Answer:
1) X stands for individual acts and y, group acts. 2) Each scenario describes a different period in minutes, but each one respecting their different amounts (individual and group acts). 3) [tex]S=\left \{ 5,10 \right \}[/tex]
Step-by-step explanation:
Completing with what was found:
1) Here is a summary of the scenario your classmate presented for the talent show:Main show The main show will last two hours and will include twelve individual acts and six group acts.Final show The final show will last 30 minutes and will include the top four individual acts and the top group act.The equations he came up with are: 12x+ 6y= 120, 4x+ y= 30
1. What do x and y represent in this situation?
X stands for individual acts and y, group acts.
Besides that, In the system of equation, they represent the time for x, and the time for y.
2. Do you agree that your classmate set up the equations correctly? Explain why or why not.
Yes, that's right. Each scenario describes a different period in minutes, but each one respecting their different amounts (individual and group acts). Either for 120 minutes or 30 minutes length. And their sum totalizing the whole period.
3. Solving the system by Elimination
[tex]\left\{\begin{matrix}12x+ 6y= 120\\ 4x+ y= 30\end{matrix}\right.\\\left\{\begin{matrix}12x+ 6y= 120\\ 4x+ y= 30\:*(-3)\end{matrix}\right.\\\left\{\begin{matrix}12x+ 6y= 120\\ -12x+ -3y= -90\end{matrix}\right.\\3y=30\Rightarrow y=10\\4x+(10)=30\Rightarrow 4x=20\Rightarrow x=5\\S=\left \{ 5,10 \right \}[/tex]
A businessman bought a fairly used radio set for 950 dollars and spent 250 dollars for repairing it before selling it for 1500 dollars. what is the percentage profit?
I believe it's a 25% profit.
950+250= 1200
1500-1200= 300
300/1200= 0.25
0.25 x 100= 25%
Answer:
I want to say 20% I could be wrong
Step-by-step explanation:
$950 + $250 = 1,200
1,200 ÷ 1500 = 0.8
0.800 > 80.0
80%
100% - 80% = 20%
Net Profit Margin = 20%
Net Profit =$300
Profit Percentage = 25%
2.4 X 10 -1 in standard form
Answer:
Step-by-step explanation:
0.24
Miranda worked Monday at her part time job and earned $71.75 for 7 hours. How much would Miranda earn after working 15 hours?
Answer:
$153.75
Step-by-step explanation:
$71.75 / 7=$10.25
$10.25 x 15 =$153.75
How many ice creams can be made with Three ice cream flavors three syrup flavors at three types
Samir, a carpenter Spent $300 on specialty tools to make toy horses for children for each horse he makes he spent $75 on supplies he charges $125 for each horse how many horses does Samir sell in order to break even ?
Assuming he spent $300 on specialty tools to make toy horses for children the number of horses that Samir sell in order to break even is 6 horses.
First step is to calculate his profit
Profit=$125-$75
Profit=$50
Now let determine how many horses does Samir sell in order to break even
Number of horse=$300/50
Number of horses=6 horses
Inconclusion the number of horses that Samir sell in order to break even is 6 horses.
Learn more here:
https://brainly.com/question/20352063
Answer:6
Step-by-step explanation:
Which of the following points is NOT a solution to the inequality: y ≥ 2x − 10?
(5,0)
(-1,1)
(4,2)
(6, -2)
Want three fractions are the same2/4 4/6 5/8 3/6 2/3 6/9
Answer:
2/4 . 4/6 . 2/3
Step-by-step explanation:
Answer:
Step-by-step explanation:
2/4=1/4
4/6=2/3
5/8
3/6
6/9=3/6
What are the solutions to the equation 3(x - 4)(x + 5) = 0?
O
O
O
x= 4 or x = 5
x= 3, x = 4, or x = -5
x= 3, x= -4, or x = 5
x = 4 or x = -5
Answer:
Step-by-step explanation:
3(x - 4)(x + 5) = 0
Dividing through by 3
(x - 4)(x + 5) = 0
(x - 4) = 0 or x + 5 = 0
x - 4 = 0 or x + 5 = 0
x = 4 or x = - 5
I really need help with this math problem
Common difference = [tex]\frac{1}{5}[/tex]
Solution:
Given arithmetic sequence:
[tex]$-2,-1\frac{4}{5} ,-1\frac{3}{5} , -1\frac{2}{5} , ....[/tex]
Let us first convert the improper fraction into mixed fraction.
[tex]$-2,-\frac{9}{5} ,-\frac{8}{5} , -\frac{7}{5} , ....[/tex]
Difference between two numbers in an arithmetic sequence is the common difference.
[tex]$a_2-a_1=-\frac{9}{5}-(-2)=-\frac{9}{5}+2=\frac{1}{5}[/tex]
[tex]$a_3-a_2=-\frac{8}{5}-\left(-\frac{9}{5}\right)=-\frac{8}{5}+\frac{9}{5}=\frac{1}{5}[/tex]
[tex]$a_4-a_3=-\frac{7}{5}-\left(-\frac{8}{5}\right)=-\frac{7}{5}+\frac{8}{5}=\frac{1}{5}[/tex]
Common difference = [tex]\frac{1}{5}[/tex].
Hence the common difference of the arithmetic sequence is [tex]\frac{1}{5}[/tex].
Common difference of the given arithmetic sequence is equal to [tex]\frac{1}{5}[/tex]
Explanation:The given arithmetic sequence is in mixed numbers. Converting them into proper fractions, we get:
[tex]First\ term = t_1 = -2\\\\Second\ term = t_2 = -1\frac{4}{5} = -\frac{(5\times1)+4}{5} = -\frac{9}{5}\\\\Third\ term = t_3 = -1\frac{3}{5} = -\frac{(5\times1)+3}{5} = -\frac{8}{5}\\\\Fourth\ term=t_4 = -1\frac{2}{5} = -\frac{(5\times1)+2}{5} = -\frac{7}{5}[/tex]
The sequence can thus be rewritten as [tex]-2, -\frac{9}{5}, -\frac{8}{5}, -\frac{7}{5}[/tex]
To find the common difference of the given arithmetic sequence, subtract any two consecutive numbers of the sequence. The difference between two consecutive numbers is always a constant and is termed as the common difference.
Hence,
[tex]d_1= t_2-t_1=(-\frac{9}{5} -(-2)= \frac{-9+10}{5}= \frac{1}{5} \\\\d_2=t_3-t_2= (-\frac{8}{5} -(-\frac{9}{5} )= \frac{-8+9}{5} = \frac{1}{5}\\\\d_3=t_4-t_3= (-\frac{7}{5} -(-\frac{8}{5} )= \frac{-7+8}{5} = \frac{1}{5}[/tex]
[tex]d_1=d_2=d_3 = d[/tex]
Common difference [tex]d=\frac{1}{5}[/tex]
Julie is 6 feet tall. If she stands 15 feet from the flagpole and holds a cardboard square, the edges of the square line up with the top and bottom of the flagpole. Approximate the height of the flagpole
Answer:
43.5 ft
Step-by-step explanation:
Given: Julie is 6 feet tall
She stands 15 feet from the flagpole.
The edges of the square line up with the top and bottom of the flagpole.
Picture drawn to show side and angle formed by Julie and flagpole.
Lets assume the height of flagpole be "h".
As given, the edges of the square line up with the top and bottom of the flagpole.
∴ Angle and base of triangle are same then ratio of corresponding sides are also equal.
Now, finding the height of flagpole by using tangent rule.
we know, [tex]tan\theta= \frac{Opposite}{adjacent}[/tex]
Remember, both the angle are equal.
∴ Ratio of opposite and adjacent leg for both right angle triangle= [tex]\frac{6}{15} : \frac{h-6}{15}[/tex]
We can put it; [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]
Solving the equation now
⇒ [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]
Multiplying both side by 15
⇒[tex]6 = \frac{15\times 15}{h-6}[/tex]
Multiplying both side by (h-6)
⇒ [tex]6\times (h-6) = 15\times 15[/tex]
Distributive property of multiplication
⇒ [tex]6h-36= 225[/tex]
Adding both side by 36
⇒[tex]6h= 225+36[/tex]
Dividing both side by 6
⇒[tex]h= \frac{261}{6}[/tex]
∴ [tex]h= 43.5\ feet[/tex]
Hence, the height of flagpole is 43.5 feet.
The height of the flagpole is given by the length of the hypotenuse side
formed by the right triangle Julie forms with the cardboard.
Response:
Height of the flagpole is 17.4 feetWhich method is used to calculate the height of the flagpole?The triangle formed by the edges of square lined up with the top and
bottom of the flagpole is a right triangle.
The altitude of the right triangle formed with the height of the flagpole as the base = 15 feet
Length of a leg of the right triangle = √(15² + 6²) = 3·√(29)
The other angle formed by the right triangle = (90° - arctan(15/6))
h × sin(arctan(15/6)) = 3·√29
[tex]h = \mathbf{\dfrac{3 \cdot \sqrt{29} }{sin(arctan(15/6))} } = 17.4[/tex]
Height of the flagpole, h = 17.4 feet
Learn more about right triangles here:
https://brainly.com/question/12399805
The speed of a boat in still water is 50km/h. It takes the same time for the boat to
travel 10km upstream as it does to travel 20km downstream. Find the speed of the
current.
The speed of a boat in still water (b) is 50km/h. It takes the same time (t) for the boat to travel 10km (x) upstream as it does to travel 20km (y) downstream. Find the speed of the current.
upstream speed (u) = speed in still water (b) - stream speed (s) = b-s = 50-s
downstream speed (d) = speed in still water (b) + stream speed (s) = 50+s
time (t) = x/u = y/d
10/(50-s) = 20/(50+s)
10(50+s) = 20(50-s)
500 + 10s = 1000 - 20s
30s = 500
stream speed (s) = 500/30 = 16.6 km/h
An experiment consists of flipping a single coin followed by rolling a six-sided cube (a die).
What is the probability of getting a head followed by a 6?
[tex]\frac{?}{?}[/tex]
Answer:[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
Okay, first, you want to find the probability of getting a head, which would be 1/2 because there are two options and we are only looking for one out of the two. Then, the probability of getting a 6 would be 1/6 because there is only one chance of getting a 6 and there are 6 options. Next, you would have to multiply both quantities to find out what the probability would be of getting both. So it would be [tex]\frac{1}{2}[/tex] ×[tex]\frac{1}{6}[/tex]=[tex]\frac{1}{12}[/tex]
Probability of getting a head followed by a 6 is 1/12
Step-by-step explanation:
There are 2 possible outcomes of tossing a coin a head and a tail.
The probability is 1 out of 2 each for head and tail.
Probability of getting a 6 when a dice is rolled is 1 out of 6 for each face i.e 1,2,3,4,5,6
So the probability of getting a head followed by 6 is 1/2*1/6 = 1/12
It can also be understood as below.
There can be 12 possible combinations once a coin is tossed and a die is rolled. Head-1, Head-2. Head-3, Head-4, Head-5, Head-6, Tail-1, Tail-2, Tail-3, Tail-4, Tail-5, Tail-6
In the list there is 1 outcome that we need. Head-6. This again gives us the chance of getting Head-6 as 1 out of 12.
If f(x) = -x2 + 6x, what is f(-3)?
Answer:
-12
Step-by-step explanation:
f(-3)= -(-3)2 + 6(-3)
= -(-6) -18
= 6 - 18
= - 12
The value of the quadratic function f(x) = -x² + 6x at x = -3 will be negative 27.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
f(x) = -x² + 6x
The degree of the function is 2. So, the function is a quadratic function.
The value of the function at x = -3 will be calculated as,
f(-3) = -(-3)² + 6(-3)
Simplify the equation, then we have
f(-3) = -(-3)² + 6(-3)
f(-3) = - 9 - 18
f(-3) = - 27
The worth of the quadratic capability f(x) = - x² + 6x at x = - 3 will be negative 27.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ5
Rewrite 3/4x+2=9/10 so that it doesn’t have fractions
The equation with no fractions is:
30x + 80 = 36
Solution:
Given that the equation is:
[tex]\frac{3}{4}x+2=\frac{9}{10}[/tex]
We have to rewrite the equation such that there is no fraction
From given expression,
[tex]\frac{3}{4}x+2=\frac{9}{10}[/tex]
Simplify the left hand side of equation
[tex]\frac{3x+8}{4} = \frac{9}{10}[/tex]
Cross multiply to get a simpler equation
[tex]10(3x+8) = 9 \times 4\\\\Simplify\ the\ above\ expression\\\\30x + 80 = 36[/tex]
Thus the equation is rewritten with no fractions
To rewrite the equation 3/4x + 2 = 9/10 without fractions, we multiply every term by the lowest common denominator (20) to get 15x + 40 = 18. Then, we isolate x by subtracting 40 from both sides to get 15x = -22. We solve for x by dividing both sides by 15, resulting in x = -22/15.
Explanation:The aim is to rewrite the equation 3/4x + 2 = 9/10 without fractions. To get rid of the fractions, we'll multiply each term by the lowest common denominator (LCD). In this case, the LCD is 20 because it's the smallest number both 4 and 10 can both go into. The equation thus becomes: 20*(3/4x) + 20*2 = 20*(9/10)
This simplifies to: 15x + 40 = 18
Now, to isolate x, we start by subtracting 40 from both sides:
15x + 40 - 40 = 18 - 40
So, 15x = -22. Finally, to solve for x, we divide by 15:
x = -22/15
Learn more about Equation Rewriting here:https://brainly.com/question/32640676
#SPJ3
what is 2x cubed plus 2x squared simplified too
Answer:
4x^4
Step-by-step explanation:
Cubed and squared are the same thing
BRAINLESS PLS
Find the value of x.
80
42
60
30
Answer:
I am pretty sure its 60 i am sorry if its wrong
Step-by-step explanation:
Solve using touch points: 620+207=
Answer:827
Step-by-step explanation:
Add 620 plus 207
what is 5/5/8 divided by 1/2/9 in simplest form
The division of 5/5/8 by 1/2/9 in simplest form is 405/88 after converting the mixed numbers to improper fractions, then multiplying by the reciprocal, and simplifying.
Explanation:To find the simplest form of the division of two mixed numbers, first, both mixed numbers must be converted to improper fractions. Dividing by a fraction is the same as multiplying by its reciprocal. So, when dividing 5/5/8 by 1/2/9, we first turn these into improper fractions.
5/5/8 becomes 45/8 (since 5*8+5=45) and 1/2/9 becomes 11/9 (since 1*9+2=11). Now the problem is 45/8 divided by 11/9. To divide these fractions, we multiply by the reciprocal: 45/8 * 9/11 = (45*9)/(8*11) = 405/88.
To simplify 405/88, we find the Greatest Common Divisor (GCD) of the numerator and the denominator, which is 1 in this case, so the fraction is already in its simplest form, which is 405/88.
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 1/2/9 is 9/2/1. So, the expression becomes 5/5/8 multiplied by 9/2/1. To multiply fractions, we multiply the numerators together and the denominators together. So, (5 x 9) / (5 x 2) x 8 / 1 = 45/10 x 8/1 = 360/10 = 36.
Jackie practices her piano for 1/2 an hour on Monday Wednesday and Friday she practices for 2/3 of an hour on Tuesday Thursday Saturday she practices for 1 hour on Sunday how many hours does Jackie practice her piano each week
Answer:
4 and a half hours
Step-by-step explanation:
half an hour ((60 x 1) / 2) for 3 of the days (30 x 3) is 90 so 1 and a half hours. then, 2/3's of an hour ((60 x 2) / 3) for 3 days (40 x 3) is 120 so 2 hours. then, adding the last hour 1.5 + 2 + 1 is 4.5 or 4 and a half hours.
Paul runs 4.8 km every morning. How many feet are in 4.8 km, given that 1 mile = 1.609 km and 1 mile = 5,280 feet?
1,769.90 feet
8,495.52 feet
12,437.42 feet
15,751.40 feet
plz help brainlist
Answer:
Step-by-step explanation:
1.609 km=1 mile
1 km=1/1.609 mile
[tex]4.8 km=\frac{4.8}{1.609} ~miles=\frac{4.8*5280}{1.609} \approx~15,751.40~ft[/tex]
Answer:
the answer is D 15,751.40
1 Kilometer is equal to 3,280.839895 feet which is approximately 3,281 feet.
multiply 3,281 feet by 4.8 = 15,748.8 which can be rounded to make 15,751.40.
In total making the correct answer choice D.
5(6x - 1) - 10x + 5 = 4(x + 10) - 4x
Answer:
x=2
Step-by-step explanation:
5(6x-1)-10x+5=4(x+10)-4x
simplify both sides
30x-5-10x+5=4x+40-4x
Simplify even further
20x=40
x=2
The perimeter of this hexagon is 52in. Each longer side measure 1 in. less than 4 times the length of a shorter side. Find the length of the labeled x.
Answer:
x=4.5 inches
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The perimeter of a hexagon is the sum of its six length sides
Let
x ----> the length of a shorter side
y ---> the length of a longer side
The perimeter of the hexagon is equal to
[tex]P=4x+2y[/tex]
[tex]P=52\ in[/tex]
so
[tex]52=4x+2y[/tex] ---->equation A
Each longer side measure 1 in. less than 4 times the length of a shorter side
so
[tex]y=4x-1[/tex] ----> equation B
substitute equation B in equation A
[tex]52=4x+2(4x-1)[/tex]
Solve for x
[tex]4x+8x=52+2\\12x=54\\x=4.5\ in[/tex]
Q(9,10) . R(-5,2) . S(-8,-2) . T (-1,2) . Parallel or Perpendicular
Answer:
Perpendicular
Step-by-step explanation:
Put all the points on a graph.
Parallel means that the lines that have the same slope and different y-intercepts. Lines that are parallel to each other will never intersect.
On the graph we made we can see that the lines will have to intersect because the points are in positions that no matter which points we chose to connect together, they would intersect with the other line.
If you had 12 pieces of licorice to share equally among 5 people, how much licorice would each person get? Be sure to show your thinking clearly.
Answer:
Each person will be getting [tex]2\frac{2}{5}[/tex] pieces of licorice
Step-by-step explanation:
If we have 12 pieces of licorice
To divide it equally among 5 people following formula will be used
Pieces to be given to each person = [tex]\frac{total\, pieces}{total\,people}[/tex]
= [tex]=\frac{12}{5} \\2.4\\[/tex]
So
Each person will be getting [tex]2\frac{2}{5}[/tex] pieces of licorice
Keywords: Algebra
Learn more about algebra at:
brainly.com/question/3739260 brainly.com/question/13168205 brainly.com/question/9607945
#learnwithBrainly
If a=2b^3 and b= -1/2c ^-2,express a in terms of c.
Answer:
Part 1) [tex]a=-\frac{1}{4c^6}[/tex]
Part 2) [tex]a=-\frac{1}{4c^{-6}}[/tex]
Step-by-step explanation:
Part 1) we have
[tex]a=2b^{3}[/tex] ----> equation A
[tex]b=-\frac{1}{2}c^{-2}[/tex] ----> equation B
substitute equation B in equation A
[tex]a=2(-\frac{1}{2}c^{-2})^{3}[/tex]
Applying property of exponents
[tex](x^{m})^{n}=x^{m*n}[/tex]
[tex]x^{-m} =\frac{1}{x^{m}}[/tex]
[tex]a=2(-\frac{1}{2}c^{-2})^{3}=2(-\frac{1}{2})^3(c^{-2})^{3}=2(-\frac{1}{8})(c^{-6})=-\frac{1}{4c^6}[/tex]
therefore
[tex]a=-\frac{1}{4c^6}[/tex]
Part 2) we have
[tex]a=2b^{3}[/tex] ----> equation A
[tex]b=-\frac{1}{2c^{-2}}=-\frac{c^{2}}{2}[/tex] ----> equation B
substitute equation B in equation A
[tex]a=2(-\frac{c^{2}}{2})^{3}[/tex]
Applying property of exponents
[tex](x^{m})^{n}=x^{m*n}[/tex]
[tex]x^{-m} =\frac{1}{x^{m}}[/tex]
[tex]a=2(-\frac{c^{2}}{2})^{3}=2(-\frac{c^{6}}{8})[/tex]
simplify
[tex]a=-\frac{c^{6}}{4}[/tex]
therefore
[tex]a=-\frac{1}{4c^{-6}}[/tex]
Kira, Bill, and Michael served a total of 134 orders Monday at the school cafeteria. Michael served 3 times as many orders as Kira. Bill served 9 more orders that Kira. How many orders did they each serve?
Answer:
Kira served 25 orders, Bill served 34 orders and Michael served 75 orders.
Step-by-step explanation:
Let Kira served x number of orders.
So, Bill served (x + 9) orders and Michael served 3x orders.
Now, it is given that Kira, Bill, and Michael served a total of 134 orders.
So, x + (x + 9) + 3x = 134
⇒ 5x + 9 = 134
⇒ 5x = 125
⇒ x = 25
Therefore, Kira served 25 orders, Bill served (25 + 9) = 34 orders and Michael served 3 × 25 = 75 orders. (Answer)
Plz help me with this the last person who did this for me got it wrong for me so i beg of u someone plz help me out with this i beg due today
a. The perimeter of the figure is 4x+34.
b. The total area of figure is 24x+40.
Step-by-step explanation:
Given,
Length of figure = 12
Width of figure = x+5+x = 2x+5
a. Perimeter = Length + Length + Width + Width
Perimeter = [tex](12)+(12)+(2x+5)+(2x+5)[/tex]
Perimeter = [tex]12+12+2x+5+2x+5 = 4x+34[/tex]
The perimeter of the figure is 4x+34.
b. Total area = Length * Width
Total area = [tex]12(2x+5) = 24x+60[/tex]
The total area of figure is 24x+40.
Keywords: area, perimeter
Learn more about perimeter at:
brainly.com/question/11207748brainly.com/question/11280112#LearnwithBrainly
Choose the number equal to: 2/3 divided by (-3)
A) -2
B) - 2/9
C) 2/9
D) 2
Answer:
-0.22222222222
Step-by-step explanation:
Which is (B)
How many thousands are in 38,000
Answer: 38
Step-by-step explanation:
Divide 38000/1000
Answer:
Step-by-step explanation: How many 10,000 are in 200,000
(SAT Prep) Find the value of x in each of the following exercises:
JIMGRANT1 CAN YOU PLEASE DO MY OTHER QUESTION AND THIS ONE.
Answer:
X=40 degrees
Step-by-step explanation:
Having trouble with RSM?
The value of angle x will be equal to 40 degrees.
What are corresponding angles?According to the equivalent angle postulate, if a transversal meets two parallel lines, the corresponding angles must be congruent.
In other words, the corresponding angles will always be identical if a transversal intersects two parallel lines. In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.
In the diagram attached with the answer below apply the corresponding angle theorem to calculate the value of x.
The value of angle x by using corresponding angle theorem will be calculated as below:-
x = 180 - 65 - 75
x = 180 - 140
x = 40
Therefore, the value of angle x will be equal to 40 degrees.
To know more about corresponding angle theorem follow
https://brainly.com/question/24839702
#SPJ5