Answer:y=42000-2000x
Step-by-step explanation:
Y is price so that’s be 42000 minus 2000 every year
Answer:
[tex]y=42,000 - 2000x[/tex]
Step-by-step explanation:
The y is the total value of the car after everything that needs to be taken account of has been accounted to. You're finding the y and what the price is after x amount of years. The initial amount is 42,000 so whatever the cost of the car has depreciated would be subtracted from it. 2,000 dollars per year means what ever x is for year, let's say 5. The amount of money that the car has depreciated over the course of 5 years would be 5 multiply by 2,000. Hopes this help!
Each side of a suspension bridge has a cable that is secured at either end of the span by two supporting towers. The cable is attached to the tops of the two towers. In the section between the two towers, the cable forms a parabolic curve. At its lowest point, the cable is 40 feet above the surface of the bridge. The towers are 450 feet apart, and the vertical distance from the surface of the bridge to the top of each tower is 500 feet. Use the left tower as the y-axis. Hint y=a(x-h)2+ k
Answer: y= 40
Step-by-step explanation:
1. The lowest point of the cable is 40 feet above the surface of the bridge.
2. The towers are 450 feet apart.
3. The vertical distance from the surface of the bridge to the top of each tower is 500 feet.
We’ll use the general form of a parabolic equation:
[ y = a(x - h)^2 + k ]
Where:
(y) represents the vertical position (height) of the cable.
(x) represents the horizontal position along the bridge.
(h) represents the horizontal position of the vertex (lowest point) of the parabola.
(k) represents the vertical position of the vertex.
Given that the lowest point of the cable is at (y = 40) feet, we have:
[ k = 40 ]
Now let’s find the vertex position ((h)). Since the towers are 450 feet apart, the midpoint between the towers corresponds to the vertex. Therefore:
[ h = \frac{{450}}{2} = 225 ]
Now we can express the equation as:
[ y = a(x - h)^2 + k ]
Next, let’s find the value of (a). At the top of each tower, the cable is at a height of 500 feet. So, when (x = 0) (left tower) or (x = 450) (right tower), we have:
At the left tower (left end of the span): [ y = 500 = a(0 - 225)^2 + 40 ] Solving for (a): [ a = \frac{{500 - 40}}{{225^2}} = \frac{{460}}{{50625}} ]
At the right tower (right end of the span): [ y = 500 = a(450 - 225)^2 + 40 ] Solving for (a): [ a = \frac{{500 - 40}}{{225^2}} = \frac{{460}}{{50625}} ]
Since the value of (a) is the same at both ends, we can use either tower to find the equation of the parabolic curve:
[ y = \frac{{460}}{{50625}}(x - 225)^2 + 40 ]
what toolkit function are discontinuous
The functions that are discontinuous are:
Step Function
Absolute Value Function
Dirichlet Function
Piecewise-defined Functions
We have,
Several functions are known to be discontinuous at certain points or intervals.
Here are a few common examples of functions that exhibit discontinuity:
- Step Function:
A step function is a piecewise-defined function that "jumps" from one constant value to another at specific points.
- Absolute Value Function:
The absolute value function, denoted as |x|, is discontinuous at x = 0, where it changes its slope abruptly.
- Dirichlet Function:
The Dirichlet function is defined as follows: D(x) = {1 for rational x, 0 for irrational x}.
This function is discontinuous at all rational numbers and irrational numbers.
- Piecewise-defined Functions:
Functions that are defined using different formulas or rules for different intervals can exhibit discontinuities at the points where the rules change.
Thus,
The functions that are discontinuous are:
Step Function
Absolute Value Function
Dirichlet Function
Piecewise-defined Functions
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help pls pls pls
4 x 10
plssss plz plz plzz so hard
Answer:
40
Step-by-step explanation:
4 x 10= 40
PlZ add brainliest.
Answer:
40 is the answer to this question
which of these equations shows a proportional relationship between x and y
F. y=-1/3x
G. y=-x+1
H. y=3/2x+3/2
J. y=2x-4
Answer:
F. y= -[tex]\frac{1}{3\\}[/tex]x
Step-by-step explanation:
A proportional relationship between x and y exists if it can be expressed in the form y/x=k or y=kx. From the choices listed, F. y= -[tex]\frac{1}{3\\}[/tex]x is the only equation expressed in this form.
The correct option is J. [tex]\( y = 2x - 4 \).[/tex]
To determine which equation represents a proportional relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex], we need to look for an equation where [tex]\( y \)[/tex] is a constant multiple of [tex]\( x \)[/tex], and passes through the origin (0,0). A proportional relationship can be expressed in the form [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of proportionality.
Let's analyse each option:
F. [tex]\( y = -\frac{1}{3}x \)[/tex]
This equation represents a proportional relationship with a constant of proportionality [tex]\( k = -\frac{1}{3} \)[/tex].
G. [tex]\( y = -x + 1 \)[/tex]
This equation does not represent a proportional relationship because it does not pass through the origin (the y-intercept is 1).
H. [tex]\( y = \frac{3}{2}x + \frac{3}{2} \)[/tex]
This equation does not represent a proportional relationship because it does not pass through the origin (the y-intercept is [tex]\( \frac{3}{2} \))[/tex].
J. [tex]\( y = 2x - 4 \)[/tex]
This equation does not represent a proportional relationship because it does not pass through the origin (the y-intercept is -4).
in terms of S, N, and A, what is the value of B in the equation S=n/2(a+b)
The value of B = [tex]\dfrac{2S-NA}{N}[/tex]
Step-by-step explanation:
The given equation,
[tex]S=\dfrac{N}{2}(A+B)[/tex]
To find, the value of B in terms of S, N and A = ?
∴ [tex]S=\dfrac{N}{2}(A+B)[/tex]
By crossmultiplication, we get
⇒ N(A + B) = 2S
⇒ NA + NB = 2S
⇒ NB = 2S - NA
⇒ B = [tex]\dfrac{2S-NA}{N}[/tex]
∴ The value of B = [tex]\dfrac{2S-NA}{N}[/tex]
Find the value for the following determinant.
5
-5
-11
Choose the solution(s) of the following system of equations:
x² + y² = 6
x² - y=6
Answer:
see attachment
Step-by-step explanation:
Answer:
2nd 4th 6th 8th or B D F H
Step-by-step explanation:
I did it on edge
2x-7=-2x+9
How do you solve this?
Answer:
4
Step-by-step explanation:
2x-7=-2x+9
2x-(-2x)-7=9
2x+2x-7=9
4x-7=9
4x=9+7
4x=16
x=16/4
x=4
15. The volume of a rectangular pyramid
is 10,500 cubic centimeters. It has a
length of 15 centimeters and a width of
85 centimeters. What is its height?
Answer:
Its height is 24.71 centimeters.
Step-by-step explanation:
Given:
The volume of a rectangular pyramid is 10,500 cubic centimeters.
It has a length of 15 centimeters and a width of 85 centimeters.
Now, to find the height.
Let the height be [tex]h.[/tex]
Volume of rectangular pyramid = 10,500 cubic centimeters.
Length (l) = 15 centimeters.
Width (w) = 85 centimeters.
Now, to get the height by putting formula:
[tex]Volume=\frac{l\times w\times h}{3}[/tex]
[tex]10500=\frac{15\times 85\times h}{3}[/tex]
[tex]10500=\frac{1275h}{3}[/tex]
Multiplying both sides by 3 we get:
[tex]31500=1275h[/tex]
Dividing both sides by 1275 we get:
[tex]24.71 =h\\\\h=24.71\ centimeters.[/tex]
Therefore, its height is 24.71 centimeters.
plz ans a,b,c and d.
Answer:
a.i) 1 piece = 20 days
1 day= 1/20 piece =0.05 of a piece
a.ii) 0.05*5 =0.25
a.iii) 0.05*10 =0.5 done.
so if the total is 1, 0.5 is half, so he has 0.5 work left
b.i)1 piece=12 days
4 days = 1/3 = 0.3333333333 of his work
b.ii)1/4=0.25
so 12*0.25 = 3 days
c.i)1/3 = 6 days
1 (work)= 6*3 = 18 days
c.ii) 1/18 = 1 day = 0.05555555555
c.iii) 0.5 since 9/18 = 1/2 = 0.5
d.i) 1 hour= 60 mins
whole tank = 60 mins
20 mins = 60/20 = 1/3 of a tank
if capacity = 1500L
1500 = 60 mins
1500/3 = 20 mins
=500 Liters
h(x) = x2 + 1 k(x) = x – 2
(h + k)(2) =
(h – k)(3) =
Evaluate 3h(2) + 2k(3) =
Answer:
(h + k)(2) = h(2) + k(2) = [tex]2^{2}[/tex] + 1 + 2 - 2 = 4 + 1 = 5
(h - k)(3) = h(3) - k(3) = [tex]3^{2}[/tex] + 1 - (3 - 2) = 10 - 1 = 9
Step-by-step explanation:
h(x) = [tex]x^2 + 1[/tex]
k(x) = x - 2
(h + k)(2) = h(2) + k(2) = [tex]2^{2}[/tex] + 1 + 2 - 2 = 4 + 1 = 5
(h - k)(3) = h(3) - k(3) = [tex]3^{2}[/tex] + 1 -(3 - 2) = 10 - 1 = 9
Maya spent 40% of her savings to pay for a bicycle that costs 85$. How much money was in her savings to begin with ?
Answer:
Total amount of saving = $212.5
Step-by-step explanation:
Let x be the amount of saving to begin with.
Given:
Maya spent = 40%
Bicycle cost = $85
We need to find the amount of savings Maya began with.
Solution:
From the statement, Maya spent 40% of her savings to pay for a bicycle that costs $85.
So, 40% of total amount = $85
[tex]40\%\times Total\ amount = \$85[/tex]
Substitute [tex]40\% = \frac{40}{100}[/tex] and total amount = x in above equation.
[tex]\frac{40}{100}\ties x = 85[/tex]
Using cross multiplication rule.
[tex]x=\frac{85\times 100}{40}[/tex]
[tex]x=\frac{8500}{40}[/tex]
x = $212.5
Therefore, amount of savings Maya began with (x) = $212.5
please help me with this
Which of the following expressions would appear farthest to the right on a number line when solved?
3-1
-2+5
4+(-2)
-4-(-2)
Answer:-2+5
Step-by-step explanation:
So basically you do simple math and you need to know that the highest number goes on the right
So basically for each one there is
3-1 that makes 2
-2+5 creates 3 because it’s a negative so you must cancel the negative out and your left with three after
And with that mind set in mind with having to cancel the negative out with the positive
4+(-2) is basically 4-2 and that makes 2
And the last one is a little bit tricky because of all the negatives involved and with this one you need to know that to negatives make a positive
So it’s -4-(-2) so because of the minus and the negative two being negatives right next to each other they cancel each other out to make the equation basically -4+2 which would ultimately make -2
So all the answers are
3-1=2
-2+5=3
4+(-2)=2
-4-(-2)=-2
And out of all those we know 3 is the highest number there so therefore it would make it the one farthest to the right on a number line when solved.
rewrite the equation
When people leave a 15% or 20% tip they often round up to the nearest multiple of 5 or 10 cents. If Kadisha always rounds up what is a 20% tip on her bill?
To calculate a 20% tip and round up, multiply the bill by 0.2, then round to the nearest 10 cents.
Explanation:To calculate a 20% tip, first, determine the total bill amount. Then, multiply the bill amount by 0.2 to find 20% of the bill. Finally, round up to the nearest multiple of 5 or 10 cents. Since Kadisha always rounds up, she should round up to the nearest 10 cents.
If the total bill is $50, to calculate a 20% tip, we multiply $50 by 0.2 to get $10, which is 20% of the bill. Then, we round up to the nearest 10 cents, making the tip $10.00.
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PLEASE HELPPP MEEEEE
Step-by-step explanation:
Given , a line passes through the points (1,-3) and (3,1)
The equation of line which passes through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is
[tex]y - y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Here [tex]x_1 = 1 , y_1= -3[/tex] and [tex]x_2 = 3 , y_2= 1[/tex]
The required equation of the line is
[tex]y+3=\frac{1+3}{3-1} (x-1)[/tex]
[tex]\Leftrightarrow y +3 =2(x-1)[/tex]
[tex]\Leftrightarrow y =2x-2-3[/tex]
[tex]\Leftrightarrow y =2x-5[/tex]
8.
Given, y varies directly with x and y=24 when x=8
Therefore,
[tex]y\propto x[/tex]
[tex]\Rightarrow y = kx[/tex].........(1)
y = 24 when x=8
[tex]\therefore 24 = 8k[/tex]
[tex]\Rightarrow k =3[/tex]
Equation (1) becomes
y= 3x
So, when x=10
y=3×10
⇒y=30
What is the circumference of a circle if the radius is 33 inches and pi is 3.14
Answer:
207.24 inches
Step-by-step explanation:
The formula for circumference is C=[tex]2[/tex][tex]\pi r[/tex]
Apply the formula here
r = 33
[tex]\pi[/tex]=3.14
C=2*3.14*33 = 207.24
Apply units!
207.24 inches
Which BEST describes the system of equations graphed on the coordinate plane?
A) Consistent
B) Inconsistent
C) Consistent and Dependent
D) Consistent and Independent
Answer:
C) Consistent and Dependent.
Step-by-step explanation:
As the system has at least ONE solution. Both lines lie over each other, which makes them dependent.
The system, therefore, is consistent and dependent.
Consider the figure.
What is JL?
The answer for the above mentioned problem is JL = 12.5
Step by step explanation:
Given:
JM = 8
KM = 6
To Find:
JL = ?
Formula to be used:
[tex]KM^2[/tex] = JM x ML
In order to find " JL" we must first find "ML",
[tex]KM^2[/tex] = JM x ML
[tex]6^2[/tex] = 8 x ML
36 = 8 x ML
36/8 = ML
ML = 4.5
Now JL = 4.5+8
= 12.5
Thus the value of JL = 12.5
a field is in the shape of a rectangle 5/6 mile long and 3/4 mile wide. what is the area of the field.
Answer: 15/24
Step-by-step explanation: 6x4=24 which is the denominator and 5x3=15 which is the numerator
Answer:
15/24
Step-by-step explanation:
The ratio of people to books in a classroom is 10:4 what is the unit ratio of people to per book ?
Answer:
[tex]2.5\ \frac{people}{book}[/tex]
Step-by-step explanation:
The correct question is
The ratio of people to books in a classroom is 10:4 what is the unit rate of people per book?
Let
x ----> the number of people
y ----> the number of books
we know that
To find out the unit rate of people per book , divide the total number of people by the total number of books
we have
[tex]x=10\ people\\y=4\ books[/tex]
so
[tex]\frac{x}{y}=\frac{10}{4}=2.5\ \frac{people}{book}[/tex]
Min is trying to place some bookmarks inside a 10000 page book. the pages that she wants to place the bookmarks on have four digits page numbers. the digits in the thousands and units places add up to 7. How many bookmarks will she need?
Final answer:
Min will need a total of 700 bookmarks for the pages where the digits in the thousands and units places add up to 7, since there are 700 four-digit page numbers meeting the criteria.
Explanation:
To determine the number of bookmarks Min needs for the pages where the digits in the thousands and units place add up to 7, we will consider all four-digit numbers that meet this criterion. This involves taking the sum of the thousands and units digits, which can equal 7 in the following ways: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1, and 7+0. Considering that for every combination of thousands and units digits, there are 10 possibilities for the hundreds digit and 10 possibilities for the tens digit, we can calculate the total number of eligible page numbers.
For 1+6 or 6+1, the number of possibilities is 2 (the two combinations) multiplied by 100 (since there are 10 choices for each of the two remaining digits), giving us 200 options.
For 2+5 or 5+2, we have another 200 options.
For 3+4 or 4+3, we get another 200 options.
For 7+0, we would only have 100 options, as there is only one combination.
Summing these up, we find Min will need 700 bookmarks: 200 + 200 + 200 + 100 = 700.
50 apple's cost $25. How much would 75 apples cost?
Answer:
$37.5
Step-by-step explanation:
(25/50) x 75 = 37.5
$25/50 .... each apple cost $0.5
0.5 x 75 = 37.5
The correct answer is 75 apples would cost $37.50.
To solve this problem, we first need to determine the cost per apple when 50 apples cost $25. We can calculate this by dividing the total cost by the number of apples:
Cost per apple = Total cost / Number of apples
Cost per apple = $25 / 50 apples
Cost per apple = $0.50 per apple
Now that we know the cost per apple is $0.50, we can calculate the cost for 75 apples by multiplying the cost per apple by the number of apples:
Cost for 75 apples = Cost per apple * Number of apples
Cost for 75 apples = $0.50 * 75
Cost for 75 apples = $37.50
Therefore, 75 apples would cost $37.50.
Identify an equation in point-slope form for the line perpendicular to
y=-3x+11 that passes through (4,-8).
Answer:
perp. : 1/3= m
y + 8 = 1/3(x -4): answer is c
y + 24/3 = (1/3)x - 4/3
y = (1/3)x - 28/3
Step-by-step explanation:
answer is c
To find the equation of a line perpendicular to y = -3x + 11 that passes through the point (4, -8), we first calculate the negative reciprocal of the original line's slope, which is 1/3. Then we apply this slope and the given point to the point-slope form equation to obtain y + 8 = (1/3)(x - 4).
The student has asked for an equation in point-slope form for a line that is perpendicular to y = -3x + 11 and passes through the point (4, -8). Firstly, we identify the slope of the given line, which is -3.
As we need a perpendicular line, we find the negative reciprocal of this slope, which is 1/3 (since the slope of perpendicular lines are negative reciprocals of each other). Now, using the point-slope form formula, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope, we plug in our values to get:
y - (-8) = (1/3)(x - 4)
This simplifies to:
y + 8 = (1/3)(x - 4)
Which is the equation of the line perpendicular to y = -3x + 11 that passes through the point (4, -8) in point-slope form.
Which expression is equivalent to 5 x + 10 y minus 15? 5 (x minus 2 y minus 3) 5 (x + 5 y minus 10) 5 (x + 2 y minus 3) 5 (x + 2 y minus 15)
Answer: 5 (x + 2y - 3)
Step-by-step explanation:
Explain how you found the volume of water in the fish tank if it was only 1/2 full with water.
You have a fish tank with the following dimensions:
Height: 3 feet
Width: 1.5 feet
Length: 2 feet
We found the volume of water by finding the volume of fish tank from given dimensions and dividing it by 2.
Step-by-step explanation:
Given,
Height of tank = 3 feet
Width of tank = 1.5 feet
Length of tank = 2 feet
We will first find the volume of tank;
Volume = Length * Width * Height
Volume = 3 * 1.5 * 2
Volume = 9 feet cubed
As we know the water is 1/2; therefore we will divide the volume of tank by 2.
Volume of water = [tex]\frac{9}{2} = 4.5\ ft^3[/tex]
We know that;
1 cubic feet = 7.481 gallons
4.5 cubic feet = 7.481*4.5 = 33.66 gallons
Keywords: volume, division
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0.599 as a percentage of 0.319
Answer: " 187. 774 % " .
_____________________________________
Step-by-step explanation:
_____________________________________
So, let's rewrite this statement as a question:
0.599 is "what percent" of: 0.319 ? ;
Set up an equation:
[tex]0.599 = (\frac{n}{100}) *0.319[/tex] ;
↔ [tex](\frac{n}{100}) * 0.319 = 0.599[/tex] ;
_____________________________________
Divide each side of the equation by: "(0.319)" ; as follows:
_____________________________________
[tex][ (\frac{n}{100}) * 0.319 ] / 0.319 = (0.599)/ (0.319)[/tex] ;
to get:
_____________________________________
[tex]\frac{n}{100} = 1.87774294671[/tex] ;
_____________________________________
Now, multiply each side of the equation by "100" ;
to isolate "n" on one side of the equation; & to solve for "n" ;
_____________________________________
[tex]100 * (\frac{n}{100)} = (1.87774294671) * 100[/tex] ;
_____________________________________
On the left-hand side of the equation; the "100's: cancel out to "1" ;
→ since: "[tex](\frac{100}{100} =1)[/tex]" ;
and we have:
→ n = 187.774294671 ;
round to three decimal places:
→ n = 187. 774 .
The answer is: 187.774 % .
_____________________________________
20 POINTS!!!!! im stuck.
Answer:
First Option
Step-by-step explanation:
An exponent is how many times you multiply a number by its self, in this case, that's 5 times
Answer:
[tex] \frac{32}{243} \\ [/tex]
Step-by-step explanation:
[tex] = ( { \frac{2}{3})}^{5} \\ \\ = \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} [/tex]
What is the sign of 3x y3xy3, x, y when x>0x>0x, is greater than, 0 and y<0y<0y, is less than, 0?
Answer: It's negative! Dude, could I please have brainiest!?!
Final answer:
The sign of the expression 3x * y^3 is negative when x is positive and y is negative because a negative number raised to an odd power remains negative.
Explanation:
The question asks about the sign of a mathematical expression where the variables have specified signs based on their values. Given that x is positive (x > 0) and y is negative (y < 0), the expression 3x * y^3 encompasses multiplying a positive number by a negative number raised to an odd power. Multiplying a positive number by a negative number results in a negative number, and raising a negative number to an odd power preserves the negative sign. Therefore, the product 3x * y^3 will be negative because y^3 maintains its negative sign while 3x is positive.