Answer:
The two different point on a segment joining the United States Capital and the White House such that the ratio of the shorter segments created by each is 1 : 3 are [tex]\vec C_{1} =(-1,7)[/tex] and [tex]\vec C_{2} = (-7,13)[/tex].
Step-by-step explanation:
At first we need to calculate the vector distance between [tex]A(x,y) = (2, 4)[/tex] and [tex]B(x,y) =(-10,16)[/tex] by following vectorial subtraction:
[tex]\overrightarrow{AB} = \vec B - \vec A[/tex] (Eq. 1)
Where:
[tex]\overrightarrow{AB}[/tex] - Vector distance between points A and B, dimensionless.
[tex]\vec A[/tex], [tex]\vec B[/tex] - Vector distance between each point and origin, dimensionless.
If we know that [tex]A(x,y) = (2, 4)[/tex] and [tex]B(x,y) =(-10,16)[/tex], then we have the following result:
[tex]\overrightarrow {AB} = (-10,16)-(2,4)[/tex]
[tex]\overrightarrow{AB} = (-10-2,16-4)[/tex]
[tex]\overrightarrow{AB} = (-12,12)[/tex]
Besides, we can find the location of any point inside the line segment by using the following vectorial equation:
[tex]\vec C = \vec A + r\cdot \overrightarrow{AB}[/tex] (Eq. 2)
Where:
[tex]r[/tex] - Segment factor, dimensionless.
[tex]\vec C[/tex] - Location of resulting point, dimensionless.
There are two different options for the location of resulting point: [tex]r_{1} = \frac{1}{4}[/tex] and [tex]r_{2} = \frac{3}{4}[/tex]. Now we proceed to find each option:
[tex]r_{1} = \frac{1}{4}[/tex]
[tex]\vec C_{1} = (2,4) +\frac{1}{4}\cdot (-12,12)[/tex]
[tex]\vec C_{1} = (2,4)+(-3,3)[/tex]
[tex]\vec C_{1} =(-1,7)[/tex]
[tex]r_{2} = \frac{3}{4}[/tex]
[tex]\vec C_{2} = (2,4) +\frac{3}{4}\cdot (-12,12)[/tex]
[tex]\vec C_{2} = (2,4) +(-9,9)[/tex]
[tex]\vec C_{2} = (-7,13)[/tex]
The two different point on a segment joining the United States Capital and the White House such that the ratio of the shorter segments created by each is 1 : 3 are [tex]\vec C_{1} =(-1,7)[/tex] and [tex]\vec C_{2} = (-7,13)[/tex].
Jacob split the cost of snacks, which was $12.24, with two friends. Before they ate, another friend joined them and paid Jacob for his fourth of the cost.
How much does Jacob need to refund each of the other two friends so that everyone pays the same amount?
Answer:
3.06
Step-by-step explanation:
12.24/4
Answer:
4.08
Step-by-step explanation:
John has 125 marbles. 35 are green; 40 are red; 20 are yellow and the rest are blue. What is the ratio of the blue marbles to all the marbles? *
40 to 30
6 to 25
25 to 6
35 to 125
Answer:
a
Step-by-step explanation:
Tristan and two of his friends purchased tickets to a school play. Tristan paid for all the tickets with a $50.00 bill and received $23.00 in change. If Tristan used a coupon for 25% off, what was the original price for one ticket?
Answer:
$36
Step-by-step explanation:
Tristan paid $50 for the tickets of the school play and was given $23 as change. The amount Tristan paid for the ticket is given as:
Price for ticket = amount paid - change = $50 - $23 = $27
Price for ticket = $27
Given that the ticket was sold at 25% off. Let x be the original price of the ticket, therefore:
x - 25% of x = $27
x - 0.25x = 27
0.75x = 27
x = 27/ 0.75
x = 36
Therefore the original price of the ticket is $36
Answer:
27.00
Step-by-step explanation:
The volume of the box is modeled by the function V (x) = 5x^2 + 5x. What is the volume when x= 4?
