Answer:
The system of equations is:
• C(x)=2400+60x
,• R(x)=120x
The number of bicycles to break even = 40
Explanation:
Let the number of bikes sold = x
• The operating cost of the store per month = $2400
,• Cost Price Per bike = $60
Thus, the total monthly cost for the store:
[tex]C(x)=2400+60x[/tex]Next, the average selling price of each bicycle is $120, therefore, the monthly revenue of the store:
[tex]R(x)=120x[/tex]The store breaks even when the cost equals its revenue.
[tex]\begin{gathered} R(x)=C(x) \\ 120x=2400+60x \end{gathered}[/tex]We then solve for x:
[tex]\begin{gathered} \text{ Subtract 60x from both sides of the equation} \\ 120x-60x=60x-60x+2400 \\ 60x=2400 \\ \text{ Divide both sides of the equation by 60} \\ \frac{60x}{60}=\frac{2400}{60} \\ x=40 \end{gathered}[/tex]The store must sell 40 bicycles in order to break even.
PLEASE HELP MUST SHOW HAND WRITEN WORK
1. Kim's age is twice that of her sister.
(a) How can you represent Kim’s age with a mathematical sentence? (2pts)
When you add Kim's age to her sister's age, you get 36. How old is each sister?
(b) Write a mathematical equation that represents the situation above. Make sure to use part “a” to help you fill in Kim’s age. (4pts)
(c) Solve the equation in the space below for Kim’s sister’s age. (4pts)
(d) What is Kim’s sister’s age? (2pts)
(e) Use that information to solve for Kim’s age. What is Kim’s age? (3pts)
Answer:
a.) Let x be Kim's sister's age. Kim's age would therefore be 2x.
b.) 2x + x = 36
c.) 2x + x = 36
3x = 36
x = 12
d.) So Kim's sister (x) is 12.
e.) Since Kim's age is 2x, Kim is 24.
Step-by-step explanation:
See above.
- What is -7- (-4)? Explain how you know.
Answer:
-3
Step-by-step explanation:
We know that,
( + ) × ( + ) = ( + )
( - ) × ( - ) = ( + )
( + ) × ( - ) = ( - )
Accordingly, let us solve the given fraction.
-7 - ( - 4 )
-7 + 4
-3
What is the area of trapezoid ABCE?A20 mB16 mEDC25 msq m
Given data:
The given figure of the trapezium.
The expression for the area of the trapezium is,
[tex]\begin{gathered} A=\frac{1}{2}(20\text{ m+25 m)(16 m)} \\ =360m^2 \end{gathered}[/tex]Thus, the area of the given trapezium is 360 sq-m.
Simplify. 14(3x−7)+34x Responses 34x−1 3 over 4 end fraction x minus 1 334x−134 3 and 3 over 4 end fraction x minus 1 and 3 over 4 34x+212 3 over 4 end fraction x plus 2 and 1 half 112x−134
The simplified form of the given expression is option c 1 1/2x - 1 3/4
Given,
The expression; 1/4 (3x - 7) + 3/4x
We have to simplify this expression;
Simplification of expressions;
To simplify a phrase, create an equivalent expression without any terms that are identical. The expression will then be rewritten using the fewest terms feasible.
Then,
1/4 (3x - 7) + 3/4x
= 1/4 × 3x - 1/4 × 7 + 3/4x
= 3/4x - 7/4x + 3/4x
= 6x/4 - 7/4
= 3x/2 - 7/4
= 1 1/2x - 1 3/4
Therefore,
The simplified form of the given expression is option c 1 1/2x - 1 3/4
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Solve for m/UVX.
Answer: m/UV X =
O
72°
42°
Submit Answer
The measure of angle UVX is 30°
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves. Angle can also refer to the length of a rotation or an angle. The arc is centered at the vertex and defined by the sides in the case of a geometric angle.
Given, measure of angle UVW = 72°
measure of angle XVW = 42°
So, the measure of angle UVX = 72° - 42° = 30°
Hence, the measure of angle UVX is 30°
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. n+(t+2) = n +(2+t) is an example of which property? |n+ (t+2)=n+(2+t) ¿es un ejemplo de esta propiedad?
Answer:
The equation is an example of the associative property of addition.
Step-by-step explanation:
Associative property of addition: changing the grouping of addends does not change the sum.
