The y-intercept of [tex]\(12x + y^3 = 2\) is at \((0, \sqrt[3]{2})\).[/tex]
To find the y-intercept of the equation [tex]\(12x + y^3 = 2\)[/tex], we first need to understand what the y-intercept represents. The y-intercept is the point where the graph intersects the y-axis, which means the x-coordinate of this point is 0.
To find the y-intercept, we set [tex]\(x = 0\)[/tex] in the equation and solve for y:
[tex]\[12(0) + y^3 = 2\][/tex]
[tex]\[y^3 = 2\][/tex]
To solve for y, we take the cube root of both sides:
[tex]\[y = \sqrt[3]{2}\][/tex]
So, the y-intercept of the equation is [tex]\((0, \sqrt[3]{2})\).[/tex]
what is the quotient of the pic
Answer:
256
Step-by-step explanation:
Answer:
Step-by-step explanation:he rate of return on Karen investment is 10%. Explanation: Given that. Bought price = P = $78500. Sale price = S =$850,000.
an = 12 – 5(n − 1)
What is the 30th term of the sequence?
Answer:
- 133
Step-by-step explanation:
To find the 30 th term substitute n = 30 into the formula, that is
[tex]a_{30}[/tex] = 12 - 5(30 - 1) = 12 - (5 × 29) = 12 - 145 = - 133
Final answer:
The 30th term of the sequence defined by an = 12 – 5(n – 1) is – 133.
Explanation:
To calculate the 30th term of the sequence given by an = 12 – 5(n – 1), we start by substituting the value of n with 30.
[tex]a_{30}[/tex] = 12 – 5(30 – 1)
[tex]a_{30}[/tex] = 12 – 5(29)
[tex]a_{30}[/tex] = 12 – 145
[tex]a_{30}[/tex] = – 133
The 30th term of the sequence is – 133.
Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x + 6)? The graph of y = f(x) will shift up 6 units. The graph of y = f(x) will shift down 6 units. The graph of y = f(x) will shift left 6 units. The graph of y = f(x) will shift right 6 units.
Answer:
The graph of y = f(x) will shift left 6 units, as shown in figure a.
Step-by-step explanation:
A translation means we are able to move the graph of a function up or down - normally called Vertical Translation - and right or left - commonly called Horizontal Translation.
If we replace the graph of y = f(x) with the graph of y = f(x + 6). It means we have added 6 units to the input, meaning the graph y = f(x) will shift left by 6 units as 6 is being added directly to the x, so it is f(x + 6).
For example, if y = x² is the original function and of 6 is directly added to x i.e. f(x + 6), making it y = (x + 6)². So, we can easily observe that there will be a horizontal translation left of 8 units, as shown in figure a.
So, the graph of y = f(x) will shift left 6 units.
Keywords: graph shift, translation
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The graph of y = f(x) will shift left 6 units. The correct option is the third one.
Which is the effect of replacing the graph of y = f(x) with the graph of y = f(x + 6)?For any function y = f(x), we define an horizontal translation of N units as:
y = f(x + N)
Where if:
N > 0, the translation is to the left.
N < 0, the translation is to the right.
Here we have:
y = f(x + 6)
So this is a translation of 6 units to the left.
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Write an equation in point slope form for the line through the given point and the given slopes
(10,-9); m=-2
Please see the attachment below.
All the information is in the problem you just have to format it into an equation.
Point slope form: [tex]y_{2}- y_{1}=m(x_{2}- x_{1})[/tex] where "m" is the slope.
The equation would look like...
y+9=-2(x-10)
Isabel will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $46 and costs an additional $0.13 per mile driven.
The second plan has an initial fee of $55 and costs an additional $0.11 per mile driven.
For what amount of driving do the two plans cost the
To compare the two plans and find the amount of driving for which they cost the same, we can set up an equation and solve for x. The two plans cost the same for 450 miles of driving.
