11) The county fair is a popular field trip destination. This year the senior class at High School A andthe senior class at High School B both planned trips there. The senior class at High School Arented and filled 3 vans and 8 buses with 322 students. High School B rented and filled 8 vansand 6 buses with 322 students. Every van had the same number of students in it as did the buses.Find the number of students in each van and in each bus.
Answers
We are given that high school A filled 3 vans and 8 buses with 322 students. Let "x" be the number of students in a van and "y" the number of students in the bus then this can be written mathematically as:
\(3x+8y=322,(1)\)High school B filled 8 vans and 6 buses with 322. Since each van and bus has the same number of students then we can write this as:
\(8x+6y=322,(2)\)We get 2 equations and 2 variables. To determine the solution we will solve for "x" in equation (1). To do that we will subtract "8y" from both sides:
\(3x=322-8y\)Now, we divide both sides by 3:
\(x=\frac{322-8y}{3}\)Now, we substitute the value of "x" in equation (2):
\(8(\frac{322-8y}{3})+6y=322\)Now, we apply the distributive law on the parenthesis:
\(\frac{2576-64y}{3}+6y=322\)Now, we multiply both sides by 3:
\(2576-64y+18y=966\)Now, we add like terms:
\(2576-46y=966\)Now, we subtract 2576 from both sides:
\(\begin{gathered} -46y=966-2576 \\ -46y=-1610 \end{gathered}\)Now, we divide both sides by -46:
\(y=-\frac{1610}{-46}=35\)Now, we substitute the value of "y" in equation (1):
\(3x+8(35)=322\)Solving the product:
\(3x+280=322\)Now, we subtract 280:
\(\begin{gathered} 3x=322-280 \\ 3x=42 \end{gathered}\)Dividing by 3:
\(x=\frac{42}{3}=14\)Therefore, there are 14 students in the van and 35 in the bus.
Related Questions
NO LINKS!! Please help with questions 3 and 4
Answers
Answers:
Problem 3) transformation is \((\text{x},\text{y})\to(\text{x}-5,\text{y}+2)\)
Problem 4) transformation is \((\text{x},\text{y})\to(\text{x}+3,\text{y}+1)\)
=====================================================
Explanation for problem 3
preimage point L is at (1, -1)
image point L' is at (-4, 1)
When going from x = 1 to x = -4, we shift left 5 units. So we'll have x-5 as part of the transformation.
When going from y = -1 to y = 1, we'll shift 2 units up and involve y+2
Since we have x become x-5, and y become y+2, the transformation is \((\text{x},\text{y})\to(\text{x}-5,\text{y}+2)\\\\\)
Let's test the transformation on point L(1,-1)
\((\text{x},\text{y})\to(\text{x}-5,\text{y}+2)\\\\(1,-1)\to(1-5,-1+2)\\\\(1,-1)\to(-4,1)\\\\\)
which helps confirm we have the correct transformation. I'll let you check the other points M and N.
-----------------------------------------------------------------
Explanation for problem 4
L has an x coordinate of x = -6L' has an x coordinate of x = -3When going from L to L', we need to shift 3 units to the right. Each x becomes x+3
L has a y coordinate of y = -4L' has a y coordinate of y = -3This tells us to shift up 1 unit. The y coordinate becomes y+1
So we can say
\(\text{x} \to \text{x}+3\\\\\text{y} \to \text{y}+1\)
which condenses to the notation
\((\text{x},\text{y})\to(\text{x}+3,\text{y}+1)\\\\\)
Let's test this transformation on point M(-5,-1) and we should get to M'(-2,0)
\((\text{x},\text{y})\to(\text{x}+3,\text{y}+1)\\\\(-5,-1)\to(-5+3,-1+1)\\\\(-5,-1)\to(-2,0)\\\\\)
This confirms the translation rule works for point M.
I'll let you check the other points L and N.
Answer:
\(\textsf{3.} \quad (x,y) \rightarrow (x-5,y+2)\)
\(\textsf{4.} \quad (x,y) \rightarrow (x+3,y+1)\)
Step-by-step explanation:
Question 3Given vertices of ΔLMN:
L = (1, -1)M = (4, 1)N = (5, -1)Given vertices of ΔL'M'N':
L' = (-4, 1)M' = (-1, 3)N' = (0, 1)From inspection of the given diagram, we can see that the two triangles are congruent since their corresponding angles and corresponding side lengths are the same.
There is no apparent reflection or rotation, so the transformation of ΔLMN to ΔL'M'N' is by translation.
To find the mapping rule for the translation, choose one pair of corresponding vertices and determine the difference between the x and y values of the translated point and the original point:
\(x_{M'}-x_M =-1-4=-5 \implies \textsf{5 units left}\)
\(y_{M'}-y_M =3-1=2 \implies \textsf{2 units up}\)
Therefore, the mapping rule for the translation is:
\((x,y) \rightarrow (x-5,y+2)\)
Question 4Given vertices of ΔLMN:
L = (-6, -4)M = (-5, -1)N = (-2 -4)Given vertices of ΔL'M'N':
L' = (-3, -3)M' = (-2, 0)N' = (1, -3)From inspection of the given diagram, we can see that the two triangles are congruent since their corresponding angles and corresponding side lengths are the same.
There is no apparent reflection or rotation, so the transformation of ΔLMN to ΔL'M'N' is by translation.
To find the mapping rule for the translation, choose one pair of corresponding vertices and determine the difference between the x and y values of the translated point and the original point:
\(x_{L'}-x_L =-3-(-6)=3 \implies \textsf{3 units right}\)
\(y_{L'}-y_L =-3-(-4)=1 \implies \textsf{1 units up}\)
Therefore, the mapping rule for the translation is:
\((x,y) \rightarrow (x+3,y+1)\)
{show steps please i’m begging it’s due in an hour }
PLEASE LET THIS GRAB UR ATTENTION IF UR AN EXPERT AT ALGEBRA I HAVE AN F
Answers
Hello!
\(slope = 2\\\\y-intercept = (0, 3)\\\\Equation: y = 2x + 3\)
We can find the slope using the slope formula:
\(slope = \frac{y_{2} - y_{1}}{x_{2}-x_{1}}\)
Plug in any two points from the table. We can use (0, 3) and (1, 5):
\(slope = \frac{5 - 3}{1-0}\)
\(slope = 2\)
Now, we can find the y-intercept by finding the y-value at which x = 0.
According to the table, when x = 0, y = 3. Thus, the y-intercept is:
\((0, 3)\)
We can write an equation using the slope and y-intercept in the format
y = mx + b where "m" is the slope and "b" is the y-intercept.
Plug in the solved values into the equation:
y = 2x + 3.
**Graphed below**
Help me please I need help x^2 - 8x + 16
Answers
The set of factors used to factor the given trinomial are -4 and -4. Therefore, option C is the correct answer.
The given trinomial is x²-8x+16.
Factors of 16 Sum of factors
-1 and -16 -1+(-16)=-17
-2 and -8 -2+(-8)=-10
-4 and -4 -4+(-4)=-8
The set of factors would used to factor the trinomial are -4 and -4.
Therefore, option C is the correct answer.
To learn more about the factorisation of polynomial visit:
https://brainly.com/question/16789195.
#SPJ1
Is -1/16 a rational number?
Answers
Answer:
yes ‐1/16 is rational number
solution ‐1/16=‐16
and every integer is a rational number
ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST FOR ANSWER
Answers
The value of term number 10, in the given sequence would be 11 / 10.
There is no minimum value in the sequence because it never reaches 1.
An explicit equation is best as opposed to a recursive equation.
How to interpret the sequence ?This sequence is given by the nth term T(n) = (n+1)/n. To find the value of the 10th term, we substitute n = 10:
T(10) = (10 + 1)/10 = 11/10
There is no minimum value in this sequence. As n increases, the values of the terms get closer to 1 but never reach it. The sequence is monotonically decreasing, and its limit as n approaches infinity is 1, but it never actually takes the value of 1.
An explicit equation for this function is more appropriate in this case because it directly provides the value of the nth term without needing any previous terms. The explicit equation for the sequence is:
T(n) = (n + 1)/n
Find out more on explicit sequence at https://brainly.com/question/29224065
#SPJ1
Given the points below, find XY. Round to the nearest hundredth.
X(-8,4) and Y (4, -6)
Answers
Answer:
15.62
Step-by-step explanation:
The length XY is found from the distance formula:
d = √((x2 -x1)² +(y2 -y1)²)
d = √((4 -(-8))² +(-6 -4)²) = √(12² +(-10)²) = √244
d ≈ 15.62 . . . units
The length of XY is approximately 15.62 units.
The function f(x) = -(x-3)² + 9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a
function of the length of the rectangle, x. What is the maximum area of the rectangle?
O3 square units
O 6 square units
O9 square units
O 12 square units
Answers
The maximum area of the rectangle is A = 9 units²
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the function for area be f ( x )
where f ( x ) = - ( x - 3 )² + 9
Let the width of the rectangle be W.
The perimeter of a rectangle is given by:
Perimeter = 2(length + width) = 12 units
12 = 2(x + width)
Simplifying this equation, we get:
6 = x + width
width = 6 - x
Now, the area of the rectangle is given by:
Area = Length x Width
Substituting the value of width in terms of x, we get:
Area = x(6 - x)
Area of rectangle A = 6x - x²
This is a quadratic function of x, which has a maximum value at the vertex of the parabola. The vertex of the parabola can be found by completing the square or by using the formula:
x = -b/(2a)
In this case, a = -1 and b = 6, so we have:
x = -6/(2(-1)) = 3
Therefore, the maximum area of the rectangle occurs when x = 3, and the value of the maximum area is:
Area of rectangle A = 3(6 - 3) = 9 square units
Hence , area of rectangle is A = 9 units²
To learn more about area of rectangle click :
https://brainly.com/question/15225905
#SPJ5
Help please Which reason is the justification for the statement that angle A ≅ angle B?
A) Vertical angles are congruent.
B) Linear angles are equal.
C) Intersecting lines form opposing angles.
D) Lines intersect at one point.
Answers
Elena wonders how much water it would take to fill her cup, so she wants to determine the diameter of the cylindrical cup. She drops her pencil in her cup and notices that it just fits diagonally. (See the diagram.) The pencil is 17 cm long and the cup is 15 cm tall. What is the diameter of the cup? Explain or show your reasoning.
Answers
Answer:
get brainly pictures in the appp store it should help you
Step-by-step explanation:
what is meaning of MRP
Answers
Answer:
MRP = Maximum retailers price
Step-by-step explanation:
Hope it helps<3The points E, F, G and H all lie on the same line segment, in that order, such that the
ratio of EF FG: GH is equal to 1: 5:3. If EH
:
= 54, find EG.
Answers
The ratio of EG = 36.
Let's assign variables to the lengths of the line segments:
EF = x
FG = 5x
GH = 3x
We know that EH = EF + FG + GH.
Substituting the given values, we have:
54 = x + 5x + 3x
Combining like terms, we get:
54 = 9x
To isolate x, we divide both sides of the equation by 9:
54/9 = x
Simplifying, we find:
6 = x
EF = 6, FG = 5(6) = 30, and GH = 3(6) = 18.
Since EG is the sum of EF and FG, we can calculate it as follows:
EG = EF + FG = 6 + 30
= 36
EG = 36.
For similar questions on ratio
https://brainly.com/question/12024093
#SPJ11
Don played a game. He scored 3 points in the
first round. After the second round, his total score
was -10. How many points did Don score in the
second round?
Answers
Which is the graph of the function f/x )= x 2 2x 3?; Which graph represents the function f/x )= 4 x?; How do you find a function on a graph?; Which is one of the transformations applied to the graph of f/x )= x2 to change it into the graph?
Answers
The graph of the function f(x) = x² + 2x + 3 is a parabola with vertex (-1, 2).
You can use the vertical line test on a graph to determine whether a relation is a function. If it is impossible to draw a vertical line that intersects the graph more than once, then each x-value is paired with exactly one y-value. So, the relation is a function.
Given, the function is f(x) = x² + 2x + 3
We have to find the graph of the function.
Let y = x² + 2x + 3
Put x = -3
y = (-3)² + 2(-3) + 3
= 9 - 6 + 3
= 9 - 3
y = 6
Put x = -2
y = (-2)² + 2(-2) + 3
= 4 - 4 + 3
y = 3
Put x = -1
y = (-1)² + 2(-1) + 3
= 1 - 2 + 3
= 4 - 2
y = 2
Put x = 0
y = (0)² + 2(0) + 3
= 0 + 0 + 3
y = 3
Put x = 1
y = (1)² + 2(1) + 3
= 1 + 2 + 3
= 3 + 3
y = 6
We can plot the graph using the points.
The graph of the function f(x) = x² + 2x + 3 is a parabola with vertex (-1, 2).
Learn more about graph of quadratic equation at :
https://brainly.com/question/16191913
#SPJ4
Ken invests $6,000 into two accounts. One account earns 8% interest and the other earns 12% interest. After one year his total interest earned from the two accounts totals $580. How much did Ken invest in the 8% account?
Answers
Answer:
2400
Step-by-step explanation:
using simple ratio
we have Account A : account B as
8:12
2:3 .....the 8% account gets
2/5 × 6000
= 2× 1200 = 2400
(2+3)^2+8/2 simplified
Answers
The given expression can be simplified to obtain (2 + 3)² + 8/2 = 29.
How to do simplification using arithmetic operation?The arithmetic operations are the fundamentals of all mathematical operations. In order to simplify a given expression various operation has to be done such as division, multiplication, addition and subtraction respectively.These operations follow a rule known as PEDMAS.
The given expression is (2 + 3)² + 8/2.
It can be solved as follows,
(2 + 3)² + 8/2
⇒ 5² + 8/2
⇒ 25 + 4
⇒ 29
Hence, the simplification of the given expression is obtained as 29.
To know more about arithmetic operation click on,
https://brainly.com/question/25834626
#SPJ1
Jack decides to coast to a stop on his bicycle, so he quits pedaling. The table represents his velocity (in meters per second) as a
function of time (in seconds). Which statement best describes the significance of V(t) having a value of zero?
A)
Jack has coasted for 20 seconds
B)
Jack's bicycle will not be moving.
C)
Jack is pedaling his bicycle again
D)
Jack has traveled at least 200 meters
Answers
Answer:
B if your doing prep
Step-by-step explanation:
math
what is the answer plz help me
Answers
348in²
Step-by-step explanation:6*8 = 48. This is the surface area of the largest rectangle.
6*9 = 54. This is the surface area of the top rectangle.
8*9 = 72. This is the surface area of the smallest rectangle.
The total is 72+54+48, so 174.
Because there are two of each rectangle, you times this number by 2.
174 * 2 = 348in².
A fish tank takes 13.5 minutes to fill at a rate 1.2 litres per minute. How many minutes would
it take 5.4 litres per minute?
Answers
Answer:
74.1 minutes is the answer
Please help this is timed! I’ll give brainliest.
Answers
Answer:
Step-by-step explanation:
Answer: merry Christmas and have a wonderful new year.
Step-by-step explanation:
A deposit of $2,960 is placed into a scholarship fund at the beginning of every six months for 13 years. The fund earns 7% annual interest, compounded biannually, and paid at the end of the six months. How much is in the account right after the last deposit?
Answers
The account will have $7240 after the last deposit.
Given that, $2960 is being deposited at the beginning of every six months for 13 years. The fund earns 7% annual interest, compounded biannually,
So,
When the amount is compounded biannually,
\(A = P(1+r/2)^{2t\)
A = final amount, P = initial amount, r = rate and t = time,
\(A = 2960(1+0.07/2)^{2(13)\)
\(A = 2960(1.035)^{26\)
\(A = 7240\)
Hence, the account will have $7240 after the last deposit.
Learn more about compound interest, click;
https://brainly.com/question/14295570
#SPJ1
Martha’s clubhouse is shaped like
a square pyramid with four congruent equilateral triangles for its sides. All of the edges are 6 feet
long. What is the total surface area of the clubhouse including the floor? Round your answer to the nearest hundredth.
A=
Answers
The total surface area of the clubhouse including the floor is approximately 95.98 square feet.
We have,
The surface area of a square pyramid can be found by adding the area of the base to the sum of the areas of the four triangular faces.
Since the base is a square, its area is 6^2 = 36 square feet.
Each triangular face is an equilateral triangle with a side length of 6 feet, so its area can be found using the formula.
A = (√(3)/4) x s²,
where s is the length of a side.
The area of each triangular face.
A = (√(3)/4) x 6² = 9 √(3) square feet.
The total surface area is then:
A = 4 x 9 √(3) + 36
A = 36 √(3) + 36 ≈ 95.98 square feet
(rounded to the nearest hundredth)
Therefore,
The total surface area of the clubhouse including the floor is approximately 95.98 square feet.
Learn more about pyramid here:
https://brainly.com/question/17615619
#SPJ1
If n<5, then n<3 true or false pls help me?!?
Answers
HELP NOW PLEASE!!!!! I will give 100 points to whoever will answer this question first
Answers
Answer:
D : 10 feet
Step-by-step explanation:
Hello I think I can help with this.
Now how I would do this given a multiple choice question is kind of use brute force with your given answers to find the solution.
So the formula for area is known as (L x W x H)
or (length x width x height)
Lets see what we are given.
We are given the length which is 12
We are also given the width which is 4 1/2
And if we multiply these we can find the surface area of the base of this rectangular prism so lets do that.
12 multiplied by 4 1/2
=
54
Alright so now we know the base of this rectangular prism is 54 ft²
Now we can start the brute force method. So we are trying to find the height in this problem since we already have the width and length and have worked that out. So now all we do is multiply what we found (54) by the possible answers until one of them gives us the answer 540 ft³.
NOW this is actually really easy because we got 54 as our answer to length x width and our total amount of area is 540.
So instead of brute force we can take an easier route and do 540 / 54 and get an easy answer of 10 which is option D :
10 feet
I hope this helps you understand this a bit better!
If you are confused or have any concerns / questions feel free to comment or message me :)
Answer:
Height = 540/(4.5*12) = 10 feet
Step-by-step explanation:
fv=100000, pmt=4000, i/y=5%, n=10, what is pv?
Answers
The Present value is $6,139.132.
We have,
FV=100000, pmt = 4000, I =5%, n=10
So, The present value formula is
PV=FV / (1 + \(i)^n\)
So, PV = 100, 000 / (1+ 5/100\()^{10\\\)
PV = 100,000 / (1+ 0.05\()^{10\\\)
PV = 100, 000/ (1.05\()^{10\\\)
PV = 100,000 / 1.6288946
PV= $6,139.132
Learn more about Future Value here:
https://brainly.com/question/14860893
#SPJ1
A tank in the shape of a hemisphere has a diameter of 20 feet. If the liquid that fills the tank has a density of 83.6 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
The total weight of the liquid in the tank is 175162 pounds
How to calculate the total weight of the liquid in the tank?To calculate the total weight of the liquid in the tank, we need to find the volume of the tank.
Since tank in the shape of a hemisphere, we will use the formula for volume of hemisphere:
V = (2/3)πr³
Where r is the radius of the hemisphere.
r = 20/2 = 10 feet
V = (2/3) * 22/7 * 10³
V = 2095.2381 cubic foot
Weight (or mass) = density * volume
Weight of the liquid = 83.6 * 2095.2381
Weight of the liquid = 175162 pounds
Learn more about volume of hemisphere on:
https://brainly.com/question/28027357
#SPJ1
find the coordinate of a triangle a(1,3) , b(2,5) and c(3,3) after being rotated about fixed point p(2,4) by 45 in clockwise direction and then translate (3,4) .
Answers
After the transformation point A will be at (5, 6.586), point B will be at (5.121, 7.121) and point C will be at (6.121, 5.121).
STEPS FOR FIND THE COORDINATEThe coordinates of a triangle after rotation and translation can be found using the following steps:
Rotation: To rotate a point (x, y) about a fixed point (a, b) by an angle θ (in this case, 45 degrees in the clockwise direction), you can use the following formulas to find the new coordinates:x' = (x - a) * cos(θ) - (y - b) * sin(θ) + a
y' = (x - a) * sin(θ) + (y - b) * cos(θ) + b
Translation: To translate a point (x, y) by a distance (dx, dy) in the x and y direction, you can use the following formulas to find the new coordinates:x' = x + dx
y' = y + dy
So for the first vertex of the triangle(1,3) after being rotated about fixed point p(2,4) by 45 in clockwise directionx' = (1 - 2) * cos(45) - (3 - 4) * sin(45) + 2 = -1.121 + 1.121 + 2 = 2.000
y' = (1 - 2) * sin(45) + (3 - 4) * cos(45) + 4 = -0.707 - 0.707 + 4 = 2.586
And after the translation (3,4) for point Ax' = 2 + 3 = 5
y' = 2.586 + 4 = 6.586
similarly for point B(2,5) will be (5.121,7.121)
and for point C(3,3) will be (6.121,5.121)
So after the transformation point A will be at (5, 6.586), point B will be at (5.121, 7.121) and point C will be at (6.121, 5.121)Learn more about coordinate of a triangle here:
https://brainly.com/question/28566332
#SPJ4
what is the opposite of 1/2
Answers
Answer:
The opposite of 1/2 is -2/1, which can also be written as -2.
valuate the
expression
12 - 3y
2
+
√²v=4] for y = 3.
2y -
Answers
The result of the formula \(12 - 3y2 + (v=4) / (2y - 2)\) for y = 3 is \(-29/2\) .
What are the ways to analyse an algebraic expression?When \(y = 3\) is used, the value of the expression \(12 - 3y2 + (v=4) / (2y - 2)\) has a value of \(-29/2\) .
To analyse an algebraic expression is to determine its value when a certain number is used in lieu of the variable. To evaluate the expression, we first replace the variable with the given number, then we use the order of operations to simplify the expression.
If \(y = 3\) , we can insert it into the expression & simplify as follows to evaluate \(12 - 3y2 + (v=4) / (2y - 2)\) for \(y = 3\) .
\(12 - 3(3)^2 + (√4) / (2(3) - 2)\) (y = 3 replacement)
\(12 - 27 + 2 / 4\s-15 + 1/2\s-29/2\)
Therefore, The result of the formula \(12 - 3y2 + (v=4) / (2y - 2)\) for y = 3 is \(-29/2\) .
Learn more about expression here:
https://brainly.com/question/953809
#SPJ1
A fair coin is flipped 10 times and lands on heads 8 times. Provide a reason to justify the difference between the experimental and theoretical
probabilities. Use the drop-down menus to explain your answer.
There should be a
Choose...
number of trials. With Choose...
flips of the coin, the experimental probability will likely
approach the theoretical probability of Choose...
Answers
Answer:
THere will be 8 heads and 2 tails
Step-by-step explanation:
I don't know
The bottom part of this block is a rectangular prism. The top part
is a square pyramid. How much paper is needed to completely
cover the block? Explain.
Answers
Answer:
Check question number 9 in that file you may be able to understand the problem
Step-by-step explanation:
