Answer:
-2
Step-by-step explanation:
Average rate of change is another term for average slope, and is found with the equation
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{2} }[/tex]
The first point is (1, 8). The second point is (2,6).
[tex]m=\frac{8-6}{1-2} \\m=-2[/tex]
During the first six months of the year, the car dealership sold 47 cars, 53 cars, 62 cars, 56 cars, 46 cars, and 48 cars. What was the average number of cars sold per month during the first six months of the year?
Answer:
52 cars
Step-by-step explanation:
During the first six months of the year the car dealership sold
53 cars
47 cars
62 cars
56 cars
46 cars
48 cars
Therefore the average number of cars sold per month can be calculated as follows
= 53+47+62+56+46+48/6
= 312/6
= 52
Hence an average of 52 cars is sold monthly
Consider the parametric equations x = 4cos(t) – 3 and y = 5sin(t) + 2. What is the rectangular form?
Answer: C on edge
Step-by-step explanation:
The rectangular form of the parametric equations x = 4cos(t) – 3 and y = 5sin(t) + 2 is shown in the option third, option third is correct.
What are parametric equations?A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.
The missing options are in the attached picture please refer to the picture.
We have two parametric equations:
x = 4cos(t) – 3 and
y = 5sin(t) + 2
From the options plug x and y values in the equation:
[tex]\rm \dfrac{(x+3)^2}{16}+\dfrac{(y-2)^2}{25}=1\\[/tex]
[tex]\rm \dfrac{(4cos(t)-3+3)^2}{16}+\dfrac{(5sin(t)+2-2)^2}{25}=1\\[/tex]
[tex]\rm \dfrac{(4cos(t))^2}{16}+\dfrac{(5sin(t))^2}{25}=1\\[/tex]
cos²t + sin²t = 1 (true)
Thus, the rectangular form of the parametric equations x = 4cos(t) – 3 and y = 5sin(t) + 2 is shown in the option third, option third is correct.
Learn more about the parametric function here:
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are 5(8y - 8) and 40y - 40 equal?
Answer:
yes
Step-by-step explanation:
5(8y-8) = 5*8y - 5*8 by distributive property. simplify that, you get 40y-40, which is equal to 40y-40.
I hope this helped, please give brainliest if this is correct! Thank you!
Based on the given information, determine which two statements are true and which is a lie. Explain what is incorrect about the “lie.”
Answer:
The first statement is a lie, second and third statement is true.
Step-by-step explanation:
Consider the provided information.
For two similar triangles, if the scale factor is a : b, then the ratio of their perimeters will be a : b.
For two similar triangles, if the scale factor of a : b, then the ratio of their areas will be [tex]a^2 : b^2[/tex].
For two similar triangles, if the scale factor is a : b, then the ratio of their altitudes will be a : b.
It is given that the ratio of perimeters is 6:1 which is incorrect as the ratio should be 3:1.
It is given that the ratio of areas is 9:1 which is correct because [tex]3^2 : 1^2=9:1[/tex].
It is given that the ratio of the altitude is 3:1 which is correct.
Hence, the first statement is a lie, second and third statement is true.
plss find this one HCF
a³,a²,a
Step-by-step explanation:
a³,a²,a
first expression
=a×a×a
second expression
=a×a
third expression
=a
HCF=a^4
4x-6y=-24 2x-3y=-6 graphed
Answer:
Step-by-step explanation:
On comparing the ratios of the coefficients, find out whether the pair of equations x – 2y =0 and 3x + 4y -20 =0 is consistent or inconsistent.
Answer:
The pair of equations is consistent
Step-by-step explanation:
A consistent system of equations has at least one solution
The consistent independent system has exactly 1 solutionThe consistent dependent system has infinitely many solutionsAn inconsistent system has no solution
In the system of equations ax + by = c and dx + ey = f, if
a = d, b = e, and c = f, then the system is consistent dependent and has infinitely many solutionsa = d, b = e, and c ≠ f, then the system is inconsistent and has no solutiona ≠ d, and/or b ≠ e, and/or c ≠ f, and [tex]\frac{a}{d}[/tex] ≠ [tex]\frac{b}{e}[/tex] , then the system is consistent independent and has exactly one solution∵ x - 2y = 0
∴ The coefficient of x ⇒ a = 1
∴ The coefficient of y ⇒ b = -2
∴ The numerical term ⇒ c = 0
∵ 3x + 4y - 20 = 0
→ Add 20 to both sides
∴ 3x + 4y - 20 + 20 = 0 + 20
∴ 3x + 4y = 20
∵ The coefficient of x ⇒ d = 3
∵ The coefficient of y ⇒ e = 4
∵ The numerical term ⇒ f = 20
∵ a ≠ d
∵ b ≠ e
∵ c ≠ f
∵ [tex]\frac{a}{d}[/tex] = [tex]\frac{1}{3}[/tex]
∵ [tex]\frac{b}{e}[/tex] = [tex]\frac{-2}{4}[/tex] = [tex]\frac{-1}{2}[/tex]
∴ [tex]\frac{a}{d}[/tex] ≠ [tex]\frac{b}{e}[/tex]
→ By using rule 3 above
∴ The pair of equations is consistent
Complete the following triangle congruence statement:
△FDE≅△
Help please thank you!!!!
