Answers
1. An acute angle is οne that is less than 90 degrees.
What is an acute angle ?An angle smaller than the right angle is called an acute angle. In οther wοrds, the angle which is less than 90 degrees fοrms an acute angle. The pοlygοns such as triangle, parallelοgram, trapezοid, etc. cοnsist οf at least οne acute angle
2. Obtuse angle: A measurement οf an angle that is greater than 90 degrees but less than 180 degrees.
3. A right angle is οne that is exactly 90 degrees.
4. A straight angle is οne that is exactly 180 degrees in length.
5. Adjacent angles are twο angles that share a cοmmοn vertex and a cοmmοn side.
6. A pair οf nοn-adjacent angles fοrmed by the intersectiοn οf twο lines are knοwn as vertical angles. They are οf equal size.
7. Cοmplementary angles are defined as twο angles that add up tο 90 degrees.
8. Twο angles that add up tο 180 degrees are referred tο as supplementary angles.
9. Angles with the same measure are said tο be cοngruent.
10. A linear pair is twο adjacent angles that fοrm a straight line and add up tο 180 degrees.
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Related Questions
the expression represents the sum of the first 200 multiples of 3. what is the sum of the first 200 multiples of 3? 803 60,300 120,600 360,000
Answers
The sum of the first 200 multiples of 3 is 60,300(B).
To find the sum of the first 200 multiples of 3, we need to calculate the arithmetic series. The formula for the sum of an arithmetic series is Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, the first term (a) is 3, and the last term (l) is 3 * 200 = 600.
Plugging these values into the formula, we get Sn = (200/2)(3 + 600) = 100 * 603 = 60,300. Thus, the sum of the first 200 multiples of 3 is 60,300(C).
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Evaluate the expression:
6² x (16 +19) — 10³
Answers
36×(35)-1000=1260-1000=260
Given f(x) = (2 - x)}, what is the value of f(18)?
Answers
(2-18)
f(18)= -16
(G.5d, 1 pt) Determine the range for the measure of AC. А 10 m B 13 m O A. 10
Answers
The length of a side must be less than the sum of the other two sides. Here, that means x < 10+13, or x < 23.
In addition, remember that the length of a side must be greater than the difference of the other two sides. That means x > 13 - 10, or x > 3.
Therefore we have two limits for the value of x: 3 and 23.
3 < x < 23
6 A movie-streaming service drafts $13 from Justin's bank account each month. Find the total changes to Justin's bank account in one year from this service.
Answers
Answer:
The amount that the movie-streaming service charges Justin's bank account each month is $13. To find out how much Justin will be charged in one year, we need to multiply this monthly charge by the number of months in a year (12):
Total charges in one year = Monthly charge x Number of months in a year
Total charges in one year = $13 x 12
Total charges in one year = $156
Therefore, the movie-streaming service will charge Justin's bank account a total of $156 in one year.
In a scale drawing, 3 millimeters represents 17 meters. Exactly how many millimeters represents 55 meters?
Answers
Work Shown:
(3 mm)/(17 m) = (x mm)/(55 m)
3/17 = x/55
3*55 = 17*x
165 = 17x
17x = 165
x = 165/17
x = 9.706 approximately
Side note: I used the cross multiplication rule for the third step.
Marcus works as a salesman at a car dealership . He is paid a base salary of $1,352.35 each month, and he receives a commission
of $133.04 for each vehicle he sells. If last month Marcus earned $3,880.11, how many cars did he sell last month?
OA. 19
OB. 71
OC. 58
OD. 38
Answers
Answer: He sold 19 cars last month
Step-by-step explanation:
set up the equasion: 1352.35 + 133.04x = 2880.11
x is the number of cars sold
solve: 2880.11 - 1352.35 is 2527.76
133.04x = 2527.75
2527.75 divided by 133.04 is 19
x = 19
Estimate a 15% tip on a dinner bill of $31.53 by first rounding the bill amount to the nearest ten dollars.
