The calculated vectors are:
[tex]\vec{A}-\vec{B}[/tex]=(3,-5,-4)
[tex]\vec{B}-\vec{C}[/tex]=(-5,4,0)
[tex]-\vec{A}+\vec{B}-\vec{C}[/tex]=(-6,4,3)
[tex]3 \vec{A}-2 \vec{C}[/tex]=(-3,-2,-11)
Calculate the following, and express your answers as ordered triplets of values separated by commas.?Generally, the equation for is mathematically given a
[tex]\vec{V}+\vec{W}=\left(V_1, V_2, V_3\right)+\left(W_1, W_2, W_3\right)\\\\\vec{V}+\vec{W}=\left(V_1+W_1, V_2+W_2, V_3+W_3\right) \text { }[/tex]
[tex]\vec{V}-\vec{W}=\left(V_1, V_2, V_3\right)-\left(W_1, W_2, W_3\right)\\\\\vec{V}-\vec{W}=\left(V_1-W_1, V_2-W_2, V_3-W_3\right)[/tex]
[tex]\alpha \cdot \vec{V}=\alpha \cdot\left(V_1, V_2, V_3\right)\\\\\alpha \cdot \vec{V}=\left(\alpha \cdot V_1, \alpha \cdot V_2, \alpha \cdot V_3\right)[/tex]
[tex]\vec{A}-\vec{B}=(1,0,-3)-(-2,5,1)\\\vec{A}-\vec{B}=(3,-5,-4) \\\\&\vec{B}-\vec{C}=(-2,5,1)-(3,1,1)\\&\vec{B}-\vec{C}=(-5,4,0) \\\\&-\vec{A}+\vec{B}-\vec{C}=-(1,0,-3)+(-2,5,1)-(3,1,1)\\-\vec{A}+\vec{B}-\vec{C}=(-6,4,3) \\\\&3 \vec{A}-2 \vec{C}=3(1,0,-3)-2(3,1,1)\\3 \vec{A}-2 \vec{C}=(3,0,-9)-(6,2,2)\\3 \vec{A}-2 \vec{C}=(-3,-2,-11)[/tex]
In conclusion,
[tex]\vec{A}-\vec{B}[/tex]=(3,-5,-4) [tex]\vec{B}-\vec{C}[/tex]=(-5,4,0) [tex]-\vec{A}+\vec{B}-\vec{C}[/tex]=(-6,4,3) [tex]3 \vec{A}-2 \vec{C}[/tex]=(-3,-2,-11)Read more about Vectors
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CQ
In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A rightarrow = (1,0, -3), rightarrow = (-2,5,1), and C rightarrow = (3,1,1). Calculate the following, and express your answers as ordered triplets of values separated by commas.
!HURRY PLSS!! 20 points!!
A transformation maps a preimage triangle to the image triangle shown in the coordinate plane below.
If the preimage triangle is reflected over the y-axis to get the image triangle, what are the coordinates of the vertices of
the preimage triangle?
The coordinates of the vertices of the preimage triangle = (4, 1), (6,1) and (6, -6).
Given the figure of the image triangle.
The coordinates of the image triangle are (-4, 1) , (-6,1) and (-6, -6).
We are asked to find the coordinates of the preimage triangle.
The preimage triangle was reflected over the y-axis .
The image triangle is lying on the 2nd and 3rd quadrants.
So the preimage triangle will lie on the 1st and 4th quadrants.
Then the coordinate (-4,1) will be the image of (4,1).
(-6, 1) will be the image of (6,1) and (-6,-6) will be the image of (6,-6).
Hence the coordinates of the vertices of the preimage triangle = (4, 1), (6,1) and (6, -6).
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Find the degree measure of each angle in the triangle
The degree measure for angle B is 28° and angle D is 62°.
We are given that:
∠ C = 90°
∠ B = ( 2 x + 10 )°
∠ D = ( 5 x + 17 )°
Now, using the angle sum property of a triangle, we get that:
∠B + ∠ C + ∠ D = 180°
Substituting the values:
2 x + 10 + 90 + 5 x + 17 = 180
7 x + 117 = 180
7 x = 63
x = 63 / 7
x = 9
∠ B = ( 2 x + 10 )
∠ B = 2(9) + 10
∠ B = 18 + 10
∠ B = 28°
∠ D = ( 5 x + 17 )
∠ D = 5 (9) + 17
∠ D = 45 + 17
∠ D = 62°
Therefore, the degree measure for angle B is 28° and angle D is 62°.
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The cost of a new robotic toy after an 8% markup can be represented by the expression
r
+
0
.
08
r
. Simplify the expression.
The simplified equation of the given statement = 1.08r.
Addition variable in math's:Even though they also have different operations, adding and subtracting variables follow the same rule: while adding or subtracting terms with the same variables, either add or subtract the coefficients and leave the result with the variable. As an example, consider an addition.
According to the given data:The original cost of the new robotic toy is given as r.
The cost of the new robotic toy after a 8% markup is: c + 0.08r to show that 8% of r was being added to r to increase the price.
Because both numbers in the equation are related to the same variable, they can be added. When r is used alone, it is considered to be 1r.
= r + 0.08r
= 1r + 0.08r
= 1.08r
The simplified equation of the given statement = 1.08r
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I understand that the question you are looking for is:
The cost of a new robotic toy after an 8% markup can be represented by the expression r+0.08r. Simplify the expression.
Nabhitha buys cookies and onions at the store.
She pays a total of $60.39.
She pays a total of $4.79 for the cookies.
• She buys 8 bags of onions that each cost the same amount.
.
.
Write and solve an equation which can be used to determine x, how much each bag
of onions costs.
The equation is 8x + 4.79= 60.39 and the value is x is $6.95
How to solve the equation ?Nabhitha pays a total of $60.39 for the cookies and onions
She pays a total of $4.79 for the cookies
She buys 8 bags of onions that each costs the same amount of money
The equation used to find the value of x is written as
8x + 4.79= 60.39
Collect the like terms
8x= 60.39 - 4.79
8x= 55.6
Divide both sides by the coefficient of x which is 8
8x/8 = 55.6/8
x= 6.95
Hence the price of each bag of onions is $6.95
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use vectors to decide whether the triangle with vertices p(3, −4, −2), q(4, −1, −4), and r(8, −3, −5) is right-angled. yes, it is right-angled. no, it is not right-angled.
Yes. It is a right-angled triangle.
What is a dot-product?The dot product, also known as the scalar product, is an algebraic operation that takes two sequences of numbers of equal length (often coordinate vectors) and outputs a single number. The dot product of two vectors' Cartesian coordinates is frequently used in Euclidean geometry. Although other inner products can be defined in Euclidean space, it is frequently referred to as the inner product (or, less frequently, projection product) of Euclidean space (see Inner product space for more).
The sum of the products of the matching entries of the two number sequences is the dot product, according to algebra. B, it is the result of adding the cosine of the angle between the two vectors and the Euclidean magnitudes of the two vectors.
The vectors that make up the triangle must first be located. The vertices are subtracted to achieve this.
QP=(2,0,-4)-(1,-3,-2)=(1,3,-2)
PR=(1,-3,-2)-(6,-2,-5)=(-5,-1,3)
RQ=(6,-2,-5)-(2,0,-4)=(4,-2,-1)
QP.PR = (1, 3, -2).(-5, -1, 3) = -5-3-6= -14
PR.RQ = (-5, -1, 3).(4, -2, -1) = -20+2-3 = -21
RQ.QP = (4, -2, -1).(1, 3, -2) = 4-6+2 = 0
Calculate the dot products to see if these vectors are perpendicular now.
