Point Q lies on segment ST, where point S is located at (- 3, - 3) and location of point T is unknown. If SQ : QT = 4 : 3, and point Q is located at (3, 0) on the segment ST, select a place on the coordinate grid to plot point T and name its coordinate.
Answers
Answer:
The location of point T is [tex]\vec T = (7.5, 2.25)[/tex]. Graph is included at the end of the explanation as attachment.
Step-by-step explanation:
The SQ : QT ratio means that there are 4 units of SQ for each 3 units of QT. Vectorially speaking, we notice that:
[tex]\overrightarrow {SQ} = \frac{4}{7}\cdot \overrightarrow {ST}[/tex] (Eq. 1)
[tex]\overrightarrow{QT} = \frac{3}{7}\cdot \overrightarrow {ST}[/tex] (Eq. 2)
Now, we eliminate [tex]\overrightarrow{ST}[/tex] by equalizing (Eq. 1) and (Eq. 2):
[tex]\frac{7}{3} \cdot \overrightarrow{QT} = \frac{7}{4}\cdot \overrightarrow{SQ}[/tex] (Eq. 3)
From Linear Algebra, we know that:
[tex]\frac{7}{3}\cdot (\vec T - \vec Q) = \frac{7}{4}\cdot (\vec Q-\vec S)[/tex] (Eq. 3b)
And we clear [tex]\vec T[/tex]
[tex]\frac{7}{3}\cdot \vec T -\frac{7}{3}\cdot \vec Q = \frac{7}{4}\cdot \vec Q -\frac{7}{4}\cdot \vec S[/tex]
[tex]\frac{7}{3}\cdot \vec T = \frac{49}{12}\cdot \vec Q - \frac{7}{4}\cdot \vec S[/tex]
[tex]\vec T = \frac{3}{7}\cdot \left(\frac{49}{12}\cdot \vec Q-\frac{7}{4}\cdot \vec S\right)[/tex]
[tex]\vec T = \frac{7}{4}\cdot \vec Q-\frac{3}{4}\cdot \vec S[/tex]
If we know that [tex]Q(x,y) = (3, 0)[/tex] and [tex]S(x, y) = (-3,-3)[/tex], then we have that [tex]T(x,y)[/tex] is:
[tex]\vec T = \frac{7}{4}\cdot (3, 0) - \frac{3}{4}\cdot (-3, -3)[/tex]
[tex]\vec T = \left(\frac{21}{4}, 0 \right) + \left(\frac{9}{4},\frac{9}{4}\right)[/tex]
[tex]\vec T = \left(\frac{21+9}{4},\frac{0+9}{4} \right)[/tex]
[tex]\vec T = \left(\frac{15}{2}, \frac{9}{4}\right)[/tex]
[tex]\vec T = (7.5, 2.25)[/tex]
At last we plot the segment with all points described on statement. We can check the result in the attachment set below.
Related Questions
What angles go with the angle pairs? Just a simple checklist please :).
Answers
Answer:
Here is the answer
Step-by-step explanation:
∠1 and ∠6 are adjacent because they share the same vertex and the same common side.
∠2 and ∠5 are vertical angles since they have pairs on opposite sides of the angle.
∠3 and ∠6 have none of the above.
∠5 and ∠3 are a linear pair because the angles are opposite of each other.
Frankie bought a new computer. He made an initial payment of $50 to the store, and he will pay $30 each month until the computer is paid off. What is the y-intercept and the slope??
Answers
PLEASE HELP ASAP 100 PTS can u also find the value of y. the options for the y questions are
square root of 55
6
16
8 sqrt 3
Answers
Answer:
The value of x is 16
Step-by-step explanation:
x=16
PLEASE helppp. What equation describes a line that is perpendicular y=-2/7x+5 and has the same y-intercept as y = 3x - 2?
