At a wedding, there are 456 people spread out amongst 45 tables. There are no empty seats. The reception hall has tables that sit 12 people or 8 people. Write a system of equations that can be used to find the number of each type of table the restaurant has.
The system of equations is [tex]\[ \begin{cases} x + y = 45 \\ 12x + 8y = 456 \end{cases} \][/tex]
How did we arrive at this equation?
Let's denote the number of 12-person tables as [tex]\( x \)[/tex] and the number of 8-person tables as [tex]\( y \)[/tex]. Since there are 45 tables in total, we can express the first equation as:
[tex]\[ x + y = 45 \][/tex]
Now, considering the total number of people seated, we know that each person at a 12-person table occupies one seat, and each person at an 8-person table occupies one seat as well. The total number of people is 456. Therefore, the second equation is:
[tex]\[ 12x + 8y = 456 \][/tex]
So, the system of equations is:
[tex]\[ \begin{cases} x + y = 45 \\ 12x + 8y = 456 \end{cases} \][/tex]
These equations represent the conditions that the total number of tables is 45 and the total number of people seated is 456, with no empty seats.
In the figure below, triangle ABC is similar to triangle PQR, as shown below: What is the length of side PQ?
A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 4, length of BC is 2. A similar right triangle; triangle PQR, which is triangle ABC enlarged and reflected across a horizontal line, is drawn near it. The right angle is at Q. Angle A is congruent to angle P and angle C is congruent to angle R. The length of QR is 12.
Answer:
Line PQ is 24
The table represents the temperature of a cup of coffee over time.
Which model best represents the data set?
A) exponential, because there is a relatively consistent multiplicative rate of change
B) exponential, because there is a relatively consistent additive rate of change
C) linear, because there is a relatively consistent multiplicative rate of change
D) linear, because there is a relatively consistent additive rate of change
Answer:
A on E2020
Step-by-step explanation:
Find the equation of the plane which has intercepts of (4,0,0) and (0,−2,0) and no z-intercept.
The equation of the plane which has intercepts of (4, 0, 0) and (0, -2, 0) and no z-intercept is [tex]\frac{1}{4}\cdot x -\frac{1}{2}\cdot y = 1[/tex].
A plane is represented by the following expression:
[tex]A\cdot x + B\cdot y + C\cdot z = 1[/tex] (1)
Where [tex]A,B, C[/tex] are real coefficients.
We need three distinct points to determine all coefficients of the plane. If we know that [tex](x_{1}, y_{1}, z_{1}) = (4,0,0)[/tex], [tex](x_{2}, y_{2}, z_{2}) = (0,-2,0)[/tex] and [tex](x_{3}, y_{3}, z_{3}) = (0, 0, 0)[/tex], then we have the following system of linear equations:
[tex]4\cdot A = 1[/tex] (2)
[tex]-2\cdot B = 1[/tex] (3)
[tex]0 \cdot C = 1[/tex] (4)
Then, the solution of this system is [tex]A = \frac{1}{4}[/tex], [tex]B = -\frac{1}{2}[/tex] and [tex]C = 0[/tex].
And the equation of the plane which has intercepts of (4, 0, 0) and (0, -2, 0) and no z-intercept is [tex]\frac{1}{4}\cdot x -\frac{1}{2}\cdot y = 1[/tex].
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Which is equivalent to (−2m + 5n)2, and what type of special product is it? 4m2 + 25n2; a perfect square trinomial 4m2 + 25n2; the difference of squares 4m2 − 20mn + 25n2; a perfect square trinomial 4m2 − 20mn + 25n2; the difference of squares
A equivalent term to [tex](-2m + 5n)^2[/tex] is a perfect square trinomial [tex]4m^2-20mn+25n^2[/tex]
What is expression?"It is a mathematical statement which consists of numbers, variables and some mathematical operations."
What is trinomial?"It is a polynomial which has only three terms."
What is perfect square trinomial?"When a trinomial can be factored into a binomial multiplied to itself, then its is a perfect square trinomial."
