Vector v is shown in the graph.Which are the magnitude and direction of v? Round the answers to the thousandths place.
Answers
Step 1:
First, draw and label the vertical and the horizontal units of the vector.
Step 2:
Write the column vector
[tex]v\text{ = }\begin{bmatrix}{4} & \\ {8} & {}\end{bmatrix}[/tex]Step 3:
[tex]\begin{gathered} \text{Magnitude of v = }\sqrt[]{v^2_x+v^2_y} \\ v_x\text{ = 8 } \\ v_y\text{ = }4 \\ \text{Magnitude of v = }\sqrt[]{8^2+4^2} \\ =\text{ }\sqrt[]{64\text{ + 16}} \\ =\text{ }\sqrt[]{80} \\ MagnitudeofV=\text{ 8.944} \end{gathered}[/tex]Step 4:
Find the direction using the formula below
[tex]\begin{gathered} tan\theta\text{ = }\frac{v_y}{v_x} \\ \tan \theta\text{ = }\frac{4}{8} \\ \tan \theta\text{ = 0.5} \\ \theta=tan^{-1}(0.5) \\ \theta\text{ = }26.565 \end{gathered}[/tex]Final answer
[tex]\begin{gathered} \text{Magnitude = 8.944} \\ \text{Direction = 26.565} \\ \mleft\Vert v\mleft\Vert\text{ = 8.944 , }\theta\text{ = 26.565}\mright?\mright? \end{gathered}[/tex]
Related Questions
Find what X equals [tex]2(x + 7) = - 4x + 14[/tex]
Answers
To solve the expression: 2(x + 7) = - 4x + 14, just follow these steps:
1. Distribute the product on the left side of the equation:
2(x + 7) = - 4x + 14
2*x + 2*7 = - 4x + 14
2x + 14 = -4x + 14
2. subtract 14 on both sides:
2x + 14 - 14 = -4x + 14 - 14
2x = - 4x
3. Add 4x on both sides:
2x + 4x = -4x + 4x
6x = 0
4. Divide both sides by 6:
6x/6 = 0
x*6/6 = 0
x*1 = 0
x=0
Then x equals 0
Find the slope of the line.
EAT
(3,1
-8-
O A.
(3-1)
O
What is the slope of the line? Select the correct choice below and, if
necessary, fill in the answer box to complete your choice.
The slope of the line is. (Type an integer or a simplified
fraction.)
B. The slope of the line is undefined.
Answers
Option A. The slope of the line is zero
How is the slope calculated?
First point = [tex](x_1,y_1)=(-3, -1)[/tex]
Second point = [tex](x_2,y_2)= (3,-1)[/tex]
Slope of the line = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\\\m =\frac{-1+1}{3+3} \\\\m = \frac{0}{3} \\\\m= 0[/tex]
Thus the slope of the line is zero.
What is a zero slope?
The slope will be 0 if time passes without any change and is called a zero slope. Here each y point in a horizontal line is identical. This implies that the slope will always be zero because the numerator of the fraction will always equal zero.A vertical line is an undefined slope where the x-points never change as the y-points rise and fall. The zero slope equation, or y = b, is the formula for a line with no slope, also known as a horizontal line.To learn more about zero slope, refer:
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The range of the function f(x)= x^2 + 2x - 8 is all real numbers..
Answers
Simplify the expression x^2+2x-8 to obtain the equation as complete square.
[tex]\begin{gathered} x^2+2x-8=x^2+2x+1-1-8 \\ =(x^2+2x+1)-9 \\ =(x+1)^2-9 \end{gathered}[/tex]The value of square terms is 0 or postive, so range of the expression x^2+2x-8 is,
[tex]\lbrack-9,\infty)[/tex]So correct option is B greater than or equal to -9.
Zena's Z-score on the chemistry final was 0.65. If the class mean on the final was 78, the the standard deviation was 12, and the distribution was normal, what was Zena's raw score?
