A. The lines with equation 3x - 4y = 6 and 3y = -4x + 9 are perpendicular
B. The lines with equation y = 1⁄2x - 7 and 6x - 12y = 24 are parallel
How do I determine if the lines are parallel or perpendicular?From the equation of lines, we can detect if they are parallel or perpendicular as follow:
Parallel lines have the same slope (or gradient). Thus, m₁ = m₂Perpendicular lines have slope that have the following property: m₁ × m₂= -1With the above information, we can obatin the answer to the questions. Details below
For question A.
We shall determine the slope of each line. This can be obtained as follow:
3x - 4y = 6
Rearrange
4y = 3x - 6
y = 3/4x - 6/4
Comparing y = 3/4x - 6/4 with y = mx + c, the slope is 3/4
3y = -4x + 9
y = -4/3x + 9/3
Comparing y = -4/3x + 9/3 with y = mx + c, the slope is -4/3
Slope (m₁) of 3x - 4y = 6 is 3/4Slope (m₂) of 3y = -4x + 9 is -4/3m₁ × m₂
3/4 × -4/3 = -1
Thus, we can say: 3x - 4y = 6 and 3y = -4x + 9 are perpendicular
For question B.
We shall determine the slope of each line. This can be obtained as follow:
y = 1/2x - 7
Comparing y = 1/2x - 7 with y = mx + c, the slope is 1/2
6x - 12y = 24
Rearrange
12y = 6x - 24
y = 6/12x - 24/2
y = 1/2x - 12
Comparing y = 1/2x - 12 with y = mx + c, the slope is 1/2
Slope (m₁) of y = 1/2x - 7 is 1/2Slope (m₂) of 6x - 12y = 24 is 1/2m₁ = m₂
Thus, we can say: y = 1/2x - 7 and 6x - 12y = 24 are parallel
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Fred earns $16.50 an hour for overtime. He worked overtime on Monday and Thursday this week. On Monday, he worked 4 hours of overtime. His total
overtime pay for the week was $123.75.
Write and solve an equation to find the number of overtime hours, h, Fred worked on Thursday.
Fred's overtime pay is $16.50 an hour. He put in extra time this week on Monday and Thursday. The equation is $123.75-4 times the x value =h and h value is 57.75 and the working hours are 3.5 hours.
Given that,
Fred's overtime pay is $16.50 an hour. He put in extra time this week on Monday and Thursday. He put in four hours of extra on Monday. He received $123.75 in overtime compensation in total for the week.
We have to determine how many overtime hours, h, Fred worked on Thursday, write an equation and solve it.
We can write the equation as
$123.75-4 times the x value =h
Here,
x value is $16.50
We get,
$123.75-4×$16.50=h
h=57.75
To check hours working
57.75/16/50
=3.5 hours.
Therefore, the equation is $123.75-4 times the x value =h and h value is 57.75 and the working hours are 3.5 hours.
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Is a triangle with vertices G(3, 2), H(8, 5), and K(0, 10) a right triangle? Justify your answer.
First you need to ubicate those vertices in a plane as follow:
Then you link the vertices with lines to form the triangle:
Knowing that a right triangle must have one angle of 90º
The answer is that yes, it is a right triangle because it has an angle of 90º in the vertice H(8,5)
Find the equation of the line that goes through the points (2, 10) and (-1, -2).
Answer:
y=4x+1
Step-by-step explanation:
Step 1: plot your points
Step 2: draw a line through them
Step 3: find the slope (RISE/RUN) = 12/3 = 4
Step 4: find the y-int = 1
y=mx+b where x and y are variables, m is the slope and b is the y-int
y = 4x + 1
Hope that helps
help needed with show work. trigonometry
Answer:
16.4 cm
Step-by-step explanation:
In a right triangle :
cosine 43 = adjacent leg / hypotenuse = 12/x
SO:
cosine 43 = 12/x then x = 12 / cos 43 = 16.4 cm
Hi can anyone help with this question? I have been stuck on this for hours
Answer:
ab = - 1
Step-by-step explanation:
GivenEquations:
1 - a tan θ = sec θ,b - cot θ = cosec θ.To find The value of abSolutionRecall the identities:
tan θ = sin θ / cos θsec θ = 1 / cos θ cot θ = cos θ/ sin θcosec θ = 1 / sin θsin² θ + cos² θ = 1(a + b)(a - b) = a² - b²Now find a and b, then find their product.
