Both slope are equal so we can say that both lines are parallel
slope, The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytical geometry ("slope equals rise over run").
Line a: 2x + y = 10
Line b:
- 6x – 3y = 3
and line
Line a: 2x + y = 10
= slope of line A is
2x + y = 10
y = -2x+10
slope = -2
- 6x – 3y = 3
-3y = 6x +3
x = -2y -1
slope = -2
in this case both slope are equal so we can say that both lines are parallel
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Sophie needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4 hours and charged her $127 for parts. The total was $227. Write and solve an equation which can be used to determine
x, the cost of the labor per hour.
Answer:
Step-by-step explanation:
(227-127)/4=x
"/" means divide.
Let f(x)=p(x)/q(x) where p(x) and p(x) are polynomials with no common factors other than 1. Describe how to find the x-intercepts and the vertical asymptotes of the function
To find the x-intercepts of a rational function of the form f(x) = p(x)/q(x), we set p(x) = 0 and solve for x. To find the vertical asymptotes, we set q(x) = 0 and solve for x.
Vertical asymptotes are vertical lines that a function approaches but never touches or crosses as the independent variable (usually denoted as x) approaches a certain value.
To find the x-intercepts of the function, we need to set the numerator of the rational function equal to zero and solve for x. This is because x-intercepts occur when the function value is equal to zero. Therefore, we can write:
p(x) = 0
Solving this equation will give us the values of x where the function intersects the x-axis. It is important to note that if p(x) has a degree greater than or equal to q(x), then the function will have a slant asymptote instead of a vertical asymptote.
To find the vertical asymptotes of the function, we need to look at the denominator of the rational function. Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a certain value. In the case of a rational function, this happens when the denominator is equal to zero. Therefore, we can write:
q(x) = 0
Solving this equation will give us the values of x where the function has a vertical asymptote. It is important to note that if the degree of q(x) is greater than the degree of p(x), then the function will have a horizontal asymptote instead of a vertical asymptote.
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What is the area of this compound figure?
Answer: 188in^2
Step-by-step explanation:
You can break the figure into 3 smaller shapes
15 x 5
10 x 5
and 9 x 7
The areas of these smaller shapes are 75, 59 and 63
adding these areas together would get you 188 in squared.
The height, h, of a projectile thrown straight up from the top of a 448-foot hill t seconds after being thrown upward with initial velocity vo ft/sec is given by
h=-16t² + vot+448. In this exercise, for a given value of vo. find the time(s) when the projectile will (a) be at a height of 576 ft above the ground and (b) crash
on the ground. Round your answers to two decimal places. Here vo= 112.
a. The projectile will be at a height of 576 ft above the ground after 1.43 seconds and after 5.56 seconds.
b. The projectile will crash on the ground after 9.84 seconds.
The solution has been obtained by solving the equation.
What is an equation?
A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.
We are given an equation as h = -16t² + v₀t + 448
Also v₀ is given as 112.
a. In order to find the time (t) the projectile will be at a height of 576 ft above the ground, we need to substitute h = 576 and v₀ = 112.
On substitution, we get
⇒h = -16t² + v₀t + 448
⇒576 = -16t² + 112t + 448
⇒36 = -t² + 7t + 28 (On dividing both sides by 16)
⇒0 = -t² + 7t - 8
⇒t² - 7t + 8 = 0
On solving the equation using the quadratic equation formula, we get
t = (7 ± √49 - 32)/2
t = 1.43 or 5.56
So, it will be at height 576 ft after 1.43 seconds and after 5.56 seconds.
b. Similarly, now we will put h = 0 and v₀ = 112.
Now, we get
⇒0 = -16t² + 112t + 448
⇒t² - 7t - 28 = 0 (On dividing both sides by 16)
On solving the equation using the quadratic equation formula, we get
t = (7 ± √49 + 112)/2
t = 9.84 or -2.84
Since, time cannot be negative, so it will crash after 9.84 seconds.
Hence, the projectile will be at 576 ft after 1.43 seconds and after 5.56 seconds and will crash on the ground after 9.84 seconds.
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Which equation represents the relationship shown in the table?
Answer:
Diatance biked = rate • time
what is the missing
equivalent ratio of 4 : 2 = 10: _
Answer:
4 : 2 = 10 : 5.
