Answers
We found for the line passing through (-1, 0) and (0, -1.5), we can see that the correct inequality is option A is -2y + 2x ≥ 7x + y + 5.
Describe Inequality?An inequality is a mathematical statement that compares two quantities or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).
Inequalities can involve variables or constants, and can be expressed in one variable or multiple variables. The solution to an inequality is the set of values that satisfy the inequality.
For example, the inequality 2x + 3 > 7 is true for values of x that are greater than 2, since if we substitute x = 2, we get 2(2) + 3 = 7, which is not greater than 7. On the other hand, if we substitute x = 3, we get 2(3) + 3 = 9, which is greater than 7, so the inequality is true for x > 2.
Inequalities have many applications in mathematics and other fields, such as economics, physics, and engineering. They are used to represent constraints in optimization problems, to model relationships between variables, and to describe ranges of possible values for a quantity or variable.
To determine the correct inequality, we need to find the equation of the line that passes through the points (-1, 0) and (0, -1.5).
The slope of the line can be calculated as follows:
m = (y2 - y1) / (x2 - x1)
m = (-1.5 - 0) / (0 - (-1))
m = -1.5
The y-intercept of the line can be found by substituting one of the points and the slope into the point-slope form of a line:
y - y1 = m(x - x1)
y - 0 = -1.5(x - (-1))
y + 1.5 = -1.5x - 1.5
y = -1.5x - 3
Now we can rewrite the inequality in the form y <= mx + b, where m is the slope and b is the y-intercept.
-2y + 2x >= 7x + y + 5 can be simplified to:
-3y >= 5x + 5
Dividing both sides by -3, we get:
y <= (-5/3)x - 5/3
Comparing this to the equation we found for the line passing through (-1, 0) and (0, -1.5), we can see that the correct inequality is option A:
-2y + 2x ≥ 7x + y + 5
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Related Questions
what is x2=20 show your work
Answers
Answer:
x=10
Step-by-step explanation:
x2=20
2*x=20
2*10=20
so, x=10
What is the greatest common factor of 9, 24, and 30
Answers
Answer: 3
Step-by-step explanation:
9/3=3
24/3= 8
30/3=10
Examine the system of equations.
2x − 4y = 6,
x − 2y = 3
How many solutions does this system of equations have?
Answers
Answer:
Step-by-step explanation:
8
six less than six times a number
Answers
Answer:
6n-6 or 6(n-1)
Step-by-step explanation:
six times a number, n, can be shown as 6n. "Six less" indicates -6. So combining the two parts leaves 6n-6. This can be simplified to 6(n-1)
A bag has 11 blue cubes, 6 red cubes, and 8 green cubes. If you draw a cube and replace it in the bag 200 times, which of the following amounts would you expect to pull? Select all that apply.
A) Pull a blue cube 88 times
B) Pull more red cubes than blue cubes
C) Pull a green cube 64 times
D) Pull a blue cube 150 times
E) Pull a red cube 10 times
Answers
Option E is incorrect in light of the provided assertion, and only options A,B,C, and D are acceptable.
What fundamentals of probability are there?Probability is simply the chance that something will happen. We can discuss the likelihood of various outcomes when we are unable to foresee how an incident will unfold.
The probability of drawing a blue cube is 11/25, the probability of drawing a red cube is 6/25, and the probability of drawing a green cube is 8/25. Since we are replacing the cube after each draw, each draw is independent and follows the same probability distribution.
To find the expected number of times we would pull a certain color cube, we can simply multiply the probability of drawing that color cube by the total number of draws:
Expected number of blue cube draws: (11/25) x 200 = 88 times. So option A is correct.
The probability of drawing more red cubes than blue cubes is a bit more complicated to calculate, but it can be done by summing the probabilities of drawing 0, 1, 2, 3, 4, 5, or 6 blue cubes and 6, 5, 4, 3, 2, 1, or 0 red cubes. However, it is easier to notice that the probability of drawing more red cubes than blue cubes is the same as the probability of drawing more blue cubes than red cubes, which is 1/2 since both events are equally likely. Therefore, option B is correct.
Expected number of green cube draws: (8/25) x 200 = 64 times. So option C is correct.
Expected number of blue cube draws: (11/25) x 200 = 88 times. So option D is correct.
Expected number of red cube draws: (6/25) x 200 = 48 times. So option E is not correct since it expects less than 48 red cube draws.
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fatouma is lifting wieghts over a 10 week training period . every week , she lifts 2 kg more than she lift the previous week . during the tenth week she lifts 120 kg . what mass did she lift during the week
Answers
Fatouma lifted 1 kg during the first week and 120 kg during the tenth week. Fatouma lifted 120 kg in 10 weeks, increasing by 2 kg each week.
What is linear equation ?Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0
Say the mass Fatouma lifted during the first week "x". According to the problem, she increases the weight she lifts by 2 kg every week. So, the mass of second week is "x + 2" kg, during the third week is "x + 4" kg, and so on.
Since there are 10 weeks of training, the mass she lifted during the 10th week is:
x + (10 - 1) × 2 = x + 18
We also know that during the 10th week, she lifted 120 kg. So, we can set up an equation:
x + 18 = 120
Solving for x, we get:
x = 102
Thus, Fatouma lifted 102 kg during the first week of training.
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know the concept of random variable and know how to use proper notations to represent them (where does the randomness come from?)
Answers
The x is a specific value that the variable can take on.
A random variable is a variable that has a numerical value, which is determined by the result of a random experiment. The numerical value is determined by a set of probabilities, which are associated with each possible outcome of the experiment. Random variables can be classified as discrete or continuous, depending on the type of outcomes that they can have. Examples of random variables include the number of heads in a series of coin tosses, the time until a traffic light changes from red to green, and the height of a randomly selected person.The randomness of a random variable comes from the fact that the outcome of the experiment that it represents is uncertain. The uncertainty arises because the experiment is subject to the effects of chance, rather than being completely determined by fixed physical laws or other deterministic factors. Because of this, it is not possible to predict with certainty what the value of a random variable will be, even if we know the probabilities associated with each possible outcome.There are many different notations that can be used to represent random variables, depending on the context and the preferences of the person using the notation. Some of the most common notations include X, Y, and Z, as well as Greek letters such as µ, σ, and ρ. When a random variable is discrete, it is often represented using a probability mass function, which is denoted by P(X=x), where x is a specific value that the variable can take on. When a random variable is continuous, it is often represented using a probability density function, which is denoted by f(x), where x is a specific value that the variable can take on.
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John wants to store his golf club inside a box. If the box has a length of 20in, width of 13 in,
and height of 11 in. If his golf club is 26 inches exactly, will it fit inside the box?
Answers
Answer: No
Step-by-step explanation:
Because the length of the box is shorter than the length of the club
20in<26in
The width of the box is also shorter than the width of the club
13in<16in
The height of the box is also shorter than the height of the club
11in<16in
But what about putting it at an angle?
So we know [tex]a^{2} +b^{2} =c^{2}[/tex]
so let's try [tex]20^{2} +13^{2} =x^{2}[/tex]
[tex]x^{2}[/tex]=569
[tex]x=\sqrt{159}[/tex]
x is near 23.85 in, but 23.85<26. So no.
please help i will give brainliest along with 20 pnts. ONLY ANSWER IF YOU KNOW IT
Answers
Giovanna deposited $1600 into two accounts, half in First Oak and half in West United.
Interest earned in First Oak account after 5 years at 6% simple interest:
= 0.06 x $800 x 5
= $240
Interest earned in West United account after 5 years at 5% compounded annually:
= $800 x (1 + 0.05)^5 - $800
= $800 x 1.27628 - $800
= $221.02
Total interest earned in both accounts:
= $240 + $221.02
= $461.02
Therefore, Giovanna will have earned $461.02 in interest from both accounts at the end of 5 years.
Jim wants to hang 4 pictures in a row on his wall. If he has 6 pictures to choose from , how many different arrangements are possible?
