The measure of [tex]$\angle CAB = 180^{\circ} - \angle ACD$[/tex]
What is the circumscribed circle?
A circumscribed circle is a circle that is drawn around a polygon such that the circle touches all the vertices of the polygon. In other words, the vertices of the polygon lie on the circumference of the circle.
Given that a circle is circumscribed around a quadrilateral ABCD, it is clear that the circle passes through all four vertices of the quadrilateral, A, B, C and, D. Also, the diameter of the circle is the diagonal AC of the quadrilateral.
The angles formed by the diameter with the tangents from the non-adjacent vertices are supplementary. That is [tex]$\angle CAB + \angle ACD = 180^{\circ}$[/tex]
Therefore, the measure of [tex]$\angle CAB = 180^{\circ} - \angle ACD$[/tex]
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find the component form of the unit vector obtained by rotating the vector counterclockwise about the origin.
The component form of the unit vector obtained by rotating the vector counterclockwise about the origin is v = ⟨ |v|cos(θ), |v|sin(θ) ⟩.
the term vector in math is defined as a quantity which has both magnitude and direction and it defines the movement of the object from one point to another.
Here we have given the unit vector and we need to find the component form from it.
As we all know that the vector is a quantity that has magnitude and direction.
Here we also know that it can be written in component form where the components are the horizontal and vertical coordinates of the endpoint of the vector measured from the origin.
And the vector with magnitude of |v| and direction of θ which has an angle measured from the horizontal axis in the counter clockwise direction then it has the following components form that can be written as
=> v = ⟨ |v|cos(θ), |v|sin(θ) ⟩.
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Which of the following types of functions have inverse functions?A.May-to-oneB.One-to-manyC.One-to-oneD.Many-to-many​
Therefore , the solution of the given problem of function comes out to be the one -to-one function is an inverse function.
What does the term function refer to?Math is the science of numbers, their variations, math and nearby tissues, shapes, and their actual and potential places. The relation between a group of inputs, each of which has a related output, is referred to as a "function." A function is an association between inputs and outputs where each input results in a single, unique output. Each function is assigned a scope, or realm, and a city or municipality. Functions are typically denoted by the letter f. (x). Input does contain an x. Procedures fall into four main categories: on functions, each processes, a few more features, within operations, as well as on functions.
Here,
Given : May -to-one function
One -to-many function
One-to-one function and
Many-to-many.
Thus, To find which is a inverse function .
So , by observing the following properties of function the one -to-one function is an inverse function.
Therefore , the solution of the given problem of function comes out to be the one -to-one function is an inverse function.
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Solve g(x) =36 given the equation g(x) = x^2 -10
x² - 10 = 36
x² = 46
x = +- sqrt(46)
Can someone help me solve the first math problem please in a quadratic b model
Answer:
i) To find the maximum height of the projectile, we need to find the highest point that it reaches before falling back to the ground. In this case, the maximum height is the vertex of the parabola. To find the vertex, we can use the formula:
x=-b/2a
(12,845)
Substituting this value back into the original height equation, we find the maximum height:
h = -5(12)^2 + 120(12) + 125 = -300 + 1440 + 125 =845
So the maximum height of the projectile is 845 meters.
ii) To find when the projectile reaches its maximum height, we need to find the x-coordinate of the vertex of the parabola. As we found above, the x-coordinate of the vertex is 12 seconds. So the projectile reaches its maximum height at 12 seconds.
susan is making a flag. she buys 3 3/4 yards of fabric. she uses 9/10 of this piece of fabric. how many yards of the 3 3/4 yards of fabric that she bought did she actually use?
On solving the provided question, we can say that by unitary method we got that the 3, 3/4 yards of fabric that she bought did she actually use
[tex]3\frac{3}{4} - 9/10 = > 31/10[/tex]
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
she buys = 3, 3/4 yards of fabric
she uses = 9/10 of this piece of fabric
the 3, 3/4 yards of fabric that she bought did she actually use
[tex]3\frac{3}{4} - 9/10\\15/4 - 9/10\\150 - 36/40\\124/40\\62/20\\31/10[/tex]
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margaret started a stamp collection. she collected 8 stamps the first day. each subsequent day she collected 8 more stamps than she had collected the previous day. if she collected stamps for 5 consecutive days, what was the average number of stamps collected per day?
