Answers
From the unit circle, we can check that [tex]\sin30^{\circ}[/tex] and [tex]\sin(-30)^{\circ}[/tex] have the same value, but opposite signs, that is:
[tex]\sin(-30)^{\circ}=-\sin(30)^{\circ}=-\frac{1}{2}[/tex].
Thus,
[tex]\displaystyle{ \cos(x-y)= \cos(-30^{\circ}-60^{\circ})=cos(-90^{\circ})[/tex].
Note that [tex]cos(-90^{\circ})[/tex] is the x-coordinate of the lowest point on the unit circle, that is (0, -1). Thus [tex]cos(-90^{\circ})=0[/tex]
Answer: 0
Related Questions
Each day, Viktor practices piano for x minutes and practices violin for 30 minutes.
To find how many minutes he will spend practicing instruments over 5 days, Viktor calculates:
x + 30 + x + 30 + x + 30 + x + 30 + x + 30
What is another way Viktor can calculate how many minutes he will practice in total over the 5 days?
Drag and drop the equivalent expression in the box.
5x + 30
x + 150
5 (x +30)
x + 30
Answers
you will distribute the 5 to both x and 30, as there are 5 thirty's and 5 x's
hope this helps
May Joan of Arc give you good tidings lol*
x + x + x + x + x + 30 + 30 + 30 + 30 + 30
And then if you add all the xs and 30s up,
5x + 150.
So therefore we now know it isn't the first, second, or third choices because those aren't remotely close.
The third one, however, is the correct choice, because:
5(x+30), if you use the distributive property, equals 5x + 150.
Joseph has $32.40. he wants to buy several comic books that each cost 2.70. how many comic books can he buy?
Answers
What is the measure of angle AXB
Answers
Answer:
70
Step-by-step explanation:
10*7=70
how would you solve this equation?
x/6-x/7=ab
Answers
To solve x/6 - x/7 = ab, find the common denominator, simplify, and then isolate x by multiplying both sides of the equation by the common denominator. The solution is x = 42ab. Always check your answer to ensure it satisfies the original equation.
Explanation:To solve the equation x/6 - x/7 = ab, one must find a common denominator for the fractions. In this case, the common denominator is 42 because 6 and 7 are both factors of 42. By converting both fractions to have the denominator of 42, we have:(7x/42) - (6x/42) = ab
This simplifies to x/42 = ab, since 7x - 6x is x. Now, multiply both sides by 42 to get x = 42ab.
If we want to solve the equation for a variable other than x, such as y, we might need to return b to denominator status, which implies that we need to divide both sides by b if b represents a multiplication factor for y.
It's also important to confirm that our manipulations haven't altered the value of the equation, which can be done by checking the answer at the end to ensure it is reasonable and satisfies the original equation.
Jen ran 1 2/3 miles in 1/4 of an hour, and Max ran 1 1/2 miles in 1 /5 of an hour. What is the average speed of each of Jen and Max? Who runs faster?
Answers
Jen: 1 2/3 = 5/3 *4 = 20/3 = 6 2/3 miles per hour
Max: 1 1/2 = 3/2 * 5 = 15/2 = 7 1/2 miles per hour
Max runs faster
Answer:
Max runs faster than Jen.
Average speed = 7.085 Miles per Hour
Step-by-step explanation:
Distance covered by Jen = [tex]1\frac{2}{3} = \frac{5}{3} \text{ miles}[/tex]
Time taken by Jen = [tex]\frac{1}{4}\text{ hours}[/tex]
Distance covered by Max = [tex]1\frac{1}{2} = \frac{3}{2} \text{ miles}[/tex]
Time taken by Jen = [tex]\frac{1}{5}\text{ hours}[/tex]
Formula:
[tex]Speed = \displaystyle\frac{Distance}{Time}[/tex]
Speed of Jen = [tex]\displaystyle\frac{\frac{5}{3} }{\frac{1}{4} } = \frac{20}{3} = 6.67 \text{ miles per hour}[/tex]
Speed of Max = [tex]\displaystyle\frac{\frac{3}{2} }{\frac{1}{5} } = \frac{15}{2} = 7.5 \text{ miles per hour}[/tex]
Hence, Max runs faster than Jen.
Average speed:
[tex]\displaystyle\frac{\text{Speed of Max + Speed of Jen}}{2} \\\\= \dsplaystyle\frac{6.67 + 7.5}{2} = 7.085\text{ Miles per Hour}[/tex]
HELP ASAP!!!!!!
