Hello from MrBillDoesMath!
Answer:
pi/2, - 3pi/2
Discussion:
The solutions of sin(t) = 1 are (pi/2) + 2*pi*n, where n = 0, -1,1, -2,2,-3,3, etc.
In particular, sin(pi/2) = 1 ( n = 0) and sin(-3pi/2) -1 ( n = -1) and those argument values lie in the interval [-2pi, 2pi]
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MrB
P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!
Final answer:
The value of t on the interval [-2π,2π] for which sin(t)=1 is only at t=π/2, since this is where the sine function reaches its maximum value within the given range.
Explanation:
The question asks: For what values of t on the interval [-2π,2π] is sin(t)=1? To answer this, we must understand when the sine function reaches its maximum value of 1. In the unit circle, θ represents the angle in radians from the positive x-axis. The sine function reaches its maximum value of 1 at an angle of θ=π/2 radians. Therefore, within the interval [-2π,2π], sin(t)=1 only at t=π/2. However, the function is periodic with a period of 2π, meaning it repeats every 2π intervals. Even though the question's range allows for multiple cycles of sine's period, only π/2 falls within those bounds with the value of sin(t) exactly equal to 1.
Why were measurements originally started?
Answer:
Measurements were needed for multiple things, such as agriculture, construction, and trade. Also, many areas developed their own systems for measuring objects making it difficult as people from different places had different results. Eventually, the same system was adopted by the majority of people.
Step-by-step explanation:
A pet store has two gray rabbit 1/8 of the rabbits at the pet store are gray how many rabbits does the pet store have
Given that two rabbits are gray and they represent 1/8 of all rabbits at a pet store, calculated using ratios, it can be inferred that the total number of rabbits is 16.
Explanation:The question is asking about the total number of rabbits in a pet store given that 1/8 of the total rabbits are gray and there are two gray rabbits. We can use this information to set up a ratio to calculate this.
To find out the total number of rabbits, we can set up a proportion where 2/total rabbits = 1/8. By cross multiplying, we find that 2 * 8 = total rabbits. Therefore, the pet store has 16 rabbits.
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The ratio of the measures of the three angles to a triangle is 2:9:4. Find the measures of the angles.
Answer:
first angle is 24
second angle is 108
third angle is 48
all the three angles of the triangle add up to 180
(its a rule)
then 2+9+4=15
180÷15=12
12×2=24
12×9=108
12×4=48
Step-by-step explanation:
i got it right
Remy drinks 214 cups of water every 145 hours.
How many cups of water does he drink in 1 hour?
Answer:
Approximately 1.5 cups/hour
Step-by-step explanation:
Divide 214 cups by 145 hours.
(214 cups)/(145 hours) = 1.47586... cups/hour
Remy drinks around 1.47 cups of water in an hour. This was calculated by dividing the total cups (214) by total hours (145).
Explanation:To solve this question, we need to calculate the rate at which Remy drinks 214 cups of water every 145 hours. This can be done by dividing the total number of cups by the total number of hours.
So, the formula we have is:Cups per hour = Total Cups / Total hours
This gives us:Cups per hour = 214 / 145
After calculating this, you will find that Remy drinks approximately 1.47 cups of water in 1 hour.
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What is the equation of this line?
a) y=2x−3
b) y=−12x−3
c) y=−2x−3
d) y=12x−3
Answer:
Not sure but i think its C. y=-2x-3
Answer:
y = 2x - 3
Step-by-step explanation:
It says to find the value of x.
Answer:
x = 23
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
the third angle forms a straight angle with 100°, hence
third angle in triangle = 180° - 100° = 80°
Summing the 3 angles gives
2x + 3 + 80 + 51 = 180
2x + 134 = 180 ( subtract 134 from both sides )
2x = 46 ( divide both sides by 2 )
x = 23
Please help me with these two problems. It's fine if you only do one though. All help is welcomed. THANK YOU!!!
Answer:
a) x=38
b) x=19
Step-by-step explanation:
a) The interior angles at L and M can be found by subtracting 134 and 84 from 180 respectively:
∠L = 180 - 134 = 46
∠M = 180 - 84 = 96
The angles of a triangle sum up to 180, so x + 46 + 96 = 180.
From this you find that x = 180 - 46 - 96 = 38
b) Because YZ and XW are parallel, ∠Y=∠W = 2x
The sum of the angles in the triangle must be 180, so
3x-5 + 90 + 2x = 180
Which simplifies to
5x +85 = 180
5x = 95
x = 19
Answer:
a) x = 38°; b) x = 19°
Step-by-step explanation:
a)
∠OLM = 180 - 134 = 46° Supplementary angles
∠OML =180 - 84 = 96° Supplementary angles
x + 46 + 96 = 180 Interior angles of triangle
x + 142 = 180
x = 38°
===============
b)
∠XWY + 3x - 5 + 90 = 180 Interior angles of triangle
∠XWY + 3x + 85 = 180
(1) ∠XWY + 3x = 95
∠XWY = 2x
(2) ∠XWY - 2x = 0 Alternate interior angles
5x = 95 [2 subtracted from (1)]
x = 19°
One day jasmine earned $25.20 for 6 hours of work. Another day, she earned $16.80 for 4 hours of work. Which function shows how much jasmine earns (c) for working (h) for hours?
Jasmine earns $4.20 per hour of work. The function that represents her earnings (c) for working h hours is c = 4.2h.
Explanation:From the provided information, we know that Jasmine earns $25.20 for working for 6 hours one day, and $16.80 for working 4 hours the next day. The rate at which Jasmine is paid can be determined by dividing her earnings by the hours she works, otherwise known as her wage rate.
For the first day:
Wage rate = $25.20/6 = $4.20 per hour
For the second day:
Wage rate = $16.80/4 = $4.20 per hour
Thus, we can conclude that Jasmine earns $4.20 per hour. Therefore, the function for Jasmine's earnings (c) for working h hours is given by:
c = 4.2h
Where 'c' represents the total earnings and 'h' represents the hours worked.
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The function that shows how much Jasmine earns (c) for working (h) hours is c = 4.20h.
Explanation:The function that shows how much Jasmine earns for working for a certain number of hours can be determined by finding the rate of earnings per hour. We can calculate the rate of earnings by dividing the total earnings by the number of hours worked. Let's use the given information to find the rate of earnings for Jasmine:
Rate of earnings for the first day: $25.20/6 = $4.20 per hour
Rate of earnings for the second day: $16.80/4 = $4.20 per hour
Therefore, the function that shows how much Jasmine earns (c) for working (h) hours is c = 4.20h.
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Three friends decide to evenly split their bill at a restaurant. The total bill is $84.99 and they will have to pay an additional $5.10 tax. One of the friends determines that each person owes $45.04. Estimate the amount each person should owe. Is the friend's calculation reasonable? Select from the drop-down menus to complete the sentence. The friend's calculation because each person should owe about .
Given : The Total Bill at the Restaurant is $84.99
Given : The Additional Tax is $5.10
⇒ Total Bill Including the Tax is : (84.99 + 5.10) = $90.09
Given : Three Friends decide to evenly split their Bill
⇒ $90.09 should be Divided into 3 Equal Parts
[tex]\mathsf{\implies The\;Amount\;each\;person\;should\;owe\;is = (\frac{90.09}{3})}[/tex]
[tex]\mathsf{\implies The\;Amount\;each\;person\;should\;owe\;is = 30.03\;Dollars}[/tex]
His Friend Calculation is not Reasonable
The friend's calculation of each person owing $45.04 is not reasonable as the correct amount should be $30.03 per person when evenly splitting a bill of $84.99 with an additional $5.10 tax.
To determine whether the friend's calculation of $45.04 each for splitting a bill of $84.99 with an additional $5.10 tax is reasonable, let's calculate the correct amount each person should owe. First, we combine the total bill and tax: $84.99 + $5.10 = $90.09. Then, we divide this total by three, as there are three friends: $90.09 / 3 = $30.03 per person.
The friend's calculation is not reasonable because each person should owe about $30.03, not $45.04. The estimate of $45.04 is significantly higher than the accurate calculation.
The earnings of a barber vary directly as the number of customers he serves. Earl serves 10 customers and earns $25.00. How much will he earn if he serves 15 customers?
A.
$38.50
B.
$39.00
C.
$36.50
D.
$37.50
Answer:
37.5
Step-by-step explanation
Th ratio is 2.5 to 1. So then I just multiplied 2.5 to 15 and got the answer!
Hope it helps, if it is right please tell me!
Answer: $37.50
Step-by-step explanation:
$25.00 / 10 = $2.50
$2.50 * 15 = $12.50
$12.50 + $25.00 = $37.50
A stem-and-leaf plot has the key 3|4 = 34. How would the value 8 be represented? 1. 3|8
2. 1|8
3. 8|0
4. 0|8
Answer:
4. 0|8
Step-by-step explanation:
key 3|4 = 34
The first digit is the tens place and the second digit is the ones place
8 can be represented as 08
0|8 would be 08
Answer:
4. 0 | 8
Step-by-step explanation:
Note that in the stem-and-leaf plot example given to us, 3 | 4 = 34.
From this, we can assume that the left side of | represents the tens place, while the right side of | represents the ones place value.
It is asking what the value 8 represents in 3 | 8. From the example that we see above, we know that the number given is 38. the value of 8 in this number represents the one's value.
0 | 8 is your best answer, for there is no tens place.
~
what percent of 20 is 6
Answer: 30 percent of 20 is 6.
_______________________________________________
Step-by-step explanation:
_______________________________________________
(n/100) * 20 = 6 ?
Solve for "n" .
_______________________________________________
Divide each side of the equation by "20" :
{ (n/100) * 20 } / 20 = 6 / 20 ;
to get:
n/100 = 6/20 ;
↔ 6/20 = n/100 ; solve for "n" ;
Look at the denominators:
20 * ? = 100 ?
100/ 20 = ? ;
100/20 = 5 ;
So, 20 * " 5" = 100 ;
Then 6* 5 = "n" (for the numerator, "n"; in : "n /100" ) ;
→ 6 * 5 = 30 ;
→ n = 30 .
_______________________________________________
Answer: 30 percent of 20 is 6.
_______________________________________________
A restaurant cook earns $8 per hour for the first 40 hours worked and $12 per hour for over time (hours worked in addition to the 40 hours a week). Last week the cook worked 60 hours. Calculate the cooks total pay for that week.
Answer:the answer is 560
Step-by-step explanation:
The reason is because you multiply to get 8 and 40 to get the amount for regular time which is 320.Then you subtract 60 from 40 which is 20.You multiply that amounnt by 12 because that is the overtime which will equal 240.Add them together and you get 560. ☺
PLEASE HELP MEH! God bless yall
Answer: -1
Step-by-step explanation:
I think because if u graph it you can count the boxes down and to the side and you get -1
Answer: D) -1
Step-by-step explanation: Use the slope formula and plug in two points form tha table.
I chose the first two (3, -5) and (6, -8)
Y2-y1/x2-x1
-8--5/6-3
Hope it helps!
Audrey's parents give her $5 to play video games at the mall.Each games costs a quarter to play.which choice is NOT a correct method for determining the total #of games she can play. A.Take the #of dollars she has and divide it by 1/4. B.Take the # of dollars she has and multiply it by 4. C.Take the # of dollars she has and divide it by 0.25. D.Take the # of dollars she has and multiply by 0.25
Answer:
Step-by-step explanation:
If answer A works then so will Answer A. The reason is because 1/4 and 0.25 are equal to one another. The only comment you should recognize is that
5/0.25 is a whole lot easier to do than 5/(1/4)
B is the same thing as C when you apply the division by fractions rule.
D is the odd method out. Instead of 20 games (5 * 4) she will only get to play 4. That because she has 5 dollars and if you multiply by 0.25 you get 1.25 games
In what direction and by how many units is the graph of f(x) = −3 cos(2x − π) + 2 vertically and horizontally shifted
Answer:
Vertical shift is 2 units top and horizontal shift is [tex]\frac{\pi }{2}[/tex] units to the right
Step-by-step explanation:
Consider the function f(x) = a cos(bx + c) + d.
In this graph, the horizontal shift is -c/b and the vertical shift is d.
Let's compare our graph, f(x) = -3 cos(2x - π) + 2 with this graph.
Here, a = -3, b = 2, c = -π and d = 2.
So, vertical shift = d = 2 units top and
horizontal shift = [tex]-\frac{c}{b} =-\frac{-\pi }{2} =\frac{\pi}{2}[/tex] units to the right.
Kassidy wants to prove that the interior angles of any triangle sum to 180°. She draws a line through one vertex parallel to the opposite side, and then she labels all the angles formed.
Drag a reason to match each statement in Kassidy's two-column proof in the table below.
Answer:
First box: A straight line measures 180 degrees
Second box: Alternate interior angles theorem
Step-by-step explanation:
All lines are straight, and therefore measure 180 degrees
You can see that the red line is parallel to the line with angles 2 and 3. Alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal. Which justifies step 2
Answer:
1.A straight line measures 180 degrees
2.Alternate interior angles theorem
Step-by-step explanation:
We have to prove that
Sum of interior angles of any triangle =180 degrees
Proof:
1.[tex]m\angle 1+m\angle 4+m\angle 5=180^{\circ}[/tex]
Reason: A straight line measures 180 degrees
2.[tex]\angle 4\cong\angle 2[/tex]
[tex]\angle 5\cong \angle 3[/tex]
Reason:Alternate interior angles theorem
3.[tex]m\angle 4=m\angle 2,m\angle 3=m\angle 5[/tex]
Reason: by definition of congruent angles.
4.[tex]m\angle 1+m\angle 1+m\angle 3=180^{\circ}[/tex]
Reason: By substitution
Hence, proved.
the sum of two numbers that differ by 3 is x, what is the value of the greater of the two numbers?
Answer:
Step-by-step explanation:
You really don't have enough information to solve this with one answer. You want a value for y and there is no what to limit it to just 1 set of values. For example if x = 23 then
x = y + y - 3
x = 2y - 3
23 = 2y - 3 Add three to both sides
23+3 = 2y Combine
26 = 2y Divide by 2
26/2 = 2y/2 Do the division
13 = y
The smaller number is 13 - 3 = 10
Their sum is 13 + 10=23 But that answer is not unique.
====================
Suppose x = 13
13 = 2y - 3 Add 3
13 + 3 = 2y
16 = 2y
y =8
The larger number = 8
The smaller number = 5
=======================
The best I can do is give you the equation which is
x = 2y - 3
Probability and Stat. Help
Answer: 0.6 (choice B)
x = number of days the book has been checked out
Check out the attached image below. I've marked 3 boxes in red to represent the bars that span from x = 9 to x = 18. The heights of these bars add up to 0.15+0.30+0.15 = 0.45+0.15 = 0.60
So if we randomly pull out a book, then the chances of picking a book that has a x value between 9 and 18 (including 9; excluding 18) is 0.60
When Tom purchased a new motorcycle, he paid a 5% sales tax. The amount of sales tax he paid was $265. What was the total cost of the motorcycle including the sales tax? Enter your answer in the box. $
Answer:
$5565 PLEASE GIVE BRAINLIEST
Step-by-step explanation:
100% ÷ 5 = 20
265 x 20 = $5300
$5300 + $265 = $5565
TO CHECK YOUR ANSWER
5565 x .05 = 265 (amount of tax)
Shana, who lives in Canada, and Pearl, who lives in Pennsylvania, were discussing the weather. Shana complained about the cold temperature of -20 C. Pearl, who lives in Pennsylvania, mentioned that her temperature was the opposite of Shana’s. Which is the correct way to represent “the opposite of Shana’s temperature is equal to Pearl’s”?
- -20 = 20
- (-20) = -20
- (20) = - 20
- -(20) = 20
Answer:
- -20 = 20
Step-by-step explanation:
The "opposite" here means we take the negative of -20 C.
So we can write - -20 which is equal to 20.
So the first option is correct, - -20 = 20.
Answer:
d
Step-by-step explanation:
6.5 divided by 6804 or 6804 divided in to 6.5 plz help
Brandon buys a radio for $46.49 in a state where the sales tax is 7%.
I couldb't understand you're question but here are possible answers and explanations
What is the total price: $49.74
$46.49 • 0.07 = 3.25
46.49 + 3.25 = 49.74
What was the sales tax amount: 3.25
$46.49 • 0.07 = 3.25
Hope this helps.
