Suppose we are given the following.
Line 1 passes through (-3, 8) and (0,4).
Line 2 passes through (4, 4) and (-4,-2).
Line 3 passes through (4, 1) and (8,4).
(a) Find the slope of each line.
Slope of Line 1-
Slope of Line 2-
Slope of Line 3-0
(b) For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2: OParallel
Line 1 and Line 3:
OParallel
Line 2 and Line 3:
OParallel
Operpendicular ONeither
Operpendicular
ONeither
OPerpendicular
Neither
Answers
Slope of line 1 is -4/3, slope of line 2 is 3/4, slope of line 3 is 3/4, and Line 1 and Line 2 are perpendicular, Line 1 and Line 3 are also perpendicular, Line 2 and Line 3 are parallel.
What is slope of a line?
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate points and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates on a line in order to determine its slope.
Slope of a line can be calculated using the formula:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here, m = slope and (x1, y1), (x2, y2) are two points on the line,
Calculating the slope of line 1 whose points are (-3, 8), (0, 4)
[tex]m = \frac{4 - 8}{0 - (-3)}[/tex]
m = -4/3
Calculating the slope of line 2 whose points are (4, 4), (-4, -2)
[tex]m = \frac{-2 - 4}{ -4 - 4}[/tex]
m = 3/4
Calculating the slope of line 2 whose points are (4, 1), (8, 4)
[tex]m = \frac{4 - 1}{ 8 - 4}[/tex]
m = 3/4
Now we know that if lines are parallel that their slope is equal and when lines are perpendicular the product of their slope is -1,
Therefore, Line 1 and Line 2 are perpendicular, Line 1 and Line 3 are also perpendicular, Line 2 and Line 3 are parallel.
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Related Questions
Mrs. Jones put this extra credit problem on the board and asked to determine the missing
length of the side of this parallelogram. What answer should the students come to?
2x+10
5x- 20
4x-1
Answers
The length of the missing side is 39 units
What is parallelogram:The parallelogram is a simple 2D-shaped quadrilateral with two pairs of parallel sides. In a parallelogram, the opposite sides and opposite angles are equal.
Here we have,
The length of the sides of a parallelogram is 2x+10, 5x- 20 and 4x-1
As we know parallel lines of a Parallelogram are equal
Take any two sides as equal and find the missing side
Let the sides with lengths be equal 2x+10, 5x- 20
=> 2x+10 = 5x- 20
=> 5x - 2x = 20+ 10
=> 3x = 30
=> x = 10
Therefore, the lengths of the 3 sides are
2x+10 = 2(10) + 10 = 30
5x- 20 = 5(10) - 20 = 30
4x-1 = 4(10) - 1 = 40 - 1 = 39
The length of the missing side is 39 units
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of the grid is blank?
bers, insert a less-than symbol (<), a greater-than symbol
pol (=) between the numbers to make a true statement.
b. 0.123 2 0.1002
Answers
0.123 < 2 > 0.1002, is the true statement after inserting symbols.
What is greater than symbol refer?
In mathematics, the larger than sign is used between two numbers to indicate that the first number is greater than the second. For instance, 10 > 5. 10 is more than 5 in this case.The greater than symbol, which consists of two strokes of equal length joined at an acute angle at the right, is always pointed toward the greater value in inequality. ( >).What is lesser than symbol refer?
In a situation when one number is less than another, a less than symbol is positioned between the two numbersWhen referring to an inequality, the less than symbol () represents the smaller value where two strokes of equal length meet at a sharp angle on the left.The reader may easily understand the message thanks to the larger than less than sign, which also decreases the time complexity.What is equal to symbol refer?
The "equal to" symbol is used to indicate that two numbers or values are equal. The greater than and less than signs are in conflict with this one. We employ the equal to symbol even while writing equations. '=' is used to indicate it.Hence, 0.123 < 2 > 0.1002, is the true statement after inserting symbols.
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the graph of a linear function is shown . which word describes the slope of the line
Answers
The slope of the line is 1/5 which is positive.
From the graph:
slope:
Slope is the steepness of a line as it moves from LEFT to RIGHT. Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line. The slope of a line is always constant (it never changes) no matter what 2 points on the line you choose.
Take any points:
(0,0) and (5,1)
slope m = y2 - y1 / x2 -x1
= 1 - 0 / 5 - 0
= 1/5
Therefore the slope of the line is 1/5 which is positive.