А-120 cubic units
B-30 cubic units
C-100 cubic units
D-45 cubic units
The volume of box at x = 4 is, 100 cubic units
What is mean by Cuboid?A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.
We have to given that;
The volume of the box is modeled by the function,
⇒ V (x) = 5x² + 5x
Now, At x = 4;
The volume of the box is,
⇒ V (x) = 5x² + 5x
⇒ V (4) = 5 × 4² + 5 × 4
⇒ V (4) = 5 × 16 + 20
⇒ V (4) = 80 + 20
⇒ V (4) = 100 cubic units
Learn more about the cuboid visit:
https://brainly.com/question/26403859
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I need help please 20 points
Answer:
5^9
Step-by-step explanation:
subtract them. base (5) stays the same
Solve for the indicated variable.
A = LW, solve for W
Anne owns a used car lot and in order to get cars to sell, she buys used cars at an
auction place. It costs $200 to attend the auction and she buys used cars at
$2,000 each. Last Tuesday, she purchased 10 cars. Which of the following
functions correctly represents this situation in function notation?
f(x) = 10x + 200
f(x) = 200x + 2,000
f(x) = 2,000x + 10
f(x) = 2,000x + 200
Answer:
It would be 2,000x+200
Step-by-step explanation:
okay it costs $200 to attend so that's a cost you are going to have to pay regardless. The $2,000 depends on how many cars you buy. So it would be 2,000 (times how ever many cars you buy) plus the $200.
on the number line between two consecutive whole numbers would square root of 7 be located at
Answer:
see explanation:
Step-by-step explanation:
We use the property that (all numbers being positive)
0 < a < b < c --> 0< a^2 < b^2 < c^2
so:
1 < 2 < sq(7) < 3 < 4 < 5
1 < 4 < 7 < 9 < 16 < 25
Find the y-intercept in the function: 3x - 2y = 6*
hi there! the y-intercept in the function is...
3 + 3x/2
hope this helped. have a good one!
Which cube is formed by folding the pattern?
Answer:
b
Step-by-step explanation:
-3a + b when a
=
-4 and b = 9.
Answer:
12+9=21
Step-by-step explanation:
In one month, Jillian made 36 local phone calls and 20 long distance calls.
What was her ratio of local calls to long distance calls for that month?
A. 2:1
B. 3:2
C. 9:4
D. 9:5
Answer:
D.
Step-by-step explanation:
Because 36:20 simplified is 9:5.
Answer:
It is D 9:5
Step-by-step explanation:
Beacuse 9x4= 36
and 5x4= 20
so 36:20 or 9:5
The graph represents the relationship between the cost of renting a trailer y for x hours,, please help
Answer:
The relationship is not proportion because the value of [tex]\frac{y}{x}[/tex] is not equivalent for each point in the relationship ⇒ C
Step-by-step explanation:
The relationship between x and y are proportional if [tex]\frac{y}{x}[/tex] = k, where k is a constantThe proportional relation represented graphically by a line passes through the origin pointLet us use the information, above to solve the question
→ From the given graph
∵ The coordinates of the points are (1, 10), (2, 20), (4, 25), (6, 40)
∵ The equation of proportion is [tex]\frac{y}{x}[/tex] = k
→ Let us check if all the points satisfy the equation or not
∵ x = 1 and y = 10
∴ [tex]\frac{10}{1}[/tex] = k
∴ 10 = k
→ Check the other points if they give the same value of k or not
∵ x = 2 and y = 20
∴ [tex]\frac{20}{2}[/tex] = k
∴ 10 = k
∵ x = 4 and y = 25
∴ [tex]\frac{25}{4}[/tex] = k
∴ [tex]\frac{25}{4}[/tex] = k
∵ x = 6 and y = 40
∴ [tex]\frac{40}{6}[/tex] = k
∴ [tex]\frac{20}{3}[/tex] = k
∵ Not all points satisfy the same value of k
∴ The relation does not represent a proportional relation
The relationship is not proportion because the value of [tex]\frac{y}{x}[/tex] is not equivalent for each point in the relationship.
