The amount we saved after paying $35.70 each for two games and $22.96 for a security program is $11.34.
What is the discount?A discount refers to an amount deducted from the normal selling price of an object.
Let x be the original price of one game and y be the original price of one security program.
Given pay $35.70 each for two games and $22.96 for a security program.
The total pay with discount
$35.70 + $22.96 = $58.66
Also, 100% - 15% = 85%
100% - 18% = 82%
here, we have
0.85 (2x) = 35.70
1.70x = 35.70
x = $21
0.82 y = 22.96
y = $28
the total pay without discount
2x + y = 2 (21) + 28
= $70
The amount saved is 70 - 58.66 = 11.34
Therefore, the amount we saved after paying $35.70 each for two games and $22.96 for a security program is $11.34.
Learn more about discounts;
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Answer:
d. $11.34
Step-by-step explanation:
Find the derivative of following function.
[tex]\\ \rm\rightarrowtail y=\dfrac{cos^2x-3\sqrt{x}+6}{sin^2x+6}\times \dfrac{tan^2x+5x}{cosec^2x+3}[/tex]
Make sure you include proper explanation and all steps .
Wrong answers aren't tolerated.
Spam/short/irrelevant answers will be deleted so don't do time pass if you don't know
[tex]\boxed{\pink{\mathscr{All\:the\:best}}}[/tex]
Answer:
[tex]\displaystyle y' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \tan^2 x + 5x \big) + \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( 2 \sec^2 x \tan x + 5 \big)}{ \big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)} + \frac{2 \cot x \csc^2 x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2 \big( \sin^2x + 6 \big)} - \frac{2 \cos x \sin x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)^2}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]:
[tex]\displaystyle (uv)' = u'v + uv'[/tex]
Derivative Rule [Quotient Rule]:
[tex]\displaystyle \bigg( \frac{u}{v} \bigg)' = \frac{vu' - uv'}{v^2}[/tex]
Derivative Rule [Chain Rule]:
[tex]\displaystyle [u(v)]' = u'(v)v'[/tex]
Step-by-step explanation:
*Note:
Since the answering box is way too small for this problem, there will be limited explanation.
Step 1: Define
Identify.
[tex]\displaystyle y = \frac{\cos^2 x - 3\sqrt{x} +6}{\sin^2 x + 6} \times \frac{\tan^2 x + 5x}{\csc^2 x + 3}[/tex]
Step 2: Differentiate
We can differentiate this function with the use of the given derivative rules and properties.
Applying Product Rule:
[tex]\displaystyle y' = \bigg( \frac{\cos^2 x - 3\sqrt{x} + 6}{\sin^2 x + 6} \bigg)' \frac{\tan^2 x + 5x}{\csc^2 x + 3} + \frac{\cos^2 x - 3\sqrt{x} +6}{\sin^2 x + 6} \bigg( \frac{\tan^2 x + 5x}{\csc^2 x + 3} \bigg) '[/tex]
Differentiating the first portion using Quotient Rule:
[tex]\displaystyle \bigg( \frac{\cos^2 x - 3\sqrt{x} + 6}{\sin^2 x + 6} \bigg)' = \frac{\big( \cos^2 x - 3\sqrt{x} + 6 \big)' \big( \sin^2 x + 6 \big) - \big( \sin^2 x + 6 \big)' \big( \cos^2 x - 3\sqrt{x} + 6 \big)}{\big( \sin^2 x + 6 \big)^2}[/tex]
Apply Derivative Rules and Properties, namely the Chain Rule:
[tex]\displaystyle \bigg( \frac{\cos^2 x - 3\sqrt{x} + 6}{\sin^2 x + 6} \bigg)' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \sin^2 x + 6 \big) - \big( 2 \sin x \cos x \big) \big( \cos^2 x - 3\sqrt{x} + 6 \big)}{\big( \sin^2 x + 6 \big)^2}[/tex]
Differentiating the second portion using Quotient Rule again:
[tex]\displaystyle \bigg( \frac{\tan^2 x + 5x}{\csc^2 x + 3} \bigg) ' = \frac{\big( \tan^2 x + 5x \big)' \big( \csc^2 x + 3 \big) - \big( \csc^2 x + 3 \big)' \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2}[/tex]
Apply Derivative Rules and Properties, namely the Chain Rule again:
[tex]\displaystyle \bigg( \frac{\tan^2 x + 5x}{\csc^2 x + 3} \bigg) ' = \frac{\big( 2 \tan x \sec^2 x + 5 \big) \big( \csc^2 x + 3 \big) - \big( -2 \csc^2 x \cot x \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2}[/tex]
Substitute in derivatives:
[tex]\displaystyle y' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \sin^2 x + 6 \big) - \big( 2 \sin x \cos x \big) \big( \cos^2 x - 3\sqrt{x} + 6 \big)}{\big( \sin^2 x + 6 \big)^2} \frac{\tan^2 x + 5x}{\csc^2 x + 3} + \frac{\cos^2 x - 3\sqrt{x} +6}{\sin^2 x + 6} \frac{\big( 2 \tan x \sec^2 x + 5 \big) \big( \csc^2 x + 3 \big) - \big( -2 \csc^2 x \cot x \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2}[/tex]
Simplify:
[tex]\displaystyle y' = \frac{\big( \tan^2 x + 5x \big) \bigg[ \big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \sin^2 x + 6 \big) - 2 \sin x \cos x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \bigg]}{\big( \sin^2 x + 6 \big)^2 \big( \csc^2 x + 3 \big)} + \frac{\big( \cos^2 x - 3\sqrt{x} +6 \big) \bigg[ \big( 2 \tan x \sec^2 x + 5 \big) \big( \csc^2 x + 3 \big) + 2 \csc^2 x \cot x \big( \tan^2 x + 5x \big) \bigg] }{\big( \csc^2 x + 3 \big)^2 \big( \sin^2 x + 6 \big)}[/tex]
We can rewrite the differential by factoring and common mathematical properties to obtain our final answer:
[tex]\displaystyle y' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \tan^2 x + 5x \big) + \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( 2 \sec^2 x \tan x + 5 \big)}{ \big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)} + \frac{2 \cot x \csc^2 x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2 \big( \sin^2x + 6 \big)} - \frac{2 \cos x \sin x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)^2}[/tex]
∴ we have found our derivative.
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Topic: Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
I need help please provide the steps
Answer:
1/[tex]\sqrt{2}[/tex] - 1/4
Step-by-step explanation:
We can write 2[tex]\sqrt{8}[/tex] as 2*[tex]\sqrt{4}[/tex]*[tex]\sqrt{2}[/tex]
That becomes 4[tex]\sqrt{2}[/tex], since the square root of 4 is 2 (±2, to be exact)
(4/(4[tex]\sqrt{2}[/tex]) - ( [tex]\sqrt{2}[/tex]/4[tex]\sqrt{2}[/tex])
1/[tex]\sqrt{2}[/tex] - 1/4
solve pls brainliest
Hi again! The answer is 200 students
Would you like me to help explain so you can do these questions on your own? :)
If you have 19 cups full of water and 45 gallons of water. what does the gallon equals to how many cups of water?
Answer:
45 divide by 19 =2 r 7 thanks
Please help!
consider the function f(x)=-(x+2)^2+4
2 + 4.
a) in what form is this quadratic function written? _________________________
b) list the values of the following parameters
a = ______
h = ______
k = ______
vertex = ___________
c) what will the a parameter do to this function?
Answer:
Below,
Step-by-step explanation:
f(x)=-(x+2)^2+4
(a) Vertex form
(b) a = -1 , h = -2 and k = 4.
vertex = (-2, 4)
(c) The value of a, -1 will invert it vertically or we can describe it as a reflection in the line y = 4. The graph will change from a U shape to a ∩ shape.
Exactly 150 years ago, students planted a tree in front of their school. Since then, the tree has grown 21 meters taller and the distance around the trunk has increased by 3 meters. Use pencil and paper. Describe how you can use this information to find at least two different unit rates. Then find these unit rates.
Answer: There are 2 different unit rates here:
The increase of the tree's height per year
The increase of the tree's trunk per year
Rate of tree's height per year
= 33m / 150 years = 0.22m per year.
Rate of tree's trunk per year
= 3m / 150 years = 0.02m per year.
There are 10 students in Class 1 and 40 students in Class 2.
All 50 students sit a test.
The mean score for the students in Class 1 was 80%
The mean score for the students in Class 2 was 70%
Find the mean score of all the students.
Answer:
72%
Step-by-step explanation:
We have 10 sudents in class 1 and 40 in the other for a total of 50 students.
The 10 in class 1 had a mean of 80 so we do 80x10=800
The mean of the class of 40 is 70, so we do 40x70=2800
we add both of those together to get 3600 then we divide that by 50 because there are 50 students in total.
3600/50=72.
Which expression is equivalent to 3 square root of x^5 y
[tex] \sqrt[3]{ {x}^{5}y } = {x}^{ \frac{5}{3} } {y}^{ \frac{1}{3} } \\ [/tex]
Thus the second option is the correct answer
I NEED HELP PLEASEEEEEEEEEEE
HELP GUYS ASAP THIS QUESTION IS DUE SOLVE
The diameter of a cylinder is 1 yd. The height is 12 ydof the cylinder? Find the volume of the cylinder.
Answer:
the volume should be 9.42
Simplify 6-2a
Thank you
Answer:
4a because first, do 6 - 2 which is 4 and combine with a.
Please mark brainliest, thanks!
Ashley is riding her bike to train for a triathlon and so far has traveled 96 miles.
She is riding at an average rate of 15 miles per hour.
Calculate the time that she has been riding her bike in hours.
Answer:
hours
Note: Write the answer in decimal form.
Answer:
6.4
Step-by-step explanation:
she has been riding her bike for 6.4 hours.
What property of operations is used to show that 12x + 6y is equivalent to(2x + y)?
Answer:
Distributive property. When you factor out a GCF, from 12x + 6y, you would get 6(2x+y).
Step-by-step explanation:
12x + 6y is equivalent to 2x + y using the distributive property of multiplication over addition.
What is Number system?A number system is defined as a system of writing to express numbers.
The distributive property states that a(b + c) = ab + ac, where a, b, and c are any real numbers.
We can apply this property to the expression 2x + y by multiplying 2x by 6 and y by 6, giving:
12x + 6y = 6(2x) + 6(y)
Then, we can use the distributive property again to simplify the expression inside the parentheses:
6(2x) + 6(y) = 6(2x + y)
Substituting this expression back into the original equation, we get:
12x + 6y = 6(2x + y)
Simplifying further by dividing both sides by 6, we obtain:
2x + y = 12x/6 + 6y/6
2x + y = 2x + y
Therefore, we have shown that 12x + 6y is equivalent to 2x + y using the distributive property of multiplication over addition.
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The length of a rectangle is 4 cm less than twice its width. The perimeter of the
rectangle is 58 cm. What are the dimensions of the rectangle?
Step-by-step explanation:
Let width be x
according to question
length = 2x-4
perimeter = 58
now,
perimeter = 2(length + width)
58 = 2(x+2x-4)
58 = 6x-8
6x = 66
x = 11
putting value of x in length
2x-4
= 2 X 11 -5
= 18
hence the dimensions of the rectangle is 18 and 11
у
6
2 Look at the coordinate plane at the right.
Choose True or False for each statement about the points in the
coordinate plane.
5
4
L
a.
3
Point J and point Khave the same
y-coordinate.
True
False
2.
1
K
b. Point K and point L have the same
x-coordinate.
True
False
O
► X
6
1
2
3
4
5
c. Point J and point L are the same
distance up from the origin.
True
False
True
False
d. The y-coordinate of point L is 5.
e.
Point is the nearest point to the
right of the origin.
True
False
Answer:
A. False
B. True
C. False
D. True
E. False
Help please I would appreciate
Answer:
66 (no other answer)
Step-by-step explanation:
The number can be divided by 2 so its even. Its a multiple of 11. It is between 20 and 79. it is a multiple of 3.
Which of the following is not a parallelogram? A. Square B. Rhombus C. Rectangle D. Right Triangle
The measures of heights (in inches) of a class of students are shown. 60, 60,54, 62, 62, 57,58, 65, 54,67, 63,57, 62, 54, 72, 66, 54, 69, 55, 61 Find the mean, median, mode, range, and standard deviation of the heights.b. A new student who is 7 feet tall joins your class. How would you expect this student’s height to affect the measures in part (a)?
Answer:Compute the variance: 49+25+16+9+1+16+36+648=27.
The variance is a measure of the dispersion and its value is lower for tightly grouped data than for widely spread data. In the example above, the variance is 27. What does it mean to say that tightly grouped data will have a low variance? You can probably already imagine that the size of the variance also depends on the size of the data itself. Below we see ways that mathematicians have tried to standardize the variance.
Step-by-step explanation:
L1S2
Area - Compound Shapes
Find the area of the shaded region in each figure. Round your answer to 2 decimal
places if required. (Use = 3.14)
PLEASE HELP I WILL MARK BRAINLIEST!
Answer:
just trust yourself
Step-by-step explanation:
Use the data below.
