Decide whether ▱ABCD
with vertices A(−2,3), B(2,3), C(2,−1),
and D(−2,−1)
is a rectangle, a rhombus, or a square.
Answers
Answer:
To determine whether a quadrilateral is a rectangle, rhombus or square, you must show that it meets the definition of that shape OR that it has properties that only that shape has.
A rectangle is a quadrilateral with four right angles. Thus, all the angles in a rectangle are equal (360°/4 = 90°). Moreover, the opposite sides of a rectangle are parallel and equal, and diagonals bisect each other.
A rhombus is a quadrilateral with all sides equal in length. The opposite angles are equal in measure. The diagonals bisect each other at right angles.
A square is a quadrilateral with all sides equal in length and all angles equal to 90 degrees4.
To determine whether ▱ABCD with vertices A(−2,3), B(2,3), C(2,−1),and D(−2,−1) is a rectangle, we can check if all angles are right angles or if the diagonals of the parallelogram are congruent.
Step-by-step explanation:
Related Questions
Convert 50 degrees into radians (NEED ASAP)
Answers
Answer:
0.872665
Step-by-step explanation:
Radians = (π / 180) x Degrees
If we put 50 Degrees into our formula we get: (π / 180) x 50 = 0.872664625997165
50 Degrees is not the only number of degrees we have converted to radians. To convert another number of degrees, simply use same formula.
^_^ ^_^
Polygon ABCD is defined by the points A(-4,2), B(-2,4), C(1,3), and D(2,2). Match the coordinates of the points of the transformed polygons to their correct values
Answers
The solutions are:
If polygon ABCD rotates 90 degrees clockwise to generate A′B′C′D′, the coordinates of D′ are (-2, 2), and the coordinates of C′′ are (3, -1), respectively.
If polygon ABCD rotates 180 degrees in a clockwise direction to generate A′′′B′′′C′′′D′′′, A′′′'s coordinates are (4, -2).
If polygon ABCD rotates 270 degrees counterclockwise to generate A′′B′′C′′D′′, B′′'s coordinates are (4, 2).
The movement of a point from its starting location to a new place is referred to as a transformation.
Every point on a shape undergoes transformation when it is altered. Reflection, rotation, dilation, and translation are examples of transformations.
Given The points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2) make up the polygon ABCD.
The new location X' is at (-y, x) if a point X(x, y) is rotated 90 degrees in the opposite direction.
The new location X' is at (y, -x) if a point X(x, y) is rotated 90 degrees clockwise.
The new location X' is at (-x, -y) if a point X(x, y) is rotated 180 degrees clockwise.
The new location X' is at (y, -x) if a point X(x, y) is rotated 270 degrees in the opposite direction.
If polygon ABCD rotates 90 degrees counterclockwise to generate A′B′C′D′, D′'s coordinates are (-2, 2)
If polygon ABCD rotates 90 degrees counterclockwise to generate A′′B′′C′′D′′, the coordinates of C′′ are (3, -1).
If polygon ABCD rotates 180 degrees in a clockwise direction to generate A′′′B′′′C′′′D′′′, A′′′'s coordinates are (4, -2).
If polygon ABCD rotates 270 degrees counterclockwise to generate A′′B′′C′′D′′, B′′'s coordinates are (4, 2).
Learn more about transformation click;
https://brainly.com/question/11709244
#SPJ4
Find the length of the segment indicated below
Answers
The length of line segment AB in the triangle using the midsegment theorem is 64.
What is the length of line segment AB?
The Midsegment Theorem states that "the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side."
From the diagram:
Midsegment = 3x + 5
Third side = 7x + 1
First, we solve for x, using the midsegment theorem:
( 3x + 5 ) = 1/2 × ( 7x + 1 )
Multiply both sides by 2:
2( 3x + 5 ) = ( 7x + 1 )
6x + 10 = 7x + 1
Collect and add like terms:
7x - 6x = 10 - 1
x = 10 - 1
x = 9
Now, we solve for line AB:
Line AB = 7x + 1
Plug in x = 9
Line AB = 7(9) + 1
Line AB = 63 + 1
Line AB = 64
Therefore, the line segment AB is 64.
Learn more about Midsegment Theorem here: brainly.com/question/30066983
#SPJ1
for what values of a and b is the following function continuous at every x?
f(x) = { -1 x ≤ -1
ax -b -1 < x < 3
9 x ≥ 3
find the values of a and b for which the function f continuous at every x.