What is angle KNL
Enter your answer in the box
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Answer:
20
Step-by-step explanation:
So in case you did not know, MNJ and KNL have the same angle measure, so to find x you would just set each of the eqautions equal to each other. distribute the 3 to (x + 14) and get 5x+ 2 = 3x + 42. subtract 2 from one side and do the same on the other side. this would leave your eqaution looking like this: 5x-40= 3x, next subtract 5x from both sides and you will get -2x=-40, then vide by -2 and x will equal 20
What is 6+6+2
need to actually ask something to give away points or the bots will report lol
Answer:
14
Step-by-step explanation:
because 6+6 is 12 and add 2 is 14
3(4x - 2) > 7x + 19
Answer:
12x-6>7x=19
Step-by-step explanation:
1. (01.01 LC)
Which of the following is a rational number? (5 points)
√2, √3. √4. √5.
Answer:
root 4 is a rational number
Step-by-step explanation:
A rational number is any number that can be expressed as a fraction of two integers, say where q is not zero.
Can someone please answer this question for me 3(7q−10)
Answer:
21q-30
Step-by-step explanation:
If u use the distributive property, 3*7 is 21, therefore it would be 21q, and 3*10 is 30, so, the final answer would be 21q-30.
I totally need help, (I just wanna see who will join)
It works :)
kte-diym-hvy
Answer:
I’m joining rn does it still work?
Step-by-step explanation:
Which point is a solution to the inequality shown in this graph?
A (6,0)
B (5,-5)
C (0,-3)
D (0,-5)
Answer:
(0,-3)
Step-by-step explanation:
Apex
which of the following explains why soft drinks are such an unhealthy choice?
A. one soft drink contains about 25% of daily caloric intake
B. one soft drink contains nearly an entire daily allowance for sugar
C. the carbonation contains unnatural additives that contribute to obesity
D. the carbonation is a preservatives that also adds sugar
Answer:
A or B
Step-by-step explanation:
A student is working two jobs over the summer to pay for a new car. The student gets paid $25 for each lawn that
is mowed ( 2 )and $15 for each pool that is cleaned (y). The student wants to earn $750 to pay for a down payment
on a car.
•What is the y-intercept
Answer:
y=50
Step-by-step explanation:
25(0)+15y=750
0+15y=750
15y=750
y=50
HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION!!!!!!!!!!
Answer:
11fl oz/per hr divided by 5.333=2.0625 or rounded to the nearest tenth 2.1 gallons per day.
Step-by-step explanation:
definition of congruence: if
Answer:
a statement that two numbers or geometric figures are congruent.
Step-by-step explanation:
Rate me please
Answer:
Definition of congruent is related to two numbers or shapes that may be equal. Congruent is like equal something can’t be congruent if it’s not equal.
Step-by-step explanation:
Melissa collects data on her college graduating class. She finds out that of her classmates,40%are brunettes ,30%have blue eyes and 5% are brunettes that have blue eyes. What is the probability that one of melissa's classmates will be a brunette or have blue eyes?
2(4+c)=67 help solve for c
Answer:
c = 29.5 or
c = 59/2
Step-by-step explanation:
2 (4 + c) = 67
8 + 2c = 67
8 - 8 + 2c = 67 - 8
2c = 59
c = 29.5
Select all that apply
Which of the following name a line in the drawing ?
Answer:
I think FC but not sure
Step-by-step explanation:
the respn os that we looc at both sides f the line and see what the letters are
Answer:
DB
Step-by-step explanation:
just did it got it correct
Pleaseee help me with my math show work please I need the work
I'm sorry the photo is on a side. I'm too lazy to text it on here lol
Help me. 1,2,3, and 4 are the only options for all letters so there is no lack of information in this picture.
Answer:
Step-by-step explanation:
a: 2
b: 4
c: 3
d: 4
e: 6
Suppose that R and S are points on the number line. If RS=9 and R lies at -6 where could S be located
Answer:
at 3
Step-by-step explanation:
because iin a number line we have positives and negatives if rlR is at nine then S is at 3