Answer:
I think the person with the greatest debt is Marcus cause he has -25 dollars in his bank account.
Step-by-step explanation:
Sara and Maria both have positive numbers as their bank amount. Samuel have to deposit 10 dollars into his bank account to not be in debt while Marcus has to deposit 25 dollars.
Someone please help me with these too://
Answer:
1.
The slope is 2
The y-intercept is -10
equation: y = 2x - 10
2.
Slope: 2.5
y-intercept: 1
Equation: y = 2.4x + 1
Step-by-step explanation:
1.
x y
2 12
4 16
8 24
10 28
from 12 to 16 you add 4
from 2 to 4 you add 2
y/x = 4/2 = 2
The slope is 2
The y-intercept is -10
equation: y = 2x - 10
I got the y-intercept because I went from 12 to 0 which is -12, and then 2 - 12 and it's -10
__________________________________________________________
2.
x y
5 4
20 10
30 14
35 16
from 4 to 10, u add 6
from 5 to 20 you add 15
y/x = 15/6 = 2.5
Slope: 2.5
y-intercept: 1
Equation: y = 2.4x + 1
I got the y-intercept because I went from 4 to 0 which is -4, and 5 - 4 is 1.
Hope this helped
What's the answer please
Answer:
6
Step-by-step explanation:
Please help, need help
Answer:
Step-by-step explanation:
ΔXYZ
m∠X = 52°, m∠Y = 106°, m∠Z = 180° - (106° + 52°) = 22°
[tex]\frac{13.2}{6.6}[/tex] = [tex]\frac{17.4}{8.7}[/tex] = 0.5
PLESASE HELP ME PLEASE AND THANK YOU
Answer:
B
Step-by-step explanation:
1*3=3
2*3=6
3*3=9
etc.
Find the total amount given the original price and tax or tip rate. Round to the nearest hundredth if necessary.
Original price: $156.67
Tax or tip rate: 6%
Answer:
Step-by-step explanation:
if we tip/tax 6% of 156.67 we will do:
156.67*(6/100)=9.40 this is the amount of tip
156.67+9.40=166.07
Jamon can type 300 words in 8 minutes. At this rate, how many words can he type in 20 minutes?
If you can buy five Nike shirts for $20, then how many can you buy with $32?
Answer:
8 nike shirts
Step-by-step explanation:
1 nike shirt is $4
You bought 50 shares of stock at $55 per share and sold them for $61 per share. The sale involves a broker’s commission of $0.30 per share. What is your profit?
a) $215
b) $285
c) $315
d) $385
Answer:
The profit made is;
b) $285)
Step-by-step explanation:
The given parameters are;
The number of shares bought, n = 50
The price each share is bought, CP = $55
The amount at which each share is sold, SP = $61
The amount the broker received per share, E = $0.30
Therefore, the amount of profit, 'P', is given as follows;
P = n × (SP - CP - E)
By substituting the values for the variables, we have;
P = 50 × (61 - 55 - 0.3) = 285
The amount made as profit, P = $285.00.
A car dealership pays a wholesale price of $12,000 to purchase a vehicle.
During a special sales event, the dealership offers a 10% discount off of the retail price. After the discount, how much will a customer pay for this vehicle? Show your work.
Answer:
$10800
Step-by-step explanation:
$12000 is the original price so let's set that as 100%. Since there's a 10% discount, you have to find out the 90% soo.
100% - $12000
90% - $12000 x 90/100 = $10800
SIMPLE INTEREST
Interest = $40
Principal = $400
Interest rate = ?
Time = 2 years
Answer:
442
Step-by-step explanation:
The cost of a car rental is $25 per day plus 22 per mile. You are on a daily budget of $90. Write and solve an inequality to find the greatest distance you can drive each day while staying within your budget. Use pencil and paper. Find 2 other two-step inequalities with the same solutions.
Answer: You can drive, at most, 2.95 miles per day.
x ≤ 2.95
Step-by-step explanation:
In a single day, you can spend at most $90
Then if C represents the cost of renting the car, then we will have the inequality:
C ≤ $90
Now let's find the equation for C.
We know that we have a fixed cost of $25 plus $22 per mile, then if you drive x miles, the total cost will be $25 plus x times $22, or:
C = $25 + x*$22.
We can now replace that in the inequality:
$25 + x*$22 ≤ $90
Now let's isolate the variable x
x*$22 ≤ $90 - $25
x*$22 ≤ $65
x ≤ $65/$22 = 2.95
x ≤ 2.95
You can drive at most, 2.95 miles per day.
To find other inequalities with the same solution we can start with the solution:
x ≤ 2.95
Now let's multiply both sides by a number (the units of the number can be dollars, in that way we can make a similar problem)
Let's multiply both sides by $10:
x*$10 ≤ 2.95*$10 = $29.5
x*$10 ≤ $29.5
Now let's add the same number in both sides, for example, $5.
x*$10 + $5 ≤ $29.5 + $5 = $34.5
x*$10 + $5 ≤ $34.5
We could write this problem as:
"To rent a cab in your city, you have an initial cost of $5, plus $10 for each mile driven. How many miles could you drive if at most you can spend $34.50?"
You could be more creative with the problem, but this is the way in which you can craft problems of this type when you already know the solution.
Someone Please help meee?
Answer:
ghk and lkh are alternate
you are looking for a z shape if that helps xx
Zellie is taking the stairs in her building from her floor to the top of the building. After 2 minutes, she was 100 steps from the bottom floor. After 5 minutes she was 196 steps from the bottom floor.
Answer:
The question seems to be incomplete, so i will think that this is a linear equation, where we can find the velocity at which she moves, and also her initial position.
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In this case we have two points:
"After 2 minutes, she was 100 steps from the bottom floor."
this can be represented with the point: (2min, 100 steps)
" After 5 minutes she was 196 steps from the bottom floor"
This can be represented with the point (5min, 196 steps)
With this, we can find the slope of this equation:
a = (196 steps - 100 steps)/(5min - 2min) = 96steps/3min = 32 steps/min
This means that she does 32 steps in one minute.
Then we can write her positon equation as:
y = (32steps/min)*x + b
where x represents the time, and b is her initial position.
If we replace x by 2 min, and y for 100 steps, we get:
100steps = (32steps/min)*2min + b
100 steps = 64 steps + b
100 steps - 64 steps = b = 36 steps.
This means that she started to take the stairs 36 steps from the bottom floor.
convert the following equation into slope intercept form
3y - 2x = 9
Answer:
the slope intercept form 3y-2x=9 is y=2/3x+3
Is this statement true or false?
p = 2 is a solution to p – 5 <20
O true
O false
Answer:
true
Step-by-step explanation:
Answer:
it is the solution
Step-by-step explanation:
because p is 2
2-5<20
-3<20 which is true
What is the solution to 3|-3x+9|=-18?
Answer:
There is no solution to the problem.
Step-by-step explanation:
Key skills: Absolute Value, Division, One Variable Equation
1) We have the equation 3|-3x+9|=-18
2) First, divide by 3 on both sides.
-18/3 is -6
3) This means --> |-3x+9| = -6
4) Absolute Value cannot be negative so there is no solution.
Hope you understood and have a nice day!! :D
The amount of money spent on a pizza for club activities varies directly with the number of pizzas bought. If $135 will pay for fifteen pizzas, then how many pizzas can be bought with $252?
Answer:
28 pizzas can be bought
Step-by-step explanation:
you have to find the unit rate of the pizzas.
so 135 divided by 15 which is 9
and then you divide 252 by 9
It is found that 28 pizzas can be bought with 252 dollar.
What is unit rate?There is an independent quantity, and a quantity that depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called the rate of increment of dependent quantity per unit increment in independent quantity.
We have been given amount of money spent on a pizza for club activities varies directly with the number of pizzas bought.
We need to find the unit rate of the pizzas
Unit rate = Total amount/ Number of pizzas
Unit rate = 35/15
Unit rate = 9
Also,Unit rate = 259/13
Unit rate = 28
Therefore, 28 pizzas can be bought.
To learn more about the unitary method, please visit the link given below;
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A.y=50+0.15x
B.y=50+0.45x
C.y=150+0.45x
D.y=150+0.15x
Answer:
D
Step-by-step explanation:
you get 150 by taking the product of 50 and 3, this eliminates answers 'a' and 'b'
since the question states the cost per mile driven is $1.50 and 'x' represents miles driven, D is the answer
Drag statements and reasons to each row to show why the slope of the line between P and Q is the same as the slope between Q and R, given that triangles A and B are similar.
hi i know i’m late but to help out any future people, the answer is
Row One: Statement: 3/2=slope Reason: Definition of Slope
Row 2: Statement: 3/2=6/4 Reason: Triangle A is similar to Triangle B
Answer:
Step-by-step explanation:
Simplify the expression 2(w+7)+6(3w−1).please help
Answer:
20w+8
Step-by-step explanation:
hope it helps..................
Answer:
20w+8
i hope this helps u :)
If Buddy the Elf stands 6'3" tall and looks up at the Empire State Building (1454' high), what is the angle of elevation if Buddy is 206' from the base of the Empire State Building?
Answer:
Step-by-step explanation:
If Buddy the Elf stands 6'3" tall and looks up at the Empire State Building (1454' high), what is the angle of elevation if Buddy is 206' from the base of the Empire State Building?
We are to find the angle of elevation which is calculated using the Trigonometric function of Tangent.
tan θ = Opposite/Adjacent
Where:
Opposite = 1454'
Adjacent = 206
tan θ = 1454'/206