Answers
By solving an inequality, we will see that option a is cheaper for more than 60 miles.
For what number of miles is option A better?We know that option A charges $25 per day plus $0.15 per mile, so the cost for x miles is given by the linear equation:
A(x) = $25 + $0.15*x
While for option B the fixed cost is $10 and the cost per mile is $0.40, so the cost equation is:
B(x) = $10 + $0.40*x
The cost of option a will be smaller when:
$25 + $0.15*x < $10 + $0.40*x
$25 - $10 < $0.40*x - $0.15*x
$15 < $0.25*x
$15/$0.25 < x
60 < x
So for 60 miles the cost is the same, for x > 60 miles the cost of option a will be smaller (because the slope is smaller).
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Related Questions
Solve for r in terms of q, s, and r. S=-qtr
Answers
To isolate a certain variable in an equation, we must perform inverse operations on both sides of the equal sign to cancel out values.
Solving the Question[tex]S=-qtr[/tex]
⇒ Right now, r is being multiplied by q and t. Divide both sides by qt to cancel these values out:
[tex]\dfrac{S}{qt}=\dfrac{-qtr}{qt}\\\\\dfrac{S}{qt}=-r[/tex]
⇒ Now, to remove the negative symbol, multiply both sides by -1:
[tex]r=-\dfrac{S}{qt}[/tex]
Answer[tex]r=-\dfrac{S}{qt}[/tex]
Is 38 / 53 and simplest form explain? Why t? Or or why not
Answers
yes 38/53 is the simplest form
Step-by-step explanation:
The fraction is already reduced.
Write an equation of the line that passes through the point (1, 4) and has a slope of -2
WIth point- intercept form
Answers
The equation of the line that passes through the point (1, 4) and has a slope of -2 is y = -2x + 6
What is slope-intercept form of a line?
The equation of the line in slope-intercept form is given by:
y = mx + c
Here,
(x, y) = Every point on the line
m = Slope of the line
c = y-intercept of the line
According to the given question:
The given line has slope m = -2 and point (1, 4) passes through the line.
By slope-intercept form general equation of line is y = mx + b where b is
y-intercept.
Substituting values of m and point (1, 4) in this equation to get value of b
y = mx + b
4 = -2(1) + b
b = 6
Hence equation of the line is y = -2x + 6
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The number of students in attendance since 2000 at Lamar Community College can be represented by the equation below, where x equals the time in years after 2000. S(x) = (x - 50)² + 19 The college creates a graph to better view the decreases and increases in attendance. Which of the following describes the end behavior of their graph? O A. As x approaches positive infinity, S(x) remains constant. OB. As x approaches positive infinity, S(x) approaches positive infinity. OC. As x approaches positive infinity, S(x) approaches zero. OD. As x approaches positive infinity, S(x) approaches negative infinity.
Answers
As domain x approaches positive infinity, S(x) approaches positive infinity. Option B is correct.
What is a graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Given expression for the attendance of the student is,
S(x) = (x - 50)² + 19
The end behavior of their graph is given as after x = 50 the graph starts heigh increasing gradient and it keeps increasing, till x = infinity, as shown in the graph.
Thus, the curve of the given equation S(x) will increase from x = 50 to x = ∞ .
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There were 234 roses growing in the back garden. If 50% of the roses were red. How many were not red?
Answers
Answer:117
Step-by-step explanation:
I’m good at math
Answer:
117 Roses
Step-by-step explanation:
234 *0.5 = 117
Determine if the triangles are similar by Angle-Angle similarity
Answers
The triangles are similar by Angle-Angle similarity since they are congruent.
What is Angle-Angle Similarity?According to the Angle-Angle Similarity Theorem, if two angles in one triangle are equal to two angles in another triangle, the triangles are similar. The triangles are similar if two pairs of corresponding angles in a pair of triangles are congruent. We know this because if two angle pairs are equal, then the third pair must be equal as well.
Two triangles with two angles, starting with Triangle 1, one measuring 47 degrees and the other measuring 53 degrees, are congruent to two angles in Triangle 2. Following the AA similarity theorem, it is assumed that Triangle 1 is similar to Triangle 2.
In this case, angle MNP = angle QPL (corresponding angles, //lines) (A)
angle QLP is common angle (A)
By AA, the 2 triangles are similar.
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2. Fill in the blanks to factor the trinomial 3x² + 13x - 10 by grouping.
3x² + 13x - 10 = 3x² -
=
3x²-x+.
_X+X-10
(3x - 2) +(3x - 2)
+
)(3x - 2)
Answers
Answer:
-2 and 15x and 5x and 5Step-by-step explanation:
You want the steps involved in factoring 3x² +13x -10 by grouping.
FactorsTo fill in the blanks, you need to know the product of the first and last coefficients, and the factor pairs of that product that have a sum equal to the middle coefficient.