Answers
The function f(x) is continuous at every x if f(x-) = f(x+) = f(x) for every x. The function is given as: f(x) = { -1 x ≤ -1ax - b - 1 < x < 39 x ≥ 3Now we will find f(x-) and f(x+):f(x-) = lim f(t) t → xf(x+) = lim f(t) t → x-In the above-given function, when x ≤ -1, then f(x) = -1.When -1 < x < 3, then we can say that f(x) = ax - b-1.When x ≥ 3, then f(x) = 9.
Therefore, we have three cases: i) lim f(t) t → -1- = -1 and lim f(t) t → -1+
\(= a - b - 1ii) lim f(t) t → 3-\)\(= a(3) - b - 1 and lim f(t) t → 3+\)\(\\ 9iii) a - b - 1 = 3a - b - 1\)
\(= a(3) - b - 1 and lim f(t) t → 3+\)
\(= 9iii) a - b - 1 = 3a - b - 1\)
For the function f(x) to be continuous at every x, the following two conditions must be satisfied: 1) f(-1) = f(-1+)
\(= f(-1-)2) f(3)\)
= f(3+) \(= a(3) - b - 1 and lim f(t) t → 3+\)
\(= f(3-)\)
The first condition, f(-1) = f(-1+)
= f(-1-) is satisfied because when x ≤ -1,
then f(x) = -1.
When -1 < x < 3, we have f(-1+) = a - b - 1 and
\(f(-1-) = -1\)
For\(f(-1) = f(-1+),\)
\(a - b - 1 = -1\)
\(= > a - b = 0\)
\(= > a = b (1)\)
When x ≥ 3,
we have f(3) = 9.f(3-)
= a(3) - b - 1 and f(3+)
= 9 For f(3)
= f(3+), 9
= 9 and no condition arises.
Now we will check the continuity at
\(x = -1+.a - b - 1 = -1 (f(-1+)= f(-1)) = > a - b = 0\)
(from equation \(1) = > a = b\) The left-hand derivative is
\(lim f(t) t → -1- = -1.\)
The right-hand derivative is
\(lim f(t) t → -1+ = a - b - 1 = a - a - 1 = -1.\)
The right-hand limit is not equal to the left-hand limit; hence the derivative does not exist at x = -1. Therefore, the function is continuous at every x if a = b and a - b - 1 = 0.The values of a and b for which the function f is continuous at every x are a = b and a - b - 1 = 0.
To know more about function visit:
https://brainly.com/question/30721594
#SPJ11
Can somebody help please?
Also there are 10 people :3
Answers
Answer:
12
Step-by-step explanation:
adding them altogether
The selected accounts from the Blue Door Corporation's accounting records are presented below for the year ended December 31, 2015: Advertising expense $ 55,000 Interest revenue $ 30,000 Common stock 250,000 Inventory 67,000 Cost of goods sold 1,085,000 Rent revenue 24,000 Depreciation expense 125,000 Retained earnings 535,000 Dividends 150,000 Salaries and wages expense 675,000 Freight-out 25,000 Sales discounts 8,500 Income tax expense 70,000 Sales returns and allowances 41,000 Insurance expense 15,000 Sales revenue 2,400,000 Interest expense 70,000 Prepare a multiple-step income statement.
Answers
Solution :
Sales Revenue
Sales $ 2,400,000
Less:
Sales discount $ 8,500
Sales returns and allowances $ 41,000
$ 48,500
Net Sales $ 2,350,500
Cost of goods sold $ 1,085,000
Gross profit $ 1,265,500
Operating expense :
Salaries expenses $ 675,000
Advertising expenses $ 55,000
Depreciation expense $ 125,000
Freight expense $ 25000
Insurance expense $ 15,000
Total operating expenses $ 895,000
Operating income $ 370,500
Non operating income
Interest revenue $ 30,000
Rent revenue $ 24,000
$ 54,000
Non Operating expenses :
Interest expense $ 70,000
Income before income tax $ 354,500
Income tax expense $ 70,000
Net income $ 284,500
How do you use numerical expressions to solve real-world problems? Write an (select) to model the situation. Simplify by using the (select) . First perform operations in (select) , then find the value of each (select) , (select) from left to right, and finally (select) from left to right.
