Answers
Required matrix representation is
| 650 -1 | | x | = | 175|
| -120 1 | | y | = | 25,080 |
What is Matrix?
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are used in various branches of mathematics, physics, engineering, and computer science to represent and manipulate data, transformations, and systems of linear equations.
A matrix is usually denoted by a capital letter, such as A, and its elements are represented by lowercase letters with subscripts, such as aij, where i and j are the row and column indices, respectively.
Matrices can be added, subtracted, multiplied, and divided by other matrices or scalars, and they obey certain algebraic laws, such as associativity, distributivity, and commutativity. Matrices can also be used to represent linear transformations, such as rotations, translations, and reflections, and to solve systems of linear equations, such as Ax = b, where A is a matrix, x and b are vectors, and the goal is to find a solution for x that satisfies the equation.
Here given system of equations are y = 650x+175 and y = 25,080-120x
The matrix representation of the system of equations is:
| 650 -1 | | x | = | 175 |
| -120 1 | | y | = | 25,080 |
where the first column corresponds to the coefficient of x and y respectively, and the second column corresponds to the variable itself. The third column corresponds to the constant term.
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Related Questions
Andy has -$45 in his checking account at the beginning of the week. At the end of the week he was paid $30 for moving the grass and $25 for vacuuming the house. How much money does Andy now have in his checking account?
Answers
Answer:
we need to add the money Andy earned to the negative balance he had. So, we have:
-$45 + $30 + $25 = $10
Therefore, Andy now has $10 in his checking account.
Answer:
Andy now has $10 in his checking account.
Step-by-step explanation:
Andy starts the week with -$45 in his checking account. When he gets paid $30 for mowing the grass and $25 for vacuuming the house, his total earnings for the week are:
$30 + $25 = $55
To find out how much money he now has in his checking account, we need to add his earnings to his starting balance of -$45. Adding a negative number is the same as subtracting a positive number, so we can write this as:
-$45 + $55 = $10
Therefore, Andy now has $10 in his checking account.
What is the price per bag of cookies
Answers
Answer: 6.3 per bag
Step-by-step explanation:
31.50 divided by 5 is 6.3!!!!
Answer: 6.3
Step-by-step explanation:
Divide 31.50 with 5
[tex]5\sqrt{31.50}[/tex]
5 goes into 3 0 times so you do 31/5. You get 6 with 1 as the remainder since 6x5 is 30. Now you do 15/5 which is 3. You get 63 but you have to add the decimal between the 6 and 3 so you will get 6.3. Hope this helped.
Nathan rolls a number cube and records the result of each roll in the table.
Number Cube
Number Rolled
Frequency
1
11
2
16
3
14
4
20
5
12
6
17
Which statements below represent the situation? Select three options.
Answers
The correct three options are:
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
The number 4 was rolled more frequently than any other number.
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
Nathan rolled the number cube a total of 90 times.
The number 4 was rolled more frequently than any other number.
The number 2 was rolled the least frequently of all the numbers.
The total number of rolls for odd numbers is greater than the total number of rolls for even numbers.
The correct statements are:
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
The number 4 was rolled more frequently than any other number.
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x^3-6x^+2x-4 divided by x+2
Answers
Answer:
Step-by-step explanation:
i literally don’t understand any of this
Answers
According to the information, he quadratic function's equation is f(x) = (47/13)x^2 + (89/13)x + 198/13 in standard form.
How to find the quadratic function's equation?To find the quadratic function's equation, we need to use the given points from the table and solve for the coefficients a, b, and c in the standard form of a quadratic function, f(x) = ax^2 + bx + c.