3(-10) = -30 = (-1)(30) = (-2)(15) = (-3)(10) = (-5)(6)
The sums of these factor pairs are 29, 13, 7, 1. The sum of interest is ...
-2 + 15 = 13
These are the values that go in the first pair of blanks.
= 3x² -2 x + 15 x -10
Factors of pairsWe want to identify the common factor for each pair of terms:
= x (3x -2) + 5 (3x -2)
Factored trinomialFinally, the common factor (3x -2) is removed and we have ...
= ( x + 5 )(3x -2)
What will the dividend income be on W number of shares of XYZ stock if XYZ distributes a $Y per share dividend?
Answers
Answer:
In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.
Step-by-step explanation:
The dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend. This is because the dividend income is calculated by multiplying the number of shares that an investor owns by the amount of the dividend per share.
For example, if an investor owns W = 100 shares of XYZ stock and XYZ distributes a $Y = 5 per share dividend, then the investor's dividend income will be 100 * 5 = 500 dollars.
In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.
Please answer fast lots of points!!!!
Answers
Answer:
Step-by-step explanation:
Solve 3+8X+6 = 5(X+2) + 3X-1
Answers
Answer: x= (−∞,∞)
Step-by-step explanation:
3+8x+6 = 5(x+2) + 3x-1
9+ 8x = 5x +10 + 3x -1
9 + 8x = 8x +9
Subtract nine on both sides
8x= 8x
x = Any number!
Sidney bought two magazines that
were each $4.95. If Sidney paid a total of
$10.59 for the two magazines with tax,
what percent tax did she pay for her s
purchase?
Answers
Answer:
Step-by-step explanation:
0.69
slope of (-3,-2) and (-1,-5)
Answers
Answer: Slope of [tex](-3, -2)[/tex] and [tex](-1, -5)[/tex] is [tex]-1.5[/tex].
Step-by-step explanation:
The slope of a line is given by, [tex]m=\frac{y_2-y_1{} }{x_2-x_1}[/tex]
Here we have,
[tex](x_{1}, y_{1}) = (-3, -2)[/tex] and [tex](x_{2}, y_{2}) = (-1, -5)[/tex]
Now put the known values in the slope formula we get,
[tex]m=\frac{(-5) -(-2) {} }{(-1) -(-3)}[/tex]
[tex]m=\frac{(-3) {} }{2}[/tex]
Slope (m) = 1.5
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Select the correct answer. about 1,500,000 bacteria are found in 1 milliliter of water of coastal ocean. how many bacteria will be there in 100 milliliters of water? a. 1.5 × 104 b. 1.5 × 105 c. 1.5 × 106 d. 1.5 × 107 e. 1.5 × 108
Answers
The amount of bacteria that will be there in 100 milliliters of water will be: 1.5 × 10⁸.
What is standard notation?A standard notation is a method of writing a given number, equation, or expression in a specific format that adheres to certain rules. 4.5 billion years, for example, is written as 4,500,000,000 years.
The main reason for converting numbers to scientific notation is to make calculations involving unusually large or small numbers easier.
Even though zeros are no longer always seemed to set the decimal point, all digits in a scientific notation number are significant.
Here, it is given that,
The number of bacteria found in 1 milliliter of water = 1,500,000.
So,
The number of bacteria in 100 milliliters of water = 1,500,000 x 100
The number of bacteria in 100 milliliters of water = 15,00,00,000
The number of bacteria in 100 milliliters of water = 1.5 × 10⁸.
Correct option: e
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C is directly proportional to D, when C-125 and D=5. Work out the value of C when D = 6. Work out the value of D when C = 4725
Answers
Answer:
d=189 when c=4725
Step-by-step explanation:
c:d
125:5
divide by 5 to find the value of c when d=1
25:1
multiply by 6 to find the value of c when d=6
150:6
4725:?
4725/25=189
189*1=189
The length of a rectangular drainage pond is changing at a rate of 8 ft/hr and the perimeter of the pond is changing at a rate of 24 ft/hr. At what rate is the width changing?
Answers
The rate of width changing will be;
⇒ 4 feet/hour
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The length of a rectangular drainage pond is changing at a rate of 8 ft/hr and the perimeter of the pond is changing at a rate of 24 ft/hr.
