The magnitude of AB based on the information is 5.1.
How to find the magnitude of AB?To show that points A, B, and C are colinear, we need to show that they lie on the same line. One way to do this is to find the direction vector of the line passing through A and B, and then check whether point C is on the same line.
The direction vector of the line passing through A and B is given by the vector AB, which is equal to OB - OA. Substituting the given values for OA and OB, we find that AB = (3i - 2i) + (-2j + 3j) = i + j.
To check whether point C is on the same line as A and B, we can find the direction vector of the line passing through C and any one of the other two points.
We can find the direction vector of the line passing through C and A, which is given by the vector CA = OA - OC = (2i + 3j) - (i + 6j + 3k) = i + (-3j - 3k).
Since the direction vectors of the lines passing through A and C and through B and C are both in the same direction, we can conclude that points A, B, and C are colinear.
To find the magnitude of AB, we can use the distance formula:
AB = √((3 - 2)² + (-2 - 3)²) = √(1² + (-5)²) = √(26) = 5.1
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Bob lifts a 15N rock through a distance of 1.7m. How much work does Bob do
Bob lifts a 15N rock through a distance of 1.7m, 25.5 J work does Bob do
What is work done?An item should be converted to energy before being moved. The use of force is one way to transfer energy. The amount of energy used by a force to move an item is referred to as the work done.
The amount of the displacement and the component of the applied force of the object in the displacement direction is the work done by a force. Pushing a block with force "F" causes the body to move more quickly, meaning that work has been completed.
Work done (W) = F × s
Where, F = force
s = displacement
Now putting the values, we get-
or, W = 15 N × 1.7 m
or, W = 25.5 N-m or Joule
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Hillary makes two transactions while at the mall: • She returns an item to get $15 back at one store. • She buys an item for $15 at another store. Which is a correct description of the two quantities that represent these transactions? A The quantities have the same magnitude, but different signs. B The quantities have the same sign, but different magnitudes. C The quantities have different magnitudes and different signs. D The quantities have both the same magnitude and the same sign.
Answer:
the correct answer to this question would be D
what is the greatest common factor of 18x^4y+3x^3y^2-39x^2y^3+12x^2y^4
The required greatest common factor in the given expression is 3x²y.
What is the greatest common factor?The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers include of.
here,
Given expression,
= 18x⁴y+3x³y²-39x²y³+12x²y⁴
Taking common 3x²y from every term,
= 3x²y(6x² + xy - 13y² + 4y³)
Where 3x²y id the greatest common factor,
Thus, In terms of the given expression 3x²y is the greatest common factor.
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Giovanni works as a tour guide during the summer. He earns $45 a day and $14 for each tour that he leads. Which function is used to find the total amount of money Giovanni will earn each day
The function that is used to find the total amount of money Giovanni will earn each day is; A = 14 + 45d
How to solve algebra word problems?The general form of the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, we are told that;
Giovanni works as a tour guide during the summer.
Amount he earns daily = $45
Amount earned for each tour = $14
Now, if the number of days he spends as a tour guide is d, then we can say that the total amount of money Giovanni will earn each day is expressed as;
A = 14 + 45d
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In △QRS , ∠R is a right angle.
If
QS
= 20 and m∠Q = 49° , what is the length of
QR
?
HELP IM TAKING MY GEOMETRY FINAL AND I DONT KNOW ANYTHING
Answer:
Bellow
Step-by-step explanation:
QS =√c2 - b2
= √202 - 15.0941916044552
= √172.16537980799
= 13.12118
Which set of coordinates models the image of the triangle after a translation along <2, −9>?
A) M’(−5, 16), N’(−2, 13), P’(0, 15)
B) M’(−1, −2), N’(2, −5), P’(4, −3)
C) M’(−5, −2), N’(−2, −5), P’(0, −3)
D) M’(−1, 16), N’(2, 13), P’(4, 15)
Answer:
b
Step-by-step explanation:
i know
The solution is Option B.
The translation of triangle MNP along T < 2 , -9 > is
M’(−1, −2), N’(2, −5), P’(4, −3)
What is Translation?
A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
The notation for translation is T(h, k) where T is the translation, h is the change in the x-axis, and k is the change in the y-axis
Given data ,
Let the translated triangle be represented as ΔM'N'P'
Now , the translation rule is T < 2 , -9 >
Let the coordinates of the triangle ΔMNP be
The coordinates of M = M ( -3 , 7 )
The coordinates of N = N ( 0 , 4 )
The coordinates of P = P ( 2 , 6 )
Now , applying the translation rule of T < 2 , -9 > for the triangle MNP , we get
The coordinates of M' = M' ( -3 + 2 , 7 - 9 )
The coordinates of M' = M' ( -1 , -2 )
The coordinates of N' = N' ( 0 + 2 , 4 - 9 )
The coordinates of N' = N' ( 2 , -5 )
The coordinates of P' = P' ( 2 + 2 , 6 - 9 )
The coordinates of P' = P' ( 4 , -3 )
Hence , the coordinates of triangle M'N'P' is M’(−1, −2), N’(2, −5), P’(4, −3)
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19. Find the surface area of the cylinder. Give your answer to two decimal places.
Answer:
1155.52cm²
Step-by-step explanation:
A cylinder's volume is π r² h, and its surface area is 2π r h + 2πr²
radius(r) = 8cm
π = 3.14
height(h) = 15
2πrh + 2πr²
=2πr(h + r)
= 2 × 3.14 × 8 ( 15 + 8)
= 50.24(23)
= 1155.52cm²
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Replace * in the monomial so It can be represented as a square monomial
*-48t+36t^2
Answer:
16
Step-by-step explanation:
36 t^2 comes from 6t
so we have
(6t - )^2 the middle term will be represented by
2 x m x 6t = -48 t
so m = -4
(6t-4)^2 would result in ' * ' = +16
Write the number shown on the calculator to 1 significant figure. 6.27
The number will be 6.00
What do you mean by an important number?
An important number is a number that has a specific significance or use in a particular situation. For example, in mathematics, some important numbers include pi, the square root of two, and the golden ratio. In finance, important numbers might include the interest rate on a loan, the exchange rate between two currencies, or the daily closing price of a stock. In politics, important numbers may include the population of a state or country, the percentage of the population that is registered to vote, or the number of seats a particular political party holds in a legislature.
Given that:
6.27 should be reduce to 1 significant figure
So as we can see before 6 we have number 2
According to rule for rounding 6 will remain 6
Hence the number will be 6.00.
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What is the vertical asymptote of the function? x = –3 x = –2 x = 0 x = 3
Answer:4
Step-by-step explanation:i did the quiz
A photo is being resized to sell at a gallery. The original photo is 4 inches by 6 inches. Using the dimensions of 3 yds by 4.5 yds, find the scale factor.
The scale factor, if The original photo is 4 inches by 6 inches, and the new photo is 3 yards by 4.5 yards, is 1.8.
What is the scale factor?The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller).
Given:
The original photo is 4 inches by 6 inches, and the new photo is 3 yards by 4.5 yards,
Calculate the scale factor as shown below,
Scale factor = Original dimension / new dimension
Scale factor = (4 × 6) / (3 × 4.5)
Scale factor = 1.8
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a biologist records the average weight of the brain and body for a number of mammal species the biologist uses the inequality [tex]60\leq 0.5x+2.5\leq 250[/tex] to determine the weight of the mammals whose brain weighs between 60 pounds(lb) and 250 lb. solve the inequality
The inequality is [tex]115\leq x\leq 495[/tex]
What is inequality?
A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">", "<", "≥". Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.
Given [tex]60\leq 0.5x+2.5\leq 250[/tex]
splitting the equation:
[tex]60\leq 0.5x +2.5[/tex] and [tex]0.5x +2.5\leq 250[/tex]
[tex]60-2.5\leq 0.5x\\57.5\leq 0.5x\\115\leq x\\x\geq 115[/tex]
also
[tex]0.5x +2.5\leq 250\\0.5x\leq 247.5\\x\leq 495[/tex]
therefore the equation is
[tex]115\leq x\leq 495[/tex]
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11.3 is 7% of what?
Answer: 157.14
Step-by-step explanation: SDHU IK
Write two expressions (with at least two terms each) that when added together have a sum of -4n + 6.
PLEASE I NEED ANSWERS TODAY.
WRITE TWO EQUATIONS
The solution of the expression would be 2(-2n + 3).