Answers
Answer:
Should be around 4.5
Step-by-step explanation:
If you round 31.53 to the nearest ten dollars, you get 30, 15 percent of 30 is 4.5
Determine whether the given sequence converges or not. If it converges, find its limit. (a) {b
n
=
n
2
+3n+1
n
2
}. The sequence {a
n
} (Write converges or diverges) and lim
n→[infinity]
a
n
= (if the sequence {a
n
} diverges in the previous blank write not exist and if converges write an integer number
Answers
According to the question The given sequence is \(\[ a_n = \frac{n^2 + 3n + 1}{n^2} \]\) and The limit simplifies to \(\[ \lim_{n \to \infty} a_n = 1 + 0 + 0 = 1 \]\) So, the sequence converges and its limit is 1.
To determine whether the sequence converges or not, we can take the limit of the sequence as n approaches infinity.
\(\[ \lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{n^2 + 3n + 1}{n^2} \]\)
Simplifying the expression inside the limit:
\(\[ \lim_{n \to \infty} a_n = \lim_{n \to \infty} \left(1 + \frac{3}{n} + \frac{1}{n^2}\right) \]\)
As n approaches infinity, both \(\(\frac{3}{n}\) and \(\frac{1}{n^2}\)\) approach zero. Therefore, the limit simplifies to \(\[ \lim_{n \to \infty} a_n = 1 + 0 + 0 = 1 \]\) So, the sequence converges and its limit is 1.
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16. What are the missing sides?
TE
4 cm
3 cm
?
?
5 cm
10 cm
Answers
Total answer is 8
1 Apply Malcolm is making chicken rice soup. The recipe calls for 5 cups of chicken broth per cup of brown rice. How many cups of brown rice are needed for 20 cups of chicken broth? Explain how you know.
Answers
Answer:
you will need 4 cups of brown rice because it says per cup of brown rice
Step-by-step explanation:
ok so,
5 cups of chicken broth= 1 cup of brown rice
so if there's 20 cups of chicken broth, then:
20/5(since 5 equals 1 cup of brown rice)
=4 cups of brown rice
Determine whether the following problem involves a permutation or combination. (It is not necessary to solve the problem.)How many different 2-letter passwords can be formed from the letters H, I, J, K, L, M, and N if no repetition of letters is allowed?
Answers
A permutation is an arrangement of outcomes in which the order does matter.
A combination is an arrangement of outcomes in which the order does not matter.
In this case, for example, the password HI is different from the password IH. In both cases, the outcomes (letters H and I) are the same, but the order of them changes the arrangement (the password). Therefore, the problem involves a permutation because the order of letters selected does matter
the growth curve shown depicts growth projections for a single population. a graph plots population size on the y axis and time on the x axis. an exponential curve shows slow population growth at first and then rapid increase over time. what would happen if the birth rate were to decline?
Answers
If the birth rate were to decline in a population, the growth curve would be affected as well. A decrease in the birth rate would cause the population growth to slow down, resulting in a change in the shape of the curve.
Initially, the exponential curve illustrates slow population growth, followed by a rapid increase over time. However, with a declining birth rate, the curve would likely transition into a logistic growth curve. This type of curve is characterized by an initial period of slow growth, followed by a phase of rapid growth, and eventually leveling off when the population reaches its carrying capacity or other limiting factors come into play.
The projections for the population growth would also be impacted by the decrease in the birth rate. Lower birth rates typically lead to slower growth rates, and in some cases, may even result in a population decline if the birth rate falls below the death rate. This change would be reflected in the updated projections for population growth over time.
In summary, if the birth rate were to decline in a population with an exponential growth curve, the curve would likely shift towards a logistic growth pattern, with slower overall growth and eventual leveling off. The projections for population growth would need to be adjusted to account for the changes caused by the reduced birth rate.
