Answers
Step-by-step explanation:
[tex] \sin(\pi - x) + \tan(x) \cos(x) (x - \frac{\pi}{2} [/tex]
[tex] \sin( - x + \pi ) + \tan(x) ( \cos(x - \frac{\pi}{2} ) )[/tex]
Sin is odd function, so if you add pi to it, it would become switch it sign.
[tex] - \sin( - x) + \tan(x) \cos(x - \frac{\pi}{2} ) [/tex]
Also since sin is again, a odd function, we can just multiply the inside and outside by -1, and it would stay the same.
[tex] \sin(x) + \tan(x) \cos(x - \frac{\pi}{2} ) [/tex]
Cosine is basically a sine function translated pi/2 units to the right or left so
[tex] \sin(x) + \tan(x) \sin(x) [/tex]
[tex] \sin(x) ( 1 + \tan(x) )[/tex]
Related Questions
A retired woman has 70,000toinvestbutneedstomake
9,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%. Set up and solve the equation for how much the woman should invest in each option to sustain exactly a $9,000 annual return.
Answers
Answer:
$51,250 at 15%$18,750 at 7%Step-by-step explanation:
The total interest earned will be the sum of the amounts earned by each account. An equation expressing this fact can be solved to find the investment amounts.
__
setupLet x represent the amount invested at the higher rate. Then 70000-x is the amount invested at the lower rate. The total earnings from the investment will be ...
0.15x +0.07(70000-x) = 9000
__
solutionSimplifying the equation gives a 2-step linear equation.
0.08x +4900 = 9000 . . . . simplified
0.08x = 4100 . . . . . . . . . . subtract 4900
x = 51,250 . . . . . . . . . . . .divide by 0.08
70000 -x = 18,750
The woman should invest $51,250 at 15% and $18,750 at 7%.
While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning
to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan
now have? Round to the nearest cent.
1 European euro =
1.3687 US dollars
Answers
Answer:
44.70 US dollars
Step-by-step explanation:
euro left=(250/1.3687)-150=32.66(rounded to nearest cents
US dollars=32.66x1.3687
=44.70US dollars
Help please I need asap
Answers
Answer: -120
Step-by-step explanation:
[tex]2\sum^{4}_{p=1} (p^{2}-9p)=2[(1^{2}-9(1))+(2^{2}-9(2))+(3^{2}-9(3))+(4^{2}-9(4))]=\boxed{-120}[/tex]
In our QR class, 43% live in Massachusetts. Of the Massachusetts residents, 67% live in
Boston. What percentage of the class lives in Boston?
Answers
Answer:
The answer will be 63%.
Step-by-step explanation:
they have all ready mentioned that.
The following table shows how far a bus has gone in t hours. Which of the following equations represents this information?
Answers
Step-by-step explanation:
You need to attach the table in order to get an answer.
What is the solution to the following equation?
-3+x= -8
A. x = -5
B. x=5
C. x = 11
D. x=-11
Answers
Add 3 to each side, -8 + 3 = -5
Answer:
[tex]\mathsf {A. x = -5}[/tex]
Step-by-step explanation:
[tex]\implies \mathsf {-3 + x = -8}[/tex]
[tex]\implies \mathsf {x = -8 + 3}[/tex]
[tex]\implies \mathsf {x = -5}[/tex]
please help me...!!!???????????????????????????????????????????
Answers
Answer: C
Step-by-step explanation:
(rx+t)/s = w [given]rx+t = sw [multiply both sides by s]rx = sw-t [subract t from both sides]x = (sw-t)/r [divide both sides by r]An equation is formed of two equal expressions. The correct option is C.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be solved for x as shown below, Therefore,
[tex]\dfrac{rx+t}{s} = w\\\\[/tex]
Using the multiplication property of equality, multiply s on both the sides of the equation,
rx + t = ws
using the subtraction property of equality, subtract t on both the sides of the equation,
rx = ws - t
[tex]x = \dfrac{sw-t+t}{r}[/tex]
Hence, the correct option is C.
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Which is the rate of change for the interval between 3
and 6 on the x-axis?
O -3
O -2
0 2
O 3
Answers
Answer: 2
Step-by-step explanation:
When x = 3, y = -2.
When x = 6, y = 4.
The average rate of change over the interval is:
[tex]\frac{-2-4}{3-6}=\frac{-6}{-3}=\boxed{2}[/tex]
Help me with this question please and thank you!! :)
Answers
[tex]A \cup B[/tex] represents the set that contains all the elements that are in at least one of the sets, so [tex]A \cup B=\{1, 2, 5, 6, 7, 8, 9, 10, 12, 16, 18, 19, 20, 21, 22, 23, 25\}[/tex].
We want the complement of this set (in other words, the set with all the elements in the universal set but not in the given set).
This set is {3, 4, 11, 13, 14, 15, 17, 24}
Determine the rank of A
Answers
Answer:
The rank of a matrix is the number of nonzero rows in the reduced matrix, so the rank is 3. option (C)
Step-by-step explanation:
Echelon Form : it is used to find the rank of matrix by reducing rows into zeros then the number of non zero rows is the rank of the matrix
[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\2&-2&-2&5&1\\1&0&-12&9&-3\\-1&1&7&-7&1\end{array}\right][/tex]
apply row operations:
R₂= R₂ - 2 R₁
[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\1&0&-12&9&-3\\-1&1&7&-7&1\end{array}\right][/tex]
R₃= R₃ - R₁
[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\-1&1&7&-7&1\end{array}\right][/tex]
R₄ = R₄ +R₁
[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\0&0&12&-9 &3\end{array}\right][/tex]
R₄ = R₄ +R₃
[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\0&0&0&0 &0\end{array}\right][/tex]
we can clearly see that after performing row operations there are 3 non zero rows,
therefore the Rank of the given matrix is 3
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A horse was galloping at average speed of 50km/hr for the first 12 minutes. For the next x minutes, the horse slowed down and it’s average speed decreases to 30km/hr. The average speed of the horse for the whole journey is 45km/h. Find its total distance travelled in kilometres
Answers
The total distance travelled is 1075.91 km.
What is average speed?The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity.
45 * (x +12)= 50* 1/5 + 1/2 *x
45x + 540= 10+ 0.5 x
44.5 x = 530
x= 11.91 (neglect the negative sign cause time can't be negative)
So, distance= 45* 23.91 = 1075.91 Km
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Find the numeral preceding and succeeding each of the following numerals. Use T as the digit for 10.
a. TTO eleven
b. 100000 nine
c. 222 three
Answers
The numeral preceding and succeeding each of the following numerals.
Now, what happens when you add 1 or subtract 1 from 100 in the familiar base 10.
Adding adds 1 to the unit digit.
Subtracting 1 gives 99 because 9 is the largest digit in base 10.
So A. 100 base 8
The largest digit in base 8 is 7, so
..., 77, 100, 101,...
B. 10000 base 7
What is the largest digit in base 7?
The largest digit in base 7 is 6, so
..., 6666, 10000, 10001, ...
Next what happens when you add 1 to 509 in base 10. 9 is the largest digit in base 9, so adding 1 makes the units digit 0, and you carry a 1 to the next digit to the left:
509 + 1 = 510.
C. 305 base 6
5 is the largest digit in base 6, so
..., 304, 305, 310, ...
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Select the correct answer.
What is the solution to this equation?
log(2x - 100) = 3
A = 1,000
B = 450
C = 550
D = 100
Answers
Jack has a rectangular piece of land, the area of which is represented by a1 = 9.5l. His brother has a different rectangular piece of land, the area of which is represented by a2 = l(14 − l). Let a represent the area in square meters and l represent the length in meters of the pieces of land. The two equations plotted on a graph meet at a point as shown in the image.
The area of the brothers’ pieces of land will be the same when the length is ______ meters.
Answers
Answer:2
Step-by-step explanation:
Answer: 13
Step-by-step explanation:
The number of cars at a car dealership is reduced by 10% in the first sales quarter of the year. If the number of cars decreased an additional 20% over the second sales quarter of the year, then by what percent did the number of cars decrease over the two sales quarters? A) 25% B) 28% C) 30% D) 45%
Answers
Answer:
B) 28%=================
Let the initial price be x.
After the first sales quarter the price is reduced by 10% and became:
x - 10% = x - 0.1x = 0.9xAfter the second sales quarter the price is reduced by 20% and became:
0.9x - 20% = 0.9x - 0.2*0.9x = 0.9x - 0.18x = 0.72xThe decrease over the two quarters is:
x - 0.72x = 0.28xThis is equivalent of 28%, hence the correct answer choice is B.
pleaseee answer people good at math
Answers
Car averages x miles per gallon means that 1 gallon is enough to drive 36 miles.
We are asked to find average miles per gallon (miles/gallon) --> average miles per gallon would be total miles driven divided by total gallons used (miles/gallon).
Total miles driven is 10+50=60.
As a car averages 25 miles per gallon in the city for 10 miles in the city it will use 10/25=0.4 gallons
What is the average value?
A data set, the arithmetic mean, also known as arithmetic average, is a measure of the central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values.
As a car averages 40 miles per gallon on the highway for 50 miles on the highway it will use
50/40=1.25 gallons;
So average miles per gallon equals to
[tex]=\frac{10+50}{0.4+1.25}\\=36[/tex]
Therefore option D is correct.
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which law would you use to simplify the expression....
Answers
Answer:
power of a power
Step-by-step explanation:
the power of a power law says that, "if a base raised to a power is being raised to another power, the exponents are multiplied and the base remains the same."
for example, for this problem, you would do:
[tex](x^4)^9\\= x^4^*^9\\= x^3^6[/tex]
On a coordinate plane, an absolute value graph has a vertex at (10, 6).
The graph of h (x) = StartAbsoluteValue x minus 10 EndAbsoluteValue + 6 is shown. On which interval is this graph increasing?
(–∞, 6)
(–∞, 10)
(6, ∞)
(10, ∞)
Answers
Answer: (10, ∞)
Step-by-step explanation:
See the graph in the attached image.
Please please help me with my math
Answers
Answer:
D
Step-by-step explanation:
In functions like this, its best to pay attention to the end points of the rays.
On the lower line:
it ends at x -1
because it is a closed circle, that means x can also equal -1.
x≤-1
On the upper line:
it starts at -1
it is an open circle, meaning x cannot be -1
x>-1
Question 2 of 11
What system of equations would you use to solve the problem below?
A test is worth 100 points. Multiple-choice questions are worth 3 points and
short-answer questions are worth 5 points. If the test has 28 questions, how
many multiple-choice questions are there?
Answers
If the number of multiple-choice questions is x and the number of short answer questions is y, then:
[tex]x+y=28\\\\3x+5y=100[/tex]
Identify how the two trianiges are congruent. Fill in the blank below the triangles with SSS, SAS, ASA, AAS, or HL. If the two triangles are not
congruent, type not congruent.
A4X4
Blank 1:
Blank 2:
Blank 3:
Blank 4:
Question 2 (1 point)
Answers
Answer:
Blank 1 = SAS
Blank 2 = HL
Black 3 = ASA
Blank 4 = SSS
SAS - when two corresponding sides and one corresponding angles are equal HL - in a right angle triangle when corresponding hypotenuse and length are equal ASA - when 2 corresponding angles and one corresponding side are equal when all the sides of triangle is equal to other.Use the moving and additivity principles to explain and she weighs why the next triangle has an area of 1/2 (b*h) Square units for the given choices of B and H. One! If it naturally with the expression b*(1/2h) and the other should fit naturally with the expression 1/2(b*h)
Answers
Answer: The given triangles have an area [tex]1/2[/tex] × [tex]base[/tex] × [tex]height[/tex]
Step-by-step explanation:
The moving principle states that if you move a shape rigidly without stretching it the area does not change whereas the additivity principle states that if you combine different shapes without overlapping them then the area is the cumulative sum of each of the figures.
Since both, the principle will give out the same answers. the arrangement for the expression can be manipulated also.
For the first triangle applying the moving principle gives,
Area [tex]=[/tex] [tex]b[/tex] × [tex](\frac{1}{2}[/tex] · [tex]h)[/tex]
For the second triangle applying the additivity principle,
Area [tex]=\frac{1}{2}[/tex] ([tex]b[/tex] · [tex]h[/tex])
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3 Three children share this chocolate equally.
What fraction does each child get?
Each child gets
CHALLENGE?
Answers
Answer: Each child gets 1/3
Step-by-step explanation: x/3
13. Find the values of x and y in the diagram below.
א
9
13
7
y
3
10
17
Answers
Answer:
x = 2
y = 4
Step-by-step explanation:
Let's start with the 7 in the middle. Subtract the 1 on its upper left to get 6.
Add the 3 on its lower left to get 10.
so, 3 - x = 1. x = 2
17 - y = 13. y = 4
12. Use the diagram to determine the value of x
Answers
Answer:
127 degrees = x
Step-by-step explanation:
A six sided polygon has interior angles that sum to
(n-2)(180) = (6-2)(180 = 720
so all of the angles in the question add to 720
98 + 133 + x + x + 155 + 80 = 720
solve for x = 127 degrees
Answer:
x = 127
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 6 , then
sum = 180° × 4 = 720°
sum the interior angles and equate to 720
x + x + 155 + 80 + 98 + 133 = 720 , that is
2x + 466 = 720 ( subtract 466 from both sides )
2x = 254 ( divide both sides by 2 )
x = 127
Graph the function f(x) = x+4 -1.
Answers
This can be simplified to [tex]f(x)=x+3[/tex], and is thus a line with a slope of 1 and a y-intercept of 3.
Find the compound interest on $4000 for 2 years and 3months at 2% per annum,
compounded annually.
Answers
Answer:
CI = $182.25
Step-by-step explanation:
Compound interest formula:
[tex]Compound \space\ Interest= P(1 + \frac{r}{100})^{n} - P[/tex] ,
where P is the principal amount ($4000), r is the interest rate (2%), and n is the time period (2 years and 3 months = 2.25 years).
Using formula:
CI = [tex]4000(1 + \frac{2}{100} )^{2.25} - 4000[/tex]
CI = $182.25
Find the nth term of this quadratic sequence
4, 16, 36, 64, 100, ...
Answers
Answer:
144, 196, 256
Mark me as brainlist, thanks me, and rate!!!
First term means that n=1, squaring it gives you 1 and if you divide that into the term, you get 4.
That makes the equation An = 4n^2
Hope this helps!
A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping. When it stopped, the boat was 18 miles from its starting point.
A triangle shows the course of a boat. Starting at the dock, it travels 18 miles to the left, then 25 miles up and to the right, and then 28 miles down and back to the dock. The angle between 25 miles and 28 miles is x degrees.
Law of cosines:
By how many degrees did the direction of the boat change when it made its first turn? Round to the nearest degree.
30 degrees
39 degrees
46 degrees
50 degrees
Answers
Answer:
Option B :39 degrees is the correct.
The nearest degree is 39°
Step-by-step explanation:
Laws of cosines relates each side with its opposite angle.
Formula for this is :
[tex]c^{2} =a^{2} +b^{2} - 2abcosC[/tex]
[tex]a^{2} = b^{2}+c^{2} - 2bccosA[/tex]
[tex]b^{2} =a^{2}+c^{2} -2accosB[/tex]
in figure a=28
b=18
c=25
Here we have to find angle between a and c that is B
So [tex]18^{2} = 25^{2} +28^{2} -2*25*28cosB[/tex]
324 = 625 + 784 - 1400cosB
1400cosB = 625 + 784 - 324
1400cosB = 1085
cosB = 0.775
∠B = 39.195° ≈ 39°
The boat change 39° when it made its first turn.
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Answer:
B 39 degrees
Step-by-step explanation:
The person above me is correct and I got proof for the people with trust issues. : )
translate algebra 2 to standard form
Answers
Adding 2x to both sides, we get [tex]\boxed{2x+y=5}[/tex]