Answers
Answer:
y = 7/2 -2
Step-by-step explanation:
if the slope of the first problem is -2/7 then its perpendicular is 7/2 (the exact opposite) and since the y- intercept is the b in Y= mx +b the intercept of the equation you’re trying to find is -2
Katy is between Houston and San Antonio. If the distance from Katy to San Antonio is 2 x x 5 miles and the distance from Katy to Houston is 4 12 x miles. The total distance from Houston to San Antonio is 120 miles . Then How far is it between each City?
Answers
Answer:
It is hard to read what you actually wrote, but i guess this is:
Distance to San Antonio = 2*5*x mi
Distance to Houston = 4*12*x mi
Distance from Houston to San Antonio = 120mi
Then we must have that:
2*5*x mi + 4*12*x mi = 120mi
(2*5 + 4*12)*x mi = 120mi
(10 + 48)*x mi = 120mi
x mi =120/58 mi = 2.06 mi
Now we can replace it in the above equations:
Distance to San Antonio = 2*5*2.06 mi = 20.6 mi
Distance to Houston = 4*12*2.06 mi = 98.88 mi
Barack Obama High School raised $42,350 for travel costs to travel to the 2021 inauguration in Washington D.C. The bus costs $11,500 to rent for the week, including fuel. If the cost per student for food and lodging is $750 for the week, how many students can attend the inauguration? Part A: Define a variable and write algebraic equation for the situation. (5)Part B: How many students can attend the inauguration.
Answers
Answer:
Approximately 41 students can attend the inauguration
Step-by-step explanation:
Let x denotes number of students who can attend the inauguration.
Cost per student for food and lodging = $ 750
So,
Total cost = $ 750 x
Also,
Amount of rent = $ 11,500
As Barack Obama High School raised $42,350 for travel costs to travel to the 2021 inauguration in Washington D.C,
[tex]750x+11,500=42,350\\750x=42,350-11,500\\750x=30,850\\x=\frac{30,850}{750}\\ x=41.1[/tex]
So, approximately 41 students can attend the inauguration
Lines a and b are parallel. What is the measure of ∠5 if ∠1 measures 116°?
Answers
please help me in this page
https://brainly.com/question/18162643
and click to thanks because i need points.
and need to ask more questions
here is your answer
The measure of ∠5 is 64°.
In other words: m∠5 = 64°.
(4, -3) and (8, -3)
Answers
Answer:
slope=0/4
Step-by-step explanation:
[tex]\frac{-3 + 3}{8-4}[/tex]
0/4
Answer:
-3 - (-3) / 8 - 4 = 0/4 = 0
Step-by-step explanation
name the following line 6 different ways
Answers
Answer:
what line??
Step-by-step explanation:
The ratios in an equivalent ratio table are 3:12, 4:16, and 5:20. If the first number in the ratio is 10, what is the second number
Answers
Answer:
I believe the answer would be 10/40. First, I simplified all of the given rations. You do this by finding the two numbers greatest common factor. For example, 3/12, 3 goes into 3 once and 3 goes into 12 four times. So that ratio would be 1/4. If you continue the pattern you would get 1/4 for all of them. Therefore, 10/40 would be correct since it's ratio would also be 1/4.
Step-by-step explanation:
6=-r/3;r
Help ASP it’s urgent
Answers
Answer:
bro what
Step-by-step explanation:
yeha
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the maths linear algebra,
here, we solve as,
6 = -r/3
=> -r = 6×3
hence, r = -18
what is the slope of the line in the graph?
Answers
Answer:
It is one. I believe, sorry if i'm wrong.
Step-by-step explanation:
Answer:
y= x +1
Step-by-step explanation:
You could use the slope formula y2-y1/x2-x1, what I did was I took the og equation y=x and I noticed it was vertically shifted by 1. Thus, y=x+1
Gi dont understand how to find Which ordered pair is a solution of the equation? y=8x+3
Answers
Answer:
(1, 11 ) is a solution
Step-by-step explanation:
To obtain a solution, choose any value of x, substitute into the equation and evaluate for y, that is
choose x = 1, then
y = 8(1) + 3 = 8 + 3 = 11
Thus (1, 11 ) is a solution
choose x = - 2 , then
y = 8(- 2) + 3 = - 16 + 3 = - 13
Thus (- 2, - 13 ) is also a solution
Lets go over the solutions.