They are perpendicular if the dot product of two vectors equals zero. As you can see, RQ.QP is zero in your triangle, which supports this. Consequently, a right-angled triangle results.
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What is a number that is at most 30
Answer: 30
Because its thirty
Julie planted t fewer trees than Logan. Logan planted 6 trees. Write an expression that shows how many trees Julie planted.
Answer: 6 - t
Step-by-step explanation:
fewer trees than Logan is another word for subtraction.
Since Julie planted t fewer, and Logan planted 6 that means
6 - t
The expression that shows how many trees Julie planted would be; 6 - t
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that Julie planted t fewer trees than Logan. Logan planted 6 trees.
Here, fewer trees than Logan means subtraction.
Since Julie planted t fewer, and Logan planted 6 that means;
the difference between them; 6 - t
Therefore, the expression that shows how many trees Julie planted would be; 6 - t
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Hexagonal chess is played on a regular hexagonal board comprised of 92 small hexagons in three colors. The chess pieces are arranged so that a player can move any piece at the start of a game.
a. What is the sum of the measures of the interior angles of the chess board?
The sum of the measures of the interior angles of the chess board is equal to 720°.
What is a polygon?A polygon can be defined as a two-dimensional geometric shape that comprises straight line segments and a finite number of sides. Also, some examples of a polygon include the following:
TriangleQuadrilateralPentagonHexagonHeptagonOctagonNonagonNote: The number of sides (n) of a hexagon is 6.
In Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:
Sum of interior angles = 180 × (n - 2)
Sum of interior angles = 180 × (6 - 2)
Sum of interior angles = 180 × 4
Sum of interior angles = 720°.
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find parametric equations and symmetric equations for the line (use the parameter t.) the line through the point (−3,3,−1) and perpendicular to both ⟨1,1,0⟩ and ⟨
The second vector that's perpendicular to the line we want (call it L) is missing; I'll denote it by ⟨a, b, c⟩.
The cross product of ⟨1, 1, 0⟩ and ⟨a, b, c⟩ is perpendicular to both of these vectors. The direction vector of L will be parallel to this cross product.
Compute the cross product.
⟨1, 1, 0⟩ × ⟨a, b, c⟩ = ⟨1•c - 0•b, 0•a - 1•c, 1•b - 1•a⟩ = ⟨c, -c, b - a⟩
Then the vector equation of L is
L(t) = ⟨c, -c, b - a⟩ t + ⟨-3, 3, -1⟩
As parametric equations, we write
x(t) = ct - 3
y(t) = -ct + 3
z(t) = (b - a) t - 1
Eliminating the parameter above, we get
x + y = (ct - 3) + (-ct + 3) = 0 ⇒ x = -y
and substituting
x = ct - 3 ⇒ t = (x + 3)/c
into z(t), we get
z = (b - a) (x + 3)/c - 1 ⇒ x = c (z + 1)/(b - a) - 3
As symmetric equations, then, we write
x = -y = c (z + 1)/(b - a) - 3
this month, a clothing store needs to finish with at least $4300 in profits Iif their total expenses will need $2900, what are the possible amounts must they make in revenue?
Answer:They need 19,000 more
Step-by-step explanation:
The midpoint of KL is M(8, 3). One endpoint is L(8, 0). Find the coordinates of the other
endpoint K.
Answer: K(8,6)
Step-by-step explanation:
M(8,3) - the midpoint of KL L(8,0) K(x,y)=?
[tex]\displaystyle\\Mx=\frac{Kx+Lx}{2}[/tex]
Multiply both parts of the equation by 2:
[tex]2Mx=Kx+Lx\\2Mx-Lx=Kx+Lx-Lx\\2Mx-Lx=Kx\\Mx=8\ \ \ \ Lx=8\\Hence,\\2(8)-8=Kx\\16-8=Kx\\8=Kx\\\\2My-Ly=Ky\\My=3\ \ \ \ Ly=0\\Hence,\\2*(3)-0=Ky\\6-0=Ky\\6=Ky\\Thus,\\K(8,6)[/tex]
9. Reason abstractly. At the green grocer, Liam
bought three pounds of apples for $3.87, bananas
for $3, grapes for $2.23, and pears for $2.37. He has
$10. Will that be enough to pay for the fruit? Why
or why not?