Now,
We know that;
⇒ Perimeter of rectangle = 2 (Length + Width)
Substitute al the values, we get;
⇒ 24 = 2 (8 + x)
⇒ 12 = 8 + x
⇒ x = 12 - 8
⇒ x = 4
Thus, The rate of width changing will be;
⇒ 4 feet/hour
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In \triangle EFG,△EFG, \angle E \cong \angle G,∠E≅∠G, GE = 17GE=17 and FG = 10FG=10. Find the length of EF. EF
Answers
In the triangle EFG, ∠E≅∠G, GE = 17 units and FG = 10 units, then the length of the side EF is 10 units
The given triangle EFG
The length of the side GE = 17 units
The length of the side FG = 10 units
The measure of angle E is equal to the measure of angle G
The equation will be
∠E≅∠G
Therefore the triangle is Isosceles triangle
The length of the side FG will be equal to the length of the side FE
The length of the side EF = The length of the side FG = 10 units
Therefore, the length of the side EF is 10 units
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Draw and label a coordinate plane so that the x-axis extends from -9 to 9 and the y-axis
extends from -6 to 6. Represent each of these points with a dot, and label the point using
its letter name.
Answers
The required given Co-ordinates are plotted in graph below.
What are Co-ordinates?The numbers on a direction lattice are utilized to find focuses. Each point can be recognized by an arranged sets of numbers; that is, a number on the x-axis called a x-coordinate, and a number on the y-hub called a y-coordinate. Requested matches are written in enclosures (x-coordinate, y-coordinate).
Explain graph.Graph is characterized as to make an outline that shows a connection between at least two things. An illustration of diagram is to make a progression of bars on charting paper
According to question:coordinates plane so that the x-axis extends from -9 to 9 and the y-axis
extends from -6 to 6
Plotted points on the graph are shown in image below.
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What is the correct prime factorization of 24? 2 ∙ 2 ∙ 6 2 ∙ 3 ∙ 3 2 ∙ 2 ∙ 3 ∙ 3 2 ∙ 2 ∙ 2 ∙ 3
Answers
Answer:
2x2x2x3
Step-by-step explanation:
Does this given information represent a function?
Answers
Aubrey and Charlie are driving to a city that is 120 mi from their house. They have already traveled 15 mi, and they are driving at a constant rate of 65 mi/h. Complete the function that models the distance they drive as a function of time. Then complete a reasonable domain for this situation.
Answers
Therefore, the solution of this problem is the domain would be
0 < t ≤ 1.61.
What is domain?A function's domain is the set of possible values that can be entered. This set reflects the values of x in a function like f. (x). Its range refers to the set of possible values that a function can accept. These are the values that are returned by the function when we enter an x value.
Here,
The remaining distance that would result from multiplying the speed by the time t will be added to the 20 miles that make up the total distance. The formula for the equation would be as follows:
120 = 15 + 65t
It would be 0 hours at the very least. When the entire 120-mile distance has been accomplished, the time limit is reached.
t ≤ (120 - 15)/65
t ≤ 1.61 hours
Therefore, the solution is the domain would be 0 < t ≤ 1.61.
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Five times a number increased by 5 is equal to 25, find the number.
Answers
Answer: the number is 4
Step-by-step explanation:
5x+5=25 is the equation
solve for x by isolating x
5x+5-5=25-5
5x=20
divide both sides by 5 to isolate x
x=4
Answer: 4
Step-by-step explanation:
5x + 5 = 25 this is what the equation is!
Then we subtract 5 on both side
5x = 20
Then divided by 5 on both side
x= 4
Find the measure of each acute angle in a right triangle where the measure of one acute angle is 8 times the measure of the other acute angle
Answers
The measure of the acute angles in the right triangle are 10 and 80 degrees.
How to find the angle of a right angle triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be named base on the position of the angles. The sides includes hypotenuse side, opposite side and adjacent side.
The sum of angles in a right angle triangle is 180 degrees.
The other measures of the right triangle are acute angles.
Any angle that measures greater than 0° and less than 90° is called an acute angle.
Hence, let's find the measure of the acute angles
let
x = measure of one acute angle
Hence,
x + 8x + 90 = 180
9x = 180 - 90
9x = 90
x = 90 / 9
x = 10
Therefore, the measure of the acute angles are 10 and 80 degrees.
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slope of the line that passes through (10, 4) and (5, 13). as a integer
Answers
The slope of the line that connects (10,4) and (5,13) is -9/5.
What is a slope?The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).Here given,
The two points are (10,4) and (5,13).
We have to find the slope that passes through the given points,
The formula to find slope(m) is,
The slope of the line that passes through (x1 , y1) and (x2,y2) is,
Slope(m) = y2 - y1 / x2 - x1
By substituting the values in x and y
Slope = 13 - 4 / 5 - 10
= 9 / -5
Slope = -9/5
= -1.8
Therefore the slope of line that passes through (10,4) and (5,13) is -9/5.
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............. i need help past due
Answers
The unit rate in acres of land planned by the workers per day is found is 16/35 acres.