Answers
Zena's raw score in the chemistry test is 85.8
How to determine the raw score of the test?From the question, the given parameters are
Mean score of the class = 78Standard deviation of the class = 12z-score of the test = 0.65The z-score of the distribution is calculated using the following z-score formula
z = (raw score - mean value)/standard deviation
Substitute the given parameters in the above equation
So, we have the following equation
0.65 = (Raw score - 78)/12
Cross multiply in the above equation
Raw score - 78 = 7.8
Add 78 to both sides
Raw score = 78 + 7.8
Evaluate
Raw score = 85.8
Hence, the raw score is 85.8
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En3. A financial advisor is paid $500 per week plus a 4% commission on all sales over $800. During oneweek, his total sales were $1,330. Find his gross earnings for the week..$541.20$531.20$521.20$551.20
Answers
For this problem we know that the salary per week is 500 and he gets a commission of 4% for each sale over 800. During one week the total sales are 1330 and we want to estimate the gross earnings for the week.
Taking in count the info given we can set up the following equation for the total amount recieved:
[tex]A=500+0.04S[/tex]Where A represent the amount recieved and S the sales. For this case S=1330 and replacing we got:
[tex]A=500+0.04\cdot1330=553.2[/tex]Statistics$ 9 45%ХIntFlorinchantemeraldataPositive and negative linear associations from scatter plots80/12so SanThe plot shown below describes the relationship between theaverage income in a city and the average rent for a 1-bedroomapartment in hat city.18001600100Average rent for a 10 dollars per month
Answers
Using the given scatter plot, let's describe the relationship between the average income in a city and the average rent for a 1-bedroom apartment in that city.
Here, the average income is represented on the x-axis while the average rent is represented on the y-axis.
Using the scatter plot, we can see that as the average income increases, the average rent also increases.
Since one variable increase as the other increases, and the points show a straight line pattern, we can say the relationship between them is a positive linear association.
Therefore, the relationship between the average income and the average rent for a 1-bedroom apartment in that city is a positive linear association.
ANSWER:
A. Positive linear association.
Can someone help me with this, please?
Answers
Hello I am quite confused by this question may you please help me solve and explain this? thank you:)
Answers
Given the mean score of a group of people in a quiz, the standard deviation of the scores of the people, and the score of a person, we can easily determine the z-score like this:
[tex]z=\frac{x-μ}{σ}[/tex]Where σ is the standard deviation, μ is the mean score and x is the score. By replacing 78 for μ, 4.2 for σ and 80 for x, we get:
[tex]z=\frac{80-78}{4.2}=0.4762[/tex]Then the z-score equals 0.4762. In this case, the score of 80 is a usual value since it is within one standard deviation of the mean.
Find the cube number
7 12
20
25
27
Answers
Answer:
712 = 360944128
20 = 8000
25 = 15625
27 = 19683
Step-by-step explanation:
A cube number is a number that is the product of three numbers which are the same. In other words, if you multiply a number by itself and then by itself again, the result is a cube number.
express (x-3)² as a trinomial in standard form
Answers
We will write it as follows:
[tex](x-3)^2=(x-3)(x-3)=x^2-3x-3x+9[/tex][tex]=x^2-6x+9[/tex]What is (a)
5(x+1)+4_4
6
Answers
Answer:
x=-1
Step-by-step explanation:
the table show how many points eduardo scored during each game use mental math to find how many points he scored
Answers
The total points scored by Eduardo in the first three games is 97.
We are given a table that shows the points scored by Eduardo during three games.
In game 1, he scored 52 points.
In game 2, he scored 19 points.
In game 3, he scored 26 points.
In game 4, he scored 10 points.
We need to find the sum of the total points scored by him in the first three games.
A summation, also known as a sum, is the outcome of adding numbers or quantities arithmetically. A summation always has an even number of terms.
The points are 52 + 19 + 26 = 97.