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There are
215 cars infront of the mall if each car has 4 wheels estimate the number of wheels infront of the mall round to nearest hundred
Answers
Answer:
It should be 860
Step-by-step explanation:
if there are 215 cars and each have 4 wheels, it should be 215 x 4 = 860
The perimeter of a rectangle is 30 cm. Its width is 3 cm. Which equation can represent the perimeter of the rectangle if L= length? (please explain how you got the answer)
A.) 3 + L = 30
B.) 3L = 30
C.) 6 + 2L = 30
D.) 6L = 30
Answers
The equation that can represent the perimeter of the given rectangle is
6 + 2L = 30, option c is correct.
Given,
width of rectangle = 3 cm
length of rectangle = L
perimeter of rectangle = 30 cm
equation of perimeter of rectangle = 2 × (L + W)
By substituting the values of width and perimeter we can get the equation,
perimeter = 2 × (L + W)
=> 30 = 2 × (L + 3)
=> 30 = 2L + 6
=> 6 + 2L = 30
Therefore, the equation of the perimeter of a rectangle is 6 + 2L = 30.
HELPPPP :Solve for x. (23x-3) degrees and 78 degrees
Arc & Angle measure formed by Chords, Secants, & Tangents
Answers
The value of x in the intersecting chords SP and PB is determined as 3.52.
What is the value x?The value of x is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.
arc SB = m∠SPB
From the diagram, we have arc SB = 78⁰
m∠JNK = 78 (interior angles of intersecting secants)
23x - 3 = 78
23x = 78 + 3
23x = 81
x = 81/23
x = 3.52
Thus, the value of x in the intersecting chords SP and PB is determined as 3.52.
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question a fair die with its faces numbered from 1 to 6 will be rolled. which of the following is the best interpretation of the probability that the number landing face up will be less than 3 ? responses for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 13. for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is one third . for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 12. for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is one half . for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 23. for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is two thirds . for three rolls of the die, a number less than 3 will land face up one time. for three rolls of the die, a number less than 3 will land face up one time. it will take three rolls of the die before a number less than 3 lands face up for the first time.
Answers
For many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.
Given that,
Only two integers (1 and 2) are smaller than 3, hence their relative frequency will be 2/6=1/3.
The best way to interpret the data is thus,
For many rolls of the die, the long- run relative frequency of a number less than three landing face up is1/3.
Hence option A is correct which is for many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.
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Need help please!
14. Write an equation of a line that is parallel to the line 2x – 3y = 6. Explain how you know that the graph of
your equation is parallel to 2x – 3y = 6.
15. A student drew the line y = 2x + 3
a. Write equations for two lines that are perpendicular to this line. Justify your answer.
b. What do you notice about the slopes of these two lines? What generalization can you make about two lines
that are both perpendicular to the same line?
Answers
Answer:
Step-by-step explanation:
14. y = -2/3x + 10. This is parallel to 2x -3y because they have the same slope.
15. y = -1/2x and y = -1/2x + 2. These are perpendicular because the slope is the opposite reciprocal to the slope of y = 2x + 3, which is 2.
The slopes of the lines of the 2 equations are the same. Because of that, we can state that 2 lines that are perpendicular to the same line are parallel. This can be further supported by the Perpendicular Transversal Theorem, which says the same thing.
Hope this helps!
the correlation between variables x and y is .50. You compute a least squares regression line wit this bivariata data. Which of the following is true?
a. the r^2 is greater than .50
b. the regression constant is positive
c. the regression coefficient is positive
d. the slope of the regression line is negative
e. all of the above
Answers
The correlation between variables x and y is 0.50 . The true option is option (c) .
that's the regression coefficient is positive for given bivariata.
Correlation: Correlation is a statistical measure of how linearly two variables are related (meaning they change together at a constant rate). The
sample correlation coefficient r quantifies the strength of the relationship.
Correlation Coefficient: The Correlation Coefficient formula is used to examine the strength of the relationship between data. The formula returns a value between -1 and 1.
Here:
1 indicates a strong positive relationship.-1 indicates a strong negative relationship.A result of zero indicates no relationship at allPearson's correlation coefficient is denoted by "r" and is
r = (n∑xy - ∑x∑y )/√( n ∑x² - (∑x )² ) ( √ n∑y² - (∑y)²)
We have given that correlation between x and y is 0.50.
cor(x,y) = √r^2 => √r^2 = 0.50 => r ^2 = (0.50)^2
=> r^2 = 0.25 > 0 but less than 0.50 ---( 1)
Regression coefficient is the constant "b" in the regression equation that gives the change in the value of the dependent variable equal to the unit change in the independent variable.
