Answer:
Option C is correct.
Step-by-step explanation:
[tex]\theta=\frac{5\pi }{6}[/tex]
We need to find reference angle and signs of sinФ, cosФ and tanФ
We know that [tex]\theta=\frac{5\pi }{6}radians[/tex] is equal to 150°
and 150° is in 2nd quadrant.
So, Ф is in 2nd quadrant.
And In 2nd quadrant sine is positive, while cos and tan are negative
The reference angle Ф' is found by: π - Ф
=> Ф = 5π/6
so, Reference angle Ф' = π - 5π/6
Ф' = 6π - 5π/6
Ф' = π/6
So, Option C Θ' = pi over 6; sine is positive, cosine and tangent are negative is correct.
9x2+4y2 = 36 The foci are located at:
Answer:
The foci are located at [tex](0,\pm \sqrt{5})[/tex]
Step-by-step explanation:
The standard equation of an ellipse with a vertical major axis is [tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex] where [tex]a^2\:>\:b^2[/tex].
The given equation is [tex]9x^2+4y^2=36[/tex].
To obtain the standard form, we must divide through by 36.
[tex]\frac{9x^2}{36}+\frac{4y^2}{36}=\frac{36}{36}[/tex]
We simplify by canceling out the common factors to obtain;
[tex]\frac{x^2}{4} +\frac{y^2}{9}=1[/tex]
By comparing this equation to
[tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex]
We have [tex]a^2=9,b^2=4[/tex].
To find the foci, we use the relation: [tex]a^2-b^2=c^2[/tex]
This implies that:
[tex]9-4=c^2[/tex]
[tex]c^2=5[/tex]
[tex]c=\pm\sqrt{5}[/tex]
The foci are located at [tex](0,\pm c)[/tex]
Therefore the foci are [tex](0,\pm \sqrt{5})[/tex]
Or
[tex](0,-\sqrt{5})[/tex] and [tex](0,\sqrt{5})[/tex]
Find the slope between (3, 2) and (-2, 3)
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
We have the following points:
[tex](x_ {1}, y_ {1}) :( 3,2)\\(x_ {2}, y_ {2}): (- 2,3)[/tex]
Substituting we have:
[tex]m = \frac {3-2} {- 2-3} = \frac {1} {- 5} = - \frac {1} {5}[/tex]
Finally, the slope is:
[tex]m = - \frac {1} {5}[/tex]
Answer:
[tex]m = - \frac {1} {5}[/tex]
help me to do this question friends
Answer:
First draw two axes x and y. Then mark all points for which x=4, this is a vertical line. Do the same for the other sides and you will find a square with side length 8.
A vessel has 13 liters 200 ml of fruit juice. in how many glass of each capacity 60 milliliters can be filled
Answer:
220 glasses.
Step-by-step explanation:
Quantity of fruit juice = 13 liters 200 ml
Number of glasses of each capacilty 60ml can be filled = ?
The quantity of fruit juice has 2 units. one is liter and the other is milliliter.
So we will convert liter into milliliter.
We have the quantity 13 liters 200 ml:
We know that:
1 liter = 1000 ml
Hence we have 13 liters so 13 will be multiplied by 1000 to convert it into milliliter.
13 * 1000 = 13000 ml
Now we have 13000 ml 200ml
Notice that we have two milliliters, so we will add both the quantities to make it one.
(13000+200)ml = 13200ml
Total quantity of fruit juice = 13200ml
Now divide the total quantity by the capacity of 60ml
=13200ml/60ml
= 220 glasses
It means that 220 glasses can be filled....
Rafeal has been given a list of 5 bands and asked to place a vote. His vote must have the names of his favorite, second favorite, and third favorite bands from the list. How many different votes are possible?
Answer:
60 different votes.
Step-by-step explanation:
This is a permutations question. There are a total of 5 bands to be voted for, and Rafeal has to vote only for 3 of the bands. It is also mentioned that the voting has to be done for the favorite, the second favorite, and the third favorite bands from the list. This means that the order of selection is important. This means that permutations will be used. Thus, 3 bands out of 5 have to be selected in an order. This implies:
5P3 = 5*4*3 = 60 possibilities.
There are 60 different votes!!!
Answer: 60 different votes are possible
Step-by-step explanation:
We have a list of 5 bands and we must choose 3 of them. In this case, the order of the election is important. Therefore this is a problem that is solved using permutations.
The formula for permutations is:
[tex]nPr=\frac{n!}{(n-r)!}[/tex]
Where n is the number of bands you can choose and you choose 3 of them.
Then we calculate:
[tex]5P3 =\frac{5!}{(5-3)!}\\\\5P3=\frac{5!}{2!}\\\\5P3 = 60[/tex]
Finally, the number of possible votes is 60
If 111 people attend a concert and tickets for adults cost $4 while tickets for children cost $3.25 and total receipts for the concert was $401.25, how many of each went to the concert?
Answer:
57 children
54 adults
Step-by-step explanation:
Let's call x the number of children admitted and call z the number of adults admitted.
Then we know that:
[tex]x + z = 111[/tex]
We also know that:
[tex]3.25x + 4z = 401.25[/tex]
We want to find the value of x and z. Then we solve the system of equations:
-Multiplay the first equation by -4 and add it to the second equation:
[tex]-4x - 4z = -444[/tex]
[tex]3.25x + 4z = 401.25[/tex]
----------------------------------
[tex]-0.75x = -42.75[/tex]
[tex]x =\frac{-42.75}{-0.75}\\\\x=57[/tex]
Now we substitute the value of x in the first equation and solve for the variable z
[tex]57 + z = 111[/tex]
[tex]z = 111-57[/tex]
[tex]z = 54[/tex]
Answer:
Number of children=57
Number of adults=54
Step-by-step explanation:
We can start by forming simultaneous equations from the information provided.
Let the number of children be x and adults be y, then the the sum of the amount collected from both children and adults=3.25x+4y=401.25
The total number of people in attendance x+y=111
Let us solve these equations simultaneously.
3.25x+4y=401.25
x+y=111
Using substitution method.
y=111-x
3.25x+4(111-x)=401.25
3.25x+444-4x=401.25
-0.75cx=-42.75
x=57
Number of children=57
Adults=111-57
=54
What is the volume of a room that is 13 feet by 9 feet by 11 feet? A. 1300 cubic feet B. 1207 cubic feet C. 1287 cubic feet D. 1200 cubic feet
Answer:
C) 1287 cubic feet
Step-by-step explanation:
To find the volume of a rectangular prism the formula is length time width times height. That means area=9*11*13 which is 1287 or C.
What is the angle of elevation of the sun if a 45 foot tall flagpole casts a 22 foot long shadow?
Answer:
the angle Ф is 63.9 degrees.
Step-by-step explanation:
A right triangle describes this situation. The height of the triangle is 45 ft and the base is 22 ft. The ratio height / base is the tangent of the angle of elevation and is tan Ф. We want to find the angle Ф:
opp
tan Ф = ---------- = 45 / 22 = 2.045.
adj
Using the inverse tangent function on a calculator, we find that the angle Ф is 63.9 degrees.
Simplify 5(x - 2) - 3x + 7.
5(x - 2) - 3x + 7.
First use the distributive property:
5(x-2) = 5x-10
Now you have:
5x - 10 - 3x +7
Now combine like terms to get:
2x - 3
Answer:
2x -3
Step-by-step explanation:
5(x - 2) - 3x + 7
Distribute the 5
5x -10 -3x+7
Combine like terms
5x-3x -10 +7
2x -3
please help anyone.
Answer:
- [tex]\frac{27}{7}[/tex]
Step-by-step explanation:
Given
f(x) = [tex]\frac{3}{x+2}[/tex] - [tex]\sqrt{x-3}[/tex]
Evaluate f(19) by substituting x = 19 into f(x)
f(19) = [tex]\frac{3}{19+2}[/tex] - [tex]\sqrt{19-3}[/tex]
= [tex]\frac{3}{21}[/tex] - [tex]\sqrt{16}[/tex]
= [tex]\frac{1}{7}[/tex] - 4
= [tex]\frac{1}{7}[/tex] - [tex]\frac{28}{7}[/tex] = - [tex]\frac{27}{7}[/tex]
Find the sum of (-4+ i) and (10 - 51).
-3+ 51
-3-51
06-41
6-61
DONE
Answer:
The correct answer is 6-4i
Answer:
6 - 4i .
Step-by-step explanation:
I will assume that (10 - 51) is ( 10 - 5i) since the other number is a complex number.
You add the real parts and the imaginary parts separately.
(-4 + i) + (10 - 5i)
= (-4 + 10) + (i - 5i)
= 6 - 4i .
After returning from a holiday to the USA, Megan has some American coins: A 25c coins and B 10c coins with a total value of $1.95, where A and B are both counting numbers. how many different values of A can Megan have?
Megan can have 7 different values of A for the number of 25c coins she possesses.
Given:
Megan has 25c coins and 10c coins with a total value of $1.95.
To find:
Number of different values of A (number of 25c coins) Megan can have.
Step-by-step solution:
Let A represent the number of 25c coins and B represent the number of 10c coins.From the given information, we can form the equation 25A + 10B = 195 (since the total value is $1.95).We know A and B are counting numbers (positive integers).Now, find the possible values of A that satisfy the equation and the conditions: A = 1, 2, 3, 4, 5, 6, 7.Therefore, Megan can have 7 different values of A for the number of 25c coins she possesses.
Find the slope of the line that passes through the points (-2,3) and (2,7)
Answer: 1
Step-by-step explanation:
A formula for the slope of a line is rise/run.
First let’s find the ‘rise’
To find the rise, we must look at the difference between the elevation of the points. We can find the rise by subtracting y1 from y2. 7-3=4, so the rise is 4
Run is the same concept. We must subtract x2 - x1.
2-(-2)=2+2=4
So the rise is 4 and the run is 4. There for rise/run = 4/4 =1
The slope of the line is 1
A thief steals an atm card and must randomly guess the correct three digit pin code from a 9 key keypad repetition of digits is allowed. That is the probability of a correct guess in the first try?
The probability of guessing a 3-digit pin correctly on the first attempt, when repetition of digits is allowed, is 1 out of 1000, or 0.001.
Explanation:The subject under scrutiny is related to the concept of probability in mathematics. To solve this, we need to consider that there are 10 possible digits (0 to 9) on the keypad for each of the 3 input spots in the pin. Since a digit can be repeated, each spot has 10 possibilities. The total number of possible pin combinations is thus 10*10*10 = 1000.
The probability of guessing the pin correctly on the first attempt would be 1 (since there's only one correct pin) divided by the total number of possibilities, which is 1000. Therefore, the probability of this happening is 1/1000 or 0.001.
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The probability of a correct guess on the first try is 1/729.
Explanation:In this scenario, the thief must randomly guess the correct three-digit pin code from a 9-key keypad where repetition of digits is allowed. To determine the probability of a correct guess on the first try, we need to calculate the ratio of favorable outcomes to total outcomes.
There are 9 possible digits to choose from, and repetition is allowed. Therefore, the number of outcomes is 9 raised to the power of 3 (since the thief needs to guess a three-digit pin code). This gives us 729 total outcomes. There is only one favorable outcome in this case, which is the correct pin code. Therefore, the probability of a correct guess on the first try is 1/729.
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How do I solve this?
Answer:
2y = 3x
Step-by-step explanation:
general formula for a straight line is given as
y = mx + b
Given 2 points (2,3) and (4,6), we can use the attached formula to calculate the slope, m of the line which connects the 2 points
m = (6-3) / (4-2) = 3/2
hence the general formula becomes
y = (3/2) x + b
Substitute one of the given points into this equation to find b.
We pick point (2,3)
3 = (3/2) (2) + b
b = 0
hence the equation is
y = (3/2)x
2y = 3x (answer)
What is the area of the sector having a radius of 8 and a central angle of 5π3
radians?
A. 320π/3 units²
B. 50π units²
C. 160π/3 units²
D. 140π/3units²
Area of a full circle is PI x r^2
Area = 3.14 x 8^2 = 200.96
Area of a sector is area * central angle / full circle
Area = 200.96 x 5PI/3 / 2PI = 160PI/3
Answer is C.
Answer:[tex]\frac{160\pi }{3} units^2[/tex]
Step-by-step explanation:
Given
Angle subtended by sector is[tex]\frac{5\pi }{3}[/tex]
radius =8 units
[tex]Area of sector=\frac{\theta }{2\pi }\pi r^2 [/tex]
[tex]A=\frac{20\times 8\pi }{3}[/tex]
[tex]A=\frac{160\pi }{3}[/tex]
what is the length of CD, given that figure ABCD is a rectangle
Answer:
where is rectangle???
Answer:
10
Step-by-step explanation:
The length of AB is 10 and the length of BC is 13. CD is parallel to AB so its 10.
Jenny and Hanan are collecting clothes for a clothing drive. Hanan collected 1/2 as many bags of clothes as Jenny did. If Jenny collected 3/ 4 of a bag of clothes, what portion of a bag of clothes did Hanan collect?
Answer:
Hanan collect [tex]\frac{3}{8}[/tex] of a bag of clothes
Step-by-step explanation:
Let
x ------> amount of clothing bag that Jenny collected
y ------> amount of clothing bag that Hanan collected
we know that
[tex]y=\frac{1}{2}x[/tex] -----> equation A
[tex]x=\frac{3}{4}[/tex] -----> equation B
Substitute equation B in equation A
[tex]y=\frac{1}{2}(\frac{3}{4})[/tex]
[tex]y=\frac{3}{8}[/tex]
therefore
Hanan collect [tex]\frac{3}{8}[/tex] of a bag of clothes
Which shows the expression x^2-1/x^2-x
Answer:
[tex]\large\boxed{\dfrac{x^2-1}{x^2-x}=\dfrac{x+1}{x}=1+\dfrac{1}{x}}[/tex]
Step-by-step explanation:
[tex]\dfrac{x^2-1}{x^2-x}=\dfrac{x^2-1^2}{x(x-1)}\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{(x-1)(x+1)}{x(x-1)}\qquad\text{cancel}\ (x-1)\\\\=\dfrac{x+1}{x}=\dfrac{x}{x}+\dfrac{1}{x}=1+\dfrac{1}{x}[/tex]
Answer:
its b on edge 2021
Step-by-step explanation:
Please please answer this correctly
Answer:
67.972 ÷ 10 = 6.7972
679.72 ÷ 10 = 67.972
6797.2 ÷ 10 = 679.72
6797200 ÷ 10 = 679720
Can you use the ASA Postulate or the AAS Theorem to prove the triangles congruent? (1)
Answer:
asa only because the two triangles are facing each other like a reflection making them congruent
ΔWZV and ΔWZY are congruent by AAS congruency
What is congruency?Congruent triangles are triangles having both the same shape and the same size.Types of congruencies are SSS, SAS, AAS, ASA, RHS.How to prove that the triangles are congruent?In the given figure there are two triangles, ΔWZV and ΔWZYConsidering ΔWZV and ΔWZY
∠WVZ = ∠WYZ (given)
∠WZV = ∠WZY ( both angles are 90° since it is given that WZ is perpendicular to VY)
WZ is common side
So ΔWZV and ΔWZY are congruent (AAS congruency)
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if X parallel Y and Y parallel Z then
Answer:
X || Z
Step-by-step explanation:
We are not told about any lines being perpendicular, so we cannot conclude any lines to be perpendicular.
Theorem:
If two lines are parallel to the same line, then the two lines are parallel to each other.
X is paralle to Y; Z is parallel to Y.
Line X and Z are parallel to the same line, Y, so lines X and Z are parallel.
Answer: X || Z
In mathematics, if lines X and Y are parallel, and lines Y and Z are parallel, then lines X and Z are also parallel. This is known as the transitive property.
Explanation:In mathematics, when we say one line is parallel to another, we mean they are moving in the same direction and they will never intersect. In the case of X being parallel to Y and Y being parallel to Z, according to the transitive property in mathematics, it follows that X would be parallel to Z. To visualize this, imagine three straight lines on a piece of paper. If Line X and Line Y never meet and continue in the same direction, and Line Y and Line Z also follow the same rule, then logically, Line X and Line Z must also be continuing in the same direction and never intersecting, hence they are essentially parallel to each other.
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Find the sum (4s/ s2-2s+1)+(7/s2+2s-3)
Answer:
It would be 7/2s, however if you want to solve it completely, you do 7 ÷ 2. It would give you 3.5 so, s = 3.5.
Which of the following are solutions to the equation below? Check all that apply (2x+3)^2=10
Answer:
Option C and E are correct.
Step-by-step explanation:
We need to solve the following equation
(2x+3)^2=10
taking square root on both sides
[tex]\sqrt{(2x+3)^2}=\sqrt{10}\\2x+3=\pm\sqrt{10}[/tex]
Now solving:
[tex]2x+3=\sqrt{10} \,\,and\,\,2x+3=-\sqrt{10}\\2x=\sqrt{10}-3 \,\,and\,\,2x=-\sqrt{10}-3\\x=\frac{ \sqrt{10}-3}{2} \,\,and\,\,x=\frac{-\sqrt{10}-3}{2}[/tex]
So, Option C and E are correct.
Answer: E .√10 - 3 / 2 or
c. -√10 - 3 / 2
Step-by-step explanation:
(2x + 3)^2 = 10
take the square root of bothside
√(2x + 3)^2 = ±√10
2x + 3 = ±√10
subtract 3 from bothside
2x = ±√10 - 3
Divide bothside by 2
x = ±√10 - 3 / 2
Either x = √10 - 3 / 2 or
x = -√10 - 3 / 2
The length of a spring varies directly with the mass of an object that is attached to it. When a 30 gram object is attached the spring stretches 9 centimeters. Which equation relates the mass of and object, m, and the length of a spring s.
A s= 3/10m
B s= 10/3m
C m= 3/10s
D m=10/3s
Answer:
A. s = 3/10 m.
Step-by-step explanation:
s = km where k is a constant , s = the length of the string and m = the mass of the object.
Substituting m = 30 and s = 9:
9 = k * 30
k = 9/30 = 3/10
So the equation is s = 3/10 m.
(05.03)Marcus loves baseball and wants to create a home plate for his house. Marcus needs to calculate the area of the home plate at the ball field so he can reconstruct it when he gets home. Calculate the area of the polygon. Pentagon with square measuring 8 inches by 5 inches and two triangles with heights of 7 inches and 6 inches.
72.5 in2
75.5 in2
83 in2
96 in2
Answer:
83 square inches
Step-by-step explanation:
Let's find the answer, you can see the attached file for clarity.
Because we have a rectangle measuring 8 inches by 5 inches, we can use the area of the rectangle as follows:
A1=base*height=(8 inches)*(5 inches)=40 square inches
Now, because we have a triangle over the square side of 8 inches long, we can divide the triangle into 2 rectangle triangles, each of them with a base of 4 inches and a height of 7 inches, obtaining:
A2=2*(base*height/2)=2*(4 inches)*(7 inches)/2=28 square inches
Doing the same for the other triangle we get 2 triangles with a base of 2.5 inches and a height of 6 inches, obtaining:
A3=2*(base*height/2)=2*(2.5 inches)*(6 inches)/2=15 square inches
The addition of all areas is:
A=A1+A2+A3=40 square inches + 28 square inches + 15 square inches
A=83 square inches.
In conclusion we have an area of 83 square inches.
Answer:
83
Step-by-step explanation:
Find the average rate of change of the function
f(x) = √x +1 on the interval 4 ≤ x ≤ 9. Recall that
the coordinates for the start of the interval are (4,
3).
What are the coordinates for the end of the
interval?
o (9,4)
o (9,3)
o (9, 82)
Answer:
Oops I went too far.
The other point is (9,4).
The average rate of change is 1/5.
Step-by-step explanation:
So I think your function is [tex]f(x)=\sqrt{x}+1[/tex]. Please correct me if I'm wrong.
You want to find the slope of the line going through your curve at the points (4,f(4)) and (9,f(9)).
All f(4) means is the y-coordinate that corresponds to x=4 and f(9) means the y-coordinate that corresponds to x=9.
So if [tex]f(x)=\sqrt{x}+1[/tex], then
[tex]f(4)=\sqrt{4}+1=2+1=3[/tex] and
[tex]f(9)=\sqrt{9}+1=3+1=4[/tex].
So your question now is find the slope of the line going through (4,3) and (9,4).
You can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] but I really like to just line up the points vertically and subtract then put 2nd difference over 1st difference. Like this:
( 9 , 4)
-( 4 , 3)
-------------
5 1
So the slope is 1/5.
The average rate of change of the function f on the interval [4,9] is 1/5.
A function describes the relationship between related variables.
The average rate of change of f(x) over 4 ≤ x ≤ 9 is [tex]\frac 15[/tex].The coordinates of the end interval is (9,4)Given that:
[tex]f(x) = \sqrt x + 1,\ 4 \le x \le 9[/tex]
The average rate of change (m) is calculated as:
[tex]m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]
[tex]m = \frac{f(9) - f(4)}{9 - 4}\\[/tex]
So, we have:
[tex]m = \frac{f(9) - f(4)}{5}[/tex]
Calculate f(4)
[tex]f(x) = \sqrt x + 1[/tex]
[tex]f(4) = \sqrt 4 + 1[/tex]
[tex]f(4) = 2 + 1[/tex]
[tex]f(4) = 3[/tex]
Calculate f(9)
[tex]f(x) = \sqrt x + 1[/tex]
[tex]f(9) = \sqrt 9 + 1[/tex]
[tex]f(9) = 3 + 1[/tex]
[tex]f(9) = 4[/tex]
So, we have:
[tex]m = \frac{f(9) - f(4)}{5}[/tex]
[tex]m = \frac{4 - 3}{5}[/tex]
[tex]m = \frac{1}{5}[/tex]
Recall that:
[tex]f(4) = 3[/tex] --- this represents the coordinate of the start interval
[tex]f(9) = 4[/tex] --- this represents the coordinate of the end interval
Hence, the coordinates of the end interval is (9,4)
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What is the order of rotational symmetry for the figure
Answer:
B. 3
Step-by-step explanation:
First of all we will define rotational symmetry.
Rotational symmetry is when a shape looks the same after some rotation or less than one rotation.
The order of rotational symmetry is how many times it matches the original shape during the rotation.
So, for the given shape the rotated shape will match the original shape three times so the order for symmetry for the given shape is 3.
Hence,
the correct answer is B. 3 ..
How many solutions does the equation 5x + 3x − 4 = 10 have? Zero One Two Infinitely many
[tex]5x + 3x -4 = 10\\8x=14\\x=\dfrac{14}{8}=\dfrac{7}{4}[/tex]
one
Answer:0ne
Step-by-step explanation:
(4 - 7n) – (20+5)
Simplify expression
(4 - 7n) – (20+5)
Simplify:
(4 -7n) - 25
Remove parenthesis:
4 - 7n -25
Combine like terms:
4-25 = -21
Now you have: -21-7n
The term with the variable is usually rearranged to be in front, so it becomes: -7n-21