What is arithmetic sequence ?A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms. One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...Using the method for locating the nth term, we may locate a particular term in an arithmetic series. Step 1: An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d. Therefore, enter the numbers a = 2 and d = 3 into the formula to determine the nth term.An ordered group of integers with a shared difference between each succeeding word is known as an arithmetic sequence.Expression 1 :
- 4n + 6
= -[tex]2^{2}[/tex] . n + 2 x 3
= 2 ( - [tex]\frac{2 * n^{2} }{2}[/tex] + [tex]\frac{2 x 3}{2}[/tex] )
= 2 ( - ([tex]2^{2-1}[/tex] * n ) + 3 )
= 2 ( - (2n) + 3 )
= 2 ( - 2n + 3 )
Expression 2 :
- 4n + 6
Rewrite 4 as 2 . 2
Rewrite 6 as 2 . 3
= - 2 . 2n + 3 . 3
= 2 ( - 2n + 3 )
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you decide to record the hair colors of people leaving a lecture at your school. what is the probability that the next person who leaves the lecture will have gray hair? express your answer as a simplified fraction or a decimal rounded to four decimal places.
The probability that the next person who leaves the lecture will have gray hair is 45/163 or 0.2760.
What is Probability?
Probability is the ratio of favorable outcomes to all other potential outcomes of an event. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
To calculate the likelihood that the next person to leave the lecture will have grey hair, one must first make an assumption about the distribution of hair colors among those in attendance. The data of the distribution of hair colors of people in the lecture are assumed below:
Blonde Red Brown Black Gray Total
24 32 29 33 45 163
The Probability of the number of people with grey hair to the total number of students in the class is used to calculate the likelihood that the next person to leave the lecture will have grey hair.
P(Gray) =45÷163 =0.2760
So therefore, the probability is 45/163 or 0.2760.
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5. The roof drawn below is made up of six pieces of lumber and is symmetrical. There is 1
foot of overhang on both sides.
Use the dimensions given in the diagram, determine how much total lumber would be
needed to create this roof (i.e. how many feet of wood does it take to build this roof?).
It is a good idea to label all of the vertices before beginning (6 marks).
Answer:
72+20sqrt3
Step-by-step explanation:
check the attached file
I NEED ANSWERS ASAP please guys this is due tomorrow and I have no idea what to do! Help!!
You could pick the question you want to answer..
The total time taken is 24 hours.
What is total time?
Total refers to a whole or full amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16. A automobile that has been totalled in an accident is irreparably damaged. Total Time is the result of multiplying the number of minutes in a day by the number of days in a given calendar month.
An inlet pipe takes 8 hours to fill a tank. An outlet pipe takes 12 hours to empty.
[tex]$\Rightarrow$[/tex] Time is taken to fill in 1 hour =1 / 8
[tex]$\Rightarrow$[/tex] Time taken to empty in 1 hour =-1 / 12
[tex]$\Rightarrow$[/tex] If both pipes are opened simultaneously tank be filled in 1 hour =1 / 8-1 / 12 =1 / 24 hours
[tex]$\therefore$[/tex] The total time taken is 24 hours.
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6 divided by 7.02 i need help
Answer: 0.85
Step-by-step explanation:
The required answer for long division for the decimal division of 6 divided by 7.02 is 0.8547 by rounded to four decimal places.
To perform long division for the decimal division of 6 divided by 7.02, follow these steps:
Step 1: Set up the division problem:
_______
7.02 | 6.00
Step 2: Place the decimal point directly above the division bar in the quotient:
0.
Step 3: Divide the first digit of the dividend (6) by the divisor (7.02). The result is 0.8547 (rounded to four decimal places).
Step 4: Multiply the divisor (7.02) by the quotient digit (0.8547) and write the result below the dividend, aligning the decimal points:
7.02
- 6.03
-----
0.99
Step 5: Subtract the result from the previous step from the dividend, and bring down the next digit (if any):
0.99
- 0.99
-----
0.00
Step 6: Since there are no more digits to bring down and the result is zero, we can conclude the division.
Therefore, the long division for the decimal division of 6 divided by 7.02 is 0.8547(rounded to four decimal places).