Let's start with (1, 11). After substituting x = 1 and y = 11, it results in the equation 11 = 11, which is a true statement. Hence, this is one solution.
Now, let's look at (-1 -5). After substituting x = -1 and y = -5, it results in the equation -5 = -5, which is also a true statement. So, this being said, (-1, -5) would also be a solution.
Hence, our two solutions are:
Both [tex](1, 11)[/tex] and [tex](-1, -5)[/tex].
Hope this helps!
LOTS OF POINTS!!
hi can you help me with the question? :)
please explain
Answers
Answer:
See below.
Step-by-step explanation:
The cubic root of 49 is 3.66, so the dot should go between 3 and 4, a little closer to 4 than to 3.
She thought the problem was square root of 49 which is 7 and placed a dot on the 7.
Sally is buying a hearing aid that costs $5,000. her insurance pays $2,900 of the cost. Sally will get a loan to pay the remaining amount. The loan interest is free, if Sally pays a minimum of $75 per month and pays off the loan in a year. To be financially responsible, Sally wants to pay off the loan in one year. What is the minimum monthly payment Sally can make each month to pay of the loan in equal payments?
Answers
Answer:
$ 175
Step-by-step explanation:
Create an equation:
5000 = ax + 2900
a > 75
x = 12 months
5000 = 12a + 2900
12a = 2100
a = 175
Point A is (5, 7), Point B is (x, y). The midpoint of AB is (17, -4). What is the value of B?
Answers
The coordinates of point B will be ( 29,-15).
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that point A is (5, 7), point B is (x, y). The midpoint of AB is (17, -4).
The coordinate of the point B is calculated as,
17 = ( 5 + x ) / 2
5 + x = 34
x = 34 - 5
x = 29
( 7 + y ) / 2 = -4
7 + y = -8
y = -8 - 7
y = -15
To know more about coordinate geometry follow
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1. The explicit formula an = 2–5(n-1) represents an arithmetic sequence. Write the recursive
formula for the sequence.
Answers
Answer:
[tex]a_n=2,\:a_n=a_{n-1}-5[/tex]
Step-by-step explanation:
If you map the sequence out, you get the following values:
a = 1, a(n) = 2
a = 2, a(n) = -3
a = 3, a(n) = -8
As you can see, the first term is 2 and the sequence is decreasing by 5 each time. Therefore, the answer is D.
Answer:
Person above is right i just did the quick check too
The answer is D
What is the value of 1
--
6^0
Answers
Answer:
2
Step-by-step explanation:
Y = 4/5x -3 perpendicular
Answers
Answer:
Y=4/5x-3
3=4/5x-y
Step-by-step explanation:
if you only have 2 gallons of gas left, you can only travel 26 more miles. If I need to travel 91 miles, how many gallons of gas would I need?
Answers
Answer:
7
Step-by-step explanation:
If 2 gallons gets you 26 miles, then you get 13 miles per gallon. If you need to go 91 miles, you divide that by the 13 per gallon, and you get 7.
If a point M at (3,-2) is reflected over the y=0 line,what would be the coordinates of M?
Answers
Answer: The coordinates of M would be (3,2).
Step-by-step explanation: I don't know how to explain but I'm 100% sure this is the answer. Your welcome :)
An account grows at an annual interest rate of r , so it grows by a factor of x = 1+ r each year. The function A(x)= 800x^4 + 350x^3 + 500x^2 + 600x gives the amount in the account after 4 years when the growth factor is x.
1) What is the total amount in the account if the interest rate for the account is 3% each year?
