Quadrilateral ABCD is a Parallelogram can be proved by many postulates. The most important three Postulates are:-
1. The two opposite side pairs are parallel.
2. The two opposing side pairs are both congruent.
3. One set of opposite sides is parallel and congruent.
In geometry, you'll frequently be required to provide evidence that a particular shape actually exists. For instance, you can be asked to demonstrate that a quadrilateral is a parallelogram after being shown it. Do not forget that a quadrilateral is a flat, four-sided shape. A quadrilateral with two sets of opposing, parallel sides is referred to as a parallelogram.
A quadrilateral ABCD is a Parallelogram
The five approaches to demonstrate that a quadrilateral is a parallelogram will be discussed first, though. You'll employ one of these five methods, depending on the data you've got to work with.
1. Establish the parallelism of the two pairs of opposite sides.
This one is just the opposite of what a parallelogram is. If you can demonstrate that the quadrilateral satisfies the requirements for a parallelogram, then it is one.
2. Establish the congruence of both pairs of opposite sides.
There will always be two opposite pairs of parallel sides in a quadrilateral if both pairs of opposite sides are congruent. They measure similarly when objects are congruent.
3. Establish that one pair of opposing sides is parallel and congruent.
The previous procedure and this one are quite comparable. It simply presents the evidence in a different manner. Actually, four toothpicks will work for this experiment. Try it by aligning two toothpicks in a parallel but opposing direction. Now join these two toothpicks to the other two toothpicks at both ends. You'll see that your second pair of toothpicks will always be parallel, regardless of how you arrange your first set.
Hence, Quadrilateral establish parallelogram.
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4 3/8 + 5 1/2= in fractions
Answer:
9 7/8
Step-by-step explanation:
1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.
2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.
3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.
Hi
Please help on question asap if the answer is correct I'll rate you five stars a thanks and maybe even brainliest!
What do you notice about the values?
0.9 amps ÷0.03v=30 ohms.
1.9amps÷0.07v=27.149 ohms
3.1. amps ÷0.10v =31 ohms
3.9. amps ÷ 0.12v =032.5 ohms
5. amps ÷0.15v=33.33 ohms
6.1. amps ÷0.19v=32.1053 ohms
In the given data, current and voltage are directly proportional, while the resistance is constant.
What is the relationship between current and voltage?The relationship between the voltage, current, and resistance in an electric circuit is described by Ohm's Law.
The law states that the voltage across a circuit is directly proportional to the current flowing in the circuit.
V ∝ I
V = IR
where;
R is the resistance, the proportionality constantFrom the given data set we can see that for each division of current by voltage we have almost a constant value of 30 ohms.
Thus, if we observe the values given in the data set, we can conclude that;
current and voltage are directly proportional, while the resistance is constant.
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At the farmers' market, Tom bought 11/12 of a pound of string beans and 1/2 of a pound of
lima beans. How many more pounds of string beans did Tom purchase?
Write your answer as a fraction or as a whole or mixed number.
pounds
PLEASE HELP WITH THIS! PLEASE! SURFACE AREA. I HAVE NO CLUE!!
Answer: 626 yd^2
Step-by-step explanation: First you need to split the figure into 2 rectangular prisms (see attached image). The tallest rectangular prism has a length of 12 yd, a width of 3 yd, and a height of 11 yd. The shorter one has a length of 12yd, a width of 4 yd, and a height of 4 yd. The surface area equation is SA=2(wl+hl+hw). First solve for the taller rectangular prism. SA=2(3x12+11x12+11x3). SA=2(36+132+33). SA=2(201). SA=402 yd^2. Now solve for the smaller rectangular prism. SA=2(4x12+4x12+4x4). SA=2(48+48+16). SA=2(112). SA=224 yd^2. Lastly, add both values together. 402+224=626 yd^2.
WhaYou is 1/5 divided by 2/6
I just need someone to draw the tree diagram for the picture below not to much
According to the information, there are thousands of different lunch options in this restaurant.
How to calculate the number of different lunches in the restaurant?To calculate the number of different lunches in the restaurant we must carry out the following mathematical procedure. We must multiply the different options as shown below:
4 green options x 5 protein options x 8 vegetable options x 4 extra options x 6 topping options = 4 x 5 x 8 x 4 x 6 = 4,800 different lunch options.