Answers
Answer:
180 possible arrangements
Step-by-step explanation:
To find the number of different arrangements possible when Jim hangs 4 pictures in a row from a set of 6 pictures, we can use the permutation formula:
nPr = n! / (n - r)!
where n is the total number of items in the set (in this case, 6), and r is the number of items being chosen (in this case, 4).
Substituting the values, we get:
6P4 = 6! / (6 - 4)!
= 6! / 2!
= (6 x 5 x 4 x 3 x 2 x 1) / (2 x 1)
= 360 / 2
= 180
Therefore, there are 180 different arrangements possible when Jim hangs 4 pictures in a row from a set of 6 pictures.
Answer:
Step-by-step explanation:
24
Ousmane envoie une carte a Arnaud par pigeon voyageur. Le pigeon vole a une vitesse de 84km/h et met 1h45 à délivrer la lettre. A quelle distance Arnaud et Ousmane vivent-ils l'un de l'autre ?
Answers
On peut commencer par utiliser la formule suivante pour calculer la distance parcourue par le pigeon voyageur :
distance = vitesse x temps
où la vitesse est donnée en km/h, le temps en heures et la distance en km.
Dans ce cas-ci, la vitesse est de 84 km/h et le temps de voyage est de 1h45, soit 1.75 heures. On peut donc calculer la distance parcourue par le pigeon :
distance = 84 km/h x 1.75 h = 147 km
Donc, la distance entre Ousmane et Arnaud est de 147 km.
Which summary about The Secret Garden includes a personal opinion?
Responses
Mary Lennox is described as a sallow, sickly, unpleasant girl.
Mary Lennox is described as a sallow, sickly, unpleasant girl.
Mr. Craven, "a miserable hunchback," has been withdrawn and depressed for ten years.
Mr. Craven, "a miserable hunchback," has been withdrawn and depressed for ten years.
Dickon and Mary secretly begin bringing Colin out into the secret garden.
Dickon and Mary secretly begin bringing Colin out into the secret garden.
Mrs. Lennox is the worst mother imaginable, and everybody knows it.
PLS HELP FAST
Answers
Answer:
"Mrs. Lennox is the worst mother imaginable, and everybody knows it."
Step-by-step explanation:
The first one uses "described", therefore isn't a personal opinion.
The second uses quotations, so isn't a personal opinion.
The third doesn't have any sort of opinion or connotation.
Therefore it must be the last one.
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165. 1% of 384. 7. Round to the nearest thousandth
Answers
Rounding to the nearest thousandth means rewrite the number and deleting all digits to the right of the rounded number. The percentage value for 165.1% of 384.7 is equals to the 42.917%.
In mathematics, a percentage is a number that represents a fraction of hundred. We have to calculate the value of 165.1% of 384.7. Percentage solution with steps:
Step 1: We make the assumption that 384.7 is 100% since it is our output value.
Step 2: We next represent the value we need with x. From step 1, it follows that 100% = 384.7.
Step 3: In the same sense, x% = 165.1.
Step 5: Now, we have a pair of simple equations:
100% = 384.7 --(1).
x% = 165.1 ---(2).
Step 6: By simply dividing equation (1) by equation 2 and taking note of the fact that both the LHS (left hand side) of both equations have the same unit (%); we have 100% /x% = 384.7/165.1.
Step 7: Taking the inverse or reciprocal in both sides, x% / 100% = 165.1/384.7
=> x = ( 165.1/384.7) × 100
=> x = 42.91655835716 ~ 42.917 (round to the nearest thousandth). Therefore, 165.1 is 42.917% of 384.7.
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Identify all expressions below that are polynomials.
Answers
Answer:
All the expressions except d are polynomials.
Pls just say a b c or d
Answers
Answer:
c
Step-by-step explanation:
[y=-z+2
y=-2²+z+1
Which ordered pair is the solution of the system?
The graph shows the system
0 (0, 2)
O (1,2)
(1,1)
(0, 1)
+
Answers
Therefore , the solution of the given problem of ordered pair comes out to be the ordered pair (1, 1/2).
