The linear equation that represents the given problem is 18x + 20y = 400.
We are given that the golf course charges $18 for a package including the full 18-hole course. The course also sells buckets of golf balls for $20 each. The golf course wants to earn a total of $400 by the end of the day. We need to find the linear equation for this situation.
Let the number of golf course packages sold be represented by the variable "x". Let the number of buckets of golf balls sold be represented by the variable "y". The equation is written below.
18x + 20y = 400
The complete question is given below.
A golf course charges $18 for a package including the full 18-hole course. The course also sells buckets of golf balls for $20 each. The golf course would like to earn $400 by the end of the day. Write a linear equation that describes the problem.
To learn more about equations, visit :
brainly.com/question/10413253
#SPJ9
Six more than three times a number is negative thirty-six.
x = 10 is the value of x as per given in the question.
What is linear equation ?A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. where x is a variable, A is a coefficient, and B is a constant. The standard form of linear equations in two variables is of the form Ax + By = C. where x and y are variables and A and B are: Equations with the highest degree of 1 are called linear equations. This means that the exponent of the variable in the linear equation is greater than 1. The graph of a linear equation is always a straight line. A linear equation is an algebraic equation in which each term has exponent 1, and the graph of this equation is always a straight line. There is a linear equation in one variable and a linear equation in two variables.Calculation3x + 6 = 36
3x = 30
x = 10
learn more about linear equation here :
brainly.com/question/11897796
#SPJ1
GCF for 4y + xy2 + 6y
The greatest common factor or GCF in the expression 4y + xy² + 6y is y.
The given expression is 4y + xy2 + 6y
GCF stands for greatest common factor
Among these three numbers ;
the variable y is common in all three of them
The factors of 4 y = 4 and y
the factors of xy² are x and y
and the factors of 6y are 6 and y
This can also be simply written by taking y common in this
for example; y ( 4 + xy + 6 )
From the above mentioned proof we can establish the fact that the variable y is common in all three of them
Thus the greatest common factor among them is y
To know more about greatest common factor or related problems you may visit the link which is mentioned below;
https://brainly.com/question/11221202
#SPJ1
what is f(x)=−x−7 cause I dont know
f(x) is a linear function whose slope is equal to -1 and y-intercept is equal to -7.
What is f(x)?
Here we have f(x) defined as:
f(x) = -x - 7
Now, we define a general linear function as:
g(x) = m*x + b
Where m is the slope and b is the y-intercept.
Now, we can rewrite f(x) as:
f(x) = (-1)*x + (-7)
So f(x) is a linear function with a slope of -1 and a y-intercept of -7.
Laern more about linear functions:
https://brainly.com/question/4025726
#SPJ1
What is X+y=6
What is 2x-y=9
The tallest tree in the United States
Coast Redwood in Jedidiah Smith State
Park in California. It is 321 feet tall.
Suppose you are 5 feet 8 inches tall and
cast a shadow that is 2 feet at a certain
time of day. About how long is the tree's
shadow at the same time of day? (convert
5 ft 8 inches to feet)
x = 113.2941 is the approximate length of the tree's shadow at the same time of a day.
What is a length?A unit of length is any arbitrarily chosen and widely accepted reference standard for measuring length. The most common units in modern use are metric units, which are used in every country on the planet. In the United States, customary units are also used. British Imperial units are still used in the United Kingdom and other countries for a variety of purposes. SI and non-SI units are subsets of the metric system.
5 feet + 8 inches is equal to 5 feet.
5 feet 8 inches is equal to 5 feet plus (8 inches) * (1 foot 12 inches).
5 feet 8 inches plus (8/12) feet equals 6 feet.
5 feet 8 inches equals 5 feet plus 2/3 feet.
5 feet 8 inches = (5 + (2/3)) feet
5 feet 8 inches = ((15/3) + (2/3)) feet
5 feet 8 inches = ((15+2)/3) feet
5 feet 8 inches = (17/3) feet
5 feet 8 inches = 5.667 feet
A/B = C/D
where
A = height of person
B = length of shadow of person
C = height of tree
D = length of shadow of tree
So we have
A = 17/3
B = 2
C = 321
D = x
A/B = C/D
(17/3)/2 = 321/x
(17/3)*x = 2*321
(17/3)*x = 642
(3/17)*(17/3)*x = (3/17)*642
x = 1926/17 the precise length of the tree's shadow
The approximate length of the tree's shadow is x = 113.2941.
To know more about length, visit:
https://brainly.com/question/8552546
#SPJ1
When two dice are rolled, find the probability of getting a 4 on each one.
step 1
the probability of get 4 in one dice is
P=1/6
so
the probability of get 4 in two dices is
(1/6)*(1/6)=1/36
answer is the third optioncomputer bag a sandwich store charges a $10 delivery fee and 450 for each sandwich. a. what is the total cost (sandwiches and delivery charge)if an office order 6 sandwiches .b. what is the total cost of x sandwiches?c. is there a proportional relationship between the number of sandwiches and the cost of the order ?explain how you know
A sandwich store charges a $10 delivery fee and $4.50 for each sandwich.
a) If an office order 6 sandwiches, the total cost is:
10 + 6(4.50) = 10 + 27 = 37
Then, the cost of the order is $37
b) The total cost of x sandwich is given by the following algebraic equation:
f(x) = 10 + 4.50x
because 10 from the delivery fee and x sandwiches cost 4.50x dollars, f(x) is the total cost.
c) The relationship between the number of sandwiches and the cost of the order is proportional, because if the numbers of sandwiches increases, the cost increases too. It can be appreciated in the function f(x), which is a linear function with a unit rate of 4.50.
The Arnold Inn offers two plans for wedding parties. Under plan A, the inn charges $30 for each person in attendance. Under plan B, the inn charges $1300 plus $20 for each person in excess of the first 25 who attend. For what size parties will plan B cost less? I do not understand how for Plan b: 1300+20(p-25). I do not understand the part p-25
ANSWER
81 people
EXPLANATION
Let p be the number of people that attend the party.
Under plan A, the inn charges $30 for each person, so the value y of a party for p people is,
[tex]y_A=30x[/tex]Then, under plan B, the cost is $1300 for a maximum of 25 people - this means that if 1 to 25 people attend the party, the cost is the same, $1300. For each person in excess of the first 25 - this means for 26, 27, 28, etc, the inn charges $20 each. The cost for plan B is,
[tex]y_B=1300+20(p-25)[/tex]The last part, (p - 25), is the part of the equation that separates the first 25 attendees. This equation works for 25 people or more, but it is okay to solve this problem. Note that for p = 25, the cost for plan A is,
[tex]y_A=30\cdot25=750[/tex]Which is less than the cost of plan B ($1300).
We have to find for what number of people attending the party, the cost of plan B is less than the cost of plan A,
[tex]y_BThis is,[tex]1300+20(p-25)<30p[/tex]We have to solve this for p. First, apply the distributive property of multiplication over addition/subtract4ion to the 20,
[tex]\begin{gathered} 1300+20p-20\cdot25<30p \\ 1300+20p-500<30p \end{gathered}[/tex]Add like terms,
[tex]\begin{gathered} (1300-500)+20p<30p \\ 800+20p<30p \end{gathered}[/tex]Now, subtract 20p from both sides,
[tex]\begin{gathered} 800+20p-20p<30p-20p \\ 800<10p \end{gathered}[/tex]And divide both sides by 10,
[tex]\begin{gathered} \frac{800}{10}<\frac{10p}{10} \\ 80For 80 people, the costs of the plans are,
[tex]\begin{gathered} y_A=30\cdot80=2400 \\ y_B=1300+20(80-25)=1300+20\cdot55=1300+1100=2400 \end{gathered}[/tex]Both have the same cost. The solution to the inequation was the number of people, p, is more than 80. This means that for 81 people the cost of plan B should be less than the cost of plan A,
[tex]\begin{gathered} y_A=30\cdot81=2430 \\ y_B=1300+20(81-25)=2420 \end{gathered}[/tex]For 81 people, plan B costs $10 less than plan A.
What is the equation of this line line PLS help
Answer: y=2x
Step-by-step explanation:
The equation of the line is y=2x.
BRAINLIST PLEASE HELP! I need to the answer this
Answer:
2, 3, 5
Step-by-step explanation:
There is no side-side congruence theorem.
There is also no angle-side-side congruence theorem.
That eliminates choices 1 and 4.
The triangles show side-angle-side-angle as congruent corresponding parts.
Also using the vertical angles at vertex C, you get angle-side-angle.
Answer: choices 2, 3, and 5.
Triangle ABC is an equilateral triangle with midpoints D, E, and F of its sides AC, BA, and CB, respectively.
A figure shows triangle ABC, in which point D is the midpoint of AC, point E is the midpoint of AB, and point F is the midpoint of CB.
Which lines are lines of symmetry of, ABC?
Answer:
A//F
CE
BD
Step-by-step explanation:
since its an equilateral triangle you can split in half easily
what are like terms
63 + 54
Answer:
There are 3 common factors of 63 and 54, that are 1, 3, and 9. Therefore, the greatest common factor of 63 and 54 is 9.
Step-by-step explanation:
In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match.
Hope this helped:)
Evaluate
107% of 700m
Answer:
834.6m
Step-by-step explanation:
780*1.07=834.6
The population of a mosquito population obeys the law of uninhibited growth.If there are 500 mosquito initially and there are 800 after 1 day. How long is it until there are 7000 mosquito?Round your answer to the nearest tenth.
The law of uninhibited growth is express as:
[tex]N(t)=N_0e^{kt}[/tex]where N(t) is the population at time t, N0 is the initial population, k is the growth rate and t is the time. In this case we know that after one day, t=1, the population is 800 and that the initial population was 500; plugging these values and solving for k we have:
[tex]\begin{gathered} 800=500e^k \\ e^k=\frac{800}{500} \\ \ln e^k=\ln\frac{8}{5} \\ k=\ln\frac{8}{5} \end{gathered}[/tex]Now that we have the growth rate, we know that the population growth in this case can be express as:
[tex]N(t)=500e^{(\ln\frac{8}{5})t}[/tex]We want to know the time it takes for the population to be 7000, to find it we equate our expression to this value and solve for t:
[tex]\begin{gathered} 7000=500e^{(\ln\frac{8}{5})t} \\ e^{(\ln\frac{8}{5})t}=\frac{7000}{500} \\ \ln e^{(\ln\frac{8}{5})t}=\ln14 \\ (\ln\frac{8}{5})t=\ln14 \\ t=\frac{\ln14}{\ln\frac{8}{5}} \\ t=5.6 \end{gathered}[/tex]Therefore, it takes 5.6 days for the population to reach 7000 individuals.
what is 60 rounded to the nearest whole number
Answer: I suppose it is still 60
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
becaus eit the whole nimber
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 2.5, 5.4
Step-by-step explanation:
[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]
Question attached as screenshot below: please help me Pre Calculus
From the given question
The volume of a cone is:
[tex]V=\frac{1}{3}\times\pi\times r^3[/tex]Now,
We are given with radius and the height of the cone
So,
We can solve for the radius as a function of water level using ratio and proportion
Then,
[tex]\begin{gathered} \frac{3}{9}=\frac{r}{h} \\ r=\frac{h}{3} \end{gathered}[/tex]Substitute the value of r into the above formula
So,
[tex]\begin{gathered} V=\frac{1}{3}\times\pi\times r^3 \\ V=\frac{1}{3}\times\pi\times(\frac{h}{3})^3 \\ V=\frac{h^3}{81}\times\pi \end{gathered}[/tex]Then,
Taking derivatives
[tex]\begin{gathered} V=\frac{h^3}{81}\times\pi \\ \frac{dV}{dt}=\frac{h^3}{81}\times\pi \end{gathered}[/tex]The,
Solving for the dh/dt
So,
[tex]\begin{gathered} \frac{dV}{dt}=10\text{ and h=3, then } \\ \frac{dh}{dt}=9.55m\text{ /s} \end{gathered}[/tex]Hence, the answer is 9.55.
help me pls!! ill mark brainliest!! Create a x/y tableequation: y=-1/3x-2
To be able to make x/y table, we substitute any number as x in the given equation y = -1/3x - 2.
Let's create a table,
x solution y
-6 -1/3(-6) - 2 = 2 - 2 0
-3 -1/3(-3) - 2 = 1 - 2 -1
0 -1/3(0) -2 = 0 - 2 -2
3 -1/3(3) - 2 = -1 - 2 -3
6 -1/3(6) - 2 = -2 - 2 -4
a 20-foot ladder is placed against a building. If the top of the ladder will lean against the building 4 square root 7 feet high, how far away from the base of the building is the bottom of the ladder located? include a sketch
First, let's draw a sketch of the problem to better understand it:
Since the distances 20, 4√7 and x create a right triangle, we can use the Pythagorean theorem to calculate the value of x.
The Pythagorean theorem states that the length of the hypotenuse squared is equal to the sum of each leg squared.
So we have:
[tex]\begin{gathered} 20^2=(4\sqrt[]{7})^2+x^2 \\ 400=16\cdot7+x^2 \\ 400=112+x^2 \\ x^2=400-112 \\ x^2=288 \\ x=\sqrt[]{288}=\sqrt[]{2\cdot12\cdot12}=12\sqrt[]{2}\text{ ft} \end{gathered}[/tex]Therefore the wanted distance is 12√2 feet (16.97 ft).
Got It? Do this problem to find out.c. The number of games won in the American Football Conferencein a recent year is displayed below. Find the median and themeasures of variability. Then describe the data.American Football Conference Wins+10 11 12 131 2 3456 7 8 9
Answer:
Explanation:
The median is the value corresponding to the line inside the box. Looking at the box plot, the line is between 8 and 9. Thus,
Median = 8.5
To find the measure of variability, we would find the interquartile range, IQR
IQR = third quartile(Q3) - first quartile(Q1)
The first quartile is the value corresponding to the left end of the box. From the box plot, it is between 5 and 6. Thus,
Q1 = 5.5
The third quartile is the value corresponding to the right end of the box. From the box plot,
Q3 = 11
Thus,
IQR = 11 - 5.5
IQR = 5.5
The range is the difference between the minimum and maximum values. On the box plot,
maximum value = 13
minimum value = 1
Range = 13 - 1
Range = 12
4x^4 - 3x^3 + 2x^2 - 5x +6 divided by (x-2)what is the remainder of this question
The remainder is 44
Explanations:The given polynomial is:
[tex]4x^4-3x^3+2x^2-5x\text{ + 6}[/tex]The function is to be divided by x - 2
The remainder of the division will be calculated using the remainder theorem
The remainder theorem states that " If a function g(x) is divided by x - a, the remainder of the division will be g(a)"
[tex]\text{Let g(x) = 4x}^4-3x^3+2x^2-5x+6[/tex]The remainder when g(x) is divided by x -2 is g(2)
[tex]\begin{gathered} g(2)=4(2)^4-3(2)^3+2(2)^2-\text{ 5(2) + 6} \\ g(2)\text{ = 4(16) - 3(8) + 2(4) -5(2) + 6} \\ g(2)\text{ = 64 - 24 + 8 - 10 + 6} \\ g(2)\text{ = 44} \end{gathered}[/tex]is (x-3) a factor of 2x^3-4x^2-6
A. yes
B. No
What is the remainder?
(no answer choice just type the answer!)
right answers only!
(x-3) is not a factor of [tex]2x^3-4x^2-6[/tex]
and the Remainder is 32 .
Using the remainder theorem, which asserts that if x is a factor in a polynomial p(x), then p(a) = 0, we may say that.
Therefore, p(x) = 2x3 - 4x2 - 6 p(3) = 0 if x - 3 is a factor.
So, p(x) = 2x³ - 4x² - 6 If x - 3 is a factor, then
p(3) = 0
So, substituting x = 3 into the equation, we have
p(3) = 2x³ - 4x² - 6
= 2(3)³ - 4(2)² - 6
= 2(27) - 4(4) - 6
= 54 - 16 - 6
= 54 - 22
= 32
Since p(3) ≠ 0.
x - 3 is not a factor
2. Since p(3) = 32,
Thus the required remainder is 32.
To know more about factors of polynomial you may visit the link which is mentioned below:
brainly.com/question/28691011
#SPJ1
A health club charges 35% a month for membership fees. Determine whether the cost of membership is proportional to the number of months. Explain your reasoning.
Yes, Because the amount charged grows by $35, a fixed amount, every time the number of months increases by 1.
What exactly does direct proportionality mean?Direct proportion, also known as direct variation, is a relationship between two quantities when their ratio equals a fixed number. The proportional symbol is used to denote it. The fact that the other quantity is inverted here means that the same symbol is really employed to denote inverse proportional.
Direct proportionality applies. This is so that the cost of the membership remains constant no matter how many months you choose to pay for. For instance, the cost is 1 x $35 if you pay for one month. The price increases to 2 x $35 if you pay for two months, which is twice as expensive.
To know more about direct proportionality visit:
https://brainly.com/question/14437120
#SPJ1
I need help in math can you please help me
We have to find the equation of a circunference with:
[tex]\begin{gathered} \text{Center}=(-3,7) \\ \text{Passes through the point P}=(-6,-2) \end{gathered}[/tex]As it is a circunference that passes through a point, we know that the distance between the center and the point must be the radius, as all points in a circunference are at the same distance from the center.
We will find then the radius, by calculating the distance:
[tex]\begin{gathered} d(C,P)=\sqrt[]{(-3-(-6))^2+(7-(-2)_{})^2} \\ =\sqrt[]{(-3+6)^2+(7+2)^2} \\ =\sqrt[]{3^2+9^2} \\ =\sqrt[]{9+81} \\ =\sqrt[]{90} \end{gathered}[/tex]Now, this means that the radius is √90.
We use the standard form for the equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h,k) is the center of the circle. In this case,
[tex](h,k)=(-3,7)[/tex]And replacing, we obtain that the equation of the circle is:
[tex]\begin{gathered} (x+3)^2+(y-7)^2=(\sqrt[]{90})^2 \\ (x+3)^2+(y-7)^2=90 \end{gathered}[/tex]Find the next two terms in this
sequence.
4, 8, -16, -32, 64, [? ], [ ]
Next two terms of the sequence 4, 8, -16, -32, 64, ?, ? are 128 and -256.
How to solve question in sequence?
Every sequence has certain logic which can be used to find next terms.
Mainly operations like addition, subtraction, multiplication, squares and cubes are used to find the logic.
Trial and error method is applied to comprehend the logic of sequence.
4, 8, -16, -32, 64, A, B.
According to the given question, the sequence can be split in two separate sequences by taking alternate terms -
1) 4, -16, 64, B
2) 8, -32, A
Now clearly the logic is:
Next term is obtained by multiplying the previous term with -4.
Let's check 4x(-4) = -16x(-4) = 64
∴ B = 64x(-4) = -256
Similarly, 8x(-4) = -32
∴ A = -32x(-4) = 128
Hence completed sequence is 4, 8, -16, -32, 64, 128, -256.
To know more about sequence visit
https://brainly.com/question/12474324
#SPJ1
In one basketball league, there are 96 players on 8 teams. In another
basketball league, there are 12 teams. All of the teams in both leagues have the same number of players. How many players are in the 12-team league?
There are 144 players in the 12-team league.
Given:
In one basketball league, there are 96 players on 8 teams.
In another basketball league, there are 12 teams.
All of the teams in both leagues have the same number of players.
we are asked to determine the number of players in the 12-team league.
⇒ 96 player - 8 teams
⇒ 12 team player = ?
⇒ 96/8 = 12 player.
each team:
⇒ 12 × 12
= 144 players in 12 teams.
Hence we get the answer as 144 players.
Learn more about Division here:
brainly.com/question/24662212
#SPJ9
What is the slope of the line described by the data in the table below/X -3 , 0 , 3 , 6Y 3, 7, 11, 15
Given the table:
X -3 , 0 , 3 , 6
Y 3, 7, 11, 15
We can write the ordered pairs of the function:
(-3, 3), (0, 7), (3, 11), (6, 15)
Any pair of ordered pairs can be used to calculate the slope, assuming they all belong to the line.
Let's pick the points (-3, 3) and (0, 7). The formula to calculate the slope is:
[tex]\begin{equation*} m=\frac{y_2-y_1}{x_2-x_1} \end{equation*}[/tex]Substituting:
[tex]m=\frac{7-3}{0+3}=\frac{4}{3}[/tex]It can be verified that the slope is 4/3 regardless of the points selected to calculate it.
Answer: 4/3
Which number is IRRATIONAL?A)V12B)136C)V64D)V144
An irrational number is a number that cannot be written as a fraction - the decimal goes on forever without repeating. Therefore:
[tex]\sqrt[]{12}=2\sqrt[]{3}=3.46410[/tex]in this case it cannot be expressed as a fraction and it is decimal, this is the correct option. So,
answer A.
A pole 7 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Rashaad measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.
The length of the guy wire, using similar triangles, is of:
43 feet.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Proportional side lengths.Equal angle measures.The height h of the tower can be found using similar triangles, as the two right triangles are similar.
The equivalent measures are given as follows:
h ft and 7 ft.3 ft and 17 ft.Hence the proportional relationship is:
h/7 = 17/3
Applying cross multiplication:
3h = 17 x 7
h = 17 x 7/3
h = 39.67 ft.
Then, applying the Pythagorean Theorem, the length of the guy wire is of:
l² = 39.67² + 17²
l = sqrt(39.67² + 17²)
l = 43 feet. (rounded down).
(the pythagorean theorem is applied as the length of the guy wire is the hypotenuse of the right triangle).
Missing InformationThe problem is given by the image at the end of the answer.
More can be learned about similar triangles at brainly.com/question/14285697
#SPJ1
For a certain company, the cost function for producing x items is C(x)=50x+250 and the revenuefunction for selling x items is R(x)=-0.5(x-90)2+4,050. The maximum capacity of the company is 110items.The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost functionC(x) (how much it spends). In economic models, one typically assumes that a company wants tomaximize its profit, or at least make a profit!Assuming that the company sells all that it produces, what is the profit function?====P(x)=Hint: Profit = Revenue - CostWhat is the domain of P(x)?Hint: Does calculating P(x) make sense when x-10 or x-1,000?The company can choose to produce either 40 or 50 items. What is their profit for each case, andwhich level of production should they choose?Profit when producing 40 items=Profit when producing 50 items=Can you explain, from our model, why the company makes less profit when producing 10 more units?
First, let's calculate the Profit functions which is P(x)=R(x)-C(x)
Let's continue simplifying the function
The profit function is a polynomial function, so the domain is all the real numbers which means x can be any real number
Domain=(-∞,∞)
Calculating x=-10 doesn't make sense because x in all the functions is the number of items, and doesn't make sense to have -10 items, so x shouldn't be negative numbers.
And Calculating x=1000 doesn't make sense either because the problem says "The maximum capacity of the company is 110 items" so if we have x=1000 we are exceeding the limit of items that the company can handle.
Now let's calculate the profit when producing 40 and 50 items (we just need to evaluate those values in the function):
The profit when the company produces 50 items is 500 and the profit when the company produces 40 items is 550.
The company should choose to produce 40 items because is a higher profit in contrast to making 50 items.
According to the function, when we replace the values in X we can see that the term (X^2) grows more than the term X and as you can see the term X^2 is negative which decreases the final result of the profit. Another way to see this is by drawing the function
As you can see the function is a parable and when the number of items "X" is very high the function tends to decrease. The function starts to grow in profit until 40 items (when you find the maximum value of profit) and then the profit function decreases.