If we start from the origin, then the vector would be v = (52, 12) as given. But suppose we shift its initial point. Doing so would preserve its direction. For example, if we move its initial point to (1, 1), we'd have to shift its terminus by the same amount (1 unit to the right, 1 unit up) so that its terminal point would be (52 + 1, 12 + 1) = (53, 13).
Option A is not correct. If we want the vector to start at (52, 12), we have to adjust the terminus by the same distance by adding (52, 12) to the terminus. This means the resulting vector would start at (52, 12) and end at (52 + 52, 12 + 12) = (104, 24).
One important thing to observe here is that the difference between the terminal and initial points always returns v. In the first example: (53, 13) - (1, 1) = (52, 12). In checking option A: (104, 24) - (52, 12) = (52, 12). So to eliminate any other answer choices, all you need to do is subtract.
Option B is correct by this "rule". (66, 7) - (14, -5) = (52, 12).
Options C and D are not. (0, 12) - (52, 0) = (-52, 12), and (64, -4) - (-12, 16) = (76, -20).
Final answer:
The initial and terminal points that correctly represent the vector v = (52, 12) in component form are option B: initial (14, -5); terminal (66, 7), as these points give the same components when subtracted (terminal - initial).
Explanation:
The student is asking about the initial and terminal points for a vector given in component form. The vector v is (52, 12), which means it has an x-component of 52 and a y-component of 12. This can be visually represented as a directed line segment with an initial point and a terminal point. The correct initial and terminal points for vector v would result in the same component form when subtracting the coordinates of the initial point from the coordinates of the terminal point (terminal - initial).
Option B has the initial point (14, -5) and terminal point (66, 7). By calculating the difference between the terminal and initial points: (66 - 14, 7 - (-5)) = (52, 12), we can see that these points correctly represent the vector v in component form. Therefore, the answer is B.
PLEASE HELP!!!!!!!! 47 POINTS!
Show work please
Answer:
Step-by-step explanation:
The installation cost is $300 and the cost per square foot is $4 . So the total price is y= 4x + 300 (where x is square foot).
slope is 4 and y intercept is 300
for 375 sqft. the cost is y= 4(375) +300 = 1800
the cost is $1800
We are supposed to use factor trees or something? Could I get a in depth explanation please?
Which option is is an example of expository writing?
Answer: Your answer would be "B" Hope this helps you!
Use a shortcut method of your choice to complete the multiplication problems.
a. 973 × 80
b. 56 × 2,000
c. 5.7 × 300
d. 0.46 × 50
Answer:
See below.
Step-by-step explanation:
a. 973 * 80
= 973 * 8 * 10
= 7784 * 10
= 77,840.
b. 56 * 2000
= 2*56 * 1000
= 112,000.
c. 5.7 * 300
= 5.7 * 3 * 100
= 17.1 * 100
= 1710.
d. 0.46 * 50
= (0.46 * 100) / 2
= 46 / 2
= 23.
Answer with Step-by-step explanation:
a. 973 × 80
= 973 × 8 × 10
= 7784 × 10
=77840
b. 56 × 2,000
=56 × 2 × 1000
=112 × 1000
=112000
c. 5.7 × 300
=5.7 × 3 × 100
=17.1 × 100
=1710
d. 0.46 × 50
=0.46 × 5 × 10
=2.3 × 10
=23
Eva makes and sells her own cranberry apple fruit punch for the holidays.
In jug A, she mixes 4 cranberry flavored cubes and 3 apple flavored cubes with some water.
In jug B, she mixes 3 cranberry flavored cubes and 2 apple flavored cubes with some water.
If you ask her for a drink that has a stronger cranberry taste, from which jug should Eva pour you drink?
Eva should pour you a drink from jug B for a stronger cranberry taste, as it has a higher ratio of cranberry to apple cubes compared to jug A, demonstrating the use of ratios in mathematics.
To decide which jug of fruit punch has a stronger cranberry taste, we should look at the ratio of cranberry flavored cubes to apple flavored cubes in both jugs. For jug A, the ratio is 4 cranberry cubes to 3 apple cubes, which simplifies to approximately 1.33 cranberry cubes for every apple cube. For jug B, the ratio is 3 cranberry cubes to 2 apple cubes, which simplifies to 1.5 cranberry cubes for every apple cube.
Since jug B has a higher ratio of cranberry to apple, it has a stronger cranberry taste compared to jug A. So, Eva should pour you a drink from jug B if you want a drink with a stronger cranberry flavor. This involves a practical application of ratios and proportions, which are key concepts in mathematics used to compare quantities.
Plzz Help!!!
√−100 =___ + ___ i
[tex]\displaystyle\bf\\\sqrt{-100}=\sqrt{100\times(-1)}=\sqrt{10^2\times(-1)}=10\sqrt{-1}=10i=\boxed{\bf0+10i}[/tex]
problem 1: the longest book toshi had read was 304 pages. she just finished kira-kira by cynthia kadohata, which is 256 pages. how much longer was the longest book toshi read than kira-kira?
Answer:
48
Step-by-step explanation:
304 - 256 equals 48
A line with a slope of -2 passes through the points (0,d) and (-8,9). What is the value of d?
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have m = -2 and the points (0, d) and (-8, 9). Substitute:
[tex]\dfrac{9-d}{-8-0}=-2\\\\\dfrac{9-d}{-8}=-2\qquad\text{multiply both sides by (-8)}\\\\9-d=16\qquad\text{subtract 9 from both sides}\\\\-d=7\qquad\text{change the signs}\\\\\boxed{d=-7}[/tex]
Georgia spends $39 on gas each week. Approximately how much money does she spend on gas each week?
$30
$40
$50
$78
The correct answer should be B. $40
I'm guessing the question is asking for a precise amount..
Hope we thought this through correctly and you get it right!,
Davinia.
What does it equal to and how
Answer:
The answer would me 15m
Step-by-step explanation:
1. you multiply both of them together in order to get the area
L x W = A
Please HELP!
How do I factorise 2x^2 - 11x -6x
please include working
Thanks!
Answer:
x(2x-17)
Step-by-step explanation:
2x^2 -11x-6x
2x^2-17x
x is common
x(2x-17)
Answer:
x(2x-17)
Step-by-step explanation:
[tex]2x^2-11x-6x\\2x^2-17x\\x(2x-17)[/tex]
Steps:
Combine Like Terms (-11x and -6x)
Factor out the common term (x)
mr.grant spent $8.40 to place an ad in the newspaper. this price included one time fee of $6.00 plus $0.08 per word.which method can be used to determine the total number of words in the ad mr.grant placed
a.(8 .4 ×6)0.08
b.(8 .4-6)÷0.08
c.(8 .4+6)÷0.08
d.(8 .4÷00.8)6
plz help me
Answer:
The cost of the one word is $30 .
Option (b) i.e [tex] \frac{8.4- 6}{0.08}[/tex] is used to determine the total number of words in the ad mr.grant placed.
Step-by-step explanation:
Let us assume that the number of words in the ad be x.
As given
Mr.grant spent $8.40 to place an ad in the newspaper.
This price included one time fee of $6.00 plus $0.08 per word.
Than the equation becomes
8.40 = 6 .00 + 0.08x
Simplify the above
8.4 = 6 + 0.08x
8.4 - 6 = 0.08x
[tex]x = \frac{8.4- 6}{0.08}[/tex]
[tex]x = \frac{2.4}{0.08}[/tex]
[tex]x = \frac{24\times 100}{8\times 10}[/tex]
[tex]x = \frac{2400}{80}[/tex]
x = $30
Therefore the cost of the one word is $30 .
Option (b) i.e [tex] \frac{8.4- 6}{0.08}[/tex] is used to determine the total number of words in the ad mr.grant placed.
A construction worker took 1over8
of the bags of cement in a load and separated them into 4 equal piles.
What fraction of the entire load of bags was in each pile?
1over32
8over4
32over1
1over2
Answer:
1/32
Step-by-step explanation:
1/8 divided by 4 = .03125
.03125= 1/32
(a^(2)-4ac+3bc)/(a^(2)-ab+bc-ac)+(a+3b)/(b-a)+(a+2c)/(a-c)
3(bc - ac - ab)/(a²-ab+bc-ac) is the simplified form of the given equation.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given an expression:
(a²-4ac+3bc)/(a²-ab+bc-ac) + (a+3b)/(b-a) + (a+2c)/(a-c)
Simplifying Using PEMDAS starts from the right:
(a²-4ac+3bc)/(a²-ab+bc-ac) + [tex]\frac{a^{2} + 3ab - ac - 3bc }{-a^{2} + ab -bc +ac }[/tex]
Taking negative common from the last term
(a²-4ac+3bc)/(a²-ab+bc-ac) - (a² + 3ab - ac -3bc)/(a²-ab+bc-ac)
Since the base is the same,
(-4ac + 3bc - 3ab +ac +3bc)/(a²-ab+bc-ac)
3(bc - ac - ab)/(a²-ab+bc-ac)
therefore, the simplified form of the given equation is 3(bc - ac - ab)/(a²-ab+bc-ac).
Learn more about Mathematical operations here:
https://brainly.com/question/20628271
#SPJ2
The solution involves evaluating a complex algebraic expression step by step after substituting given values for variables.
Given the expression, (a2-4ac+3bc)/(a2-ab+bc-ac)+(a+3b)/(b-a)+(a+2c)/(a-c), substitute a = 1, b = 0.0211, and c = -0.0211 to simplify.
After substitution, perform the necessary calculations to evaluate the expression step by step.
if f(1) = -5 and f(n) = f(n-1) +7, find the first four terms and the common difference of the sequence
Answer:
- 5, 2, 9, 16 and d = + 7
Step-by-step explanation:
to obtain the first four terms substitute n = 2, 3, 4 into the recursive formula
f(1) = - 5 ← given
f(2) = f(1) + 7 = - 5 + 7 = 2
f(3) = f(2) + 7 = 2 + 7 = 9
f(4) = f(3) + 7 = 9 + 7 = 16
common difference d = 16 - 9 = 9 - 2 = 2 - (- 5) = 7
Jasper used 15 inches of blue ribbon,14 of yellow ribbon,and 3 feet of red ribbon to decorate his box of cookies.How many inches of ribbon did jasper use?
Answer:65 inches
Step-by-step explanation:
15+14+36=65
Jasper used a total of 65 inches of ribbon.
Explanation:To calculate the total length of ribbon used by Jasper, we need to convert the 3 feet of red ribbon to inches.
Since 1 foot is equal to 12 inches, 3 feet would be equal to 12 x 3 = 36 inches. Then, we can add up the lengths of all three ribbons: 15 inches of blue ribbon + 14 inches of yellow ribbon + 36 inches of red ribbon = 65 inches of ribbon.
Learn more about Calculating length here:https://brainly.com/question/34290733
#SPJ2
Suppose f(x) =x2. What is the graph of g(x) = f(2x)
The function g(x) is [tex]\rm4x^2[/tex] and the graph is attached in the question the correct option is B.
What is the linear graph?Linear Graph Linear means straight and a graph is a diagram that shows a connection or relation between two or more quantities.
The given graph is;
[tex]\rm f(x)=x^2[/tex]
The graph of g(x) = f(2x) is given by;
[tex]\rm g(x) = f(2x)\\\\g(x) = f(2x)^2\\\\g(x)=4x^2[/tex]
Hence, the function g(x) is [tex]\rm4x^2[/tex] and the graph is attached in the question the correct option is B.
Learn more about graphs here;
https://brainly.com/question/21981889
#SPJ2
In triangle FGH, FH=10 units and GH=26 units. Which is the length of FG?
Final answer:
To find the length of FG in triangle FGH, we can use the Pythagorean Theorem. By substituting the given values into the formula and solving for FG, we find that FG is approximately 27.9 units.
Explanation:
To find the length of FG, we can use the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In this case, FH and GH are the two sides of the right triangle FGH, and FG is the hypotenuse. So we have FH² + GH²= FG².
Substituting the given values, we have 10² + 26² = FG². Simplifying this equation, we get 100 + 676 = FG². Adding the numbers gives us 776 = FG². And taking the square root on both sides, we find that FG ≈ 27.9 units.
Please help simplify!!
Answer:
a) -5n9
Step-by-step explanation:
CAN U PLZZZZ MARK ME BRAINIEST!!!! I REALLY NEED IT
Slope of (15,130) and (1,160)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (15, 130) amd (1, 160). Substitute:
[tex]m=\dfrac{160-130}{1-15}=\dfrac{30}{-14}=-\dfrac{15}{7}[/tex]
Hi there! :)
Step-by-step explanation:
[tex]Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]
[tex]\frac{160-130}{1-15}=\frac{30}{-14}=\frac{30/2}{-14/2}=\frac{15}{-7}=-\frac{15}{7}[/tex]
Therefore, the slope is -15/7.
Final answer is -15/7.
Hope this helps!
Have a nice day! :)
:D
-Charlie
Thank you so much! :)
:D
10. You have two jobs. You earn $8 for each hour x that you work as a restaurant host and $6 for each hour y that you work as a hair washer. Your earnings for the pay period are $144.
a. Write an equation in standard form that models your earnings.
b. Find the x- and y-intercepts.
c. You worked 10 hours as a hair washer. How many hours did you work as a host?
Answer:
Step-by-step explanation:
The equation in standard form is:
8x + 6y = 144
To find the y-intercept, isolate y.
8x + 6y = 144
Subtract 8x from both sides.
6y = -8x + 144
Divide both sides by 6.
y = -4/3x + 24
From this, we know (0, 24) is the y-intercept because b, which in this case, is the y value for the y-intercept.
To find the x-intercept, input y as 0.
0 = -4/3x + 24
Subtract 24 from both sides.
-24 = -4/3x
Multiply both sides by 3/-4.
18 = x
The x -intercept is (18, 0).
Input 10 for y because that's how many hours you worked as a hair washer.
8x + 6(10) = 144
Simplify.
8x + 60 = 144
Subtract both sides by 60.
8x = 84
Divide both sides by 8.
x = 10.5
You worked 10.5 hours as a host.
During the first year, ABC's stock starts at $100 and increases 100%. During the second year, its stock prices goes down 25% from its price at the end of the year. What is the price of the stock, in dollars, at the end of the second year?
Answer:
$150
Step-by-step explanation:
$100 + 100% = $200 in the first year
$200 - 25% = $150 in the second year
marcus has 12 slices of bread for each sanwich he uses 2 slices for sandwich
how many sandwiches can he make
Answer: Marcus can make 6 sandwiches.
Step-by-step explanation:
If you have 12 slices of bread and use 2 for each sandwich you would do 12/2, which equals 6.
Round answer to the nearest tenth. . An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 175 feet. What was the speed of the vehicle before the brakes were applied?
Answer:
v2 - v02 = 2ad
v = final speed = 0 (came to a full stop)
v0 = initial speed (what you want to solve for)
d = stopping distance = 175 feet
Then
v0 = √(-2ad) [Remember a is negative, so the argument of the square root is positive.]
But as you can see, we need the acceleration.
If we knew the time it took to come to a full stop, we could still answer the question. Either way, we need more information than just the stopping distance.
Step-by-step explanation:
The speed of the vehicle before the brake were applied was about 83.7 feet/s
Further explanationAcceleration is rate of change of velocity.
[tex]\large {\boxed {v^2 = u^2 + 2ad}[/tex]
[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]
[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]
a = acceleration ( m/s² )
v = final velocity ( m/s )
u = initial velocity ( m/s )
t = time taken ( s )
d = distance ( m )
Let us now tackle the problem!
This problem is about accelerated motion.
Given:
final speed of the vehicle = v = 0 feet/s
length of skid marks = d = 175 feet
maximum deceleration = a = 20 feet/s² ( assumption )
Unknown:
initial speed = u = ?
Solution:
[tex]v^2 = u^2 - 2ad[/tex]
[tex]0^2 = u^2 - 2(20)(175)[/tex]
[tex]u^2 = 7000[/tex]
[tex]u = \sqrt{7000}[/tex]
[tex]u = 10\sqrt{70} \texttt{ feet/s}[/tex]
[tex]u \approx 83.7 \texttt{ feet/s} [/tex] (rounded to the nearest tenth)
[tex]\texttt{ }[/tex]
Conclusion:The speed of the vehicle before the brake were applied was about 83.7 feet/s if we assume that maximum deceleration of the vehicle is about 20 feet/s²
[tex]\texttt{ }[/tex]
Learn moreVelocity of Runner : https://brainly.com/question/3813437Kinetic Energy : https://brainly.com/question/692781Acceleration : https://brainly.com/question/2283922The Speed of Car : https://brainly.com/question/568302Answer detailsGrade: High School
Subject: Physics
Chapter: Kinematics
Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle
Please help
What is a function? Can the following set of ordered pairs represent functions? Why or why not? A =(-4,-4), (2,0), (6,4) ,(10,2) B=(9,3), (9,-3), (4,2), (5,-2) C=(-3,7), (-2,7), (1,7),(0,7)
Answer:
A and C represent a function and B doesn't represent.
Step-by-step explanation:
A function is a relation that maps one output value of y for each input value of x.
A. Ordered pairs can be written as relation
-4→-4;2→0;6→4;10→2.Here each input value of x determines one output value of y and this set of ordered pairs represents function.
B. Ordered pairs can be written as relation
9→3;9→-3;4→2;5→-2.Here for input value x=9 there are 2 output values of y (y=3 or y=-3). This set of ordered pairs doesn't represent function.
C. Ordered pairs can be written as relation
-3→7;-2→7;1→7;0→7.There is exactly one y for each x, then this set of ordered pairs represents function.
what equation describes a line passing through (-6,-5) that is perpendicular to a line described by y=-2/3x?
The equation of the line passing through (-6,-5) and perpendicular to y=-2/3x is y=(3/2)x+4.
Explanation:To find an equation of a line passing through the point (-6,-5) that is perpendicular to the line described by y=-2/3x, we first need to determine the slope of the perpendicular line. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of our line will be the negative reciprocal of -2/3, which is 3/2.
Now, using the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can substitute our point (-6, -5) and slope 3/2 into the formula:
y - (-5) = (3/2)(x - (-6))
Simplifying this, we get:
y + 5 = (3/2)(x + 6)
y + 5 = (3/2)x + 9
Subtracting 5 from both sides, we get the final equation of the line:
y = (3/2)x + 4
Joshua receive a $70 gift card to use at a clothing store. He buys a pair of jeans for $36 and 8 pair of socks. He does not use the entire amount of the gift card. Write and solve an inequality to find s , the price of each pair of socks?
Larry uses his credit card to purchase a new video game system for $445.07 he can pay off off up to $200 per month the card has an annual rate of 13.6% compounded monthly how much total interest will he pay
Larry will pay a total interest of $45.07 when using his credit card to purchase the video game system.
To calculate the total interest Larry will pay when using his credit card to purchase a video game system for $445.07, with a monthly payment limit of $200 and an annual rate of 13.6% compounded monthly, we can follow these steps:
1. Calculate the total amount to be paid off by subtracting the monthly payment from the total purchase amount:
Total amount to be paid off = $445.07 - $200 = $245.07
2. Determine the number of months it will take to pay off the balance by dividing the total amount to be paid off by the monthly payment:
Number of months = $245.07 / $200 = approximately 1.22535 months (round up to the nearest whole month, which is 2 months)
3. Calculate the monthly interest rate by dividing the annual rate by 12 (since it's compounded monthly):
Monthly interest rate = 13.6% / 12 = 1.1333%
4. Use the formula for compound interest to find the total interest paid:
Total interest = Total amount paid - Total principal amount
Total principal amount = $445.07
Total amount paid = $200 * 2 = $400
Total interest = $400 - $445.07 = $45.07
Therefore, Larry will pay a total interest of $45.07 when using his credit card to purchase the video game system.
evaluate the expression for z=3 , 45z + 4,565 + 9,078 ÷ 89
Answer:
4802
Step-by-step explanation:
z=3 , 45z + 4,565 + 9,078 ÷ 89 = 45 * 3 + 4,565 + 9,078 ÷ 89 = 135 + 4,565 + 102 = 4802
Rachel paints 5 1 2 512 square meters of wall space in 1 3 13 hour. What area of wall space can she paint in 1 hour? One 200-gram bag of rice costs $8.12. How much does 1 kilogram of rice cost? (Note that 1000 g = 1 kg.) John ran 1 2 12 mile in 5 minutes, and Al ran 1 3 13 mile in 4 minutes. Which runner ran at a faster rate? At a certain store, a half-gallon jug of milk costs $2.95, and a gallon jug of milk costs $5.95. Which milk has a cheaper price: the half-gallon or gallon jug? A package of nine 12-ounce cans of cola costs $7.50. A half-gallon bottle of the same cola is sold for $2.90. Which cola has a cheaper price, the cans or the bottle?
Rachel can paint 16.5 square meters in 1 hour. 1 kilogram of rice costs $40.60. John ran at a faster rate. The half-gallon jug of milk and the half-gallon bottle of cola are cheaper.
Explanation:Rachel paints 5 1/2 square meters of wall space in 1/3 hour, so we have to calculate how much she could paint in a whole hour. We multiply the speed (5.5/1/3) by the desired timeframe (1) to get 16.5 square meters. Therefore, Rachel can paint 16.5 square meters in 1 hour.
One 200-gram bag of rice costs $8.12. To find out how much 1 kilogram of rice costs, we divide 1000 by 200 to get 5 and then multiply this by $8.12 to find that 1 kilogram of rice costs $40.60.
John ran 1/2 mile in 5 minutes, while Al ran 1/3 mile in 4 minutes. To find out who ran faster, we need to calculate each runner's speed in miles per minute. John's speed is 1/2 / 5 = 0.1 mile per minute, while Al's is 1/3 / 4 = 0.083 mile per minute. Therefore, John ran at a faster rate.
A half-gallon jug of milk costs $2.95, and a gallon jug of milk costs $5.95. To compare, we should double the price of the half-gallon to reflect the same quantity as the gallon. $2.95 x 2 = $5.90, which is less than $5.95. Therefore, the half-gallon jug of milk is cheaper.
A package of nine 12-ounce cans of cola costs $7.50, whereas a half-gallon of the same cola costs $2.90. A half-gallon is 64 ounces, which is roughly equivalent to 5.33 cans of cola (64/12). Therefore, a half-gallon of cola costs the equivalent of $4.00 in cans (5.33 x $1.40 [the pricing per single can]). Therefore, the half-gallon bottle of cola is cheaper.
Learn more about Rate Comparison here:https://brainly.com/question/28572142
#SPJ12