Answer:
all real numbers or [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
since both f(x) and g(x) are polynomials, neither of them have restrictions on their domains. Since they can be defined for all real numbers. It's not like the square root which has a domain of (0, infinity), or log x which is defined only from (0, infinity). So adding these two polynomials would result in a domain of all real numbers.
Davion wants to buy 4 tickets to a basketball game. He sees that there is a discount for$25 off his entire purches at check out, so the tickets would him $215 before tax. what was the original price of each tickets?
The original price of each tickets is; $60 per ticket
What is the original Price?We are told that $215 is what it costs after the discount. Thus, we add the amount taken off, back on to get;
$215 + $25 = $240
Now, since he wants to buy 4 tickets, then we divide the amount above by 4 to get the cost of each individual ticket.
Original Cost of each individual ticket = 240/4 = $60
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3y−13≥−9 and 3y−13≤−1
Use in interval notation please
Step-by-step explanation:
3y-13>-9
3y-13<-1
3y>4
3y<12
12>3y>4
y=2,3,4
Answer:
[tex]\left[ \dfrac{4}{3},4 \right][/tex]
Step-by-step explanation:
Inequality 1
[tex]3y-13\geq -9[/tex]
Add 13 to both sides:
[tex]\implies 3y-13+13\geq -9+13[/tex]
[tex]\implies 3y\geq 4[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3y}{3}\geq \dfrac{4}{3}[/tex]
[tex]\implies y \geq \dfrac{4}{3}[/tex]
Therefore, y is equal to or bigger than 4/3.
Inequality 2
[tex]3y-13\leq -1[/tex]
Add 13 to both sides:
[tex]\implies 3y-13+13\leq -1+13[/tex]
[tex]\implies 3y\leq 12[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3y}{3}\leq \dfrac{12}{3}[/tex]
[tex]\implies y\leq 4[/tex]
Therefore, y is equal to or smaller than 4.
Therefore, the solution to the inequalities in interval notation is:
[tex]\left[ \dfrac{4}{3},4 \right][/tex]
What is the inverse of the function f(x) = 1/9x+2
Hello,
f(x) = 1/9x + 2 ⇔ y = 1/9x + 2 ⇔ 1/9x = y - 2 ⇔ x = 9(y - 2)
x = 9y - 18
⇒ f⁻¹(x) = 9x - 18
[tex]\frak{Hi!}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
If we have a function, we can find its inverse if we do the
following-:
[tex]\tiny\bullet[/tex] replace f(x) with y.
[tex]\boldsymbol{\sf{y=\displaystyle\frac{1}{9}x+2}}[/tex]
[tex]\tiny\bullet[/tex] switch the places of x and y
[tex]\boldsymbol{\sf{x=\displaystyle\frac{1}{9}y+2}}}[/tex]
[tex]\bullet[/tex] solve for y
[tex]\boldsymbol{\sf{x\times9=\frac{1}{9}y\times9+2\times9}}[/tex]
[tex]\boldsymbol{\sf{9x=y+18}}[/tex]
[tex]\boldsymbol{\sf{-y=-9x+18}}[/tex]
[tex]\boldsymbol{\sf{y=9x-18}}}[/tex]
[tex]\boldsymbol{\sf{f(x)^{-1}=9x+18}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
PLEASE HELP!!!!!!!!!!!!!!!!!!!! ASAP PLEASE!!!!!!!!!!!!!!!!!!!!!!!
Answer:
729
Step-by-step explanation:
I have not done this in some time so the terms may be a bit unconventional, but they work. The key to this is multiplying by -3.
1*(-3) = -3
-3*(-3) = 9
And so on.
1, -3, 9, -27, 81, -243, 729
Math 2 Of high school
Answer:
B. BC = 18 so ∆ABC ~ ∆DEF by SASStep-by-step explanation:
[tex] \bf \cfrac{AB}{DE} = \cfrac{BC}{EF} [/tex]
[tex] \bf \cfrac{15}{10} = \cfrac{BC}{12} [/tex][tex]\bf \cfrac{3}{2} = \cfrac{BC}{12} [/tex][tex]\bf BC = \cfrac{3}{2} \times 12 [/tex][tex]\bf 3 \times 6[/tex][tex]\bf BC = 18[/tex][tex] \bf \angle B = \angle \: E[/tex]So, ∆ABC ~ ∆DEF by SAS.
------------------------------------Is UVW=Xyz?if so, name the postulate that applies
By critically observing the two triangles, we can deduce that they: B. might not be congruent.
The properties of similar triangles.In Geometry, two triangles are said to be similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.
By critically observing the two triangles, we can logically deduce that the three angles of both triangles are congruent in accordance with AAA similarity postulate:
<U ≅ <X<V ≅ <Y <W ≅ <ZHowever, AAA isn't a congruence postulate and as such all similar triangles might not be congruent.
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GOE
ASSI
Collect Data from Our Solar System
Fill in the table. To obtain each planet's distance from the sun and orbital period, click its name.
DONE
"include all given digits
Distance from the sun (au)
Orbital Period (years)
Venuss
Sun
9.72.a
Mercury Venus Earth
Mars
Orbital Period: 0.616 years
Jupiter Saturn Uranus Neptune
ΝΑ
ΝΑ
Answer:
Mercury - 0.39 and 0.242
Venus - 0.72 and 0.616
Earth - 1 and 1
Mars - 1.52 and 1.88
Uranus - 19.18 and 84.00
Neptune - 30.06 and 165.00
The distance between Mercury, Venus, Earth, Mars, Uranus, and Neptune from the sun is 0.39, 0.72, 1, 1.52, 19.18, and 30.06 respectively.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
The distance between each planet from the sun will be given as
Mercury - 0.39 and 0.242
Venus - 0.72 and 0.616
Earth - 1 and 1
Mars - 1.52 and 1.88
Uranus - 19.18 and 84.00
Neptune - 30.06 and 165.00
Hence, the distance between Mercury, Venus, Earth, Mars, Uranus, and Neptune from the sun is 0.39, 0.72, 1, 1.52, 19.18, and 30.06 respectively.
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MO, MN, and ON are the midsegments of △JKL.
Triangle M N O is inside triangle J K L. Points M, N, and O are the midpoints of sides J K, J L, and K L.
What is the perimeter of △JKL?
6
9.5
11.5
19
Applying the midsegment theorem, the perimeter of triangle JKL is: D. 19.
What is the Perimeter of a Triangle?The perimeter of triangle JKL = JK + JL + KL
Find the lengths of JK, JL, and KL using the triangle midsegment theorem.
JK = 2(3.5) = 7 units
JL = 2(4) = 8 units
KL = 2(2) = 4 units.
Perimeter of triangle JKL = 7 + 8 + 4
Perimeter of triangle JKL = 19 units.
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Answer: D. 19
Step-by-step explanation: Answer is correct on Edge. Trust Me! :)
MO, MN, and ON are the midsegments of △JKL.
Triangle M N O is inside triangle J K L. Points M, N, and O are the midpoints of sides J K, J L, and K L.
Q: What is the perimeter of △JKL?
A: D. 19
6.2.4 practice for modeling geometric systems
The recursive function of a ball with a 67% rebound is a(n) = 0.67a(n-1)
The recursive function of a ballThe rebound is given as:
r = 67%
Express as decimal
r = 0.67
So, the recursive function is:
a(n) = Previous height * r
This gives
a(n) = a(n-1) * 0.67
Evaluate
a(n) = 0.67a(n-1)
Hence, the recursive function is a(n) = 0.67a(n-1)
Complete the tableBasketball
The initial height is given as:
a(1) = 54
So, we have:
a(2) = 0.67 * 54 = 36.18
a(3) = 0.67 * 36.18 = 24.24
Tennis ball
The initial height is given as:
a(1) = 58
So, we have:
a(2) = 0.67 * 58 = 38.86
a(3) = 0.67 * 38.86 = 26.04
Table-tennis ball
The initial height is given as:
a(1) = 26
So, we have:
a(2) = 0.67 * 26 = 17.42
a(3) = 0.67 * 17.42 = 11.67
Hence, the complete table is:
Bounce n Height
First bounce 1 Basketball: 54 inches
Tennis ball: 58 inches
Table tennis ball: 26 inches
Second bounce 2 Basketball: 36.18 inches
Tennis ball: 38.86 inches
Table tennis ball: 17.42 inches
Third bounce 3 Basketball: 24.24 inches
Tennis ball: 26.04 inches
Table tennis ball: 11.67 inches
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Missing part of the question
A ball is dropped such that each successive bounce is 67% of the previous bounce's height.
In a small town in the Himalayas, the average snowfall each month is 6 inches. July is the month with the lowest average snowfall, of 1 inch. Construct a function that models this behavior. During what period is there more than 10 inches of snowfall?
A coffee shop owner wants to examine the number of customers who pass in front of his store in the morning from 7:00am to 7:30am. Suppose that the mean number of customers during this time window is 200. What is the probability that more than 210 people will pass in front of his store
The probability that more than 210 people will pass in front of his store is 0.2272.
In the question, we are given that a coffee shop owner wants to examine the number of customers who pass in front of his store in the morning from 7:00 A.M to 7:30 A.M.
We are asked to find the probability that more than 210 people will pass in front of his store if the mean number of customers during this time is 210.
This experiment follows a Poisson Distribution with a mean (λ) = 200, and the random variable X = 210.
To find the probability that more than 210 people will pass in front of his store, we will find P(X > 200).
P(X > 200) = 1 - P(X ≤ 210).
Now, P(X ≤ 210) can be calculated using the function poissoncdf(200,210) on the calculator.
As to find the probability of a Poisson Distribution P(X ≤ x), for a mean = λ, we use the calculator function poissoncdf(λ,x).
The value of poissoncdf(200,210) = 0.77271.
Thus, the value of P(X > 210) = 1 - 0.77271 = 0.22729.
Thus, the probability that more than 210 people will pass in front of his store is 0.2272.
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Given: 9x > -36. Choose the solution set. {x | x < -4} {x | x < 4} {x | x > 4} {x | x > -4}
[tex]\bf{9x > -36 }[/tex]
Divide both sides by 9.
[tex]\bf{\dfrac{9x}{9} > \dfrac{-36}{9} }[/tex]
[tex]\bf{x > -4 \ \ \to \ \ \ Answer}[/tex]
{ Pisces04 }Answer:
{x | x > -4}
Step-by-step explanation:
{a few basic reminders: > means greater than; < means less than; ≥ means greater than or equal to; ≤ means less than or equal to
for example: 4 < 7
4 ≤ 4
4 ≥ 3
4 > 3}
When we see an inequality, such as 9x > -36, we are trying to figure out what possible numbers x can be to make this statement true.
We can either use logic / words (see below), or in a much more efficient manner, we can solve this algebraically [as though it were an equation]
So, like when working with any other variable, we want to isolate x:
9x > -36
÷9 ÷9
x > -4
just in case none of this makes sense (it can be quite confusing at first),
here's how we can think about it logically
we know that whatever multiplies with 9 must be more than -36, and because -4 multiples with 9 to be exactly -36, any number greater than -4 also will be greater than -36
meaning that x must be more than -4, which we express as: x > -4
So, the solution set (solution set means set of possible solutions) is
{x | x > -4}
hope this helps!! have a lovely day :)
Kayden buys bottles of grapefruit juice at the corner store. Assume each bottle of juice is the same price. The proportional relationship between the number of juice bottles bought, j, and the total cost in dollars and cents, c, can be represented by the equation c=0.41j. What is the constant of proportionality from the number of bottles of juice brought to the total cost, in dollars and cents?
An equation is formed of two equal expressions. The value of the constant of proportionality is 0.41.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given there exists a proportional relationship between the number of juice bottles bought, j, and the total cost in dollars and cents. Therefore,
c ∝ j
c = kj
As the relation is represented by the equation c=0.41j. Therefore, the value of the constant of proportionality is 0.41.
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3. A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:
(i) exactly 3 girls ?
(ii) atleast 3 girls ?
(iii) atmost 3 girls ?
Answer:
i 4 boys
ii 3 boys
III 5 boys
n is less than 15 and greater than or equal to 3 On a number line
The number line that represents the solution set of the inequality can be seen below.
How to graph the inequality?
Here we have the inequality:
15 > n ≥ 3
Then we need to have a open dot at the number 15 on the number line, and then a line that goes to the left until the value 3, where we must have a closed dot (because n = 3 is a solution of the inequality). The number line can be seen below.
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Find the length of UC
Answer:
18
Step-by-step explanation:
Entire length =105 + 82 =187
subtract 22
subtract 96
subtract 51 result =18
The length of a rectangle is 6 less than twice the width. If the perimeter is 60 inches, find the length and width.
Answer:
w = 12
l = 18
Step-by-step explanation:
Hello!
Recall the perimeter of a rectangle is twice the sum of the length and the width of the rectangle.
[tex]P = 2(l + w)[/tex]Let w be the width. The length is 6 less than twice the width. That means, l is 2w - 6.
Plug it into the formula and solve, given that P is 60.
Solve for w[tex]P = 2(l + w)[/tex][tex]60 = 2(2w - 6 + w)[/tex][tex]60 = 2(3w - 6)[/tex][tex]60 = 6w - 12[/tex][tex]72 = 6w[/tex][tex]w = 12[/tex]The width is 12 inches. We can plug in 12 for 2w - 6 to find the length.
Solve for l[tex]l = 2w - 6[/tex][tex]l = 2(12) - 6[/tex][tex]l = 24 - 6[/tex][tex]l = 18[/tex]The length is 18 inches.
The width is 12 inches, and the length is 18 inches.
Solve the equation. QUESTION 1!
Answer:
Simplifying
x2 + 6x + 13 = 20
Reorder the terms:
13 + 6x + x2 = 20
Solving
13 + 6x + x2 = 20
Solving for variable 'x'.
Reorder the terms:
13 + -20 + 6x + x2 = 20 + -20
Combine like terms: 13 + -20 = -7
-7 + 6x + x2 = 20 + -20
Combine like terms: 20 + -20 = 0
-7 + 6x + x2 = 0
Factor a trinomial.
(-7 + -1x)(1 + -1x) = 0
Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:
Simplifying
-7 + -1x = 0
Solving
-7 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7
Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7
Combine like terms: 0 + 7 = 7
-1x = 7
Divide each side by '-1'.
x = -7
Simplifying
x = -7
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:
Simplifying
1 + -1x = 0
Solving
1 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1
Combine like terms: 0 + -1 = -1
-1x = -1
Divide each side by '-1'.
x = 1
Simplifying
x = 1
Solution
x = {-7, 1}
Step-by-step explanation:
hope this helps if not let me know have a blessed day
Which line segment could be the diameter of this circle?
Answer:
K-A would make a circle because it goes across
Watch help video
A middle school took all of its 6th grade students on a field trip to see a play. The
students filled 1219 seats, which was 53% of the total number of seats in the theater.
How many total seats were in the theater?
Answer:
2300
Step-by-step explanation:
53%=1219
100=X
X=[(1219)(100)]/53=2300
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
53% = 1219
100% = 2300
The total number of seats in the theater is 2300
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of seats filled by all the students = 1219
1219 is 53% of the total seats in the theater.
This means,
53% = 1219
Now,
Total number of seats in the theater = 100%
53% = 1219
Multiply 100/53 on both sides.
100/53 x 53% = 100/53 x 1219
100% = 2300
Thus,
The total number of seats in the theater is 2300
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Evaluate the expression for x = 1 and y = 5 : 3 (3x + 5y)
Hello,
[tex]3(3x + 5y)[/tex]
if x = 1 and y = 5 :
[tex]3(3 \times 1 + 5 \times 5) = 3(3 + 25) = 3 \times 28 = 84[/tex]
⊰__________________________________________________________⊱
Answer:
84Step-by-step explanation:
[tex]\large\displaystyle\text{$\begin{gathered} \sf {Substitute \ the \ values-\!\!:} \\ \sf{3(3*1+5*5)} \\ \sf{3(3+25)=3(28)=84} \end{gathered}$}}[/tex]
[tex]\pmb{\tt{done \ !!}}[/tex]
⊱__________________________________________________________⊰
Evaluate the given question
The value of the given expression is 1/16
Exponential functionsGiven the exponential function below as shown;
(1/2)^4
This means the product of 1/2 in 4 places. This can be expressed as;
(1/2)^4 = 1/2 * 1/2 * 1/2 *1/2
(1/2)^4 = 1/4 * 1/4
(1/2)^4 =1/16
Hence the value of the given expression is 1/16
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What is the expression of g(x) when we perform the following sequence of transformations onto the parent function fx=x2+2x:
a) Compress horizontally by a factor of 3 with respect to its axis of symmetry
b) Shift right 1 unit
The transformed function is:
[tex]g(x) = ( (x + 1)/3 - 2)^2 + 2*( (x + 1)/3 - 2)[/tex]
How to get the function g(x)?
The parent function is:
[tex]f(x) = x^2 + 2x[/tex]
Here the axis of symmetry is at:
[tex]x = -2/2*1 = -1[/tex]
So first we need to apply a horizontal compression by a factor of 3 with respect to the line x = -1.
Here we can, for the moment, define a new variable that is zero when x = -1, let's define:
z = x + 1.
x = z - 1
Writing our function in terms of z, we get:
[tex]f(z) = (z - 1)^2 + 2*(z - 1)[/tex]
Now we can apply a compression by a factor of 3 around the origin. Then we have:
[tex]f(z/3) = (z/3 - 1)^2 + 2*(z/3 - 1)[/tex]
Returning to the original variable, we have:
[tex]f((x+1)/3) = ( (x + 1)/3 - 1)^2 + 2*( (x + 1)/3 - 1)[/tex]
Now we want to shift it one unit to the right, then we have:
g(x) = f( (x + 1)/3 - 1)
Replacing the actual function we get:
[tex]g(x) = f((x+1)/3 - 1) = ( (x + 1)/3 - 1 - 1)^2 + 2*( (x + 1)/3 - 1 - 1)\\\\g(x) = ( (x + 1)/3 - 2)^2 + 2*( (x + 1)/3 - 2)[/tex]
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What package of toothpaste has the lower unit price?
Package Price Unit Price
6.2 oz $2.95
8.0 oz $3.13
Answer:
6.2 oz is lower
Step-by-step explanation:
Two increased by a number is dozen. Find the number.
The number is 5 if two increased by a number is a dozen. In other words, the correct answer is 5 by solving equations.
Step 1: Write the given information as an equation. "Two increased by a number" can be represented as 2 + x, where x is the unknown number.
Step 2: Translate "Two increased by a number is a dozen" into an equation. The word "a dozen" refers to the number 12.
[tex]2 + x = 12.[/tex]
Step 3: Solve the equation for x. To isolate x, subtract 2 from both sides of the equation:
[tex]2 + x - 2 = 12 - 2.[/tex]
This simplifies to x = 10.
Step 4: Verify the solution. Substitute the value of x back into the original equation:
2 + 10 = 12.
This equation is true, so x = 10 is indeed the solution.
Therefore, the number is 10.
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if x=2 y=4 a=3 b=6 and c=2 find the value of
xty=5
2a+5b-4c
(4c-3b)a÷2
5x2square+4y2squre-5
Answer:
I didnt know but i worked it out and searched it up and i got this
Step-by-step explanation:
(2a+4c-5b+2a+5b-4c)
Which linear inequality is graphed with y > –x – 2 to create the given solution set?
y > x + 1
y < x – 1
y > x – 1
y < x + 1
The Linear inequality that is graphed with y > –x – 2 to create the given solution set is; y < x + 1
How to interpret Inequality Graphs?From the attached graph of inequalities, we see that one of the lines has its' y - intercept as -2 with a slope of -1. Thus, the equation in slope intercept form is; y = -x - 2.
The shaded region will have the inequality; y > -x - 2.
The other line has its' y - intercept as 1 and a slope of 1.
Thus, the equation of line is; y = x + 1.
The shaded part is above the line and as such the inequality region is represented by the inequality y < x + 1.
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Answer:
D
Step-by-step explanation:
33. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
33. Passes through (1, 5) and (4, 11)
Answer:
The linear equation for the line which passes through the points given as (1,5) and (4,11), is written in the point-slope form as y=2x+3.
Step-by-step explanation:
A condition is given that a line passes through the points whose coordinates are (1,5) and (4,11).
It is asked to find the linear equation which satisfies the given condition.
Step 1 of 2
Determine the slope of the line.
The points through which the line passes are given as (1,5) and (4,11). Next, the formula for the slope is given as,
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute 11&5 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and [tex]$4 \& 1$[/tex] for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]$$\begin{aligned}m &=\frac{11-5}{4-1} \\m &=\frac{6}{3} \\m &=2\end{aligned}$$[/tex]
Step 2 of 2
Write the linear equation in point-slope form.
A linear equation in point slope form is given as,
[tex]$$y-y_{1}=m\left(x-x_{1}\right)$$[/tex]
Substitute 2 for [tex]$m, 1$[/tex] for [tex]$x_{1}$[/tex], and 5 for [tex]$y_{1}$[/tex] in the above equation and simplify using the distributive property as follows,
[tex]$$\begin{aligned}&y-5=2(x-1) \\&y-5=2 x-2 \\&y=2 x-2+5 \\&y=2 x+3\end{aligned}$$[/tex]
This is the required linear equation.
what is the measure of angle d1°
Answer:
40
Step-by-step explanation:
Please help with this!!
Answer:
Step-by-step explanation:
Forming linear equations and solving:Cost = fixed rate + number of guests* cost per meal.
Let x be the number of guests.
a) Pin hall:
Fixed rate = $ 500
Cost per meal = $15
Cost = 500 + 15*x
[tex]\sf \boxed{\bf C = 500 + 15x}[/tex]
Bloom place:
Fixed rate = $350
Cost per meal = $18
[tex]\sf \boxed{\bf C = 350 +18x}[/tex]
b) Given the charges are same at both halls.
350 + 18x = 500 + 15x
18x = 500 + 15x - 350
18x = 150 + 15x
18x -15x = 150
3x = 150
x = 150 ÷ 3
x = 50
When the number of guests is 50, the cost is same at both the halls
Hello!
Forming the equations :
y = mx + b
m = rate per hour
b = fixed charge
[tex]\fbox {y = 15x + 500}[/tex]
[tex]\fbox {y = 18x + 350}[/tex]
Solving for number of guests at which cost is the same :
15x + 500 = 18x + 350
3x = 150
x = 25 guests