A car starts from an office building, which is 5 miles east and 2 miles south of the town center. The car travels 6 miles north, makes a left turn and then travels 8 miles. What is the car’s final position? What single translation vector moves the car from its starting position to its final position?
Answers
Answer:
[tex]\displaystyle \binom{-8}{6}[/tex]
Step-by-step explanation:
The car's starting position is 2 miles south of the town center. If it travels 6 miles north, then it will be 4 miles north of the town center.
The car's starting position is 5 miles east of the town center. If it travels 8 miles west, it will be 3 miles west of the town center.
Therefore, its final position is 4 miles north and 3 miles west of the town center.
If the car travels 6 miles north from it's starting position, the y-value of the vector will be 6, as the car is moving in a positive direction along the y-axis.
If the car travels 8 miles left, the x-value of the vector will be -8, as the car is moving in a negative direction along the x-axis.
Therefore, the single translation vector that moves the car from its starting position to its final position is:
[tex]\displaystyle \binom{x}{y}=\binom{-8}{6}[/tex]
Related Questions
Identify the center and the radius of each circle.
C. X^2+2x+1+y^2+4y+4=9
Answers
Answer:
[tex]Center =(-1,\: -2),\: radius = 3\: units[/tex]
Step-by-step explanation:
[tex] x^2 +2x + +1 + y^2++4y+4=9[/tex] (Given equation of circle)[tex]\implies (x^2 +2x + +1) + (y^2++4y+4)=(3)^2[/tex][tex]\implies (x+1)^2 + (y+2)^2=(3)^2[/tex]Comparing the above equation with standard form of circle i.e. [tex](x-h)^2+(y-k)^2=r^2[/tex], we find:[tex]h=-1, \: k = -2,\: r = 3[/tex][tex]Center =(h, \: k )=(-1,\: -2),\: radius = 3[/tex]Illustrate on a number line the solution set of each pair of simultaneous inequalities. x>-2;-4 <x <2
Answers
The intersection region will be between -2 <x <2 or x ∈ (-2, 2) if the two inequalities are x>-2 and -4 <x <2
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.
We have two inequalities:
x>-2 and
-4 <x <2
or
x ∈ ( -2, ∞) and x ∈ (-4, 2)
The intersection region will be(from the graph)
x ∈ (-2, 2)
Thus, the intersection region will be between -2 <x <2 or x ∈ (-2, 2) if the two inequalities are x>-2 and -4 <x <2
Learn more about the inequality here:
brainly.com/question/19491153
#SPJ1
NEED TO PASS HELP WILL GIVE BRAINLY!!!
Answers
Answer:
[tex]\bigodot[/tex] None of the other answers are correct.
Step-by-step explanation:
[tex]2b^2-3b+85=-5[/tex] (Given)[tex]\implies 2b^2-3b+85+5=0[/tex][tex]\implies 2b^2-3b+90=0[/tex]Comparing it with the general form of quadratic equation [tex]ax^2+bx+c=0,[/tex] we find:a = 2, b = -3, c = 90Next, we find the value of the discriminant [tex] b^2-4ac[/tex][tex] b^2-4ac= (-3)^2-4(2)(90)=9-720=-711<0[/tex][tex] \because b^2-4ac<0[/tex], which means the roots of the given quadratic equation are non-real or imaginary.Thus, last option is the correct answer.Please help. I dont understand a thing. lol
Answers
Answer:
39 in²
Step-by-step explanation:
Area of triangle = 1/2 * b * h, where,
b = Base of Triangle
h = Height of triangle
Area of 4 triangles = 4 * 1/2 * 3 in * 5in
Area of 4 triangles = 2 * 3 in * 5 in
Area of 4 triangles = 30 in²
Area of square = a², where,
a = Each side of square.