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The graph of a non-invertible function passes through the points (- 1, 2), (0, 6) and (3, - 4) How is the inverse of this function graphed ? Drag a phrase or group of coordinates into each box to correctly complete the statement.
Answers
Answer:
The order of ordered pairs of a function and its inverse reverse. The graph of the inverse of this function passes through the points (2,-1), (6,0), (-4,3).
Explanation:
I just took the test.
As per the graph, the non-invertible functions pass through the point of (-1, 2)), (0,6), and (3, - 4).
The inverse of the function on the graph will be depicted by the Y = X. The graph of the inverse passes through the vertical line test for the inverse function. While the graph of the inverse function will pass through the (2,-1), (6,0), (-4, 3)Learn more about the graph of a non-invertible function that passes through the point.
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−7.5(x−3)=3.75 What is the value of x? Enter your answer as a decimal.
Answers
Answer:
x=2.5
Step-by-step explanation:
What goes on the lines I don’t understand the problem
Answers
Answer:
Step-by-step explanation:
a). Let the number of spoons = x
And number of forks = y
Total number of spoons and forks bought by Perry = 10
x + y = 10 --------(1)
Cost of one spoon = $5
Cost of one fork = $3
Therefore, total cost of x spoons and y forks = $(5x + 3y)
5x + 3y = 42 -------(2)
b). Now we can convert these equations into the slope-intercept form.
x + y = 10 ⇒ y = -x + 10
Table for input output values,
x 2 4 6
y 8 6 4
5x + 3y = 42
3y = -5x + 42
y = \(-\frac{5}{3}x+14\)
x 0 3 6
y 14 9 4
Point of intersection of these lines will be (6, 4).
Find all the solutions of (1+i)z^5+i=0
Answers
The solutions to the equation (1+i)z^5 + i = 0 are:
z ≈ 0.382 + 0.924i, -0.682 + 0.731i, -0.618
To find the solutions of the equation (1+i)z^5 + i = 0, we can rearrange the equation and solve for z.
Let's start by subtracting i from both sides:
(1+i)z^5 = -i
Next, divide both sides by (1+i):
z^5 = -i / (1+i)
To simplify the right side, we can multiply the numerator and denominator by the conjugate of (1+i), which is (1-i):
z^5 = (-i)(1-i) / (1+i)(1-i)
z^5 = (i - i^2) / (1^2 - (i^2))
z^5 = (i + 1) / (1 + 1)
z^5 = (i + 1) / 2
Now, we need to find the fifth roots of (i + 1) / 2. This involves finding the complex numbers that, when raised to the power of 5, result in (i + 1) / 2.
To find the fifth roots, we can use De Moivre's theorem. De Moivre's theorem states that for any complex number r∠θ, the nth roots are given by the formula: r^(1/n)∠(θ/n).
In this case, (i + 1) / 2 can be written as r∠θ, where:
r = sqrt((1/2)^2 + 1^2) = sqrt(1/4 + 1) = sqrt(5/4) = sqrt(5) / 2
θ = arctan(1 / (1/2)) = arctan(2)
Using De Moivre's theorem, we can find the fifth roots as follows:
z = (sqrt(5) / 2)^(1/5)∠(arctan(2) / 5) + 2πk/5
where k is an integer from 0 to 4.
Calculating the values:
For k = 0:
z_1 = (sqrt(5) / 2)^(1/5)∠(arctan(2) / 5)
z_1 ≈ 0.382 + 0.924i
For k = 1:
z_2 = (sqrt(5) / 2)^(1/5)∠(arctan(2) / 5 + 2π/5)
z_2 ≈ -0.682 + 0.731i
For k = 2:
z_3 = (sqrt(5) / 2)^(1/5)∠(arctan(2) / 5 + 4π/5)
z_3 ≈ -0.618 - 0.854i
For k = 3:
z_4 = (sqrt(5) / 2)^(1/5)∠(arctan(2) / 5 + 6π/5)
z_4 ≈ 0.886 - 0.466i
For k = 4:
z_5 = (sqrt(5) / 2)^(1/5)∠(arctan(2) / 5 + 8π/5)
z_5 ≈ 0.032 - 1.137i
Therefore, the solutions to the equation (1+i)z^5 + i = 0 are:
z ≈ 0.382 + 0.924i, -0.682 + 0.731i, -0.618
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find the surface area of that part of the plane that lies inside the elliptic cylinder
Answers
The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder \(\frac{x^2}{25} +\frac{y^2}{9}\) is 15π√150 and this can be determined by using the given data.
We are given the two equations are:
10x + 7y + z = 4---------(1)
\(\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)\)
equation(1) is written as
z = 4 - 10x - 7y-----------(3)
The surface area is given by the equation:
A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)
compare equation(4) with equation(3) we get the values of ∂f/∂x and
∂f/∂y
∂f/∂x = -10
∂f/∂y = -7
substitute these values in equation(4)
A(S) = ∫∫√[(-10)² + (-7)² + 1]dA
A(S) = ∫∫√[100 + 49 + 1]dA
A(S) = ∫∫√[150]dA
A(S) = √150 ∫∫dA
Where ∫∫dA is the elliptical cylinder
From the general form of an area enclosed by an ellipse with the formula;
comparing x²/a² + y²/b² = 1 with x²/25 + y²/9 = 1, from that we get the values of a and b
a = 5 and b = 3
So, the area of the elliptical cylinder = πab
Thus;
A(S) = √150 × π(5 × 3)
A(S) = 15π√150
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a coin is altered so that the probability that it lands on heads is less than 1 2 12 and when the coin is flipped four times, the probability of an equal number of heads and tails is 1 6 16. what is the probability that the coin lands on heads?
Answers
The probability that the coin lands on heads is D = (3±√3)/6
Probability is a branch of mathematics that studies the likelihood of a random event occurring. For example, when a coin is tossed into the air, the possible outcomes are Head and Tail.
Let x be the probability of flipping heads. As a result, the probability of flipping tails is 1- x.
The probability of flipping two heads and two tails is equal to the number of ways to flip it multiplied by the product of the probabilities
(4+2)x2(1-x)2 = 1/6
6x2(1-x)2 = 1/6
x2(1-x)2 = 1/36
x(1-x) = ±1/6
As for the desired probability x, both x and 1 - x are nonnegative, we only need to consider the positive root, hence
x(1-x) = 1/6
6x2 – 6x +1 = 1/6
Using the quadratic formula, we can determine that the roots of this equation are
(3±√3)/6
Therefore the probability that the coin lands on heads is D = (3±√3)/6
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Quantitative Problem 1t You deposit \( \$ 2,300 \) into an account that pays \( 6 \% \) per year. Your plan is to withdraw this amount at the end of 5 years to use for a down payment on a new car. How
Answers
You will be able to withdraw approximately $3,076.32 at the end of 5 years.
To calculate the amount you will be able to withdraw at the end of 5 years, we can use the future value formula for compound interest.
The formula for calculating the future value (FV) of a present value (PV) invested at an annual interest rate (r) for a certain number of years (t) is:
\(FV = PV * (1 + r)^t\)
Given:
PV = $2,300
r = 6% = 0.06 (decimal representation)
t = 5 years
Substituting these values into the formula, we get:
FV = $2,300 * \((1 + 0.06)^5\)
Calculating the expression inside the parentheses:
\((1 + 0.06)^5 = 1.338225\)
Multiplying the present value by this factor:
FV = $2,300 * 1.338225
FV ≈ $3,076.32
Therefore, you will be able to withdraw approximately $3,076.32 at the end of 5 years.
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You deposit $2,300 into an account that pays 6% per year. Your plan is to withdraw this amount at the end of 5 years to use for a down payment on a new car. How much will you be able to withdraw at the end of 5 years? Do not round intermediate calculations. Round your answer to the nearest cent
If a stadium has 50,000 seats, how many concert tickets would have to be sold for the event to be 85% sold out?
Answers
Answer:
7,500 tickets would be sold for 85% to be sold out.
What is x-x?
Anyone who answers that in 7 minutes will be given marks
Answers
Answer:
0
Step-by-step explanation:
x and x are same terms.
Answer:
x is the cofficient term in algebra equations
Step-by-step explanation:
nd when they both are cancelled out they r equal to 0
HOPE IT HELPS
Write an equation for a line wrich passes through the point (3,-2) and is perpendicular to the line 3x+7y=9.
Answers
The equation of a line passing through the point (3,-2) and perpendicular to the line 3x+7y=9 will be derived. The explanation will describe the steps to find the equation using the given information.
To find the equation of a line perpendicular to 3x+7y=9, we need to determine the slope of the given line and then find the negative reciprocal to obtain the perpendicular slope. The negative reciprocal of a slope is obtained by taking the negative reciprocal of the fraction representing the slope.The given line, 3x+7y=9, can be rearranged into slope-intercept form (y = mx + b) by solving for y:
7y = -3x + 9
y = (-3/7)x + 9/7
The slope of the given line is -3/7. To find the negative reciprocal, we flip the fraction and change the sign, resulting in the perpendicular slope of 7/3. Now that we have the perpendicular slope, we can use the point-slope form of a line to find the equation. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the values from the given point (3,-2) and the perpendicular slope of 7/3, we have:
y - (-2) = (7/3)(x - 3)
Simplifying the equation:
y + 2 = (7/3)(x - 3)
Expanding the equation:
y + 2 = (7/3)x - 7
Moving the constant term to the other side:
y = (7/3)x - 7 - 2
Simplifying further:
y = (7/3)x - 9
Therefore, the equation of the line that passes through the point (3,-2) and is perpendicular to the line 3x+7y=9 is y = (7/3)x - 9.
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The scale factor of two similar polygons is given. Find the ratio of their perimeters and the ratios of their areas.
1) 3:1
2) 7/4
Answers
The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.
Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,
To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.
1) So, perimeter = 3:1
The ratio of areas between two similar polygons is equal to the square of the scale factor.
Since the scale factor is 3:1, the ratio of their areas is:
(Ratio of areas) = (Scale factor)² = 9/1 = 9:1
Similarly,
2) Perimeter = 7:4
Area = 49/16
Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.
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Let A and B be independent events with P(A)=0.7 and P(B)=0.2. Compute (a) P(A∩B) (b) P(A∪B) (c) P(A ′
∪B ′
Answers
Based on the given data, the probabilities are (a) P(A∩B) = 0.14, (b) P(A∪B) = 0.76, and (c) P(A'∪B') = 1.1.
P(A∩B) can be found by multiplying the probabilities of the individual events since A and B are independent. Therefore, P(A∩B) = P(A) * P(B) = 0.7 * 0.2 = 0.14.
P(A∪B) represents the probability of either event A or event B occurring. To calculate this probability, we can use the formula P(A∪B) = P(A) + P(B) - P(A∩B). Since A and B are independent, P(A∩B) = 0.14. Therefore, P(A∪B) = 0.7 + 0.2 - 0.14 = 0.76.
P(A') represents the complement of event A, which is the probability of A not occurring. Since A and B are independent, the complement of A (A') and the complement of B (B') are also independent. To find P(A'∪B'), we can calculate the probability of either A' or B' occurring. Using the complement rule, P(A') = 1 - P(A) = 1 - 0.7 = 0.3, and P(B') = 1 - P(B) = 1 - 0.2 = 0.8. Since A' and B' are also independent, we can use the same formula as in part (b) to find P(A'∪B'), which is P(A') + P(B') - P(A'∩B'). However, since A' and B' are independent, the intersection of their complements (A'∩B') will have a probability of 0, as the occurrence of A' does not affect the occurrence of B', and vice versa. Therefore, P(A'∩B') = 0, and P(A'∪B') = P(A') + P(B') = 0.3 + 0.8 = 1.1.