Answer:
It will not be enough money to pay for the fruit
Step-by-step explanation:
Reason:
3+3.87+2.23+2.37= $11.47
$11.47-10= $1.47
hes missing $1.47
Which point is located at -3 1/2
Explanation:
The value -3 1/2, aka -3 & 1/2, is between -3 and -4. It's at the exact midpoint of those values.
Think of it like how 3 & 1/2 is between 3 and 4.
Or you can rewrite it in decimal form: -3 & 1/2 = -3.5
The expression 53(1−x) gives the discounted price of a pair of shoes, where x is the percent of the discount written in decimal form. what does 1−x represent in the expression?
So, 1−x represents the percent of original price being paid as we know that if percentage is given in decimal form, then to get the percent of original.
What is decimal form?The decimal number framework has 10 digits which range from 0 to 9 with the base 10 and transformation from paired to decimal can assist us with better figuring out the compound parallel numbers. The decimal numeral framework is the standard framework for meaning number and non-whole number numbers. It is the augmentation to non-whole number quantities of the Hindu-Arabic numeral framework. The approach to meaning numbers in the decimal framework is frequently alluded to as decimal documentation. Numerous numeral frameworks of antiquated civilizations utilize ten and its powers for addressing numbers, perhaps on the grounds that there are ten fingers on all fours began counting by utilizing their fingers. Models are first and foremost the Egyptian numerals, then the Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, and Chinese numerals.
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Which inequality is represented by the graph?
Answer:
Step-by-step explanation:
x < 0
Answer : x is less than or equal to 0
First, the direction of the number line in the graph is the negative number side, so it has to be 0 or less.
If it is less than 0, the dot that starts at the point 0 must have a hollowed out part in the middle. If it is 0 or less, the dot that starts at the point 0 is completely filled with no hollowed middle part.
Since the dot is completely blacked out, the answer is the second option.
3. Two quantities, p and q, are in direct proportion. The sum of the values of q when p = 6 and when p = 11 is 51.
(a) Find an equation connecting p and q. (b) Find the value of p when q = 72.
Step-by-step explanation:
this just means
q = k×p
and we need to find k.
the sum of both q values when p = 6 and p = 11 is then
k×6 + k×11 = 51
17k = 51
k = 51/17 = 3
so, our equation is
q = 3p
and when q = 72
72 = 3p
p = 72/3 = 24
use these two graphs to answers questions for 4 and 5
why do these graphs represent functions? explain.
The 2 graphs are of parabolas .
A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola. Also, an important point to note is that the fixed point does not lie on the fixed line. A locus of any point which is equidistant from a given point (focus) and a given line (directrix) is called a parabola. Parabola is an important curve of the conic sections of the coordinate geometry.
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Each year a certain amount of money is deposited in an account that pays an annual
the interest rate so that at the end of each year the balance in the account is multiplied by a
the growth factor of z = 1+r. $500 is deposited at the start of the first year, and an additional $200
is deposited at the start of the next year, and $600 at the start of the following year.
b. What is the amount (to the nearest cent) in the account at the end of three years if the
interest rate is 2%?