22, 16, 18, 14, 16, 34, 20
Mean:
Median:
Mode:
Range:
Step-by-step explanation:
mean = sum of all data points / number of data points
(22+16+18+14+16+34+20)/7 = 140/7 = 20
median is the number, where half of the data points are smaller, and the other half are larger.
first we need to sort the data points
14, 16, 16, 18, 20, 22, 34
median = 18
mode is the data point occurring most often.
mode = 16 (occurring 2 times, while the others occur only once).
range is the difference between the largest and the smallest data point.
range = 34 - 14 = 20
HELP!! I’m in class I just need help with the fill in blanks segment help me please
Answer:
First Blank: “controlled” Second Blank: "a Different" Third Blank: "the same" Last Blank: "Height of the ramp"
Step-by-step explanation:
Pleas help me (and pls don't ban my question this time Brainly)
Answer:
d = 7.2
Step-by-step explanation:
12 + d = -4.8
subtract 12 from both sides and you get
d = 7.2
Answer:
-16.8
Step-by-step explanation:
The equation can be solved by performing the inverse of the operation that is done to the variable. Here, 12 is added to the variable. The inverse of that operation is addition of the "additive inverse", or "opposite" of 12:
12 + d = -4.8 . . . . . . given equation
12 -12 +d = -4.8 -12 . . . . . the same operation is done to both sides
d = -16.8
The value of d that makes the equation true is -16.8.
_____
The addition (subtraction) property of equality tells you that adding (subtracting) the same number from both sides of an equation will not change the value of the variable.
Keeram ordered 15 1/2 kg of juniper berries for her store. But 2/7 of them arrived bruised and mushy how many kg of useable berries did she receive?
Answer:
11.07~
Step-by-step explanation:
2/7 of 15.5 is 4.42857142857 which we can round to 4.43. We can then just do 15.5-4.43 to get our answer of 11.07.
the dimensions of a rectangular dining room are 18 feet by 16 feet long if a scale factor 1/4 is used to make a scale model of the dining room what is the area of the dining room in the scale model.
calculate the sides of the rectangle in scale factor model
Length: 18 * 1/4 = 4.5 feet
Width: 16 * 1/4 = 4 feet
Rectangle area in scale factor model:
Length * Width
4.5 * 4
18 feet²
Answer:
Given dimensions of a rectangular dining table:
width = 18 ftlength = 16 ftIf a scale factor of [tex]\dfrac14[/tex] is used, then we need to multiply each measurement by [tex]\dfrac14[/tex]:
[tex]\implies \textsf{width}=18 \times \dfrac14[/tex]
[tex]=4.5 \textsf{ units}[/tex]
[tex]\implies \textsf{length}=16 \times \dfrac14[/tex]
[tex]=4 \textsf{ units}[/tex]
Therefore, the scale model of the dining room will be 4.5 by 4 units.
Find f(2) if f(x)=2x+1
[tex]f(x) =2 x+1 \\\\ \text{If x = 2,}\\\\f(2) = 2(2) +1 = 4+1 = 5[/tex]
Answer:
5
Step-by-step explanation:
plug 2 in for x
f(2) = 2(2) + 1
f(2) = 5 [Asnwer]
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
Ben and Cam are scuba diving. Ben is 15.8 meters below the surface of the water. Cam is 4.2 meters below
Ben. Andrew is a further 16 meters.
Part 1 Write an expression That'll allow you to find Andrew's depth.
Part 2: What's Andrew's depth?
Answer:
27.6
Step-by-step explanation:
1) Say bens depth is x
Cam's depth is x + 4.2
Andrew's depth is x + 4.2 + 16 or x + 11.8
1) andrew's depth = x + 11.8, where x is 15.8.
Therefore, his depth is 27.6 meters.
-9 more than a number results in -20
Answer:
-9+x=-20
Step-by-step explanation:
I am not so positive on this one, but if you are not doing inequalities, then this should be correct.
"More than" would insinuate that you are adding. In this class, you would have a number to replace that x, but since no number was given, you place the x in its place. x=-11, because when you "add" -9 with something to get -20, it would have to be -11. Negative numbers can be confusing because when you subtract a negative number by another negative, you end up with a negative. Like in this case. Normally, you would just put -11, so it would look like -9 - 11 = -20. But since this says "more than", unless you are doing inequalities, you add.
If you are doing inequalities, then your answer should be this:
-9 > x = -20
I hope this helps!
-No one
A mom shared $490 between her 2 daughters in the ratio of 4 : 3 respectively. Calculate how much money is the larger share?
Step-by-step explanation:
let ratio be 4x and 3x
sum : 490$
4x+3x = 490
7x=490
x=490/7
Hence x = 70
first daughter gets = 4x =4 x 70 = 280
second daughter gets =3x = 3x 70 = 210
first daugter gets the larger share
Events that cannot happen at the same time are called?
Anona poured 5.6 cups of
water into her dog's water bowl
this morning. If her dog drinks 27 fluid ounces of the water,
how many fluid ounces of water
will be left in the bowl?
Answer:
Step-by-step explanation: 5.6 would be the add on to 27 so since it included the key word '' left'' you'd substract the two and you'd get your answer, just use calculator. You got this!!!
Go sub to clan fbib !!!!!