Answers
The magnitude and direction of the vectors are
11. <0,4> :
Magnitude = 4
Direction = 90°
12. <-3,0>:
Magnitude = 3
Direction = 0°
13. <6,5>:
Magnitude = √(61)
Direction = 39.8°
14. <3,7>:
Magnitude = √58
Direction = 66.8°
15. <-2,1>:
Magnitude = √5
Direction = -26.57°
16. <-10,13>:
Magnitude = √(269)
Direction = -37.57°
17. <2,-5>:
Magnitude = √(29)
Direction = -68.2°
18. <8,-4>:
Magnitude = √(80)
Direction = -26.57°
19. <-4.-6>:
Magnitude = √(52)
Direction = 56.3°
20. <-1,9>:
Magnitude = √(82)
Direction = -83.66°
We are asked to find the magnitude and direction of the vectors given as <x, y>. We have the formulas for magnitude and direction of the vectors.
Magnitude = √(x²+y²)
and direction, θ = tan⁻¹(y/x)
11. The vector is <0,4>
Magnitude = √(0²+4²) = 4
Direction = tan⁻¹(4/0) = tan⁻¹∞ = 90°
12. The vector is <-3,0>.
Magnitude = √(-3²+0²) = 3
Direction = tan⁻¹(0/-3) = tan⁻¹0 = 0°
13.The vector is <6,5>
Magnitude = √(6²+5²) = √(61)
Direction = tan⁻¹(5/6) = 39.8°
14. The vector is <3,7>
Magnitude = √(3²+7²) = √58
Direction = tan⁻¹(7/3) = 66.8°
15.The vector is <-2,1>
Magnitude = √(-2²+1²) = √5
Direction = tan⁻¹(1/-2) = -26.57°
16.The vector is <-10,13>
Magnitude = √(13²+-10²) = √(269)
Direction = tan⁻¹(-10/13) = -37.57°
17.The vector is <2,-5>
Magnitude = √(2²+-5²) = √(29)
Direction = tan⁻¹(-5/2) = -68.2°
18.The vector is <8,-4>
Magnitude = √(8²+-4²) = √(80)
Direction = tan⁻¹(-4/8) = -26.57°
19.The vector is <-4.-6>
Magnitude = √(-4²+-6²) = √(52)
Direction = tan⁻¹(-6/-4) = 56.3°
20. The vector is <-1,9>
Magnitude = √(-1²+9²) = √(82)
Direction = tan⁻¹(9/-1) = -83.66°
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Related Questions
7x+12=x-6
I need help!!!!
Answers
Answer:
x = -3
Step-by-step explanation:
You have to isolate x:
7x + 12 = x - 6
7x = x - 6 - 12 = x - 18
6x = -18
x = -3
Can anyone Solve 2.5 ≤ 25
Answers
Answer:
true
Step-by-step explanation:
2.5≤25
Compare 2.5 and 25.
True
You have $50 in your bank account. Each week you plan to deposit $8 from your allowance and $20 from your paycheck. The equation b=50+(20+8)w gives the amount b in your account after w weeks. How many weeks from now will you have $210 in your bank account?
Answers
If you have $50 in your bank account and each week you plan to deposit $8 from your allowance and $20 from your paycheck. The number of weeks from now that you will have $210 in your bank account is: 5.71w.
Number of weeksThe given equation is:
b=50+(20+8)w
Where:
b is the amount in your account after w weeks.
w = Number of week
Hence,
b = 50+(20+8)w
b = 50+28w
b-50 = 28w
(b-$50)/28 = w
(210-$50)/28 = w
160/28 = w
5.71 = w
Therefore we can conclude that you will have the amount of $210 in your account in 5.71 weeks.
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Now answer the question:
Juan and his children went into a grocery store and he bought $4 worth of apples and
bananas. Each apple costs $1 and each banana costs $0.50. He bought a total of 6
apples and bananas altogether. Determine the number of apples, x, and the number
of bananas, y, that Juan bought.
Juan bought apples and
bananas.
Answers
X=2 and Y=4
Answer:
2 apples and 4 bananas
Step-by-step explanation:
Given info:
He bought $4 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. He bought a total of 6 apples and bananas altogether.Question given:
Determine the number of apples, x, and the number of bananas, y, that Juan bought.
Solution:
Since, we know that;
apples = x
bananas = y
Cost of each apple = $1 & Cost of each banana = $ 0.50
Total = 6
The equation that represents the following information:
x + y = 6
x + 0.5y = 4
We can multiply the top equation by -1 so it becomes -x -y = 6
-x - y = 6
x + 0.5y = 4
Now, we can use elimination to cancel out the x.
-0.5y = -2
y = 4
Because y=4, x must be 2 since x+y=6. So,
x = 2 and y = 4
Which means;
Juan bought 2 apples and 4 bananas.
~kavinsky
Data were collected on the distance a baseball will travel when hit by a baseball bat at a certain speed. The speed, s, is measured in miles per hour, and distance, y, is
measured in yards. The line of fit is given by ý = 3.98 +53.59s.
If the ball travels for a duration of 5 seconds, what is the predicted distance of the ball?
O 267.95 feet
O271.93 feet
O 283.87 feet
O287.85 feet
Answers
The predicted distance of the ball is 271.93 feet.
What is speed?The speed of an item, which is a scalar quantity in everyday usage and kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time. Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
Given Data
The speed, s, is measured in miles per hour, and distance, y, is
measured in yards.
The line of fit is given by ý = 3.98 +53.59s.
When s = 5 sec
y = 3.98 + 53.59(5)
y = 3.98 + 267.95
y = 271.93
The predicted distance of the ball is 271.93 feet.
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Suppose an online store has an item on sale for 10% off the original price. By what perceny does the store have to increase the price of the item in order to sell it for the original amount
Answers
The most appropriate choice of percentage will be given by-
The store have to increase the price of the item by [tex]11\frac{1}{9}[/tex] % in order to sell it for the original amount.
What is Percentage?
Percentage is a ratio expressed as a percentage of 100.
Let the original price be x
Percentage decrease in price due to sale = 10%
Decrease in price due to sale = [tex]\frac{10}{100} \times x[/tex]
= [tex]\frac{x}{10}[/tex]
New price = ([tex]x - \frac{x}{10}[/tex])
= [tex]\frac{10x-x} {10}[/tex]
= [tex]\frac{9x}{10}[/tex]
Now,
Increase in price from [tex]\frac{9x}{10}[/tex] to [tex]x[/tex] = [tex]\frac{x}{10}[/tex]
Percentage by which the store have to increase the price of the item in order to sell it for the original amount =
[tex]\frac{\frac{x}{10} }{\frac{9x}{10} } \times 100[/tex]
=[tex]\frac{x}{10} \times \frac{10}{9x} \times 100[/tex]
= [tex]\frac{100}{9}[/tex]
= [tex]11\frac{1}{9}[/tex] %
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q=p(r+s)
Solve for p
Answers
About how many times heavier is the largest dog when compared with the smallest dog?
Answers
The number of times heavier that the largest dog is when compared with the smallest dog is B. 41.
How to illustrate the information?It should be noted that from the information given, the biggest dig is the St Bernard and it has 145 pounds.
Also, it should be noted that the smallest dog is Yorkie and it had 3.5 pounds. Therefore, it should be noted that the number of times heavier will be:
= Weight of biggest fog / Weight of smallest dog
= 145 / 3.5
= 41.
It is 41 times heavier.
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A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. Find the probability that a given class period runs between 51.5 and 51.75 minutes.
Answers
A statistics professor plans classes so carefully that lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes.The Probability that a given class period runs between 51.5 and 51.75 minutes is 0.025.
What is density?The density of a place refers to the quantity of things—which may include people, animals, plants, or objects—there are in it. Divide the number of objects by area's measurement to determine density. A country's population density is calculated by dividing its total population by its area, expressed in the square kilometers or miles.
A flat distribution with the same probability density for each number is called a uniform distribution. The area beneath the distribution's graph must be 1. This distribution has a range of 10.0 and runs from 46.0 to 56.0 minutes (56.0-46.0). Since the density must be 1/10, 10.0*0.1 Equals 1.0.
Multiply the range between the numbers by the probability density to get the likelihood of being between two numbers
range: 50.75-50.5 = 0.25
0.25*0.1 = 0.025
P(50.5 < x < 50.75) = 0.025
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The first three terms of an arithmetic sequence are x, 2x + 4, 5x. Find the value of x.
Answers
The value of x for the given arithmetic sequence is x = 4.
What is an arithmetic sequence?A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Given,
First three terms of an arithmetic sequence are x, 2x + 4, 5x
The difference of 1 and 2 term equals the difference of 3 and 2 term.
⇒ 2x + 4 - x = 5x - 2x - 4
⇒ x + 4 = 3x - 4
⇒ 2x = 8
⇒ x = 4
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What is the slope of the line passing through (-2, 5) and (3, -4)
Answers
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-2)}}} \implies \cfrac{-9}{3 +2}\implies {\Large \begin{array}{llll} -\cfrac{9}{5} \end{array}}[/tex]
Mandy and 6 of her teammates each sold an equal number of
shirts to raise money for their tennis team. If a total of 56 shirts
were sold, how many shirts did each person sell?
Answers
Each person will sell 8 shirts if 56 shirts were sold
How to calculate the number of shirts sold by each person ?Mandy and 6 of her teammates each sold an equal number of shirt
Mandy is one person, let add 1 plus six to get the total number
1 + 6
= 7
The total number of shirts sold is 56 shirts
Since there are 7 people, the number of shirt that each person will sell can be calculated by dividing 56 by 7
= 56/7
= 8
Hence 8 shirts will be sold by each person
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find the x intercepts of f(x)=x^4+x^3-4x^2-4x
Answers
The x intercepts are 0, 1, -2, 2.
What is intercepts?
The term "intercept" refers to the x- and y-intercepts of of a given equation. The x-intercept is the point at which a line crosses the x-axis and the y-intercept is the point at which a line crosses the y-axis.
In the linear equation, we have the general form as y=mx+b
where m and b are constants.
We have to find the x intercept of the given function.
Given equation is [tex]x^{4} +x^{3} -4x^{2} -4x[/tex]
put this equation equals to 0
x^{4} +x^{3} -4x^{2} -4x = 0
[tex]x(x^{3} +x^{2} -4x-4)=0[/tex]
from this x = 0
x =1 is also the root of the equation
we get [tex]x^{2} -4=0[/tex]
from this
x = -2, 2
The intercept are 0,1,2,-2.
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The point P(6,4) is rotated 270° clockwise around the origin. What are the coordinates of the resulting point, P'?
Answers
Check the picture below.
Hi can someone please help me out?
Happy Halloween!
Answers
Answer:
A=14
B=pi 7^2
Step-by-step explanation:
All you need to do is put pi symbol on calculator and x by 7 squared to get answer
find the ratio of 15k to 65k
Answers
Answer:
Step-by-step explanation:
If its 15000:65000
Then we divide both sides by 1000 first :
15 : 65
Then we divide both sides by 5 :
3 : 13
This is simplified
If K is a unit then it will be 3k : 13k by doing the above steps but skipping the first.
Hope this helped and have a good day
Think About the Process The length of cell A is 4 x 10^-5 length to cell B's length? Use pencil and paper. Is it easier to find notation or in standard form? Explain your reasoning. m. The length of cell B is 0.000002 the ratio when the numbers m. What is the are expressed ratio of cell A's in scientific
Answers
Ratio of length of cell A to the length of cell B will be 20 : 1.
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
Given that;
Length of cell A = 4 x 10⁻⁵
Length of cell B = 0.000002 = 2 x 10⁻⁶.
Now,
Length of cell B into scientific notation = 2 x 10⁻⁶
Hence, The ratio of the length of cell A to cell B = 4 x 10⁻⁵ / 2 x 10⁻⁶
= 2 x 10⁻⁵⁺⁶
= 2 x 10¹
= 20
Thus, Ratio of length of cell A to the length of cell B is 20 : 1.
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On a piece of paper, graph y + 2 > -3x - 3. Then determine which answer
choice matches the graph you drew.
A
D
(0,-5)
• A. Graph A
• B. Graph B
C. Graph C
D. Graph D
Answers
Answer:
D
Step-by-step explanation:
The line needs to be dotted since the boundary is not included.
Eliminate A and C.The line should be shaded above because of the > sign.
Eliminate B.:) Please help!!!!!!
Answers
Answer:
1/2, 1/5, 1/7, 1/9, 1/28
7/14, 7/21, 7/42, 7/49
10/18, 10/20, 10/50, 10/100
is the relation in this graph a function ?
Answers
Answer:
No it's not a function
Step-by-step explanation:
You can use the vertical line test to determine whether it's a function or not. If the vertical line touches the graph at more than one point, the graph is not a function therefore the answer is no.
Two splice plates are cut from a piece of sheet steel that has an overall length of 18 3/4 in. The plates are 10 1/2 in. and 6 15/16 in. long. How much material remains from the original piece if each saw cut removes 1/16 in.?
Answers
Total material remains from original piece if overall length of sheet is
[tex]18\frac{3}{4}[/tex] in and two plates are cut of length [tex]10\frac{1}{2}[/tex] in and [tex]6\frac{15}{16}[/tex] in ,two saw of length 1/16 in is 35 / 16 in.
As given,
Overall length of steel sheet=[tex]18\frac{3}{4}[/tex] in
=(75 /4) in
=(300 /16)in
Length of two plates is [tex]10\frac{1}{2}[/tex] in and [tex]6\frac{15}{16}[/tex] in
Total length of two plates=[tex]10 \frac{1}{2} + 6\frac{15}{16}[/tex]
=(21 /2) +(95/16)
=(168 +95)/16
=263 /16
Total length of saw cut=(1/16) +(1/16)
=2/16
Material remains from original piece=(300/16) - (263/16 +2/16)
= 35 /16
Therefore, total material remains from original piece if overall length of sheet is [tex]18\frac{3}{4}[/tex] in and two plates are cut of length [tex]10\frac{1}{2}[/tex] in and [tex]6\frac{15}{16}[/tex] in ,two saw of length 1/16 in is 35 / 16 in.
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(-2,-5) (-3,5) fin the slope from the pair of points
Answers
The slope of the line from the pair of given points would be [tex]m = 5[/tex].
Hope this helps!
In a game of cornhole, Sasha tossed a bean bag and it landed at the edge of the hole. The hole can be represented by the equation x2 + y2 = 5, and the path of the bean bag can be represented by y = 0.5x2 – 1.5x – 4. To which points could she have tossed her bean bag?
A. (–1, –2) or (–2, 1)
B. (1, –2) or (2, 1)
C. (–1, 2) or (–2, –1)
D. (1, 2) or (2, –1)
Answers
The points are (1, -2) or (2, 1).
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
The equation for the hole
x² + y² = 5.............(1)
and, equation for bean bag can be represented by
y = 0.5x² – 1.5x – 4............................(2)
By solving above two equation we get
0.25 [tex]x^4[/tex] + 1.5 x³ -0.75 x² -12 x +11 =0
we het x1=1 and x2 = 2
then y1= -2 and y2 = 1
hence, the points are (1, -2) or (2, 1).
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Find the perimeter of the triangle
Answers
Answer:30 in.
Step-by-step explanation:13+5+12
Bill and ross are twins, their brother mark was born on the same day as twins but is three year older. if mark was born in 1990, in what year did the three boys get total age 21
Answers
Step-by-step explanation:
x = age of one of the twin boys
when they had together 21 years of age,
Bill was x years old
Ross was x years old
Mark was x+3 years old
so, we have
x + x + (x + 3) = 21
3x + 3 = 21
3x = 18
x = 6
Bill and Ross were 6 years old.
Mark was 6+3 = 9 years old.
Mark was born in 1990.
1990 + 9 = 1999
so, it was 1999 when they had together 21 years of age.
write a part to part and a part to whole ratio for each problem situation of the 250 students surveyed, 142 prefer carrots and 97 prefer peas
Answers
∵ There are 142 who prefer carrots
∵ There are 250 all
∴ The fraction represents who prefer carrots is
[tex]\frac{142}{250}[/tex]We must simplify the fraction by divide up and down by the same number until getting the simplest form
∵ 142 and 250 can divide by 2
[tex]\therefore\frac{\frac{142}{2}}{\frac{250}{2}}=\frac{71}{125}[/tex]∵ 71 and 125 can not divide by any number
∴ The fraction is 71/125
∴
∵ There are 97 who prefer peas
∵ There 250 all
∴ The fraction represents who prefer peas is
[tex]\frac{97}{250}[/tex]∵ 97 and 250 can not divide by the same number
∴ The fraction is 97/250
∴ The ratio is 97: 250
HELP I WILL GIVE YOU POINTS!
Describe in words the one transformation that maps
ΔABC to ΔA'B'C'
∆ABC to ∆A′B′C′
. Make sure that you include specific details (Reflection – over which axis, Rotation – direction, degrees, and center of rotation, Translation – direction(s) and number of units). 15 points
Answer:
ΔABC
∆ABC
is transformed by a:
Type of Transformation:
Details of transformation:
Answers
The description of the one transformation that maps ∆ABC to ∆A'B'C' is a rotation counterclockwise, 90 degrees, with the center at the origin
What is a rotation transformation?A rotation transformation can be described as the angular motion of a rigid, geometric figure around a point
The vertices on the triangle ∆ABC are;
A(-5, -2), B(-7, -4), C(-5, -5)The vertices on the triangle ∆A'B'C' are;
A'(2, -5), B'(4, -7), C'(5, -5)The rotation of a point A(x, y), 90° counterclockwise about the origin gives the point A'(-y, x)
The reflection of a point (x, y) across the y–axis gives the point A'(-x, y)
Therefore;
The coordinates of the vertices of∆ABC following a 90° counterclockwise rotation gives;
A(-5, -2) → A'(2, -5)
B(-7, -4) → B'(4, -7)
C(-5, -5) → C'(5, -5)
Therefore;
The transformation that maps ∆ABC to ∆A'B'C' is therefore a rotation of 90° counterclockwise about the origin
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what is equivlent 10x-30
Answers
Answer:10(x-3)
Step-by-step explanation:
Just divide 10 on both sides and be done with it
10/10x-30/10
move ten to the left
10(x-30/10)
10(x-3)
-2x+4=y ( ,-2)
Help
Complete the missing value in the solution to the equation
Answers
Answer:
3
Step-by-step explanation:
let unknown point (x, -2)
-2(x)+4=-2
-2x=-6
x=3
m^2+7m-51/4=0 by completimg square
Answers
By completing squares, we will see that the two solutions of the quadratic equaiton are:
m = -7 + √(145)/2
m = -7 - √(145)/2
How to solve by completing squares?Here we have the quadratic equation:
m^2 + 7m - 51/4 = 0
If we multiply both sides by 4, we will get
4m^2 + 28m - 51 = 0
Now, remember the relation:
(a + b)^2 = a^2 + 2ab + b^2
Then to complete the squares we can write:
(2m)^2 + 2*14*m + (14)^2 - (14)^2 - 51 = 0
(2m + 14)^2 - 14^2 - 51 = 0
(2m + 14)^2 = 145
We already completed squares, now the solutions are:
2m = -14 ± √145
m = (-14 ± √145)/2
m = -7 + √(145)/2
m = -7 - √(145)/2
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