1 - a tan θ = sec θ1 - a sin θ / cos θ = 1 / cos θ cos θ - a sin θ = 1a sin θ = cos θ - 1a = (cos θ - 1) / sin θb - cot θ = cosec θb - cos θ/ sin θ = 1 / sin θb = cos θ/ sin θ + 1 / sin θb = (cos θ + 1) / sin θab = (cos θ - 1) / sin θ × (cos θ + 1) / sin θ = (cos² θ - 1) / sin² θ = - sin² θ / sin² θ = - 1what is an equation of the line that passes through the point (8,-7) and is parallel to the line x+2y=18
Answer: The equation of line parallel to given line passing through (8,-7) is:
Step-by-step explanation:
Given line is:
5x+4y=16
first of all, we have to convert the equation of given line in slope-intercept form
Dividing both sides by 4
Slope intercept form is:
The slope of given line is:
Let m1 be the slope of line parallel to given line
"The slopes of two parallel lines are equal"
The equation of line parallel to given line will be:
Putting the value of slope
Putting the point (8,-7) in the equation
Putting the value of b
Hence,
The equation of line parallel to given line passing through (8,-7) is:
What is the value of -3/15-s+ 25³ when s=-3?
Answer:
=[tex]\frac{78139}{5}[/tex]
Step-by-step explanation:
[tex]-\frac{3}{15}-(-3)+25^{3} \\=\frac{78139}{5}[/tex]
What is an equation of the line that passes through the point (-4,8)(−4,8) and is parallel to the line x+y=6x+y=6?
The equation of the line that passes through the point; (-4, 8) and is parallel to x + y = 6 as required in the task content is; x + y = 4.
What is the equation of the line that passes through the given point and is parallel to the given line?It follows that the equation of the line that passes through the given point and is parallel to the given line is to be determined.
By expressing the given linear equation in slope-intercept form; it follows that we have;
x + y = 6
y = -x + 6
Hence, the slope of the equation by comparison with; y = mx + c is; -1.
Therefore, the slope of the required equation is same as the two lines are said to be parallel.
Ultimately, the required equation from point-slope form of an equation is;
( y - 8) = -1 ( x - (-4))
y - 8 = -x - 4
x + y = -4 +8
x + y = 4.
Ultimately, the required equation is; x + y = 4.
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For each ordered pair, determine whether it is a solution to 5x + 2y = -1. (x, y) (1, − 3) (2,8) (-4, -6) (-3,7) what is the soulsion
The following ordered pairs are the solutions to 5x+2y=-1 :
(1,-3) and (-3,7)
Given we have the ordered pairs and the equation.
To find out whether the ordered pair is a solution or not, we just need to replace the x and y values from the ordered pair (x,y) and check if both the sides equate.
a. (1,-3)
5x+2y=-1
5(1)+2(-3) = -1
consider L.H.S
5-6
= -1
Therefore, L.H.S = R.H.S
hence the ordered pair (1,-3) is a solution to 5x+2y=-1.
b. (2,8)
5x+2y=-1
5(2)+2(8) = -1
consider L.H.S
10+16
= 16
Therefore, L.H.S ≠ R.H.S
hence the ordered pair (2,8) is not a solution to 5x+2y=-1.
c. (-4,-6)
5x+2y=-1
5(-4)+2(-6) = -1
consider L.H.S
-20-12
= -32
Therefore, L.H.S ≠ R.H.S
hence the ordered pair (-4,-6) is not a solution to 5x+2y=-1.
d. (-3,7)
5x+2y=-1
5(-3)+2(7) = -1
consider L.H.S
-15+14
= -1
Therefore, L.H.S = R.H.S
hence the ordered pair (2,8) is a solution to 5x+2y=-1.
Therefore the ordered pairs which are solutions to 5x+2y=-1 are:
(1,-3) and (-3,7)
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2. Each year a certain amount of money is deposited in an account which pays an
annual interest rate of r so that at the end of each year the balance in the account is
multiplied by a growth factor of x = 1+r. $500 is deposited at the start of the first
year, an additional $200 is deposited at the start of the next year, and $600 at the
start of the following year.
a. Write an expression for the value of the account at the end of three years in
terms of the growth factor x.
b. What is the amount (to the nearest cent) in the account at the end of three
years if the interest rate is 2%?
3. Consider the polynomial function p given by p(x) = 5x³ + 8x²-3x + 1. Evaluate the
function at x = -2.
Answer:
2a. ((500x +200)x +600)x
2b. $1350.68
3. -1
Step-by-step explanation:
2. You want to know the balance in an account at the end of 3 years with deposits at the beginning of successive years being $500, $200, and $600, and with deposits having an annual growth factor of x. You want (a) an expression for the balance in terms of x, and (b) the balance when x=1+2%.
3. You want the value of p(-2) for p(x) = 5x³ +8x² -3x + 1.
2. Account Balancea. Expression$500 is deposited at the beginning of the first year. The problem statement tells us that this has been multiplied by growth factor x by the end of the year, so the balance at that point is 500x.
At the beginning of the second year, $200 is added to the account, and the entire amount is multiplied by the growth factor for the year. That makes the balance at the end of the second year be ...
(500x +200)x
Then $600 is added, and again the account grows by a factor of x. At the end of the third year, the balance is ...
balance = ((500x +200)x +600)x
b. Balance for r=2%The growth factor is given as x = 1 +r. When r = 2%, this becomes x = 1.02. Then the balance at the end of year 3 is ...
((500·1.02 +200)·1.02 +600)·1.02 = 1350.68
The amount in the account at the end of three years is $1350.68.
__
3. Polynomial valueThe value of p(x) = 5x³ +8x² -3x +1 for x=-2 is found by substituting -2 where x is found. Evaluation can be easier by rewriting the polynomial to Horner form:
p(x) = ((5x +8)x -3)x +1
p(-2) = ((5(-2) +8)(-2) -3)(-2) +1 = ((-2)(-2) -3)(-2) +1 = (1)(-2) +1 = -1
The value of the function for x=-2 is -1.
__
Additional comment
You will note that the expression in problem 2 is also written in Horner form. If it were expanded, it would be 500x³ +200x² +600x. Evaluation takes fewer steps when Horner form is used.
HI NEED THIS ASAPP GRAOHS OF INVERSE FUNCTIONS
Answer: D (last bubble)
Step-by-step explanation:
slope of f is 2/3
inverse of 2/3 is 3/2
that is graph h
these graphs are symmetrical around the line y = x
what set of numbers dose -17 belong to?
A. integers, rational numbers, real numbers
B. rational numbers, real numbers
C. whole numbers, integers, real numbers
D. whole numbers, integers, rational numbers, real numbers
A
-------------------------------------------------------
bc it is an integer but not whole numbers
Write an algebraic expression that matches Six less than a number
ANSWER
x - 6
EXPLANATION
We want to write an algebraic expression that matches the statement:
Six less than a number.
First, let that unknown number be x.
So, 6 less than x.
Since it means that we are taking 6 from x, we subtract 6 from x.
That will be:
x - 6
Solve z3 = 8.
answers are
z = −4
z = 4
z = ±2
z = 2
Answer:
I'll assume z3 is actually z^3
z = 2
Step-by-step explanation:
z*z*z = 8
(2)*(2)*(2) = 8
find the volume of this triangular prism
Answer:
The volume would be [tex]396cm^3[/tex].
Step-by-step explanation:
Answer:
792 cm
Step-by-step explanation:
99*8
What is the equation of the line?
Answer:
Thr equation is y=x-1
Step-by-step explanation:
The y intercept is negative 1 so that eliminates options 1 and 3 and the slope goes up which leaves only option 2 left
The directions on a seed packet say to plant the seeds 1 7/8 inches apart. What is the decimal equivalent of this mixed number?
Enter your answer in the box.
Answer:
1 7/8 inches is 1.875 in decimal form.
Prove the identity.
(csc²x - 1) secx = cosx csc x
Sanjay a is making punch. he uses 1/3 c of pineapple juice for every 3/4 c of orange juice. how many cups of pineapple juice does he need if he uses 3 c of orange
Sanjay a is making punch. he uses 1/3 c of pineapple juice for every 3/4 c of orange juice Then 4/3 cups of pineapple juice does he need if he uses 3 c of orange
equation of direct proportion between x and y
x1/y1 = x2/y2
as per given ,
let x= quantity of pineapple juice and y= quantity of orange juice
x1= 1/3 , y1 = 3/4
x2 = ? and y2 =3
x1/y1 = x2/y2
(1/3)/ (3/4) = x2/3
4/9= x2 /3
4/3 = x2
Hence ,Sanjay a is making punch. he uses 1/3 c of pineapple juice for every 3/4 c of orange juice Then 4/3 cups of pineapple juice does he need if he uses 3 c of orange
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You want to sample our class. You split the class by gender and select 5 students of each gender. What type of sample is this?
this type of sample is called fractions
Step-by-step explanation:
Andrew would like to put six different Rubik's cubes onto 3 shelves. The order of the cubes does not matter.