Based on the above, we can infer that 4,800 different lunch options can be created with the available ingredients.
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Ali has X paintings He buys two more paintings.
How many Paintings does he now have?
Answer:
X+2
Hope this helps
Which equation choice could represent the graph shown below?
1) F(x) = (x - 4)(x + 1)(x - 6)
2) F(x) = (x - 4)(x - 1)(x - 6)
3) F(x) = (x - 4)(x - 1)(x + 6)
4) F (x) = (x + 4(x - 1)(x - 6)
The algebraic equation of the cubic function set on Cartesian plane is f(x) = (x + 6) · (x - 1) · (x - 4). (Correct choice: 3)
What equation does represent a cubic function?
In this problem we find the representation of a cubic function set on Cartesian plane, whose definition as algebraic equation is shown below:
f(x) = a · (x - r₁) · (x - r₂) · (x - r₃)
Where:
a - Lead coefficient.r₁, r₂, r₃ - Roots of the polynomial.Graphically speaking, the roots of the polynomials are the points of the curve on x-axis. If we know that a = 1, r₁ = - 6, r₂ = 1 and r₃ = 4, then the algebraic equation of the cubic function is:
f(x) = (x + 6) · (x - 1) · (x - 4)
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Answer:
3) f(x) = (x - 4)(x - 1)(x + 6)
Step-by-step explanation:
The x-intercepts of a function are the points at which the curve crosses the x-axis, so when f(x) = 0.
From inspection of the given graph, the curve crosses the x-axis at:
x = -6x = 1x = 4According to the Factor Theorem, if f(x) is a polynomial and f(a) = 0, then (x - a) is a factor of f(x).
Therefore, as f(x) = 0 when x = -6, x = 1 and x = 4, then (x + 6) and (x - 1) and (x - 4) are factors of the polynomial.
Therefore, the equation of the function is:
f(x) = (x - 4)(x - 1)(x + 6)One of the authors received a credit card bill for $2,559, but it included a charge of $1,825 th
values of the absolute and relative errors.
The value of the absolute error is $
The value of the relative error is%. (Round to the nearest integer as needed)
The absolute error is $1825, the relative error is 2
What is an absolute and relative error?An absolute error is a determinant of how large an error is. A relative error defines how good or bad an error is.
The formula for determining an absolute error is;
Absolute error = measured value - actual valueThe formula for determining a relative error is:
Relative error = absolute error ÷ actual valueFrom the parameters given:
The absolute error can be computed as:
Absolute error = 2559 - (2559 - 1825)
Absolute error = 2559 - 734
Absolute error = $1825
The relative error = 1825 ÷ 734
The relative error = 2.4
The relative error ≅ 2 (as an integer)
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which cellphone srvice provider was the first to be established in south africa
The first cellphone service provider to be established in South Africa was Vodacom. Vodacom was launched on April 1, 1994, and it became the country's first cellular network operator.
The company was a joint venture between Telkom, the national telecommunications company of South Africa, and Vodafone, a global telecommunications giant.
Vodacom introduced the GSM network to South Africa, providing mobile voice and data services to customers across the country. Its launch marked a significant milestone in the telecommunications industry in South Africa, as it brought mobile communication to the masses and revolutionized the way people connect and communicate.
Since its inception, Vodacom has played a pivotal role in the development of the telecommunications sector in South Africa. It has continually expanded its network coverage, introduced innovative services, and played an active role in bridging the digital divide in the country.
Today, Vodacom remains one of the leading mobile network operators in South Africa, providing a wide range of mobile services to millions of customers.
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The probable question may be:
Which cellphone service provider was the first to be established in south africa
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The value of side TS is,
⇒ TS = 28
First, we are going to divide the figure and named new points X and Y as:
Now, we know that TS is the sum of TX and XS.
TS = TX + XS
Additionally, TX has the same length of HJ, so:
TX = HJ = 14
Now, we want to know the length of YK, and we can calculate it using the following equation:
LK = LY + YK
LY = HJ,
so, LY = 14
And, 42 = 14 + YK
42 - 14 = YK
28 = YK
Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:
XS = YK/2
XS = 28/2
XS = 14
Therefore, TS is equal to:
TS = TX + XS
TS = 14 + 14
TS = 28
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Which of the following is an example of a statistical experiment?
A Twenty people in a neighborhood are asked if they want more streetlights on the street.
OB. More streetlights are installed on one street and people are then asked if they like the change.
OC. The number of accidents on the street is compared to last year's rate.
OD. People are asked to call a number to comment about the need for new streetlights.
Answer:
B. More streetlights are installed on one street and people are then asked if they like the change.
Step-by-step explanation:
An experiment is a type of research method that involves manipulating one or more variables and measuring their effects on other variables. In this case, the experiment is to change the color of the product packaging and see how many people like the change. This is because the outcome of the experiment (the number of people who like the change) depends on chance and can be measured using numerical data. The other options are not experiments, but surveys or observations. Surveys involve asking people questions and collecting their opinions or preferences. Observations involve watching and recording people's behavior or reactions without interfering with them.
The box plots show the data distributions for the number of customers who used a coupon each hour for two days of a store sale. What is the difference of the medians? 0 2 4 7
The difference of medians is given as follows:
2.
What does a box and whisker plot shows?A box and whisker plots shows these five metrics from a data-set, listed and explained as follows:
The minimum non-outlier value.The 25th percentile, representing the value which 25% of the data-set is less than and 75% is greater than.The median, which is the middle value of the data-set, the value which 50% of the data-set is less than and 50% is greater than%.The 75th percentile, representing the value which 75% of the data-set is less than and 25% is greater than.The maximum non-outlier value.The median for each day is given as follows:
Day 1: 6.Day 2: 8.Hence the difference is given as follows:
8 - 6 = 2.
Missing InformationThe box plot is given by the image presented at the end of the answer.
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can somebody please help me with this asap!
The diameter of the second pile of phosphate is 53.5 ft.
We have,
Conveyor belt:
Cone shape:
Diameter = 48.6 ft
Radius = D/2 = 24.3 ft
Height = 15.3 ft
Volume.
= 1/3 x π x r² x h
= 1/3 x 3.14 x 24.3 x 24.3 x 15.3______(1)
Shorter conveyor belt:
Cone shape:
Diameter = D
Height = (15.3 - 2.7) = 12.6 ft
Volume.
= 1/3 x π x (D/2)² x h
= 1/3 x 3.14 x (D/2)² x 12.6_______(2)
Since (1) and (2) are equal.
24.3 x 24.3 x 15.3 = (D/2)² x 12.6
(D/2)² = 717.02
D²/4 = 717.02
D² = 717.02 x 4
D² = 2868.09
D = 53.55
D = 53.5 ft
Thus,
The diameter of the second pile of phosphate is 53.5 ft.
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22. Which of the following is NOT a rational expression?
O(x+3)(2x-1)
x+3
O3x²+3x
4x+5
3x+4√x-7
2x+2
2x²-3x³+5
5x
The correct expression which is not a rational expression,
⇒ (x+3)(2x-1) / (x+3)
We have to given that;
All the expressions are,
⇒ (x+3)(2x-1) / (x+3)
⇒ (3x²+3x) / (4x+5)
⇒ (3x+4√x-7) / (2x+2)
⇒ (2x²-3x³+5) / 5x
Since, A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.
Hence, We can simplify all the expressions as,
⇒ (x+3)(2x-1) / (x+3)
⇒ (2x - 1)
Hence, It is not a rational expression.
⇒ (3x²+3x) / (4x+5)
⇒ 3x (x + 1) / (4x + 5)
Hence, It is a rational expression.
⇒ (3x+4√x-7) / (2x+2)
⇒ (3x + 4√x - 7) / 2 (x + 1)
Hence, It is a rational expression.
⇒ (2x²-3x³+5) / 5x
Hence, It is a rational expression.
Thus, The correct expression which is not a rational expression,
⇒ (x+3)(2x-1) / (x+3)
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Gabe learns more than just
math in Mrs. Zemla's class. Today he
learned that buying a car is a bad
investment because a car's value decreases
each year. So when Gabe was looking to
buy a 2024 Porsche Boxster for $54792,
he also reasearched the projected resale
value of the vehicle. He found that the
vehicle is expeced depreciate 19% each
year after the car is purchased. What is
the expected vaule of the car 7 years after
it was purchased?
The expected value of the car 7 years after it was purchased is $47,029.12.
To solve this problem, we need to calculate the expected value of the car after 7 years. To do this, we need to use the formula for calculating the value of a depreciating asset:
Value after n years = Initial Value - (Initial Value × (Depreciation Rate/100)×n)
In this case, the initial value of the car is $54792, the depreciation rate is 19%, and n = 7. Thus, the expected value of the car 7 years after it was purchased is:
Value after 7 years = 54792 - (54792 × (19/100)×7)
Value after 7 years = 54792 - (54792 × 0.19×7)
Value after 7 years = 54792 - 7762.88
Value after 7 years = $47,029.12
Therefore, the expected value of the car 7 years after it was purchased is $47,029.12.
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Find the amount accumulated after
investing a principle P for t years at an
interest rate compounded k times per year.
P = $40,500 r = 3.8% t = 20 k = 12
Hint: A = P(1 + £)kt
A = $[?]
The solution is: the amount accumulated after investing a principle P for t years at an interest rate compounded k times per year is $86496.26.
Here, we know,
The whole sum borrowed (or invested), exclusive of interest and dividends.
We have,
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
The formula for the amount A accumulated after investing a principle P for t years at an annual interest rate r compounded k times per year is:
A = P * (1+r / k)^kt
given that,
P = $40,500 r = 3.8% t = 20 k = 12
Substituting the given values into this formula, we have:
A = $40,500 * (1 + 0.038 / 12)^12*20
A = $40,500 * 2.1357
A = $86496.2599
A = $86496.26 (rounded to the nearest cent)
Therefore, the amount accumulated after investing a principle P for t years at an interest rate compounded k times per year is $86496.26.
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Your brain needs caffeine! You decide to walk from home to the coffee shop located at point (-8,-5). What coordinate would you be standing on if you stood on a point “K” so that it directed the line segment in a ratio of 5:2?
The coordinates you would be standing on would be coordinate (-5.71, -3.57).
How to calculate the coordinatesTo discover the arrangement of point "K" that partitions the line section interfacing the beginning point to the coffee shop in a proportion of 5:2, we are able to utilize the concept of the area equation.
We should expect the starting point to be meant as A with orchestrates (- x1, - y1), and the café is implied as B with works with (- x2, - y2). The ratio of 5:2 suggests that segment AB is divided into two parts and five parts, each accounting for 7 percent of the length.
The x-direction of point K can be determined as:
xK = (5 * x2 + 2 * x1)/7
Basically, the y-direction of point K can be determined as:
yK = (5 * y2 + 2 * y1) / 7
Stopping within the arranges of the coffee shop (-8, -5) as (-x2, -y2) and accepting the beginning point as the beginning (0, 0), we have:
xK = (5 * (-8) + 2 * 0) / 7 = -40/7 ≈ -5.71
yK = (5 * (-5) + 2 * 0) / 7 = -25/7 ≈ -3.57
Hence, in case you stood on point K, you'd be around at coordinate (-5.71, -3.57).
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Identify one example of each angle pair in the diagram to the right.
Alternate exterior angles are ∠9 and (∠1 + ∠2)
Consecutive interior angles are ∠7 and ∠4
Consecutive exterior angles are ∠9 and ∠∠3
Vertical angles are ∠2 and ∠5
Linear pairs are ∠7 and ∠8
We have,
Alternate exterior angles: Pairs of angles on opposite sides of a transversal line, formed by two parallel lines, and located outside the intersected lines.
Consecutive interior angles: Pairs of angles on the same side of a transversal line, formed by two parallel lines, and located between the intersected lines.
Consecutive exterior angles: Pairs of angles on the same side of a transversal line, formed by two parallel lines, and located outside the intersected lines.
Vertical angles: Pairs of non-adjacent angles formed by the intersection of two lines, sharing the same vertex and having equal measures.
Linear pair: A pair of adjacent angles formed by the intersection of two lines, sharing a common side, and whose measures add up to 180 degrees.
So,
Alternate exterior angles
= ∠9 and (∠1 + ∠2)
Consecutive interior angles
= ∠7 and ∠4
Consecutive exterior angles
= ∠9 and ∠∠3
Vertical angles
= ∠2 and ∠5
Linear pair
= ∠7 and ∠∠8
Thus,
Alternate exterior angles are ∠9 and (∠1 + ∠2)
Consecutive interior angles are ∠7 and ∠4
Consecutive exterior angles are ∠9 and ∠∠3
Vertical angles are ∠2 and ∠5
Linear pairs are ∠7 and ∠8
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This may be hard to put together, but I need help with an angle equation. I'm looking for example equations and how to do these types of equations. *please note that this equation is completely random and probably ends with an ugly number. it's just an example of a type of problem*
Example: (2x - 4) x=7 so (2x (x=7) - 4) =18
Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $22,000 over the next 3 years. What amount must be deposited quarterly into an account that earns 4.7% interest, compounded quarterly, in order to reach your goal? Round your answer to the nearest cent, if necessary.
The initial deposit needed for the account is given as follows:
$19,257.37.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
[tex]A = 22000, t = 3, r = 0.0447, n = 4[/tex]
Hence the initial deposit P is obtained as follows:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]22000 = P\left(1 + \frac{0.0447}{4}\right)^{4 \times 3}[/tex]
1.142657P = 22000
P = 22000/1.142657
P = $19,257.37.
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The graph below displays a fire department's
response time, which measures the time from when
the alarm is sounded at the firehouse to the time the
first fire engine leaves the station.
Fire Department Response Times
0.4
Relative Frequency
10
02
0
10
20 30 40 50 60 70 80 90
Response Time (Seconds)
Which of the following correctly describes the shape of
the distribution?
uniform
skewed left
skewed right
roughly symmetric
The correct description of the shape of the distribution is D. Roughly Symmetric.
What is a symmetric distribution ?Symmetric distribution is an often-referenced term in statistics, representing a type of probability with data segments evenly dispersed around the mean. This denotes the perfect mirror image of the right and left halves when the distribution is split; arriving at an equal size and shape on either side when drawn at the midpoint of the line.
Looking at the distribution of a fire department's response time, we can see that the distribution is roughly symmetric because the values on the left seem to match those on the right.
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Write an expression to represent: 6 times the difference of 5 and x
Answer:
6 * (5 - x)
Step-by-step explanation:
This expression calculates the difference between 5 and x, and then multiplies it by 6. The difference is obtained by subtracting x from 5, and then the entire result is multiplied by 6.
A cruise ship can cover 19 nautical miles in 437 minutes. How many nautical miles will it travel in 345 minutes?
The cruise ship will travel approximately 15 nautical miles in 345 minutes.
How did we get the value?Use a proportion to solve this problem. Let "d" be the number of nautical miles the cruise ship will travel in 345 minutes. Then:
19 nautical miles / 437 minutes = d nautical miles / 345 minutes
To solve for "d", cross-multiply:
19 nautical miles x 345 minutes = d nautical miles x 437 minutes
Then, divide both sides by 437 minutes to isolate "d":
d nautical miles = (19 nautical miles x 345 minutes) / 437 minutes
Simplifying this expression, we get:
d nautical miles = 15 nautical miles (rounded to the nearest whole number)
Therefore, the cruise ship will travel approximately 15 nautical miles in 345 minutes.
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At a football game, a vender sold a combined total of 233 sodas and hot dogs. The number of hot dogs sold was 51 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
The vendor sold 142 sodas and 91 hotdogs.
According to the question:
The vendor sold 233 sodas and hotdogs combined
The number of hot dogs sold was 51 less number of sodas sold
To find:
Number of sodas sold(S)
Number of hotdogs sold(H)
From the question, it is clear that:
S + H = 233 ...(i)
S - H = 51 ...(ii)
These two are simultaneous linear equations.
Adding equations (i) and (ii):
S + H + S - H = 233 + 51
2S = 284
S = 284/2
S = 142
Substitute this value of S in equation (i):
142 + H = 233
H = 233 - 142
H = 91
Therefore, the vendor sold 142 sodas and 91 hotdogs.
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Part of the population of 5,250 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 8 of them are infected. How many elk are likely to be infected? Based on the sample, there will likely be infected elk in the wildlife preserve.
The likely population of the infected elk in the wildlife preserve is 840.
What is the likely population of the infected elk?A sample is a smaller group of the population. A sample is a representation of the population.
The fraction of infected elks in the sample to the total sample would be the same of the infected elks in the population to the total population of the elks.
Population of the infected elk = (infected elks in the sample / total sample) x number of elks in the preserve
(8/50) x 5250
= 0.16 x 5250 = 840
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ill mark brainliest !
Answer:
Since the line is vertical and passes through the point (3, -5), it is a vertical line with undefined slope.
Step-by-step explanation:
the martins bought a condominium for $85,000. assuming that the value of the condo will appreciate at most 5% a year, how much will the condo be worth in 5 years?
Answer:
Step-by-step explanation:
Answer:181,250
Step-by-step explanation:
Basically, the cost would go up 5 percent, and you’re asking how much it would go up in 5 years. So 5x5=25, so you’d multiply 145,000 by 25%, which is 36,250. So, you’d add that to 145,000 which would get you 181,250.
(b) The co-ordinates of three points are A(7, 4), B(-1, -2) and C(3t, 5-4t). (i) Find the value of t if the three points are collinear.
Answer:
Step-by-step explanation:
To determine the value of t if the three points A(7, 4), B(-1, -2), and C(3t, 5-4t) are collinear, we can use the concept of slope. If the points are collinear, the slopes between any two pairs of points should be equal.
The slope between points A and B is given by:
m₁ = (y₂ - y₁) / (x₂ - x₁)
= (-2 - 4) / (-1 - 7)
= (-6) / (-8)
= 3/4
Now, let's calculate the slope between points B and C:
m₂ = (y₂ - y₁) / (x₂ - x₁)
= (5 - (-2)) / (3t - (-1))
= (7) / (3t + 1)
Since the points are collinear, the slopes m₁ and m₂ should be equal. Therefore, we can set up the equation:
3/4 = 7 / (3t + 1)
To solve for t, we can cross-multiply and solve the resulting equation:
4(7) = 3(3t + 1)
28 = 9t + 3
25 = 9t
t = 25 / 9
Therefore, the value of t that makes the points A(7, 4), B(-1, -2), and C(3t, 5-4t) collinear is t = 25/9.
Answer:
6/7
Step-by-step explanation:
If the three points are collinear, then the slope of the line passing through any two of the points should be the same as the slope of the line passing through the other two points.
Let's find the slope of the line passing through points A and B:
slope AB = (y2-y1)/(x2-x1)
= (-2-4)/(-1-7)
= -6/-8
= 3/4
Now let's find the slope of the line passing through points B and C:
slope BC = (y2-y1)/(x2-x1)
= (5-4t-(-2))/(3t-(-1))
= (7-4t)/(3t+1)
Since the three points are collinear, slope AB = slope BC:
3/4 = (7-4t)/(3t+1)
Cross-multiplying and simplifying:
12t + 4 = 28-16t
28t = 24
t = 24/28
t = 6/7
Therefore, the value of t is 6/7 if the three points A, B, and C are collinear.
Can someone please answer and provide an explanation for these problems?
The area of the sector is: 21) 177.0 cm² 22) 58.6 in.²
The missing sides are: 23) 12 24) 8
How to Find the Area of a Sector of a Circle?The area of the sector of any circle is given as:
Area = ∅/360 * πr², where r is the radius.
21. ∅ = 120°
r = 13 cm
Substitute:
Area = 120/360 * π * 13² = 177.0 cm²
22. ∅ = 105°
r = 8 in.
Substitute:
Area = 105/360 * π * 8² = 58.6 in.²
Since the lines appear tangents in the circles given, then the triangle formed is a right triangle, therefore, we will apply the Pythagorean Theorem in each case:
23. Missing side = √[(9 + 6)² - 9²]
Missing side = 12
24. Let the missing side be x. Therefore, we have:
12 + x = √(16² + 12²)
12 + x = 20
12 + x - 12 = 20 - 12
x = 8
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