Using the point (-7, 209):
209 = a(-7)^2 + b(-7) + c
Using the point (-5, 113):
113 = a(-5)^2 + b(-5) + c
Using the point (-2, 29):
29 = a(-2)^2 + b(-2) + c
Now we have three equations with three variables. We can solve for a, b, and c using a system of linear equations. First, simplify each equation:
49a - 7b + c = 209
25a - 5b + c = 113
4a - 2b + c = 29
Then, we can solve for b in terms of a and substitute in the other equations to eliminate b:
b = 7a + c/7 - 29/7
Substituting into the second equation:
25a - 5(7a + c/7 - 29/7) + c = 113
Simplifying:
10a + c = 80
Substituting into the third equation:
4a - 2(7a + c/7 - 29/7) + c = 29
Simplifying:
-3a + c = 33
Now we have two equations with two variables. We can solve for c in terms of a and substitute back into one of the previous equations to solve for a:
c = 3a + 33
Substituting into the second equation:
10a + (3a + 33) = 80
Simplifying:
13a = 47
a = 47/13
Now we can substitute a back into one of the previous equations to solve for c:
c = 3(47/13) + 33 = 198/13
Finally, we can substitute a and c into the standard form of a quadratic function:
f(x) = (47/13)x^2 + (7(47/13) - 198/13)x + 198/13
Simplifying:
f(x) = (47/13)x^2 + (89/13)x + 198/13
Therefore, the quadratic function's equation is f(x) = (47/13)x^2 + (89/13)x + 198/13 in standard form.
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The polynomial of degree 4, P(x) , has a root of multiplicity 2 at x=3 and a root of multiplicity 1 at x=0 and x=-1. it goes through point (5,12).
Answers
P(x) = k(x-3)^2 x(x+1)
where k is some constant.
To find the value of k, we use the fact that P(5) = 12. Substituting x=5 into the equation for P(x), we get:
P(5) = k(2)^2 (5)(6) = 120k
Setting this equal to 12, we have:
120k = 12
k = 1/10
So the polynomial is:
P(x) = (1/10)(x-3)^2 x(x+1)
Therefore, the polynomial of degree 4, P(x), with a root of multiplicity 2 at x=3 and a root of multiplicity 1 at x=0 and x=-1, and which goes through point (5,12), is given by:
P(x) = (1/10)(x-3)^2 x(x+1)
Note that the point (5,12) is not a root of the polynomial, but rather a point on the graph of the polynomial.
Alg 2 graphic quadratics in intercept form
Answers
The calculated key features of the quadratic functions 1 to 6 are listed below
Completing the key features of the graphsFunction 1: y = 1/2(x + 4)(x - 2)
Expand
y = x^2/2 + x - 4
From the function, we have
a = 1/2 (coefficient of x^2 term)
p = -b/2a (x-coordinate of the vertex)
p = -(1)/2(1/2)
p = -1
q = f(p) (y-coordinate of the vertex)
q = 1/2(1 + 4)(1 - 2)
q = -5/2
From the function, we have
x-intercepts = (-4, 0) and (2, 0)
This also means that the axis of symmetry is
x = -1
The quadratic function opens up because the coefficient of the x^2 term is positive.
Next, we have
Vertex = (-1, -5/2)
For the y-intercept, we have
y-intercept = f(0)
y-intercept = 1/2(0 + 4)(0 - 2)
y-intercept = -4
Slope to a point one unit from the vertex can be found by taking the derivative of the function:
f(x) = x^2/2 + x - 4
f'(x) = x + 1
At x = -2 (one unit to the left of the vertex), the slope is -1
i.e. f'(-2) = -2 + 1 = -1
At x = 0 (one unit to the right of the vertex), the slope is 1.