Answers
Answer:
2431.311498
Step-by-step explanation:
Given the model:
A(x)= 800x^4 + 350x^3 + 500x^2 + 600x
x = growth factor = (1 + rate)
If rate = 3% ; x = (1 +. 3%) = (1 + 0.03 = 1.03
Hence,
A(1.03)= 800(1.03)^4 + 350(1.03)^3 + 500(1.03)^2 + 600(1.03)
= 2431.311498
This is the amount in account after 4 years, if the interest rate is 3% and growth rate = (1 + rate)
Applying the formula, it is found that the total amount in the account will be of $2,431.3.
The amount in the account after 4 years is given by:
[tex]A(x) = 800x^4 + 350x^3 + 500x^2 + 600x[/tex]
In which the growth factor is x = 1 + r, in which r is the interest rate, as a decimal.
In this problem, interest rate of 3%, hence [tex]r = 0.03, x = 1 + r = 1 + 0.03 = 1.03[/tex].
Then:
[tex]A(1.03) = 800(1.03)^4 + 350(1.03)^3 + 500(1.03)^2 + 600(1.03) = 2431.3[/tex]
The total amount in the account will be of $2,431.3.
A similar problem is given at https://brainly.com/question/22995738
1
Use the converse of the pythagorean theorem to decide if the given lengths will form a right triangle. Answer Yes or No.
10,8,6
NEXT
Answers
Answer:
Yes
Step-by-step explanation:
The pythagorean theroem is: A^2 + B^2 = C^2
I tried this and it works so yes, the right traingle can be made.
The 2 legs are, 64 and 36, while the hyptenouse is 100.
Can anyone tell me how to break apart the following number: 6359
Answers
Answer:
6000 + 300+ 50 +9
Step-by-step explanation:
Start by focusing on the thousands place. Then switch to hundreds then to tens and finally to ones place.
Number 1 please ITS URGENT HELP PLSPLS
Answers
Answer:
The area of B is 8 cm²
Step-by-step explanation:
From the diagram, we can tell that the scale factor is 2 because the length of A is 6 cm and the length of B is 12 cm so the scale factor is 2. Since diagram A's area is 4 cm², all we need to do is multiply the diagram A's area by 2. That gives diagram B's area which is 8 cm²
brainliest for correct answer please help me
Answers
Answer:
b
Step-by-step explanation:
The power, P, of a gear varies directly with its radius, r. If the power of a certain gear is 550 and the radius for that gear is 11 find the radius (r) of a gear whose power is 715. Identify the constant of variation, direct variation equation, and radius (r).
Answers
Answer/Step-by-step explanation:
Given that P varies directly with r, the equation for this direct variation would be:
[tex] P = rk [/tex],
Where,
P = power
r = radius
k = constant of variation.
If P = 550, when r = 11, constant of this direct variation is calculated as follows:
Plug in the values of P and r into the variation equation to find k.
[tex] 550 = 11k [/tex]
Divide both sides by 11
[tex] \frac{550}{11} = {11k}{11} [/tex]
[tex] 50 = k [/tex]
Constant of variation = 50
To find the radius (r) of the gear whose power (P) = 715, substitute P = 715 and k = 50 in the variation equation.
[tex] P = rk [/tex]
[tex] 715 = r*50 [/tex]
[tex] \frac{715}{50} = \frac{50r}{50} [/tex]
[tex] \frac{715}{50} = \frac{50r}{50} [/tex]
[tex] 14.3 = r [/tex]
r = 14.3
The average age of 3girls is 17years 4months.The average 2 of them is 17years 3months. How old is the third girl?
Answers
Answer:
17 years 2months
Step-by-step explanation:
Beacause the last girl is young
Need help, Write the equation of the line that passes through the points (-2, -3) and (8,3) first in point-slope form, and then in slope-intercept form.
Answers
Answer:
the slope intercept formula would be: y=3/4x-3. Hope this helps!
Step-by-step explanation:
What is the slope of a line that is perpendicular to the line y=-1/3x-6
OA. 3
OB. 1/3
OC. -1/3
O D. 3
Answers
Answer:
3
Step-by-step explanation:
3 is the complete oposite of -1/3 in terms of slopes, therefore they are perpendicular to each other.