The average number of stamps collected per day was 24.
1st day: 8 stamps
2nd day: 8 + 8 = 16 stamps
3rd day: 16 + 16 = 32 stamps
4th day: 32 + 32 = 64 stamps
5th day: 64 + 64 = 128 stamps
Total number of stamps collected
= 8 + 16 + 32 + 64 + 128
= 248 stamps
Average number of stamps collected per day
= 248 / 5
= 24 stamps
Margaret started a stamp collection and collected 8 stamps on the first day. On the second day she collected 8 more stamps, for a total of 16. On the third day she collected 16 more stamps, for a total of 32. On the fourth day she collected 32 more stamps, for a total of 64. On the fifth day she collected 64 more stamps, for a total of 128. In total, she collected 248 stamps over the five days. The average number of stamps collected per day was 24.
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assume the average test score from the last year's class was 85 points with a standard deviation of 9. about what proportion of students earned a 70 points or higher?
About 96.17% of the students who took the test earned a 70 points or higher
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The z score of a normal distribution is given by:
z = (raw score - mean)/standard deviation
The average test score from the last year's class was 85 points with a standard deviation of 9. Hence:
Mean = 85, standard deviation = 9
For a score of 70 points or higher:
z = (70 - 85) / 9 = -1.67
P(z > -1.67) = 1 - P(z < -1.67) = 1 - 0.0383 = 0.9617 = 96.17%
96.17% of the students earned a 70 points or higher
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an urn contains 6 white balls and 15 red balls. a sample of four balls is selected at random from the urn. what is the probability that the sample contains two white balls and two red ones?
The probability that the sample contains two white balls and two red ones is 0.264. There are multiple draws without replacement.
How to calculate probability?Probability of an event can be expressed as
P(A) = n(A) / n(S)
Where
P(A) is the probability of an event An(A) is the number of favorable outcomesn(S) is the total number of events in the sample spaceAn urn contains 6 white balls and 15 red balls. A sample of four balls is selected at random from the urn. Find the probability that the sample contains two white balls and two red ones!
It means that there will be multiple draws without replacement.
The total balls are 6 + 15 = 21 balls.
The probability of drawing two white balls and two red ones is
= P(1st is white ∩ 2nd is white ∩ 3rd is red ∩ 4th is red)
= P(1st is white)*P(2nd is white)*P(3rd is red)*P(4th is red)
= (6/21)*(5/20)*(15/19)*(14/18)
= 0.044
There are 6 possible orders (WWRR, WRWR, WRRW, RWWR, RWRW, RRWW). So, the probability in any order would be
= 0.044 × 6
= 0.264
Hence, the probability of drawing two white balls and two red ones in any order is 0.264.
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The diagram shows a prism.
1m
2m
front
1m
2m
2m
side
front elevation
Draw the front elevation and the side elevation.
of the prism on the grids.
Use a scale of 2 squares to 1 m.
side elevation
Therefore , the solution of the given problem of triangle comes out to be height = 2 meters = 4 squares.
Explain the triangle.Triangles are polygons due to their 3 sides and three vertices. It is an essential geometric form. Triangle ABC is a triangle whose corners are at coordinates A, B, and C. The discovery of a single plane and triangle in geometric shapes occurs when four elements are not collinear. Due to its upper right corner and three corners, triangles are classified as polygons. The corners of a triangle are the three spots at which it intersects. You may get 180 degrees by multiplying the triple triangle angles.
Here,
Drawn using the Required Elevation's Construction Method
The scale is presented as 2 squares per meter.
The front elevation plane has a total of 16 squares, which is the quantity of cubes in the plane.
Front elevation: There are 4 squares in the front elevation's width.
Closest to the observer, there are 4 + 1 squares within the front portion.
The slant surface has 3 by 4 squares as the number of squares.