For example: A+(B+C) = (A+B)+C.
hi i need some help. on the “select” part, the options are 1997-2006.
From the given table that represents the population in a small coastal communityfor the period 1997 to 2006, let's answer the following questions.
(a) Average rate of change of the population between 1999 and 2002.
To find the average rate of change, apply the formula below:
[tex]Average=\frac{y2-y1}{x2-x1}[/tex]Where:
x1 = 1999
x2 = 2002
y1 = the population in 1999 = 1,336
y2 = the population in 2002 = 1,483
Thus, we have:
[tex]\begin{gathered} Average=\frac{1483-1336}{2002-1999} \\ \\ Average=\frac{147}{3} \\ \\ Average=49 \end{gathered}[/tex]Therefore, the average rate of change of the population between 1999 and 2002 is
49
(b) What was the average rate of change of the population between 2001 and 2005.
To find the average rate of change, apply the formula:
[tex]Average=\frac{y2-y1}{x2-x1}[/tex]Where:
x1 = 2001
x2 = 2005
y1 = population in 2001 = 1591
y2 = population in 2005 = 801
Thus, we have:
[tex]\begin{gathered} Average=\frac{801-1591}{2005-2001} \\ \\ \text{Average}=\frac{-790}{4} \\ \\ \text{Average}=-197.5 \end{gathered}[/tex]Therefore, the average rate of change in the population between 2001 and 2005 was -197.5
(c) For what period of time was the population increasing.
From the given table, we can see the table was increasing from 1997 to 2001
The population was increasing from 1997 to 2001
(d) For what period was the population decreasing.
From the table, the population was decreasing from 2002 to 2006
The population was decreasing from 2001 to 2006
ANSWER:
• (a) 49
,• (b) -197.5
,• (c) 1997 to 2001
,• (d) 2001 to 2006
Consider the polynomial function p(x)=-4x³-6x²+16+24. find the end behavior of the graph of p(x). explain your answer
I will ask my question here
is p(x)
[tex]\begin{gathered} p(x)=-4x^3-6x^2+16x+24 \\ \lim _{x\to\infty}-4x^3-6x^2+16x+24=\lim _{x\to\infty}-4x^3=-4\lim ^{}_{x\to\infty}x^3=-4\infty=-\infty \\ \\ \end{gathered}[/tex]bye :)
X=
////////////////////////////
Answer: [tex]x=15[/tex]
Step-by-step explanation:
By the consecutive interior angles theorem,
[tex]150+3x-15=180\\\\3x-15=30\\\\3x=45\\\\x=15[/tex]
Jai left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Jai is xx minutes after he left his house, until he got back home. How many blocks is it from the store to the bank?
Considering the Graph and reading the distance blocks from the store to the bank we see a progression of 3blocks
This is further explained below.
What is the distance?Generally, There is a concept referred to as distance that may be used to quantify, either quantitatively or qualitatively, the distance that separates two items or sites.
When speaking about physics or using the phrase in everyday language, "distance" may either refer to a literal measurement or an estimate based on a number of other parameters.
Both meanings are appropriate when discussing or using the term.
The progression of existence and events that occur in what seems to be an unstoppable order beginning in the past, continuing through the present, and moving into the future is what we refer to as time.
Time may be broken down into three distinct parts: the past, the present, and the future.
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Lavania is studying the growth of a population of fruit flies in her laboratory. After 6 days, she had nine
more than five times as many fruit flies as when she began the study. If she observes 20 fruit flies on the first
day of the study, write and evaluate an expression to find the population of fruit flies Lavania observed after
6 days.
The expression to find the population of fruit flies on 6th day in Lavania's laboratory can be (9+5x) where x is the number of fruit flies on the first day. After evaluating the expression, the number of fruit flies on 6th day will be 109.
According to the question,
We have the following information:
Lavania observes 20 fruit flies on the first day of her study.
On 6th day, the number of fruit flies would be nine more than 5 times as many fruit flies as when she begun her study.
Now, let's take the number of fruit flies on first day to be x.
So, we have:
x = 20
Now, the expression to find the number of fruit flies on 6th day would be:
9+5x
Now, putting the value of x:
9+5*20
9+100
109
Hence, the required expression is (9+5x) and the number of fruit flies on 6th day are 109.
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6 more than the difference of p and 3
Do not simplify any part of the expression.