Explanation:To compare the two plans and find the amount of driving for which they cost the same, we need to set up an equation. Let's assume the amount of driving is represented by the variable x. The total cost for Plan 1 can be calculated as:
Total cost = $46 + $0.13x
The total cost for Plan 2 can be calculated as:
Total cost = $55 + $0.11x
We can set the two equations equal to each other and solve for x:
$46 + $0.13x = $55 + $0.11x
$0.02x = $9
x = $9 / $0.02 = 450
Therefore, the two plans cost the same for 450 miles of driving.
What is the constant of proportionality in the equation y=3xy=3xy, equals, 3, x?
Answer:
k=3
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In this problem we have
[tex]y=3x[/tex]
therefore
The constant of proportionality is k=3
Answer:
k=3
Step-by-step explanation:
i went on knan and it worked
1. 4/5 - (-3/10)=
2. 5.5 - 8.1=
3. -5 - 5/3=
4. -8 3/8 - 10 1/6=
5. -4.62 - 3.51=
Answer:
Step-by-step explanation:
4/5-(-3/10)=4/5+3/10=8/10+3/10=11/10
5.5-8.1=-2.6
-5-5/3=-15/3-5/3=-20/3
-8 3/8-10 1/6=-67/8-61/6=-445/24
-4.62-3.51=-8.13
4. What is the equation of the midline of the sinusoidal function?
The midline equation for the sinusoidal function is y = 4 sin(ωx + ∅) - 3, derived by calculating the amplitude and vertical shift within the general function equation.
A function is a mathematical expression, rule, or law that defines the relationship between one variable and another. In mathematics, functions play a crucial role in representing physical relationships and various mathematical concepts. One specific type of function is the sinusoidal function, characterized by its repetitive pattern within a specific time interval.
The general form of a sinusoidal function is given by the equation:
y = A sin(ωx + ∅) + c
Here, A represents the amplitude, ω is the argument, ∅ is the phase difference, and c is the vertical shift known as the midline.
To find the equation of the midline, we use the formula:
A = (Maximum value - Minimum value) / 2
Given that the maximum value is 1 and the minimum value is -7, the amplitude (A) is calculated as:
A = (1 - (-7)) / 2 = 4
The vertical shift (c) is determined to be -3. Substituting these values into the general equation, we obtain the equation of the midline for the sinusoidal function:
y = 4 sin(ωx + ∅) - 3
In summary, the equation of the midline for the sinusoidal function is y = 4 sin(ωx + ∅) - 3.
The amplitude and vertical shift inside the general function equation are used to obtain the midline equation for the sinusoidal function, which is y = 4 sin(ωx + ∅) - 3.
A mathematical phrase, rule, or law that establishes the connection between two variables is called a function.
Functions are essential to the representation of both mathematical concepts and physical relationships in mathematics.
The sinusoidal function is one particular kind of function that is distinguished by its repeating pattern inside a predetermined time frame.
The following formula provides the generic form of a sinusoidal function:
sin(ωx + ∅) + c = A
In this case, amplitude is denoted by A, argument by ω, phase difference by ∅, and vertical shift, or midline, by c.
We utilise the to determine the midline's equation.
A is equal to (Maximum - Minimum) / 2.
A = (1 - (-7)) / 2 = 4 is the formula for calculating the amplitude (A), given that the maximum value is 1 and the minimum value is -7.
It is found that the vertical shift (c) is -3. The equation of the midline for the sinusoidal function is obtained by substituting these values into the general equation: y = 4 sin(ωx + ∅) - 3
In conclusion, y = 4 sin(ωx + ∅) - 3 is the equation of the midline for the sinusoidal function.
Let p = 5. Enter > , < , or = to compare the expressions. 4p4 2p−3
Answer:
The given expression at p = 5 can be written as:
[tex]4(p^4) > 2p -3[/tex]
Step-by-step explanation:
Here, the given expressions are:
[tex](4p^4 ), (2p-3)[/tex]
Now, substitute the value of p = 5 in both the given expressions, we get:
[tex]4(p^4) = 4(5^4) = 4 (625) = 2,500\\\implies 4(p^4) = 2,500[/tex]
Similarly,
[tex](2p-3) = 2(5) - 3 = 10 -3 = 7\\\implies 2p - 3 = 7[/tex]
So,now comparing both the values at p = 5, we get:
2,500 > 7
[tex]\implies 4(p^4) > 2p -3[/tex]
Hence, the given expression at p = 5 can be written as:
[tex]4(p^4) > 2p -3[/tex]
1) For the data in the table, does y vary directly with x? If it does, write an equation for the direct
variation.