Answer:
What is the amount (to the nearest cent) in the account at the end of three years if the interest rate is 2%? $1,350.68
Step-by-step explanation:
DATA:
Deposits (at beginning of year):
Year 1 = $500
Year 2 = $200
Year 3 = $600
growth factor: z = 1 + r
interest rate is 2% so replace r with 2%. Growth factor equation is now:
z = 1 + 2%
z = 1.02
Year 1 account balance end of year = account balance + growth factor
= $500 + 1.02
= $ 510 account balance at end year 1
Year 2 account balance end of year = (previous year ending balance + current year deposit) * growth factor
= ($510 + $200) * 1.02
= $724.20
Year 3 account balance end of year = (previous year ending balance + current year deposit) * growth factor
= ($724.20 + $600) * 1.02
=$1,350.684
rounded: = $1,350.68 (This answer assumes no money has been withdrawn at any time.)
write the slope-intercept form of the equations of the line described
1. through (1,3), perpendicular to y=x-4
2. through (3,1), parallel to y=-x-4
1. The equation of the perpendicular line is: y = -x + 4
2. The equation of the parallel line is: y = -x + 4
What are the Equations of Parallel and Perpendicular Lines?The equations of two lines that are parallel to each other will have the slope (m), while the equations of two lines that are perpendicular to each other will have slope values that are negative reciprocals of each other.
The slope-intercept form for the equation of a line is, y = mx + b, where b is the y-intercept and m is the slope of the line.
1. The slope (m) of y = x - 4 is 1. The line that is perpendicular to y = x - 4 would have a slope (m) of -1.
Substitute (a, b) = (1, 3) and m = -1 into y - b = m(x - a):
y - 3 = -1(x - 1)
Rewrite in slope-intercept form:
y - 3 = -x + 1
y = -x + 1 + 3
y = -x + 4
2. The slope (m) of y = -x - 4 is -1. The line that is parallel to y = -x - 4 would have a slope (m) of -1.
Substitute (a, b) = (3, 1) and m = -1 into y - b = m(x - a):
y - 1 = -1(x - 3)
Rewrite in slope-intercept form:
y - 1 = -x + 3
y = -x + 3 + 1
y = -x + 4
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I need this answered in the next 5 maybe 10 minutes
Six times a number is 36
x^6= 36
6x = 36
6^x= 36
6 + x = 36
Answer:
6x = 36 is the correct expression.
Answer:
6x=36 so we divide both side by 6, then we will gate the x =6
Step-by-step explanation:
6x= 36 so the x value become 6Ex) what is the ratio? Of 5:35
Answer:
1:
Step-by-step explanation:
5 divided by 5 is 1, and 35 divided by 5 is
The function f is defined as follows
f(x)=-2x^2-2
if the graph of f is translated vertically upward by 5 units, it becomes the graph of function h
FIND THE EXPRESSION FOR H(X)
h(x)=?
Answer:
h(x)=-2x²+3
Step-by-step explanation:
Add 5 to -2x²-2.
-2x²-2+5=-2x²+3
h(x)=-2x²+3
Hope this helps!
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Question Progress
Homework Progress
10/41
Expand and simplify (x+3)(x + 5)
Answer:
x2 + 8x + 15
Step-by-step explanation:
First - take the first terms of the brackets (so, x and x) and multiply them together: for this example that gives x2.
Outside - take the two outermost terms of the brackets (x and 5) and multiply them together: for this example that gives 5x.
Inside - take the two innermost terms of the brackets (3 and x) and multiply them together: for this example that gives 3x.
Some people may draw lines between terms when doing this (as seen in the diagram above) leaving you with a “crab claw” around the brackets.
Write down everything you have worked out as one long expression:
x2 + 5x + 3x + 15
Then, we will simplify this expression by grouping any “like” terms (this just means adding together any bits with x where they have the same power).
This leaves us with our final answer, which is:
x2 + 8x + 15
Please answer fast
Thank you!
Answer:
see explanation
Step-by-step explanation:
the perimeter (P) is the sum of the 4 sides
(a)
P = a + b + c + d
= x + 7 + 2x + 2 + 8x + x + 10 ← collect like terms
= 12x + 19
(b)
If x = 4 , then
P = 12x + 19 = 12(4) + 19 = 48 + 19 = 67
(c)
If x = 2 , then
P = 12x + 19 = 12(2) + 19 = 24 + 19 = 43
(d)
P = a + b + c + d
= x² + 4x + 8 + 2x² + x ← collect like terms
= 3x² + 5x + 8
Look at the table showing different prices for cans of soup.
