Part (a)
The resultant vector is the vector formed by adding the two vectors a and b. So we effectively add the corresponding components.
You can use the parallelogram law as a visual alternative.
Adding a and b leads to
a+b = (3i-2j) + (pi-2pj)
a+b = (3i+pi) + (-2j-2pj)
a+b = (3+p)i - (2+2p)j
Define vector d to be d = a+b so we can use it later below.
Recall that parallel vectors point in the same direction. This means the ratio of their components or coordinates are equal.
We can say the following
(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)
(3+p)/(2) = (-(2+2p))/(-3)
Let's solve for p
(3+p)/(2) = (-(2+2p))/(-3)
(3+p)/(2) = (2+2p)/3
3(3+p) = 2(2+2p) .... cross multiply
9+3p = 4+4p
4p+4 = 3p+9
4p-3p = 9-4
p = 5
Answer: p = 5========================================================
Part (b)
Since p = 5, from part (a), we can determine vector b
b = pi - 2pj
b = 5i - 2*5j
b = 5i - 10j
Then add vectors a and b to get
a+b = (3i-2j) + (5i - 10j)
a+b = (3i+5i) + (-2j - 10j)
a+b = (3+5)i - (2+10)j
a+b = 8i - 12j
Or we can say
a+b = (3+p)i - (2+2p)j .... from part (a)
a+b = (3+5)i - (2+2*5)j ... plugging in p = 5
a+b = 8i - 12j
Note the ratio of the components of vector d and vector c are such
(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)
8/2 = -12/(-3)
4 = 4
This helps confirm the answer
You could also graph the vectors c = 2i - 3j and d = 8i - 12j to note the two lines produce the same slope -3/2. We can see that -12/8 = -3/2. Lines of the same slope are parallel lines
Answer: 8i - 12ja.
The value of p is 5
Since vector a = 3i - 2j and vector b = pi - 2pj, the resultant of vectors a and b is R = a + b
= 3i - 2j + pi - 2pj
= (3 + p)i - 2(1 + p)j
Since R is aparallel to vector c = 2i - 3j, it implies that the cross product of R and c is zero.
The cross product of two vectors a and b is a × b = absinФ where a and b are the magnitudes of a and b and Ф is the angle between them.
So, R × c = [(3 + p)i - 2(1 + p)j] × [2i - 3j]
= (3 + p)i × 2i + (3 + p)i × (-3j) + (-2(1 + p)]j × 2i + (-2(1 + p)]j×(-3j)
= 0 - 3(3 + p)k - 4(1 + p)(-k) + 0
= -3(3 + p)k + 4(1 + p)k
= [-3(3 + p) + 4(1 + p)]k
= [-9 - 3p + 4 + 4p)]k
= [-9 + 4 - 3p + 4p)]k
= [-5 + p]k
[-5 + p]k = RcsinФ.
Since R and c are parallel, Ф = 0°
So, Rcsin0° = Rc × 0 = 0
So, [-5 + p]k = 0
-5 + p = 0
p = 5
The value of p is 5
b.
The resultant of vectors a and b is R = 8i - 12j
Since p = 5 and the resultant of vectors a and b is R = (3 + p)i - 2(1 + p)j
Substituting the value of p = 5 into r, we have
R = (3 + p)i - 2(1 + p)j
R = (3 + 5)i - 2(1 + 5)j
R = 8i - 2(6)j
R = 8i - 12j
So, the resultant of vectors a and b is R = 8i - 12j
Learn more about resultant of vectors here:
https://brainly.com/question/14358602
What is the value of x?
Enter your answer in the box.
Answer:
111°
Step-by-step explanation:
The polygon given is a heptagon having 7 sides.
Sum of interior angles of a 7-sided polygon = (n - 2)*180
= (7 - 2)*180
= 5*180 = 900°
Therefore:
126° + 158° + 120° + 125° + 121° + 139° + x° = 900°
Solve for x
789° + x° = 900°
Subtract 789 from each side
x = 900° - 789°
x = 111°
Which property was used to simplify the expression?
4(b+2) = 4b+8
distributive property
commutative property
associative property
inverse property
Answer:
distributive
Step-by-step explanation:
they took the number outside of the parentheses and multiplied by the inside
675 grams of sweets were distributed among 9 children. How much sweet was given to each child?
Answer:
75 Sweets
Step-by-step explanation:
To get the answer you have to divide the number of sweets by the number of children. If there are 675 grams and 9 children, then you divide 675/9 to get your answer of 75 sweets.
Each child was given 75 grams of sweets as per linear equation when distributed.
What is a linear equation?A linear equation is an equation where the highest degree of the variable is one.
Given, there are a total of 675 grams of sweets.
There are a total of 9 children among which the sweets is to be distributed equally.
Therefore, each children will get sweets of
(675 ÷ 9) grams
= 75 grams.
Therefore, each child will get 75 grams of sweets when it is distributed equally.
Learn more about a linear equation here: https://brainly.com/question/18467717
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How many solutions can be found for the equation 4x + 5 = 10? (4 points)
a. Zero
b. One
c. Two
d. Infinitely Many
Write an equation for each of the four types of slopes.(in slope intercept form) 9th grade geometry HELP
Answer:
y=x+3
y=-2x+3
y=3
y=0/3x+2
Step-by-step explanation:
Multiply the polynomial x (3x-1)(2x+5) also what is the degree of the polynomial
Answer:
Result after multiplication of polynomial is: [tex]6x^3+13x^2-5x[/tex]
Degree of polynomial = 3
Step-by-step explanation:
The given polynomials are:
[tex]x(3x-1)(2x+5)[/tex]
In order to multiply the given polynomials we have to work step by step. First of all the polynomials in the bracket will be multiplied and then their result will be multiplied with x.
So, multiplying the polynomials in round brackets first
[tex]=x(3x-1)(2x+5)\\= x\{3x(2x+5)-1(2x+5)\}\\=x\{6x^2+15x-2x-5\}\\=x(6x^2+13x-5)[/tex]
Now multiplying with x
[tex]= 6x^3+13x^2-5x[/tex]
Degree of a polynomial is the highest exponent of variable in the polynomial.
In the acquired result, the highest exponent of x is 3 so the degree is 3.
Hence,
Result after multiplication of polynomial is: [tex]6x^3+13x^2-5x[/tex]
Degree of polynomial = 3
When a number n is divided by 10000, the quotient is 1 and the remainder is 2011. The quotient and the remainder when n is divided by 2011 are respectively.
Answer:
[tex]Remainder = 1956[/tex]
[tex]Quotient = 5[/tex]
Step-by-step explanation:
Given
[tex]Dividend = n[/tex]
[tex]Divisor = 10000[/tex]
[tex]Quotient = 1[/tex]
[tex]Remainder = 2011[/tex]
Required
Determine the quotient and remainder when the divisor is 2011
First, we need to determine the value of n.
The relationship between the given parameters is:
[tex]Dividend = Quotient * Divisor + Remainder[/tex]
Substitute values in the above:
[tex]n = 1 * 10000 + 2011[/tex]
[tex]n = 10000 + 2011[/tex]
[tex]n =12011[/tex]
So, we divide 12011 by 2011 and record the quotient and divisor:
[tex]\frac{12011}{2011} =[/tex]
The integer division of 12011 and 2011 is 5.
The remainder is calculated using:
[tex]Dividend = Quotient * Divisor + Remainder[/tex]
Where
[tex]Dividend = 12011[/tex]
[tex]Quotient = 5[/tex]
[tex]Divisor = 2011[/tex]
So, Remainder =:
[tex]Remainder = 12011 - 2011* 5[/tex]
[tex]Remainder = 12011 - 10055[/tex]
[tex]Remainder = 1956[/tex]
Hence:
[tex]\frac{12011}{2011} = 5\ Remainder\ 1956[/tex]
hurryyyyyyyyyyy 5/6 - 1/4=
yes subtraction
Step-by-step explanation:
(5x4)/(6x4) - (1x6)/(4x6)
=20/24 - 6/24
= (20-6)/24
=14/24
=7/12
give me brainliest
someone pls help and dont troll
Answer: A
Step-by-step explanation:
2x + 9 = 15
2x = 6
x = 3
2x+9 = -15
2x = -24
x = -12
Which side of DEF is the longest?
Answer:
Letter B
Segment DF
Step-by-step explanation:
For the Noah and Andres question: To make orange fizz Noah mixes 4 scoops of powder with 6 cups of water. Andre mixes 5 scoops of powder with 8 cups of water what would that look like on a double number line? Sorry this is long
Answer:
On the number line:
a) 0.6666666667 scoops per powder
b) 0.625 scoops per powder
Step-by-step explanation:
For the Noah and Andres question:
To make orange fizz Noah mixes 4 scoops of powder with 6 cups of water.
Unit rate = scoops per cup
= 4 Scoops/6 cups
= 2/3 scoops per powder
= 0.6666666667 scoops per powder
Andre mixes 5 scoops of powder with 8 cups of water what would that look like on a double number line?
Unit rate = scoops per cup
= 5 Scoops/8 cups
= 0.625 scoops per powder
What’s the answer for 5x + 12
6x
Answer:
8
Step-by-step explanation:
21x+12=180
21x= 168
x=8
Step-by-step explanation:
Both the angles added together create 180 degrees so,
15x+12+6x = 180
21x+12=180
21x=168
x=8
What is the measure of angle b?
A) 54
B) 46
C) 126
D) 136
Evaluate the expression 4^3÷(7-3) × 2 PLEASE HURRY AND HELP ME I DONT HAVE MUCH TIME TILL ITS DUE
Answer:
The answer is 32.
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Pls help I will give u 50 points
Answer:
y=13.50x
Explanation:
Answer:
Step-by-step explanation:
stop the cappppppppppp
Anna made a scale drawing, in inches, of a building using a scale of 1:600. Her scale drawing was 6 inches long. Greg made a scale drawing of the same building using a scale of 1:300. How long, in inches, was Greg's scale drawing? A 2 B 3 C 12 D 50
you'll get 30 points.
Answer:
C.12
Step-by-step explanation:
Answer:
i dont exactly know but the answer is C ?
Step-by-step explanation:
3(1-2x)>3-6x what is x plz show work
Answer:
The answer is 0.
Search up "Linear Equation Calculator" and use one of those to get the work.
Answer:
No solution
Step-by-step explanation:
3(1-2x)>3-6x
3-6x > 3-6x
3 3
Can Somebody Help With Geometry?
Answer:
SAS
Step-by-step explanation:
II side (given)
Angles between the congruent sides (vertically opposite angle)
III side (given)
Hence by, SAS the Triangles are congruent.
Find the product of the two binomials below
(x-8) (x+4)
WILL MARK branniest answer if gotten right
Answer:
Line MN is the answer
Step-by-step explanation:
Image SQ as a line that extends forever, if you took line segment and also made it extend forever, then it would become parallel to line segment SQ, never touching or intersecting and going at the same angle.
You spend $23 to spend on 4 avocados. After buying them you had $11. How much did each avocado cost? Write an equation about this.
Answer: Each avocado cost $3
Equation: 23 - 4x = 11
Answer:
$3 per avocados
Step-by-step explanation:
23-11= 12. 12 divided by 4 = 3
rewrite this expression
[tex] \sqrt[5]{x} [/tex]
Which Figure is a rotation of the Blue Figure?
A
B
C
D
Tom's recipe requires 8 cups of sugar to make 40 sugar cookies. How many
sugar cookies will 120 cups of sugar make? *
During a 60-minute period, a traffic engineer counted 66 trucks and cars that crossed a bridge. The ratio of trucks to cars that travel across the bridge is usually 3:8. The equation 3 8 = t 66 − t 3 8 = t 66 − t can be used to predict the number of trucks, t, the engineer should have counted. How many trucks should the engineer have counted?
Answer:
18
Step-by-step explanation:
t = Number of trucks counted
c = Number of cars
Ratio of trucks to cars = [tex]\dfrac{t}{c}=\dfrac{3}{8}[/tex]
Total number of cars and truck = 66
[tex]t+c=66[/tex]
Divide the left and right side by the number of cars
[tex]\dfrac{t+c}{c}=\dfrac{66}{c}\\\Rightarrow \dfrac{t}{c}+1=\dfrac{66}{c}\\\Rightarrow \dfrac{3}{8}+1=\dfrac{66}{c}\\\Rightarrow \dfrac{11}{8}=\dfrac{66}{c}\\\Rightarrow c=66\times \dfrac{8}{11}\\\Rightarrow c=48[/tex]
Total number of cars is 48
so
[tex]t=66-c\\\Rightarrow t=66-48\\\Rightarrow t=18[/tex]
Total number of trucks counted is 18.
If you go shopping and a pair of jeans cost $50.00 but they are on sale for 50% off or 1/2 off what is the price of the jeans
Answer:
$25
Step-by-step explanation:
you just subtract 25 from 50 since 25 is half of 50.
What is the image of (0,7) after a reflection over the x-axis
Answer:
(0, - 7 )
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y ), thus
(0, 7 ) → (0, - 7 )
What is the difference between ordering numbers, comparing numbers, and comparing amounts?
Answer:
different definitions
Step-by-step explanation:
ordering numbers can be seen as arranging the numbers by a certain characteristics. for example, you could order numbers from least to greatest
comparing numbers can be seen as looking into two or more numbers rather than the entire group of numbers. for example, if there were the numbers 1, 2, 3, 4, 5, 6, you could say that 2, 4, 6, are even numbers
comparing amounts could be determined by worth but not the numerical values. for example, you could have a gallon of milk and a quart of orange juice but just by the size of the container, a gallon of milk is bigger and holds more than a quart of orange juice
What is the measure of A, in degrees?
Answer:
Um... D
Step-by-step e xplanation:
Write an equation of the line passing through point P(4,0) that is parallel to the line -x + 2y = 12.