Step-by-step explanation:
Let's put this in a fraction way. 4/2 = 2, and 10/5 = 2. Likewise, we can keep going and putting things that equal to 2. (e.g. 42 : 21)
an isosceles trapezoid has a height of 4 cm and bases 3cm and 7cm long. how long are its diagonals
The length of the diagonal of an isosceles trapezoid is 2.83 cm
An isosceles trapezoid is a quadrilateral with two parallel sides and two non-parallel sides of different lengths.
In this case, the non-parallel sides are the bases, which are 3cm and 7cm long. The height is the perpendicular distance between the two bases and is given as 4cm. To find the length of the diagonals, we can use the Pythagorean theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse (the longest side).
In an isosceles trapezoid, the diagonals are equal in length and bisect each other. Let's call the length of the diagonal d. We can draw a right triangle with one leg being half of the trapezoid's height (2cm), the other leg being half of the difference between the two bases (2cm), and the hypotenuse being the length of the diagonal d. Using the Pythagorean theorem, we get:
(2cm)² + (2cm)² = d²
4cm² + 4cm² = d²
8cm² = d²
d = √(8cm²)
d = 2√(2)cm
d = 2.83cm
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The figure shown has two parallel lines cut by a transversal:
A pair of parallel lines is shown, crossed by a transversal. Angles are identified as 1, 2, 3, 4, 5, 6, 7, and 8. Angles 1-4 are on the top line clockwise from upper left. Angles 5-8 are on the lower line clockwise from upper left.
Which angle is an alternate interior angle to ∠3?
∠5 is the alternate interior angle of ∠3.
What is transversal?
A transversal is a line that, at two different points in the geometry, cuts through two lines in the same plane. Various types of angles in pairs, including consecutive interior angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.
When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairs of that transversal. Alternate interior angles are what they are called.
Line m and line n are parallel and line l is transversal.
The alternate pairs of that transversal are ∠3 and ∠5.
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Two sides of a triangle are
shown. Find the range of
values of the third side.
8, 5
< X <
The range of values for the third side must be 5 < C < 13 this means that the third side must be a value greater than 5 and less than 13.
What is triangle?
A triangle is a two-dimensional geometric shape with three sides and three angles. It is a basic polygon and one of the simplest shapes in geometry. Triangles come in different types based on the length of their sides or the measure of their angles, such as equilateral triangles (all sides are equal), isosceles triangles (two sides are equal), scalene triangles (no sides are equal), right triangles (one angle measures 90 degrees), and obtuse triangles (one angle measures greater than 90 degrees).
The third side of a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for a triangle with sides A, B, and C, we have:
A + B > C
B + C > A
A + C > B
For the given sides of 8 and 5, the range of values for the third side can be found by considering the two inequalities:
5 + C > 8
8 + C > 5
Adding the two inequalities, we get:
13 > C
So the range of values for the third side must be:
5 < C < 13
This means that the third side must be a value greater than 5 and less than 13.
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Find the distance travelled by rahul, if he takes 6 rounds of a square field of side=120m
The distance travelled by Rahul, if he takes 6 rounds of a square field of side = 120m is 2880 meters.
We are given that Rahul takes 6 rounds of a square field of side length 120m. To find the total distance he travels, we need to calculate the perimeter of the square field and multiply it by the number of rounds.
The perimeter of a square is the sum of the lengths of its four sides. Since the side length of the square field is 120m, the perimeter is:
4 * 120m = 480m
This is the distance Rahul covers in one round around the square field.
To find the total distance he covers in 6 rounds, we multiply the distance covered in one round by the number of rounds:
480m * 6 = 2880m
So, Rahul covers a total distance of 2880 meters.
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Hexagonal prism B is the image of hexagonal prism A after dilation by a scale factor of 2. If the surface area of hexagonal prism B is 172 cm^2, find the surface area of hexagonal prism A, the preimage.
Hexagonal prism A has a surface area of 43 cm2.
What is the surface area equation?A three-dimensional shape's surface area is the total area on its surface. A cuboid's surface area is calculated by adding the areas of each of its six rectangular sides. The cuboid's length, width, and height may all be identified, and the formula SA=2lw+2lh+2hw can be used to determine its surface area (SA).
The surface area of a hexagonal prism is given by the formula:
SA = 2B + PH
where B is the base's surface area, P is its perimeter, and H is the prism's height.
Since prism B is a dilation of prism A with a scale factor of 2, its surface area is four times the surface area of prism A. So we can write:
SA_B = 4×SA_A
where SA_B is the surface area of prism B and SA_A is the surface area of prism A
We are given that SA_B = 172 cm², so we can substitute this value into the equation above to find SA_A:
172 = 4×SA_A
SA_A = 43 cm²
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does a parallelogram have 2 pairs of parallel sides
Answer:
A parallelogram is a quadrilateral with 2 pairs of parallel sides
At a restaurant, Table A's bill of €72 is split equally
between the people at the table. Table B has two more
people than Table A, and its bill of €108 is also split
equally between the people at the table. Each person at
Table A pays the same amount as each person at Table B.
How many people were at Table A?
There were total 4 people at table A and each of them pay €18.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Table A's bill of €72 is split equally.
and, Table B has two more people than Table A and its bill of €108 is also split equally.
let number of people at table A be x and at table B be (x+2).
So, the number of people
x/ 72 = (x+2)/108
108x = 72x + 144
108x - 72x = 144
36x= 144
x=4
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Keisha must choose a shirt and a pair of pants for today's outfit. She has 4 shirts and 2 pairs of pants to choose from. How many different outfits can she make?
answer: 12
explanation:
at a football match , there are 29800 people correct to the nearest 100.
at the end of the football match, the people leave at a rate of 400 people per minute , correct to the nearest 50 people
calculate the lower bound for the number of minutes it takes for all the people to leave
The lower bound for the number of minutes it takes for all the people to leave is 67 minutes.
What is lower bound?
Lower bound refers to the smallest possible value in a range or interval of values. In the context of measurements or estimates, it represents the minimum value that a quantity or measurement is expected to be, based on the precision or accuracy of the measuring instrument or method.
To calculate the lower bound for the number of minutes it takes for all the people to leave, we need to use the following formula:
Lower bound = (total number of people - 0.5) / departure rate (in people per minute)
Using the given information, we have:
Total number of people = 29800 (correct to the nearest 100)
Departure rate = 400 (correct to the nearest 50)
To ensure we have a conservative estimate, we will round down the total number of people to 29750 and round up the departure rate to 450.
Therefore, the lower bound for the number of minutes it takes for all the people to leave is:
Lower bound = (29750 - 0.5) / 450
= 66.1 (rounded up to the nearest minute)
So the lower bound for the number of minutes it takes for all the people to leave is 67 minutes.
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hat
The distance around a circle is 36
meters long. What is the diameter of the
circle?
Answer: [tex]36/\pi[/tex] or approximately 11.4592
Step-by-step explanation:
The distance around a circle equals its circumference.
The circumference equation is: C = 2[tex]\pi[/tex] * r where r = radius.
Now, we know that the distance around the circle is 36 so C = 36
Using the equation, we have 36= 2[tex]\pi[/tex]*r
Now, we solve for r by dividing by 2[tex]\pi[/tex] to both sides.
r = [tex]36/2\pi[/tex] which equals [tex]18/\pi[/tex] which is approximately 5.7296
Now, since radius is half of the diameter, we need to multiply this by 2.
This finally gives us the answer of diameter = [tex]36/\pi[/tex] which is approximately 11.4592
Find the values of x, y, and z
The value of x, y and z in the trapezoid are solved to be
x = 6.3
y = 6.7
z = 5
What are similar polygons?This is a term used in geometry to mean that the respective sides of the polygons are proportional and the corresponding angles of the polygon are congruent
Hence assuming the corresponding angles of the polygon are congruent then the side should be in proportions
Examining the figure the constant of proportionality from the quadrilateral is
10 / 24 = 0.417
hence we solve for the dimensions as follows
x = 16 * 0.417 = 6.3
y = 16 * 0.417 = 6.67
z = 12 * 0.417 = 5
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2/3 thrids subtract 1/4
Answer: 5/12
Step-by-step explanation:
2/3 - 1/4 = 5/12
Answer:
1.75
Step-by-step explanation:
1. Students in Mrs. Henderson's third grade class are working on times tables, and they demonstrate mastery by
passing tests. Sofia has passed 4 tests so far. Her classmate, Jacob, has passed 8 of them. From now on, Sofia plans
to take and pass 3 tests per week. Meanwhile, Jacob plans to do 1 per week. At some point, Sofia will catch up to
Jacob. How long will it take?
The number of weeks when Sofia will catch up to Jacob will be 2 weeks.
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
Let 'x' be the number of weeks and 'y' be the total test. Then the equations are given as,
y = 4 + 3x ...1
y = 8 + x ...2
From equations 1 and 2, then we have
4 + 3x = 8 + x
3x - x = 8 - 4
2x = 4
x = 2
The number of weeks when Sofia will catch up to Jacob will be 2 weeks.
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Neeeeeed hellppppppppll
Answer:yes
Step-by-step explanation:correct becuase
Answer:
Answer is ADB
Step-by-step explanation:
I believe that's the answer
in the country of united states of heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.6 inches, and standard deviation of 6.5 inches. a) what is the probability that a randomly chosen child has a height of less than 40.65 inches? answer
The probability that a randomly chosen child has a height of less than 68.15 inches is 0.9162, the probability that a randomly chosen child has a height of more than 54.4 inches is 0.6255.
Simply put, probability is the liability that commodity will do. When we do not know how an event will turn out, we can bandy the liability or liability of several issues. Statistics is the study of events that follow a probability distribution.
a) We need to find p(x<68.15)
Standardize x to z, we have, z = (68.15-μ)/σ
=(68.15-57)/8.1
=1.38
Reading from standard normal tables,
p(z<1.38) =0.9162.
Therefore, the probability that a randomly chosen child has a height of less than 68.15 inches is 0.9162.
b) We need to find p(x>54.4)
Standardize x to z, we have, z = (54.4-μ)/σ
=(54.4-57)/8.1
=-0.32
Reading from standard normal tables,
p(z>-0.32) = 0.6255
Therefore, the probability that a randomly chosen child has a height of more than 54.4 inches is 0.6255.
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Use a trigonometric ratio to solve for z. Round to two decimal places as necessary.
The value of z in the triangle using trigonometric ratio is; z = 10.90
How to use trigonometric ratios?The three basic trigonometric ratios from which others are derived are;
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
From the diagram, we can easily see that z is the opposite side of the given angle and 13 is the hypotenuse. Thus;
z/13 = sin 57
z = 13 * sin 57
z = 13 * 0.83867
z = 10.90
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ayuda ES URGENTE 911
Answer: B D I J M
Step-by-step explanation: you just gotta see if any of the two answers work an if they don’t it’s nethier!
1. Which equation has a quotient of 1 1/5?
A 5÷6=
B 6÷5=
C 4÷5=
D 5÷4=
Answer:
none of them do
Step-by-step explanation:
5/6=0.83
6/5=1.2
4/5=0.8
5/4=1.25
11/5=2.2
3x - 5 = -3 is the answer positive or negative
Answer:
x = 2/3
0r 0.6(6)
both are positive
Step-by-step explanation:
3x - 5 = -3 is the answer positive or negative?
3x - 5 = -3
3x = -3 + 5
3x = 2
x = 2/3
0r 0.6(6)
The area of a square is numerically 60 more than the perimeter. Find the length of the side?
A. 10 B. 200 C. 40 D. 50
The length of the side is 10 units.
Solving Word Problems:To solve word problems, we try to assign variables to the quantities involved and use the given information to interpret the situation as a mathematical equation. Mathematical equations can then be solved using various techniques, so we get a solution which is then reinterpreted into the situation.
Now, According to the question:
Let the length of the side is 'L'
The area of a square is numerically 60 more than the perimeter.
Then, P = perimeter = 4L
A = area = [tex]L^2[/tex]
A = P + 60 ⇒
[tex]L^2[/tex] = 4L + 60
[tex]L^2[/tex] - 4L - 60 = 0
(L - 10)(L + 6) = 0
L = 10 or -6
L must be positive,
Since s can't be negative, L = 10 units.
Hence, The length of the side is 10 units.
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which of the following approaches to building a multiple linear regression model involves taking all of the possible independent variables, and then systematically eliminating insignificant ones until only significant ones remain? forward selection. stepwise regression. backward elimination. back-checking for aic
The approaches to building a multiple linear regression model is option (C) Backward elimination
Here the multiple linear regression model involves taking all of the possible independent variables, and then systematically eliminating insignificant ones until only significant ones remain
We know the independent variable is the variable that does not depends on any other variables
Here the given elimination methods is eliminating insignificant ones until only significant ones remain
In the backward elimination method starts with explanatory variables in the regression model then starts to eliminates the least significant ones will eliminates one by one
Therefore, the suitable approach is backward elimination method
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Brianna’s parents built a swimming pool in the backyard. Brianna days that the distance around the pool is 120 feet. Is she correct? Explain why or why not. 40ft 20ft
Brianna is correct, the distance around a rectangular pool with dimensions of 40 feet by 20 feet is 120 feet, which can be calculated by adding up the lengths of all four sides: (40 + 20 + 40 + 20) feet = 120 feet.
Brianna is correct, the distance around a rectangular pool with dimensions of 40 feet by 20 feet is indeed 120 feet. To calculate the distance around the pool, we need to add up the lengths of all four sides, which are equal in length. In this case, the length and width of the pool are both 40 feet and 20 feet, respectively. So, to find the distance around the pool, we add up these four lengths:
40 feet + 20 feet + 40 feet + 20 feet = 120 feet
Therefore, the total distance around the pool is 120 feet.
To determine the distance around the pool, Brianna needs to measure the length and width of the pool. If the pool is rectangular, she can measure the length and width and add up the lengths of all four sides to find the total distance around the pool. If the pool is a different shape, Brianna would need to measure the lengths of each side and add them up to find the total distance around the pool. This information can then be used to calculate the amount of stone needed for the edging around the pool. By knowing the total distance around the pool, Brianna's parents would have a good estimate of how much stone they need to buy for the edging, which is typically sold by the linear foot.
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The complete question is:
In the backyard, Brianna's parents constructed a swimming pool. The pool's circumference, according to Brianna, is 120 feet.
40 Ft
20 Ft
1. Is she correct? Explain why or why not. (You must mention the following in your explanation: If she is right, demonstrate the steps she took to determine the pool's circumference. Determine the right distance and demonstrate all effort if she is mistaken.)
2. So that her parents will know how many feet of stone to purchase for the pool's edging, describe (using words this time) how Brianna would calculate the distance around the pool.
There are 2.75 ounces of cream cheese in one slice of cheesecake. How
many ounces are there in a cake with 8 slices?
A. 22 ounces
B. 21.6 ounces
C. 16 ounces
D. 10.75 ounces
Answer:
Step-by-step explanation:
2.75 x 8 = 22
3cos²∅ (1+tan²∅) = 3
Answer:
Reflection Paper on "Freedom Riders"
Ankit Mishra
title movie
freedom riders
instructions create a reflection paper that summarize the documentary and how brougth about social changes and lead to the Civil rigths act of 1964
please help me
2,3 pages
Please read the instructions please I need your help watch the movie and the instructions
Reflection Paper on "Freedom Riders" Documentary
The "Freedom Riders" is a powerful documentary that recounts the story of a group of civil rights activists who rode buses across the American South in 1961 to challenge the segregated public transportation system. The film provides a vivid and moving account of their journey and the challenges they faced along the way, from beatings and arrests to bombings and arson attacks. Through interviews with surviving freedom riders and archival footage, the film sheds light on the bravery and determination of these activists and the impact they had on the civil rights movement.
The freedom riders were inspired by the nonviolent protest movement led by Dr. Martin Luther King Jr. and other civil rights leaders. They believed that segregation was a moral wrong and that they had a duty to resist it through nonviolent means. Despite the danger they faced, the freedom riders refused to back down, putting their lives on the line for the cause of justice and equality.
The bravery of the freedom riders had a profound impact on the civil rights movement. Their actions galvanized support for the cause and drew national attention to the issue of segregation. The freedom rides sparked a wave of protests and civil disobedience across the South, and helped to build momentum for the passage of the Civil Rights Act of 1964. This landmark legislation banned segregation in public places and made it illegal to discriminate against someone on the basis of race, color, religion, sex, or national origin.
The "Freedom Riders" documentary serves as a powerful reminder of the sacrifices made by those who fought for civil rights in the United States. It highlights the courage and determination of the freedom riders and the impact they had on the country. It is an important film that teaches us about the past and the struggles of those who fought for justice and equality.
In conclusion, the "Freedom Riders" documentary is a powerful reminder of the sacrifices made by those who fought for civil rights in the United States. It highlights the bravery and determination of the freedom riders and the impact they had on the civil rights movement. The film serves as a testament to the power of nonviolent protest and the importance of standing up for what is right, even in the face of opposition. The lessons of the freedom riders should inspire us all to continue working towards a more just and equal society.
Ankit Mishra
3cos²∅ (1+tan²∅) = 3
This equation involves trigonometric functions and can be simplified using trigonometric identities.
Starting with the right-hand side of the equation, we have 3. On the left-hand side, we have the expression 3cos^2(θ)(1 + tan^2(θ)).
We can simplify the expression as follows:
cos^2(θ) = 1 - sin^2(θ)
and
tan^2(θ) = sin^2(θ) / cos^2(θ)
Substituting these identities into the expression on the left-hand side, we get:
3(1 - sin^2(θ))(1 + sin^2(θ) / (1 - sin^2(θ))
Expanding the product and simplifying, we get:
3
Thus, the equation is true and holds true for all values of θ.