Answers
There are numerοus real-life situatiοns which are easily sοlved with the help οf numerical expressiοns such as when we need tο find hοw much discοunt is applied tο a prοduct, tο find the area οf a rectangular park, tο find the amοunt οf ingredients required tο bake a cake and many mοre.
What are numerical expressiοns?We knοw that numerical expressiοns are the expressiοns that cοntains numbers and οperatiοns namely additiοn, subtractiοn, multiplicatiοn and divisiοn.
Nοw, numbers are required in οur life tο make it easier.
Fοr e.g. If we need tο find the number οf candies which are tο be distributed amοng the class οf 50 students, where each student get 2 candies each.
We dο nοt start cοunting the numbers but instead use numerical expressiοns as,
Number οf students in the class = 50
Number οf candies each student gets = 2
Tοtal number οf candies required = 50 × 2 =100.
Sο, we see that in place οf using the time-cοnsuming methοd οf cοunting, we used numerical expressiοns which saved the time and was easy tο apply.
In this way, there are numerοus real-life situatiοns which are easily sοlved with the help οf numerical expressiοns such as when we need tο find hοw much discοunt is applied tο a prοduct, tο find the area οf a rectangular park, tο find the amοunt οf ingredients required tο bake a cake and many mοre.
Learn more about numerical expressions on:
https://brainly.com/question/28491899
#SPJ1
Quality control finds on average that 0.026% of the items from a certain factory are defective. One month, 4000 items are checked How many items are expected to be defective? Round your answer to the nearest whole number
help quick pls<33
Answers
The number of items that are expected to be defective is; 1
What is the number of defective Items?We are told that on average that 0.026% of the items from a certain factory are defective.
Now, if 4000 items are checked, the number of defective items would be gotten by multiplying the percentage of defective items by the number of items checked.
Thus;
Number of defective items = 0.026% * 4000 = 1.04 approximately 1
Read more about defective items at; https://brainly.com/question/2500024
when rounding to the nearest hundred what is the greatest whole number that rounds to 500?
Answers
Answer:
499
Step-by-step explanation:
Suppose that a batch of 10 items contains 3 that are defective and 7 that are not defective. If X is the number of defective items in a randomly drawn sample of 3 items from the batch. Find P(X > 1). 11/60 23/60 37/60 49/60
Answers
In a batch of 10 items contains 3 that are defective and 7 that are not defective. If X is the number of defective items in a randomly drawn sample of 3 items from the batch then P(X > 1) = 37/60.
To find the probability that X is greater than 1, we need to calculate the probability of getting 2 or 3 defective items in the sample of 3 items.
First, let's find the probability of getting exactly 2 defective items.
We can choose 2 defective items out of the 3 in the batch in (3 choose 2) = 3 ways. The probability of choosing a defective item is (3/10), and the probability of choosing a non-defective item is (7/10).
Therefore, the probability of getting 2 defective items is (3 choose 2) * (3/10)^2 * (7/10)^1.
Next, let's find the probability of getting exactly 3 defective items.
We can choose all 3 defective items in (3 choose 3) = 1 way. The probability of choosing a defective item is (3/10), and the probability of choosing a non-defective item is (7/10).
Therefore, the probability of getting 3 defective items is (3 choose 3) * (3/10)^3 * (7/10)^0.
To find the probability that X is greater than 1, we add the probabilities of getting exactly 2 defective items and exactly 3 defective items:
P(X > 1) = P(X = 2) + P(X = 3)
= (3 choose 2) * (3/10)^2 * (7/10)^1 + (3 choose 3) * (3/10)^3 * (7/10)^0
Calculating the values, we find:
P(X > 1) = 0.377
Therefore, the correct answer is 37/60.
To know more about probability refer here:
https://brainly.com/question/31828911
#SPJ11
scientific research on popular beverages consisted of 65 studies that were fully sponsored by the food industry, and 35 studies that were conducted with no corporate ties. of those that were fully sponsored by the food industry, 13 % of the participants found the products unfavorable, 22 % were neutral, and 65 % found the products favorable. of those that had no industry funding, 36 % found the products unfavorable, 17 % were neutral, and 47 % found the products favorable. what is the probability that a participant selected at random found the products favorable? if a randomly selected participant found the product favorable, what is the probability that the study was sponsored by the food industry? if a randomly selected participant found the product unfavorable, what is the probability that the study had no industry funding?
Answers
To find the probability that a participant selected at random found the products favorable, we can calculate the weighted average of the favorable responses from both the industry-sponsored and non-industry-funded studies.
For the industry-sponsored studies, 65% of participants found the products favorable, and for the non-industry-funded studies, 47% found the products favorable. Since there were 65 industry-sponsored studies and 35 non-industry-funded studies, the overall probability is:
(65/100) * 0.65 + (35/100) * 0.47 = 0.4225 + 0.1645 = 0.587 or 58.7%
If a randomly selected participant found the product favorable, we can use Bayes' theorem to calculate the probability that the study was sponsored by the food industry given this favorable response. The calculation is:
P(Industry-sponsored | Favorable) = (P(Favorable | Industry-sponsored) * P(Industry-sponsored)) / P(Favorable)
P(Favorable | Industry-sponsored) = 0.65
P(Industry-sponsored) = 65/100
P(Favorable) = 0.587
P(Industry-sponsored | Favorable) = (0.65 * (65/100)) / 0.587 ≈ 0.719 or 71.9%
Similarly, if a randomly selected participant found the product unfavorable, we can use Bayes' theorem to calculate the probability that the study had no industry funding given this unfavorable response. The calculation is:
P(No industry funding | Unfavorable) = (P(Unfavorable | No industry funding) * P(No industry funding)) / P(Unfavorable)
P(Unfavorable | No industry funding) = 0.36
P(No industry funding) = 35/100
P(Unfavorable) = 1 - P(Favorable) = 1 - 0.587 = 0.413
P(No industry funding | Unfavorable) = (0.36 * (35/100)) / 0.413 ≈ 0.305 or 30.5%
To learn more about Bayes' theorem - brainly.com/question/29598596
#SPJ11
An auditing software can identify 63.7% of misreporting issues in accounting ledgers. Let X be the number of accounting misreporting transactions identified by the software among 50 randomly selected transactions for the last 3 months.
Determine the probability that no misreported transactions are found.
Determine the probability that less than 10 misreported transactions are found.
Determine the probability that at least half of the transactions are misreported.
If the firm applying the auditing software as a test run finds no misreporting, it will receive a $200 compensation, but if there are less than 10 misreported transactions it will have to pay a fee of $50, and if the misreported transactions represent more than half of the transactions then the fee will be $100. Determine the expected monetary gain (assuming that the auditing software is correct when identifying a misreporting).
Answers
The auditing software can identify 63.7% of misreporting issues in accounting ledgers. The probability that no misreported transactions are found is 1 - 63.7% = 36.3%. The probability that at least half of the transactions are misreported is 1 - P(X 25) = 1 - P(X 24) P(X 24) = _(i=0)24 (50C_i) (0.363)i (1 - 0.363)(50 - i) 0.0001. The expected monetary gain is approximately -$49.8.
Given that an auditing software can identify 63.7% of misreporting issues in accounting ledgers. Let X be the number of accounting misreporting transactions identified by the software among 50 randomly selected transactions for the last 3 months.Probability that no misreported transactions are found:X follows a binomial distribution with n = 50 and p = 1 - 63.7% = 36.3%.P(X = 0) = (1 - p)^n = (1 - 0.637)^50 ≈ 0.0002Probability that less than 10 misreported transactions are found:
P(X < 10) = P(X ≤ 9)P(X ≤ 9)
= P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 9)P(X ≤ 9)
= ∑_(i=0)^9 (50C_i ) (0.363)^i (1 - 0.363)^(50 - i) ≈ 0.99
Probability that at least half of the transactions are misreported:
P(X ≥ 25)P(X ≥ 25)
= P(X > 24)P(X > 24)
= 1 - P(X ≤ 24)P(X ≤ 24)
= ∑_(i=0)^24 (50C_i ) (0.363)^i (1 - 0.363)^(50 - i) ≈ 0.0001
Expected monetary gain:Let Y be the amount of money that the firm gets to earn or pay. The probability distribution of Y can be shown below:Outcomes: $200, -$50, -$100
Probabilities: P(X = 0), P(0 < X < 10), P(X ≥ 25)P(X = 0)
= 0.0002P(0 < X < 10)
= 0.99 - 0.0002 = 0.9898P(X ≥ 25)
= 0.0001E(Y)
= ($200 x P(X = 0)) + (-$50 x P(0 < X < 10)) + (-$100 x P(X ≥ 25))E(Y)
= ($200 x 0.0002) + (-$50 x 0.9898) + (-$100 x 0.0001)≈ -$49.8
Therefore, the expected monetary gain is approximately -$49.8.
