Please help! I know me have 10 minutes! Find all solutions to 20cos(2pi/5 x) = 10✔️2
Answers
Answer: A
Step-by-step explanation:
You have:
[tex]20cos(\frac{2\pi }{5} x)=10\sqrt{2}[/tex]
Begin by dividing both sides by 20 to get:
[tex]cos(\frac{2\pi }{5} x)=\frac{\sqrt{2} }{2}[/tex]
Take the arccosine of both sides to get:
[tex]arccos(cos(\frac{2\pi }{5} x))=arccos(\frac{\sqrt{2} }{2})[/tex]
[tex]\frac{2\pi }{5} x=arccos(\frac{\sqrt{2} }{2} )[/tex]
First of all, lets find the right side. Cosine of what gives sqrt 2 over 2? That would be pi/4, plus 2npi. Another solution would be 7pi/4, plus 2npi. We have:
[tex]\frac{2\pi }{5} x=\pi /4+2n\pi[/tex]
[tex]\frac{2\pi }{5} x=7\pi /4+2n\pi[/tex]
Isolate 'x' to get:
[tex]x=\frac{5}{2\pi } (\pi /4+2n\pi)=\frac{5}{8} +5n[/tex]
[tex]x=\frac{5}{2\pi } (7\pi /4+2n\pi)=\frac{35}{8} +5n[/tex]
Related Questions
5. A bank has outstanding loans worth $10,000. Some were loan at 10% and some
were loaned at 7%. If the income from these loans was $820, how much was
loaned at 10%?
Answers
The total amount of the outstanding loan that the bank loaned at 10% interest rate is $4,000.
What are the linear equations that represent the question?a + b = $10,000 equation 1
0.1a + 0.07b = 820 equation 2
Where:
a = amount loaned at 10%b = amount loaned at 7%How much was loaned at 10%?Multiply equation 1 by 0.07
0.07a + 0.07b = 700 equation 3
Subract equation 3 from equation 2
0.03a = 120
Divide both sides of the equation by 0.03
a = 120 / 0.03
a = $4000
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Maria, age 28, wants to pay no more than $300 a year in life insurance. what is the face value of the largest 20-year term policy she can buy without spending more than $300 annually? annual life insurance premium (per 1,000 dollars of face value) for age 28. a 10-year term for female is 1.28, 15 year term for female is 1.54, 20 year term for female is 1.89, and whole life for female is 9.46. a. $234,000 b. $158,000 c. $11,000 d. $567,000
Answers
The face value of the largest 20-year term policy which Maria can buy without spending more than $300 annually is $158,000.
What is face value?Face is the term used in finance, is used for the amount which has to be paid to the policyholder at the time of maturity.
Maria, age 28, wants to pay no more than $300 a year in life insurance.
The period for this policy is 20-year term.
Annual life insurance premium (per 1,000 dollars of face value) for age 28.
A 10-year term for female is 1.28, A 15 year term for female is 1.54, A 20 year term for female is 1.89, A whole life for female is 9.46.For the 20 year term for female is 1.89 and annular premium is $300. Thus, the face value is,
[tex]\rm Face \; Value=\dfrac{300}{1.89}\times1000\\\rm Face \; Value\approx158000[/tex]
Thus, the face value of the largest 20-year term policy which Maria can buy without spending more than $300 annually is $158,000.
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Answer: B
on edge
Step-by-step explanation:
The more people living in an area, the more likely it is that public buses will be used. city a has a population of 51,242 and covers an area of 89.22 mi2. city b has a population of 50,178 and covers an area of 8.12 mi2. which statement about use of public buses in the cities is most likely true? the residents of city a are more likely to use public buses because their city has a greater population density. the residents of city b are more likely to use public buses because their city has a greater population density. the residents of both cities are equally likely to use public buses because both population densities are about the same. the residents of both cities are unlikely to use public buses because both population densities are too high.
Answers
The population density of city-B is greater, so, the public bus must be used for city-B.
What is the population density?Population density (in agriculture: standing stock and standing crop) is a measurement of population per unit area.
The total population of city A= 51,242
The total area of city A =89.22 mi^2
The population density of city A is given by;
[tex]\rm Population \ density=\dfrac{Total \ population }{Total \ Area}\\\\ Population \ density=\dfrac{51,242}{89.22}\\\\ Population\ density=574.3331[/tex]
The total population of city B = 50178
The total area of city B =8.12 mi^2
The population density of city B is given by;
[tex]\rm Population \ density=\dfrac{Total \ population }{Total \ Area}\\\\Population \ density=\dfrac{50178}{8.12}\\\\Population \ density=6179.55665[/tex]
Hence, the population density of city-B is greater, so, the public bus must be used for city-B.
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Answer:
b is the answer
Step-by-step explanation:
The length of the base of a triangle is four more than twice the height. the area of the triangle is 80 m^2. find the lengths of the base and the height of the triangle.
can someone help me out with this? none of my friends understand this question either.
Answers
A furniture store has a sale during which the sale price of a sofa is 1/3 off its original price. The original price
of the sofa is $1,029. A customer can get an additional 5% discount off the sale price for paying with cash. At
checkout, a 6.5% sales tax on the final price is added to the cost of the sofa. What is the total cost of the sofa,
including sales tax, for a customer paying with cash?
Answers
Answer:
$694.06
Step-by-step explanation:
OG price= 1,029
discount=.05
sales tax =.065
1/3(og price)=1/3(1029)=343
one third of $1,029 is 343, hence we take off $343 from the orginial price
1029-343= $686--> sales price
.05*salesprice= .05*686=34.3
subtract 5% discount: 686-34.3= $651.71
=find 6.5% tax: .065*651.71= $42.36
add 6.5% tax: 651.81+42.36=694.06
What is the value of 0.23? Enter your answer in the box.
Answers
0.2 * 0.2 * 0.2 = 0.008
Your final answer should be 0.008
(6x1000)+(1x10)+(8x1/1)+(9x1/10)+(4/100)=
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's evaluate ~
[tex]\qquad \tt \dashrightarrow \:(6 \times 1000) + (1 \times 10) + (8 \times \frac{1}{1} ) + (9 \times \frac{1}{10} ) + \frac{4}{100} [/tex]
[tex]\qquad \tt \dashrightarrow \:6000 + 10 + 8 + \frac{9}{10} + \frac{4}{100} [/tex]
[tex]\qquad \tt \dashrightarrow \: \dfrac{600000 + 1000 + 800 + 90 + 4}{100} [/tex]
[tex]\qquad \tt \dashrightarrow \: \dfrac{601894}{100} [/tex]
or
[tex]\qquad \tt \dashrightarrow \:{6018.94}{} [/tex]
Which of the following is the equation of a line in slope-intercept form for a
line with slope = { and y-intercept at (0.-2)?
y
O A. y=-x-2
ОВ
O B. y=x-2
{
O C. y=-x+
OD. y=-2x
2
SUBMIT
Answers
Answer:
Option B is the correct answer
Step-by-step explanation:
Hope it helps you in your learning process.
mode is 7. find the missing value for this list: 1,4,7,5,7,X,3,6,3,5,9
Answers
Answer:
the missing value is 7
Step-by-step explanation:
mode means the highest occuring number and from the figures above, the numbers the occured the most are 3,5and7. they appeared two times and since from the question it's said that 7 is the mode, it means that 7 should occure more than 3 and 5. so the missing value is 7.
Help please! Put a step-by-step explanation.
No links.
Answers
Answer:
70 degrees
Step-by-step explanation:
Angles directly opposite are equal
Help!! The angle measurements in the diagram are represented by the following expressions.
∠
A
=
5
x
+
3
4
∘
∠A=5x+34
∘
start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 5, x, plus, 34, degrees, end color #11accd
∠
B
=
2
x
+
7
6
∘
∠B=2x+76
∘
Answers
Answer:
[tex]\boxed{\bf \angle A=84^o}[/tex]
Step-by-step explanation:
From the given diagram, we can see that ∠B & ∠C are corresponding angles, which means that they are equal. The two angles that form a straight line are supplementary angles (the sum of two supplementary angles is 180°).
