If R is (-4, 7) and S is (-2, 12), what is the component form of the vector R.S?
(8,84)
(2,5)
(-6, 19)
(-3,9.5)
Answers
Answer:
(2, 5)
Step-by-step explanation:
Given:
R = (-4, 7)S = (-2, 12)To find the components of [tex]\overrightarrow{RS}[/tex] we need to go from R to O and then O to S. Remember that [tex]\overrightarrow{RO}[/tex] is the negative of [tex]\overrightarrow{OR}[/tex]. Therefore:
[tex]\begin{aligned} \displaystyle \overrightarrow{RS} & =\overrightarrow{RO}+\overrightarrow{OS}\\& = \overrightarrow{OS}-\overrightarrow{OR}\\& =\binom{-2}{12}-\binom{-4}{7}\\& =\binom{2}{5}\end{aligned}[/tex]
Therefore, the component form (x, y) of the vector [tex]\overrightarrow{RS}[/tex] is (2, 5)
Related Questions
One Solution
No Solutions
Infinitely Many Solutions
2+y=3
−2x − y = −6
Answers
Answer:
it is -6. . . . . . . . . . . . . . . . .. ... . . . . . . .
AB = 10 in; AD = 6 in
A=
30sqrt3 in2
30 in2
60 in2
Answers
Answer: 30
Step-by-step explanation:
If we were to draw diagonal BD, then we would create two congruent triangles, and we could find the area of each using the formula [tex]A=\frac{1}{2} ab \sin C[/tex].
However, since there are two triangles, we can double this, giving us [tex]A=ab \sin C[/tex].
So, the area is [tex]A=(10)(6)(\sin 30^{\circ})=\boxed{30}[/tex]
A line that passes through the point (x,y), with a y-intercept of b and a slope of m, can be represented by the equation y = mx + b.
A line is drawn on the coordinate plane that passes through the point (3,-6) and has a slope of 4. The y-intercept of the line is .
Answers
Answer:
b= -18
Step-by-step explanation:
x=3, y= -6, m=4
y=mx+b
-6 = 4 x 3 + b Solve for b
-6 = 12 + b
-6-12 = b
b= -18
Answer:
b = -18
Step-by-step explanation:
Slope y-intercept form: y =mx +bSlope = m = 4
Plugin the value of slope in the above equation.
y = 4x + b
Now, the line passes through the point (3 , -6). Substitute x and y coordinates in the above equation.
-6 = 4*3 + b
-6 = 12 + b
b = -6 - 12
b = -18
[tex]\sf \boxed{\bf y-intercept = -18}[/tex]
ristina and Lamar use a ruler and protractor to draw triangles with given conditions. Part A Cristina is asked to construct a triangle with a 45° angle and a 65° angle. How many different triangles could she draw with these conditions? A any number of triangles B exactly two triangles C exactly one triangle D no triangle Part B Lamar is asked to construct a triangle with two angles measuring 45° and 65°, with the side length between those angles 4 centimeters long. How many different triangles could he draw with these conditions? A any number of triangles B exactly two triangles C exactly one triangle D no triangle
Answers
Answer:The sum of the interior angles in any triangle must be equal to 180 degrees
In this problem we have a triangle with a 45 degree angle and a 65 degree angle
so
The measure of the third side must be equal to
The triangle is a 45°-65°-70°
Remember that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
In this problem
I can have as many triangles whose internal angles are congruent and their sides are proportional
therefore
More than one triangle can be drawn with these conditions
Step-by-step explanation:
I need help with this
Answers
Answer:
1. obtuse angle
2. Right angle
3. Adjacent angle
4. Supplementary angle
5. Acute angle
6. Straight line
7. Complementary angle
8. Vertical Angle
9. linear
10. Vertex
Step-by-step explanation:
1. Obtuse angle are angle that measures greater than 90 degree but less and 180 degree
2. Right angle are angle that measures exactly 90 degree
3. Adjacent angle are angles that has a common vertex and share a common side
4. Straight angle is a pair of angle whose sum is 180 degree.
5. Acute angle is an angle greater than 0 degree but less than 90 degree
6. straight line measure exactly 180 degree
7. Complementary angle is a pair of angle whose sum is 90 degree.
8. Vertical Angle is a pair of angle made by intercepting lines with congruent opposite side
9. Linear is a pair of adjacent, supplementary angles.
10. Vertex is an common end point that two rays meet to form an angle.
A line contains points F, G, H, I, J. The space between F G is 2. The space between H and I is 1. The space between F and I is 7.
If FG = 2 units, FI = 7 units, and HI = 1 unit, what is GH?
Answers
Based on the segment addition postulate, the length of GH is: 4 units.
What is the Segment Addition Postulate?The segment addition postulate states that if a line segment is divided into smaller parts, the sum of the length of the smaller parts equals the length of the line segment.
FG = 2 unitsFI = 7 unitsHI = 1 unitGH = ?FI = FG + HI + GH [segment addition postulate]
7 = 2 + 1 + GH
7 = 3 + GH
7 - 3 = GH
4 = GH
GH = 4 units.
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Answer:
B- 4 units
Step-by-step explanation:
In how many years will $7000 yield an interest of $4620 at 22% simple interest?
Answers
Answer:
3 Years
Step-by-step explanation:
7000*22% = 1540
4620/1540 = 3
1540 = the yearly interest
so it will take 3 years of $1540 of interest to get $4620.
Normally you would also have to take into account the interest plus the base varible but since it specifically says 7000 it makes it a simple problem.
hope this helped
CHARLES' LAW CALCULATION.
Answers
1.The temperature will be, T2= 169.8 K
2. The volume if the temperature is 318 K is 0.170 L
What is Charles Law?Charles's law, a statement that the volume occupied by a fixed amount of gas is directly proportional to its absolute temperature, if the pressure remains constant.
Given: V1= 250 ml=0.25L
V2=150 ml= 0.15 L
T1= 10 °C=283 K, T2=?
Now using Charles law
V1/T1=V2/T2
0.25/283=0.15/T2
T2= 169.8 K
2. T1= 20 °C= 293 K
V1= 160 cm³
T2= 318 K
V2=?
Using Charles Law,
V1/T1=V2/T2
0.16/293=V2/313
0.170 L=V2
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Select the correct answer. The vertices of a triangle are A(7, 5), B(4, 2), and C(9, 2). What is m<ABC
Answers
Answer: [tex]45^{\circ}[/tex]
Step-by-step explanation:
[tex]\angle ABC[/tex] is formed by [tex]\overline{AB}[/tex] and [tex]\overline{BC}[/tex], so we can begin by finding their slopes.
[tex]m_{\overline{AB}}=\frac{2-5}{4-7}=-1\\m_{\overline{BC}}=\frac{2-2}{9-4}=0[/tex]
This means that:
[tex]\tan \left(\angle ABC \right)=\left| \frac{-1-0}{1-(0)(-1)} \right|\\\tan \left(\angle ABC \right)=1[/tex]
As [tex]\angle ABC[/tex] is acute, this means [tex]m\angle ABC=\boxed{45^{\circ}}[/tex]
Problem #2
Using the perpetual inventory system, journalize the entries for the following transactions:
a) Sold merchandise on account for $12,000, terms 1/10, n/30. The cost of the merchandise sold was $6,500.
b) Sold merchandise on account for $9,500 to customers who used a VISA card. The cost of the merchandise sold was
$5,300.
c) The customer in a) returned merchandise which was sold for $1,000 and that we had purchased for $780.
d) Purchased merchandise on account for $8,500, credit terms 1/15, n 45, FOB destination. The appropriate company paid
the Freight costs of $500.
Answers
The perpetual inventory system is an inventory management method that records when stock is sold or received in real-time.
How to depict thejournal?
a. Debit Accounts Receivable 12000
Credit Sales 12000
Debit Cost of Merchandise Sold 6500
Credit Merchandise Inventory 6500
b. Debit Cash 9500
Credit Sales 9500
Debit Cost of Merchandise Sold 5300
Credit Merchandise Inventory 5300
c. Debit Cash 2900
Credit Sales 2900
Debit Cost of Merchandise Sold 1700
Credit Merchandise Inventory 1700
d. Debit Credit Card Expense 385
Credit Cash 385
e. Debit Credit Card Expense 75
Credit Cash 75
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Evaluate 1/2 X (6 X 4)÷3 + 2 show your work to find the answer pls hurry
Answers
So, when we evaluate 1/2 × (6 × 4) ÷ 3 + 2 = 8
To answer the question, we must use the rules of arithmetic in mathematical operations
What are mathematical operationsMathematical operations are operation which include
addition, subtraction, multiplication and division. Rules of arithmetic in mathematical operationsIn arithmetic, we follow the rule PEMDAS where
P - parentheses E - exponents M - multiplication D - division A - addition and S - subtractionSo, to evaluate 1/2 × (6 × 4) ÷ 3 + 2, we follow this rule.
So, 1/2 × (6 × 4) ÷ 3 + 2 = 1/2 × 24 ÷ 3 + 2
= 12 ÷ 3 + 2
= 6 + 2
= 8
So, 1/2 × (6 × 4) ÷ 3 + 2 = 8
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rectangle with area of 12 square units is dilated by a scale factor of 3. What is the area?
Answers
Answer:
36 units²
Step-by-step explanation:
rectangle with area of 12 square units is dilated by a scale factor of 3. What is the area?
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
we use the inverse formula
12 * 3 =
36 units²
-----------------------
check
36 : 12 = 3
the answer is good
What is the simple interest on N450 for 2 years at 3%?
Answers
Answer:
Simple Interest = PTR/100
P=450
T=2
R=3%
Simple Interest = PTR/100
=450×2×3\100
=27
Hence the interest is 27.
How much will a sum of ¥4000 amount to in 1 1/2 yrs at 10% per annum compound interest,interest being paid half-yearly
Answers
Answer:
¥4630.50
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = 4000r = 10% = 0.1n = 2t = 1.5Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=4000\left(1+\dfrac{0.1}{2}\right)^{2 \times 1.5}[/tex]
[tex]\implies \sf A=4000\left(1.05\right)^{3}[/tex]
[tex]\implies \sf A=4630.50[/tex]
Answer:
¥4630.50
Step-by-step explanation:
Here,
P = ¥4000n = 1 1/2 = 3/2 yearsr = 10% per annumATQ, as well,the interest is payable in half-yearly.
We know that,
[By this formula,it could easily solved][tex] \boxed{\rm \: A = P \bigg(1+ \cfrac{ \cfrac{r}{2} }{100} \bigg) {}^{2n} }[/tex]
Substitute the values
[tex]A = 4000 \bigg(1 + \cfrac{5}{100} \bigg) {}^{2 \times \frac{3}{2} } [/tex]
Now solve.
[tex]A = 4000 * (21/20)^3[/tex]
[tex] \implies \: A = 4000 \times \cfrac{21}{20} \times \cfrac{21}{20} \times \cfrac{21}{20} = \cfrac{21 \times 21 \times 21}{2} [/tex]
[tex] \implies \: A = \: \yen \: 4630.50[/tex]
Hence,the sum of ¥ 4000 will be amounted to ¥4630.50 in 1 1/2 years.
[tex] \rule{225pt}{2pt}[/tex]
This question arises:Why we used that formula?
Reason:
The compound interest is calculated half-yearly, the formula changes a little.In this case for r we write r/2 and for n we write 2n because a rate of r% per annum is r/2% half-yearly and n years = 2n half year So this is the reason.
It cost a boy $13.50 to take a girl out for the evening. Sixty percent of this was for the theater tickets. What was the cost of each ticket ?
Answers
It cost a boy $13.50 to take a girl out for the evening. Sixty percent of this was for the theater tickets. What was the cost of each ticket?
Solution:60% of $13.50 is 0.6*13.50 = 8.10
Cut this figure in half to get 8.10/2 = 4.05
So the cost of each ticket was $4.05
Answer:The cost of each ticket is $4.05.
학습을 계속하다
Does anyone know how to do this I’m really confused
Answers
The size of the unknown angle "x"
Solution:The given polygon is a Pentagon so the sum of interior angle will be,
[tex]\large\boxed{Formula: ( n − 2 ) × 180}[/tex]
n means the number of sides
Let's substitute the values according to the formula.
[tex](5-2)×180[/tex]
[tex]=540°[/tex]
Now, we can find the sum of one interior angle.
[tex]\large\boxed{\frac{sum \: of \: interior \: angles}{n}}[/tex]
n means the number of sides.
Let's substitute the values according to the formula.
[tex]x=\frac{540}{5}[/tex]
[tex]\large\boxed{x= 108°}[/tex]
Therefore, the size of the unknown angle "x" is 108°
Find the surface area and lateral surface area of the cylinder. Round your answers to the nearest tenth.
3 yd
Surface area:
Lateral surface area:
Answers
A cylinder is a three-dimensional structure formed by two parallel circular bases. The lateral and the total surface area of the cylinder are 113.1 yd² and 169.7 yd².
What is a cylinder?A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.
Lateral area of the cylinder = Area of the curved surface
= 2πR × H
= 2 × π × 3yd × 6yd
= 36π yd²
= 113.0973 yd² ≈ 113.1 yd²
The total surface area of the cylinder
= Area of the two bases + Area of the curved surface
= 2(π × 3²) + 113.0973 yd²
= 56.54866 yd² + 113.0973 yd²
= 169.6459 yd² ≈ 169.7yd²
Hence, the lateral and the total surface area of the cylinder are 113.1 yd² and 169.7 yd².
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Find cos 20 if theta is in the first
quadrant and tan 0 = 40/9
Answers
If the value of the angle θ is 77.32°. Then the value of cos 2θ will be the negative 0.90.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The trigonometric equation is given below.
tan θ = 40/9
tan θ = 4.444
Then the angle θ will be
θ = tan⁻¹(4.444)
θ = 77.32°
Then the value of cos 2θ will be
cos 2θ = cos (2 x 77.32°)
cos 2θ = cos 154.64°
cos 2θ = - 0.9036
cos 2θ ≅ - 0.90
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Dean started with 5 meters
of yarn. He used 300
millimeters of yarn each day
for 5 days. How many
meters of yarn does Dean
have left?
Answers
Answer:
3.5 meter is the answer.
Answer:
3.5 Meters
Step-by-step explanation:
5 Meters is equivalent to 5000 millimeters
1 day = 300mm
5 days = (300*5)
= 1500 mm
= 5000 mm - 1500 mm
Yarn left = 3500 mm
= 3.5 Meters
EN=NG, which of the following statements CANNOT be true? F M E R NP Q A. MN is a perpendicular bisector. OB. FM = MG O C. Pis a midpoint. O D. MN is a midsegment. G
help dawg
Answers
Answer:A. MN is a perpendicular bisector.
Hope that helps
Step-by-step explanation:
What’s the second step to solving 2x-4=26
Answers
Answer:
The second step is to isolate the variable by multiplication or division
Step-by-step explanation:
so it should be solving the x
Answer:]
A two-step equation is an algebraic equation that takes you two steps to solve. You've solved the equation when you get the variable by itself, with no numbers in front of it, on one side of the equal sign.
:] Correct me if i'm wrong :]
pls help me with 5,6,7,8,9,10,11.Its 7th grade maths i really need help.I'll
also give brainliest
Answers
The missing areas and dimensions of the given squares, rectangles, and triangles are:
2. 36 cm²
3. 21 cm²
4. 9 cm²
5. 5 cm
6. 10 cm
7. 4 cm
8. 8 cm
9. 7 cm
10. 7
11. 10
What is the Area of a Square, Rectangle, and a Triangle?Area of a square = s²
Area of a rectangle = (length)(breadth)
Area of a triangle = 1/2(base)(height).
2. Area of square = s² = 6² = 36 cm².
3. Area of a rectangle = (length)(breadth) = (3)(7) = 21 cm².
4. Area of a triangle = 1/2(base)(height) = 1/2(3)(6) = 9 cm².
5. Area of a rectangle = (length)(breadth)
60 = (12)(breadth)
Breadth = 60/12
Breadth = 5 cm.
6. Area of a triangle = 1/2(base)(height)
35 = 1/2(7)(height)
Height = (35)(2)/7
Height = 10 cm
7. Area of a square = s²
16 = s²
s = √16
s = length = 4 cm
8. Area of a triangle = 1/2(base)(height)
40 = 1/2(10)(height)
Height = 40/5
Height = 8 cm.
9. Area of a square = s²
49 = s²
s = √49
s = length = 7 cm
10. Area of a rectangle = (length)(breadth)
84 = (12)(breadth)
Breadth = 84/12
Breadth = 7 cm.
11. Area of a triangle = 1/2(base)(height)
35 = 1/2(7)(height)
Height = 70/7
Height = 10 cm.
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Please show your work! I'll give you brainliest as well as a 5 star rating, thanks!