i.e. f'(0) = 0 + 1 = 1
When the above steps is repeated for the remaining functions, we have the following results:
Function 2: y = 1/2x(x - 8)
The features are:
a = 1/2, p = 4, q = -8x-intercepts = (0, 0) and (8, 0)Axis of symmetry: x = 4Opens up or down: UpVertex = (4, -8)y-intercepts = (0, 0)Slope to pt one unit from vertex: -1 and 1Function 3: y = (x + 2)(x - 2)
The features are:
a = 1, p = 0, q = -4x-intercepts = (-2, 0) and (2, 0)Axis of symmetry: x = 0Opens up or down: UpVertex = (0, -4)y-intercepts = (0, -4)Slope to pt one unit from vertex: -2 and 2Function 4: y = -1/3(x + 1)(x - 5)
The features are:
a = -1/3, p = 2, q = 3x-intercepts = (-1, 0) and (5, 0)Axis of symmetry: x = 2Opens up or down: DownVertex = (2, 3)y-intercepts = (0, 5/3)Slope to pt one unit from vertex: 2/3 and -2/3Function 5: y = 4(x + 2)(x + 1)
The features are:
a = 4, p = -3/2, q = -1x-intercepts = (-2, 0) and (-1, 0)Axis of symmetry: x = -3/2Opens up or down: UpVertex = (-3/2, -1)y-intercepts = (0, 8)Slope to pt one unit from vertex: -8 and 8Function 6: y = -(x - 3)(x - 3)
The features are:
a = -1, p = 3, q = 0x-intercepts = (3, 0)Axis of symmetry: x = 3Opens up or down: DownVertex = (3, 0)y-intercepts = (0, -9)Slope to pt one unit from vertex: 2 and -2Read more about quadratic functions at
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Write 4 as a logarithm with a base 4
Answers
Answer: Algebra Examples
Logarithm base 4 of 4 is 1.
Step-by-step explanation:
unity
The value of log 4 to the base 4 is equal to unity. The Antilogarithm of the logarithmic value of 4 is equal to 4.
Suppose you want to save $7,500 to go on a dream vacation in three years. You can save for your vacation by either depositing one single lump of money into a savings account and letting it accumulate interest or by making regular monthly payments.
Answers
You would need to deposit approximately $8,267.40 initially to reach your goal of $7,500 in three years, assuming an annual interest rate of 3%.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
If you have three years to save for a dream vacation and want to save $7,500, there are two main approaches you can take: making regular monthly payments or depositing one single lump sum into a savings account.
Option 1: Regular Monthly Payments
If you decide to make regular monthly payments towards your vacation savings, you will need to calculate how much you need to save each month to reach your $7,500 goal. To do this, you need to divide the total amount you want to save by the number of months you have to save.
In this case, you have 36 months (3 years x 12 months/year) to save $7,500, so:
$7,500 ÷ 36 = $208.33 per month
So, you would need to save approximately $208.33 per month for 36 months to reach your goal of $7,500.
Option 2: Single Lump Sum Deposit
If you decide to deposit one single lump sum into a savings account, you will need to calculate how much you need to deposit initially to reach your $7,500 goal in three years, assuming a certain rate of interest.
The amount you need to deposit will depend on the interest rate you can earn on your savings. For example, if you can earn an annual interest rate of 3%, the calculation would be:
Initial deposit = Future value of $7,500 at 3% interest over 3 years
Using a financial calculator or spreadsheet, you can determine that the future value of $7,500 at 3% interest over 3 years is approximately $8,267.40.
Therefore, You would need to deposit approximately $8,267.40 initially to reach your goal of $7,500 in three years, assuming an annual interest rate of 3%.
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Write the following series in sigma notation. 8+18+28+38+48
Answers
Answer:
in the image
Step-by-step explanation:
using the arithmetic formula
a = ao + d(n-1)
we can find the sum of this formula added up 5 times
Identify the shapes that make up the figure at the left. Then find the perimeter and area of the figure to the nearest hundredth.
Answers
Rectangle, semi circle, semi circle
Perimeter: 60.8
Area: 64.2
What is perimeter and area?In mathematics, the two key characteristics of two-dimensional forms are area and perimeter. The difference between area and perimeter is how much room each type of shape takes up.