[tex]\bf 5x+34^o+\angle C=180^o[/tex]
[tex]\bf 5x+34^o+\angle B=180^o[/tex]
[tex]\bf 5x+34^o+2x+76^o=180^o[/tex]
Now, let's solve for x :-
[tex]\bf (5x+34^o)+(2x+76^o)=180^o[/tex]
[tex]\bf (5x+2x)+(34+76)=180^o[/tex]
[tex]\bf 7x+110=180^o[/tex]
[tex]\bf (7x+110)-110^o=180-110^o[/tex]
[tex]\bf 7x=70^o[/tex]
[tex]\bf \cfrac{7x}{7} =\cfrac{70}{7}[/tex]
[tex]\boxed{\bf x=10^o}[/tex]
Now, in order to find ∠A will substitute the value of x into the expression:-[tex]\bf \angle A=5x+34^o[/tex]
[tex]\bf \angle A=5(10)+34^o[/tex]
[tex]\bf \angle A=84^o[/tex]
______________________
How many Cube Bs will fit into Cube A? Enter the max amount.
Answers
Answer:
8
Step-by-step explanation:
The answer is 8 because 1/2 times 1/2 times 1/2 is 1/8, which means that 8 B cubes can fit into cube A.
Jaime has a board that is 8 feet long. He cuts the board into three equal pieces. How long is each piece.
SHOW WORK PRETTY PLEASE WITH SUGARCANE JUICE!!!
Answers
Each piece is 2 ft and 8 inches long.
Explanation:
12 inches are in a foot, so 12 times 8 equals 96.You then divide 96 by 3 which is 32.So 32 inches is 12in+12in+8in= 2feet 8 inches
please help me i will give brainliest
Answers
Answer:
Look below
Step-by-step explanation:
We know QS is parallel to RT, so that will be the first one. We also know that r is congruent to s, so add that if possible
Next, we have to use the alt. int. angles are congruent theorem, so we can say that angle QTR and angle SOT are congruent due to this rule.
Next we have to use reflexive property, and the only thing that fits is the transversal intersecting the parallel lines. So we can say that QT is congruent to TQ.
Then we can say that triangle SQT and triangle ROT are congruent due to SAS.
Finally, we can say angle QTS is congruent to angle TQR because of corresp. parts of congruent triangles are congruent(CPCTC for short)
I hope this helped!
It would be greatly appreciated if you marked this answer as brainliest!
Hunter earned a grade of 66% on his multiple choice math final that had a total of 200 problems. How many problems on the final exam did Hunter get wrong?
Answers
There are 68 problems on the final exam did Hunter get wrong.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Hunter earned a grade of 66% on his multiple choice math final that had a total of 200 problems.
Now,
Since, Hunter earned a grade of 66% on his multiple choice math final that had a total of 200 problems.
Hence, The correct problem = 66% of 200
= 66/100 x 200
= 66 x 2
= 132
Thus, The incorrect question = 200 - 132
= 68
Therefore, There are 68 problems on the final exam did Hunter get wrong.
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#SPJ2
D
Question 6
11 pts
Use the previously created equation to solve for the verbal description (give your
answer to the nearest cent and include commas and decimal points). For example,
12,345,67
The value of a car purchased for $20,000 decreases at a rate of 12% per year. What
will be the value of the car after 3 years?
Question 7
79°F
Answers
Select all the expressions that equal 4×106.
(2×108)(2×10-2)
40×105
40 6
400,000
1. 2×1093×102
Answers
Answer:
None of the expressions are equal to 4*106
Step-by-step explanation:
(2×108)(2×10-2) does not equal 4*106
40×105 does not equal 4*106
40 6 does not equal 4*106
400,000 does not equal 4*106
2×1093×102 does not equal 4*106
Of the hats in Tammy's Hat Shop, 3/8 are green and another 1/4 are blue. What fraction of the hats are either green or blue?
Answers
Answer:
5/8
Step-by-step explanation:
Since it’s either, that is essentially saying ‘or’Because of this we add the fractions togetherThis gives [tex]\frac{3}{8} +\frac{1}{4}[/tex]Find a common denominator1/4 = 2/83/8 + 2/8 = 5/8PLEASE HELP ASAP! WILL GOVE BRAINLIEST!!! I NEED THIS DONE PLEASE FOLLOW DIRECTIONS!