What exactly are ordered pairs?"Ordered pairs" are two separate variables that are arranged in a way that suggests a specific sequence. The coordinates for x and y in an order pair are represented, respectively, by the main and second components. The sample following uses close parentheses to indicate the ordered combination.
Here, The formulae are as follows:
=>y = -z + 2 ...(1)
=> y = -2x² + z + 1 ...(2)
Equation (1) can be substituted for equation (2) to find the value of z:
=> Z = x² + 1/2 - z + 2 = -2x² + z + 1
=> 2z = 2x² + 1
We can now enter this value of z into equation (1) and find the value of y:
=> y = -z + 2
=> y = -(x² + 1/2) + 2
=> y = -x² + 3/2
As a result, the equation system can be expressed as:
=> z = x² + 1/2
=> y = -x² + 3/2
When x=0:
=> z = 0² + 1/2 = 1/2
=> y = -0² + 3/2 = 3/2
Therefore, there is no answer for the ordered pair (0, 3/2).
When x=1:
=> z = 1² + 1/2 = 3/2
=> y = -1² + 3/2 = 1/2
The answer is the ordered pair (1, 1/2).
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How do I solve this I don’t get it
Answers
Surface area , Lateral area and volume of triangular prism area 262.25 square in, 231 square in and 156.25 cubic in respectively.
The meaning of the triangular prismWith two triangular bases and three rectangular sides, a triangular prism is a kind of polyhedron. Alternatively, because it has five faces overall, it may be thought of as a pentahedron in which the bases' edges and vertices are connected by three rectangular sides.
Surface area of triangular prism:Given, base (b) =5 in ,
the height of the triangle (h) = 6.25 in
length of a prism (l) = 12 in
and the hypotenuse of the right triangle = 8 in
The surface area of a right triangular prism = b×h + (S1 + S2 + h)L
On substituting the values, we get
SA = (5 × 6.25) + [(5 + 6.25 + 8) × 12]
⇒ SA = 60 + (30 × 11)
⇒ SA =262.25 square in
Therefore, the total surface area of a right triangular prism is 262.25 square in.
Lateral area of triangular prism:Lateral Area = ( S1 + S2 + S3 ) × l
On substituting the values, we get
LA=(5+6.25+8)×12
LA=(19.25)×12
LA=231 square in
Therefore, the lateral surface area of a right triangular prism is 231 square in.
Volume of triangular prism:the base area = (1/2) × (b×h) = (1/2) × (5 ×6.25) =15.625 square in
The length of the prism is, L = 12 in
Using the volume of the triangular prism formula,
The volume of the given triangular prism = base area × length of the prism = 15.625 ×10=156.25 cubic in
Hence, The volume of the given triangular prism is 156.25 cubic in.
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The table shows four transactions (in dollars) for a bank account. Positive numbers represents deposits, and negative numbers represent withdrawals. The balance before the transactions is $75.50. What could the transaction for 11/7 be if the final balance in the bank account is $86.92? Date Amount 11/4 50.68 11/4 -22.16 11/7 11/11 56.65 End Balance 86.92
Answers
Answer:
11/7: +9.42
Step-by-step explanation:
The price of a new car is $28,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 6%/year compounded monthly. (Round your answers to the nearest cent.)
(a) What monthly payment will she be required to make if the car is financed over a period of 36 months? Over a period of 60 months?
36 months=$
60 months=$
(b) What will the interest charges be if she elects the 36-month plan? The 60-month plan?
36-month plan =$
60-month plan=$
Answers
With a 25% down payment, the interest for the 60-month plan therefore equals $3,372.60.
what is compound interest ?A loan's or investment's principle and any accrued interest from earlier periods are both considered when calculating compound interest. In other words, it is the interest charged on a deposit or loan that is computed on both the initial principal and the cumulative interest. This means that the principal amount is increased by the interest earned during each period, and the succeeding interest is computed using the new sum. This causes the investment or debt to grow over time and can have a big impact on the amount received or due in comparison to simple interest calculations.
given
(b) The amount funded can be subtracted from the total amount paid over the loan term to determine the interest fees.