In how many ways can Andrew do this if a shelf can have zero cubes?
What if each shelf must have at least one cube?
Answer:
540
Step-by-step explanation:
helpppp meeee pleaseee
For Items 12–14, use the figure shown.
Two vertical parallel lines are intersected by two diagonal transversals, one slanting up and one slanting down. They intersect the left line at the same point, creating 6 angles, starting at the bottom left of the right line and moving clockwise, they are: 3, 2, 1, left parenthesis 4 y times 3 right parenthesis, left parenthesis 3 x times 9 right parenthesis, and left parenthesis 5 x right parenthesis. The line slanting up intersects the right vertical line creating 4 angles, starting at the bottom left and moving clockwise, they are: 6, 4, 5, and left parenthesis 9 x times 3 right parenthesis. The line slanting down intersects the right vertical line creating 4 angles, starting at the bottom left and moving clockwise, they are: 8, 7, left parenthesis 7 y times 6 right parenthesis, and 9.
What is m∠2?
A. 12
B. 18
C. 45
D. 120
Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.
Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.
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Write a story about temperatures that this expression could represent: 27+(-11)
Draw a number line diagram and write an expression to represent this situation: “On Tuesday at lunchtime, it was 29ºC. By sunset, the temperature had dropped to 16ºC.”
(this is summit learning btw)
The temperature “On Tuesday at lunchtime, it was 29ºC
i.e., 29 - 16.
Given,
Write a story about temperatures that this expression could represent:
27+(-11)
Now, According to the question:
1. The temperature is 27 degree C in the morning and reduced 11 degree C in the evening , the difference in temperature is 27 + (-11)
2. “On Tuesday at lunchtime, it was 29ºC. By sunset, the temperature had dropped to 16ºC.”
Again, Similarly
= 29 - 16
About Number line,
Draw a number line and allocate a point 16 degree C on the left side
and, 29 allocate a point on the right side.
Hence, The temperature “On Tuesday at lunchtime, it was 29ºC
i.e., 29 - 16.
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To win a trivia game, Nevan must score 90 points.
Each correct answer is worth 1 3/4 points, and each incorrect answer is worth −1/4 points.
If he gets 58 questions correct and 22 questions incorrect, does Nevan win? How many points does he score?
Answer: no he does not win he got 67 points not 90 or more
Step-by-step explanation:
What is x^3 pls help
Answer:
its x^3 or 1
Step-by-step explanation:
there's nothing else you can do with it
also it might be 1 because x by itself is 1 so x^3 is considered 1^3
Janell is standing on a set of bleacher and throws a ball in the air at an initial velocity of 35 ft/s. The height of the ball, h, at t seconds is modeled by the equation h=-16t^2+35t+6. How many seconds will it take the ball to reach the ground?
The time taken by the ball to reach the ground is 0.067 seconds
Given,
The initial velocity of the ball (speed) = 35 feet/second
The height of the ball (distance), h = -16t² + 35t + 6
We have to find the time, (t in seconds) taken by the ball to reach the ground.
Speed = distance/time
So, Time = distance/speed
Here,
Time = (-16t² + 35t + 6) / 35
We have to solve the equation first.
-16t² + 35t + 6 = 0 is in quadratic form. So, we can solve this by using quadratic formula.
Quadratic formula = [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Here,
a = -16, b = 35, c = 6
Now,
[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
= [tex]\frac{-35(+-)\sqrt{35^{2}-4(-16)(6) } }{2(-16)}[/tex]
= [tex]\frac{-35(+-)\sqrt{1225 +384} }{-32}[/tex]
= (-35±√1609) / -32
= (-35±40.11) / -32
Now,
Solve for:
(-35 + 40.11) / -32 = 5.11/-32 = -0.15
Solve for
(-35 - 40.11) / -32 = -75.11 / -32 = 2.35
Lets take the height as 2.35 feet.
Now,
Time = distance/speed
Time = 2.35/35 = 0.067
Therefore, the time taken by the ball to reach the ground is 0.067 seconds.
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Please do number one please thank you
Answer:
Step-by-step explanation:
Hypothesis: you live in a state that borders California
:]
Ellos ____ en la casa. (To express location)
Answer: Estan
Step-by-step explanation: I know spanish
Question 4 (10 point)
Answer:
25
Step-by-step explanation:
25 is the square root of 625
Answer:
25
Step-by-step explanation:
[tex]\sqrt{625} = \sqrt{25^{2} } = 25[/tex]