I'm pretty sure it's 6>p-3
I need help 9th grade math
Answer:
A. y - 2 = 2/3 (x - 0)
Step-by-step explanation:
Round your answer to the nearest hundredth.A = 8.4 in²Calculate the diameter of the circle.O 3.27 inO 4.20 inO 1.75 inO2.89 in
The area of a circle can be calculated as follows:
[tex]A=\pi r^2[/tex]Using the area given in the problem and solving for the radius r:
[tex]\begin{gathered} A=8.4 \\ 8.4=\pi r^2 \\ \frac{8.4}{\pi}=r^2 \\ \sqrt{\frac{8.4}{\pi}}=r \\ 1.635=r \end{gathered}[/tex]Finally, the diameter is twice the radius:
[tex]\begin{gathered} d=2r \\ d=2*1.635 \\ d=3.27\text{ in} \end{gathered}[/tex]Then the answer is the first option 3.27 in
How does the graph of 2y−x=1 compare with the graph of 3y−x=1?
a.
The graph of 2y−x=1 has a steeper slope than the graph of 3y−x=1.
b.
The graph of 3y−x=1 has a steeper slope than the graph of 2y−x=1.
c.
The graph of 2y−x=1 crosses the x-axis farther to the left than the graph of 3y−x=1.
d.
The graph of 2y−x=1 crosses the x-axis farther to the right than the graph of 3y−x=1.
The way in which the graph of 2y − x = 1 compare with the graph of 3y − x = 1 is that: A. the graph of 2y − x = 1 has a steeper slope than the graph of 3y − x = 1.
What is a steeper slope?In Mathematics, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.
How to interpret the slope?Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
x and y are the points.m is the slope or rate of change.c is the intercept.For the graph of 2y − x = 1, the slope is given by:
2y − x = 1
2y = x + 1
y = x/2 + 1/2
Slope, m₁ = 1/2 or 0.5.
For the graph of 3y − x = 1, the slope is given by:
3y − x = 1
3y = x + 1
y = x/3 + 1/3
Slope, m₂ = 1/3 or 0.3.
Therefore, m₁ > m₂ (steeper slope).
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due wensday but prefered be done now
The correct statement about the function is the y-intercept is (0.71), and 71 represents the starting temperature.
What is the y-intercept?
A graph can be described as a pictorial representation of data. A graph has a y-axis and a x-axis. The x-axis in this question represents time and the y-axis is the temperature.
The function shown in the graph is a linear function. This is because the curve is a straight line. The y-intercept is the point where the line crosses the y-axis. The y-intercept is the value of the data set when x is zero. The y-intercept represents the initial temperature or the starting temperature.
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Hello, I just need help with part b and it's dealing with combinations
According to the combination method, there are 6 ways for the selection to be made if one worker is to be a receptionist, one a secretary, and one a technical typist.
Combinations:
A combination is all about grouping. The number of different groups which can be formed from the available things can be calculated using combinations.
The standard form for calculating the combinations is,
[tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]
where,
0 ≤ r ≤ n.
This formula is sometimes also called as ncr formula.
Given,
An executive hires 3 office workers from 8 applicants.
Here we need to find how many ways can the selection be made if one worker is to be a receptionist, one a secretary, and one a technical typist.
Here we have to split the problem like the following,
We know that the total number of office workers is 3.
Like, if one worker is to be a receptionist, the the combination is like,
So, the value of n = 3 and r = 1.
Then, according to the ncr formula,
=> ³C₁ = [tex]\frac{3!}{1!(3-1)!}[/tex]
=> 3!/1!2!
=> (3 x 2 x 1) / 1 x 2 x 1
=> 3
Similarly, if one worker is to be a secretary,
Here the value of n = 2 (Because we have already select one person as receptionist) and r = 1
So,
=> ²C₁ = (2!)/1!(2-1)!
=> (2x1)/ 1 x 1
=> 2
Similarly, if one worker is to be a technical typist,
Here the value of n = 1 (Because we have already select one person as receptionist) and r = 1
So,
=> ¹C₁ = 1
Therefore, the total number of possible ways are,
=> 3 x 2 x 1
=> 6
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Find the indicated measure. Assume that all segments that appear to be tangent are tangent.
We are asked to determine the arc length of HJ. To do that we will use the following formula:
Given two secant lines that intercept outside a circle as follows:
We have the following relationship:
[tex]\angle x=\frac{1}{2}(\text{mCD-mAB)}[/tex]Substituting the values we get:
[tex]29=\frac{1}{2}(96-\text{mHJ)}[/tex]Now, we multiply both sides by 2:
[tex]58=96-mHJ[/tex]Now, we subtract 96 from both sides:
[tex]58-96=-\text{mHJ}[/tex]Solving the operations:
[tex]-38=-\text{mHJ}[/tex]Now, we multiply both sides by -1:
[tex]38=\text{mHJ}[/tex]Therefore, the measure of the arc length of HJ is 38.
Determine the product of (x-2)^3
The profuct of the given expression (x-2)³ is (x³ - 6x² + 12x - 8).
What are expressions?An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) You can think of expressions as being similar to phrases. Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing. For instance, the mathematical expression for "4 added to 2" will be 2+4.So, (x-2)³:
Do, the product as follows:
(x-2)³Perfect cube root formula: (a - b)³ = a³ - 3a²b + 3ab² -b³
x³ - 3x² · 2 + 3x · 2² -2³Simplify:
x³ - 6x² + 12x - 8Therefore, the profuct of the given expression (x-2)³ is (x³ - 6x² + 12x - 8).
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A 12-ft-by-15-ft rectangular swimming pool has a 3-ft-wide no-slip surface around it. What is the outer perimeter of the no-slip surface?.
The outer perimeter of the no-slip surface is equal to 78 feet.
Perimeter is a term used to describe the sum of the outside edge lengths or it can also be described as the whole of the outer edge or boundary.
The outer perimeter of this swimming pool can be determined by adding 3 feet twice to all the sides of the rectangular swimming pool and then adding these sides together.
Since it is a 12-ft-by-15-ft rectangular swimming pool, this means that two sides of this swimming pool are 12 feet and two sides of this pool are 15 feet, therefore;
12 + 6 = 18
15 + 6 = 21
Now the perimeter can be determined by adding all the sides as follows;
18 + 21 + 18 + 21 = 78 feet
Hence, the outer perimeter of the no-slip surface is calculated to be 78 feet.
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Which one of these expressions doesn’t have a value less than 1 please help thank you if u do
The most appropriate choice for exponent will be given by-
Fourth option is correct
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2\times 2\times 2 \times 2[/tex], here, 2 is multiplied by itself 4 times.
If [tex]a^m = a\times a\times a \times.....\times a[/tex] (m times), a is the base and m is the index.
The laws of index are
[tex]a^m \times a^n = a^{m + n}\\\\\frac{a^m}{a^n} = a^{m-n}\\\\a^0 = 1\\\\(a^m)^n = a^{mn}\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\a^mb^m = (ab)^m[/tex]
Here,
For first option
[tex]\frac{4^{11}}{4^{14}}\\\frac{1}{4^{14 - 11}}\\\frac{1}{4^3}\\\frac{1}{64} < 1[/tex]
For second option
[tex](5^4)^2 \times 5^{-11}\\5^8 \times 5^{-11}\\5^{8-11}\\5^{-3}\\(\frac{1}{5})^3\\\frac{1}{125} < 1[/tex]
For the third option,
[tex](2^3)^{-2}\\2^{-6}\\(\frac{1}{2})^6\\\frac{1}{64} < 1[/tex]
For the fourth option
[tex]\frac{(3^5)^2}{3^4}[/tex]
[tex]\frac{3^{10}}{3^4}\\3^{10 - 4}\\3^6\\ 729 > 1[/tex]
Fourth option does not have an expression greater than 1
Fourth option is correct.
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400 x 600x 800x150x120
Answer:
3.456e+12
or
3,456,000,000,000
Step-by-step explanation:
400 x 600 = 240,000
240,000 x 800 = 192,000,000
192,000,000 x 150 = 28,800,000,000
28,800,000,000 x 120 = 3,456,000,000,000
hope this helps you :D
Which rational number also belongs to the set of whole numbers
A 0.3333
B. -9
C. 0
D. 5/6
Answer:
0
Step-by-step explanation:
Whole numbers are 0.1.2.3... Follows that pattern forever.
What is 25% of 130? Round to one decimal place ___________
Answer:
32.5
Step-by-step explanation:
What is 25% of 130?
0.25 * 130 = 32.5
State which graph would most appropriately represent the given situation
Since we are measuring bank preference, we want to see the data in order of importance, then, the pareto chart is the most useful graph in this situation
b
2x - 15
3x + 5
Line a || Line b.
Use the diagram to write an equation and solve for x
Answer:
x= −20
Step-by-step explanation:
The solution is x = 38
The equation to measure the value of x is ( 2x - 15 )° + ( 3x + 5 )° = 180° and the value of x = 38 from the two angles
What are angles in parallel lines?
Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.
We can conclude three factors determining parallel lines ,
Alternate angles are equal
Corresponding angles are equal
Co-interior angles add up to 180°
Same side exterior angles are supplementary
Given data ,
Let the first angle be represented as A
Now , the value of A is = ( 2x - 15 )°
Let the second angle be represented as B
Now , the value of B is = ( 3x + 5 )°
The angles A and B are on the same side of the exterior angles
And , lines a and b are parallel
So , When two parallel lines are intersected by a transversal, the angles that are exterior to the parallel lines and on the same side of the transversal line are supplementary
Substituting the values in the equation , we get
( 2x - 15 )° + ( 3x + 5 )° = 180°
On simplifying the equation , we get
2x - 15 + 3x + 5 = 180
5x - 10 = 180
Adding 10 on both sides of the equation , we get
5x = 190
Divide by 5 on both sides of the equation , we get
x = 190/5
x = 38
Therefore , the value of x is 38
Hence , the value of x from the equation is 38
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Ben earned 625.5 points out of 700 on an essay and 65out of 70 on an assignment. In order to earn an A in theclass, he needed to average a 91 on these twoassignments. Did Ben earn an A?
We were told that Ben earned 625.5 points out of 700 on an essay. Expressing his score in the essay in terms of percentage, it becomes
625.5/700 x 100 = 89.29%
Also, he scored 65 out of 70 on an assignment. Expressing his score in the assignment in terms of percentage, it becomes
65/70 x 100 = 92.86%
We would find the average between the two percentages
Average = sum of percentages/number of percentages
Average = (89.29 + 92.86)/2
Average = 91.075
Average is approximately 91%
Since in order to earn an A in the class, he needed to average a 91 on these two
assignments and he got an average of 91%, then we can conclude that he got an A
find the trig graph equation
Step-by-step explanation:
I assume, based on what I see, that the solid line is just cos(x), right ?
and we need to find the equation that draws the dotted line, correct ?
the notation is strange, as it seems we need to find a multiplication factor for x in the cos function.
but there is no multiplication factor that moves the cosine wave by pi to the left or to the right (so that the max. happens, where originally the minimum happens, and vice versa).
so, we need to add (or subtract) pi in the cosine function.
the rest is clear :
the normal distance between min. and max. of the cosine function is 2 (between +1 and -1). the target is 4. so we need to multiply by 2.
and since the values of that function have to be between -4 and 0 (instead of -2 and +2), we have to subtract overall 2.
giving us the function :
y = 2×cos(pi + x) + -2
Question 2 of 10
Use the quadratic formula to find the solution to the quadratic equation given
below.
9
ײ − 3x + 9/4 =0
PLEASE HELP
Answer:
using the quadratic formula
Step-by-step explanation:
x= 3/2
2x²-11x-21=0.using factorization method
The factors of the quadratic equation are found as the 7 and -3/2
What is termed as the factorization method?To factorize a number, use the factorization formula. Factorization is defined as the process of converting one entity into the a product of another entity, as well as factors, that when multiplied together yield the original number. The factorization method employs the basic factorization formula to simplify any algebraic and quadratic equation, where the equations are depicted as the product of factors rather than expanding the brackets.For the given question, the quadratic equation is give as;
2x² - 11x - 21 = 0
Find the factors of -21×2 = 42 such that on subtraction it gives -11.
2x² - 14x + 3x - 21 = 0
Take 2x common from the first two terms and 3 from the last two terms.
2x(x - 7) + 3(x - 7) = 0
Take (x - 7) common from the terms.
(x - 7)(2x + 3) = 0
Then,
x - 7 = 0
x = 7
and, 2x + 3 = 0
x = -3/2
Thus, the factors of the quadratic equation are found as the 7 and -3/2.
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