The total sum paid for the 36-month plan is:
The amount paid is monthly payment multiplied by the number of payments ($630.70 x 36 = $22,743.60).
These are the interest fees:
Interest costs equal Total paid - Financed amount ($22,743.60 - $21,000) to equal $1,743.60.
Hence, the 36-month plan's interest costs come to $1,743.60.
(ii) The total sum paid for the 60-month plan is:
Amount paid equals Monthly Payment * Number of Payments, or $406.21 * 60, for a total of $24,372.60.
These are the interest fees:
Interest costs are calculated as follows: Total paid - Total financed: $24,372.60 - $21,000 = $3,372.60
With a 25% down payment, the interest for the 60-month plan therefore equals $3,372.60.
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FIND THE MISSING SIDES OF THE KITE
Picture for more info!
Thank you.
Answers
The required sides of kite are √61, √61, √221 and √221 units.
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse in a right-angled triangle equals the total of the squares of the other two sides. The formula for this theorem is c² = a² + b², where c is the hypotenuse and a and b are the triangle's two sides. Pythagoras theory triangles are another name for these triangles.
According to question:In ΔAOD
AD = [tex]\sqrt{5^2+6^2} = \sqrt{61}[/tex] units
In ΔAOB
AB = [tex]\sqrt{5^2+6^2} = \sqrt{61}[/tex] units
In ΔBOC
BC = [tex]\sqrt{5^2+14^2} = \sqrt{221}[/tex] units
In ΔDOC
DC = [tex]\sqrt{5^2+14^2} = \sqrt{221}[/tex] units
Thus, required sides of kite are √61, √61, √221 and √221 units.
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The relation between hours studied and LSAT scores in a random sample of students is found to be S = 130 + 2.2h. How will a student’s score be affected if she studies for 10 hours?
Answers
Answer:
We can use the given equation to find the expected LSAT score (S) for a student who studies for 10 hours:
S = 130 + 2.2h
S = 130 + 2.2(10)
S = 130 + 22
S = 152
Therefore, if a student studies for 10 hours, we would expect her LSAT score to be 152.
y < 2x + 3
x+y≥ 3
x < 4
Write an ordered pair that is a solution to the systems.
Answers
The solution to the system of equations is (2, 1). To find this solution, we must first solve the first equation, Y < 2x + 3, for x.
What is subtracting?Subtracting involves taking the difference between two numbers. It is the opposite of addition and is represented by the '-' sign.
We can do this by subtracting 3 from both sides of the equation, which gives us Y - 3 < 2x.
We then divide both sides of the equation by 2, which gives us
Y - 3/2 < x.
Next, we must solve the second equation, x + y ≥ 3, for y. To do this, we subtract x from both sides of the equation, which gives us y ≥ 3 - x.
Finally, we must set both equations equal to each other,
Y - 3/2 = 3 - x.
We can then solve for x by adding 3/2 to both sides of the equation, which gives us
x = 2.5.
We can then plug this value for x into the second equation, which gives us y ≥ 3 - 2.5.
We then solve for y by subtracting 2.5 from both sides of the equation, which gives us y = 0.5.
Since the value for x must be less than 4, we must round down the value of x to 2. This means that the solution to the system of equations is (2, 1).
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Sophie has a small cube-shaped box. Its volume is 64 cubic centimeters.
What is the area of one face of the box?
Answers
Answer:
The answer to your problem is, [tex]16cm^{2}[/tex]
Step-by-step explanation:
Sophie has a small cube shaped box.
Volume of the box is [tex]64cm^{3}[/tex]
We have to find the area of one face of the box.
Let one side of the box is x
Then volume = [tex]x^{3}[/tex] = 64
x³ = 4³
= 4
Now area of one face of the cube = x²
then area = 4² = 16 cm²
Thus the answer to your problem is, [tex]16cm^{2}[/tex]
a coin is flipped 6 times. if more heads are flipped than tails, the probability that all 6 are heads is , what is the value of ?
Answers
The probability that all 6 flips result in heads is 1/64
The given coin is flipped 6 times. The number of heads and tails could vary from 0 to 6.Let H be the number of heads and T be the number of tails. Then the possible values of H and T are, H=0 and T=6 H=1 and T=5 H=2 and T=4 H=3 and T=3 H=4 and T=2 H=5 and T=1 H=6 and T=0
For the given question, it is given that more heads are flipped than tails.So the possible values of H are 4, 5 and 6.So the total number of possible outcomes with more heads than tails is the sum of the possible outcomes with 4, 5 and 6 heads which is, 1+6+15 = 22 (from the combinations formula)Now, the probability that all 6 flips result in heads, given more heads are flipped than tails is,
P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T)P(H > T) = 22/64
P(all 6 are heads | H > T) = 1/21 (there is only one possibility where all 6 flips are heads)
P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T) = (22/64) × (1/21) = 1/64
Therefore, the probability that all 6 flips result in heads, given more heads are flipped than tails is 1/64.
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what is the mean of the sample means? the mean of the sample means is equal to the population mean, divided by the square root of the sample size. the mean of the sample means is equal to the population mean,divided by the sample size. the mean of the sample means is equal to the population mean, divided by the population standard deviation. the mean of the sample means is equal to the population mean. the mean of the sample means is undefined because all possible sample means can never be found.
Answers
The mean of the sample means is equal to the population mean.
The mean of the sample means is the average of all sample means taken from the population. It is an estimate of the population mean. The sample mean is calculated by taking the sum of all values in the sample and dividing it by the sample size. The mean of the sample means is equal to the population mean, as all sample means come from the same population and therefore have the same mean. It is not affected by the sample size or the population standard deviation. Therefore, the mean of the sample means is equal to the population mean.
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The prism-shaped roof has equilateral triangular bases. Use the model you created in question #1 to calculate the height of the roof, to the nearest tenth of a foot, if the side lengths each measure 25 feet. In your final answer, include all necessary calculations. You may include a sketch as part of your work
Answers
The height of the roof is approximately 21.6 feet, to the nearest tenth of a foot.
To calculate the height of the roof, we need to use the formula for the volume of a prism with a triangular base. This is given by V = 1/3 B h, where B is the area of the base and h is the height of the prism.
In this case, we know that the base is an equilateral triangle with side length 25 feet. The area of an equilateral triangle with side length s is given by A = √3/4 s². Therefore, the area of the base of the prism is:
B = √3/4 (25 ft)²
B = 25√3/4 ft²
Now, we need to use the model to determine the height of the prism. We can do this by measuring the height of one of the triangular faces. The model is not provided, so I cannot provide specific measurements. However, we can use the Pythagorean theorem to relate the height of the triangular face to the height of the prism:
h² = (25 ft)² - (1/2 s)²
h² = 625 ft² - (1/2 (25 ft))²
h² = 625 ft² - 156.25 ft²
h² = 468.75 ft²
h ≈ 21.6 ft
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Can anybodyhelp me with these please? I need help please!
Answers
1: The measure of arc JML is: arc JML = 176°
3: m∠WXY = 59°
5: The measure of the arc is: arc FE = 54°
7: The measure of the angles are: m∠A = 79° and m∠B = 112°
9: The value of x is: x = 9
How to find the angle or arc measure in a circle?
No. 1
The measure of inscribed angle is half the measure of its intercepted arc. That is:
∠ JKL = 1/2 * arc JML
88 = 1/2 * arc JML
arc JML = 2 * 88
arc JML = 176°
No. 3
arc WY = 360 - 86 - 156 = 118° (sum of angles in a circle)
m∠WXY = 1/2 * arc WY
m∠WXY = 1/2 * 118
m∠WXY = 59°
No. 5
An angle inscribed in a semicircle is a right angle. Thus, m∠DFE = 90°
m∠EDF = 180 - 90 - 63 = 27° (sum of angles in a triangle)
m∠EDF = 1/2 * arc FE
27° = 1/2 * arc FE
arc FE = 2 * 27
arc FE = 54°
No. 7
The opposite angle in a cyclic quadrilateral add up to 180°. That is:
m∠A + m∠C = 180°
m∠A + 101 = 180
m∠A = 180 - 101
m∠A = 79°
m∠B + m∠D = 180°
m∠B + 68 = 180
m∠B = 180 - 68
m∠B = 112°
No. 9
67 = 1/2 * (16x - 10)
67 * 2 = (16x - 10)
16x - 10 = 134
16x = 134 + 10
16x = 144
x = 144/16
x = 9
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If f(x) is a function and f(1) = 5, then which of the following could not be true?
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If f(x) is a functiοn and f(1) = 5, then f(1) = 1 cοuId nοt be true.
Thus οptiοn a is cοrrect.
Define functiοn.A functiοn is a reIatiοn between twο sets, caIIed the dοmain and the range, such that fοr each eIement in the dοmain, there is exactIy οne eIement in the range. A functiοn maps each eIement in the dοmain tο a unique eIement in the range.
In οther wοrds, a functiοn is a ruIe οr a fοrmuIa that assοciates each input vaIue with a unique οutput vaIue. The input vaIues are the dοmain οf the functiοn, and the οutput vaIues are the range. Functiοns are οften denοted by a symbοI such as f(x), where x is an eIement in the dοmain and f(x) is the cοrrespοnding eIement in the range.
In mathematicaI anaIysis, the generaI cοncept οf functiοn, appIicatiοn οr mapping refers tο a ruIe that assigns tο each eIement οf a first set a singIe eIement οf a secοnd set.
Using this definitiοn, severaI eIements οf the dοmain can resuIt in the same eIement οf the range οf the functiοn.
But, the same eIement οf the dοmain, can nοt have different vaIues οf the range οf the functiοn.
Therefοre, the fοIIοwing expressiοn can nοt be true:
f (1) = 1
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Complete Question:
If f(x) is a function and f(1) = 5, then which of the following could not be true?
a. f(1) = 1
b. f(2) = 1
c. f(5) = 5
you are making cookies and missing a key ingredient eggs. you have most of the other ingredients, except you only have 1.33 cups of butter. the recipe calls for two cups of butter and three eggs to make six dozen cookies. how many eggs do you need use all of the butter?
Answers
By using equation in two variable we need to use 2 eggs to make all the cookies with 1.33 cups of butter.
To make six dozen cookies, the recipe calls for two cups of butter and three eggs. We can use proportionality to solve this question: If 2 cups of butter require 3 eggs to make 6 dozen cookies, then 1.33 cups of butter require x eggs to make all of the cookies.
x eggs = (1.33 cups of butter x 3 eggs)/(2 cups of butter). x = 1.99 eggs. Since we cannot use .99 eggs to make cookies, we would need to round up to the nearest whole number of eggs.
Therefore, we need to use 2 eggs to make all the cookies with 1.33 cups of butter.
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Let Θ be an angle in standard position. What is the terminal point (x,y) of Θ= π on the unit circle?
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In the present scenario, the angle of Θ= π terminates in the second quadrant, where the x-coordinate is negative and the y-coordinate is positive.
the terminal point (x, y) of Θ= π on the unit circle can be calculated with the help of the following steps:
Step 1: Firstly, let’s recall the unit circle, which is a circle having a radius of 1 unit, and it is centered at the origin of a coordinate plane.
Step 2: Draw the angle of Θ= π on the unit circle. We can see that this angle has been formed by rotating in the clockwise direction along the unit circle from its initial position on the positive x-axis.
Step 3: As we know that the terminal point (x, y) of an angle in standard position is given by (cos Θ, sin Θ). Therefore, we can apply this formula to calculate the coordinates of the terminal point for the given angle of Θ= π on the unit circle.
Here, cos π= -1 and sin π= 0. Thus, the coordinates of the terminal point are (-1, 0). Hence, the correct answer is (-1, 0).Note: The coordinates of the terminal point for an angle in standard position can be negative, positive, or zero, based on the quadrant in which the angle terminates.
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