Answer:
Step-by-step explanation:
A dependent variable in an expression is one whose value can be determined only when the value of other variable (i.e independent) is known.
A. The cost at the fitness center depends on the number of months (x).
The cost is the dependent variable, and number of months (x) is the independent variable.
f(x) = 100 + 40x
Example, the cost paid for 12 months can be determined as;
f(12) = 100 + 40(12)
= 100 + 480
= 580
Thus, $580 would be paid for 12 months at the fitness center.
B. The lettuce is sold at $1.69 per pound. The cost depends on the number of pounds of lettuce bought.
The cost is the dependent variable, while the number of pounds of lettuce (x) bought is the independent variable.
So that;
f(x) = 1.69x
The cost of 10 pounds of lettuce can be determined as;
f(x) = 1.69(10)
= 16.9
Thus, the cost of 10 lb of lettuce is $16.90.
What is the equation in slope-intercept form of a line that passes through the point (4, 5) and has a slope of 1/2?
Answer:
1/2x + 5
Step-by-step explanation:
The y intercept is 5 & the slope is already given!
Help Me! ASAP! Determine whether each equation has no solution, one solution or infinitely many solutions. Choose No Solution, One solution, or Infinitley Many Solutions for each equation.
Answer:
Step-by-step explanation:
(1). One solution
(2). Infinitely Many Solutions
(3). One solution
(4). No Solution
Answer:
1. 1 solution, 2. Infinite solutions, 3. 1 solution, 4. No solution
Step-by-step explanation:
Please please please help
Part A: Marguerite rented a truck at $125 for 2 days. If she rents the same truck for 5 days, she has to pay a total rent of $275. Write an equation in the standard form to represent the total rent (y) that Marguerite has to pay for renting the truck for x days. (4 points) Part B: Write the equation obtained in Part A using function notation. (2 points) Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
(10 points)
Answer:
:)
Step-by-step explanation:
Part A: To get an equation into standard form to represent the total amount rented (y) that Marguerite has to pay for renting the truck for x amount of days, we use the formula for the equation of a straight line.
Remember that the equation of a straight line passing through points is ( x_{1} , y_{1} ) and the points ( x_{2} , y_{2} ) is given by
y - y_{1} / x - x_{1} = y - y_{2} / x - x_{2}
Knowing that Marguerite rented a truck at $125 for 2 days, we know if she rents the exact same truck for 5 days, she has to pay a total of $275 for the rent.
This means that the line modeling this situation crosses points at (2, 125) and (5, 275).
The equation modeling the total rent (y) that Marguerite has to pay for renting the truck for x days is given by
y - 125 / x - 2 = 275 - 125 / 5 - 2 = 150 / 3 = 50
But if you are writing the equation in standard form it would be
50x - y = -25
Part B:
When writing the function using function notation it means you are making y the subject of the formula and then replacing the y with f(x).
If you remember that from part A, we have that the equation for the total rent which is y that Marguerite has to pay for renting the truck for x amount of days is given by
y = 50x + 25.
Writing the equation using the function notation would give us this
f(x) = 50x + 25
Part C:
To graph the function, we name the x-axis the number of days and name the y-axis total rent. The x-axis is numbered using the intervals of 1 while the y-axis is numbered using the intervals of 50.
The points of (2,125) and of (5,275) are marked on the coordinate axis and a straight line is drawn to pass through these two points.
Which of these is not an equation?
A
3b = 5
B
43(4x + 7y)
C
78 = 3p - 37
D
a - 17 = 1,825,026
Option B is not an equation since it doesn't have the "=" sign. [It's an expression]
Hope it helps!
What is the answer to (8y -6
Answer:
Step-by-step explanation:
Incomplete presentation of question. Did you want to factor out the greatest common factor (which is 2), obtaining 2(4y - 3)? Or something else? Also: please note that if you use the left parenthesis ) , you MUST also use the right parenthesis ( .
What is the solution to the system below?
x + y = 5
x - y = 3
( x, y ) = ( 4, 1 )
hope it helps!
Answer:
x= 4
y= 1
Step-by-step explanation:
by adding 2 equations
2x = 8
x= 4
by sub. in Equation 1
4+y=5
y = 5-4
y= 1
Read and write each number in expanded form
6,203,103
Answer:
6,000,000+200,000+3,000+100+3
Step-by-step explanation:
• A trapezoid is one or two ____
and a _____
combined!
Use the formula ______
where:
. b1 is the ____
. b2 is the ____
and
• h is the ___
of the trapezoid.
Third time posting. Explain it too
Answer:
D. x-5 / x+4
Step-by-step explanation:
(-3x³ +9x² +30x) / (-3x³ -18x² - 24x)
=-3x (x²-3x-10) / -3x(x²+6x+8)
=-3x(x+2)(x-5) / -3x(x+2)(x+4)
=x-5 / x+4
Answer:
oooooooof
Step-by-step explanation:
H = -16t^2 + 84t + 100 what is maxium height
Answer:
[tex]H=210.25\ \text{units}[/tex]
Step-by-step explanation:
Given that,
[tex]H = -16t^2 + 84t + 100[/tex] ...(1)
We need to find the maximum height
For maximum height, put dH/dt = 0
[tex]\dfrac{d(-16t^2 + 84t + 100)}{dt}=0\\\\-32t+84=0\\\\t=\dfrac{84}{32}\\\\t=2.625\ s[/tex]
Put t = 2.625 in equation (1)
[tex]H = -16(2.625)^2 + 84(2.625) + 100\\\\=210.25\ \text{units}[/tex]
Hence, the maximum height [tex]=210.25\ \text{units}[/tex]
P L E A S E H E L L P P P P P P P P !! WILL MARK BRAINLIEST
Answer:
D or the last one
Step-by-step explanation:
Answer: its the last one
Step-by-step explanation:
its the last one
i hope i helped
if i did pls mark BRAINLIEST!!
k
What is the equation of a line that passes through the points (–3, 4) and (2, 8)?
Answer:
=5
Step-by-step explanation:
4-9= -5
2-3 = -1
=5
.....
Answer:
y = \frac{4}{5}x + \frac{32}{5}
Step-by-step explanation:
(x₁ , y₁) = (-3, 4) & (x₂ , y₂) = (2 , 8)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]
[tex]= \frac{8-4}{2-[-3]}\\\\= \frac{8-4}{2+3}\\\\= \frac{4}{5}[/tex]
m = 4/5 ;
Equation of the line: y - y₁ = m(x - x₁)
[tex]y - 4 = \frac{4}{5}(x - [-3])\\\\y - 4 = \frac{4}{5}(x +3)\\\\y - 4 = \frac{4}{5}x + \frac{4}{5}*3\\\\ y = \frac{4}{5}x + \frac{12}{5}+4\\\\ y = \frac{4}{5}x + \frac{12}{5} + \frac{4*5}{1*5}\\\\ y =\frac{4}{5}x + \frac{12}{5} +\frac{20}{5}\\\\ y = \frac{4}{5}x + \frac{32}{5}[/tex]
what is 2.23607 as a fraction
Answer:
559/250
Step-by-step explanation:
Answer:
223607/100000
Step-by-step explanation:
I'm not sure if this is what you wanted, but 2.23607 is 223607/100000 as a fraction because the decimal is in the 100,000th place. It can't be simplified any more, but if you were to round it would be 559/250. Hope this helps you!
Solve the equation for x.
- 1/2 x - 3 = 4
Answer:
Step-by-step explanation:
It is -14
What Is the solution to the system of equations? Y=-3x-2
5x+2y=15
Answer:
x,y=-19,55
Step-by-step explanation:
plug in y.
5x+2(-3x-2)=15
5x-6x-4=15
-x=19
x=-19.
Plug in.
y=-3(-19)-2
y=55
correct is B.
Hope this helps :D
What is 69+69 please fast I need for test
Answer:
138
Step-by-step explanation:
Thats the answer bcus yea
Answer:
you can't rickroll be with 69
Step-by-step explanation:
but it is 138
A rectangular block of metal is 25cm long, 11cm wide and 9cm high. The metal block is melted down and all of the metal is used to make a cube. Work out the length of each side of the new cube formed
Answer:
29.03 cm
Step-by-step explanation:
Step one:
given
A rectangular block of metal is
25cm long
11cm wide and
9cm high.
The volume of the block is
= 25*11*9
= 2475cm^3
Required
The dimension of an equivalent cube
we know that volume of cube
v=l^3
24475=l^3
cube root both sides
l= ∛24475
l= 29.03 cm
Answer:
13.5cm
Step-by-step explanation:
Tried the other answer and got it wrong and saw the right one.
what is 4 2/3 in a proper fraction.
Answer:
14/3(I believe you mean improper fraction)
Step-by-step explanation:
4 mutiply 3 plus 2
Write the equation of a line
that passes through: (0, 2) and (-1, 1)
Answer:
y = x + 2
Step-by-step explanation:
slope = Δy / Δx = (1-2) / (-1 - 0) = 1
pass (0,2): y intercept = 2 b=2
y = mx + b
equation: y = x + 2
Find the equation of the line specified.
The line passes through the points (-2, 3) and (-4,7)
a. y = -2x-1
y = -4x-1
b. y = -2x +3
d. y = -2x + 7
C.
Please select the best answer from the choices provided
Answer:
A……
Step-by-step explanation:
Which THREE pairs of measurements are possible side lengths for a 30-60-90 triangle?
C= 30, B = 90, A = 60
1. AB+4, BC = 4√3
2. 2√3, AC = 2
3. AB = 3, AC = 3√3
4. BC = 10, AC = 4√3
5. AB = 7, AC = 14
6. AB = 11, BC = 11√3
Answer:
1, 5 and 6.
Step-by-step explanation:
The sides of this triangles has lengths in the ratio x : √3x : 2x where 2x is the hypotenuse.
When C = 30, the side AB is the small leg (=x).
When B = 90, the hypotenuse is AC ( =2x).
When A = 60, the larger leg is BC (=√3x).
1. AB = 4, BC = 4√3 :- Are possible legs.
5 AB = 7, AC = 14. :- AB = small leg, AC = hypotenuse.
6. AB = 11, BC = 11√3:- AB = small, BC = larger leg.
Answer:
1, 5, and 6
Hope this helps!
Step-by-step explanation:
If a factory can produce 250 desks in 5 days, how many desks will it produce in 15 days?
Answer:
750 would be ur answer
Step-by-step explanation:
happy new year!
Answer:750 desks
Step-by-step explanation: I would start by setting up an equation. 5d=250 (d means days). Then, to isolate the d, I would divide both sides of the equation by 5. I would get d=50. So there are 50 desks made daily. To find out the number of desks made in 15 days, I would just multiply both sides of the equation d=50 by 15 and I would get 15d=750. That means, there are 750 desks produced in 15 days. I hope this helps you out a bit!
HELP FAST!! WILL GIVEV BRAINLIEST
Answer:
-2, -4, -1.5
Step-by-step explanation:
-6x+10>16
-6x>6
x<-1
(anything less than -1)
Answer:-4, -2, -1.5
Step-by-step explanation: First, simplify the equation. You should get -6x+10>16
Then, substitute the values into the place of x. If they are greater than 16, they are solutions. -4, -2, and -1.5 work. Hope this helps you!
Guys please help me with this question
Answer:
Colin will have to wait for 2 hours for the pond to completely empty
Step-by-step explanation:
Volume of a Prism
The volume of a prism of base area Ab and height H is computed with the formula:
V=Ab.H
We are given a pond in the shape of a prism with a trapezoidal base (front view).
The area of a trapezoid of bases b1 and b2, and height a, is given by:
[tex]\displaystyle A_b=\frac{b_1+b_2}{2}.a[/tex]
The parallel bases of the trapezoid have measures of b1=0.6 m and b2=1.4 m, and the height is a=2 m, thus the area is:
[tex]\displaystyle A_b=\frac{0.6+1.4}{2}*2[/tex]
[tex]A_b=2\ m^2[/tex]
The height of the prism is H=1m, thus the volume of the pond is:
[tex]V=2\ m^2*1\ m[/tex]
[tex]V=2\ m^3[/tex]
It's also known the level of the pond goes down by 20 cm (0.2 m) in the first 30 minutes. Note at this moment the level is still at the rectangular prism zone of the pond, thus the volume of water is calculated as the area of the face of water by the height it went down:
[tex]V_w=1\ m*2\ m*0.2\ m = 0.4\ m^3[/tex]
The pond still has this volume of water:
[tex]V_p=2\ m^3-0.4\ m^3=1.6\ m^3[/tex]
The pond was drained [tex]0.4\ m^3[/tex] in 30 minutes, thus the rest of the water will be taken out in
[tex]\frac{1.6}{0.4}*30 =120\ min[/tex]
Thus, Colin will have to wait for 2 hours for the pond to completely empty
Which is the input value produces the same output value for the two functions on the graph ?
Answer:
X = - 2
Hope it's help you.... ^_^
What are the zeros of this function? Circle them on the graph.
Given:
The graph of a function.
To find:
The zeros of this function on the graph.
Solution:
We know that, zeros are the values at which the values of the function is 0. It means, the points where the graph of function intersect the x-axis are know as zeros of the function.
From the given graph it is clear that, the graph intersect the x-axis at two points.
Therefore, the marked points on the below graph are the zeros of the function.
Help please it’s urgent!
Transform the quadratic function defined by y=ax2+bx+c into the form y=a(x-h)2+k 1.Y=x2-6x-3 2.Y=5x2-20x-5
Answer:
1) y = (x-3)²-12
2) y = 5(x-2)²-9
Step-by-step explanation:
Given the quadratic expressions
y=x²-6x-3
We are to transform it in the form y=ax²+bx+c
y=(x²-6x)-3
Complete the square of the expression in parenthesis
y = (x²-6x + (6/2)² - (6/2)²)-3
y = (x²-6x+3²-3²)-3
y = (x²-6x+9-9)-3
y = (x²-6x+9)-12
y = (x²-3x-3x+9)-12
y = x(x-3)-3(x-3)-12
y = (x-3)(x-3)-12
y = (x-3)²-12
Hence the transformation is y = (x-3)²-12 where a = 1 and k = -12
For the quadratic equation
y=(5x²-20x)-5
y = 5(x²-4x)- 5
Complete the square of the expression in parenthesis
y = 5(x²-4x+4-4)- 5
y = 5(x²-4x+4)-9
y = 5(x-2)²-9
Hence the transformation is y = 5(x-2)²-9 where a = 5 and k = -9
A volunteer group is planting trees at 6 different parks. They planted 70 trees at each park.
How many trees did the group plant in all?
Answer:
420 trees
Step-by-step explanation:
6 volunteers × 70 trees planted by each = 420 trees planted in total.
What is the simplified expression for (screenshot)
A. 3/4
B. 4/3
C. 4²/3
D. 3³/4
Answer:
B. 4/3
Step-by-step explanation:
[tex] \frac{ {4}^{ - 3} . {3}^{4} . {4}^{2} }{ {3}^{5} . {4}^{ - 2} } \\ \\ = \frac{ {4}^{ - 3} . {4}^{2 + 2} }{ {3}^{5 - 4}} \\ \\ = \frac{ {4}^{ - 3} . {4}^{4} }{ {3}^{1}} \\ \\ = \frac{ {4}^{4 - 3} }{ {3}^{1}} \\ \\ = \frac{ {4}^{1} }{ {3}^{1}} \\ \\ = \frac{4}{3} [/tex]
Answer:
B. 4/3
Step-by-step explanation:
(4^-3 . 3^4 . 4^2)/(3^5 . 4^-2)
4^-3 . 4^2/ 4^-2 . 3^4/ 3^5
4^(-3+2-(-2)) . 3^(4-5)
4^1 . 3^-1
4 . 1/3 = 4/3