Mathematical concepts like area and perimeter are crucial because they are applied to daily living. Any size and form, whether regular or irregular, can use this. Each design has a unique area and perimeter calculation. Forms like triangles, squares, rectangles, circles, spheres, etc. should be known to you. Here, the boundaries and surfaces of all forms are explained.
perimeter= 60.8
each of the three shapes' perimeters separately, then sum them all up to get 60.8.
area= 64.2
Calculate the area of each of the three shapes separately, then sum them all up to get 64.2.
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The complete question attached below,
The required size and perimeter of the Area are respectively 27.42 and 64.26 square units.
What is Perimeter of the shape?A shape's perimeter is its circumference. How are perimeters determined? By adding the lengths of each side of a shape, the border may be obtained.
A shape comprised of two circles and a rectangle has been provided.
the size of a circle = 12 - 6 = 6
then radius = 3 units
Perimeter = 3+3+3+3+3+3+π(3)
= 18 + 3.14(3)
= 18 + 9.42
= 27.42 units
and
Area = area of rectangle + area of two half circles
= 12(3) + π(3)²
= 36 + 28.26
= 64.26 sq units.
Therefore, the shape's needed area and perimeter are respectively 27.42 and 64.26 square units.
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Twenty four blood samples were selected by taking every seventh blood sample from racks holding 199 blood samples from the morning draw at a medical center
A)calculate the FPCF for this sample
B)Should the population be considered effectively infinite
DO BOTH A AND B URGENT
Answers
A) The FPCF for this sample is 0.899. B) The sample size is about 12% of the population size, which is relatively large.
A) The FPCF (Finite Population Correction Factor) is used to adjust for the impact of a finite population on the sampling distribution. The formula for the FPCF is:
FPCF = [tex]\sqrt{((N-n)/(N-1))}[/tex]
where N: size of the population and n: size of the sample.
In this case, the population size is N = 199, and the sample size is n = 24. Therefore, the FPCF can be calculated as follows:
FPCF = [tex]\sqrt{((199-24)/(199-1))}[/tex] = 0.899
So, the FPCF for this sample is 0.899.
B) In general, a population can be considered effectively infinite when the sample size is no more than 5-10% of the population size. In this case, the sample size is n = 24, and the population size is N = 199. Therefore, the sample size is about 12% of the population size, which is relatively large.
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HELP I NEED THIS ASAPPP!!!
Mr. Harris graded papers at the end of the school day. The table below shows how many papers he graded in minutes.
Minutes Number of papers graded
4 2
16 8
20 10
24 12
At this rate, how many papers will Mr. Harris grade in 60 minutes?
30 papers
36 papers
48 papers
52 papers
Answers
The number of papers that will be graded in 60 minutes is 30 papers.
What is proportion?Proportion refers to the relationship or comparison between two or more quantities or values. It expresses how one quantity relates to another in terms of size, magnitude, or scale. Proportions are often used to describe the relative sizes or ratios of different elements within a whole or between different parts of a whole.
We have that;
2 papers are graded in 4 minutes
1 paper will be graded in 1 * 4/2
= 2 minutes
If 1 paper is graded in 2 minutes
x papers are graded in 60 minutes
x = 30 papers
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Let x represent one number and let y represent the other number. Use the following conditions to write a system of nonlinear equations. Solve the system and find the numbers.
The sum of two numbers is 11 and the product of the two numbers is 30
The two numbers are:
(use a comma to separate answers as needed)
Answers
Answers:
There are 2 answers:
1. 6,5
2. 5,6
Step-by-step explanation:
The SUM of two numbers IS 11:
x + y = 11
The PRODUCT of two numbers IS 30:
xy = 30
The system we get is
x + y = 11
xy = 30
Now solve the system:
There are 2 possible solutions:
(6,5) and (5,6)
Triangle ABC is shown. Use the graph to answer the question. triangle ABC on a coordinate plane with vertices at 1 comma negative 2, 9 comma negative 2, 5 comma 2 Determine the coordinates of the image if triangle ABC is translated 5 units down. A′(−4, −2), B′(4, −2), C′(0, 2) A′(1, −7), B′(9, −7), C′(5, −3) A′(1, 3), B′(9, 3), C′(5, 7) A′(6, −2), B′(14, −2), C′(10, 2)
Answers
if triangle ABC is translated 5 units down, the image's coordinates are A′(1, 7), B′(9, 7), and C′(5, 3).
The x and y coordinates of each of a triangle's vertices must be added to or subtracted from to translate the triangle on a coordinate plane.
Triangle ABC must be translated five units lower in this situation. Thus, we must deduct 5 from the y coordinates of each of its vertices.
A(1, -2) changes to A' (1, -7) B(9, -2) changes to B' (9, -7) C(5, 2) changes to C' (5, -3)
As a result, if triangle ABC is translated 5 units down, the image's coordinates are A′(1, 7), B′(9, 7), and C′(5, 3).
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options.
NEED ASAP
Answer choices:
y(y + 5) = 750
y2 – 5y = 750
750 – y(y – 5) = 0
y(y – 5) + 750 = 0
(y + 25)(y – 30) = 0
Answers
The equations that can be used to solve for y in the given situation are:
(A) y(y + 5) = 750
(B) y² – 5y = 750
(D) y(y – 5) + 750 = 0
What is a rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°).
A rectangle has equal and parallel opposite sides.
A rectangle has two dimensions—length and width—because it is a two-dimensional form.
The rectangle's longer side is its length, while its shorter side is its breadth.
So, the area formula of the rectangle:
750 = l * w
750 = x * (x-5)
750 = x² - 5x
x² - 5x - 750 = 0
Equations in the options that are similar:
(A) y(y + 5) = 750
(B) y² – 5y = 750
(D) y(y – 5) + 750 = 0
Therefore, the equations that can be used to solve for y in the given situation are:
(A) y(y + 5) = 750
(B) y² – 5y = 750
(D) y(y – 5) + 750 = 0
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Correct question:
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options.
NEED ASAP
Answer choices:
a. y(y + 5) = 750
b. y2 – 5y = 750
c. 750 – y(y – 5) = 0
d. y(y – 5) + 750 = 0
e. (y + 25)(y – 30) = 0
find the answer to 9/16 in decimal form
Answers
Answer:
0.5625
Step-by-step explanation:
Which inequality is true?
A 0.23 < 0.089
B 1.035 > 1.04
© 2.358 < 2.369
D 99.863 > 99.901
Answers
Answer:
C
Step-by-step explanation:
We Can see from the < pointing to the higher side.
Help plsSSSSSSSSSSSSSSSSSSSSSSS
Answers
Step-by-step explanation:
[tex]\triangle ADB[/tex] is equilateral, so [tex]m\angle DBA=60^{\circ}[/tex].
Using linear pairs, [tex]m\angle DBC=120^{\circ}[/tex].
Answer: J (120)
Step-by-step explanation: Since triangle ABD is given to be an equalatiral triangle, we know that every interior angle is 60 degrees. Since line ABC is a straight line we know that if we subtract the lines angle (180) by the interior angle it goes through (60) we get the measure of angle DBC: 120 degrees
Calculate the area of the shape
Answers
Answer:
Step-by-step explanation:
Just divide the total shape into three shapes one rectangle and two triangles and then calculate the area
Hope this helps: )
Solve the systems by elimination.
x -y = 11
5x + 6y = -44
Answers
Answer: (6,-5)
Step-by-step explanation:
Select the best answer for the question.
4
ol
0
-1 2
-3
-1
15. Multiply
0
A. -6
3
4
1
-4
0
-3 1
Answers
Answer:
40 -12-3 15 multiply all of them and u get your answer
can someone help me do this (will give brainliest if possible
Answers
Answer:
4) ∠1 and ∠2, ∠2 and ∠3
5) ∠1 and ∠3
6) x = 10
Step-by-step explanation:
Adjacent angles are two angles that share a common vertex and a common side, but do not overlap.