In summary, the probabilities are: (a) P(A∩B) = 0.14, (b) P(A∪B) = 0.76, and (c) P(A'∪B') = 1.1. The independence of events A and B allows us to calculate these probabilities using simple mathematical operations and rules of probability.
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How can a diagram show you that corresponding parts of two triangles are congruent without providing specific angle measures or side lengths?
Answers
Then look up your question
There you go
By using congruency definitions, we can show that corresponding parts of two triangles are congruent.
What is Congruent Triangles?Congruent triangles have the same corresponding angle measures and side lengths.
Given two triangles,
We can show that corresponding parts of two triangles are congruent by showing both the triangles congruent, then by CPCT we'll get the corresponding parts of congruent triangles are congruent.
Hence, By using congruency definitions, we can show that corresponding parts of two triangles are congruent.
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you spin two wheels with equal size wedges labeled with numbers 1 through 6. what is the probability that either wheel lands on an odd value ?
Answers
The probability that either of spin two wheel lands on an odd value is 1.
Define the term probability?Probability is a way to gauge how likely something is to happen. Even though no event can be predicted with absolute certainty, probability can be used to express how likely it is that it will happen.For the stated question-
Total number marked on the wheel (1 to 6) = 6 numbers.
Total odd number (1, 3, 5) = 3 numbers
Probability of of getting odd number on one wheel = 3/6 = 1/2.
Let the probability of of getting odd number on one wheel P(A).
Then, Probability of of getting odd number on second wheel P(B).
Then,
Only only wheel have the odd number,
P(A∩B) = 0.
Thus,
Probability that either wheel lands on an odd value;
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∪B) = 1/2 + 1/2 - 0
P(A∪B) = 1
Thus, probability that either wheel lands on an odd value is 1.
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preform the indicated operation 2 3/8 × 5 3/4
Answers
Answer:
It is 13 21/32 hope this helps
why do we use the 2's complement representation to handle subtraction instead of direct subtraction? (again, you may search the internet for an answer) g
Answers
We use the 2's complement representation to handle subtraction instead of direct subtraction because it simplifies the implementation of subtraction in digital circuits and makes it more efficient.
The 2's complement representation allows us to represent negative numbers by taking the complement (flipping all the bits) of the positive number and adding 1. This means that we can perform addition and subtraction using the same hardware circuitry, by simply inverting the bits of the subtrahend (the number being subtracted) and adding it to the minuend (the number being subtracted from). For example, to subtract 5 from 7, we can represent 5 as 00000101 in binary, take its 2's complement to get 11111011, and then add it to 7 (represented as 00000111) to get the result 00000010, which represents the number 2. Using direct subtraction, we would have to perform a borrow operation when subtracting each bit, which is more complex and time-consuming than using the 2's complement representation. Furthermore, the 2's complement representation has the useful property that it preserves the order of numbers under addition and subtraction, which makes it easier to compare and manipulate signed numbers in computer programs.
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It’s state if they are similar and if so state how they are
Answers
For similar triangle is:
For similar triangle:
\(\begin{gathered} \angle A=\angle X \\ \angle B=\angle Y \\ \angle C=\angle Z \end{gathered}\)and
\(\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XY}\)So
\(\angle L=59\)both triangle then :
\(\frac{LE}{LM}=\frac{ED}{MN}=\frac{LD}{LN}\)LE=11 , LD=9 , LM=90, LN=110
\(\begin{gathered} \frac{ED}{MN}=\frac{LD}{LN} \\ \frac{ED}{MN}=\frac{9}{10} \end{gathered}\)For similar triangle ratio of ED and MN is 9/10