Symbolically it can be expressed as:
bₓᵧ= r σ ₓ /σ ᵧ
where x and y are correlated
σ ₓ --> standard deviation of X
σᵧ ---> standard deviation of y
We know that standard deviations is square root value of variance of observations. we also know square root any quantity is always positive or zero.
Using the above fact about standard deviations and correlation coefficient (r) is also positive we see that bₓᵧ is postive.
Hence, Regression cofficient is positive.
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pluto is the furthest planet in our solar system and moves in an orbit at an average of 5900 million km from the sun. find this distance in standard form.
Answers
Answer: 5.9 × 10 to the power of 9
2. Choose the correct answer.
Which theorem, term, or corollary is represented by the picture? The bold lines in the pictures represent the hypothesis of the theorem or corollary.
CPCTC
Corollary 1 to the Isosceles Triangle Theorem
Corollary 2 of the Isosceles Triangle Theorem
Isosceles Triangle Theorem
Converse to the Isosceles Triangle Theorem
Answers
The theorem (A) CPCTC represents the given condition of the triangle.
What is CPCTC?According to the formula CPCTC, which stands for "corresponding portions of congruent triangles are congruent," if two or more triangles are congruent, their corresponding angles and sides must also be congruent.
When demonstrating the congruence of triangles or other shapes, the term CPCT is employed.
When a student is asked to demonstrate that two angles or two sides are congruent, CPCTC is frequently employed at the end of the proof or close to it.
So, in the given triangle:
The angles are bold and the lines are not bold.
This represents that it is proved first that the angles are congruent.
And through CPCTC, we are concluding that the sides of the triangles are also congruent.
Therefore, the theorem (A) CPCTC represents the given condition of the triangle.
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a painter leans a ladder against a vertical wall. the top of the ladder is 15 meters above the ground. when the bottom of the ladder is moved 3 meters farther away from the wall, the top of the ladder is 11 meters above the ground. what is the length of the ladder? round to the nearest hundredth of a meter.
Answers
From the ground the length of the ladder is 15 feet.
Step-by-step explanation:
From the Pythagorean Theorem, the situation described can be expressed mathematically as:
x² +9² = (x+3)²
or,
x² + 81 = x² + 6x + 9
Now, cancelling equal terms on either side of the equation and reducing gives:
x = 12
Since the ladder is defined to be 3 feet longer than the distance of its foot to the wall the ladder’s length must be:
12 feet + 3 feet
=15 feet
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factor -1/2 out of 1/2x+6.
Answers
Answer:
-1/2(x - 12). Hope this helped out for you!
which of the following is not needed to determine the minimum sample size required to estimate a population proportion?
a. Standard Deviation
b. Margin of Error
c. α
d. z α/2
Answers
Answer:
Step-by-step explanation:
margin of error
in the moring the temputure starts out around 50 F As the day gose on the temperature rises first slowly then more quickly it stays constant for an hour before droping slowly select the graph that best represents this description
Answers
express the interval shown on the number line in inequality notation.
Answers
The given interval shown on the number line in inequality notation as (3, 6).
What are inequalities on a number line?
Inequalities on a number line allow us to visualise the values that are represented by an inequality.
To represent inequalities on a number line we show the range of numbers by drawing a straight line and indicating the end points with either an open circle or a closed circle.
An open circle shows it does not include the value.
A closed circle shows it does include the value.
The left endpoint is 3. The right endpoint is 6. Both endpoints are open holes, meaning we do not include them as part of the green shaded solution region. If x is a solution, then the solution can be described as
3 < X < 6 which converts to the interval notation (3, 6) . The curved parenthesis says "do not include the endpoint".
Note: this is not ordered pair notation (x,y).
The given interval shown on the number line in inequality notation as (3, 6).
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You have a summer job that pays time and a half for overtime. That means if you work
more than 40 hours in a week, your hourly wage for the extra hours is 1.5 times your
rate of $12 per hour.
How much will you get paid if you work 47 hours?
Answers
You have a summer job that pays time and a half for overtime. That means if you work more than 40 hours in a week, your hourly wage for the extra hours is 1.5 times your rate of $12 per hour.
If you work for 47 hours you will get paid $606.
Define overtime. What does overtime pay mean?
The amount of time spent working past the regular working day is known as overtime. The word is also applied to the compensation for this period of extra time.
Employees covered by the Act must receive overtime compensation, unless they are exempt, at an overtime rate that is at least time and a half their usual rates of pay for hours worked beyond 40 in a workweek.
Solution Explained:
Given,
Normal rate = $12 per hour
Overtime rate = 1.5 times more than the normal rate per hour
= (15 X 12) / 10 = $18 per hour
First we will see the normal total pay for 40 hours
= 40 X 12 = $480
The overtime pay = 7 X 18 = $126
Therefore, the pay for 47 hours is = 126 + 480 = $606
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Yo! Please quickly help me solve this! Select the equivalent expression (2^5/x^2)^4
( Would give more points if I had more, but THANK YOU!! )
Answers
Answer:
(2⁵/x²)⁴
(32/X²)
32⁴+x⁶
1,048,576 + X⁶
Step-by-step explanation:
i don't know if this is right. this is all I know
Compare -2.655 and 4 square root
Answers
Answer:
-2.655 < -√4
Step-by-step explanation:
-√4 = -2
-2.655 < -2
I assume that's what the question is asking for?
Charlie is making copies of fliers to advertise his new club at school. The cost for 25 copies is $3.75. What is c, the total cost Charlie will pay for 40 copies?
Answers
The total cost for Charlie to make 40 copies of flyers is $6
Given the fact that 25 copies of flyers is costing him $3.75, we will then need to find the cost of each copy of the flyer. The figure is calculated using unit rates as follows:
25x = 3.75
x = 3.75/25
x = 0.15
so each copy of a flyer will cost him $0.15
To make 40 copies of flyers, Charlie will need to spend:
$0.15 × 40 = $6
So the amount of money Charlie will have to spend in order to make a copy of 40 flyers is $6
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Answer: Charlie will pay 6$.
Step-by-step explanation:
Select all the equations equivalent to
6x9=12
a )2x + 3 = 4
B)0x + 9 = 6
C)6x + 12 = 9
D) 3= 2x + 4
E)3x + 9 = 6
F)6x=3
Answers
Equation which is equivalent to the given equation 6x + 9 = 12 is given by 2x + 3 = 4.
As given in the question,
Given equation is equal to :
6x + 9 = 12
Simplify by writing each number into prime factors of the given equation 6x + 9 =12 to get the equivalent equation,
( 2 × 3 )x + ( 3 × 3 ) = ( 2 × 2 × 3 )
3 is the common factor in all we get,
3 ( 2x + 3) = 3(4)
Divide by 3 both the side of the equation we get,
2x + 3 = 4
Therefore, equation which is equivalent to the given equation 6x + 9 = 12 is given by 2x + 3 = 4.
The complete question is:
Which equation is equivalent to the equation 6x + 9 = 12?
A. x +9=6
B. 2x + 3 = 4
C. 3x + 9 = 6
D. 6x + 12 = 9
E. 6x = 3
F. 3 = 2x + 4
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Tori and her two best friends are all dressing up as superheroes for Halloween
this year. Their costumes are almost ready, but each person still needs to
make a cape. If each cape uses 4 feet of cloth, how many yards of cloth will
they use for the 3 capes?
Answers
Answer:
4×3=12
Step-by-step explanation:
that is the answer
Factor each of the following.
x^3−8=0
Answers
Answer:
(x - 2)(x² + 2x + 4) = 0
Step-by-step explanation:
x³ - 8 ← is a difference of cubes and factors in general as
a³ - b³ = (a - b)(a² + ab + b²) , then
x³ - 8
= x³ - 2³
= (x - 2)(x² + 2x + 2²) = (x - 2)(x² + 2x + 4)
Find the equation of the parabola with the given x-intercepts and point on the graph. Use y = a(x-p)(x-q).