To know more about probability Visit:
https://brainly.com/question/31828911
#SPJ11
292,000 after several years decrease by 8%
Answers
After several years of an 8% decrease, the house's value is $268,640 currently.
What is a percentage decrease?In this situation, the percentage decrease refers to the fractional devaluation of the property value.
We can compute the percentage decrease by directly determining the amount (absolute value in dollars) of the decrease or by indirectly determining the value after the decrease, using mathematical operations.
The initial value of the house = $292,000
The percentage decrease in value = 8%
The Decrease Value = $23,360 ($292,000 x 8%)
The Current Value of the house = $268,640 ($292,000 - $23,360) or {$292,000 x (1 - 8%)}
Thus, the house decreased by $23,360 or 8% and is currently worth $268,640.
Learn more about percentage decreases at https://brainly.com/question/2692313
#SPJ1
In order to make a profit, a retailer will mark up the cost of an item. If the cost of the item is $42 but it is sold for
$89, what is the mark up rate for the item?
Round your answer to the whole percent.
Answers
4. When you convert from feet to inches, you are doing which of the following?
changing the measurement unit
Determining mass
Determining capacity
Determining volume
Answers
Answer:
A) Changing the measurement unit.
Step-by-step explanation:
"Changing the measurement unit" is the correct answer because when you convert from feet to inches, you are essentially changing the unit of measurement from a larger unit (feet) to a smaller unit (inches) within the same system of measurement (length or distance). It involves multiplying the value in feet by a conversion factor to obtain the equivalent value in inches. This process is commonly used in math, science, and everyday life when dealing with different units of measurement.
The main purpose of descriptive statistics is to Multiple Choice summarize data in a useful and informative manner. make inferences about a population. determine if the data adequately represent the population. gather or collect data.
Answers
Descriptive statistics are used to summarize data in a useful and informative manner.
What is Statistics?This type of statistics provides meaningful information about the data set by organizing and presenting it in an easily understandable format. Descriptive statistics can be used to summarize the data in the form of tables, graphs, and charts. It can also be used to provide detailed information about the data set, such as the mean, median, mode, standard deviation, and range.
Descriptive statistics can also be used to make inferences about a population. This is done by comparing the data collected from a sample to the characteristics of the population. By understanding the characteristics of the population, researchers can make accurate predictions about the behavior of the population.
Descriptive statistics can also be used to determine if the data adequately represent the population. This involves analyzing the sample size, data accuracy, and the assumptions made about the population. If the data does not accurately represent the population, then researchers have to make changes to their data collection process or revise their assumptions about the population.
Finally, descriptive statistics can be used to gather or collect data. This involves designing surveys, experiments, and other data collection methods. By using descriptive statistics to collect data, researchers can ensure that the data is valid and reliable.
To know more about statistic click-
https://brainly.com/question/15525560
#SPJ1
\large f\left(x\right)=2\left(x+5\right)^2-7
Answers
Which word could you use to describe the author's purpose in an argument?
Convince
Describe
Entertain
Inform
Write the equation of the line, in slope-intercept form, with the
following information:
slope: -1
y-intercept: (0, -1)
Answers
Answer:
y = -x -1
Step-by-step explanation:
x1= 0, y1= -1
\(slope = \frac{x - x1}{y - y1} = \frac{x - 0}{y - ( - 1)} = \frac{x}{y + 1} \)
-1 = x/(y+1)
-1 (y+1) = x
y+1 = -x
y= -x -1
What type of model does the data suggest?
х
0
1
2
3
4
y
2.5
5
10
20
40
O
A.
constant
O
B. exponential
C. linear
O
D. quadratic
Answers
Answer:
D HOPE THIS HELPS YOU!!
ANSWER IS D
Step-by-step explanation:
Show that the helium ground state wavefunction Ψ(1,2)= 2
1
1s(1)1s(2)[α(1)β(2)−β(1)α(2)] is normalised, that is, show that ∬[Ψ(1,2)] 2
dτ 1
dτ 2
=1 The integration variable dτ is a product of the volume dv and spin dγ variables.
Answers
The helium ground state wavefunction Ψ(1,2) = 2√(1s(1)1s(2)[α(1)β(2)−β(1)α(2)]) is normalized.
How can we show that the integral of Ψ(1,2) squared over all variables equals 1?To show that the wavefunction Ψ(1,2) is normalized, we need to calculate the integral of Ψ(1,2) squared over all variables and demonstrate that the result is equal to 1.
The integral is given by:
\(∬[Ψ(1,2)]^2 dτ₁dτ₂\),
where dτ₁ is the volume element for particle 1, dτ₂ is the volume element for particle 2, and dτ = dv dγ is the product of the volume dv and spin dγ variables.
To simplify the integral, we can first square the wavefunction Ψ(1,2) and then integrate over the spatial and spin coordinates. Since the spin variables are orthogonal, the spin part of the integral will evaluate to 1.
The spatial part of the integral can be calculated by considering the overlap of the hydrogenic 1s orbitals for both particles.
This overlap depends on the inter-particle distance and can be solved using the radial wavefunction for the 1s state. After performing the integration, we find that the spatial part evaluates to 1/2.
Multiplying the spatial part by the spin part, we obtain a final result of 1/2 * 1 = 1, demonstrating that the wavefunction Ψ(1,2) is normalized.
Learn more about wavefunction
brainly.com/question/29089081
#SPJ11
Write the prime factorization of 21. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
Answers
The prime factorization of the number 21 is:
21 = 3*7
How to write the prime factorization?We want to write the prime factorization of 21.
To do so, we just need to divide the number by prime numbers.
The first prime number we can try is 2, if we divide by 2 we get:
21/2 = 10.5
This is not an integer, so 2 is not a factor.
The next one is 3:
21/3 = 7
Now we can rewrite:
21 = 3*7
Where 3 and 7 are prime numbers, so that is the prime factorization.
Learn more about prime factorizations:
https://brainly.com/question/1081523
#SPJ1
An inscribed angle is an angle whose vertex is a point on a circle and whose sides are two _____ of the circle
Answers
An inscribed angle is formed by two chords of a circle that intersect at a vertex located on the circle.
The angle itself is formed by the two sides of the angle, which are the line segments connecting the vertex to the endpoints of the chords. The property that makes inscribed angles interesting is that the measure of an inscribed angle is half the measure of the intercepted arc on the circle.
This relationship holds true for any inscribed angle in a circle, making it a useful concept in geometry for solving problems involving angles, arcs, and circles.
To know more about geometry visit-
brainly.com/question/30283669
#SPJ11
In a video game, the player can choose their character. The choices are from 8 animals and 4 humans. Players can also let the game randomly choose their character. If a player does the random selection, what is the probability that a human character will be chosen? Enter your answer as a fraction in simplest form in the box.
Answers
The probability of a human character being chosen when the selection is done randomly is 1/3.
To find the probability of a human character being chosen when the selection is done randomly, we need to determine the total number of possible character choices and the number of choices that correspond to a human character.
There are 8 animals and 4 humans, making a total of 8 + 4 = 12 possible character choices.
Since the selection is done randomly, each character has an equal chance of being chosen. Therefore, the probability of selecting a human character is the number of human characters divided by the total number of character choices.
The probability of selecting a human character is:
Number of human characters / Total number of character choices
Substituting the values:
4 / 12
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4:
4 / 12 = 1 / 3
Therefore, the probability of a human character being chosen when the selection is done randomly is 1/3.
For more questions on probability
https://brainly.com/question/30460538
#SPJ8
Questions 7 and 8 please. Really need help thank you!!
Answers
Answer:
7) sin 60° = 25√3/Z
0.8660 = 25√3/Z
Z = 50
8) using the Pythagorean theorem:
50² = (25√3)² + y²
2500 = 1875 + y²
y² = 625
y = 25
Answer:
z = 50
y = 25
Step-by-step explanation:
Using the 30, 60, 90 triangle rule
you can figure this out.
The rule says
With a 30, 60, 90 triangle
Given the shorter leg, (side across the 30 degree angle,
To find longer leg (side across the 60 degree angle):
Multiple shorter leg by radical 3.
To find hypotenuse (side across the 90 degree angle):
Multiple shorter leg by 2.
Thus
Shorter leg (side opposite 30 degree): 25
Longer leg (side opposite 60 degree):
25 radical 3
Hypotenuse(side opposite 90 degree): 50
______ has at least one solution, and an inconsistent system has no solution.
Answers
The statement "Consistent system of equations has at least one solution, and an inconsistent system has no solution" is true.
In the context of systems of linear equations, a consistent system refers to a system where there exists at least one solution that satisfies all the equations in the system. This means that the equations can be simultaneously satisfied by a set of values for the variables.
On the other hand, an inconsistent system refers to a system of equations that has no solution. This occurs when the equations are contradictory or cannot be satisfied simultaneously by any values for the variables.
Therefore, a consistent system guarantees the existence of at least one solution, while an inconsistent system does not have any solution.
To know more about Consistent system refer here:
https://brainly.com/question/12791933
#SPJ11
6. Given the implicit curve x^2-ln(x/y)=1 , Write the linear approximation () of the tangent line at (1,1) A) L(x)=-x-2 B) L(x)= -x+2 C) L(x)= -x-1 D) L(x)= -x+1
Answers
Answer:
B) L(x) = -x + 2
Step-by-step explanation:
To find the tangent at (1,1), we differentiate x² - ln(x/y) = 1 with resect to x.
So, x² - ln(x/y) = 1
x² - (lnx - lny) = 1
x² - lnx + lny = 1
differentiating both sides with respect to x, we have
d{x² - lnx + lny]/dx = d1/dx
dx²/dx - dlnx/dx + dlny]/dx = d1/dx
2x - 1/x + 1/y(dy/dx) = 0
1/y(dy/dx) = 1/x - 2x
dy/dx = y(1/x - 2x)
dy/dx evaluated at (1,1) is
dy/dx = y(1/x - 2x)
= (1)(1/1 - 2(1))
= 1 - 2
= -1
This is the gradient of the tangent line.
To find the equation of the tangent line, we use (y - y')/(x - x') = m where y' = 1, x' = 1 and m = gradient of line = dy/dx = - 1
(y - y')/(x - x') = m
(y - y')/(x - x') = dy/dx
(y - 1)/(x - 1) = -1
cross-multiplying,
y - 1 = -1(x - 1)
expanding the bracket, we have
y - 1 = -x + 1
adding + 1 to both sides, we have
y -1 + 1 = -x + 1 + 1
y = -x + 2
So, L(x) = -x + 2
A sample of two items is selected without replacement from a batch. Describe the ordered sample space for the following batch:
(a)The batch contains 3 defective items and 10 good times.Hint: suppose we denote defective item by ‘d’ and good item as ‘g’, so one possible outcome could be "dg".
(b)The batch contains the items {a, b, c, d}.
Answers
For both scenarios, a sample is selected without replacement from a batch of items. In the first scenario, the batch contains 3 defective items ('d') and 10 good items ('g'). The ordered sample space consists of all possible ordered pairs of items: {dd, dg, gd, gg}. In the second scenario, the batch contains the items {a, b, c, d}. The ordered sample space also consists of all possible ordered pairs of items: {aa, ab, ac, ad, ba, bb, bc, bd, ca, cb, cc, cd, da, db, dc, dd}.
In the first scenario, the ordered sample space is derived by considering all possible combinations of the two items selected from the batch. Since the selection is done without replacement, the first item can be either defective ('d') or good ('g'). For each case, the second item can also be defective or good, depending on what was chosen as the first item. Therefore, the ordered sample space consists of four possibilities: dd, dg, gd, and gg.
In the second scenario, the batch consists of four distinct items: a, b, c, and d. Again, the ordered sample space is obtained by considering all possible combinations of the two items selected without replacement. Since there are four items, there are 16 possible combinations. Each combination is represented by an ordered pair of the selected items, such as aa, ab, ac, and so on.
To know more about ordered sample space, click here: brainly.com/question/29189463
#SPJ11
Find the inverse of the radical function
Answers
Heya~
\(\sf{What~is~312~x~12~?}\)
Explain into your own answers ~
Thanks~
Answers
Answer:
312x12 or \(2^{5} *3^{2}*13\)
is 3744
Step-by-step explanation:
can you help me please
Answers
wrong one -----/////