Answer:
(10 + x) liters represents the total number of liters in the mixture
Step-by-step explanation:
Here, we want to find and expression representing the total number of liters in the solution; we proceed as follows;
The simple answer here is the sum of the liters of both solutions.
Mathematically, that would be 10 + x liters
We should understand that we do not have anything to do with the concentration of either solution and thus, the total amount in liters of both will be 10 + x liters
Expand and simplify
(2x2 + 3)(4x + 5) - 8x(x - 2)
Use S = n^2 to find the sum of 1 + 3 + 5 + . . . + 701.
Answer:
123201
Step-by-step explanation:
This is an arithmetic sequence of common difference 2 and starting value 1,
So we can use the formula for an arithmetic sequence if we know what is the order of the last term.
Then first use the formula for the nth term to find "n":
[tex]a_n=a_1+(n-1)d[/tex]
where d = 2, first term = 1 and last term = 701
[tex]a_n=a_1+(n-1)d\\701=1+(n-1)*2\\700=(n-1)*2\\350=n-1\\n = 351[/tex]
Knowing this, we can estimate the partial sum:
[tex]S=n\,\frac{a_1+a_n}{2} \\S=351\,\frac{1+701}{2} \\S=351\,*\,351\\S = 123201[/tex]
One cattle farmer plans to grow his cattle population 2% each year, modeled by the function f(t) = 100(1.02)t. Another farmer intends to add 20 cattle per year, modeled by the function g(t) = 100 + 20t. For this application, the domain is restricted to t ≥ 0. If the farmers become partners, which function represents the total cattle they will have after t years? h(t) = 200(21.02)t h(t) = 200(20.4)t h(t) = 100(1.02)t + 20t + 10 h(t) = 2,000t(1.02)t + 100
Answer:
h(t) = 100(1.02)t + 20t + 10
Step-by-step explanation:
I got it right on the test : )
Answer:
h (t) = 100(1.02)t + 20t + 100
Step-by-step explanation: edge 2021
took the unit test got it right.
HELP!!!
on thursday, mabel handled 90 transactions. anthony handled 10% more transactions than mabel. cal handled 2/3 of the transactions that anthony handled, and Jade handled 16 more transactions than cal. how many transactions did jade handle?
Answer:
82
Step-by-step explanation:
Mabel = 90Anthony = 90 + 10% = 90 +90*0.1 = 99Cal = 2/3*99 = 2*33 = 66Jade = 16 + 66 = 82Rewrite the given inequality as two linear inequalities. ∣8x+9∣<4
Answer:
[tex]8x+9<4[/tex] and [tex]8x+9>-4[/tex].
Step-by-step explanation:
The given inequality is
[tex]|8x+9|<4[/tex]
We need to rewrite the given inequality as two linear inequalities.
We know that |8x+9|>0 but (8x+9) can be positive or negative.
For [tex]|8x+9|<4[/tex], the value of (8x+9) must be lies between -4 and 4.
i.e., [tex]-4<8x+9<4[/tex]
If 8x+9 positive, then
[tex]8x+9<4[/tex] ...(1)
If 8x+9 negative, then
[tex]8x+9>-4[/tex] ...(2)
Therefore, the two inequalities are [tex]8x+9<4[/tex] and [tex]8x+9>-4[/tex].
The formula for calculating the density of an object is D=-, where m is mass and v is volume.
m
Rewrite the formula in terms of m. Then rewrite the formula in terms of v.
Answer:
M= D x V, V= M x D
Step-by-step explanation:
You just do the opposite of division since the original is:
Density= Mass/ Volume
A soccer ball with a diameter of 8.6 inches is shipped in a box that is a square prism and has a side length of 9.5 inches. How much volume is available to be filled with packing material if the shipping company wants the box completely full? Round your answer to the nearest tenth.
524.5 in^3
774.2 in^3
5,115.8 in^3
1805.6 in^3
1190.2 in^3
Answer:
A 524.5 in^3
Step-by-step explanation:
A study was done by an online retail store to determine the rate at which users used its website. A graph of the data that was collected is shown: A line graph with Number of Months on the x axis and Number of Users, in thousands, on the y axis. The x axis has a scale from 0 to 36 with an increment of 4. The y axis has a scale of 0 to 60 with increments of 6. A straight line connecting 0, 0 and approximately 36, 54 is drawn. What can be interpreted from the range of this graph? v
Answer:
A graph of the data that was collected is shown: A line graph with Number of Months on the x axis and Number of Users, in thousands, on the y axis. The x axis has a scale from 0 to 36 with an increment of 4. The y axis has a scale of 0 to 60 with increments of 6. A straight line connecting 0, 0 and approximately 36, 54 is drawn. What can be interpreted from the range of this graph? v .
Answer:
c
Step-by-step explanation:
The graph of f(x) = 0.5x is replaced by the graph of g(x) = 0.5x + k. If g(x) is obtained by shifting f(x) up by 5 units, then what is the value of k?
Answer:
k = 5
Step-by-step explanation:
The value of k is added to each y-coordinate, so represents the amount of up-shift. If the shift up is 5 units, then k=5.
Answer:
k = 5
Step-by-step explanation:
I got it right on the quiz
2,802,136 expanded complete the expanded form
Answer:
200000+800000+0+2000+100+30+6
Step-by-step explanation:
2,000,000
800,000
0
2,000
100
30
+ 6
_________
prove cos x / 1+sinx = tan ( π\4 - x/2)
Answer:
[tex]\displaystyle \frac{\cos x}{1 + \sin x} = \tan\left(\frac{\pi}{4} - \frac{x}{2}\right)[/tex].
Overview of the steps:
Apply the double-angle identity of sines and cosines to the left-hand side of the equation.Apply the Pythagorean identity to the left-hand side of the equation.Apply the angle sum and difference identity of sines and cosine to the right-hand side of the equation.Step-by-step explanation:
Double-angle identity of sines and cosines:
[tex]\cos (2\,\alpha) = \cos^2\alpha - \sin^2\alpha = (\cos\alpha + \sin\alpha)\, (\cos\alpha - \sin\alpha)[/tex].[tex]\sin(2\,\alpha) = 2\, \sin\alpha\, \cos\alpha[/tex].Pythagorean identity for the sine and cosine of the same angle:
[tex]1 = \cos^2\alpha + \sin^2\alpha[/tex].
Angle sum and difference identity of sines and cosines:
[tex]\sin(\alpha - \beta) = \sin\alpha\, \cos\beta - \cos\alpha \, \sin\beta[/tex].
[tex]\cos(\alpha - \beta) = \cos\alpha\, \cos\beta + \sin\alpha \, \sin\beta[/tex].
Consider [tex]x[/tex] as the sum of two angles of size [tex](x/2)[/tex]. Start by applying the double-angle identity to the left-hand side.
[tex]\begin{aligned} \text{L.H.S.}&= \frac{\cos(x)}{1 + \sin(x)} \\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{1 + 2\, \sin(x / 2)\, \cos(x / 2)}\end{aligned}[/tex].
Apply the Pythagorean identity to rewrite the "1" in the denominator as [tex]\left(\cos^2(x / 2) + \sin^2(x / 2)\right)[/tex].
[tex]\begin{aligned} \text{L.H.S.}&= \frac{\cos(x)}{1 + \sin(x)} \\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{1 + 2\, \sin(x / 2)\, \cos(x / 2)}\\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{\sin^2(x/2) + 2\,\sin(x/2)\, \cos(x/2) + \cos^2 (x/2)}\end{aligned}[/tex].
Note that the denominator is now a perfect square. On the other hand, the numerator is in the form [tex](x^2 - y^2)[/tex], which is equal to [tex](x + y)\, (x - y)[/tex]. Rewrite and simplify this expression:
[tex]\begin{aligned} \text{L.H.S.}&= \frac{\cos(x)}{1 + \sin(x)} \\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{1 + 2\, \sin(x / 2)\, \cos(x / 2)}\\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{\sin^2(x/2) + 2\,\sin(x/2)\, \cos(x/2) + \cos^2 (x/2)} \\[1em] &= \frac{(\cos(x/2) + \sin(x/2))\, (\cos(x/2) - \sin(x/2))}{\left(\sin(x/2) + \cos(x/2)\right)^2} \\ &= \frac{\cos(x/2) - \sin(x/2)}{\sin(x/2) + \cos(x/2)}\end{aligned}[/tex].
The tangent of an angle is equal to the ratio between its sine and its cosine. Apply the angle sum and difference identity of sine and cosine to the right-hand side.
Note, that the sine and cosine of [tex](\pi/4)[/tex] are both equal to [tex]\left(\sqrt{2}/2\right)[/tex].
[tex]\begin{aligned}\text{R.H.S.} &= \tan\left(\frac{\pi}{4} - \frac{x}{2}\right) \\ &= \frac{\sin((\pi/4) - (x/2))}{\cos((\pi/4) - (x/2))}\\ &= \frac{\left(\sqrt{2}/2\right)\, \cos(x/2) - \left(\sqrt{2}/2\right)\, \sin(x/2)}{\left(\sqrt{2}/2\right)\, \cos(x/2) + \left(\sqrt{2}/2\right)\, \sin(x/2)} \\ &= \frac{\cos(x/2) - \sin(x/2)}{\cos(x/2) + \sin(x/2)}\end{aligned}[/tex].
Therefore:
[tex]\displaystyle \text{L.H.S.} = \frac{\cos(x/2) - \sin(x/2)}{\sin(x/2) + \cos(x/2)} =\text{R.H.S.}[/tex].
[tex]\displaystyle \frac{\cos x}{1 + \sin x} = \tan\left(\frac{\pi}{4} - \frac{x}{2}\right)[/tex].
The perimeter of a rectangular window is 43 feet. The width of the window is 5 ft more than the length. Find the width of the window
Answer:
13.25 ft
Step-by-step explanation:
Let w represent the width of the window. Then w-5 represents the length, and the perimeter is ...
P = 2(L+W)
43 = 2((w-5) +w) = 4w -10
53/4 = w = 13.25 . . . feet
The width of the window is 13.25 ft.
Calculate the distance between (6 − 5i) and ( 1 + 3i).
A: /113
B: /29
C: /53
D: /89
Answer: D
Step-by-step explanation:
i just had this question on a quiz and it said the correct answer was /89
can someone please help me with this?!
Answer:
26) Let the first number be x.
Sum of three consecutive even numbers:
[tex]x+(x+2)+(x+4)=-84[/tex]
[tex]x+x+2+x+4=-84\\[/tex]
[tex]3x+6=-84[/tex]
Subtract 6 from both sides:
[tex]3x+6-6=-84-6[/tex]
[tex]3x=-90[/tex]
Divide both sides by 3:
[tex]\frac{3x}{3}=\frac{-90}{3}[/tex]
[tex]x=-30[/tex]
To find the other two numbers, add 2 and 4 respectively:
[tex](-30+2=-28)(-30+4=-26)[/tex]
27) Let the first number be x.
Sum of three consecutive odd integers:
[tex]x+(x+2)+(x+4)=141[/tex]
[tex]3x+6=141[/tex]
Subtract 6 from both sides:
[tex]3x+6-6=141-6\\3x=135[/tex]
Divide both sides by 3:
[tex]\frac{3x}{3}=\frac{135}{3}\\x=45[/tex]
To find the other two numbers, add 2 and 4 respectively:
[tex](45+2=47)(45+4=49)[/tex]
28) Let the first number be x.
Sum of four consecutive integers:
[tex]x+(x+1)+(x+2)+(x+3)=54[/tex]
[tex]4x+6=54[/tex]
Subtract 6 from both sides:
[tex]4x+6-6=54-6\\4x=48[/tex]
Divide both sides by 4:
[tex]\frac{4x}{4}=\frac{48}{4}\\x=12[/tex]
To find the other three numbers, add 1, 2 and 3 respectively:
[tex](12+1=13)(12+2=14)(12+3=15)[/tex]
29) Let the first number be x.
Sum of four consecutive integers:
[tex]x+(x+1)+(x+2)+(x+3)=-142[/tex]
[tex]4x+6=-142\\[/tex]
Subtract 6 from both sides:
[tex]4x+6-6=-142-6[/tex]
[tex]4x=-148[/tex]
Divide both sides by 4:
[tex]\frac{4x}{4}=\frac{-148}{4}\\x=-37[/tex]
To find the other three numbers, add 1, 2 and 3 respectively:
[tex](-37+1=-36)(-37+2=-35)(-37+3=-34)[/tex]
Write the word form of the following decimals. 432.98
Answer: Four hundred and thirty two point nine - eight.
Step-by-step explanation:
Hey there! I'm happy to help!
With the numbers before the decimal, you just say it normally. After the decimal, you just name the digits.
So, you would call this number four hundred thirty-two point nine eight.
Have a wonderful day! :D
If simplifying the following problem, what
would be the correct first and third
steps?
8 - 4 [5(2-2)] + 3
Answer: First step would be doing the () first. The third step would be 4 times 0. I think so, forgive me if I’m wrong.
Step-by-step explanation:
Eight avocados cost $4.
How much do 16 avocados cost?
How much do 20 avocados cost?
How much do 9 avocados cost?
16 avocados costs = $8, 20 avocados costs = $10 and 9 avocados costs = $4.5
What is the Cost?The amount of money that a company spends on the creation or production of goods or services.
Given that, Eight avocados cost $4.
Therefore, each of them costs = 4/8 = 1/2
So, 16 avocados = 16*1/2 =$8
20 avocados = 20*1/2 =$10
9 avocados = 9*1/2 =$4.5
Hence, 16 avocados costs = $8, 20 avocados costs = $10 and 9 avocados costs = $4.5
For more references on Cost, click;
https://brainly.com/question/15135554
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3g-9+11g-21 simplyfy
Answer:
g = 15/7
Step-by-step explanation:
3g - 9 + 11g - 21
group like terms
3g + 11g = 21 + 9
14g = 30
g = 30/14
g = 15/7
The flow-rate of your current sink faucet is 2.7 gallons per minute. If you purchase a fancy low-flow faucet for $294, the flow rate would decrease by 39%. Assuming you use your faucet for an average of 1,558 minutes per month and water costs $0.006 per gallon, compute the payback period (in months) of such a purchase.
Answer:
23
Step-by-step explanation:
**LOOK AT PHOTO** Whats the answer and what are the steps?
Answer:
[tex]a=2K-b[/tex]
Step-by-step explanation:
[tex]K=\frac{a+b}{2}[/tex]
Switch sides:
[tex]\frac{a+b}{2}=K[/tex]
Multiply both sides by 2:
[tex]\frac{2\left(a+b\right)}{2}=2K[/tex]
[tex]a+b=2K[/tex]
Subtract b from both sides:
[tex]a+b-b=2K-b[/tex]
[tex]a=2K-b[/tex]
Robert is building model cars as well as model trains. The cars take 4 hours to build while the trains take 6 hours
to build. He is hoping to build as many as possible before the next model fair exhibition. If he has 100 free hours
until the fair, how many can he build? Write the inequality for this problem. Let cars be the domain and trains the
range.
10 cars and 10 trains in 100 hours
it approximately take him 10 hours to build one car and one train how 6+4=10 how many times can 10 go into 100 10 times hope this helps a little
Find the derivative of the function. y = sin−1(6x + 1)
If you don't know the derivative of the inverse of sine, you can use implicit differentiation. Apply sine to both sides:
[tex]y=\sin^{-1}(6x+1)\implies\sin y=6x+1[/tex]
(true for y between -π/2 and π/2)
Now take the derivative of both sides and solve for it:
[tex]\cos y\dfrac{\mathrm dy}{\mathrm dx}=6[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=6\sec y[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac6{\cos\left(\sin^{-1}(6x+1)\right)}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac6{\sqrt{1-(6x+1)^2}}[/tex]
Solve y over negative 6 + 5 = 9. (1 point)
This should be your equation - (y/-6) + 5 = 9
Answer:
y/-6 = 4 <y = -24 <
Answer:
[tex]y=-24\\[/tex]
Step-by-step explanation:
Write the equation
[tex]\frac{y}{-6} +5=9[/tex]
Subtract 5 from both sides
[tex]\frac{y}{-6} =4[/tex]
Multiply both sides by -6
[tex]y=-24\\[/tex]
Hope this helps! : )
The translation rule is (x,y) (x+_,y+_)
Answer:
see below
Step-by-step explanation:
The question is not clear but I will provide info based on given
Translation of
(x, y) → (x + a, y+ b)means sliding by a points to left/right and by b points to up/down
Eli is making smoothies. Each smoothie uses 1/2 cup of yogurt. How much yogurt does he need to make 20 smoothies?
Answer:
40 smoothies
Step-by-step explanation:
if a 1/2 is one then times it by two
Answer:
40 smoothies
Step-by-step explanation:
There are 450 seats in a theatre. 48% of the seats are occupied. How many seats are not occupied?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{234}}}}}[/tex]
Step-by-step explanation:
Total seats in a theatre = 450
Finding the total occupied seats
[tex] \dashrightarrow{ \sf{48\% \: of \: 450}}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{48}{100} \times 450}} [/tex]
[tex] \dashrightarrow{ \sf{216}}[/tex]
Finding the seats that are not occupied
[tex] \longrightarrow{ \sf{450 - 216 = 234}}[/tex]
Hope I helped!
Best regards! :D
Kyanna has 4 pears, 6 apples, and 3 oranges. Write a ratio to show oranges to pears.
Answer:
3:4
Step-by-step explanation:
Which of the following statements best describes a theorem?
A. A theorem cannot be proven.
B. A theorem can be false.
C. A theorem is always true.
D. A theorem is never true.
Answer:
a
Step-by-step explanation:
A theorem cannot be proven.
A college library has five copies of a certain text on reserve. Three copies (1, 2, and 3) are first printings, and the remaining two (4, and 5) are second printings. A student examines these books in random order, stopping only when a second printing has been selected. One possible outcome is 4, and another is 214. (a) List the outcomes in S. (b) Let A denote the event that exactly one book must be examined. What outcomes are in A
Answer:
S = { (4), (5), (1,4), (1,5), (2,4), (2,5), (3,4), (3,5), (1,2,3,4), (1,2,3,5), (2,1,3,4) (2,1,3,5), (3,1,2,4), (3,1,2,5) }
A ={(4), (5)}
Step-by-step explanation:
Given that:
Among the three copies, (1,2,3) are the first printings, and (4,5) are the second printings.
A student who examines these books in random order stops when a second printing has been selected.
Thus, we can compute the sample space associated with these experiments as:
S = { (4), (5), (1,4), (1,5), (2,4), (2,5), (3,4), (3,5), (1,2,3,4), (1,2,3,5), (2,1,3,4) (2,1,3,5), (3,1,2,4), (3,1,2,5) }
Suppose A represents the event that we must examine exactly one book.
Then the outcomes of A are:
A ={(4), (5)}
How many proportional relationships are shown in the coordinate plane below?
Choose 1 answer:
(Choice A)
0
(Choice B)
1
(Choice C)
2
(Choice D)
3
Answer:
D. 3
Step-by-step explanation:
We can see from the graph that there are 3 lines. All 3 lines look linear, and if a line is linear, x and y are proportional. Therefore, if all 3 lines are linear, then we have 3 proportional relationships.