2. x-int: (-4,0) , (-10, 0)
P (-6,-12)
Answers
Answer:
y = 1.5(x + 4)(x + 10)=========================
Givenx- intercepts (-4, 0) and (-10, 0),Point P (- 6, - 12).SolutionThe given translates as:
p = - 4, q = - 10, x = - 6, y = - 12Use given x - intercepts to get the equation:
y = a(x + 4)(x + 10)Use the coordinates of P to find the value of a:
- 12 = a(-6 + 4)(-6 + 10)- 12 = a*(-2)*4- 12 = - 8aa = - 12 / - 8a = 1.5The equation of this parabola is:
y = 1.5(x + 4)(x + 10)Answer:
[tex]\textsf{Intercept form}: \quad y=\dfrac{3}{2}(x+4)(x+10)[/tex]
[tex]\textsf{Standard form}: \quad y=\dfrac{3}{2}x^2+21x+60[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
If the x-intercepts are (-4, 0) and (-10, 0) then:
p = -4q = -10Substitute the values of p and q into the formula:
[tex]\implies y=a(x-(-4))(x-(-10))[/tex]
[tex]\implies y=a(x+4)(x+10)[/tex]
To find a, substitute the given point on the curve P (-6, -12) into the equation:
[tex]\implies -12=a(-6+4)(-6+10)[/tex]
[tex]\implies -12=a(-2)(4)[/tex]
[tex]\implies -12=-8a[/tex]
[tex]\implies a=\dfrac{-12}{-8}[/tex]
[tex]\implies a=\dfrac{3}{2}[/tex]
Substitute the found value of a into the equation:
[tex]\implies y=\dfrac{3}{2}(x+4)(x+10)[/tex]
Expand to write the equation in standard form:
[tex]\implies y=\dfrac{3}{2}(x^2+14x+40)[/tex]
[tex]\implies y=\dfrac{3}{2}x^2+21x+60[/tex]
HELLLLPPP WILL GIVE BRAINLIST HELP PLEASE DUE SOON
Answers
Rahul invested $1,100 in an account paying an interest rate of 3 3/8% compounded
quarterly. Caleb invested $1,100 in an account paying an interest rate of 3 1/4%
compounded daily. After 8 years, how much more money would Rahul have in his
account than Caleb, to the nearest dollar?
Answers
Answer:
$13
Step-by-step explanation:
You want to know how much more Rahul's investment of $1100 at 3 3/8% compounded quarterly for 8 years is worth than Caleb's investment of $1100 at 3 1/2% compounded daily for 8 years.
Rahul's accountThe amount in Rahul's account is given by ...
A = P(1 +r/n)^(nt) . . . . . P invested at rate r compounded n times per year
A = $1100(1 +0.03375/4)^(4·8) = $1100(1.0084375^32) ≈ $1439.33
Caleb's accountThe same formula is used for Caleb's account, but with different numbers.
A = $1100(1 +0.0325/365)^(365·8) ≈ $1426.61
DifferenceThe difference in account values is ...
Rahul's - Caleb's = $1439.33 -1426.61 = $12.72 ≈ $13
Rahul will have about $13 more in his account.
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What is the first time after 1 PM at which the inute hand and hour hand of a clock point in exactly opposite directions?
Answers
Answer:
9 : 30
Step-by-step explanation:
1 PM - 1 hour = 12 PM
12 PM - 2 hours = 10 PM
10 PM - 20 minutes = 9 : 40
9 : 40 PM - 10 minutes = 9 : 30 PM
So, it is 9 : 30 PM
Given that y varies directly as x, write an equation
for the relationship if y=-4 when x=10.
A) y=-4x+10
B) y=-0.4x
C) y=0.4x
D) y=-2.5x
Answers
X^2 - x - 6 simplified
Answers
(02.04 MC)
(Multiple Choice Worth 2 points)
For the function f(x) = -(x + 1)² + 4, identify the vertex, domain, and range.
O The vertex is (-1, 4), the domain is all real numbers, and the range is y ≥ 4.
O The vertex is (-1, 4), the domain is all real numbers, and the range is y ≤ 4.
O The vertex is (1, 4), the domain is all real numbers, and the range is y ≥ 4.
O The vertex is (1, 4), the domain is all real numbers, and the range is y ≤ 4.
Answers
The vertex is (-1, 4), the domain is all real numbers, and the range is y ≤ 4.
What are the domain and range of a function?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
if you use the foil method it will come out to -(x^2+2x+1)+4. then distribute the negative and simplify the equation (add the four) the equation comes out to be -x^2-2x+3.
The vertex is at -b/(2A).
The vertex is at x=2/(2*-1), which is -1. plug -1 into the original equation to find y, (y=-(-1)^2-2*(-1)+3) which is y=4. so the vertex is at (-1,4).
since the parabola opens down (negative a value) and has a maximum at 4, y is always less than or equal to 4. x is all real numbers as it goes on forever. so b is your answer.
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