For given question,
We have been given a quadratic expression [tex](-2m + 5n)^2[/tex].
We need to find to find an equivalent expression to given expression.
Consider given expression,
[tex]\Rightarrow (-2m + 5n)^2 = (2m)^2-2(2m)(5n)+(5n)^2\\\\\Rightarrow (-2m + 5n)^2 =4m^2-20mn+25n^2[/tex]
We can observe that a trinomial [tex]4m^2-20mn+25n^2[/tex] is a perfect square trinomial.
Therefore, an equivalent term to [tex](-2m + 5n)^2[/tex] is a perfect square trinomial [tex]4m^2-20mn+25n^2[/tex]
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How many possible outcomes exist when two fair coins are flipped and a three-section spinner is spun?
Answer:
12
Step-by-step explanation:
find the equation of parallel line:
find the equation of perpendicular line:
Answer:
the person on top is right.
Step-by-step explanation:
what is the factored form of 64g^3+8
“You are collecting email addresses from 74 customers per day, which is about 90% of the daily goal of emails per day.”
Final answer:
To find the daily email goal when 74 is 90%, we divide 74 by 0.9, leading to approximately 82.22 emails. The importance of email is underscored by the billions of users and emails sent daily, highlighting its role in business communication.
Explanation:
The student's question pertains to the calculation of a daily email collection goal based on the collection of email addresses from 74 customers, which they've stated is 90% of that goal.
To find the total daily goal, we can set up a proportion where 90% (or 0.9) of the goal equals 74 customers. We use a simple algebraic equation to solve for the total goal (G): 0.9 * G = 74. Dividing both sides by 0.9 gives us G = 74 / 0.9, which gives us the total goal as approximately 82.22 customers per day.
It's important to understand the context and relevance of emails in our daily lives. As of 2023, there are over 4.2 billion email users globally with up to 60 billion emails sent daily.
This vast number shows the significance of email communication, especially in business communication, making it a fundamental skill to manage effectively. With an average office worker receiving 120 emails daily, it becomes clear why being effective with email correspondence is crucial.
Two cylinders are similar. The radius of cylinder A is 5.6 inches. The radius of cylinder B is 1.4 inches. If the height of cylinder B is 4 inches, what is the height of cylinder A
Answer:
C ✔️
Step-by-step explanation:
"16 inches"
Luis wants to buy a home priced at $315,000. He plans to finance this amount less the down payment required. His mortgage payment would then be $2100. Luis has an annual income of $91,500 and $65,000 in savings. Luis has a car payment of $370, a student loan payment of $165 and a credit card payment of $45. Use a 20% down payment and the 28/36 ratio to determine if Luis is eligible for a loan. What would you advise him to do if he is not eligible?
Solution:
Annual income of Luis= $ 91,500
[tex]\frac{28}{36}[/tex] ratio states that maximum of 28 % of your gross monthly income should be spent on housing finances and not more than 36% of your total monthly income should be spent on loans.
36% of $ 91,500= 0.36 × 91,500=$ 32,940(Annualy)
Total money that luis can use for loan as a monthly payment =$ [tex]\frac{32940}{12}=2745[/tex] $
Amount that Luis spent on loan Monthly =car payment of $370, a st udent loan payment of $165 and a credit card payment of $45= $ 370 + $ 165 + $ 45=$ 580
Amount that can be used for housing debt = $ 2745 - $ 580= $2165
Down Payment =
20 % of $315,000=0.20 × 315,000 =$ 63,000
Remaining amount for home that Luis has to pay = $ 315,000 - $ 63,000= $252,000 (not given in how many months or years Luis has to pay this amount )
Mortgage payment = $ 2100
Calculated Mortgage payment on $ 91,500 using 28% rule = 0.28 × 91,500=$25620 (Yearly)
Amount that Luis can use for Mortgage payment monthly=$ [tex]\frac{25620}{12}=2135[/tex] $(Calculated) Monthly
So, Money saved = 2135-2100=$ 35
If Monthly income allowable for Debt(i.e if $ 252,000 is divided into months) > or exceeds $ 2165, then Luis is not eligible for Loan.
If Monthly income allowable for Debt (i.e if $ 252,000 is divided into months )< or Less than $ 2165, then Luis is eligible for Loan.
The advise that i will give to Luis is that he should make full payment of his car debt, and stop being Extravagant i.e start saving more money if he wants to Possess a home.
The function f(x)=15000(0.96)^x represents the value in dollars of a vehicle x years after it has been purchased new. What is the average decrease in value per year between years 5 and 10? Please show all work!
To find the average decrease in value per year between years 5 and 10 of a vehicle, we plug in x=5 and x=10 into the given function, subtract the values, and divide by 5.
Explanation:To find the average decrease in value per year between years 5 and 10, we need to calculate the difference in value between those two years and then divide it by the number of years.
First, we find the value of the vehicle in year 5 by plugging in x = 5 into the function:
f(5) = 15000(0.96)^5
solving this equation gives us the value of the vehicle in year 5.
Next, we find the value of the vehicle in year 10 by plugging in x = 10 into the function:
f(10) = 15000(0.96)^10
solving this equation gives us the value of the vehicle in year 10.
Finally, we subtract the value in year 10 from the value in year 5 and divide by 5 (the number of years) to get the average decrease in value per year.
Which is an odd monomial function? A.y=2x^3 B.1/x C.5x^-9 D.3
The ratio of the perimeters of two similar triangles is 3:7. Find the ration of the areas! Please help, I am really not sure. And please explain well in terms that I can understand and draw a visual as well.
x 5,7,9,11,13
.................................
y 14,16,18,20,22
Write the rule for the relationship between x and y
y=?
△FSB∼△ZDR .
What is the value of x?
Enter your answer.
How many units?
△FSB∼△ZDR
What is the value of x?
Enter your answer in the box.
____UNITS
A bag contains 5 gray tiles and 2 blue tiles. Jenny reached into the bag and picked a tile randomly, and then without replacing it, picked a second tile. If you know that she picked a blue tile with her first pick, what is the probability that she picked a gray tile with her second pick? A) 1 6 B) 1 7 C) 5 6 D) 5 7
Answer:
the anwer would be c
which of the following function is f(x) if f^-1(x)=5x-19
Answer: F(x)=x-19/5
Step-by-step explanation:
which best describes your ability to calculate the volume of prisms, cylinders, pyramids, and cones?
A.I know the correct formulas to find the volumes of a ll of these figures.
B.I know the correct formulas to find the volume of at least half of these figures.
C.I can find the volume of these figures when the formulas are given to me.
I know the correct formulas to find the volumes of a ll of these figures. best describes to calculate the volume of prisms, cylinders, pyramids, and cones
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Volume of prism is Surface area multiplied by height, or more simple:
V=1/2×(l×w×h)
Volume of cylinder = πr²h
where r is the radius of cylinder and h is the height of the cylinder
Volume of pyramid = 1/3×l×w×h
Where l is length of pyramid, w is width of pyramid and h is height of the pyramid.
Volume of cone = 1/3πr²h
r is the radius of cone and h is the height of the cone
Hence, I know the correct formulas to find the volumes of a ll of these figures. best describes to calculate the volume of prisms, cylinders, pyramids, and cones
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A baker has a bin filled with 30 cups of flour. His signature cake requires one and a half cups of flour. Determine which graph and which equation represent the amount of flour in the bin, F, after he bakes c signature cakes.
The equation for the flour left in the bin after baking c number of cakes is F = 30 - 1.5*c. This equation can be graphed with flour left, F, on the vertical axis and the number of cakes, c, on the horizontal axis, producing a downward sloping line.
Explanation:The subject of this question is mathematics and it focuses on linear equations and graphical representations. To answer this question, consider that the baker uses one and a half cups of flour for each cake. So, if he bakes 'c' amount of cakes, then the total flour used will be 1.5*c cups. If he started with 30 cups of flour in the bin, after making 'c' cakes, the flour remaining, F, in the bin will be given by the equation F = 30 - 1.5*c. This is a linear equation and its graph would be a line with a negative slope (because the amount of flour decreases as more cakes are baked). On the graph, the vertical axis (y-axis) could be the amount of flour left 'F', and the horizontal axis (x-axis) would be the number of cakes 'c'. The line would start from the point (0,30) (since initially, when no cakes are baked, there are 30 cups of flour) and slope downwards.
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Jen has 2 meters of taffy. She wants to give each of her 3 best friends an equal amount of taffy. How many centimeters of taffy will each friend get?
Write your answer as a mixed number in the form a b/c.
Answer:
[tex]66\frac{2}{3}[/tex] centimeters.
Step-by-step explanation:
Jen has 2 meters of taffy.
She wants to give each of her 3 best friends an equal amount of taffy.
First we convert 2 meters to centimeters.
1 meter = 100 centimeters
2 meters = 100 × 2 = 200 centimeters.
Now divide 200 cm to 3 friends
Each friend get = [tex]\frac{200}{3}[/tex]
= [tex]66\frac{2}{3}[/tex]
Each friend will get [tex]66\frac{2}{3}[/tex] centimeters of taffy.
-2⁄3 a − 6 = 12 a =?????????????/
How do you figure how far Leanne walks if she walks a speed of
3 and one third miles in two hours
if the apr on a credit card is 22.2% what is the monthly interest rate
Solution:
APR =Annual Percentage rate
It is the amount of money charged as interest on a sum that you borrow from bank.The interest can be paid monthly or annualy. If you pay the balance at the end of each month that you have borrowed from credit card ,there is no need to pay interest.To find the monthly interest rate , we just divide the value of APR by 12 .
As Yearly interest rate i.e APR on credit card = 22 .2 %
Then , Monthly interest rate = [tex]\frac{22.2}{12}= 1.85[/tex]%
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < x + 2
y > x + 2
Answer:
y > 3x+2
Step-by-step explanation:
We have 2 points so we can find the slope
m = (y2-y1)/(x2-x1)
= (2--7)/(0--3)
= (2+7)/(0+3)
= 9/3
= 3
The y intercept is 2, so we can write the equation of the line using the slope intercept form (y=mx+b)
y = 3x+2
The line is dotted so we use either < or > (If it were solid we would use ≤ or ≥)
Since it is shaded above , y is greater than.
y > 3x+2
One factor of f(x)= 4x^3-4x^2-16x+16 is (x – 2). What are all the roots of the function? Use the Remainder Theorem.
The graph shown is the solution set for which of the following inequalities?
y ≥ x + 1
y ≥ |x| + 1
y ≥ |x - 1|
Answer:
The correct option is C) [tex]y\geq |x+1|[/tex]
Step-by-step explanation:
The graph of [tex]y=|x|[/tex] is shown in figure-1
In option (1) [tex]y\geq x+1[/tex] .....(2)
the graph of equation (2) is shown in figure-2
In option (2) [tex]y\geq |x|+1[/tex] .....(3)
the graph of equation (3) is shown in figure-3
In option (3) [tex]y\geq |x+1|[/tex] .....(4)
the graph of equation (3) is shown in figure-4
As this is shifted 1 unit to right side
So, this figure is correct as it is matches the provided figure
Therefore, the correct option is C) [tex]y\geq |x+1|[/tex]
PLEASE HELP WILL GIVE 30 POINTS AND BRAINLIEST.
Write the statement for the problem in mathematical language. Use x for the tens digit and y for the unit digits in the two digit numbers.
Find the two-digit number which is greater than the product of its digits by 26
The statement is ?
The number is ?
How many ways can a person select 3 videotapes from a collection of 10 tapes?
One is dollar is currently worth 84.1 Japanese yen. If you exchange 4,205 for US dollars, how much will you have?