Answer:
Yes, y varies directly with x.
[tex]y=\frac{11}{8} x[/tex]
Step-by-step explanation:
[tex]\frac{y}{x}=\frac{11}{8} =\frac{22}{16} =\frac{33}{24}[/tex]
Hence [tex]y[/tex] varies directly with [tex]x[/tex].
[tex]\frac{y}{x}=\frac{11}{8} \\\\ y=\frac{11}{8} x[/tex]
What is g + 11 >_ -1
Answer:
g>=-12
Step-by-step explanation:
g+11>=-1
g>=-1-11
g>=-12
What is 19,000 using exponents
Answer:
I think its 19,000/1
Step-by-step explanation:
I don't think there is any explanation :)
The price of a train ticket consists of an initial fee plus a constant fee per stop.
The table compares the number of stops and the price of a ticket (in dollars).
Stops Price (dollars)
3 6.50
7 12.50
11 18.50
What is the initial fee?
The initial fee of a train ticket, given a constant fee per stop, can be calculated by finding the constant fee per stop and subtracting the total of this fee for a given number of stops from the total price for those stops. By this calculation, the initial fee is $2.50.
Explanation:To determine the initial fee that is related to the price of a train ticket, which consists of an initial fee plus a constant fee per stop, we should first calculate the cost per stop. We can do this by subtracting the price of a ticket for 3 stops from the price of a ticket for 7 stops. So, we get $12.50 - $6.50 = $6.00. We find the difference in the number of stops, which is 7 - 3 = 4 stops. Divide the total price difference by the difference in the number of stops to get the constant fee per each stop: $6.00 / 4 stops = $1.50 per stop. Now we know the constant fee for each stop, so we subtract that from the total price for 3 stops to find the initial fee: $6.50 - ($1.50 * 3) = $2.50. So, the initial fee is $2.50.
To find the initial fee, we need to determine the additional cost per stop. We can do this by using the formula y = mx + b, where y represents the price of the ticket, x represents the number of stops, m represents the constant fee per stop, and b represents the initial fee.
Using the given data, we can set up two equations using the points (3, 6.50) and (7, 12.50).
By subtracting these two equations, we can determine the value of b, which represents the initial fee. Thus, the initial fee is $3.
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the circumference of a circle is 18.41 feet. WHat is the approximate length of the radius.
Answer:
The answer can be calculated by doing the following steps;
Step-by-step explanation:
Answer:
The approximate length of the radius is 3 feet
Step-by-step explanation:
Given:
circumference of a circle = 18.41 feet
To Find:
approximate length of the radius = ?
Solution:
Let the radius of the circle be r
We know that the circumference of the circle C is given by the formula
C =[tex]2 \pi R[/tex]
Substituting the values, we get
18.41 =[tex]2\times \pi \times R[/tex]
Rearraning the above equation we get
R=[tex]\frac{14.41}{ 2\times \pi}[/tex]
R=[tex]\frac{18.41}{6.28}[/tex]
R= 2.93
R= 3 (approx)
Ryan has $40 in the bank. He writes
a check for $64.75 and then uses his
check card to buy gas for $40. What is
his new balance?
Show work and explain clearly
Assume you drink eight sodas per week & they cost $1.59
each. How much money can you accumulate over the course of
a year if you opt to save the money instead?
The money can you accumulate over the course of a year if you opt to save the money instead will be $82.68.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
It is also known as the product. If the object n is given to m times then we just simply multiply them.
Assume you drink eight sodas per week & they cost $1.59 each.
We know that there are 52 weeks in a year.
The money can you accumulate over the course of a year if you opt to save the money instead will be
⇒ $1.59 × 52
⇒ $82.68
The money can you accumulate over the course of a year if you opt to save the money instead will be $82.68.
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What is the length of jy?