Therefore, the pairs of adjacent angles in the given diagram are:
∠1 and ∠2∠2 and ∠3∠3 and ∠4∠4 and ∠5∠5 and ∠1Vertical angles are pairs of non-adjacent angles that are formed when two lines intersect. Vertical angles are congruent,
Therefore, the pair of vertical angles in the given diagram are:
∠1 and ∠3As ∠1 and ∠3 are the same measure:
⇒ m∠1 = m∠3
⇒ (9x)° = 90°
⇒ 9x = 90
⇒ 9x ÷ 9 = 90 ÷ 9
⇒ x = 10
Therefore, the value of x is 10.
Answer:
4) ∠1 and ∠2, ∠2 and ∠3.
5) ∠1 and ∠3.
6) x = 10.
Step-by-step explanation:
Explanations are given in attachment!
Simplify -4x(1-3)-2x+2)
Answers
(1-3)-2x+2 = -2x + 3
Now we can simplify the entire expression:
-4x(-2x + 3)
Multiplying -4x by each term inside the parentheses:
= (-4x * -2x) + (-4x * 3)
Simplifying:
= 8x^2 - 12x
Answer:
The answer is 6x + 2
Step-by-step explanation
I did all the work and I passed on this test so i know this is the answer.
Solve the equation for y in terms of x, and replace y with function notation f(x). Then find f(2).
y+3x^2=5
f(x)=?
f(2)=?
Answers
Answer:
[tex]f(x)=-3x^2+5[/tex]
[tex]f(2) = -7[/tex]
Step-by-step explanation:
Given equation:
[tex]y+3x^2=5[/tex]
To solve the equation for y in terms of x, simply subtract 3x² from both sides of the equation:
[tex]\implies y+3x^2-3x^2=5-3x^2[/tex]
[tex]\implies y=-3x^2+5[/tex]
Replace y with the function notation f(x):
[tex]f(x)=-3x^2+5[/tex]
Finally, to find the value of f(2), substitute x = 2 into the function:
[tex]\begin{aligned}\implies f(2)&=-3(2)^2+5\\&=-3(4)+5\\&=-12+5\\&=-7\end{aligned}[/tex]
Answer:
[tex]f(2) = - 7[/tex][tex] f(x) = 5 - 3x^2[/tex]Step-by-step explanation:
To find:-
The value of [tex]f(2)[/tex]Answer:-
We are here a given a equation, with some steps to follow, in order to find out the value of [tex]f(2)[/tex].
Step 1 :- Solve the equation in terms of y ,
The given equation to us is,
[tex]\longrightarrow y + 3x^2 = 5\\[/tex]
To solve for y , we need to transpose 3x² from LHS to RHS , by doing this , the sign changes from positive to neagative .
[tex]\longrightarrow y = 5 - 3x^2 \\[/tex]
Step 2 :- Replace y with function notation [tex]f(x)[/tex]
Just simply replace y here with f(x) as ,
[tex]\longrightarrow f(x) = 5 - 3x^2\\[/tex]
Step 3 :- Find f(2) .
To calculate the value of f(2) , we need to put x = 2 , in the above equation as ,
[tex]\longrightarrow f(2) = 5 - 3(2)^2\\[/tex]
Simplify,
[tex]\longrightarrow f(2) = 5 - 3(4)\\[/tex]
[tex]\longrightarrow f(2) = 5 - 12\\[/tex]
[tex]\longrightarrow \boxed{ \boldsymbol{f(2) = -7 }} \\[/tex]
Hence the required answer is -7 .
Rachel cycled a total distance of 59,136ft on a bicycle path surrounding a lake. She cycled 4 laps, where each lap was the same length. What was the length of each lap around the lake? Write your answer in miles.
