Answers
Answer
Tan (7π/3) = √3
csc (-330°) = 2
Explanation
tan (7π/3) Note: π radians = 180°
tan [(7 x 180°)/3]
tan 420° = tan (420 - 360)° = Tan 60°
tan 60° = √3
∴ tan (7π/3) = √3
csc (-330°) = csc (-330° + 360°)
csc (30°) = 1/sin (30°) = 1 ÷ 1/2 = 2
∴ csc (-330°) = 2
Related Questions
Sharma draws a floor plan of the local supermarket on a coordinate plane.
Answers
Solution
For this case we can do the following:
Coordinates
Dairy 1,0
Produce 3,3
Bakery 6,2
Frozen foods 2,6
Part A
B. (3,5)
Part B
D. (2,2)
I’m not sure if this correct is there no decimal? But it’s asking for a decimal format.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
1.6 x 10^7
decimal format = ?
Step 02:
decimal format:
10^7 ====> move decimal point 7 places right
1.6 x 10^7 = 16,000,000
The answer is:
16,000,000
please help methe cube of one more than two times a number as an algebraic expression
Answers
[tex](1+2x)^3[/tex]
Explanation
Step 1
Let
x, a number
2x, two times a number,
cube=exponent 3
Step 2
replace
one more than two times a number =1+2x
the cube of one more than two times a number=
[tex](1+2x)^3[/tex]Simply The Expression 12+3(7y-8)
Answers
First we use the distributive property to eliminate the parenthesis:
[tex]\begin{gathered} 12+3(7y-8)=12+3(7y)+3(-8) \\ =12+21y-24 \end{gathered}[/tex]Now we add similar terms and we get the following:
[tex]12+21y-24=21y-12[/tex]Notice that 21 and 12 are divisible by 3, therefore, we have::
[tex]21y-12=3(7y-4)[/tex]Finally, the simplifed expression of 12+3(7y-8) is 3(7y-4)
I need help solving this math problem by using substitution method
Answers
To solve by substitution method:
1. Substitute the x in the first equation by the value of x given in the second equation:
[tex]-3(-5y)-6y=45[/tex]2. Solve y:
[tex]\begin{gathered} 15y-6y=45 \\ 9y=45 \\ \\ \frac{9}{9}y=\frac{45}{9} \\ \\ y=5 \end{gathered}[/tex]3. Use the value of y to find x:
[tex]\begin{gathered} x=-5y \\ x=-5(5) \\ x=-25 \end{gathered}[/tex]Then, the solution for the given system of equations is: x= -25 and y=5 (-25,5)hello can you tell me what I need to do to get the answer please
Answers
We'll first sort the data in ascending order:
[tex]30,\text{ 88, 90, 96}[/tex]The median is the number in the "middle" of a sorted list of numbers. Since in ths case we have two "middle" numbers because we have four data point, we just need to average them. That is:
[tex]\frac{88+90}{2}=89[/tex]And so, 89% is the median of the quiz grades given.
find three rational numbers between 3/4 and 0.750.75 is a repeating decimal
Answers
3/4 can be written in decimal form as,
[tex]\frac{3}{4}=0.75[/tex]0.75 is a repeating decimal. So, 0.75 with repeating decimal can be written as 0.757575.
We have to find three rational numbers between 0.75 (3/4) and 0.757575.
So, three rational numbers between 0.75 (3/4) and 0.757575 should have values in between 0.75 (3/4) and 0.757575 itself.
So, three rational numbers between 3/4 and 0.75 are 0.753, 0.754 and 0.756.
Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probability that a randomly selected book has fewer than 169 pages if the mean is 194 pages and the standard deviation is 25 pages? Use the empirical rule. Enter your answer as a percent rounded to two decimal places if necessary.
Answers
15.85%
Explanations:According to the empirical rule for normal probability;
• 68% of given, data falls within 1σ of the mean
,• 95%, of the given data falls within 2σ of the mean
,• 99.7% of all data falls within 3σ of the mean
This rule shows an even distribution among the mean
From the data, we can say that 34% of the data is within μ±1σ
Given the following data
Mean = 194 pages
Standard deviation = 25
Hence 1 standard deviation of the mean will be 194 - 25 = 169 showing that 34% of data fall in that range
Since we need the probability that a randomly selected book has fewer than 169 pages, we use the normal distribution property which states:
50% of the data is left of the mean of which 34% fall within 1 standard deviation, hence the remaining would fall fewer than 169.
Pr(a randomly selected book has fewer than 169 pages) = 50% - 34% = 16%
To determine the final probability, we will subtract the half of 0.3(100-99.7) to have:
Pr(a randomly selected book has fewer than 169 pages) = 16 - 0.3/2
Pr(a randomly selected book has fewer than 169 pages) = 16 - 0.15
Pr(a randomly selected book has fewer than 169 pages) = 15.85%
find the missing angle measures of each polygon in 8
Answers
The sum of the interior angles of a pentagon is 540°
angle H +angle I + angle J + angle K +angle L=540°
we substitute the values
100+143+85+92 angle L= 540°
angle L= 540-100-143-85-92
angle L=120°
Write an equation describing the relationship of the given variables Y varies directly as the square root of x and when x=81, y=45
Answers
Solution
Step 1:
[tex]\begin{gathered} If\text{ y varies directly as square root of x.} \\ We\text{ have,} \\ y\text{ }\propto\sqrt[]{x} \end{gathered}[/tex]Step 2:
Plug in constant k to change the proportionality sign into an equal sign.
[tex]\begin{gathered} y\text{ }\propto\sqrt[]{x} \\ y=k\sqrt[]{x} \end{gathered}[/tex]Step 3:
Substitute the values of x = 81 and y = 45 to find the value of constant k.
[tex]\begin{gathered} \text{y = k}\sqrt[]{x} \\ 45\text{ = k}\sqrt[]{81} \\ 45\text{ = 9k} \\ \text{Divide both sides by 9 to find the value of k.} \\ k\text{ = }\frac{45}{9} \\ k\text{ = 5} \end{gathered}[/tex]Step 4:
Write an equation describing the relationship of the given variables.
[tex]\begin{gathered} \text{y = k}\sqrt[]{x} \\ y\text{ = 5}\sqrt[]{x} \end{gathered}[/tex]Final answer
[tex]\text{y = 5}\sqrt[]{x}[/tex]hey can you tell me how to find a domain of a function and what does real numbers mean
Answers
Solution
Basically the domain represent all the possible values that the function can assume on the x axis
And the real numbers represent all the possible numbers from - infinity to infinity
For example:
f(x)= 2x+1
The domain is all the real numbers since the function is defined for all the possible values of x
In the other hand:
[tex]g(x)=\frac{1}{x-1}[/tex]For this new function the domain is all the real numbers except x=1 since we can' divide by 0
A quality control inspector found 9 defective machine parts out of 500 manufactured.a) What percent of the machine parts manufactured were defective? b) What percent of the machine parts manufactured were NOT defective?
Answers
a) In order to calculate what percent of the machine parts manufactured were defective, you proceed as follow:
divide the defective machine between the total number of machines:
9/500 = 0.018
next, you multiply the previous result by 100:
0.018 x 100 = 1.8%
Hence, 1.8% of the total number of machines were defective
b) In this case you have:
subtract total machine and defective ones:
500 - 9 = 491
divide the previoues result by the number of toal machine:
491/500 = 0.982
multiply the previoues result by 100:
0.982 x 100 = 98.2
Hence, 98.2% of the total number of machine were NOT defective.
which of the following are like terms?3y^5 ,2x^53y^5, 2y^56y^2, 2z3y^4, 4x^3
Answers
1) Like terms have the same variable and the same exponent. Therefore we can add, subtract, and combine them when operating polynomials.
2) Examining the options, we can state that:
3y^5, 2y^5
We can add those, subtract them, and so on.
3) So the answer is 3y^5, 2y^5 for they have the same variable,
what is the difference of the rational expressions below? *photo
Answers
Answer: C.
[tex]\frac{-2x+1}{x^2}[/tex]Explanation
Given
[tex]\frac{3x+1}{x^2}-\frac{5}{x}[/tex]We have to find the minimum common denominator, which in our case is x². Then, we divide this denominator over the denominator of each term in the given equation, multiply it times the numerator, and place the result as follows:
[tex]\frac{3x+1}{x^{2}}-\frac{5}{x}=\frac{3x+1-5x}{x^2}[/tex]Simplifying by adding similar terms we get:
[tex]=\frac{1-2x}{x^2}[/tex]17. Multistep The height of a trapezoid is 8 in. and its area is 96 in. Onebase of the trapezoid is 6 inches longer than the other base. What are thelengths of the bases? Explain how you found your answer.
Answers
The area of a trapezoid is computed as follows:
A = h*(a + b)/2
where h is the height, and a and b are the length of the bases.
One base of the trapezoid is 6 inches longer than the other base, then:
a = b + 6
Replacing with A = 96, h = 8, and a = b + 6, we get:
96 = 8*(b+ 6 + b)/2
96 = 8*(6 + 2b)/2
What is f( 1) for the function given?f(x) = 3x + 811
Answers
the given expression i s
[tex]f(x)=x^2-3x+8[/tex]for f(-1) , put x = -1 in the equation.
[tex]f(-1)=(-1)^2-3(-1)+8[/tex]f(-1) = 1 + 3 + 8 = 12
so the answer is
f(-1) = 12
A rope is 60 inches in length must be cut into two pieces one piece must be twice as long as the other find the length of each piece round your answers to the nearest inch if necessary
Answers
Let x be the length of one piece and y be the length of the other piece. Then, we can write:
[tex]x+y=60\ldots(A)[/tex]since one piece must be twice long than the other, we can write
[tex]2x=y\ldots(B)[/tex]and we have 2 equations in 2 unknows.
Solving by substitution method.
By substituting equation B into equation A, we get
[tex]x+(2x)=60[/tex]which gives
[tex]\begin{gathered} 3x=60 \\ x=\frac{60}{3} \\ x=20 \end{gathered}[/tex]Now, in order to obtain y, we must substitute this result into equation B. It yields
[tex]\begin{gathered} y=2x\Rightarrow y=2(20) \\ y=40 \end{gathered}[/tex]Therefore, the answer is x= 20 inches and y= 40 inches.
1/2x - 7 = 1/3(× - 12)what ia the value of x?
Answers
Distributing:
[tex]\begin{gathered} \frac{1}{2}x-7=\frac{1}{3}x-\frac{1}{3}\cdot12 \\ \frac{1}{2}x-7=\frac{1}{3}x-4 \end{gathered}[/tex]1/3x is adding on the right, then it will subtract on the left.
7 is subtracting on the left, then it will add on the right
[tex]\begin{gathered} \frac{1}{2}x-\frac{1}{3}x=-4+7 \\ \frac{1\cdot3-1\cdot2}{6}x=3 \\ \frac{1}{6}x=3 \end{gathered}[/tex]1/6 is multiplying on the left, then it will divide on the right
[tex]\begin{gathered} x=3\cdot6 \\ x=18 \end{gathered}[/tex]Judy drew an isosceles triangle.One side of the triangle was 6 incheslong. The other side of the triangle was 9 inches long. What couldbe the length of the third side of the triangle Judy drew? Explainyour reasoning.
Answers
Isosceles triangles Have two sides that have the same measure, and one of them is different.
So, we can have two situations:
6 - 6 - 9
or
9 - 9 - 6
The measure of angle a below is(Hint: Slide 3)42°78°
Answers
The measure of the angle = 78 - 42 = 36
The angle 78 is interior angle for the shown triangle
so, the angle 78 is the sum of the angles of the triangle except the adjacent angle to 78
Describe howfactoring can help you find the x-interceptsof the graph of the quadratic functiony=x2 - 4x + 3.
Answers
hello
the quadratic equation given is
[tex]x^2-4x+3=0[/tex]now let's find two factors to the equation and proceed to solve the equation.
to do this, i'll write down the standard form of a quadratic equation out
[tex]ax^2+bx+c=0[/tex]to solve this by factorization, we need to find two numbers that when they're multiplied will give us the value of c but when added will give the value of b
in this case, our value of b = -4 and c = 3
two numbers that will give us the desired value are (-1, -3)
[tex]x^2-4x+3=(x-1)(x-3)[/tex]the factorized form of the equation would be (x - 1)(x - 3)
The ones with the X’s are the only ones i cannot get the answer for. please help
Answers
Order the winning scores from least to greatest, and do so with the losing scores.
[tex]\begin{gathered} winning \\ 14,16,16,16,17, \\ 20,20,20,21,21,23,23,24,24,24,26,27,27,27,27,27,29 \\ 30,31,31,31,31,32,32,33,34,34,35,35,35,37,38,38,39 \\ 42,46,48,49, \\ 52,55 \end{gathered}[/tex]As for the losing scores,
[tex]\begin{gathered} losing\text{ } \\ 3,6,7,7,7,7,7,9 \\ 10,10,10,10,10,10,10,13,13,14,14,14,16,16,16,16,17,17,17,17,17,17,17,19,19 \\ 20,21,21,21,21,23,24,24,25,26,29 \\ 31 \end{gathered}[/tex]Therefore, the correct diagram for the losing scores is
As for the winning scores,
How many 5-letter arrangements of the letters T, E, X, A, S can be created if eachletter is used only once?What is the answer?
Answers
ANSWER
120
EXPLANATION
We have to find the number of permutations of 5 letters in 5 spots:
[tex]_5P_5=\frac{5!}{(5-5)!}=5!=5\cdot4\cdot3\cdot2\cdot1=120[/tex]One positive number is 5 more than another. The sum of their squares is 53. What is the larger number?
Answers
7
1) Let's write this
1st number: x
2nd number: y+5
So the positive number and the 1st number have the following relationship x = y +5
2) So we can write, and expand that binomial:
y² +(y+5)² = 53
y² + y² +10y +25 = 53 Combine like terms
2y² +10y -28 =0
We can now solve it:
[tex]\begin{gathered} y=\frac{-10\pm\sqrt[]{100-4(2)(-28)}}{2(2)} \\ y_1=2 \\ y_2=-7 \end{gathered}[/tex]3) As -7 is 9 units lower than 2, then it does not suits us. So let's use that prior relationship to find the other number
x =y+5
x = 2 +5
x=7
Hence, the larger number is 7 and the smaller one is 2
Two linear functions are represented below , f(x) by a table , and g(x) by a graph .which function has the greater rate of change
Answers
The rate of change of a function is equal to the derivative of that function.
So, we can proceed by finding the derivative of functions f and g. The one with the greatest derivative will then have the greatest rate of change.
Function f(x).
From the table, we can observe that
x=0-->f(x)=4 and x=5-->f(x)=7
Let's see if this function is a line. Remember that to define a line we only need two points, we can take (x,f(x))=(0,4),(5,7) so as to facilitate the solution.
[tex]\begin{gathered} (0,4),(5,7) \\ f(x)-f(x_1)_{}=\frac{(f(x_2)_{}-f(x_1)_{})}{(x_2-x_1)}(x-x_1) \\ \Rightarrow f(x)-4=\frac{(7-3)}{(5-0)}(x-0) \\ \Rightarrow f(x)-4=\frac{4}{5}x \end{gathered}[/tex]Now, let's verify that this equation models the information displayed in the table:
x=-10-->f(x)=-2
Instead of the installment plan, suppose the Sanchez family went to the bankand borrowed $273 with 8% interest.
Answers
8. Amount of interest: $273*8% = $21.84
9. Total amount: $273 + $21.84 = $294.84
Find the equation of the line passing through the points (-2,3) and (1, -3). Write the equation in slope-intercept form. A) y = -2x + 3 B) y = 2x + 7 C) y = 2x - 5 D) y = -2x - 1
Answers
The coordinates are given (-2,3) and (1, -3).
The equation formed from the coordinates is
[tex]y-3=\frac{-3-3}{1+2}(x+2)[/tex][tex]y-3=\frac{-6}{3}(x+2)[/tex][tex]y=-2x-4+3[/tex][tex]y=-2x-1[/tex]Hence the correct option is D .
Which pair of functions are inverses of each other?O A. f(x) = and g(x) = 6 x3B. f(x) = 1 + 6 and g(x) = 5x - 6C. f(x) = 7x- 2 and g(x) = x+2O D. f(x) = -2 and g(x) = 2+2SUBMIT
Answers
Explanation:
To find the inverse of a function, we need to replace f(x) by y, then solve the function for x, and finally interchange the variables x and y.
So, the inverse function for each option is:
Option A.
[tex]undefined[/tex]Hi yea thank you thank goodness for your help today please
Answers
Given:
[tex]h(t)=3300-54t-300e^{-0.18t}[/tex]Find-:
(1)
Velocity at the instant when t = 6 sec.
(2)
The time when velocity is -45 meter per sec
Explanation-:
Velocity is define as a:
[tex]\begin{gathered} v(t)=\frac{dh(t)}{dt} \\ \\ v(t)=h^{\prime}(t) \end{gathered}[/tex]The value of the h'(t) is:
[tex]\begin{gathered} h(t)=3300-54t-300e^{-0.18t} \\ \\ h^{\prime}(t)=-54-300(-0.18)e^{-0.18t} \end{gathered}[/tex]Value is:
[tex]\begin{gathered} h^{\prime}(t)=54e^{-0.18t}-54 \\ \\ v(t)=h^{\prime}(t) \\ \\ v(t)=54e^{-0.18t}-54 \end{gathered}[/tex]At t=6 velocity is:
[tex]\begin{gathered} v(t)=54e^{-0.18t}-54 \\ \\ v(6)=54e^{-0.18\times6}-54 \\ \\ v(6)=54e^{-1.08}-54 \\ \\ v(6)=54\times0.333-54 \\ \\ v(6)=18.333-54 \\ \\ v(6)=-35.66 \end{gathered}[/tex]At t=6 velocity is -35.66 meters per sec.
(b)
Velocity is -45 meter per second then time is:
[tex]\begin{gathered} v(t)=54e^{-0.18t}-54 \\ \\ v(t)=-45\text{ then time is:} \\ \\ -45=54e^{-0.18t}-54 \\ \\ 54-45=54e^{-0.18t} \\ \\ 9=54e^{-0.18t} \\ \\ \frac{9}{54}=e^{-0.18t} \\ \\ 0.166=e^{-0.18t} \end{gathered}[/tex]Taking log both side then,
[tex]\begin{gathered} \ln0.166=\ln e^{-0.18t} \\ \\ \ln0.166=-0.18t\ln e \\ \\ -1.79175=-0.18t \\ \\ t=\frac{-1.79175}{-0.18} \\ \\ t=9.95 \end{gathered}[/tex]So, the time is 9.95 second
Three friends went to a school play. Each ticket was$5. They each spent different amounts of money on food and drink. Chris$5, Ben $3 and Danica$6 which is these expression can be used to find out the total amount of money all three friends spent on tickets, food, and drink(3+5*(5+6) (3*5)+(5+3+6)(3+5)+(5*5*6)
Answers
Answer:
(3*5) + (5 + 3 + 6)
Explanation:
To know the total amount of money that they spend, we need to sum the amount that they spend on tickets to the amount that they spend on food and drink.
So, if each ticket cost $5 and they are 3 friends, the total amount that they spend on tickets can be calculated as:
3*5
On the other hand, if Chris spent $5, Ben $3, and Danice $6, the total amount that they spent on food and drink is:
5 + 3 + 6
Therefore, the expression to calculate the total amount that they spent is:
(3*5) + (5 + 3 + 6)