Answers
Answer:
281.3
Step-by-step explanation:
If the shapes are similar then the linear scale factor is :
15÷20 = 0.75
The area scale factor will be 0.75²
The area scale factor is 0.5625
500 × 0.5625 = Area of shaded rectangle
Area of shaded rectangle = 281.25
To the nearest tenth = 281.3
Hope you understood and brainliest please
Answer:
[tex]281.3 m^{2}[/tex]
Step-by-step explanation:
I've done this before I have the work attached below in a screenshot. Sorry that it's not much but I hope it helps!
Please feel free to comment, give feedback, ask questions, and correct me if I am wrong!
Have a great day
:)
EASY POINTS
NEED HELL ASAP WIT THIS
Answers
Answer:
5
Step-by-step explanation:
You just multiply the indices by the power so 1/6 x 6 = 1 and 5 to the power of 1 is just 5.
a circular garden has a diameter of 12 yards whag is the area of the garden use 3.14
Answers
Step-by-step explanation:
the area of a circle is
pi × r²
r is the radius (= half of the diameter) of the circle.
radius in our car is 12/2 = 6 yd
and we are to use 3.14 as pi.
so we get as area
3.14 × 6² = 3.14 × 36 = 113.04 yd²
what is the smallest number when divided by 24 and 12 leaves remainder 12
Answers
Answer:
The smallest number is two 2
The bearing
of P from Q is 0.60°. What is the bearing
of Q from P
Answers
Answer:
MMm mmm mmm mmm sh get wicked mmm mmm mm like what u saying mmm mmm mmm gla mmmm
Step-by-step explanation:
(URGENT) Madelina wants to make a prediction using a linear model with a correlation coefficient of 0.55. Which statement best describes how accurate she can expect her prediction to be? Her prediction will probably be close to the actual value. Her prediction will be unlikely to be close to the actual value. Her prediction will be somewhat likely to be close to the actual value. Her prediction will very likely be close to the actual value.
Answers
A correlation coefficient of 0.55 indicates that her prediction will probably be close to the actual value.
What is correlation coefficient?The correlation coefficient shows the relationship between two variables. It can be used to describe how to variables increase or decrease.
Thus, a correlation coefficient of 0.55 indicates that her prediction will probably be close to the actual value.
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This list shows the lengths in feet of the 25 longest bridges in the United States.
1010
1470
1600
2000
2800
1053
1495
1632
2150
3500
1200
1596
1750
2150
3800
1207
1600
1800
2300
4200
1380
1600
1850
2310
4260
Jamie made a frequency table of the bridge data.
U.S. Bridges
Length (ft)
Tally
Frequency
(first interval)
|||| ||
7
(last interval)
||
2
Based on the tallies and frequencies for the first and last intervals, how many intervals of what length did Jamie use?
a.
4 intervals of 1000 feet
c.
6 intervals of 500 feet
b.
5 intervals of 1000 feet
d.
7 intervals of 500 feet
Please select the best answer from the choices provided
A
B
C
D
Answers
The length of the intervals of the given frequency table is
500 ft.
The given list shows the lengths in feet of the 25 longest bridges in the United States.
we have to determine the median and mode of the bridge data.
The median is the middle number of the data set arranged in ascending order.
1010, 1053, 1200, 1207, 1380, 1470, 1495, 1596, 1600, 1600, 1600, 1632, 1750, 1800, 1850, 2000, 2150, 2150, 2300, 2310, 2800, 3500, 3800, 4200, 4260.
The median is 1750.
Mode is the number that appears most often in the data set.
1010, 1053, 1200, 1207, 1380, 1470, 1495, 1596, 1600, 1600, 1600, 1632, 1750, 1800, 1850, 2000, 2150, 2150, 2300, 2310, 2800, 3500, 3800, 4200, 4260
The mode is 1600.
Therefore the correct option is Median: 1750, Mode: 1600
So the length of the intervals of the given frequency table is
500 ft.
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After a 35% reduction, you purchase a new television for $136.5. What was the price of the television before the reduction?
A) First write an equation you can use to answer this question.
B) Solve your equation in part [A] to find the original price of the television.
Answers
Answer:
See Below
Step-by-step explanation:
35% off means you pay 65%
sooo A) .65 x = 136.50 where x = original price
B) x = 136.50/.65 = $210 original price