What is meant by rate of doing work?Power refers to the rate of work completion. It is a measure of how much energy is used up each unit of time. The joule per second (J/s) is the unit of power in the SI system.Force applied across a distance is called work. Examples such work include dragging down a confined helium balloon, driving a vehicle up a steep hill, and lifting an article against the gravitational attraction of the Earth. Energy manifests mechanically as work.For the mentioned question-
Total acres of land planted = 2/5 acres.
Total time taken = 7/8 days.
Thus, unit rate in acres per day = Total acres of land planted / Total time taken
unit rate in acres per day = (2/5) / (7/8)
unit rate in acres per day = (2*8)/(5*7)
unit rate in acres per day = 16/35
Thus, unit rate in acres of land planned by the workers per day is found is 16/35 acres.
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*URGENT* I need help with 5,6,7 please answer correctly and quickly
Answers
Answer:
Step-by-step explanation:
(5). ( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~~~~~
( 4 , 8 )
y = [tex]\frac{1}{7}[/tex] x - 5 ; slope m = [tex]\frac{1}{7}[/tex]
Slope of line ⊥ to the given line is opposite reciprocal to [tex]\frac{1}{7}[/tex] and equal to ( - 7)
y - 8 = - 7( x - 4 )
(6).
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
m = [tex]\frac{ y_{2} -y_{1} }{ x_{2} -x_{1} }[/tex]
y = mx + b
~~~~~~~~~~~~
( 4 , 3 )
( 5 , 1 )
m = [tex]\frac{1-3}{5-4}[/tex] = - 2
y - 3 = - 2( x - 4 )
y = - 2x + 11
(7). y = - [tex]\frac{1}{2}[/tex] x + 2
which statement about the graph of y=3x+5 is correct?
Answers
The correct statement regarding the linear function y = 3x + 5 is given as follows:
The line passes through the ordered pair (0,5) and has a slope of 3.
What are the slope and the intercept of the linear function?The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
The slope and the intercept are given as follows:
m is the slope, representing the rate of change of the linear function.The intercept is of b, representing the numeric value of the function when the input is of zero, hence the line passes through the ordered pair (0,b).In this problem, the function is defined as follows:
y = 3x + 5.
Hence the coefficients have the values given as follows:
m = 3, b = 5.
Missing InformationThe statements are given by the image shown at the end of the answer.
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3. The coordinate (4, 3) is the solution to which system of equations?
Answers
The coordinate (4, 3) is the solution of the following system of equations:
y = 1/2x + 1 and y = -x + 7
y = x - 1 and y = 1/4x + 2
The solution implies that the coordinate is the: point of intersection.
What is the Solution to a System of Equations?The solution to a system of equations are the coordinate of the point where the two lines that represent the equations of the system intersect each other. The coordinate of x and the coordinate of y, when plugged into any of the equations would be true.
The graph of the system of equations, y = x - 1 and y = 1/4x + 2 shows that both equations intersect at the point with the coordinate (4, 3) [see the graph in figure 1].
Also, the graph in figure two shows that y = 1/2x + 1 and y = -x + 7 also intersect at (4, 3).
Therefore, we can state that, the system of equations with (4, 3) as the solution are:
y = 1/2x + 1 and y = -x + 7
y = x - 1 and y = 1/4x + 2
The solution means point of intersection.
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The graph shows the results of a survey that asked people to choose their favorite
dinner foods. One of the persons surveyed is chosen at random.
What is the probability that she chose Potatoes?
Answers
Answer:
7.5%
Step-by-step explanation:
a probability is always
desired cases / totally possible cases
the totally possible cases is everybody in the survey :
24+18+14+10+8+6 = 80
the desired cases are everybody having potatoes a favorite food : 6
the probability the picked person prefers potatoes is
6/80 = 3/40 = 0.075 = 7.5%
The volume of a cylinder having height one and half of the radius is 12,936 m3 what minimum square cm of paper is needed to cover the curved surface area of the cylinder? The answer should be 1848m2. please solve my question.
Answers
Answer:
Lateral Surface Area = 1848 m^2 (does not include the top and bottom)
Step-by-step explanation:
Vol Cylinder = pi*r^2 *h
h = (3/2)r
Vol = pi*r^2((3/2)r) [We are told that the volume is 12,936 m^3]
pi*r^2((3/2)r) = 12,936 m^3
pi*(3/2)*(r^3) = 12,936 m^3
pi*r^3 = (12,936 m^3)*(2/3)
pi*r^3 = 8,624 m
r^3 = (8,624 m)/(3.14)
r^3 = 2745.1
r = 14.0 m
Lateral Surface = 2*(pi)*r*h [Lateral is just the curved portion of the right cylinder.
Lateral Surface Area = 2*(3.14)*(14.0)(21.0)
Lateral Surface Area = 1848 m^2
(a) Write 7.97 x 10 ^-6 as an ordinary number.
Answers
Answer:
0.00000797
Step-by-step explanation: