Given:
The compound inequality is
[tex]9<3x+6\leq 15[/tex]
To find:
The solution for the given compound inequality in interval notation.
Solution:
We have,
[tex]9<3x+6\leq 15[/tex]
Subtracting 6 from each side, we get
[tex]9-6<3x+6-6\leq 15-6[/tex]
[tex]3<3x\leq 9[/tex]
Divide each side by 3.
[tex]\dfrac{3}{3}<\dfrac{3x}{3}\leq \dfrac{9}{3}[/tex]
[tex]1<x\leq 3[/tex]
Here, 1 is not included in the solution set and 3 is included in the solution set.
Therefore, the solution in interval notation is (1,3].
Evaluate the integral of the quantity x divided by the quantity x to the fourth plus sixteen, dx . (2 points) one eighth times the inverse tangent of the quantity x squared divided by 4, plus C one fourth times the natural log of x to the 4th power plus 16, plus C one fourth times the inverse tangent of the quantity x squared divided by 4, plus C the product of negative one fourth and 1 over the quantity squared of x squared plus 16, plus C
Answer:
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c[/tex]
Step-by-step explanation:
Given
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx[/tex]
Required
Solve
Let
[tex]u = \frac{x^2}{4}[/tex]
Differentiate
[tex]du = 2 * \frac{x^{2-1}}{4}\ dx[/tex]
[tex]du = 2 * \frac{x}{4}\ dx[/tex]
[tex]du = \frac{x}{2}\ dx[/tex]
Make dx the subject
[tex]dx = \frac{2}{x}\ du[/tex]
The given integral becomes:
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du[/tex]
Recall that: [tex]u = \frac{x^2}{4}[/tex]
Make [tex]x^2[/tex] the subject
[tex]x^2= 4u[/tex]
Square both sides
[tex]x^4= (4u)^2[/tex]
[tex]x^4= 16u^2[/tex]
Substitute [tex]16u^2[/tex] for [tex]x^4[/tex] in [tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du[/tex]
Simplify
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]
In standard integration
[tex]\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)[/tex]
So, the expression becomes:
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)[/tex]
Recall that: [tex]u = \frac{x^2}{4}[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c[/tex]
Once sales tax is included, a $62 hammock ends up costing $67.58. What is the sales
tax percentage?
NEED ASAP WILL GIVE BRAINLIEST
Answer:
9%
Step-by-step explanation:
subtract 62 from 67.58 to get 67.58-62=5.58divide 62 by 5.58and your final answer is 9%what are 3 equivalent fractions of 5/6
Answer:
Answer is 10/12 , 15/18 , 20/24 , 25/30 .
Step-by-step explanation:
1. 5/6 { Multiply both numerator and denominator with 2 }
5/6 = 10/12
2. 5/6 { Multiply both numerator and denominator with 3 }
5/6 = 15/18
3. 5/6 { Multiply both numerator and denominator with 4 }
5/6 = 20/24
4. 5/6 { Multiply both numerator and denominator with 5}
5/6 = 25/30
PLZZZZZZZZZZ HELP!!!!!!!!
Answer:
b
Step-by-step explanation:
cause a negative number is to the left of zero and a positive to the right
10 points and will be marked BRAINLIEST if the answer you give is correct!
Answer:
the one on the bottom and Lewis made one less of whatever Bryan made
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
bryan- 7x4=28
lewis- 6x4=24
28+24=52
PLEASE HELP. I WILL GIVE BRAINLIEST TO THE PERSON WHO ANSWERS BOTH PARTS OF THE QUESTION.
Parking at the posh center costs d dollars per hour during the off hours and an extra $3 per hour during peak hours. During holidays, the basic rate of d doubles. Write an expression for how much it would cost to park for 3d hours on a holiday during peak hours.
Then, if the basic off-hours parking rate is $2.50 per hour, how much would a person pay to park for 3d hours in the situation described above?
PLEASE HELP. I WILL GIVE BRAINLIEST TO THE PERSON WHO ANSWERS BOTH PARTS OF THE QUESTION.
THINGS TO REMEMBER:
the variable d represents dollarsCosts an extra $3 per hour during peak hoursWhile holiday's are going on the amount of d doublesFind how much parking would cost on a holiday during peak hour's-----
Question: Write an expression for how much it would cost to park for 3d hours on a holiday during peak hours.
-----
Answer: 3d × 2 or 3d + 3d
-----
Explanation: This is because during holidays the amount of d doubles. However since this is on a holiday DURING peak hours it would be 3d × 2
-----
Question 2: Then, if the basic off-hours parking rate is $2.50 per hour, how much would a person pay to park for 3d hours in the situation described above?
-----
Answer: $15
-----
Explanation: Since d represents dollars we would multiply 2.50 times 3 which would give us 7.5 then we double this since it is during holidays giving us $15
-----
NOTE: I AM SO SORRY IF THIS IS WRONG AND I MISSED SOMETHING. IF IT IS WRONG THEN PLEASE MAKE SURE TO TELL ME SO I CAN FIGURE OUT WHAT I MISUNDERSTOOD
Again I'm sorry but I hope I helped a little bit.
Pls help I need this and I don’t get it
Answer:
C.
Step-by-step explanation:
Hi there!
To find the answer to this, plug the number values in for n and then solve.
For the answer to be correct, the sum has to be less than 26.
Answers B and D both have numbers that would be equal to 26, so they aren’t right.
Answer A has numbers that would go over 26.
Every number in C can be added to 15 and the sum would be less than 26.
I hope this helps!
The triangles are similar. Complete the similarity statement
Answer:
ABC
Step-by-step explanation:
Answer:
YZX ~ ABC
Step-by-step explanation:
For Angle Y, there is one curved line, so you must go to the other triangle and find which angle has one curved line too, in this case that is angle A. Then, Angle Z has three curved lines, and in the other triangle, Angle B has three curved lines, so you now have AB, which only leaves C left. So your final answer is ABC.
I need help with this
Answer:
They multiplied by 100
Step-by-step explanation:
1 x 1.5 = 1.5
10 x 1.5 = 15
100 x 1.5 = 150
HELP ME PLS I NEED ANSWERS
what is the answer to
24(4 goes up)+7
Answer:
23
Step-by-step explanation:
Write your answer with no spaces and any fraction with “/“
Answer:
The slope is 1/2
Step-by-step explanation:
Hi!
Disclaimer: Just for this response, I'm going to write it the same way you write a fraction out on paper just so it's easier to see.
First, you plot the two coordinates on the graph:
(0,0) and (2,1)
The formula for slope is [tex]\frac{y1 - y2}{x1 - x2}[/tex]
Now we plug in numbers accordingly:
[tex]\frac{0 - 1}{0 - 2}[/tex]
Simplify:
[tex]\frac{-1}{-2} \\[/tex]
Simplify:
[tex]\frac{1}{2}[/tex]
Let me know if you have any questions
What is the Answer pls help
Answer:48ft
Step-by-step explanation:
Write 31/24 as a decimal rounded to the nearest tenth
Answer:
1.3
Step-by-step explanation:
just divide 31 by 24
This will give you the decimal: 1.291666667
Since the number 2 is right of the decimal point, it is in the tenths place.
Therefore, since the number next to the 2 is 9, you would round the 2 up and get 1.3 as your answer.
(25 + 19) + 15 = (19 + 25) + 15
What property is that equation
Answer:
Commutative Property
Step-by-step explanation:
It looks like Associative property which is when you change the GROUP, but actually it’s commutative because it didn’t change any numbers in the group, just the order of where they were.
Associative: (25 + 19) + 15 = (15 + 19) + 25
Commutative: (25 + 19) + 15 = (19 + 25) + 15
It didn’t change the numbers, only the order. Therefore, it would be commutative property
Answer:
25+19=44
44+15=59
19+25=44
44+15=59
what is the slope of a line that passes through the point (3,29.25)
Answer:
The slope is 9 3/4 or 9.75
Step-by-step explanation:
slope= rise/run or y/x
29.25/3=9.75 or 9 3/4
For what value of x is the following expression
sinx
undefined for Os x <211?
1+COS X
Answer:
ti 5
Step-by-step explanation:
its 5
? Help if you know how to do this
Answer:
[tex]x = 2.5[/tex]
Step-by-step explanation:
Given
[tex]AC = 2x - 1[/tex]
[tex]AB = 2x + 1[/tex]
[tex]BC = 2\sqrt{7[/tex]
[tex]\angle A = 60^{\circ}[/tex]
Required
Find x
To find x, we make use of cosine formula which states:
[tex]a^2 = b^2 + c^2 - 2bcCosA[/tex]
In this case:
[tex]BC^2 = AB^2 + AC^2 - 2*AB*BC*CosA[/tex]
Substitute values
[tex](2\sqrt{7})^2 = (2x + 1)^2 + (2x-1)^2 - 2*(2x + 1)*(2x - 1)*Cos(60^{\circ})[/tex]
Evaluate all exponents
[tex]4*7 = (4x^2 + 4x + 1)+(4x^2 - 4x + 1) - 2(4x^2 - 1)*cos(60^{\circ})[/tex]
Open brackets
[tex]28 = 4x^2 + 4x + 1+4x^2 - 4x + 1 - (8x^2 - 2)*cos(60^{\circ})[/tex]
Collect Like Terms
[tex]28 = 4x^2 +4x^2+ 4x - 4x+ 1 + 1 - (8x^2 - 2)*cos(60^{\circ})[/tex]
[tex]28 = 8x^2+ 2 - (8x^2 - 2)*cos(60^{\circ})[/tex]
Substitute 0.5 for cos(60)
[tex]28 = 8x^2+ 2 - (8x^2 - 2)*0.5[/tex]
Open bracket
[tex]28 = 8x^2+ 2 - 4x^2 + 1[/tex]
Collect Like Terms
[tex]8x^2- 4x^2 + 2 + 1 - 28 = 0[/tex]
[tex]4x^2 -25 = 0[/tex]
Collect Like Terms
[tex]4x^2 =25[/tex]
Divide both sides by 4
[tex]x^2 =\frac{25}{4}[/tex]
[tex]x^2 =6.25[/tex]
Take positive square root of both sides
[tex]x = \sqrt{6.25[/tex]
[tex]x = 2.5[/tex]
4. The side lengths of a square are each 5p. By adding 1 to the length and subtracting 1 from the width, a rectangle is made. What is the area of the rectangle?
O4p2 - 2
25p2 + 1
25p - 10p - 1
25p2 - 1
Answer:
D. 25p² - 1
Step-by-step explanation:
Each side length of a square = 5p
Length of rectangle = 5p + 1
Width of the rectangle = 5p - 1
Area of rectangle = Length × Width
Area of rectangle = (5p + 1)(5p - 1)
= 5p(5p - 1) +1(5p - 1) (distributive property)
= 25p² - 5p + 5p - 1
Area = 25p² - 1
An advertising agency notices that approximately 2 in 50 potential buyers of a product sees a given magazine ad, and 1 in 7 sees a corresponding ad on television. One in 100 sees both. One in 5 actually purchases the product after seeing the ad, 1 in 10 without seeing it. What is the probability that a randomly selected potential customer will purchase the product
Answer:
the probability that a randomly selected potential customer will purchase the product is 0.11728
Step-by-step explanation:
Given the data in the question;
by hypothesis, let the event be given as;
M = buyers sees a given magazine ad of the product
T = buyers sees a given television ad of the product
[tex]P_{A}[/tex] = buyer purchases the product after seeing the ad
[tex]P_{A"}[/tex] = buyer purchase the product without seeing the ad
from the information given in the question;
P(M) = (2/50 ) = 0.04, P(T) = ( 1/7) = 0.1428, P(M∩T) = (1/100) = 0.01,
P([tex]P_{A}[/tex]) = (1/5) = 0.2, p( [tex]P_{A"}[/tex] ) = (1/10) = 0.1
now, the probability that the buyer sees the ad of the product will be;
P( M ∪ T ) = P( M) + P(T) - p( M ∩ T)
P( M ∪ T ) = 0.04 + 0.1428 - 0.01
P( M ∪ T ) = 0.1728
The probability that the buyer does not see the ad of the product will be;
P( M ∪ T )' = 1 - P( M ∪ T )
= 1 - 0.1728
= 0.8272
Now, the probability that a randomly selected potential customer will purchase the product will be;
P(P) = P([tex]P_{A}[/tex]) P( M ∪ T ) + p( [tex]P_{A"}[/tex] )P( M ∪ T )'
P(P) = (0.2)(0.1728) + (0.1)(0.8272)
= 0.03456 + 0.08272
P(P) = 0.11728
Therefore, the probability that a randomly selected potential customer will purchase the product is 0.11728
Find a, please do not guess or if your not sure. i need help not guesses for points. (it’s geometry)
Answer:
[tex]\huge\boxed{\boxed{a=6}}[/tex]Step-by-step explanation:
to understand thisyou need to know about:trigonometryPEMDASequationtips and formulas:sin(30°)=½sin(x)=opp/hypolet's solve:[tex] step - 1 : define[/tex]
[tex] \sin( {30}^{o} ) = \frac{a}{12} [/tex]
[tex] step - 2 : solve[/tex]
[tex] \tt substitute \: the \: value \: of \: \sin( {30}^{o} ) \\ \tt \frac{1}{2} = \frac{a}{12} [/tex][tex] \tt cross \: multiplication : \\ \tt2a = 12 [/tex][tex] \tt divide \: both \: sides \: by \: 2 : \\ \tt \frac{2a}{2} = \frac{12}{2} \\ \therefore a = 6[/tex]Can you help me with my math?
Answer:
y = -3x - 1
Step-by-step explanation:
First find the slope then the Y-intercept
n - 89 > 171. what inequality below true. 1. n=82. 2. n=105. 3. n=268. 4. n=300. 5. n=312
Answer:
1. Assume the contrary, namely that √2 + √3 + √5 = r, where r is a rational number.
Square the equality √2 + √3 = r − √5 to obtain 5 + 2
√6 = r2 + 5 − 2r
√5. It follows
that 2√6 + 2r
√5 is itself rational. Squaring again, we find that 24 + 20r2 + 8r
√30
is rational, and hence √30 is rational, too. Pythagoras’ method for proving that √2 is
irrational can now be applied to show that this is not true. Write √30 = m
n in lowest
terms; then transform this into m2 = 30n2. It follows that m is divisible by 2 and because
2( m
2 )2 = 15n2 it follows that n is divisible by 2 as well. So the fraction was not in lowest
terms, a contradiction. We conclude that the initial assumption was false, and therefore
√2 + √3 + √5 is irrational.
Step-by-step explanation:
In triangle ABC, point D is the centroid, and BD=6. Find BE
Answer:
where is the image that can show the triangle?? how can we answer your question if its incomplete?
Decrease £14120 by 4% Give your answer rounded to 2 DP.
Answer:
(14120/100)*96 = £13,555.20
Step-by-step explanation:
Answer:
£13,555.20
Step-by-step explanation:
14120*4=56480
56480+14120=70,600
then 70,600+20
on a cauculaiter it will give you 70,620 but it is 70,600.20
then 14,1000.50-1,555.30=13,55.20
hope it is helpfull
P(AB)fxufucufgcidgfyzyfgx
Answer:
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Answer:
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Step-by-step explanation:
i need help asap due tonight
Answer:
The top right one 3(x+4)=30
Step-by-step explanation:
Answer:
The answer should be the one on the top right.
Step-by-step explanation:
So we know that the whole entire model equals 30, and each of the three sections are s+4. So, in order to get 30, the equation has to have something to do with three times s+4. We can eliminate the one on the top left because the model does not have a 12 involved. We can also eliminate the bottom left because it only represents one of the three s+4s. The bottom right can be taken off because the 3 in that equation is only multiplied to s, and not s+4. The top right works because it is saying that s+4 multiplied by 3 times is equal to 30. There you go! I hope this helps❤️
100 PTS!! Will give Brainliest...
Q. Select ALL transformations from the parent graph of the function f(x)=|x+7|−3
Shifted down 3
Shifted right 7
Shifted up 3
Shifted up 7
Shifted left 7
Shifted left 3
Shifted right 3
Shifted down 7
Answer:
shifted left 7 & shifted down 3
Step-by-step explanation:
A regular price of a bathing suit is $89.99. What is the new price of the bathing suit when it is 70% off the regular price?
Answer:
$26.99
Step-by-step explanation:
i multiplied $89.99×.7 to get $62.993 and subtracted that from the regular amount.
hope this is right and helps :)
Answer:
Step-by-step explanation:
89.99(1-70/100)
89.99(30/100)
$26.997
$27 (rounded to nearest cent)
Al sumar 2x+5y-4z+9 y 2x-4y+6 se obtiene?
Answer: (Responder)
4x + y + 15 – 4z
Step-by-step explanation: (Explicación paso a paso)
(2x + 5y – 4z) + (9 + 2x – 4y + 6)
Group Like Terms (Agrupar términos similares)
2x + 2x + 5y – 4y – 4z + 9 + 6
Add Similar Elements (Agregar elementos similares)
4x + 5y – 4y – 4z + 9 + 6
4x + y – 4z + 9 + 6
Add The Numbers (Suma los números)
4x + y + 15 – 4z