Answers
Rachel cycled each lap around the lake that was 2.8 miles long.
What is unit rate?
A unit rate is a ratio in which the denominator is 1. It is a rate that compares a quantity to one unit of another quantity.
First, we need to convert the total distance cycled from feet to miles since the length of each lap is likely to be expressed in miles.
1 mile = 5280 feet
Therefore,
59,136 ft ÷ 5280 ft/mile = 11.2 miles
So, Rachel cycled a total of 11.2 miles around the lake.
Since she cycled 4 laps of the same distance, we can divide the total distance by 4 to get the length of each lap:
11.2 miles ÷ 4 = 2.8 miles per lap
Therefore, Rachel cycled each lap around the lake that was 2.8 miles long.
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Anton surveys 80 students at his school and finds that 55% of them have mobile phones. He also finds that 98% of 50% adults have mobile phones. How many more adults than students ?
Answers
Answer:
13
Step-by-step explanation:
Student: 80 * 55% = 44
Adult: 50 * 98% = 49
49-44=5
Given vectors u = (2, 5) and v = (-5, -2), find the difference u - v and
represent the difference graphically in two different ways.
Answers
The difference between two vectors [tex](u - v )[/tex] = [tex](7,7)[/tex].
What is vectors?An entity with both magnitude and direction is referred to as a vector. A vector can be visualized geometrically as a directed line piece, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.
Therefore subtracting [tex]u-v[/tex] we get
[tex]u-v = (2,5)-(-5,-2\\ = (2+5,5+2)\\=(7,7)[/tex]
The distinction between u and v can be graphically represented in two ways:
The next step is to create the vector [tex]u-v[/tex], which begins at the same location as [tex]u[/tex] and ends at [tex]v[/tex].
In an algebraic sense, the vectors u and v can be represented as points in a coordinate plane, and the vector u - v as a line connecting these places.
The following figure shows the construction with negative velocities
In this case, the vectors u and v are represented by location A and point B, respectively.
Therefore the difference between two vectors [tex](u - v )[/tex] = [tex](7,7)[/tex].
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y = y₁ = m(x − x₁)
Show your work in the space provided below.
1. Find the equation of the line that has a slope of -4 and passes through the point (-3, 7).
Show your work below:
2. Find the equation of the line that passes through the points (4, -3) and (8,9).
Show your work below:
Answers
Answer:
see below
Step-by-step explanation:
The equation y - y₁ = m(x − x₁)
1. y - 7 = -4(x - -3)
y - 7 = -4(x + 3)
y = -4x - 12 + 7
y = -4x - 5
2. y - y₁ = m(x − x₁)
9 - -3 = m(8 - 4)
12 = 4m
m = 12/4 = 3
y = mx + b
-3 = 3(4) + b
b = - 3 - 12
b = -15
y = 3x - 15
I put a picture please help
Describe the transformation of LM to L'M'.
O A. LM is translated 5 units left and 2 units down to L'M':
O B. LM is translated 5 units right and 2 units up to L'M
O C. LM is reflected over the x-axis to L'M'.
O'D. LM is reflected over the y-axis to L'M
SUBMIT
Answers
The option that Describe the transformation of LM to L'M'. is: LM is translated 5 units left and 2 units down to L'M'. Answer: option A.
What is the transformation about?To determine the transformation from LM to L'M', we need to identify how much LM has been translated horizontally and vertically. From the graph, we can see that L has been moved 5 units to the left to reach L', and M has been moved 2 units down to reach M'.
Looking at the graph, we can see that L is moving leftward and downward, while M is moving leftward. This indicates a translation.
Furthermore, the distance that L and M move is 5 units horizontally and 2 units vertically. This means that LM is translated 5 units left and 2 units down to L'M'.
Therefore, the correct answer is OA. LM is translated 5 units left and 2 units down to L'M'.
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