Which equations are equivalent to Y=2/3X-4 when written in slope-intercept form? Check all that apply. A =3X-2Y=4. B=2X-3Y=12. C-4(2X-3Y)=-4(12). D=2(X+6)=3Y. E=2X-3Y=4
Answer:
B 2X-3Y=12
C -4(2X-3Y)=-4(12)
Step-by-step explanation:
y = 2/3 x -4
multiply by 3
3y = 2x -12 factor out a 2 3y = 2(x-6)
subtract 2x from each side
-2x+3y = -12
multiply by -1
2x-3y = 12
multiply by -4
-4(2x-3y) = -4(12)
The slope-intercept form: y = mx + b.
The standard form: Ax + By = C.
We have:
[tex]y=\dfrac{2}{3}x-4[/tex] multiply both sides by 3
[tex]3y=2x-12[/tex] subtract 2x from both sides
[tex]-2x+3y=-12[/tex] change the signs
[tex]2x-3y=12\to\boxed{B.}[/tex] multiply both sides by (-4)
[tex]-4(2x-3y)=-4(12)\to\boxed{C.}[/tex]
Answer: B and C.A. 3x - 2y = 4 - NOT
D. 2(x + 6) = 3y → 2x + 12 = 3y → 2x - 3y = -12 - NOT
E. 2x - 3y = 4 - NOT
mr. wilson paid $45 for honey. this amount includes a tax of 8%. what was the cost of the honey before tax?
Answer:
$3.60
Step-by-step explanation:
Answer:
$41.40
Step-by-step explanation:
You just have to do $45.00-8%
What is 3 and 5? And show how to solve plz
Answer:
3. 9n + 6 = 78
5. see below
Step-by-step explanation:
3.
Let the number of adults be n. Each adult ticket costs $9, so the cost of n adult tickets is 9n. There is only one child, and a child's ticket is $6, so the cost of the child's ticket is 6. Adding the costs, you get 9n + 6. The total cost is $78, but the expression representing the total cost is 9n + 6, so 9n + 6 must equal 78. That is the equation.
9n + 6 = 78
5.
Sam bought equal gifts for his two children. The two gifts had the same price, x. He received a discount of $125. How much did each of the two gifts cost before the discount?
if two lines are the same slope and diffrent y-intercepts then the lines are
Answer:
The lines would be parallel
Step-by-step explanation:
They have the same slope, but they sit on different y values. Therefore, they are parallel.
What is the shortest driving distance from the animal shelter to the stadium?
Answer:
7 miles
Step-by-step explanation:
Four miles plus 3 miles = 7 miles
The shortest driving distance from the animal shelter to the stadium can be found using a map or a GPS system, which considers all possible routes and chooses the one with the least distance.
Explanation:The shortest driving distance between two locations, in this case, from an animal shelter to a stadium, can be discovered by using geographical tools such as a map or GPS system. These tools can provide data on distance with respect to various routes, allowing you to choose the shortest one.
For example, assume the animal shelter is at Place A, and the stadium is at Place B. The GPS system will analyze all possible routes from A to B, consider traffic conditions, road detours, and provide you with the option that covers the least amount of miles/kilometers and saves the most time. This is considered the shortest driving distance.
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What are the posible rational zeros of f(x)= x4 +6x^3-3x^2+ 17x-15
[tex]w(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0[/tex]
The posible rational zeros of w(x) are:
[tex]\pm\text{dividers of}\ a_0\ \text{and}\ \pm\dfrac{\text{dividers of}\ a_0}{\text{dividers of}\ a_n}[/tex]
[tex]f(x)=x^4+6x^3-3x^2+17x-15\to a_n=1,\ a_0=-15[/tex]
[tex]\text{dividers of}\ a_0= 15:\ \ 1,\ 3,\ 5,\ 16\\\text{dividers\ of}\ a_n=1:\ \ 1[/tex]
Answer:
[tex]\{\pm1,\ \pm3;\ \pm5;\ \pm15\}[/tex]
The sun of the roots of 3x^2+11x-4=0
[tex]ax^2+bx+c=0\\\\x_1,\ x_2-the\ roots\\\\x_1+x_2=\dfrac{-b}{a}\\-------------------------\\\text{We have}\ 3x^2+11x-4=0\\\\a=3,\ b=11,\ c=-4\\\\\text{Substitute:}\\\\x_1+x_2=\dfrac{-11}{2(3)}=-\dfrac{11}{6}\\\\Answer:\ \boxed{-\dfrac{11}{6}}[/tex]