Area of square = (3 in) ²
Area of square = 9 in²
Total surface area of pyramid = 30 inch² + 9 inch²
Total surface area of pyramid = 39 in²
Answer:
39 in^2 (Please mark me brainliest)
Step-by-step explanation:
3*3+3*2*5
=39
8x+5y=16 8x+10y=56 what strategy could you apply to use the linear combination method to solve the system?
Answers
Answer:
elimination
Step-by-step explanation:
Consider the diagram.
2 triangles are connected at their hypotenuse to form a rectangle. The rectangle has a length of 7 meters and width of 6 meters.
Mia plans to build a fence to divide her rectangular garden into two triangular areas. Use the diagram to find the length of fence she will need to divide the garden. Round up to the nearest hundredth.
Mia will need a fence that is
meters long.
Answers
The length of fence she will need to divide the garden is 9.22 m.
What is a Rectangle?A Rectangle is a quadrilateral having four sides and four right angles in which both sides are parallel and opposite to each other.
Pythagoras TheoremThe Pythagorean Theorem states that the sum of the squared sides of a right triangle equals the length of the hypotenuse squared.
Let us consider the length of the fence be 'x'
Using Pythagoras Theorem,
x² = 6² + 7²
[tex]x^{2} =36+49\\x^{2} = 85[/tex]
x = 9.22 m
So, the length of fence is 9.22 m.
Learn more about rectangle here:
brainly.com/question/2687959
#SPJ1
Answer:
9.22
Step-by-step explanation:
edge
Using the slope formula, find the slope of the line through the given points.
(6,9) and (4,3)
Answers
Answer:
Slope is 3.
Step-by-step explanation:
Slope formula
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
m ... slope
Two points on the line are (x1, y1) and (x2, y2).
Now let's insert the coordinates of points (6,9) and (4,3) in the slope formula.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}\\\\m = \frac{9 - 3}{6 - 4}\\\\m = \frac{6}{2}\\\\m = 3[/tex]
You could also do [tex]m = \frac{3-9}{4-6}[/tex] and would get the same result.
In how many ways can we color the $8$ vertices of an octagon each red, green, or blue, so that no two adjacent vertices are the same color
Answers
There are 258 ways to color the octagon such that no two adjacent vertices are the same color
How to determine the number of ways?The given parameters are:
Sides, n = 8 --- the sides of an octagonColors, r = 3 i.e. red, green and blueSince no two adjacent vertices are the same color, we use the following chromatic polynomial of an octagon equation
Ways = (r - 1)⁸ + (r -1)
Substitute 3 for r
Ways = (3 - 1)⁸ + (3 -1)
Evaluate
Ways = 258
Hence, there are 258 ways to color the octagon
Read more about combination at:
https://brainly.com/question/11732255
#SPJ1
I need help PLEASE HELPP
Answers
Answer:
1 and 5 are corresponding angle
8 and 4 are corresponding angle
4 and 6 are alternate interior angle
2 and 8 are alternate exterior angle
7 and 3 are corresponding angle
2 and 6 are corresponding angle
3 and 5 are alternate interior angle
1 and 7 are alternate exterior angle
The elevator at the local mall has a weight limit of 1,800 pounds and requires that the maximum person allowance be no more than nine people. let represent the number of people. write an inequality to describe the maximum allowance of people allowed in the elevator at one time.
Answers
Answer: 9? I’m not sure but it seems like it’s 9 as it mentions it in the problem
Why is apr an important tool for consumers
Answers
Answer:
APR, or annual percentage rate, is your interest rate stated as a yearly rate. An APR for a loan can include fees you may be charged, like origination fees. APR is important because it can give you a good idea of how much you'll pay to take out a loan.
What is the value of x?
29
12
7.3
25.2
Answers
Answer:
25.2
Step-by-step explanation:
Secant-Tangent Formula:
(whole secant) x (external part) = (tangent)^2
(41+12) * 12 = x^2
( 53) * 12 = x^2
636= x^2
Taking the square root of each side
sqrt(636) = x
25.2=x
Answer:
25.2
Step-by-step explanation:
This is an intersection of a tangent and a secant.
Prove .. help me pls
Answers
Answer:
Step-by-step explanation:
i just dont know the answer
Answers
Answer:
(3,7) (4,4) (1,2)
Step-by-step explanation:
180 degrees: (x, y) —> (-x, -y)
Find x if f(x)=2x-7 and f(x) = 18.
Answers
Answer:
x = 12.5
Step-by-step explanation:
f(18)=2x-7
18+7=2x
25=2x
x=12.5
Give brainiest please!
Hope this helps :)
grace likes jeffery what will she do ?
Answers
Answer:
2,964
Step-by-step explanation:
52 x 57 = 2,964
Joe has 7/8 yards of string. What is the maximum number of 1/16 yards of string Joe can be cut from the string? 11 points
Answers
Answer:
14
Step-by-step explanation:
7/8 = 14/16
How do you add these two consecutive triangular numbers?
TR(4)+TR(3)
Answers
The n-th trianglar number is given by
[tex]T_n = \dfrac{n(n+1)}2[/tex]
Then
[tex]T_4 + T_3 = \dfrac{4\times5}2 + \dfrac{3\times4}2 = \boxed{16}[/tex]
Alternatively, the triangular numbers are defined recursively by
[tex]\begin{cases}T_1 = 1 \\ T_n = T_{n-1} + n & \text{for } n>1\end{cases}[/tex]
This means
[tex]T_1=1[/tex]
[tex]T_2 = T_1 + 2 = 3[/tex]
[tex]T_3 = T_2 + 3 = 6[/tex]
[tex]T_4 = T_3 + 4 = 10[/tex]
so that
[tex]T_3+T_4=\boxed{16}[/tex]
The coordinates of the endpoints of the diameter of a circle are (-1, 5) and (3, -1). The center of the circle has coordinates
Answers
Answer: (1,2)
Step-by-step explanation:
The center of the circle is the midpoint of the diameter, so using the midpoint formula, we get the answer to be [tex]\left(\frac{-1+3}{2}, \frac{5-1}{2} \right)=\boxed{(1,2)}[/tex]
Write an equation in slope-intercept form for the line with slope 8 and y-intercept 9.
Answers
Answer:
y = 8x + 9
Step-by-step explanation:
Slope-intercept form of an equation is a fill-in-the-blank formula for writing an equation of a line. It is in the form:
y = mx + b
where m is the slope and b is the y-intercept (hence the name) In the problem slope is given, fill it in for m, next to the x. Y-intercept is given in the question also, fill it in in place of b.
y = 8x + 9
Can one of u guys help me I need help asap
Answers
Answer:
See below ~
Step-by-step explanation:
The three inequalities (listed below) have been plotted on a graph :
y ≤ 8y ≥ -3x + 4y > 2x - 4Which of the following options have the same value as 10% of 33?
Choose 3 answers:
0.1.0.33
® 10.33
©
1
10
33
0.1.33
10
100
33
3o
Answers
Answer:
1
Step-by-step explanation:
Two stores have movies to rent.
• The first store charges a $10.50-per-month membership fee plus
$1.50 per movie rented.
• The second store has no membership fee but charges $2.50 per movie
rented.
What is the minimum number of movies a person would need to rent in a month
for the first store to be a better deal?
Answers
Answer:
4 movies because ďòê ánş vianna sausage says so i dont know im barely passing math myself
HELP ASAP THIS IS DO TOMORROW!
Answers
Answer:
The volume of the box is 250cm³
Step-by-step explanation:
V = Length * Width * Height
V = 5cm * 5cm * 10cm
V = 250cm³
The volume of the given box (rectangular prism).
Solution:[tex]V = whl[/tex]
[tex]V = 10 \times 5 \times 5[/tex]
[tex]\large\boxed{\sf{V = 250 \: {cm}^{3}}}[/tex]
Therefore, the volume of the given box (rectangular prism) is 250 cubic centimeters.
A group of 3 people are sharing chocolates.Each person wants 8 chocolates and each box has 4 chocolates.How many boxes do they need?
Answers
Answer:
6
Step-by-step explanation:
you times it and you get the answer
Can someone please help me with b and C questions
Answers
Answer:
(b) 33919
(c) 8 ¹/₃
Step-by-step explanation:
⇒ 317 × 107 = (300 + 10 + 7)(100 + 7)
= 300(100 + 7) + 10(100 + 7) + 7(100 + 7)
= 30000 + 2100 + 1000 + 70 + 700 + 49
= 30000 + 2000 + 100 + 1000 + 70 + 700 + 40 + 9
= 30000 + 2000 + 1000+ 700 + 100 + 70 + 40 + 9
= 30000 + 3000 + 800 + 110 + 9
= 30000 + 3000 + 800 + 100 + 10 + 9
= 30000 + 3000 + 900 + 10 + 9
= 33919
[tex]\begin{aligned} 5\frac{2}{3}+3\frac{1}{2}-\frac{5}{6}&=\dfrac{5 \times3+2}{3}+\dfrac{3 \times 2+1}{2}-\dfrac{5}{6}\\\\&=\dfrac{17}{3}+\dfrac{7}{2}-\dfrac{5}{6}\\\\& =\dfrac{17 \times 2}{3\times 2}+\dfrac{7\times 3}{2\times 3}-\dfrac{5}{6}\\\\ & = \dfrac{34}{6}+\dfrac{21}{6}-\dfrac{5}{6}\\\\ & = \dfrac{34+21-5}{6}\\\\ & = \dfrac{50}{6}\\\\&=8\frac{1}{3}\end{aligned}[/tex]
A person invests 8000 dollars in a bank. The bank pays 6.25% interest compounded daily. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 10800 dollars
Answers
Answer:
4.8 years
Step-by-step explanation:
10 800 = 8000 e^(i t) i = decimal interest per year t = years
10800/8000 = e^(.0625 t) ln both sides
.300 = .0625 t
t = 4.8 years
RIGHT triangular prisms A and B are congruent. What is the volume of prism B? A) 420 in3 B) 1080 in3 C) 2160 in3 D) 32400 in3
Answers
Answer: B
Step-by-step explanation:
The diameter of a cylindrical construction pipe is 3 ft. If the pipe is 12 ft long,
what is its volume?
Use the value 3.14 for π, and round your answer to the nearest whole
number.
Be sure to include the correct unit in your answer.
Answers
Work Shown:
d = 3 = diameter
r = d/2 = 3/2 = 1.5 = radius
h = 12 = height or length of the pipe
pi = 3.14 approximately
V = volume of the cylinder pipe
V = pi*r^2*h
V = 3.14*(1.5)^2*12
V = 84.78
V = 85
The cylindrical pipe's volume is about 85 cubic feet.
Logan's solution and reasoning for solving an equation are shown below:
Given
Step 1: x-10-50 Reason 1: Given
Step 2
x-10+10=50+10 Reason 2 Addition Property of Equality
Step 3
60
Reason 3 Simplity
Step 4:
<= 60
Reason 4: Division Property of Equality
Step 5.
x = 40
Reason 5: Simplity
Choose which reason is incorrect.
O Reason 2
O Reason 3
O Reason 4
O Reason 5
Answers
Answer:
Logan's solution and reasoning for solving an equation are shown below:
Given
Step 1: x-10-50 Reason 1: Given
Step 2
x-10+10=50+10 Reason 2 Addition Property of Equality
Step 3
60
Reason 3 Simplity
Step 4:
<= 60
Reason 4: Division Property of Equality
Step 5.
x = 40
Reason 5: Simplity
Choose which reason is incorrect.
O Reason 2
O Reason 3
O Reason 4
Step-by-step explanation:
