Algebra 2 Word Problem: Set up using 3 variables & 3 equations:
"A friend e-mails you the results of a recent high school swim meet. The e-mail states that 24 individuals placed, earning a combined total of 53 points. First place earned 3 points, second place earned 2 points, and third place earned 1 point. There were as many first-place finishers as second and third-place finishers combined."
A: Write a system of THREE equations that represents how many people finished in each place.
B: How many swimmers finished in first place, second and third?
Final answer:
To solve the word problem, we define three variables representing the number of first-, second-, and third-place finishers, respectively. We set up three linear equations based on the information provided, and by solving the system, we determined that 10 swimmers finished in first place, 8 in second, and 6 in third.
Explanation:
Setting Up the Equations
Let's denote the number of first-place finishers as x, second-place finishers as y, and third-place finishers as z. According to the information provided:
Total number of individuals placed: x + y + z = 24
Total points earned: 3x + 2y + z = 53
The number of first-place finishers equals the number of second and third-place finishers combined: x = y + z
This is our system of three equations.
Solving the System of Equations
To solve for the number of swimmers in each place, use the substitution or elimination method:
Since x = y + z, substitute x in the first two equations.
You'll get two equations with two variables (y and z).
Solve these equations to find the values of y and z.
Finally, substitute the found y and z back into x = y + z to get the value of x.
By solving this system, we find that 10 swimmers finished in first place, 8 swimmers finished in second, and 6 swimmers finished in third.
What is the solution to the equation 9(w-4)-7w=5(3w-2)
Answer:
2
Step-by-step explanation:
Is the coordinate (-2,-4) a solution to the equation y= 3x-2.
Simplify.
5√7+√7-2√7
3√7
3√21
4√21
4√7
Answer: 4 sqrt 7
Step-by-step explanation:
He is correct, the answer is the one above.
Option (D) To simplify the expression 5√7 + √7 - 2√7, combine like radicals by adding their coefficients to get the simplified form, which is 4√7.
The student is asked to simplify the expression 5√7 + √7 - 2√7. To simplify an expression that involves like radicals, combine them by adding or subtracting their coefficients, just as you would combine like terms in algebra.
The expression simplifies as follows:
Combine the terms with like radicals: (5 + 1 - 2)√7
Simplify the coefficients: 4√7
Therefore, the simplified form of the expression is 4√7.
Lisa ate 1/3 of pizza. Kate ate 4/12 of same pizza. What fraction did they eat altogether
You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You never withdraw money from the account. How much money will be in the account after 4 years?
Answer:
A=2000(1+0.05)^4=2,431.01
Step-by-step explanation:
Use the relationships in the diagram below to write an equation and solve for X
Which ordered pairs in the form (x,z) are solution to the equation 3x-4y?
PLEASE HELP!!!
Lena is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges
$115
and allows unlimited mileage.
Company B has an initial fee of
$55
and charges an additional
$0.80
for every mile driven.
For what mileages will Company A charge less than Company B?
Use
m
for the number of miles driven, and solve your inequality for
m
.
To calculate the unit price of an item, divide the total number of units by the total price.
True or False?
Answer:
Its really false!!!!!
Step-by-step explanation:
Triangle LMN is congruent to triangle HIJ. Angle L measures 35 degrees angle M measures 65 degrees and angle H measures 2x + 10 degrees. Find the value of x.
Answer: The value of x is 12.5°.
Step-by-step explanation:
Since we have given that
ΔLMN ≅ ΔHIJ
So, According to "Congruency rules":
∠L = ∠H -------------------------------------(1)
∠M = ∠I
∠N = ∠J
∠M = 65° , ∠L = 35° and ∠H = (2x+10)°
From eq(1), we get that
[tex]2x+10=35^\circ\\\\2x=35-10\\\\2x=25\\\\x=\dfrac{25}{2}\\\\x=12.5^\circ[/tex]
Hence, The value of x is 12.5°.
Each set of ordered pairs represents a function. Write a rule that represents the function.
1. (0,0),(1,4),(2,16),(3,36),(4,64)
2. (0,0),(1,0.5),(2,2),(3,4.5),(4,8)
The number of students at marita's school decreased to 98% of last year's number currently there are 1170 students how many students were there last year round to the nearest whole number
There were about 1194 students at Marita's school last year.
To find the number of students last year when the current number is 1170 and represents 98% of last year's number, you can set up a simple equation.
Let "x" represent the number of students last year.
According to the given information, the current number of students is 98% of last year's number, which can be expressed as:
1170 = 0.98x.
To find the value of "x," you need to divide 1170 by 0.98:
[tex]\(x = \frac{1170}{0.98} = 1193.877\).[/tex]
Rounding to the nearest whole number, last year's number of students was approximately 1194.
So, there were about 1194 students at Marita's school last year.
Solve the inequality. Graph the solutions. h – 2 < –1
Write two equations in standard form that are equivalent to the given equation.
1.5x+10y=15
2.-9x-12y=6
3.-2x+4y=-5
Equivalent equations can be created by multiplying or dividing the original equation by any nonzero constant. Lifting the coefficients of the given equations accordingly can create multiple equivalent equations.
Explanation:To create two equations that are equivalent to the given equation 1.5x + 10y = 15, we can multiply the entire equation by a nonzero constant. By multiplying by 2, we obtain 3x + 20y = 30. Conversely, dividing the original equation by 3 gives us 0.5x + 3.3333y = 5.
Applying the same concept to the second equation -9x - 12y = 6, multiplying by 2 gives us -18x - 24y = 12, and dividing by 3 gives us -3x - 4y = 2.
For the third equation -2x + 4y = -5, multiplying by any nonzero constant yields an equivalent equation. Multiplying by 2, we get -4x + 8y = -10, and dividing by 2 gives us -1x + 2y = -2.5.
Under a dilation, a figure is enlarged and its orientation is preserved. Choose the statement that best describes the dilation.
A.
The image is along the same ray as the preimage but is farther from the center of dilation.
B.
The image is along the opposite ray from the preimage but is farther from the center of dilation.
C.
The image is along the same ray as the preimage but is closer to the center of dilation.
D.
The image is along the opposite ray from the preimage but is closer to the center of dilation.
Answer: C) The image is along the same ray as the preimage but is closer to the center of dilation.
A cone has a diameter of 10 inches. If its height is twice its radius, about what is the volume of the cone in cubic inches? Use 3.14 for π.
Answer with Step-by-step explanation:
The volume of cone is given by:
V=[tex]\dfrac{1}{3}\times \pi r^2h[/tex]
Where r is the radius of cone and h is height
r=d/2 where d is the diameter
Hence, here r=5 in.
height is twice its radius ⇒ h=10 in.
V=[tex]\dfrac{1}{3}\times 3.14\times 5^2\times 10[/tex]
V=261.66 in³
Hence, Volume of cone is:
261.66 in³
In the function y=1/2x^2 , what effect does the number 1/2 have on the graph, as compared to the graph of the function y=x^2 ?
A. It shrinks the graph vertically to 1/2 its original height.
B. It stretches the graph vertically by a factor of 2.
C. It stretches the graph horizontally by a factor of 2.
D. It shrinks the graph horizontally to 1/2 its original width.
In the function y=1/2x^2 , what effect does the number 1/2 have on the graph, as compared to the graph of the function y=x^2 ?
A. It shrinks the graph vertically to 1/2 its original height.
B. It stretches the graph vertically by a factor of 2.
C. It stretches the graph horizontally by a factor of 2.
D. It shrinks the graph horizontally to 1/2 its original width.
Answer:
D isn't the correct answer. It's "It shrinks the graph vertically to 1/2 its original height."
Step-by-step explanation:
I'm not sure why though this is right because I graphed it, and I don't see how that could be the right answer.
Answer:
Option A - It shrinks the graph vertically to 1/2 its original height.
Step-by-step explanation:
Given : In the function [tex]y=\frac{1}{2} x^2[/tex]
To find : What effect does the number [tex]\frac{1}{2}[/tex] have on the graph, as compared to the graph of the function [tex]y=x^2[/tex] ?
Solution :
The parent function is [tex]y=x^2[/tex]
We have given that [tex]\frac{1}{2}[/tex] number is multiply to the parent function.
When the unit is multiply to the function gives you vertical stretch or compression
i.e, f(x)→ bf(x), o<b<1 then the function is vertically compressed.
[tex]y=\frac{1}{2} x^2[/tex] As [tex]0<\frac{1}{2}<1[/tex] means there is vertical compression or shrinks.
Therefore, Option A is correct.
It shrinks the graph vertically to 1/2 its original height.
D=20-1.95c how would I work this out correctly
A bacteria culture begins with 15 bacteria which double in amount at the end of every hour. How many bacteria are grown during the 12th hour?
please help with this #15
What is 57 divided by 4241
The result of dividing 4241 by 57 is approximately 74.40.
To divide 4241 by 57, we perform the division as follows:
74
____________
57 | 4241
- 3996
_______
245
- 228
______
170
- 171
______
-1
The quotient is 74 with a remainder of 1.
Therefore, [tex]\( \frac{4241}{57} = 74 \)[/tex].40 with a remainder of 1.
Complete question:
What is 4241 divided by 57?
Mae currently has a balance of $8,484.79 in an account earning simple interest. Seventeen years ago she opened the account with an initial deposit of $4,854. What is the interest rate on the account?
4.4%
2.5%
10.3%
5.9%
Kathleen and Arnob both run from the park entrance along a loop. Kathleen starts walking from the park entrance and gets a 5-mile head start on Arnob. The graph shows how far they have both traveled.
How many minutes does it take Arnob to catch up to Kathleen?
a. 9.8
b. 10
c. 73.5
d. 75
For this case, the first thing we must do is define variables.
We have then:
x: time in minutes
y: distance traveled.
We then have the following equations:
For Kathleen:
[tex] y = (\frac{1}{15}) x + 5
[/tex]
For Arnob:
[tex] y = (\frac{2}{15}) x
[/tex]
By the time Arnob reaches Kathleen we have:
[tex] (\frac{1}{15}) x + 5 = (\frac{2}{15}) x
[/tex]
From here, we clear the value of x.
We have then:
[tex] (\frac{2}{15}) x - (\frac{1}{15}) x = 5
[/tex]
[tex] (\frac{1}{15}) x = 5
x = (15) * (5)
x = 75 min
[/tex]
Answer:
it takes Arnob to catch up to Kathleen 75 minutes:
d. 75
What multiplies to make 12 and adds up to 16
Student earned a 70% on a test with 50 questions how many questions were correct
Your class hopes to collect at least 325 cans of food for the annual food drive. There were 135 cans donated the first week and 89 more the second week.
a. Write an inequality that describes this situation. Let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass your goal.
b. How many cans are needed to meet or surpass your goal?
Guys i need help. My niece has come over my house and she need help with this question any help?
Loves from KIM.
A ladder that is 21 feet long is propped against a building. The bottom of the ladder was placed 4 feet from the base of the building. How high up on the building does the ladder reach? Round the answer to the nearest tenth of a foot.
4.1 feet
17.0 feet
20.6 feet
21.4 feet
Answer:
C
Step-by-step explanation:
I took test on Edg
Part 1 : When solving systems of equations, how do you determine what method to use?
Part 2 : Choose 1 system of equations from the choices below. Then, solve the system and post your solution, showing your steps so that other students can see which method you chose.
–y + 3x = 6
y = –6x + 12
6x – 4y = 54
–9x + 2y = –69
2y = x + 1
–2x – y = 7
...?
To solve systems of equations, select a method based on the system's setup; using substitution, we solve the given system and find the solution to be (2, 0).
Explanation:When solving systems of equations, one must choose the method that best fits the problem's constraints. Methods include substitution, elimination, and graphing. The method selected often depends on how the equations are presented and which method allows for the most straightforward calculation.
Choosing the system –y + 3x = 6 and y = –6x + 12, we can solve it using substitution since the second equation is already solved for y:
Substitute the expression for y from the second equation into the first.So –(–6x + 12) + 3x = 6.Simplify to get 6x – 12 + 3x = 6.Combine like terms to get 9x – 12 = 6.Add 12 to both sides to get 9x = 18.Divide by 9 to find x = 2.Plug x back into the second equation to get y = –6(2) + 12, hence y = 0.Our solution is (x, y) = (2, 0).
Use linear approximation to estimate 15^.25 ...?