1 + r = 1.5

r = 1.5 - 1

Rate of change, r = 0.5.

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Using the formula, we can conclude that the 15th term in the following sequence is 59.

A progression or sequence of numbers known as an arithmetic sequence maintains a consistent difference between each succeeding term and its predecessor.

The common difference in that mathematical progression is the constant difference.

n: The method for determining the nth term is used to locate a particular term in an arithmetic series.

Step 1:

An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.

Therefore, enter the values a = 2 and d = 3 into the formula to determine the nth term.

So, the formula is:

an = a + (n – 1)d

Now, insert the values as follows:

an = a + (n – 1)d

a15 = 3 + (15 – 1)4

a15 = 3 + (14)4

a15 = 3 + 56

a15 = 59

Therefore, using the formula, we can conclude that the 15th term in the following sequence is 59.

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Correct question:

Find the 15th term in the sequence if a1= 3 and d= 4

The average rate of change from 2020 to 2010 of the median individual income is 157.

The average rate at which one item is changing in relation to another is known as the average rate of change. An average rate of change function, put simply, is a calculation that divides the amount of change in one thing by the corresponding amount of change in another.

The average rate of change is given by the formula:

R = f(b) - f(a) / (b - a)

where, f(b) and f(a) are values of the function at b and a respectively.

Here, the value of the functions are:

f(b) = 31675

f(a) =30105

b = 2020

a = 2010

Substituting the values in the equation we have:

R = (31675 - 30105)/ (2020 - 2010)

R = 1570/10 = 157

Hence, the average rate of change from 2020 to 2010 of the median individual income is 157.

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Answer: 158

Step-by-step explanation: The average rate of change from 2020 to 2010 of the median individual income is 157.

What is average rate of change?

The average rate at which one item is changing in relation to another is known as the average rate of change. An average rate of change function, put simply, is a calculation that divides the amount of change in one thing by the corresponding amount of change in another.

The average rate of change is given by the formula:

R = f(b) - f(a) / (b - a)

where, f(b) and f(a) are values of the function at b and a respectively.

Here, the value of the functions are:

f(b) = 31675

f(a) =30105

b = 2020

a = 2010

Substituting the values in the equation we have:

R = (31675 - 30105)/ (2020 - 2010)

R = 1570/10 = 157

Every point of an open set in R2 is a limit point, but only the boundary points of a closed set are limit points.

Every point of every open set E in R2 is a limit point of E. This is because an open set is characterized by the fact that all of its boundary points are included in the set. Therefore, all of the points in the set are limit points because they are all on the boundary of the set.

For closed sets in R2, the answer is not the same. A closed set is characterized by the fact that it is determined by its boundary points and all of its interior points. Therefore, only the boundary points of a closed set are limit points, while the interior points are not.

Every point of an open set in R2 is a limit point, but only the boundary points of a closed set are limit points.

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The rate of change on a slope graph is 25.

How do you find the rate of change on a slope graph?

The rate of change for a line is the slope, the rise over run, or the change in over the change in. The slope can be calculated from two points in a table or from the slope triangle in a graph.

The average rate of change formula is used to find the slope of a graphed function. To find the average rate of change, divide the change in y-values by the change in x-values.

Given :

Y - variations = 0 , 25 , 50 ,75 , 100 , 125..........

X - variations = 0 , 1 , 2 , 3 , 4 , 5 , 6 .........

Thus , we can formulate the points as,

(0,0) , (1,25) , (2,50) , (3,75) and so on ...

for rate of change of graph with (x1 , y1) and (x2 , y2) as co-ordinate point we know that,

rate of change = (y2-y1)/(x2-x1)

Similarly ,by taking any two points(let (0,0) and (1,25)) from formulated points , we can say that

rate of change = (25-0)/(1-0)

rate of change = 25

Hence , the rate of change on a slope graph is 25.

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There are 5 × 3 = 15 possible ordered pairs. Therefore, n(B × C) = 15.

In mathematics, the Cartesian product is a binary operation that takes two sets and forms a set consisting of all possible ordered pairs of elements from the two sets. The resulting set is often denoted by A × B, where A and B are the two original sets.

Formally, if A and B are two sets, the Cartesian product A × B is defined as:

A × B = {(a, b) : a ∈ A and b ∈ B}

This means that the Cartesian product contains all possible ordered pairs (a, b) where a is an element of A and b is an element of B. For example, if A = {1, 2} and B = {x, y}, then A × B would be {(1, x), (1, y), (2, x), (2, y)}.

The Cartesian product B × C is the set of all ordered pairs (b, c) where b is an element of B and c is an element of C. Since B has 5 elements and C has 3 elements, there are 5 × 3 = 15 possible ordered pairs. Therefore, n(B × C) = 15.

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Answer:

Since we are given the standard deviation of the sample, we can use the formula:

variance = standard deviation^2

Substituting the given value:

variance = 10.3695^2 kg^2

Calculating:

variance ≈ 107.495 kg^2

Therefore, the variance of the weights of the 10 subjects is approximately 107.495 kg^2.

Answer:

  (c)  8

Step-by-step explanation:

You want the x-coordinate of the point where the lines on the graph cross.

The equilibrium point, as the problem statement tells you, is the point where the two lines have the same x- and y-values. That is the point where the lines cross.

The problem statement also tells you that the x-coordinate represent the number of games, in thousands, that will be sold at the price represented by the y-coordinate. By asking for the number of games sold, the question is asking for the x-coordinate of the point where the lines cross.

The lines cross at a grid intersection that is 4 squares right of the y-axis. The label 10 on the 5th square tells you that each square represents 2 (thousands). Hence the x-coordinate of the equilibrium point is ...

  8 . . . . . (thousands of games sold)

The Probability (less than 4) when the spinner is spun once is 0.5, the correct option is D.

When probability is in terms of area or volume or length etc geometric amounts (when infinite points are there), we can use this definition:

E = favorable event

S = total sample space

Then:

P(E) = [tex]\dfrac{A(E)}{A(S)}[/tex]

where A(E) is the area/volume/length for event E, and similar for A(S).

Given that;

Spinner is divide in eight sections that has 3blue, 1 red, 2 purple, 2 yellow

Now,

The coloured spinner is divided into = 8 colour sections

The P event;

=4/8

=1/2

=0.5

Therefore the probability of event will be 0.5.

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The missing side length of the figure is given as follows:

6 cm.

The segment addition postulate is a geometry axiom that states that a segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.

For this problem, we have that:

Hence the missing side length of the figure is obtained as follows:

16 - 10 = 6 cm.

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The number of customers who queued for more than 20 minutes was 11 customers .

The median queuing time was 11 minutes .

The number of customers who queued for more than 20 minutes would be found by the formula :

= Number of customers at 25 minutes - Number of customers at 20 minutes

= 100 - 89

= 11 customers

The median queuing time would be the queuing time at 50 customers which according to the cumulative frequency graph is 11 minutes .

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(a) 0.52, (b) -0.54, (c) 0.68, (d) -0.71, (e) -1.44 - Percentiles for standard normal distribution using z-table.

(a) To find the 71st percentile, we search for the z-score that relates to a combined area of 0.71 to one side of the mean. From the standard typical circulation table, we find that the nearest z-scores are 0.67 and 0.72, with relating areas of 0.7486 and 0.7642, individually. To interject, we utilize the equation:

z = z1 + (z2 - z1) * ((p - p1)/(p2 - p1))

where z1 and z2 are the nearest z-scores in the table, p1 and p2 are the comparing regions, and p is the ideal total region (0.71). Connecting the qualities, we get:

z = 0.67 + (0.72 - 0.67) * ((0.71 - 0.7486)/(0.7642 - 0.7486)) = 0.52

Consequently, the 71st percentile is z = 0.52.

(b) To find the 29th percentile, we search for the z-score that compares to a combined area of 0.29 to one side of the mean. From the standard ordinary conveyance table, we find that the nearest z-scores are - 0.53 and - 0.52, with relating areas of 0.2981 and 0.3050, individually. To add, we utilize the recipe:

z = z1 + (z2 - z1) * ((p - p1)/(p2 - p1))

where z1 and z2 are the nearest z-scores in the table, p1 and p2 are the comparing regions, and p is the ideal total region (0.29). Connecting the qualities, we get:

z = - 0.53 + (- 0.52 - (- 0.53)) * ((0.29 - 0.2981)/(0.3050 - 0.2981)) = - 0.54

Consequently, the 29th percentile is z = - 0.54.

(c) To find the 76th percentile, we search for the z-score that relates to an aggregate area of 0.76 to one side of the mean. From the standard ordinary appropriation table, we find that the nearest z-scores are 0.73 and 0.77, with relating areas of 0.7673 and 0.7794, separately. To interject, we utilize the equation:

z = z1 + (z2 - z1) * ((p - p1)/(p2 - p1))

where z1 and z2 are the nearest z-scores in the table, p1 and p2 are the comparing regions, and p is the ideal total region (0.76). Connecting the qualities, we get:

z = 0.73 + (0.77 - 0.73) * ((0.76 - 0.7673)/(0.7794 - 0.7673)) = 0.68

Consequently, the 76th percentile is z = 0.68.

(d) The 24th percentile compares to a z-score of - 0.71, meaning 24% of the standard ordinary conveyance misleads its left.

(e) The seventh percentile relates to a z-score of - 1.44, meaning 7% of the standard typical conveyance misleads its left.

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The given sum of money in cents as 375 cents.

Money is any item or medium of exchange that is accepted by people for the payment of goods and services, as well as the repayment of loans.

Given that, person has a toonie, a loonie, and three quarters.

1 Toonie = 2 dollars

1 Loonie = 1 dollar

3 quarters = 0.75 dollars

So, sum of money = 2+1+0.75

= 3.75 dollars

1 Toonie = 200 cents

1 Loonie = 100 cents

3 quarters = 75 cents

Sum of money = 200+100+75

= 375 cents

1 Toonie = 8 quarters

1 Loonie = 4 quarters

So, in quarters = 8+4+3

= 15 quarters

Therefore, the given sum of money in cents as 375 cents.

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On expanding the expression, we get -

{x³ - 2x²y + xy² - x²y + 2xy² - y³}

Given is the expression as -

(x - y) (x² - 2xy + y²)

The given expression is -

(x - y) (x² - 2xy + y²)

x {x² - 2xy + y²} - y {x² - 2xy + y²}

x³ - 2x²y + xy² - x²y + 2xy² - y³

Therefore, on expanding the expression, we get -

{x³ - 2x²y + xy² - x²y + 2xy² - y³}

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Answer:

Step-by-step explanation:

a) the probability of having exactly 10 days of precipitation in the month of April

Answer:

3/4

Step-by-step explanation:

Answer:4/7*1/4

trust me >:)

Answer:

3000 liters

Step-by-step explanation:

To calculate the volume of the tin can, we can multiply its dimensions:

Volume = 2m × 1.5m × 1m = 3 cubic meters

Since a liter is equivalent to 0.001 cubic meters, we can convert the volume of the tin can to liters:

Volume (in liters) = 3 cubic meters × 1000 liters/cubic meter = 3000 liters

Therefore, the tin can can hold 3000 liters of kerosene oil.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

The statement that is NOT true about brake drum inside diameter measurements with a brake drum micrometer is B.

If the drum diameter is less than specified, replace the drum. In fact, if the drum diameter is less than the minimum specified limit, the drum can be machined to a larger diameter to restore its proper dimension. This will depend on the manufacturer's recommendations, and the minimum thickness limits of the drum should also be checked to ensure it is within safe tolerances.

                          The other statements are true: A. The drum should be cleaned before measuring the diameter, to avoid errors due to dirt or rust. C. The diameter should be measured at two locations around the drum, usually at the top and bottom of the friction surface, to check for taper or out-of-roundness. D. The drum diameter variation should not exceed 0.035 in (0.009 mm), to ensure proper brake function and minimize vibration or noise.

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Answer:

Step-by-step explanation:

4p + 2 (5p - 4)

Expand:-

Combine like terms (4p + 10p = 14p) :-

-Hope this helps! :)

Answer:

2(7p-4)

Step-by-step explanation:

Answer:

1. is 216

2. 100000

3. 81

Step-by-step explanation:

The “power” of a number indicates how many times the base would be multiplied by itself to reach the correct value.

Step-by-step explanation:

x + 2 > 5

x > 5-2

x> 3.

TO FND THE VALUE OF X

2 IS PART OF THE SOLUTION AND 5 TOO also >

with the absence of > you can not find x since the question will be algebraic.

The selling price of the bicycle is equal to R1,102.

In Mathematics, profit can be defined as a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.

Mathematically, the amount of profit made from selling a bicycle can be calculated by using the following function:

Profit made = Cost price - Selling price

Making selling price the subject of formula, we have:

Selling price = Cost price - Profit made

Selling price = R1489 - R387.

Selling price = R1,102.

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The equation describing the relationship between the elapsed time and the amount of glucose remaining in the bag is: g = 120 - 1.02t

What is an equation ?

In mathematics, an equation is a statement that shows the equality between two expressions containing variables. It is typically written as a combination of numbers, variables, and mathematical symbols, such as addition, subtraction, multiplication, and division.

Here is a table comparing the elapsed time with the amount of glucose given to the patient:

Time (minutes) Glucose remaining in bag (cc)

0 120

1 119.98

2 119.96

3 119.94

4 119.92

... ...

t 120 - 1.02t

The equation describing the relationship between the elapsed time and the amount of glucose remaining in the bag is: g = 120 - 1.02t

where g represents the amount of glucose remaining in the bag in cc and t represents the elapsed time in minutes.

Hence,  The equation describing the relationship between the elapsed time and the amount of glucose remaining in the bag is: g = 120 - 1.02t

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The differential equation for the amount of salt A(t) in the tank at time t is  12 - A(t)/(200 + 3t)  and the amount of salt in the tank when it is full is 290.72 pounds.

To set up a differential equation for the amount of salt A(t) in the tank at time t, we need to determine how the amount of salt changes over time. The rate of change of the amount of salt in the tank is determined by the difference between the rate at which salt flows into the tank and the rate at which salt flows out of the tank.

Since the incoming brine contains 3 pounds of salt per gallon, the rate at which salt flows into the tank is 3 pounds per gallon times 4 gallons per minute, or 12 pounds per minute. Since the mixture flows out of the tank at a rate of 1 gallon per minute, the rate at which salt flows out of the tank is A(t)/V(t), where V(t) is the volume of the mixture in the tank at time t.

Since the volume of the mixture in the tank at time t is the sum of the initial volume and the volume of incoming brine minus the volume of outgoing mixture, we have:

V(t) = 200 + 4t - t = 200 + 3t

Therefore, the rate at which salt flows out of the tank is A(t)/(200 + 3t) pounds per minute. Thus, the differential equation for the amount of salt A(t) in the tank at time t is:

dA/dt = 12 - A(t)/(200 + 3t)

To find the amount of salt in the tank when it is full, we need to find the time t when the tank is full. The tank is full when its volume is 500 gallons, so we have:

200 + 4t - t = 500

Simplifying this equation, we get:

3t = 300

t = 100

Therefore, the tank is full after 100 minutes. To find the amount of salt in the tank when it is full, we can solve the differential equation for A(t) using an appropriate initial condition (i.e., the amount of salt in the tank at t=0):

dA/dt = 12 - A(t)/(200 + 3t)

A(0) = 90

Solving this differential equation, we get:

A(t) = 360 - 270e^(-t/300)

Therefore, the amount of salt in the tank when it is full (i.e., after 100 minutes) is:

A(100) = 360 - 270e^(-1/3)

which is approximately 290.72 pounds.

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Event A: Choosing a student who is a girl

Event B: Choosing a student who is a senior

Therefore, the events are not mutually exclusive because one student can be a girl and a senior at the same time.

Probability is a measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to happen.

The correct equation is:

P (G or S) =  P(G) + P(S) - P(G and S)

= 800/1400 + 300/1400 - 200/1400

= 900/1400

= 9/14

This means that 9 out of 19 students is either a girl or a senior.

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An equation of the line that passes through the points (−4, −7) and (1, −7) is y = -7.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (-4, -7), a linear equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-7) = (-7 - (-7))/(1 - (-4))(x - (-4))

y + 7 = (-7 + 7)/(1 + 4)(x + 4)

y + 7 = 0/5(x + 4)

y + 7 = 0

y = -7.

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