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4 sheets of paper cost's $14 how much will with be for 11 1/2 sheets of paper?
Answers
4 sheets of paper cost's $14 how much will with be for 11 1/2 sheets of paper?
we have that
Applying proportion
14/4=x/11 1/2
Convert 11 1/2 to an improper fraction
11 1/2=23/2
substitute
14/4=x/(23/2)
x=(23/2)*(14/4)
x=$40.25
therefore
teh answer is $40.25
if a (9,18) and b = (1,12) what is the length of ab
Answers
To calculate the lenght of AB we'll use the formula for distance between two points.
Remember that the disnatce between points
[tex]\begin{gathered} (x_1,y_1) \\ \text{and} \\ (x_2,y_2) \end{gathered}[/tex]is:
[tex]\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Using this, and the data given,
[tex]\begin{gathered} AB=\sqrt[]{(1_{}-9)^2+(12-18)^2} \\ \rightarrow AB=\sqrt[]{(-8)^2+(-6)^2} \\ \rightarrow AB=10 \end{gathered}[/tex]This way, the lenght of AB is 10 units
Which of the following is the coordinate of the minimum?O (-9,-4)O (4,-6)0 (0,2)O (9,5)O (1,3)
Answers
In this case the answer is very simple.
The minimums are represented by the valleys.
Analyzing the graph we can say that the minimum would be:
(4 , -6)
That is the solution.
i need help asap with these questions please worth 100 of my grades
Answers
Joy's investment of $3600 grows to $4800 in 48 weeks. What simple interest did she earn?
Answers
Answer:
answer
down
below
8 294 400
please help i dont have as much time
Answers
Answer:
f(2) = -7
Step-by-step explanation:
f(x) = -2x-3
f(2) = -2(2)-3
f(2) = -4-3
f(2) = -7
(3.22x10^3)-(2.96x10^3)
Answers
The value of (3.22 - 2.96)×10³ is 0.26×10³.
What is scientific notation?We use scientific notation for writing large numbers in compact form.
Scientific notation is written in base multiplied by 10 raised to some power where 0 ≤base < 10 scientific notation also has an alternative name which is known as engineering notation.
We know when we have numbers in scientific notation with the same exponent value we can do arithmetic operations to the base.
∴ (3.22x10³) - (2.96x10³).
= (3.22 - 2.96)×10³.
= 0.26×10³.
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A certain group of women has a 0.97% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
Answers
The probability that a randomly selected women does not have red/ green color blindness is 0.9903.
The probability of a woman has red/ green color blindness is,
P (Color blindness) = 0.0097.
The probability that a randomly selected women does not have red/ green color blindness is,
P (No Color blindness) = 1 - P (Color blindness)
= 1 - 0.0097
= 0.9903
Thus, the probability that a randomly selected women does not have red/ green color blindness is 0.9903.
Hence the probability that the women does not have red/green color blindness is 0.9903.
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Work these out mentally2/5 of 10 mm3/4 of 40 km 5/6 of $12
Answers
This can be solved by multiplying.
- 2/5 of 10 mm
[tex]\frac{2}{5}\times10=\frac{20}{5}=4[/tex]Answer: 4 mm
- 3/4 of 40 km
[tex]\frac{3}{4}\times40=\frac{40\times3}{4}=\frac{120}{4}=30[/tex]Answer: 30 km
- 5/6 of $12
[tex]\frac{5}{6}\times12=\frac{5\times12}{6}=\frac{60}{6}=10[/tex]Answer: $10
A line includes the point (7,5)has a slope of 1.What is its equation in slope intercept form?
Answers
Given:
Point( 7, 5)
x = 7 and y=5
slope(m) = 1
We need to first find the intercept.
Substitute x=7, y=5 and m=1 into y=mx + b and solve for intercept(b)
5 = 1(7) + b
5 = 7 + b
5 - 7 = b
-2 = b
Now, form the equation by substituting the value of the slope and intercept into y=mx + b
y = x - 2
what is the image point of (-7 6) after a rotation of 270 degrees counterclockwise
Answers
270° counterclockwise about the origin. Check the picture below.
Kevin needs to rent tables for his party. There will be 26 people at his party. Each table can seat 4 people. How many tables does Kevin need to order? Write a multiplication and division sentence that will help you answer the question. Use n for the unknown. __ x __ =___ ___÷___=____
Answers
Answer:
6.5
Step-by-step explanation:
Well if you do 4 x n=26 26/4=n
point a is to the left of point B on the horizontal number line what could be the valves of point a and point B
Answers
Answer:
If point A is to the left of point B, point A is less than B. Therefore, the values of point A and B could be:
A = 7 and B = 9
A = -8 and B = -5
A = -10 and B = 2
Because 7 is less than 9, -8 is less than -5, and -10 is less than 2.
Use the rule to complete the input/output table. Rule: the output is t-3•Input t: 17, 20, 22, 24•output r: On the home work it’s set as a table
Answers
Step 1
Write the rule
r = t - 3
Step 2:
Find each output for corresponding input.
When t = 17
r = 17 - 3 = 14
When t = 20
r = 20 - 3 = 17
When t = 22
r = 22 - 3 = 19
When t = 24
r = 24 - 3 = 21
Step 3
Final answer
16.What is the equation of the vertical asymptote for the function f(x) = x-1,x+4(A) x=1(B) x=-1(C) x=4(D) x=-417.
Answers
The vertical asymptotes is when the denominator is 0
Hence we have
[tex]\begin{gathered} x+4=0 \\ x=-4 \end{gathered}[/tex]X=-4 is the vertical asymptote
The right option is D
Hi, can you help me answer this question please, thank you!
Answers
We were given the following information:
Sample of men = 80, 45% of the sample owned cats (36 men owned cats)
Sample of women = 80, 55% of the sample owned cats (68.75 women owned cats)
The significance level is 0.025
We will calculate the test statistics as shown below:
[tex]undefined[/tex]Find the area of the shaded region.6005 cmA = [?] cm2Enter a decimal rounded to the nearest tenth.
Answers
To determine the area of the shaded region we first need to calculate the area of the whole circle, then we need to calculate the area of the circular sector of 60º, then finally we will calculate the area of the triangle and subtract the area of the triangle from the area of the circular sector, this will be the area of the part that isn't painted. Finally we can subtract the area that isn't painted by the area of the circle to determine the shaded region.
To calculate the area of the circle we will do as follows:
[tex]A_{\text{circle}}=\pi\cdot r^2=\pi\cdot5^2=25\cdot\pi=78.5[/tex]The circular sector can be calculated by the following expression:
[tex]A_{\text{sector}}=\frac{60\cdot\pi\cdot r^2}{360}=\frac{\pi\cdot5^2}{6}=\frac{25\cdot\pi}{6}=13.08[/tex]All of the sides of the triangle are equal, so we can use the following expression:
[tex]A_{\text{triangle}}=\frac{l^2\sqrt[]{3}}{4}=\frac{5\cdot\sqrt[]{3}}{4}=2.163[/tex]Now we will subtract the area of the triangle from the area of the sector to determine the area that isn't shaded.
[tex]A_{\text{blank}}=13.1-2.163=10.937[/tex]To finish we will subtract the area that isn't shaded from the area of the circle.
[tex]A_{\text{shaded}}=78.54-10.937=67.6[/tex]The area of the shaded region is 67.6 cm²
Which polynomial is prime?O 3x²+3x²-2x-2O 3x-2x²+3x-4O4x²+2x²+6x +3O4x³+4x²-3x-3
Answers
Explanation:
Concept:
If the only factors a polynomial are 1 and itself, then that polynomial is prime.
The first polyonial will be factorised below as
[tex][/tex]