Given:
The two endpoints of a vector are P = (2, 9) and Q = (4, 14).
To find:
The component form and magnitude of vector PQ .
Solution:
A vector is defined as
[tex]v=\left<x_2-x_1,y_2-y_1\right>[/tex]
Where, [tex](x_1,y_1)[/tex] is the initial point and [tex](x_2,y_2)[/tex] is the terminal point.
Two endpoints of a vector are P = (2, 9) and Q = (4, 14). So, the vector PQ is
[tex]\overrightarrow{PQ}=\left<4-2,14-9\right>[/tex]
[tex]\overrightarrow{PQ}=\left<2,5\right>[/tex]
Component form of vector PQ is [tex]\left<2,5\right>[/tex].
The magnitude of a vector [tex]v=\left<a,b\right>[/tex] is
[tex]|\vec{v}|=\sqrt{a^2+b^2}[/tex]
The magnitude of vector PQ is:
[tex]|\overrightarrow{PQ}|=\sqrt{2^2+5^2}[/tex]
[tex]|\overrightarrow{PQ}|=\sqrt{4+25}[/tex]
[tex]|\overrightarrow{PQ}|=\sqrt{29}[/tex]
Therefore, the correct option is A.
What 3D figure is a paper towel carboard tube?
Answer:
An 11 inch tall roll of paper towels has an inner cardboard tube with a diameter of 1.5 inches.
Step-by-step explanation:
Naomi‘s parents want to have $50,000 say to her college education if they invest $20,000 today in earn 7% interest compounded annually about how long will it take them to save the $50,000
Answer:
13 years
Step-by-step explanation:
Given data
A=50,000
P=20,000
r= 7%
t=??
The compound interest formula is given as
A=P(1+r)^t
Calculate time, solve for t
t = ln(A/P) / r
t= ln(50000/20000)/0.07
t= ln(2.5)/0.07
t= 0.916/0.07
t= 13.0
Hence the time is 13 years
A 22.5 cm straw fits diagonally inside an 18 cm high can of soft drink what is the radius of the can
Answer:
6.75cm
Step-by-step explanation:
The straw fits diagonally inside the can so it makes a right angled triangle with height and base of the can ( which is the diameter of the can)
So, hypotenuse = length of straw = 22.5cm
perpendicular = 18cm
base = diameter of can(d)
Using pythagoras theorem
h² = p² + b²
(22.5)² = 18² + d²
506.25 = 324 + d²
d² = 506.25 - 324
d² = 182.25
d = 13.5cm
Now radius = d/2 = 13.5/2 = 6.75cm
The teacher gave 36 gold stickers to the first student, 45 gold stickers to the second student, 54 gold stickers to the third student, and 63 gold stickers to the fourth student. If this pattern continues, how many gold stickers will the teacher give to the fifth student?
Answer:
69
Step-by-step explanation:
the sequence is to add 6 to previous value
Anyone help me? Please, whoever will be marked as brainliest.
Answer:
∠BAC=∠DAC(given)
AC=AC(common)
∠ACB=∠ACD( 90°each)(complementary angles)
So, ΔBAC≅ΔDAC (ASA)
Step-by-step explanation:
Pls mark me brainliest if u don't mind
20 points+brainliest!
Which statements about the factors of the terms in the expression 12 x + 18 x y minus 24 y are true? Select three options.
The factors common to 12x and 18xy are 1, 2, 3, 6, x, and y.
The factors common to 12x and 18xy are 1, 2, 3, 6, and x.
The factors common to 12x and 24y are 1, 2, 3, 4, 6, and 12.
The GCF of the expression is 6xy.
The GCF of the expression is 6.
Answer:
C, D, E
Step-by-step explanation:
Solve the equation.
−6p=48
p=
Please help I suck at math
Equations -
[tex] - 6p = 48[/tex]
Divide -6p using inverse operations!
[tex]\frac{ - 6p}{ - 6} = p[/tex]
[tex] \frac{48}{ - 6} = - 8[/tex]
[tex]p = - 8[/tex]
[tex] - 8 \times - 6 = 48[/tex]
Tyler spent a relaxing afternoon watching movies. He watched movies for 2 1/2 hours. His brother watched the movies for 3/4 of the amount of time that Tyler did. What equation can be used to find out how much time Tyler’s brother spent watching movies?
Answer:
1 3/4
Step-by-step explanation:
Frist he turned the proper fraction into an inproper which came to be 5/2. Then he subtracted 5/2 out of 3/4 Then after that you get 7/4 but then you make it a proper fraction you will get 1 3/4
Answer:
3/4 X 2 1/2
Step-by-step explanation:
Which quadrilateral has two sides
measuring 3 inches and two sides measuring
8 inches, with four 90° angles?
Answer:
A rectangle
because it has to opposite and two congruent sides
the length of a rectangle is 7 centimeters less than the width. What are the dimensions of the rectangle if its area is 228 square centimeters?
Answer:
L=12cm
W=19cm
Step-by-step explanation:
Hope this helps someone!!
A tabletop in the shape of a trapezoid has an area of 7,205 square centimeters. Its longer base measures 115 centimeters, and the shorter base is 105 centimeters. What is the height?
Answer:
The height is 65.5 cm
Step-by-step explanation:
[tex]h=2*\frac{A}{a+b} \\\\h=2*\frac{7205}{115+105} \\\\h=2*\frac{7205}{220} \\\\h=2*\frac{131}{4} \\\\h=65.5[/tex]
PLEASE HELP ME I WILL GIVE 25 POINTS PLUS BRAINLIEST URGENT PLEASE HELP!
caroline babysat for two families the nelson and the smiths. use the information below to compare her earings.
nelson a = 6.25h, where a represents the amount she earned and h represents the number of hours she babysat.
smiths : $39 for 6 hours
witch statement is true?
A. Caroline earns $6.25 an hour babysitting for the smiths.
B. Caroline earns $6.50 an hour babysitting for the nelsons.
C. Caroline earns more money per hour from the smiths.
D. Caroline earns more money per hour from the nelsons.
Please helppppp??!!!???!
Answer:
56
Step-by-step explanation:
Which expression is equivalent to m + 3m + 3(m - 1)
Answer:
7m-3
Step-by-step explanation:
first, distribute
m+3m+3m-3
then, combine all like terms
m+6m-3
7m-3
i hope this helps! have a nice day!
Find the area of the figure shown below:
a
34 square units
b
220 square units
c
480 square units
d
960 square units
Answer:
.................hshs
Which statements are true about the graph?
Select all that apply.
An architect is making a plan for a new circular playground. If the playground needs to be surrounded by a fence and the diameter of the playground is 25 meters, how much fencing needs to go up?
Answer:
78.54 m
Step-by-step explanation:
To obtain how much circular fence, we obtain the Circumference of the circular playground.
The Circumference of a circle, C = 2*pi*r
pi = 3.14 ; r = diameter / 2 = 25 /2 = 12.5 m
C = 2 * 3.14 * 12.5
C = 78.539816
Hence, the fencing which need to go up is ;
78.54 m
Ramrio walks into a store that advetises a sale of 30% off everything in the store He writes the following expression to caculate the sale price
Answer:
dhasij
Step-by-step explanation:
sdafjiaj;
This is a One-Step Equations problem, please help
Read the problem.
Sara and Elizabeth have exchanged 60 text messages. Sara sent 42 of the messages.
Shade the grid to show the fraction of the text messages that Sara sent.
What percent of the text messages did Sara send? You can use your model to help.
Answer:
I think that Sarah sent 70 percent of the text messages , so you have to shade 70 of them .
I need help with this problem please
n must be 0, since x ⁿ = 1 for all positive, real x if n = 0. So the answer is A.
4 points
Which expression is equivalent to 3-5314 ?
Answer:
use an app called math w*y that should help you
Step-by-step explanation:
A deli offers bag lunches with 2 bread choices and 3 meat choices, as shown in this tree diagram. What is the probability that someone will randomly choose a turkey sandwich?
Answer:
its 2/3 i think
Step-by-step explanation:
please help ! mathhhhh
Answer:
72
Step-by-step explanation:
if you subtract 4 each time then it would look like:
202-4=198
198-4=194
etc. ...
76-4=72
13. A cone with a radius of 3 inches and a height of 7 inches has the same radius as a cylinder. If the cylinder's volume is two times the volume of the cone, what is the height of the cylinder? Use 3.14 for pi
Answer:
Step-by-step explanation:
r = 3 in
h = 7 in
volume of cone = ⅓πr²h = 21π in³
cylinder has radius r = 3 and height h.
volume of cylinder = πr²h = 9πh in³
volume of cylinder is two times the volume of cone
9πh = 2×21π
9h = 42
h = 42/9 = 4⅔ in
Help me? Giving Brain
Answer:
D) 1 1/2 inches
Step-by-step explanation:
15 1/3 times 1 1/2 = 23 inches sqaured
Round 3.44570830811 to the nearest hundred-thousandth.
Answer:
3.44571
Step-by-step explanation:
The hundred thousands place is the fifth number after the decimal.
Answer:
3.44571
Step-by-step explanation:
The 5th number after the decimal is in the hundred thousandth place. to the right of the 0 in the hundred thousandth place there is an 8 which is greater than 4 so we round up the 0 is now a 1 and the rest of the numbers after it are gone
PLEASE HELP !!!!!!!!!!!!!!
Answer:
reflection and translation
After 5 games Adrian Peterson has rushed for 498 yards. If he gains 4.5 yards per carry, how many carries will it take for him to reach 1200 yards
Answer:
156 carries
Step-by-step explanation:
Given that:
5 games = 498 yards
Number of yards Gained per carry = 4.5 yards
Target number of yards = 1200
Number of yards left to reach target :
1200 - 498 = 702 yards
Number of carries required = number of yards / yards per carry
Number of carries required = 702 / 4.5
= 156 carries