Starting with the equation:
[tex]\tan (\theta)=1[/tex]take the inverse tangent function to both sides of the equation:
[tex]\begin{gathered} \arctan (\tan (\theta))=\arctan (1) \\ \Rightarrow\theta=\arctan (1) \\ \therefore\theta=\frac{\pi}{4} \end{gathered}[/tex]Yet another value can be found for this equation to be true since the period of the tangent function is π:
[tex]\begin{gathered} \theta_1=\frac{\pi}{4} \\ \theta_2=\frac{\pi}{4}+\pi=\frac{5}{4}\pi \end{gathered}[/tex]Starting with the equation:
[tex]7\tan (\theta)=-15[/tex]Divide both sides by 7:
[tex]\Rightarrow\tan (\theta)=-\frac{15}{7}[/tex]Take the inverse tangent to both sides of the equation:
[tex]\begin{gathered} \Rightarrow\arctan (\tan (\theta))=\arctan (-\frac{15}{7}) \\ \Rightarrow\theta=\arctan (-\frac{15}{7}) \\ \therefore\theta=-1.13416917\ldots \end{gathered}[/tex]The tangent function has a period of π. Since the value that we found for theta is not between 0 and 2π, then we can add π to the value:
[tex]\begin{gathered} \theta_1=-1.13416917\ldots+\pi \\ =2.007423487\ldots \end{gathered}[/tex]We can find another value for theta such that its tangent is equal to -15/7 by adding π again, provided that the result is less than 2π:
[tex]\begin{gathered} \theta_2=\theta_1+\pi \\ =5.14901614\ldots \end{gathered}[/tex]Therefore, for each equation we know that:
[tex]\begin{gathered} \tan (\theta)=1 \\ \Rightarrow\theta=\frac{\pi}{4},\frac{5\pi}{4} \end{gathered}[/tex][tex]\begin{gathered} 7\tan (\theta)=-15 \\ \Rightarrow\theta=2.007423487\ldots\text{ , }5.14901614\ldots \end{gathered}[/tex]Starting with the equation:
[tex]\tan (\theta)=1[/tex]take the inverse tangent function to both sides of the equation:
[tex]\begin{gathered} \arctan (\tan (\theta))=\arctan (1) \\ \Rightarrow\theta=\arctan (1) \\ \therefore\theta=\frac{\pi}{4} \end{gathered}[/tex]Yet another value can be found for this equation to be true since the period of the tangent function is π:
[tex]\begin{gathered} \theta_1=\frac{\pi}{4} \\ \theta_2=\frac{\pi}{4}+\pi=\frac{5}{4}\pi \end{gathered}[/tex]Starting with the equation:
[tex]7\tan (\theta)=-15[/tex]Divide both sides by 7:
[tex]\Rightarrow\tan (\theta)=-\frac{15}{7}[/tex]Take the inverse tangent to both sides of the equation:
[tex]\begin{gathered} \Rightarrow\arctan (\tan (\theta))=\arctan (-\frac{15}{7}) \\ \Rightarrow\theta=\arctan (-\frac{15}{7}) \\ \therefore\theta=-1.13416917\ldots \end{gathered}[/tex]The tangent function has a period of π. Since the value that we found for theta is not between 0 and 2π, then we can add π to the value:
[tex]\begin{gathered} \theta_1=-1.13416917\ldots+\pi \\ =2.007423487\ldots \end{gathered}[/tex]We can find another value for theta such that its tangent is equal to -15/7 by adding π again, provided that the result is less than 2π:
[tex]\begin{gathered} \theta_2=\theta_1+\pi \\ =5.14901614\ldots \end{gathered}[/tex]Therefore, for each equation we know that:
[tex]\begin{gathered} \tan (\theta)=1 \\ \Rightarrow\theta=\frac{\pi}{4},\frac{5\pi}{4} \end{gathered}[/tex][tex]\begin{gathered} 7\tan (\theta)=-15 \\ \Rightarrow\theta=2.007423487\ldots\text{ , }5.14901614\ldots \end{gathered}[/tex]Which answer is equivalent to
OA.
B. √
(4
OB.
C.
16
49
D.
16
49
3/16
349
√16
(49
? Please helpppp
Answer:
C [tex]\sqrt \frac{16}{49}[/tex]Step-by-step explanation:
looking at all the stress you're in I knew I had to help so all your lists are bunched up, so I went of the picture C is correct because B 4 and 7 aren't even a part of the question itself and A has 16 and 49 but it doesn't have sqrt so it's not = to the question and D is not correct either because it doesn't have one sqrt it has two on top of each other. HOPE THIS HELPED!
(a) Find an angle between 0° and 360° that is coterminal with 600°.(b) Find an angle between 0 and 2n that is coterminal withЗп2
Coterminal Angles are angles that share the same initial side and terminal sides.
Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.
QUESTION A
The angle is given as 600°.
To find the coterminal angle between 0° and 360°, we subtract 360° from the angle.
Therefore,
[tex]\text{Coterminal angle = 600 - 360 = 240}\degree[/tex]The coterminal angle is 240°.
QUESTION B
The angle is given as
[tex]-\frac{3\pi}{2}[/tex]To get an angle between 0 and 2π, we will add 2π to it.
Hence, we have
[tex]\begin{gathered} \text{Coterminal angle = 2}\pi-\frac{3\pi}{2} \\ =\frac{\pi}{2} \end{gathered}[/tex]The coterminal angle is π/2.
the triangles below are similar. Find the value of x.
Answer:
x=9
Step-by-step explanation:
both sides are 14 and the other triangle is 7 so 14/7=2 and 18/2=9
an instructor has graded 22 exam papers submitted by students in a class of 23 students, and the average so far is 73. how high would the score on the last paper have to be to raise the class average by 1 point?
The next score have to be 96 to raise the class average by 1 point.
Explanation :
Let the score of the last paper be x, then
(22(73) + x)/23 = 74
22(73) + x = 74 x 23
1606+ x = 1702
x = 1702- 1606 = 96
x = 96
The next score have to be 96 to raise the class average by 1 point.
Solution in math :
An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values that, when used to replace the unknowns, cause the equation to equal itself. You can solve an equation numerically or symbolically.When an equation is solved numerically, only numbers are accepted as solutions. When an equation is solved symbolically, the solutions can be represented by expressions. The distinction between known variables and unknown variables is generally made in the statement of the problem, by phrases such as "an equation in x and y", or "solve for x and y", which indicate the unknowns, here x and y. Any solution, all solutions, or a solution that meets additional properties, such as belonging to a particular interval, may be found by solving an equation, depending on the context. An optimization problem is one where the goal is to identify the solution that meets a particular criterion best. A solution is a tuple of values, one for each unknown, that satisfies all of a given set of equations or inequalities. The solution set of a given set of equations or inequalities is the set of all of its solutions. There are no values of the unknowns that satisfy all equations and inequalities simultaneously if the solution set is empty.To learn more about how to find value of x refer :
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The vertices of a figure are W(-6,-2), X(-2,-2), Y(-2,-6), and Z(-5, -6).. Rotate the figure 270°
counterclockwise about the origin.
W'(-2 , 6), X'(-2 , 2), Y'(-6 , 2), Z'(-6 , 5).
This is the vertices after the 270° counterclockwise rotation.
What does counterclockwise rotation mean ?Counterclockwise is a turn to the left, opposite the direction of the hands on a clock.Given vertices,
W(-6,-2), X(-2,-2), Y(-2,-6), and Z(-5, -6).
Here we have to rotate 270°.
We know that,
Rotating a point 90° counterclockwise: (x, y) → (-y, x).
Rotating a point 180° counterclockwise: (x, y) → (-x, -y).
Rotating a point 270° counterclockwise: (x, y) → (y, -x).
So here we are rotating the figure 270°,
W(-6,-2)→ W'(-2 , 6)
X(-2,-2)→ X'(-2 , 2)
Y(-2,-6)→ Y'(-6 , 2)
Z(-5, -6)→ Z'(-6 , 5)
The vertices after rotating 270° counterclockwise about origin is:
W'(-2 , 6), X'(-2 , 2), Y'(-6 , 2), Z'(-6 , 5).
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The simple interest charged on a 65 day loan of $1250 is $7.75. Find the annual simple interest rate in precent for this loan round to the nearest tenth of a percent. Use 360 days in 1 year
We have a loan of 65 days.
The principal is $1250 and the interest is $7.75.
We have to find the annual simple interest rate.
We can express the interest of a loan of this type as:
[tex]I=r\cdot\frac{t}{360}\cdot P[/tex]where r = annual interest rate, t = period of the loan in days, I = interest and P = principal.
Then, we can rearrange the equation and replace with the values:
[tex]\begin{gathered} I=r\cdot\frac{t}{360}\cdot P \\ r=\frac{I\cdot360}{t\cdot P} \\ r=\frac{7.75\cdot360}{65\cdot1250} \\ r=\frac{2790}{81250} \\ r\approx0.03433846 \\ r\approx3.4\% \end{gathered}[/tex]Answer: the annual simple interest rate is 3.4%.
Debra earns $12.45 per hour and worked 26 34 hours last week. What is her gross pay?
the 10th and 15 term of an AP are - 5 and - 7 1/2 respectively what is the sum of the first 20 terms ? I really need the answer pls A 60 B -105 C -52 1/2 D -20
Answer:
B
Step-by-step explanation:
before finding the sum we require to find first term and common difference.
the nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₁₀ = - 5 and a₁₅ = - 7 [tex]\frac{1}{2}[/tex] = - 7.5 then
a₁ + 9d = - 5 → (1)
a₁ + 14d = - 7.5 → (2)
subtract (1) from (2) term by term to eliminate a₁
0 + 5d = - 2.5
5d = - 2.5 ( divide both sides by 5 )
d = - 0.5
substitute d = - 0.5 into (1) and solve for a₁
a₁ + 9(- 0.5) = - 5
a₁ - 4.5 = - 5 ( add 4.5 to both sides )
a₁ = - 0.5
the sum to n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
here a₁ = - 0.5 and d = - 0.5 , then
S₂₀ = [tex]\frac{20}{2}[/tex] [ (2 × - 0.5) + (19 × - 0.5) ]
= 10 (- 1 -9.5)
= 10 × - 10.5
= - 105
Find the probability of at least 6 failuresin 7 trials of a binomial experiment inwhich the probability of success in anyone trial is 9%.p=[?1%Round to the nearest tenth of a percent.
X=
//////////////////////////////
Answer: [tex]x=90[/tex]
Step-by-step explanation:
Using the alternate exterior angles theorem,
[tex]180-x=x\\\\180=2x\\\\x=90[/tex]
When and where does the story The circuit take place?
Answer:
Mexico to the United States in 1947
Step-by-step explanation:
There are 10 books are arranged on a shelf. If 4 books you are choosing are in alphabetical order,how many different groups of books could be chosen? Determine if it is permutation orcombination then solve.A). 24B). 210C). 3,628,800D). 5040
The problem says you have 10 books arranged on a shelf and then you are choosing 4 books in alphabetical order.
Given that you are choosing books with an order (alphabetical) it means the order does matter, then it is a permutation (which is an ordered combination).
In this case, no repetitions are allowed because you can't repeat a book in the selection, they'll be 4 different books from the shelf, the formula you have to use is:
[tex]\frac{n!}{(n-r)!}\begin{cases}n=\text{total number of books} \\ r=\text{ number of books you are choosing}\end{cases}[/tex]Then n=10 and r=4, replace these values:
[tex]\frac{10!}{(10-4)!}=\frac{3628800}{720}=5040[/tex]Then, can be chosen 5040 different groups of books.
The answer is option D.
You have read 4 of the books shown. Which choice shows 2 ways of writing the fraction of these books that you read?
Using proportions, two ways of writing the fraction of these books that you read is:
4/12 and 1/3.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations, especially multiplication or division.
One example of application of proportions is for relative frequencies, as a relative frequency is given by the number of successes in the sample divided by the sample size.
In the context of this problem, it is found that:
The number of successes on the sample is of 4, as you have read 4 books.The sample size is of 12, as there is a total of 12 books.Hence the relative frequency is:
4/12.
12 is divisible by 4, hence the fraction can be simplified as follows:
1/3.
Missing informationThe number of books is missing, and is of 12. (researching the problem on a search engine).
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most states run a lottery game in which players may select a three digit number, then later that day a televised drawing randomly selects a winning three digit number. suppose you select one three digit number and buy a ticket. what is the probability that your three digit number is an exact match with the winning three digit number?
The probability that the selected three digit number is an exact match with the winning three digit number = 1/1000
The 10 digits are 0, 1, 2, 3, 4, 5, 6,7, 8, 9. From these 10 digits 3 digits are selected.
Total number of ways of selecting a three-digit number = Number of ways of selecting a digit from 10 digits for each place(one's, ten's and hundred's place)
Thus a three-digit number can be selected in 10 x 10 x 10 = 1000 ways.
So there are 1000 possibilities for a three digit number.