A. 4.5
B. 18
C. 6
D. 3
Answer:
D.3
Step-by-step explanation: The full line is equivelent to 3 if you look
What is the slope of the line perpendicular to the line y = -3/4x + 1?
A) -4/3
B) -3/4
C) 3/4
D) 4/3
Answer:
the answer is D.) 4/3
Step-by-step explanation:
when you look for a slope that is perpendicular to the slope you are given you take the reciprocal and change the sign
Answer:
4/3
Step-by-step explanation:
Because perpendicular means negative reciprocal.
Anita is filling a small pool for her kids. Currently, there are 60 gallons of water in the pool and she is filling the pool at a rate of 50 gallons every 5 minutes. The pool holds 200 gallons of water.
Which equation represents the amount of minutes ( m) that it will take to fill the pool?
The equation which represents the amount of minutes.m that it will take to fill the pool is 200 = 60 + 10m
Which equation represents the amount of minutes ( m) that it will take to fill the pool?
Let
m = amount of minutes that it will take to fill the pool
Gallons of water in the pool = 60 gallons
Capacity of the pool = 200 gallons
Additional gallons added per minutes = 50 gallons / 5
= 10 gallons per minutes
The equation:
200 = 60 + 10m
200 - 60 = 10m
140 = 10m
Divide both sides by 10
m = 140/10
m = 14 minutes
Therefore, it takes Anita 14 minutes to fill the pool.
find the linear regression equation for the transformed data?
(1, 13) 1.114
(2, 55) 1.740
(3, 349) 2.543
(4, 2407) 3.381
(5, 16, 813) 4.226
Answer:
y = 0.7865x + 0.2413
Step-by-step explanation:
[tex]\begin{array}{rrc}\mathbf{x} & \mathbf{y} & \mathbf{\log(y)}\\1 & 13 & 1.114\\2 & 55 & 1.740\\3 & 349 & 2.543\\4 &2407 & 3.381\\5 &16813 & 4.226\\\end{array}[/tex]
I plotted both your original and transformed data in Excel and asked it to display the regression equation for the transformed data.
Your original data are the blue line plotted against the left-hand axis.
Your transformed data are the red line, plotted against the right-hand axis.
The linear regression equation is
y = 0.7865x + 0.2413
The answer is y = 0.7865x + 0.2413
The Linear regression equation for the transformed data:
We transform the predictor (x) values only. We transform the response (y) values only. We transform both the predictor (x) values and response (y) values.
Find the linear regression equation for the transformed data?
(1, 13) 1.114
(2, 55) 1.740
(3, 349) 2.543
(4, 2407) 3.381
(5, 16, 813) 4.226
X Y Log(y)
1 13 1.114
2 55 1.740
3 349 2.543
4 2407 3.381
5 16813 4.226
The linear regression equation is y = 0.7865x + 0.2413
The graph is plotted below:
Original data are the blue line plotted against the left-hand axis and transformed data are the red line, plotted against the right-hand axis.
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What is 28/185 in simplest form
What is 28/185 in simplest form
Answer:
0.1513...
Step-by-step explanation:
the slope of y+4=3/5(x-7
Answer:
3/5
Step-by-step explanation:
Answer:
slope = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y + 4 = [tex]\frac{3}{5}[/tex](x - 7) ← is in point- slope form
with slope m = [tex]\frac{3}{5}[/tex]
how many times dose 10 go into 450
Answer:
10 go into 450 45 times
Step-by-step explanation:
Willie sold 2 rolls of plain and 2 rolls of shiny for a total of $80. Arjun sold 8 rolls of plain and 10 rolls of shiny for a total of $360. What is the cost of each kind
One roll of plain costs $20 and one roll of shiny costs $20 also.
Step-by-step explanation:
Let,
Cost of one roll of plain = x
Cost of one roll of shiny = y
According to given statement;
2x+2y=80 Eqn 1
8x+10y=360 Eqn 2
Multiplying Eqn 1 by 4
[tex]4(2x+2y=80)\\8x+8y=320\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](8x+10y)-(8x+8y)=360-320\\8x+10y-8x-8y=40\\2y=40[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{40}{2}\\y=20[/tex]
Putting y=20 in Eqn 1
[tex]2x+2(20)=80\\2x+40=80\\2x=80-40\\2x=40[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{40}{2}\\x=20[/tex]
One roll of plain costs $20 and one roll of shiny costs $20 also.
Keywords: linear equation, elimination method
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solve -2-2(-7+b)=-8b+24
Answer:
b = 2Step-by-step explanation:
[tex]-2-2(-7+b)=-8b+24\qquad\text{use the distributive property}\\\\-2+(-2)(-7)+(-2)(b)=-8b+24\\\\-2+14-2b=-8b+24\qquad\text{combine like terms}\\\\(-2+14)-2b=-8b+24\\\\12-2b=-8b+24\qquad\text{subtract 12 from both sides}\\\\12-12-2b=-8b+24-12\\\\-2b=-8b+12\qquad\text{add}\ 8b\ \text{to both sides}\\\\-2b+8b=-8b+8b+12\\\\6b=12\qquad\text{divide both sides by 6}\\\\\dfrac{6b}{6}=\dfrac{12}{6}\\\\b=2[/tex]
Use the key features of the polynomial f(x) = -9x3 + 8x2 - 16x + 3 to describe its end behavior.
The left side continues up, and the right side continues up.
The left side continues down, and the right side continues down.
The left side continues up, and the right side continues down.
The left side continues down, and the right side continues up
Answer:
The left side continues up, and the right side continues down.
Step-by-step explanation:
[tex]f(x) = -9x^3 + 8x^2 - 16x + 3[/tex]
To find the end behavior, determine the highest degree and leading coefficient
Highest degree is 3 and leading coefficient is -9
highest degree 3 is odd and leading coefficient is negative
As x->-infinity , y -> infinity
As x->infinity , y ->-infinity
The left side continues up, and the right side continues down.
Answer:
Correct answer is C.
Step-by-step explanation:
Someone please help!
If r and p are perpendicular:
1 + 2 = 90°
3 = 90°
4 + 5 = 90°
6 = 90°
If any one of these are true, r and p must be perpendicular
Answer:
Yes
Step-by-step explanation:
First you will have to find out the scale
Then you will find out the numbers that are
Perpendicular
Luke sells you cars for $12 each. His expenses are $3.50 per car, plus $34 for tools. How many cars must he sell for his revenue to equal his expenses?
Answer:
Step-by-step explanation:
x = number of cars
12x = 3.50x + 34
12x - 3.50x = 34
8.5x = 34
x = 34/8.5
x = 4 <=====he would have to sell 4 cars
In this case, Luke must sell [tex]\(\boxed{4}\)[/tex] cars for his revenue to equal his expenses.
To determine how many cars Luke must sell for his revenue to equal his expenses, let's define the variables and set up the equation.
Let x be the number of cars Luke sells.
Revenue:
Luke sells each car for $12, so his revenue for selling x cars is:
[tex]\[ \text{Revenue} = 12x \][/tex]
Expenses:
Luke's expenses include $3.50 per car and a fixed cost of $34 for tools. So his total expenses for x cars are:
[tex]\[ \text{Expenses} = 3.50x + 34 \][/tex]
We need to find the number of cars x such that his revenue equals his expenses:
12x = 3.50x + 34
To solve for x subtract 3.50x from both sides:
12x - 3.50x = 34
8.50x = 34
Now, divide both sides by 8.50:
[tex]\[ \text{Expenses} = 3.50x + 34 \][/tex]
x = 4
Therefore, Luke must sell [tex]\(\boxed{4}\)[/tex] cars for his revenue to equal his expenses.
How many days is 45% of 31 days
Answer:
45% of 31 days is 13.95 days, theres your answer.
Suppose that y varies inversely with x, and y=2 when x=10.
(A) write an inverse variation equation that relates x and y
(b) find y when x= 4
Answer:
see explanation
Step-by-step explanation:
Given that y varies inversely with x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
(A)
To find k use the given condition y = 2 when x = 10
k = yx = 2 × 10 = 20, thus
y = [tex]\frac{20}{x}[/tex] ← equation of variation
(B)
When x = 4, then
y = [tex]\frac{20}{4}[/tex] = 5