Answer:
m = -5/4
General Formulas and Concepts:
Algebra I
The slope of the perpendicular line is the negative reciprocal of the original slope.
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Slope-Intercept Form (Original): y = 4/5x + 9
Step 2: Break Original Function
Slope m = 4/5
y-intercept b = 9
Step 3: Find slope of perpendicular line
Take the negative reciprocal.
Perpendicular Slope m = -5/4
The line segment joining the points ( 3,-4) and (1,2) is trisected at the points P and Q . If the coordinates of P and Q are (p , -2 ) and ( 5/3 , q ) respectively, find the values of p and q.
Answer:
P = 7/3 and q = 0
Step-by-step explanation:
The given parameters are;
The endpoints of the segment are, (3, -4) and (1, 2)
The points that trisect the given points are P and Q with coordinates (p, -2) and (5/3, q) respectively
Therefore, we have;
The first point of the trisection cuts 1/3 of the length from one point and the second point of the trisection cuts 2/3 of the length from the same point
The coordinates of P or Q = (3 - (3 - 1)/3, -4 - (-4 - 2)/3) = (7/3 , -2)
Therefore, given that the y-coordinate value of the derived point coincides with the y-coordinate value of the point P, (p, -2) and there is only one point with x = -2 on the line, we have that the coordinate of the point P is (p, -2) = (7/3 , -2)
∴ P = 7/3
Similarly we have the second point of the trisection, Q, given as follows;
We are already given the x-coordinate value of the point Q as the 5/3 in (5/3, q)
Point Q = (5/3, q) = (3 - 2×(3 - 1)/3, -4 - 2×(-4 - 2)/3) = (5/3 , 0)
Point Q = (5/3, q) = (5/3 , 0)
∴ q = 0.
plz help
Simplify:
- 1.2+15.45
Answer:
- 1.2+15.45=14.43
Step-by-step explanation:
In a video game, two objects move around the screen according to the equations r = 4cos(0) and r= -1 +
2cos(0). Which coordinates represent a possible collision point of the objects?
Answer:
The correct option is;
[tex]\left ( -2,\dfrac{2 \cdot \pi }{3} \right)[/tex]
Step-by-step explanation:
The given parameters are
The equation of motion of one (the first) object is r = 4·cos(θ)
The equation of motion of the other (the second) object is r = -1 + 2·cos(θ)
Equating both equations gives;
4·cos(θ) = -1 + 2·cos(θ)
4·cos(θ) - 2·cos(θ) = -1
2·cos(θ) = -1
cos(θ) = -1/2
θ = Arccos(-1/2) = 120° = 2·π/3
Therefore, the two equations are equal when θ = 2·π/3 for which we have;
r = 4·cos(2π/3) = -2 and r = -1 + 2·cos(2π/3) = -2
∴ r = 4·cos(2π/3) = -1 + 2·cos(2π/3) = -2
The coordinate that represents a possible collision point of the objects in the form (r, θ) is therefore [tex]\left ( -2,\dfrac{2 \cdot \pi }{3} \right)[/tex]
Hence, The coordinate that represents a possible collision point of the objects in the form (-2, [tex]\frac{2\pi }{3}[/tex])
Given that ,
The first object is moving around the screen r = 4 cos(0)
The second object is moving around the screen r = -1 + 2cos(0)
We have to find ,
The coordinates represent a possible collision point of the objects.
According to the question,
Coordinate represent collision points to object ,
Equating both equations ;
4·cos(θ) = -1 + 2·cos(θ)
4·cos(θ) - 2·cos(θ) = -1
2·cos(θ) = -1
cos(θ) = -[tex]\frac{1}{2}[/tex]
θ = [tex]cos^{-1} (\frac{1}{2} )[/tex] = 120°
[tex]\theta[/tex] = [tex]\frac{-2\pi }{3}[/tex]
Therefore, the two equations are equal when θ = [tex]\frac{2\pi }{3}[/tex]
We have;
r = 4·cos([tex]\frac{2\pi }{3}[/tex]) = -2
And r = -1 + 2·cos([tex]\frac{2\pi }{3}[/tex]) =
r = -2
r = 4·cos([tex]\frac{2\pi }{3}[/tex]) = -1 + 2·cos([tex]\frac{2\pi }{3}[/tex])
r = -2
The coordinate that represents a possible collision point of the objects in the form (r, θ) is therefore r = -2 and [tex]\theta = \frac{2\pi }{3}[/tex] .
Hence, The coordinate that represents a possible collision point of the objects in the form (-2, [tex]\frac{2\pi }{3}[/tex]) .
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An amount P at 6% for 5 years compounded monthly increased to $15000.00. What is P? (Round answer to cents)
Answer:
$20,232.75
Step-by-step explanation:
I hope it helped
If 40 percent is 240 what is 25 percent
Answer:
150
Step-by-step explanation:
maybe it could be like this
0.40x = 240
we could get x = 600
then 0.25x = 600 × 0.25 = 150
You are ordering planks of
wood that are 8' long each.
You need 15 pieces cut 3' long,
and 9 pieces cut 4' long. How
many planks of wood should
you order?
you need 10 8' planks of wood because 15x3= 45+9x4= 77, then 77÷8= 9.625, but you can't get .625 of a plank, so 10. hope you get a good grade!
dillon pays x dollars to get a haircut.he gives the stylist a 20% tip the expression representing his total cost is x + 0.2x
Answer:
[tex]y=x+0.2x[/tex]
Step-by-step explanation:
Step one:
given data
we are told that Dillon paid $x for a haircut.
and gave a tip of 20% of the amount he paid, this is expressed as
=20/100*x
=0.2x
Let the total amount he paid, that is haircut plus tip be y
the expression for the total amount is
[tex]y=x+0.2x[/tex]
here x represents the amount he paid
0.2 represents 20% of the haircut
2x+3=6x-5 Solve the eqution
Answer:
2
Step-by-step explanation:
2x+3=6x-5
2x-6x=-5-3
-4x=-8
X=8/4
X=2
So the final answer is 2
In a two-digit number, the units digit is six less than three times the tens digit. Four times the units digit minus five times the tens digit equals 11. Find the digits.
Answer:
The tens digit = 5
The units digit = 9
The two digit number is 59
Step-by-step explanation:
Let the tens digit be represented by x
The units digits be represented by y
In a two-digit number, the units digit is six less than three times the tens digit.
y = 3(x) - 6
y = 3x - 6
Four times the units digit minus five times the tens digit equals 11.
4(y) - 5(x) = 11
4y - 5x = 11
We substitute
4(3x - 6) - 5x = 11
12x - 24 - 5x = 11
Collect like terms
12x - 5x = 11 + 24
7x = 35
x = 35/7
x = 5
y = 3x - 6
y = 3(5) - 6
y = 15 - 6
y = 9
Hence,
The tens digit = 5
The units digit = 9
The two digit number is 59
Answer:
5=tens 9=units
Step-by-step explanation:
I think its this
Does this table represent a direct variation?
Answer:
yes, correct me if im wrong
Step-by-step explanation:
No it is not a direct variation or A
Asia is a chef in a restaurant. To prepare for dinner service, she chops 7 1/2 onions in 1/6 of an hour. What is Asia's rate of chopping in onions per hour?
Asia is a chef in a restaurant. To prepare for dinner service, she chops 7 1/2 onions in 1/6 of an hour. Asia's rate of chopping onions is 30 onions per hour.
From the information given;
Asia chops [tex]\mathbf{7 \dfrac{1}{2} \ onions }[/tex] in [tex]\mathbf{\dfrac{1}{6} \ hours}[/tex]So, the onion is given in mixed fraction which can be converted to an improper fraction as: [tex]\mathbf{\dfrac{15}{2}\ onions}[/tex]
Now,
if Asia chops [tex]\mathbf{\dfrac{15}{2}\ onions}[/tex] in [tex]\mathbf{\dfrac{1}{6} \ hours}[/tex] Then Asia will chop (x) onions in 1 hour.We can cross multiply the above two equations to determine the number of onions Asia will chop per hour as follows:
[tex]\mathbf{(x) \times \dfrac{1}{6} \ hours = \dfrac{15}{2} \ onions \times 1 \ hour}}[/tex]
Making (x) the subject of the formula:
[tex]\mathbf{(x)=\dfrac{ \dfrac{15}{2} \ onions \times 1 \ hour}{ \dfrac{1}{6} \ hours }}}[/tex]
[tex]\mathbf{(x)={ \dfrac{15}{2} \ onions } \times { \dfrac{6}{1} }}}[/tex]
(x) = 15 onions × 3
(x) = 30 onions per hour.
Therefore, Asia's rate of chopping onion is 30 onions per hour.
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If Asia chops 7 1/2 onions in 1/6 hour, therefore, using proportion, the rate of chopping onions per hour is: 45 onions per hour.
Applying the knowledge of proportion and fractions, we can determine Asia's chopping rate of onions per hour.
Given:
Number of onions chopped in 16 hour = 7 1/2 onionsLet number of onions chopped in 1 hour be xUsing proportion, we have the following:
[tex]7\frac{1}{2} = \frac{1}{6} \\\\x = 1[/tex]
Cross multiply[tex]\frac{1}{6} \times x = 7\frac{1}{2} \times 1\\\\\frac{x}{6} = \frac{15}{2}[/tex]
Multiply both sides by 6[tex]\frac{x}{6} = \frac{15}{2}\\\\x = \frac{15}{2} \times 6\\\\x = 45[/tex]
Therefore, if Asia chops 7 1/2 onions in 1/6 hour, therefore, using proportion, the rate of chopping onions per hour is: 45 onions per hour.
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a) Write 7.1 x 10² as an ordinary number.
Answer:
710 is the answer.
Step-by-step explanation:
7.1 x 10^2
10^2= 10 x 10 = 100
so,
7.1 x 100 = 710
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.21 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
will give crown if answered correctly..
Answer:
what is a crown
Step-by-step explanation:
they should stop eating out
ax+by=c What is the equivalent equation
If his heartbeat has increased by 8 beats per minute after 20 minutes of working out how much will his heartbeat have increased after 30 minutes of working out
Answer:
12 beats per minute after 30minutes
Step-by-step explanation:
Since we are told by how much his heartrate increased in 20 minutes, we can simply calculate how much it increased in 10 minutes and add that amount to the current heart rate to know how much his heartrate increased after 30 minutes of working out. Since 10minutes would be half of the 20minutes we simply divide the beats per minute by 2.
8 / 2 = 4 beats per minute after 10 minutes
Now we simply add this to the beats per minute at the 20minute mark to calculate the beats per minute at 30minutes
8 + 4 = 12 beats per minute after 30minutes
Kendra posts a photo on her social media account.In the first hour, 2 friends share the photo.In the second hour, each of those friends has 2 friends who share the photo.The pattern continues. How many photos do people share in hour
1. 32
2. 64
3. 12
4. 9
Answer:
Step-by-step explanation:
The answer is 64 because If you multiply 2x2x2x2x2x2 It equals 64
what is the slope. please hurry up
Answer:
The slope is 1/2
Step-by-step explanation:
m=y²-y¹/x²-x¹
m=2-1/4-2
m=1/2
Which of the following equation(s) has a graph that is perpendicular to the line x + 2y = 14? Select all that apply.
A. 2x - y = -7
B. 7y = 14x + 2
C. x + 2y = 7
D. 14y = 7x + 2
Answer:
A
Step-by-step explanation:
not sure.................pero tama sagot ko
4) A cell phone company would like to run a promotion for a limited time. The cellphone
company is activating a phone line for $40. People will have to pay $50 each month for
phone service. Which equation can be used to find y, the amount that someone will pay
for x months?
y = 40x + 10
y = 40x + 50
y = 40 + 50x
y = 10x + 40
Write an equation of the line that passes through each pair of points (5,-3), (2,5)
Answer:
8x+(-27)=y
Step-by-step explanation:
To find an equation of a line, you use the formula mx+b=y
M=slope
x=x cooridnates
y=y coordinates
b=y intercept
Slope:
You use the formula y2-y1/x2/x1 to find slope.
5-(-3)/2-5
5+3/-3
8/-3
8
Y intercept:
8(5)+b==3
40+b=-3
b=-37
Equation: 8x+-37=y
The equation of the line that passes through each pair of points (5,-3), (2,5) is 3y = -8x+31
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, a line passes through each pair of points (5,-3), (2,5)
We know that, the equation of a line passing through two points (x1, y1) and (x2, y2) is given by,
(y-y1) = (y2-y1)/(x2-x1)(x-x1)
Where, (y2-y1)/(x2-x1) is, representing the slope of the line.
Here, x1 = 5, x2 = 2 and y1 = -3, y2 = 5
Equation of the line =
(y+3) = (5+3)/(2-5)(x-5)
y+3 = -8/3(x-5)
3y+9 = -8x+40
3y = -8x+31
Hence, The equation of the line that passes through each pair of points (5,-3), (2,5) is 3y = -8x+31
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PLSS HELP ASP Nick bought raffle tickets to try to win a prize. He paid $3.00 for $12 tickets.
What is the cost per raffle ticket?
A $0.20 per ticket
B $0.25 per ticket
C $4.00 per ticket
D $5.00 per ticket
Answer:
c.
Step-by-step explanation:
$4 a ticket
12÷3=4
I hope this was helpful
Really stupid question, but how do you add a comment lol. There’s no enter button or anything (I’m on an iPad) if that helps.
Answer:
You just do
Step-by-step explanation:
Answer:
just click the thing that says "Ask blah blah about this question..."
Step-by-step explanation:
Derek made 15 baskets. This was triple the number of baskets he made on Saturday
Which equation can be used to find, x, the number of baskets Derek made on Saturday?
A) x-3 = 15
B) x/3 = 15 (the x is in fraction form x over three just so u know)
C) x+3 = 15
D) 3x = 15
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The equation can be used to find, x, the number of baskets Derek made on Saturday.
3x = 15
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of baskets made = 15
This was triple the number of baskets he made on Saturday.
This means,
3x = 15
Number of baskets made on Saturday = x
Now,
3x = 15
Divide both sides by 3.
x = 5
The number of baskets made on Saturday is 5.
Thus,
The equation can be used to find, x, the number of baskets Derek made on Saturday.
3x = 15
Option D is the correct answer.
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What is the answer to this question above?
Answer:
is it multiple choice
Step-by-step explanation:
Answer:
x is 10 y is 5.8
Step-by-step explanation:
x=y+4.2=10
in the equation, y = 0.007x, how many inches of rain falls in 6 minutes?
Answer:
X represents the value you can multiply with the slope to get the answer.
y = 0.007x
= 0.007(6)
= 0.042
Therefore, 0.042 inches of rain falls in 6 minutes.
(Find common denominator first.)
3/2 + b=7/4
Answer:
b = 1/4
Step-by-step explanation:
Take the given fractions : 3/2 and 7/4 and find a common denominator.We will use 4 as a common denominator.
In order for the denominator of 3/2 to get to 4, you need to multiply by 2.3 × 2 = 6 2 × 2 = 4
New fraction: 6/4Now we have the equation 6/4 + b = 7/4
7/4 - 6/4 = 1/4
What is the constant of proportionality in the equation y=3I
Answer:
31
Step-by-step explanation:
y=kx
HELPPPPP its geo and I need help
Answer:
61
Step-by-step explanation:
first we set <B and <E equal to each other to find x (they are equal because it is a given in the phrase below the pics)
5x + 8 = 7x - 12
5x + 20 = 7x
20 = 2x
10 = x
now we know x is 10, so substitute it into an equation to find the measure of the vertex of the triangles
5(10) + 8 = 58
subtract 58 from 180 to find what the base angles are combined
180 - 58 = 122
since there are two congruent base angles (the base angles of isosceles triangles are always congruent), we have to divide 122 by 2 to find the measure of a base angle
122 ÷ 2 = 61
<F is a base angle, so <F is 61
Why is the function below called a rational function?
f(x) =x+3
——
x-2
Simplify
x + x + y x y?
Answer: [tex]2x+y^2[/tex]
Step-by-step explanation:
[tex]x\:+\:x\:+\:y\:\cdot \:y[/tex]
[tex]x+x+yy[/tex]
[tex]2x+yy[/tex]
[tex]2x+y^2[/tex]
Answer:
2(x)+[tex]y^{2}[/tex]