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Please HELP PLEASE PLEASE
nj bought a car for $20,000. two years later, the car has depreciated to a value that is 81% of what he paid. which equation(s) represent the exponential relationship?
V = 20,000 * 0.81^2 and V = 20,000 * (1 - 0.19)^2 are the equation(s) that represent the exponential relationship.
The value of the car two years later is represented by the variable V. The initial value of the car is represented by the constant 20,000. The relationship between the value of the car two years later and the initial value of the car is exponential, because the value of the car decreases by a fixed percentage each year.
One equation that represents this relationship is:
V = 20,000 * 0.81^2
This equation says that the value of the car two years later is equal to the initial value of the car multiplied by the decay factor of 0.81 raised to the power of 2. The decay factor represents the percentage by which the value of the car decreases each year.
Another equation that represents this relationship is:
V = 20,000 * (1 - 0.19)^2
This equation says that the value of the car two years later is equal to the initial value of the car multiplied by (1 - 0.19) raised to the power of 2. The term (1 - 0.19) represents the percentage by which the value of the car remains after it has depreciated.
Both of these equations represent the exponential relationship between the value of the car two years later and the initial value of the car.
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Assume that when adults with smartphones are randomlyselected, 45% use them in meetings or classes. If 6 adult smartphone users are randomly selected, find the probability that exactly 2 of them use their smartphones in meetings or classes. Round to 4 decimals
P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.
what is probability?The possibility or likelihood of an event occurring is expressed numerically as probability. Probabilities are expressed as ratios (0 to 1) and percentages (0 to 100). It is founded on the likelihood that something will occur. The theoretical probability is built on the fundamental principle of probability justification. For instance, there is a 12 percent chance of receiving heads while flipping a coin.
P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.
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-2y + 3 =21 solve linear equations
Answer:
y= -9
Step-by-step explanation:
Subtract 3 from both sides
-2y + 3-3= 21-3
-2y=18
Divide both sides by the same factor
-2y/-2 = 18/-2
y= -9
Answer: y = -9
Step-by-step explanation:
-2y+3=21
-2y=21-3
-2y=18
Divide that by -2:
y=-9
Find the value of x using the picture
The value of x is 91/9.
What is the value of X triangle?
The two angles' combined angles are subtracted from 180 degrees. A triangle's total angles are always equal to 180 degrees. When you remove the total of the two angles from 180 degrees, note the difference you discovered. This is what X is worth. The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.
(9x+1)+ 88
Remove parentheses: (a)=a
9 x+1+88=180
Add the numbers: 1+88=89
9 x+89=180
Move 89 to the right side
9 x=91
Divide both sides by 9
[tex]\frac{9 x}{9}=\frac{91}{9}$$[/tex]
Simplify
[tex]x=\frac{91}{9}$$[/tex]
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Answer:
x = 5
Step-by-step explanation:
You want the value of x where one of the base angles in an isosceles triangle is marked (9x+1)° and the vertex angle is marked 88°.
Base angleEach base angle of an isosceles triangle is the complement of half the vertex angle. This one is ...
9x +1 = 90 -(88/2)
9x = 45 . . . . . . . . . . subtract 1
x = 5 . . . . . . . . . divide by 5
what is the total surface area of the triangular prism in square centimeters?
A 240 cm^2
B 368 cm^2
C 320 cm^2
D 344 cm^2
Answer:
D
Step-by-step explanation:
base area = (6 · 4)/2 = 24/2 = 12 cm²
half base length = 6 : 2 = 3 cm
leg = [tex]\sqrt{3^2+4^2} = \sqrt{9 + 16} = \sqrt{25} = 5[/tex] cm
perimeter = (5·2) + 6 = 10 + 6 = 16 cm
lateral area = 16 · 20 = 320 cm²
surface area = (2 · 12) + 320 = 24 + 320 = 344 cm²
evaluate 4.56×36÷0.12
Answer:
1,368
Step-by-step explanation:
4.56x36=164.16
164.16/0.12=1368
Answer:
1368
Step-by-step explanation:
1368
9. If the perimeter of the square above is 24, what is the area of the circle? Leave your answer
in terms of pi.
The area of the circle would be 36π.
What is the area of a circle?
If the circle has a radius then the area of the circle can be computed by using the formula
area = π * radius²
The perimeter of the square = 24
4 * side = 24
Side of a square = 24/4 = 6
Side of a square = radius of the circle
Substituting the radius of 6 into this formula gives:
area = π * 6²
Which simplifies to:
area = π * 36
Hence, the area of the circle would be 36π.
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In circle C, mCG= 148°, mCD = 86°, and m∠EPF = 116°. What is the measure of arc FG?
Answer:
The measure of arc FG is 148°
Step-by-step explanation:
Since the measure of an arc is equal to the measure of the central angle that subtends it, and the measure of central angle CG is 148°, the measure of arc FG is 148°. This is because the arc FG is subtended by the central angle CG.
write an equation for the line for each graph
The equation of each of the lines are:
1. y = 1/3x - 1
2. y = 3x + 1
3. y = 2/3x - 1
4. y = 3x
5. y = -2/3x - 1
6. y = 1/3x - 1
7. y = -3x + 2
How to Write the Equation of a Line?To write the equation of a line, find the following:
Slope (m) = rise/runy-intercept (b) = the point where the line intersects the y-axis.1. Slope (m) = rise/run = 1/3
y-intercept (b) = -1.
To write the equation, substitute m = 1/3 and b = -1 into y = mx + b:
y = 1/3x - 1
2. Slope (m) = rise/run = 3/1 = 3
y-intercept (b) = 1.
To write the equation, substitute m = 3 and b = 1 into y = mx + b:
y = 3x + 1
3. Slope (m) = rise/run = 2/3
y-intercept (b) = -1.
To write the equation, substitute m = 2/3 and b = -1 into y = mx + b:
y = 2/3x - 1
4. Slope (m) = rise/run = 3/1 = 3
y-intercept (b) = 0.
To write the equation, substitute m = 3 and b = 0 into y = mx + b:
y = 3x
5. Slope (m) = rise/run = -2/3
y-intercept (b) = -1.
To write the equation, substitute m = -2/3 and b = -1 into y = mx + b:
y = -2/3x - 1
6. Slope (m) = rise/run = 1/3
y-intercept (b) = -1.
To write the equation, substitute m = 1/3 and b = -1 into y = mx + b:
y = 1/3x - 1
7. Slope (m) = rise/run = -3/1 = -3.
y-intercept (b) = 2.
To write the equation, substitute m = -3 and b = 2 into y = mx + b:
y = -3x + 2
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Two occupations predicted to greatly increase in number of jobs are pharmacy technicians and network systems and data communication analysts. The number of pharmacy technician jobs predicted for 2003 through 2014 can be approximated by 7.4x-y=-254 The number of network and data analyst jobs for the same years can be approximated by 12.4x-y=-231. For both equations, x is the number of years since 2003 and y is the number of jobs in thousands.
a. Use addition method to solve the following system of equations
{7.4x-y=-254
{12.4x-y=-231
The solution, rounded to the nearest whole number is: ?
Pls help!!!
Number of years since 2003 x=5 years and number of jobs in thousand y=288.
What is addition method of algebra?In this method two equation are added or subtracted depending on the sign of variables. After adding or subtracting we create a new equation with one variable. Therefore, we easily get the solution.
Why is addition method called elimination method?while using addition method of algebra, we either add or subtract two equations to obtain a new equation by eliminating one variable. Hence, this method is called elimination method.
Given equation, 7.4x-y= -254
12.4x-y = -231
using addition method
-5x= -23
after solving x=4.6
x= 5 (nearest whole number)
y = 288.04
y =288
hence, number of years 5
number of jobs in thousand =288
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maria has type b blood. she can safely receive blood transfusions from people with blood types o and b. what is the probability that a randomly chosen person from the united states can donate blood to maria?
The probability that a randomly chosen person from the united states can donate blood to maria is 0.50
considering blood to be of types A,B,AB and O
further all blood groups are equi probable
Probability of blood type A = probability of blood type B = probability of blood type AB = probability of blood type O = x
Probability of blood type A + probability of blood type B + probability of blood type AB + probability of blood type O = 1
⇒ 4x = 1
⇒ x = 1/4
Probability that a random person will have blood of type B or O = x+x
= 1/4 + 1/4
= 1/2
= 0.50
Hence we get the required answer.
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