Prices for Soup
Price A
Price B
Price C
$3.87 for 3
$2.38 for 2
$8.75 for 7
The prices in order from greatest to least unit rate is Price A>Price C>Price B.
Given a table that showing different prices for cans of soup as shown in attached image.
Here, we will calculate the price of 1 quantity of each type of soup.
The Price of 3 quantities of soup price A=$3.87
Now, we will find the price of soup A for the 1 quantity.
The Price of 1 quantity of soup price A=$3.87/3=$1.29
The Price of 2 quantities of soup price B=$2.38
Now, we will find the price of soup B for the 1 quantity.
The Price of 1 quantity of soup price B=$2.38/2=$1.19
The Price of 7 quantities of soup price C=$8.75
Now, we will find the price of soup C for the 1 quantity.
The Price of 1 quantity of soup price C=$8.75/7=$1.25
Hence, the prices in order, from greatest to least unit rate from the given table which is shown in attached image is Price A>Price C>Price B or $1.29>$1.25>$1.19.
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Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.
If you have three points A, B , and C , then A, B, C are noncollinear.
The given conjecture "If you have three points A, B , and C , then A, B, C are noncollinear" is false.
How to Interpret Conditional Statements?Notice that the given conjecture does not necessarily be always true.
To be precise, there are no reasons as to why A, B and C must be noncollinear.
They could lie on the same line.
Therefore, the given conjecture "If you have three points A, B , and C , then A, B, C are noncollinear" is false.
A Counterexample of the given statement is; A, B, C are three points that lie on the same line and so they are collinear.
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Una ciclopista para andar en bicicleta tiene 17/6 de km ¿cuantos km se recorren al dar dos vueltas a la pista
The number of kilometers when the person goes twice is 17km.
How to compute the value?From the information, it should be noted that the bicycle lane to ride a bicycle is 17/6 km.
Therefore, the number of kilometers when the person goes twice will be:
= 17/6 × 2
= 17 km
Therefore, the number of kilometers when the person goes twice is 17km.
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The angle lies in which quadrant?
tan<0 and csc<0 are in Quadrant II
a washer and a dryer cost combined. the cost of the washer is three times the cost of the dryer. what is the cost of the dryer?
$250 is the cost of the dryer.
What do we mean by cost?
The amount of money spent by a company on the creation or production of goods or services is referred to as the cost.It does not include the profit margin. From the standpoint of a seller, the cost is the amount of money spent to produce a good or product.To find the cost of the dryer:
The dryer is priced at x dollars.The washer costs 3 times as much.Then,
3x + x = 10004x = 1000x = 250Therefore, $250 is the cost of the dryer.
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The correct question is given below;
A washer and a dryer cost $1000 combined. The cost of the washer is three times the cost of the dryer. What is the cost of the dryer?
john is playing a game with a standard deck of playing cards. he wants to draw a jack on the first try. which of the following statements is true?
John is playing a game with a standard deck of playing cards - this statement is true.
What is the purpose of playing cards?playing a card game, set of cards that are numbered or outlined (or both) and are utilized for messing around, for schooling, for divination, and for conjuring. Generally, Western playing a card game are made of rectangular layers of paper or slight cardboard stuck together to frame a level, semirigid material. Some have proposed that the playing a card game previously worked as "play cash" and addressed the stakes utilized for other betting games, and later turned out to be essential for the actual games. Others have proposed associations between playing a card game and chess or dice games, yet this is again theoretical. Different games, for example, a 25-card variation of Euchre which involves the Joker as the most elevated trump, make it one of the main in the game. Frequently, the Joker is a special case, and subsequently permitted to address other existing cards.
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