The cost, c(x), for a taxi ride is given by c(x) = 3x + 2.00, where x is the number of minutes. On a piece of paper, graph c(x) = 3x + 2.00. Then determine which answer matches the graph you drew, including the correct axis labels.
Answers
The y-intercept of 2.00 indicates that even if the ride was 0 minutes, there is still a flat fee of $2.00.
What is a slope?If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of a line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
The characteristics of the graph of the equation c(x) = 3x + 2.00.
The graph of c(x) = 3x + 2.00 is a straight line with a slope of 3 and a y-intercept of 2.00.
The x-axis represents the number of minutes, and the y-axis represents the cost in dollars.
The slope of 3 indicates that for every additional minute of the taxi ride, the cost increases by $3.
The y-intercept of 2.00 indicates that even if the ride was 0 minutes, there is still a flat fee of $2.00.
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Related Questions
What is the solution to 2h+8>3h-6
Answers
2h-3h>-6-8
-h>-14
h<14
Answer h∈(-∞;14)
helpppppppppppppppppppppp
Answers
Explanation:
1) given:
y = (x + 3)^2 + (x + 4)^2
2) expand the binomials:
y = x^2 + 6x + 9 + x^2 + 8x + 16
3) add like terms:
y = 2x^2 + 14x + 25
4) take common factor 2 of the first two terms:
y = 2 (x^2 + 7x) + 25
5) complete squares for x^2 + 7x
x^2 + 7x = [x +(7/2)x ]^2 - 49/4
6) substitue x^2 + 7x = (x + 7/2)^2 - 49/4 in the equation for y:
y = 2 [ (x + 7/2)^2 - 49/4] + 25
7) take -49/4 out of the square brackets.
y = 2 (x + 7/2)^2 - 49/2 + 25
8) add like terms:
y = 2(x + 7/2)^2 + 1/2
And that is the vertex for of the given expression.
HOW ARE RESTRICTIONS AND DISCONTINUITIES CREATED IN RATIONAL EXPRESSIONS? HOW CAN THEY BE ACCOUNTED FOR GRAPHICALLY?
Answers
Graphically, this is usually represented by a dashed vertical line indicating a vertical asymptote.
In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator zero, as division by zero is undefined. Graphically, these are represented as vertical asymptotes or holes. They can be accounted for by noting the x-values where the denominator equals zero.
Explanation:In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator of the expression equal to zero, as division by zero is undefined. A rational expression is a ratio of two polynomials, typically written in the form P(x)/Q(x), where P(x) and Q(x) are polynomial expressions and x is a variable.
For example, in the rational expression (x+2)/(x-3), x-3 is the denominator. The restriction is determined by setting the denominator equal to zero. If x-3 equals zero, then the value of x that makes this true is 3. Therefore, x cannot be 3 as this would make the denominator zero, creating a discontinuity in the rational expression.
Graphically, discontinuities in rational expressions are represented as vertical asymptotes or holes. A vertical asymptote occurs when the denominator of the fraction is zero but the numerator is not. A hole occurs when both the numerator and the denominator are zero at the same point. These can be accounted for by noting the x-values where the denominator equals zero.
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What is the solution to the system of equations below? Y=-4/5x-6 & y=-30
Answers
-30=-4/5x-6
And then solve for x:
Add 6 on both sides.
-24=-4/5x
Then multiply by the reciprocal of -4/5.
-5/4*-24=-5/4*-4/5x
x=30
But then you are gonna want to plug 30 in for x in y=-4/5x-6 to make sure that it is the same as y=-30.
The solution of the system is y = -30 and x = 30.
How to solve the system of equations?Here we have two equations:
y = -(4/5)*x - 6
y = -30
The second equation can be replaced in the first one, so we get:
-30 = -(4/5)*x - 6
Now we can solve that for x.
-30 + 6 = -(4/5)*x
24*(5/4) = x = 30
So the solution of the system is y = -30 and x = 30.
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Please help me !! Thank you!!
Answers
2. yes. The cost is proportional to the number of tickets, hence a linear function of the number of tickets.
3. no. The population is modeled by an exponential function.
4. yes. Distance is proportional to time at a constant speed.
5. yes. (maybe) In the context of this question, "at a constant rate" is presumed to mean "by a constant amount". In that case, growth is linear.
If the rate expressed as a constant percentage (say, 3%) per year, then growth is exponential, not linear.
Dan and Dawn purchased a house for $69,500. They had to make a down
payment of 20%. How much was the amount of the mortgage they obtained?
a. $13,900
b. $69,500
c. $55,600
d. $76,450
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Answers
One reading list had a total of 12 fiction and nonfiction books. Compared to the first list, there are twice as many fiction books and 3 times as many nonfiction books making a total of 28 books on the second reading list. Write a system of linear equations and find the number of fiction and nonfiction books on the first list.
Answers
x = fiction books
y = nonfiction books
We write the system of equations that best suits the problem.
We have then:
x + y = 12
2x + 3y = 28
Solving the system:
x = 8
y = 4
Answer:
x + y = 12
2x + 3y = 28
the number of fiction and nonfiction books on the first list are:
8 fiction books
4 nonfiction books
Answer:
(8,4)
Step-by-step explanation:
yes
please help thank you
Answers
When doing ratios, if you know the proportion of the length and width you just multiply that ratio to the origingal value
Choose the option that correctly completes the statement.
The measure of an exterior angle of a triangle is _____ the sum of the measures of the remote interior angles.
less than
greater than
equal to
Answers
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
Explanation:The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
For any triangle, the sum of the measures of the three interior angles is always 180 degrees. An exterior angle is formed by extending one side of the triangle. The sum of the measures of the exterior angle and its corresponding remote interior angles is always 180 degrees. Therefore, the measure of an exterior angle is equal to the sum of the measures of the remote interior angles.
Final answer:
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
Explanation:
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
For example, if one of the remote interior angles of a triangle measures 40 degrees, then the corresponding exterior angle measures 40 degrees as well. The sum of the measures of the other two interior angles would be 140 degrees, making the exterior angle equal to 40 degrees.
Therefore, the correct option that completes the statement is equal to.
A bank's monthly charge for maintaining an account is $.45 for each check written plus a service charge of $12.50. If x represents the number of checks written during the month, which function models this situation?
A) f(x) = x + 12.50
B) f(x) = 0.45x -12.50
C) f(x) = 12.50x + 0.45
D) f(x) = 0.45x + 12.50
Answers
The correct model for the bank service cost based on the number of checks written during a month is f(x)=0.45x + 12.50.
Explanation:The question is asking for a model that would represent the cost of a bank service based on the number of checks written during a month. The bank charges $0.45 for each check, which is a variable cost that will change depending on the number of checks, represented by x. Additionally, they also have a monthly fixed service charge of $12.50, which is paid regardless of whether or not a check is written that month.
So, the amount paid every month is $0.45 multiplied by the number of checks, plus $12.50. In function format, that will be represented as $0.45x + $12.50, which is equivalent to the option D i.e f(x)=0.45x + 12.50. So, the correct model for the situation is D.
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Charlie is trying to hold on to his toy fire truck.
His brother Noah is pulling with a force of 8 N on a bearing of 023° and his brother Jude with a force of 5 N on a bearing of 155°.
What force does Charlie need to exert to keep the toy in equilibrium?
If you could explain it using Cartesian vectors, that would be the best.
Answers
Charlie needs to apply a force in the opposite direction of the resultant vector sum of his brothers' forces. By converting the forces into Cartesian vectors based on the bearings, we can calculate the components of Charlie's required force to maintain equilibrium.
Explanation:Step 1: Break down the forces into their x and y components
The force exerted by Noah can be broken down into its x and y components using the following equations:
F_x_Noah = F_Noah × cos(θ_Noah) = 8 N × cos(023°) ≈ 7.13 N
F_y_Noah = F_Noah × sin(θ_Noah) = 8 N × sin(023°) ≈ 3.71 N
The force exerted by Jude can be broken down into its x and y components using the following equations:
F_x_Jude = F_Jude × cos(θ_Jude) = 5 N × cos(155°) ≈ -4.95 N
F_y_Jude = F_Jude × sin(θ_Jude) = 5 N × sin(155°) ≈ -0.58 N
Step 2: Sum the x and y components of the forces
To find the net force in the x-direction, we sum the x-components of the forces exerted by Noah and Jude:
F_x_net = F_x_Noah + F_x_Jude ≈ 7.13 N - 4.95 N ≈ 2.18 N
To find the net force in the y-direction, we sum the y-components of the forces exerted by Noah and Jude:
F_y_net = F_y_Noah + F_y_Jude ≈ 3.71 N - 0.58 N ≈ 3.13 N
Step 3: Calculate the magnitude of the net force
The magnitude of the net force can be calculated using the Pythagorean theorem:
F_net = √(F_x_net^2 + F_y_net^2) ≈ √(2.18 N^2 + 3.13 N^2) ≈ 3.74 N
Step 4: Find the angle of the net force
The angle of the net force can be calculated using the following equation:
θ_net = atan(F_y_net / F_x_net) ≈ atan(3.13 N / 2.18 N) ≈ 55.6°
Step 5: Calculate the force Charlie needs to exert
In order for Charlie to keep the toy fire truck in equilibrium, he needs to exert a force that is equal in magnitude and opposite in direction to the net force. Therefore, the force Charlie needs to exert is 3.74 N at an angle of 55.6° + 180° = 235.6° (since the net force is acting in the third quadrant).
While training for a marathon, Sean runs at least 28 miles a week. He has already ran 6 miles this week. The inequality shown can be used to find m, the number of miles Sean still needs to run this week. m + 6 ≥ 28 Which inequality represents the solution set for this situation? A) m ≥ 22 B) m ≤ 22 C) m ≤ 34 D) m ≥ 34
Answers
Explanation : Just l like a normal equation , we need to isolate the variable to get its value. We can do that by simply substracting 6 from both sides of the equation :
m + 6 >= 28
m + 6 - 6 >= 28 - 6
6 - 6 cancel out so we end up with
m >= 22
I hope you understood my brief explanation. And please consider marking this awnser as Branliest if you think it deserves it. Thank you so :)
Answer: A) m ≥ 22
Step-by-step explanation:
Hi, to answer this question we simply have to solve the inequality given for m (miles ran per week).
m + 6 ≥ 28
Subtracting 6 from both sides:
m+6-6 ≥ 28 -6
m ≥ 22
Sean still needs to run 22 miles this week.
So, the correct option is A) m ≥ 22
Feel free to ask for more if needed or if you did not understand something.
It's been estimated that if you consume an extra 3,500 calories, you will gain 1 pound of fat. one can of soda contains 40 grams of sugar. sugar has 4 calories per gram. if a person drinks a six-pack of soda every day, how many pounds will he or she gain in 1 year?
Answers
1 can of soda---------------> 40 grams of sugar
if 1 gram sugar------------------------------------>has 4 calories
40 grams (1 can of soda)-----------------------> X
X=40*4=160 calories
then
1 can of soda--------------> has 160 calories
six-pack of soda every day--------------> 6*160=960 calories every day
in one year------------> 960*365=350400 calories in one year
if 3500 calories----------------> 1 pound of fat
350400 calories----------------X
X=350400/3500=100.11 pound
In one year she or he will gains 100.11 pound of fat
the answer is 100.11 pound
The simplest form of square root of eighty can be written as a times square root of b, where a = and b = .
Answers
The correct answer is:
A=4
B=5
hopes this helps you and future people!
Answer:
a = 4 and b = 5
Step-by-step explanation:
The simplest form of square root of eighty can be written as:
[tex]\sqrt{80}=\sqrt{2\times2\times2\times2\times5}[/tex]
Now as it is a square root function, we will pair up the four 2's in two pairs.
And will take out [tex]2\times2[/tex] outside the square root.
Making the answer = [tex]2\times2\sqrt{5}[/tex]
or [tex]4\sqrt{5}[/tex]
So, a = 4
and b = 5
Which unit should be studied to review symbols from set theory? Unit 1 Unit 3 Unit 5 Unit 7
Answers
a wheel has a radius of 12 cm approximately how far does it travel in 2 revolutions
Answers
Hello!
S=R*THETA
so s= is what you are looking for.
givens;
radius=12cm=.12m
theta(RADIANS ONLY)=2pi*2revs=4pi
s=.12*4pi=for an approximate answer of 1.50796m travelled
hope this helps. any questions please ask. thank you
A child designs a flag in the shape of a rhombus, as shown in the diagram below. Which expression can be used to determine the side length of the rhombus?
Answers
The answer is the first option: 10/Cos(30°)
Explanation:
1. As you can see in the figure attached, there is a right triangle and its hypotenuse (which is represented with the letter "x") is the side you want to calculate. So, you have:
Cos(α)=Adjacent leg/Hypotenuse
α=30°
Adjacent leg=(20 in)/2=10 in
Hypotenuse=x
2. When you substitute these values into the formula, you obtain:
Cos(α)=Adjacent leg/Hypotenuse
Cos(30°)=10/x
3. Therefore, you obtain the expression to determine the side length of the rhombus by clearing the hypotenuse "x", as below:
x=10/Cos(30°)
Answer:
A
Step-by-step explanation:
10/cos30 degree
Write an equation that is perpendicular to y = -7x + 2 and passes through (7 , 5)
Answers
The slope of a line perpendicular to another line is the negative reciprocal, that is, [tex]m_{perp} = \frac{-1}{m} [/tex].
For your equation, the slope is –7. That means the slope of its perpendicular line must be [tex]- \frac{-1}{7} = \frac{1}{7} [/tex].
Now, we must also find such a line that passes through (7, 5). It is easiest to write this in point-slope form, [tex]y-y_1=m(x-x_1)[/tex].
We get [tex]y-5= \frac{1}{7} (x-7)[/tex]. Technically, we are done, but it is customary to convert this into slope-intercept form, [tex]y=mx+b[/tex].
[tex]y-5= \frac{1}{7} (x-7)\\\\y= \frac{1}{7}x-1+5\\\\y= \frac{1}{7}x+4[/tex].
And that's our final answer. We can verify the solution graphically. See attached.
In general, our steps are:
1) Find the slope of the given line if it is not given directly.
2) Find the slope of the perpendicular line (the negative reciprocal).
3) Identify the point it must pass through.
4) Substitute the values into the point-slope form.
5) Write the equation in slope-intercept form.
Every morning, a deli offers a “commuter special” in which customers can select a pastry, beverage, and a copy of one of the local papers and pay $1.00. Their options are listed in the table.
Last Tuesday, the deli did not have any muffins. How did that affect the number of possible combinations?
A. It decreased the number of combinations by 1.
B. It decreased the number of combinations by 4.
C. It decreased the number of combinations by 8.
D. It decreased the number of combinations by 10.
Answers
Answer: C
c. It decreased the number of combinations by 8.
Jason is buying a home theater system on layaway for $349. If he makes a down payment of $25 and pays $54 each week will it take Jason to pay for the home theater system?
Answers
First, you would take 349 and subtract 25 from it.(349-25=324) This gets rid of the down payment.
Next, you would divide 324 by 54. (324÷54=6)
It would take him 6 weeks!
Hope this helped! And make sure to check my calculations!
Godspeed
-Song
Jason will take 6 weeks to pay off the home theater system on layaway after making an initial down payment of $25 and weekly payments of $54.
The student's question is about how long it will take Jason to pay for a home theater system using a layaway plan. Jason has made an initial down payment of $25 and will make weekly payments of $54.
To calculate the time it will take to pay off the remaining balance, we subtract the down payment from the total cost: $349 - $25 = $324. Then, we divide the remaining balance by the weekly payment amount: $324 / $54 = 6. This means it will take Jason 6 weeks to pay off the home theater system on layaway.
He perimeter of this pentagon is 280 cm. find the lengths of the sides.
Answers
280 / 5 which equals 56 cm
Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = –6. Which function could Heather be writing?
Answers
Heather's quadratic function must have a double root at x = -6, suggesting a function of the form y = a(x + 6)² here 'a' is a nonzero coefficient. The orientation and width of the parabola depend on the value of 'a'.
Since Heather's quadratic function represents a parabola that touches but does not cross the x-axis at x =
–6, her function must have a double root at x= –6. To achieve this, the quadratic function should be in the form y = a(x + 6), where a is a non-zero coefficient.
The function that Heather could be writing will have a vertex at the point (-6, 0), as the parabola touches the x-axis at this point. Thus, a possible function can be y = (x + 6), if we assume a coefficient of 1 for simplicity. If a is negative, the parabola will open downwards, while a positive a will make the parabola open upwards. However, the exact value of a will depend on other conditions Heather might have, such as the position of the parabola in relation to the y-axis or specific points it must pass through.
There's a 40% chance of rain on Tuesday and a 50% chance of rain Friday. What percent will it rain both Tuesday and Friday?
p.s. this is a probability question I think
Answers
50% or 50/100 which is in decimal format 0.5.
P( tueday AND friday) <----- AND is a keyword, means product
P(tuesday) AND P(friday)
0.4 * 0.5
0.2 or 0.2 * 100 or 20% chance that it will rain on both days.
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Answers
A rectangle has a length of 12 millimeters and a width of 17 millimeters.
What is the effect on the perimeter when the dimensions are multiplied by 12?
a. The perimeter is increased by a factor of 12.
b. The perimeter is increased by a factor of 48.
c. The perimeter is increased by a factor of 144.
d. The perimeter is increased by a factor of 576.
Answers
ok so original perimeter = 12 +12 + 17 +17 = 58 mm
if dimensions are multiplied by 12:
12*12 = 144 and 17*12 = 204
new perimeter = 144 +144 +204 +204 = 696 mm
696 / 58 = 12
so the perimeter increased by a factor of 12, answer is A
Answer:
The perimeter is increased by a factor of 12.
Option (a) is correct .
Step-by-step explanation:
Formula
Perimeter of a rectangle = 2 (Length + Breadth)
As given
A rectangle has a length of 12 millimeters and a width of 17 millimeters.
Perimeter of a rectangle = 2 × (12 + 17)
= 2 × 29
= 58 millimeters ²
As given
when the dimensions are multiplied by 12 .
New Length = 12 × 12
= 144 millimeter
New Breadth = 17 × 12
= 204 millimeter
Thus
New Perimeter of a rectangle = 2 × (144 + 204)
= 2 × 348
= 696 millimeter²
[tex]\frac{New\ perimeter\ of\ a\ rectangle}{Perimeter\ of\ a\ rectangle} = \frac{696}{58}[/tex]
[tex]\frac{New\ perimeter\ of\ a\ rectangle}{Perimeter\ of\ a\ rectangle} = 12[/tex]
Therefore the perimeter is increased by a factor of 12.
Option (a) is correct .
Write a polynomial function of f of least degree with rational coefficients a leading coefficient of 1 and the given zeros -5 2i
Answers
y = (x + 5)(x + 2i)(x - 2i) = (x - 5)(x^2 + 4)
which expands to
y = x^3 + 5x^2 + 4x + 20
find the nonpermissible replacement for y in this expression Y+7/Y-3
Answers
Final answer:
The nonpermissible value for y in the expression (Y+7)/(Y-3) is 3, because it would make the denominator zero, resulting in an undefined expression.
Explanation:
The question is asking to find the nonpermissible value for y in the expression (Y+7)/(Y-3). In algebra, nonpermissible values are values for the variable that would make the denominator of a fraction equal to zero. We set the denominator of our expression equal to zero and solve for y.
Steps to find the nonpermissible value:
Identify the denominator of the expression, which is (Y-3).
Set the denominator equal to zero: Y - 3 = 0.
Solve for y: Y = 3.
Therefore, the nonpermissible replacement for y is 3, as substituting this value into the denominator would create a division by zero, which is undefined in mathematics.
an internet company charges a one time setup fee of 44.99 and a monthly fee of 29.99 for internet service the company is offering a 25 percent discount on the monthly fee for the first year
Answers
yark
Given the geometric sequence 100, 50, 25, ..., find the 7th term.
Answers
T(7)=100(1/2)^6=1.5625
The distance between 2 points is found by ________ the x terms and squaring the result, _________ the y terms and squaring the result, taking the sum of the results and then finding the square root of the sum.
subtracting; subtracting
adding; adding
adding; subtracting
subtracting; adding
Answers
The goal is to find the legs of the right triangle, so you can find the hypotenuse. The hypotenuse is the distance between the two points. See the attached image.
Answer:
A)
subtracting; subtracting
Step-by-step explanation: