Explanation:
Each person is x years old. Adding those unknown ages gets us x+x = 2x
We can think of it like x being one box, so x+x represents having two boxes which shortens to 2x.
Cheyenne is on her school swim team.
She has won 6 of her 15 events so far
this year. Which equation can be used
to determine how many events she will
need to win in a row to have an overall
win rate of 75%?
The equation that can be used to determine how many events Cheyenne will need to win in a row to have an overall win rate of 75% is x+6=(3/4)×15.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that there is a total of 15 events. And in order to win 75% of the event, Cheyenne need to win,
The number of matches Cheyenne needs to win = 75% of 15
= 11.25 ≈ 12 events
Since Cheyenne has already won 6 events out of 15, she needs to win 6 more events.
Hence, the equation that can be used to determine how many events Cheyenne will need to win in a row to have an overall win rate of 75% is x+6=(3/4)×15.
Learn more about Equation:
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How many minuteds does it take to make one balloon sculpture? How many balloons are used in one sculpture
Answer:
It will take 5 minutes to make one balloon structure. 7 balloons are used in 1 sculpture For part b the answer would be: Tom's unit rate for balloons used per minute would be 1.4
Step-by-step explanation:
Consider the following function.
f(x) = 1 + 5/x - 4/x2
(a) Find the vertical asymptote(s).
(b) Find the interval where the function is increasing.
Find the interval where the function is decreasing.
(c) Find the local maximum and minimum values.
(d) Find the interval where the function is concave up.
Find the interval where the function is concave down.
Find the inflection point.
(e) Use the information from parts (a)-(d) to sketch the graph of f.
Answer:
See below
Step-by-step explanation:
I assume the function is [tex]f(x)=1+\frac{5}{x}-\frac{4}{x^2}[/tex]
A) The vertical asymptotes are located where the denominator is equal to 0. Therefore, [tex]x=0[/tex] is the only vertical asymptote.
B) Set the first derivative equal to 0 and solve:
[tex]f(x)=1+\frac{5}{x}-\frac{4}{x^2}[/tex]
[tex]f'(x)=-\frac{5}{x^2}+\frac{8}{x^3}[/tex]
[tex]0=-\frac{5}{x^2}+\frac{8}{x^3}[/tex]
[tex]0=-5x+8[/tex]
[tex]5x=8[/tex]
[tex]x=\frac{8}{5}[/tex]
Now we test where the function is increasing and decreasing on each side. I will use 2 and 1 to test this:
[tex]f'(2)=-\frac{5}{2^2}+\frac{8}{2^3}=-\frac{5}{4}+\frac{8}{8}=-\frac{5}{4}+1=-\frac{1}{4}[/tex]
[tex]f'(1)=-\frac{5}{1^2}+\frac{8}{1^3}=-\frac{5}{1}+\frac{8}{1}=-5+8=3[/tex]
Therefore, the function increases on the interval [tex](0,\frac{8}{5})[/tex] and decreases on the interval [tex](-\infty,0),(\frac{8}{5},\infty)[/tex].
C) Since we determined that the slope is 0 when [tex]x=\frac{8}{5}[/tex] from the first derivative, plugging it into the original function tells us where the extrema are. Therefore, [tex]f(\frac{8}{5})=1+\frac{5}{\frac{8}{5}}-\frac{4}{\frac{8}{5}^2 }=\frac{41}{16}[/tex], meaning there's an extreme at the point [tex](\frac{8}{5},\frac{41}{16})[/tex], but is it a maximum or minimum? To answer that, we will plug in [tex]x=\frac{8}{5}[/tex] into the second derivative which is [tex]f''(x)=\frac{10}{x^3}-\frac{24}{x^4}[/tex]. If [tex]f''(x)>0[/tex], then it's a minimum. If [tex]f''(x)<0[/tex], then it's a maximum. If [tex]f''(x)=0[/tex], the test fails. So, [tex]f''(\frac{8}{5})=\frac{10}{\frac{8}{5}^3}-\frac{24}{\frac{8}{5}^4}=-\frac{625}{512}<0[/tex], which means [tex](\frac{8}{5},\frac{41}{16})[/tex] is a local maximum.
D) Now set the second derivative equal to 0 and solve:
[tex]f''(x)=\frac{10}{x^3}-\frac{24}{x^4}[/tex]
[tex]0=\frac{10}{x^3}-\frac{24}{x^4}[/tex]
[tex]0=10x-24[/tex]
[tex]-10x=-24[/tex]
[tex]x=\frac{24}{10}[/tex]
[tex]x=\frac{12}{5}[/tex]
We then test where [tex]f''(x)[/tex] is negative or positive by plugging in test values. I will use -1 and 3 to test this:
[tex]f''(-1)=\frac{10}{(-1)^3}-\frac{24}{(-1)^4}=-34<0[/tex], so the function is concave down on the interval [tex](-\infty,0)\cup(0,\frac{12}{5})[/tex]
[tex]f''(3)=\frac{10}{3^3}-\frac{24}{3^4}=\frac{2}{27}>0[/tex], so the function is concave up on the interval [tex](\frac{12}{5},\infty)[/tex]
The inflection point is where concavity changes, which can be determined by plugging in [tex]x=\frac{12}{5}[/tex] into the original function, which would be [tex]f(\frac{12}{5})=1+\frac{5}{\frac{12}{5}}+\frac{4}{\frac{12}{5}^2 }=\frac{43}{18}[/tex], or [tex](\frac{12}{5},\frac{43}{18})[/tex].
E) See attached graph
Here is the list of numbers.
5
11
16
24
29
From the list, write down a multiple of 3.
Plz write down the answer.
Answer:
From the list the multiple of 3 is 24
help me please hhhhhjjkk
Answer:
x=11
Step-by-step explanation:
This is an exterior angle theorem question.
To answer this question, you must know what the exterior angle theorem is:
An exterior angle of a triangle is equal to the sum of the two opposite interior angles. (not my definition)
So first, you need to add the two opposite interior angles.
3x+8+2x+9 is equal to 5x+17.
Then, you make an equation setting 5x+17 equal to the exterior angle.
5x+17 = 8x-16.
To solve this equation, first add 16 on both sides
→5x+33 = 8x
Then, subtract 5x on both sides
→ 33 = 3x
Finally, divide both sides by 3 to get x=11
I need help with math
[tex] \frac{1}{5} + \frac{3}{4} \times \frac{3}{5} = \\ [/tex]
[tex] \frac{1}{5} + \frac{9}{20} = \\ [/tex]
[tex] \frac{4}{20} + \frac{9}{20} = \\ [/tex]
[tex] \frac{13}{20} \\ [/tex]
..Find the slope of a line that contains the points (0,1) and (1,3)
Answer:
m=2
Step-by-step explanation:
m=y2-y1/x2-x1
m=3-1/1-0
m=2/1
m=2
Answer:
2
Step-by-step explanation:
because i got it right on the quiz
Identify the x-intercept and y-intercept of the line 3x - 6y = – 12.
Answer:
x=32
Step-by-step explanation:
What is the solution to this question im putting all my points on it. 3(a- 4) + 1 =9-a
please help ill mark brainliestO
Answer:
8 cm
Step-by-step explanation:
According to the condition,
[tex]\dfrac{PQ}{RS} = \dfrac{QT}{ST}\\\\\implies \dfrac{9}{3} = \dfrac{QT}{4}\\\\ \implies 3 =\dfrac{QT}{4}\\\\\implies QT = 3 \times 4 = 12~ \text{cm}\\\\\text{Hence}~ QS =QT - ST = 12 -4 = 8~ \text{cm}[/tex]
(a) $21,000.00 is to be divided in the ratio 5:7:9 respectively for three siblings Antony, Terry
and Jack. Calculate how much money each sibling will get.
Answer:
See below for answer
Step-by-step explanation:
Set up the equation 5x+7x+9x=2100 and solve for x:
5x+7x+9x=2100
21x=2100
x=100
Now multiply the proportion by 100:
5:7:9 * 100 = 500:700:900
This means that Antony will get $500, Terry will get $700, and Jack will get $900.
can someone pleasw helppppppp meee
Answer:
D. Modes are 2, 5, and 6
Step-by-step explanation:
The mode represents the most frequently occurring value in a data set. A data set may have more than one mode. It is one of the measures of central tendency..
Which expression is equivalent to squareroot 100?
A10
B10^2
C50
D50^2
Answer:
10^2=100
because all u would do is put down 10 two times and then u just multiply those 2 numbers
Step-by-step explanation:
Please help me solve this question I'm stuck on
The answer to the question is
D) ($9. 60, $9. 84)
ayden evaluated the expression a ÷ (2 + 1.5) for a = 14. He said that the value of the expression was 8.5. Select all the statements that are true.
Jayden's solution is incorrect.
Jayden added inside the parentheses before dividing.
Jayden substituted the wrong value for a.
Jayden divided 14 by 2 and then added 1.5.
Jayden added inside the parentheses before multiplying.
Answer:
Jayden's solution is incorrect.
Jayden divided 14 by 2 and then added 1.5
Jayden substituted the wrong value for a.
help i dont know what this means
The youth group is going on a trip to the state fair. The trip costs $64. Included in that price is $12 for a concert ticket and the cost of 2 passes, one for the rides and one for the game booths. Each of the passes costs the same price. Write an equation representing the cost of the trip, and determine the price of one pass. Solve your equation by showing your work and steps.
Answer:
12+26x=64
Step-by-step explanation:
64-12=52
52/2=26
$26 per pass
equation 12+26x=64
x=2 in this case x is representing the number of passes
12 is the ticket
and 64 is total cost
Does each relation represent a function? Choose Yes or No.
(1, 3), (2, 5), (2, 7), (4, 9)
(1, 3), (2, 5), (3, 7), (4, 9)
(1, 3), (1, 5), (1, 7), (1, 9)
(1, 3), (2, 3), (3, 3), (4, 3)
Answer:
No, Yes, No, Yes
Step-by-step explanation:
A function is where each input (the first value in the ordered pair) only has one output (the second value in the ordered pair)
1.
List of inputs: 1, 2, 2, 7
List of outputs: 3, 5, 7, 9
For the input value of 2, there is more than one output. 2 is mapped to both 5 and 7, so this is not a function
2.
Inputs: 1, 2, 3, 4
Outputs: 3, 5, 7, 9
Each input only has one output, so this is a function
3.
Inputs: 1, 1, 1, 1
Outputs: 3, 5, 7, 9
For the input value of 1, there is more than one output. 1 is mapped to 4 values, so this is not a function
4.
Inputs: 1, 2, 3, 4
Outputs: 3, 3, 3, 3
Each input is only mapped to one output, so this is a function
261,256,251,...
Find the 50th term.
Find the 50th term.
Answer:
16
Step-by-step explanation:
261 - 256 - 251
-5 by step
to 50th term there is 49 -5's from 261.
261 + 49.(-5) = 261 - 245 = 16
Answer:
16
Step-by-step explanation:
The sequence appears to be an arithmetic sequence. To find the 50th term we should create a general formula for the sequence.
General formula of an arithmetic sequence: [tex]a_n=a_1+(n-1)d[/tex]
where An = nth term, a1 = first term , n = number of terms and d = common difference.
The first term is 261 so a1 = 261
The common difference appears to be -5
( 256 - 261 = -5 ) and ( 251 - 256 = -5 )
so d = -5
We want to find the 50th term so n = 50
We then plug all of this in to get the 50th terms
Formula : [tex]a_n=a_1+(n-1)d[/tex]
a1 = 261 , n = 50 and d = -5
[tex]a_n=261 + (50-1)-5[/tex]
subtract 1 from 50
[tex]a_n=261+(49)(-5)[/tex]
multiply 49 and -5
[tex]a_n=261-245[/tex]
subtract 245 from 261
[tex]a_n=16[/tex]
The 50th term is 16
-2/7 × 9.75 what is answer
Answer:
-2.78
Step-by-step explanation:
You first divide and then multiply.
The given triangles are similar. Find x.
Answer:
9
Step-by-step explanation:
Each side is being multiplied by 1.5.
3 times 1.5 is 4.5.
7 times 1.5 is 10.5.
6 times 1.5 is 9.
-3, 9, -27, 81 find the next term
Answer: The next term is -243.
Answer:
-243
Step-by-step explanation:
The common ratio in this geometric sequence is -3. Therefore, the next term will be 81(-3) = -243.
factor and solve the zeros for the following x^2+10x-75=0
Because Aaron, age 32, is a smoker, he must pay more for life insurance. Given that Company A charges 20% more for smokers, Company B charges 18% more for smokers, Company C charge 25% more for smokers and Company D charges 15% more for smokers, Aaron decides to buy his $250,000 policy from Company B. Which of the following statements is true? A 5-column table with 3 rows titled Annual Insurance Premiums (per 1,000 dollars of face value) 10 year term. Column 1 is labeled age with entries 30, 31, 32. Column 2 is labeled Company A with entries 1.30, 1.57, 1.86. Column 3 is labeled Company B with entries 1.29, 1.55, 1.86. Column 4 is labeled Company C with entries 1.40, 1.64, 2.07. Column 5 is labeled Company D with entries 1.49, 1.88, 2.25. a. Aaron is paying the smallest premium possible with Company B. b. Aaron is paying $93 more in premiums than he would with Company A. c. Aaron is paying $129 more in premiums than he would with Company C. d. Aaron could have chosen any company because the premiums are all the same. Please select the best answer from the choices provided A B C D
Answer:
answer B
Step-by-step explanation:
becuase b is bad for you
Solve the equation for the variable 49-2/3x=32-1/6x
Answer:
No Solutions
Step-by-step explanation:
I believe it's no solutions. 47/3x can never equal 31/6x. Even if you try to cross multiply it (282x = 9x), you'll see that x must equal to 0.
Therefore, x has no solutions.
Answer:
Can you give the answers please but i think it is 49-2/3 32-1/6 the answer is 27.5
Step-by-step explanation:
Dean ran 5 miles this week and wants to know how many kilometers he ran. His work is below.
Answer:
Dean ran 8.0467 kilometers
Step-by-step explanation:
First, you need to know how much kilometers are in a mile. 1 mile is 1.60934 kilometers, so once you found that out, then you would do 1.60934x5 which gets you 8.0467. Hope it helps!
3. Tom's entered a snowman building contest in which the person who builds the tallest
snowman wins. Currently, the record is 13.4 feet high. If Tom's snowman is currently 9 feet
high, how many more feet does he need to build on, in order to win the competition
tom's snowman has to increase by anything greater than 4.4 ft
Answer:
4.5 feet
Step-by-step explanation:
9+4.5=13.5
13.5>13.4
square root of the quantity x minus 3 end quantity plus 5 equals x
Answer:
x =1 if understood it correctly
Step-by-step explanation:
how many times as large is the 4 in the tenthousands place as the 4 in the ones place
WILL GIVE BRAINLIEST
Answer:
answer choice is B
Step-by-step explanation:
Use mathaway and scan the problem
Please help i rlly need itttt
Answer:
The value of x is the value where the line crosses the x-axis!
________________________________________________________
Hope this helps!!
Please tell me if I have made a mistake!!
I enjoy learning from them:)
Answer:
x = y - b/m (with the obvious restriction m ≠ 0 )
Step-by-step explanation:
If
y = mx + b
subtracting b from both sides
y - b = mx
dividing both sides by m
y - b/m = x
flipping the sides (to make it look more normal)
x = y - b/m