A figure skater needs a total score of at least 90 to move on to the next round. Her total score is the average of four judges’ scores. The first three judges’ scores were 83, 88, and 92. The figure skater found out she made it to the next round.
What is the minimum score the fourth judge could have given her?
Answers
(83 + 88 + 92 + x) / 4 > = 90
(263 + x) / 4 > = 90....Multiply both of sides by 4, then eliminating the 4 on the left.
263 + x > = 90 * 4
263 + x > = 360
x > = 360 - 263
x > = 97
So, the minimum score would be '97' for your answer.
solve the equation for y:
x=2y-3
Answers
You have to add the 3 over and then divide both of the sides by 2 to isolate the y.
Solve the equation. Explain each step and identify the property used to reach each step.
0.6x + 0.8 = 1.4
Answers
The value of x is 1 after applying the property of the subtraction and division if the equation is 0.6x + 0.8 = 1.4.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The linear equation is:
0.6x + 0.8 = 1.4
Subtract 0.8 on both sides
0.6x = 1.4 - 0.8 (Subtraction property of the equality)
0.6x = 0.6
Divide by 0.6 into both sides
x = 1 (Division property of equality)
Thus, the value of x is 1 after applying the property of the subtraction and division if the equation is 0.6x + 0.8 = 1.4.
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What is the average speed of a runner if he ran 2 1/3 of a mile in 20 minutes?
Answers
in 20 minutes. So you multiply 20 by 3 you get 60. Then you multiply 2 by 3 you get 6. Then you multiply 1/3 x 3 and you get 1. 6=1=7 Hope This Helps
Answer:
The average speed of the runner is 7 miles per hour.
Step-by-step explanation:
Given:
Distance ran by [tex]2\frac{ 1}{3} miles[/tex]
Time taken by the runner = 20 minutes.
To find:
The average speed of a runner=?
Solution:
Now, we know that ,
distance = speed x time
Then, [tex]2\frac{ 1}{3} miles[/tex] = average speed x 20 minutes
=> average speed = [tex]\frac{(2 \frac{1}{3} miles)}{(20 minutes)}[/tex]
=> average speed = [tex](\frac{(2 x 3 + 1)}{3} miles)}{(20\times\frac{1}{60} hours)[/tex]
=> average speed=[tex]\frac{(\frac{(6+1)}{3})}{(\frac{20}{60})}[/tex]
=> average speed = [tex]\frac{ (\frac{7}{3})}{(\frac{1}{3})}[/tex]
=>average speed = [tex]\frac{7}{3}\times\frac{3}{1}[/tex]
=>average speed = 7
It took a truck, which is moving at 60 mph, 8 hours to get from Boston to Washington DC. How long will it take a car to get from Boston to Washington DC, if it travels at 75 mph?
Answers
For this case we have that by definition the time is given by:
[tex]t=\frac{d}{v}[/tex]
Where the variable "d" represents the distance and "v" represents the speed.
So, first we need to know the total distance:
[tex]d=(v)(t)[/tex]
[tex]d=(60)(8)[/tex]
[tex]d=480 mi[/tex]
Then, the time for 75mph is given by:
[tex]t=\frac{480}{75}[/tex]
[tex]t=6,4[/tex]
Answer:
6,4 hours
Answer:
6.4 hours
Step-by-step explanation:
60*8/75=
480/75=
6.4
Please Hurry Again!!
Which Exponent Property would you apply FIRST to simplify this problem
(4^5 × 4^−7)^2
A Power to Power Property
B Quotient Property
C Product Property
D Zero Exponent Property
Answers
______________________________________
Specifically, you would begin by using the "Product Property"; by simplifying the value in parentheses:
______________________________________
(4⁵ * 4⁻⁷) = 4⁽⁵⁺⁽⁻⁷⁾⁾ = 4⁽⁵⁻⁷⁾ = 4⁻² ;
______________________________________
If f(x) = 2x−5, then what is the value of f(2) + f(5)
Answers
so
f(2)+f(3)=-1+5=4
The budget for a film production includes the following employee pay scales: $15,000 for each technical crew member (e.g. camera, lighting, sound), and $10,000 for each support staff (e.g., drivers, craft services, production assistants). A minimum of 20 employees is needed, but the locations can accommodate a maximum of 50 people. There must be at least 12 technical crew members to shoot the film, and there must be at least half as many crew members as support staff. Which combination of employees will minimize the cost, and what is the minimum feasible cost?
Answers
Final answer:
The minimum cost combination of film production employees is 12 technical crew members and 24 support staff members, with a minimum feasible cost of $420,000.
Explanation:
To determine the combination of employees that will minimize the cost, let's set up variables for technical crew members (T) and support staff members (S).
The pay scales are $15,000 for each technical crew member (T) and $10,000 for each support staff member (S).
The objective is to minimize the cost C, where C = 15,000T + 10,000S.
From the constraints provided:
There must be a minimum of 20 employees: T + S ≥ 20.The maximum number of people that can be employed is 50: T + S ≤ 50.There must be at least 12 technical crew members: T ≥ 12.There must be at least half as many crew members as support staff: T ≥ 0.5S.To minimize the cost while satisfying all constraints, we should aim to hire as few technical crew members as possible, given they are more expensive.
If T = 12 (the minimum), we can solve for S using T ≥ 0.5S, which gives us S ≥ 24.
However, S must be even due to the constraint T ≥ 0.5S and hence we can set S = 24 as a candidate solution, resulting in the minimum number of employees (12 + 24 = 36).
We also need to ensure that S ≤ 2T to satisfy the condition T ≥ 0.5S; with T = 12, the maximum S can be is 24.
The minimum feasible cost is determined by plugging T = 12 and S = 24 into the cost equation:
C = 15,000(12) + 10,000(24) = 180,000 + 240,000 = $420,000.
Write the doubles fact you used to solve the problem. 7+8
Answers
What is the solution to the proportion? m/18 15/12 A. m=10 B. m=14.4 C. m=22.5 D. m=27
Answers
m/18 = 15/12
m12 = 270
m = 270 /12 = 22.5
C. m = 22.5
Find the area of the model!!! ASAP PLEASE
Answers
area of a square is S^2
2.6^2 = 6.76 square cm
A recipe calls for31/4 cups of sugar.amy has already put in 31/9 cups . How many more cups does she need
Answers
A family of four goes to a movie theater and spends $30.50.They buy 2 tickets for children at $3.50 per ticket,2tickets for adults,and 3 boxes of popcorn at $2.50 per box.What is the cost of one adult movie ticket?
Answers
Without actually calculating, how much greater is the product of 98x50 than the product of 97x50
Answers
98x50 is greater than 97x50 by 50
☺☺☺☺
−8x+5−2x−4+5x− when x=2
Answers
= -5x + 1
so when x = 2 then
-5x + 1
= -5(2) + 1
= -9
hope it helps
-9
Harriet made a list of all her monthly expenses. What is Harriet’s total cost for housing in a month?
eating out = $40
cell phone bill = $55
rent = $370
car insurance = $48
groceries = $160
renter’s insurance = $27
gas = $60
Total Housing=$______
Answers
Brandon rode his bike 90% of the distance that Carlee did this week. He rode 58.5 miles. How many miles did Carlee ride?
Answers
To find out how many miles Carlee rode, you need to divide the distance Brandon rode (58.5 miles) by 0.9 (representing 90%). The result is that Carlee rode 65 miles.
Explanation:The problem requires you to determine the distance that Carlee biked based on the information provided. Given that Brandon rode his bike 90% of the distance Carlee did, and he rode 58.5 miles, to calculate the distance Carlee traveled, you would divide the distance Brandon rode by 0.9 (which represents 90%).
So, the calculation would be: 58.5 ÷ 0.9 = 65.
Therefore, Carlee must have biked 65 miles in total given the information provided.
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a veterinary student estimated the weight of a snapping turtle to be 147 pounds. the actual weight was 175 pounds. what is the percent error between the actual weight of the turtle and the estimated weight
Answers
Mrs. Gordon measured three rectangular rooms she wants to tile. What is the total rooms? the family room is 25 ft by 16 ft the kitchen is 15 ft by 12,75 ft the laundry room is 10.5 ft by 10.5 ft. I have to describe the steps i would have to take to solve this problem
Answers
family room 25 x 16 = 400
kitchen 15 x12.75= 191.25
laundry room 10.5 x 10.5 = 110.25
Then add them up 400+191.25+ 110.25= 701.5 sq ft
13. Which equation has no solution? (1 point) 5v + 3 = 5v – 5 2x – 4 = 2x + 7 – x 2y + 5 – y = 2y – 3(y – 6) 7z + 9 = –7z – 6
Answers
It simplifies down to 3 = -5 which isn't true so, no solutions!
On the first day of school, the school bookstore sold 348 notebooks, some at 25¢ each and the rest at 38¢ each. The total amount of money paid for the notebooks was $100.91. How many of each kind were sold?
Answers
Final answer:
The bookstore sold 107 notebooks at 38¢ each and 241 notebooks at 25¢ each. A system of equations was used to determine the number of each notebook sold.
Explanation:
Let's denote the number of notebooks sold at 25¢ each as [tex]x[/tex] and the number of notebooks sold at 38¢ each as [tex]y[/tex] .
We are given two pieces of information:
The total number of notebooks sold is [tex]348: x + y = 348[/tex]The total amount of money collected is [tex]$100.91: 0.25x + 0.38y = 100.91[/tex]We can set up a system of two equations to represent this information:
[tex]x+ y = 348[/tex] (Equation 1)
[tex]0.25x + 0.38y = 100.91[/tex] (Equation 2)
Now, we can solve this system of equations to find the values of x and y.
Multiply Equation 1 by 0.25 to make the coefficients of x in both equations the same:
[tex]0.25x + 0.25y = 87[/tex] (Equation 3)
Now, subtract Equation 3 from Equation 2 to eliminate [tex]x[/tex] :
[tex]( 0.25x + 0.38y ) - ( 0.25x +0.25 y) = 100.91 - 87[/tex]
[tex]0.13 y = 13.91[/tex]
[tex]y = 107[/tex]
Now that we have the value for y, substitute it back into Equation 1 to find x:
[tex]x + 107 = 348[/tex]
[tex]x = 241[/tex]
Hence , the solution is x = 241 and y = 107, meaning 241 notebooks were sold at 25¢ each and 107 notebooks were sold at 38¢ each.
The graph shows the total fare, y, for a taxi ride with respect to the miles traveled, x.
What is the y-intercept and what does it represent?
Question options:
The y-intercept is 3 and it represents the initial fee before any miles are traveled.
The y-intercept is 3 and it represents the cost of traveling 1 mile.
The y-intercept is 0 and it represents the initial fee before any miles are traveled.
The y-intercept is 20 and it represents the cost of the cab ride.
Answers
If you don't know why 3 represents the initial fee picture this. You get into the taxi and have not traveled any miles, but instead of starting out at zero, the money meter shows $3.00. The cost of every mile you travel is added to the initial $3.00.
Hope this helps!
and May the Force Be With You
-Jabba
Find the value of x so that the function has the given value.
m(x)=4x+15 m(x)=7
Answers
4x = -8
x = -2
The value of x so that the function is equal to -2
Given the following function
m(x) = 4x + 15
m(x) = 7
Since both of them are m(x), hence;
4x + 15 = 7
Subtract 15 from both sides
4x + 15 - 15 = 7 - 15
4x = -8
Divide both sides by 4
4x/4 = -8/4
x = -2
Hence the value of x so that the function is equal to -2
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Hannah says that 2.11 is a rational number. Gus says that 2.11 is a repeating decimal.
Answers
Answer:
Yes, she is correct.
Step-by-step explanation:
A real number that can be expressed as [tex]\frac{p}{q}[/tex],
Where,
p and q are integers,
Such that, q ≠ 0,
is called a rational number.
A terminating decimal is always a rational number,
Thus, 2.11 is a rational number,
Verification :
2.11 = [tex]\frac{211}{100}[/tex]
Where,
Both 211 and 100 are integers,
Such that 100 ≠ 0.
The value 2.11 is a rational number and not a repeating decimal.
Given the number 2.11 ;
Rational numbers Can be expressed in the form p/q ; where q ≠ 0. However, irrational numbers cannot be be expressed in the form p/q. 2.11 is written into two decimal places ; therefore it can be expressed thus ;(2.11 × 100) ÷ 100 [tex] \frac{211}{100} [/tex][tex]since \: 2.11 = \frac{211}{100} [/tex]
Then, we can conclude that 2.11 is a rational number
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What does 39.75 divided by 8 equal
Answers
39.75
÷ 8
____
4.96875