The front aspect of the supplied diagram is depicted in the drawing that is attached.
A side elevation;
Following the same format as before, we have the side elevation as follows;
The side elevation's lower side is 2 meters wide, or 4 squares.
The side elevation is 2 meters high, or 4 squares.
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Help, needed ASAP, thank you!!
Answer:
mt =84
mns = 78
Step-by-step explanation:
since mn=124 , ns=80 , ts=72
then mt= 360-(124+80+72)=84
if we draw a line from m to s
then angle msn=124÷2=62 (inscribed angle)
and angle smn=80÷2=40 ( // // )
then angle mns=180-(62+40)=78
Help with only even problems please no odd problems
Write an exponential function in the form y=ab^x that goes through points (0,13) and (2,637)
Answer:
y=13(7)^x
Step-by-step explanation:
x = 0, y = 13, so we know that a = 13.
13b^2 = 637 ==> x=2 and y=637
b^2 = 49 ==> divide both sides by 13
b = 7 ==> take the square root on both sides
y = 13 * 7^x ==> plug in 7 for b in y = 13b^x
Answer: y=13(7)^x
The Fleet Feet training log is shown at the right. Deana ran 462 miles. Her weekly mileage rate was greater than Pavel's rate but less than Alberto's rate. Complete the training log. How many weeks could it have taken her to run 462 miles?
Deana whose running rate is greater than Pavel's but less than Alberto ran 33 miles per week
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
The number of miles Pavel ran is,
= 672/21.
= 32 per week.
The number of miles Alberto ran is,
= 420/12.
= 35 miles per week.
Now, The rate per week must be an integer and it should be 33 or 34.
So, The number that divides 462 completely is 33.
Therefore, The number of miles Deana ran is 33 miles per week.
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Which of the following is the solution set of the inequality x/4 < (5x-2)/3 - (7x-3)/ 5 ?
A. (4, 00)
B. (- [infinity], 4)
C. (4, infty)'
D. (- [infinity], 4)
The solution set of the inequality " x/4 < (5x-2)/3 - (7x-3)/ 5 is C: (4, infinity).
x/4 < (5x-2)/3 - (7x-3)/ 5
taking the LCM of the right-hand side of the given inequality which is 15.
Now multiply 15 by both sides of the inequality
15 . x/4 < [ 15 . (5x-2)/3 ] - [ 15. (7x-3)/ 5 ]
15. x/4 < [ 5 . (5x -2) ] - [ 3 . (7x -3) ]
15. x /4 < ( 25x - 10 ) - ( 21x - 9 )
15. x/4 < 25x - 10 - 21x + 9
15. x/4 < 4x - 1
Now multiply boh sides with 4
4 (15 . x/4) < 4. (4x - 1)
15 . x < 16x - 4
15x < 16x - 4
4 < - 15x + 16x
4 < x
x > 4
Hence, all real numbers x that are greater than 4 are the solution of the given inequality.
Therefore, the solution set of the given inequality is (4, infinity).
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Using the sample formulas, find the mean, variance, and standard deviation for the grouped data displayed in the following table. x f 0 to less than 4 19 4 to less than 8 21 8 to less than 12 15 12 to less than 16 11 16 to less than 20 8 20 to less than 24 6 Carry out all calculations exactly, round to 2 decimal places the final answers only. Mean
Therefore, the answer to the above median problem is a) z-score = 1.50, b) age 34 has SD=1.5, and C. option B is correct.
Define median.The median value is the number that exactly lies in the middle of a dataset that has been arranged. The gap between the minimum and maximum 50% of the data is a maximum likelihood measure or average. Depending on whether you have an odd or possibly even amount of data points, different formulas are used to calculate the median and mode.
Here,
The average age is 36, it is stated.
2.5 standard deviations
a) The z-score is (34 - 28.3)/3.8 = 1.50.
b) Analysis
A 34-year-old is 1.50 standard deviations well above average in age.
c) The right answer is B.
Consequently, the provided issue of median's solution yields
Option B is right since age 34 has an SD of 1.5 and a C, and z-score is 1.50.
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What does ∆ x mean in math?
In mathematics, the symbol ∆ (delta) is often used to indicate a change or difference in a quantity.
When used in the context of Calculus, ∆x (delta x) is a notation that represents the change in the independent variable x, often used in the study of limits, derivatives and integrals. It is defined as the difference between two nearby values of x, for example x2 - x1.
Also, In physics and engineering, the notation ∆x is used to refer to the change in position or displacement of an object. It is defined as the final position minus the initial position of an object.
In general, ∆x is used to represent a small change or difference in a variable, usually used in the context of calculus and physics.
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inclusive or exclusive or? a: you must take chemistry or physics to graduate b: you can have a complimentary coffee or tea question 3 options: a is exclusive, b is inclusive both are exclusive a is inclusive, b is exclusive both are inclusive
If you have two options, A and B, exclusive means only one option is required (A or B) while inclusive means both options are available (A and B).
To calculate the answer to this question, we need to consider what the words “exclusive” and “inclusive” mean. Exclusive means that one option is required and the other is not, while inclusive means that both options are available. In the case of the question a, the answer is exclusive because you must take either chemistry or physics to graduate. In the case of question b, the answer is inclusive because you can have either a complimentary coffee or tea.
To illustrate the difference between exclusive and inclusive with a formula, we can use the following:
Exclusive: A + B = A
Inclusive: A + B = A + B
This formula demonstrates that if you have two options, A and B, exclusive means only one option is required (A or B) while inclusive means both options are available (A and B).
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One large box and two small boxes weigh a total of 100 pounds. One large box and four small boxes weigh a total of 150 pounds. The weight limit of a trailer is 1500 pounds. Write an inequality that represents the numbers of large, x, and small, boxes that can be loaded in the trailer.
The inequality that represents the numbers of large, and small, boxes that can be loaded in the trailer is 2x + y ≤ 60
What is inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given that, One large box and two small boxes weigh a total of 100 pounds. One large box and four small boxes weigh a total of 150 pounds.
Let the weights of large and small boxes be x and y respectively.
x + 2y = 100
x = 100-2y...(i)
x + 4y = 150
x = 150-4y...(ii)
Solving eq(i) and eq(ii)
100 - 2y = 150 - 4y
2y = 50
y = 25
Put y = 25 in eq(i)
x = 100-50
x = 50
Therefore, weights of large and small boxes are 50 and 25 pounds respectively.
Now,
Since, weight limit of a trailer is 1500 pounds
Establishing the inequality,
50x + 25y ≤ 1500
or,
2x + y ≤ 60
Hence, the inequality that represents the numbers of large, and small, boxes that can be loaded in the trailer is 2x + y ≤ 60
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I took a loan from the bank and I paid an interest of 1,500 at what rate and I pay if the loan was 5000 for 3 years
Answer:
Step-by-step explanation:
To calculate the rate :
Interest = P x R x T
100
Here, P = 5000, T = 3, I = 1500
Therefore,
1500 = 5000 x R x 3
100
1500 = 150 R
1500 = R
15
10 = R
Thus, the rate is 10%
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Giovanna used the calculations below to determine the height of a stack of 7 books that are each 2 5/8 inches thick. What was her error?O 7(2 5/8)O 7 (2 + 5/8)O 14 + 5/8O 14 5/8
Giovanna's error is that she should have added the fractions instead of adding the whole numbers and the fraction. The correct calculation is 14 7/8 inches.
2 5/8 + 2 5/8 + 2 5/8 + 2 5/8 + 2 5/8 + 2 5/8 + 2 5/8
= (2 + 2 + 2 + 2 + 2 + 2 + 2) + (5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8)
= 14 + (5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8)
= 14 + (7/8)
= 14 7/8
Giovanna made an error when calculating the height of a stack of 7 books that are each 2 5/8 inches thick. The correct calculation was 14 7/8 inches, however, she calculated 14 + 5/8 inches. This is incorrect because it is necessary to add the fractions together in order to get the correct answer. To calculate the height of the stack of books, we need to add each book's thickness together. Since each book is 2 5/8 inches thick, we start by adding the whole numbers: 2 + 2 + 2 + 2 + 2 + 2 + 2 = 14. Then, we add the fractions: 5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8 = 7/8. Adding these together gives us 14 + 7/8 = 14 7/8. Thus, the correct answer is 14 7/8 inches.
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judith surveyed some students at her school about their favorite primary color. yellow 2 red 5 blue 3 what is the experimental probability that the next student judith talks to will pick red? write your answer as a fraction or whole number. p(red)
The experimental probability that the next student Judith talks to will pick red is 1/2.
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.
Given that,
Yellow = 2
Red = 5
Blue = 3
Finding the experimental probability
Total number of trials = 2+5+3 = 10
Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes
Probability = red/ Total number of trials = 5/10 = 1/2
Thus, the experimental probability that the next student Judith talks to will pick red is 1/2.
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Answer:
1/2
Step-by-step explanation:
how to multiply fraction with one fraction having the lcm and two other fractions being a factor of it
Multiplying fractions can be a tricky task, but with the right steps, it can be easily accomplished.
To multiply two fractions together, first find the least common multiple (LCM) of the two fractions.
Once you have the LCM, divide it by each of the two fractions and multiply the resulting numbers together. This will give you the final answer to your multiplied fractions.
Let's look at an example. Suppose you wanted to multiply 3/4 and 5/8 together. First, you would need to find the LCM of 3/4 and 5/8. The LCM in this case would be 24.
Now divide 24 by 3/4 and 5/8 to get 32/24 and 30/24 respectively. Multiplying 32/24 and 30/24 together would give you 960/576 as the answer.
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a triangle has dimensions 5, 8, and 10. a similar triangle is drawn with a scale factor of 0.5. what are the dimensions of the new triangle?
a. 10, 16, 20
b. 5.5, 8.5, 10.5
c. 2.5, 4, 5
d. 5, 8, 10
Answer is c. 2.5, 4, 5
Step-by-step explanation:
To find the dimensions of the new triangle,
we need to apply the scale factor of 0.5 to the original triangle's dimensions.
This means we need to multiply each dimension by 0.5.
Original Dimensions: 5, 8, 10
New Dimensions:
5 x 0.5 = 2.5,
8 x 0.5 = 4
10 x 0.5 = 5
Therefore, the dimensions of the new triangle are 2.5, 4, 5.
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Simplify the expression. 3.8−4.9n−3n+6
Answer:
-7.9n+9.8
Step-by-step explanation:
add em
Answer:
9.8 - 7.9n
Step-by-step explanation:
To simplify, we need to have the least amount of terms possible. To do this here, we need to group like terms. We will start by rearranging our equation to group our like terms, like this:
3.8 + 6 - 4.9n - 3n
Then, we will combine our liker terms, giving us:
9.8 - 7.9n
That is the most simplified we can get. So our simplified equation is
9.8 - 7.9n.
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Triangle proportionality theorem and the segment addition postulate, indicates that A_F : AT = A_F : 4×A_F, therefore;
A_F : AT = 1 : 4
What is the triangle proportionality theorem statement?The triangle proportionality theorem states that a segment drawn in a triangle, such that it is parallel to one side of the triangle and intersects the other two sides at two distinct points, then the proportion in which the segment divides the other two sides are the same.
The specified details of the triangle ΔABC are;
The location of the point D = AB, the location of the point B = AC
The point of intersection of the angle bisector of angle ∠A and DE = F
The point of intersection of the angle bisector of angle ∠A and BC = Point T
AD = 1, DB = 3, AE = 2, EC = 4
Drawing a line CU parallel to DE from point C to intersect AB at U, according to the triangle proportionality theorem, we get;
AE : EC = 2 : 4 = AD : DU = A_F : FV
AD : DU = 1 : 2
A_F : FV = 1 : 2
Therefore; FV = 2 × A_F
FV : VT = DU : BU = 2 : 1
FV = 2 × VT
2 × VT = 2 × A_F by substitution property, therefore;
FV = 2 × A_F
AT = A_F + FV + VT (segment addition postulate)
Therefore; AT = A_F + 2 × A_F + A_F = 4×A_F
A_F : AT = A_F : 4 × A_F = 1 : 4
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x/4 - 3/8y = 3
5/3x - y/2 = 12
Any method is fine :)
Answer:
(6, - 4 )
Step-by-step explanation:
[tex]\frac{x}{4}[/tex] - [tex]\frac{3}{8}[/tex] y = 3
multiply through by 8 ( the LCM of 4 and 8 ) to clear the fractions
2x - 3y = 24 → (1)
[tex]\frac{5}{3}[/tex] x - [tex]\frac{y}{2}[/tex] = 12
multiply through by 6 ( the LCM of 3 and 2 ) to clear the fractions
10x - 3y = 72 → (2)
multiplying (1) by - 1 and adding to (2) will eliminate y
- 2x + 3y = - 24 → (3)
add (2) and (3) term by term to eliminate y
8x + 0 = 48
8x = 48 ( divide both sides by 8 )
x = 6
substitute x = 6 into either of the 2 equations and solve for y
substituting into (1)
2(6) - 3y = 24
12 - 3y = 24 ( subtract 12 from both sides )
- 3y = 12 ( divide both sides by - 3 )
y = - 4
solution is (6, - 4 )
What is the base if the portion is $4,570 and the rate is 55%?
Answer:
8309.09
Step-by-step explanation:
Base = Total
So we know that 4570 is 55% of the total
55% = 55/100 = 0.55
It is the same as:
4570 = 0.55 * total
Total = 4570/0.55 = about 8309.09
Hope this helps :)
Let me know if this is correct or not
Have a great day!
Semicircles of diameter 2'' are lined up as shown. What is the area, in square inches, of the shaded region in a 1-foot length of this pattern?
The shaded region is made up of the area of a rectangle minus the areas of the semicircles. The semicircles have a diameter of 2 inches, so the radius of each semicircle is 1 inch.
The area of each semicircle can be found using the formula pir^2, where r is the radius. So the area of each semicircle is pi1^2 = pi square inches.
The area of the rectangle is found by multiplying the length by the width: 1 foot * 12 inches/feet = 12 square inches.
The shaded region is the area of the rectangle minus the area of the semicircles. So the area of the shaded region is 12 square inches - 2* pi square inches = 12 - 2* pi square inches.
It's important to note that the length of the shaded region is given in feet (1-foot) but the area of the semicircles and the rectangle is given in square inches.
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isabelle has a recipe for granola that is currently written to make 15 cups. she wants to increase the yield to 50 cups to prepare for family vacation. isabelle needs to determine the percentage that she will multiply her original quantities by to determine her new measurements. what this percentage is known as?
So Isabelle will have to multiply all the quantities in her recipe by a factor of 3.33 (or 333%) to increase the yield to 50 cups.
The percentage that Isabelle needs to multiply her original quantities by to increase the yield from 15 cups to 50 cups is known as the "scaling factor".
To find the scaling factor, you can divide the desired yield by the original yield and multiply by 100 to express it as a percentage:
Scaling factor = (50 cups / 15 cups) x 100% = 3.33 x 100% = 333%
So Isabelle will have to multiply all the quantities in her recipe by a factor of 3.33 (or 333%) to increase the yield to 50 cups.
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What is the property of regular graph Mcq?
A graph is called a regular graph if the degree of each vertex is equal.
N complete vertices make up an (N-1) regular graph.
Proof: Each vertex in a complete network with N vertices is connected to each of the (N-1) remaining vertices. Therefore, each vertex's degree is (N-1). The graph is hence (N-1) Regular.
If the degree of each vertex is equal, a graph is said to be a regular graph. If the degree of each vertex is K, a graph is said to be K regular.
A regular graph in graph theory is one in which every vertex has the same number of neighbors or the same degree of valency. The stronger requirement that each vertex's indegree and outdegree be equal must also be met by a regular directed graph.
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