Answers
Answer:
I'm not sure but
Step-by-step explanation: The area is 9.5 feet.
Find the MAD for this data set
Answers
Answer:
O.8 is the answer
Step-by-step explanation:
The coordinates of the vertices of a polygon are (1, 2), (1, -1), (-6, -1) and (-6,2). What is the perimeter of the polygon
Answers
Check the picture below.
It takes you 1/4 hours to walk 1/3 of a mile.
How long will it take you to walk 2 1/2? Miles?
PLS HELP ASAP
Answers
Answer:
15/8 Hours
Step-by-step explanation:
To start, I would find see how long it takes to walk a mile.
1/3 · 3 = 1
1/4 · 3 = 3/4
So we now know that walking one mile takes 45 minutes. Next, I multiplied 1 mile by 2.5 and repeated the same process with the time.
3/4 · 5/2 = 15/8
Therefore, it takes 15/8 hours to walk 2.5 miles.
26% of 42 is what number
Answers
Answer:
10.92
Step-by-step explanation:
26% is equivalent to 0.26 (% is in terms of 100, so if you divide the percent by 100, you gte the decimal form)
You just multiply the decimal form by the number and your result is the answer
0.26x42=10.92
What specific measure of a geometric figure is shown in the image?
Answers
Answer:
A 140 degree angle. Think about where 90 degree angle is, where 180 degree angle is, and recognize that 140 degree angle is in between those. Also, when it's saying side length, it's just saying how long the line itself is;)
Step-by-step explanation:
Answer:
A 140° angle
Step-by-step explanation:
It can be seen that the angle between 2 rays is being measured. Conveyor scale indicates 140° angle.
Hope this helps
A quadratic equation of the form 0=ax2 bx c has a discriminant value of -16. how many real number solutions does the equation have?
Answers
The quadratic equation will have no real solutions.
Given quadratic equation is: [tex]ax^{2} +bx+c=0[/tex]
What is the discriminant of a quadratic equation?The discriminant(D) of a quadratic equation is [tex]D=b^{2}-4ac[/tex]. It depicts the nature of the roots.
[tex]D > 0[/tex] the roots are real and distinct.
[tex]D=0[/tex] the roots are real and equal.
[tex]D < 0[/tex] the roots will be imaginary.
We have [tex]D=-16[/tex] which is negative.
So, the roots will be imaginary.
So, the given quadratic equation will have no real solutions.
Hence, the given quadratic equation has no real solutions.
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MAKE THIS INTO A TESTABLE QUESTION!!
"What do milkweed bugs eat"
pleasd help
Answers
Answer: what do milky buggies munch on UWU
Step-by-step explanation:
The book fair is selling erasers for $0.17 each. If Brandon spent a total of $2.21 on erasers, how many erasers did he purchase?
Answers
Answer
The answer is 13
Step-by-step explanation:
I divided 2.21 by 0.17
Answer:
13 Erasers
Step-by-step explanation:
2.21 ⁒ 0.17 = 13
Hope this helps :)
28.2
с
45.8
В
о
mzB =
Answers
Answer:
17.6
I hope this helps :)
Determine if \sqrt{41}
41
is rational or irrational and give a reason for your answer.
Answers
Assume √41 is rational, so that there exist integers p, q such that
[tex]\sqrt{41} = \dfrac pq[/tex]
and p/q is irreducible. Taking squares, this would mean
[tex]41 = \dfrac{p^2}{q^2} \implies p^2 = 41q^2[/tex]
This tells us that 41 is a factor of p², which in turn means 41 is a factor of p because 41 is prime. We can consequently write p = 41n for some integer n. But then
[tex]p^2 = (41n)^2=41q^2 \implies 41n^2 = q^2[/tex]
which says 41 also divides q² and hence divides q as well. In other words, p/q is reducible, so we have a contradiction.
What is the value of x in the equation −6 + x = −3? (5 points) Group of answer choices −9 −3 9 3
Answers
Answer:
The value of x is 3
Step-by-step explanation:
=> −6 + x = −3
=> x = -3+6
=> x = 3
So first you add the 6 to both sides
-6 + x = -3
+6 +6
The 6 will cancel
So your answer is
x= 3