From this only one choice matches exactly with the winning number.
So the number of favorable outcome = 1
Hence, The probability that the selected three digit number is an exact match with the winning three digit number = 1/1000
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Draw a slope triangle, from point B, whose horizontal leg is along the x-axis. What are the lengths of the vertical and horizontal legs of your slope triangle?
Horizontal leg = 6 units
Vertical leg is 4 units
Lets Represent the diagonal as line AB where A and B are the endpoints of the line segment
The coordinates of point A is ( 12,4)
The coordinates of point B is ( 6,0)
Slope = ( Y2 - Y1 ) / (X2 -X1) = (0 - 4) / ( 6 - 12) = -4 / -6 = 2/3
or simply.
slope = rise / run = vertical leg/ horizontal leg = 4/6 = 2/3
ANSWER
Horizontal leg = 6 units
Vertical leg is 4 units
Slope = 2/3
A 12-ft-by-15-ft rectangular swimming pool has a 3-ft-wide no-slip surface around it. What is the outer perimeter of the no-slip surface?.
The outer perimeter of the no-slip surface is 78 feet if the swimming pool has a 3-ft-wide no-slip surface around it.
The outer perimeter of an area or land can be described as the whole of its outer edge or can be described as the sum total of the outside edge lengths.
We can find the outer perimeter of this swimming pool by adding 3 feet twice to all the sides of this rectangular swimming pool followed by the addition of these sides together.
As the swimming pool is 12-ft-by-15-ft, this represents that two sides of this rectangular swimming pool are 15 feet and the other two sides are 12 feet, therefore;
12 + 6 = 18
15 + 6 = 21
Now we can find the perimeter by the addition of all the sides as follows;
18 + 18 + 21 + 21 = 78 feet
Therefore, the outer perimeter of the no-slip surface is found to be equal to 78 feet.
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Point T is located at (2, 5). Point A is located at (-3, 1.5). Point A is the midpoint of segment TB.
Point B is the midpoint of segment TY. What are the coordinates of point Y?
Using the midpoint, the coordinates of point Y in the line segment TY is (-18, -9).
How to use midpoint to find coordinates?Point T is located at (2, 5). Point A is located at (-3, 1.5). Point A is the midpoint of segment TB.
Therefore, the mid point formula can be represented as follows:
(xₙ, yₙ) = (x₁ + x₂ / 2, y₁ + y₂ / 2)
Hence, let's find the coordinates of point B.
(-3, 1.5) = (2 + x₂ / 2 , 5 + y₂ / 2)
2 + x₂ / 2 = - 3
cross multiply
2 + x₂ = -6
x₂ = -6 -2
x₂ = - 8
1.5 = 5 + y₂ / 2
3 = 5 + y₂
y₂ = 3 - 5
y₂ = -2
Therefore, the coordinates of B is (-8, -2)
Hence, let's find the coordinate of point Y. The coordinates of point B is the mid point of segment TY.
(-8, -2) = (2 + x₂ / 2 , 5 + y₂ / 2)
(-8, -2) = (2 + x₂ / 2 , 5 + y₂ / 2)
2 + x₂ / 2 = - 8
-16 = 2 + x₂
x₂ = -18
-2 = 5 + y₂ / 2
-4 = 5 + y₂
-4 - 5 = y₂
y₂ = -9
Therefore, the coordinates of y is (-18, -9)
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q - r - 3s = p solve for q
Answer:
q = p + r + 3s
Step-by-step explanation:
q - r - 3s = p solve for q
q - r - 3s = p
add r to both sides:
q - r - 3s + r = p + r
q - 3s = p + r
add 3s to both sides:
q - 3s + 3s = p + r + 3s
q = p + r + 3s
you are driving a 30 foot bus on a highway at 45 mph. the road is dry and visibility is good. a safe distance between you and the vehicle ahead of you should be at least:
Which of the following equations have no solutions?Choose all answers that apply:-60x + 32 = 32x + 60 -60x + 32 = 32x - 60 -60x + 32 = -60x - 32-60x + 32 = -60x + 60
Answer:
-60x + 32 = -60x - 32
Step-by-step explanation:
The first step to solve this question is combining the like terms in each option.
In those that we end up with:
0x = c
In which c != 0, we have no solution. So
-60x + 32 = 32x + 60
-60x - 32x = 60 - 32
-92x = 28
No 0x, so it has solution
-60x + 32 = 32x - 60
-60x - 32x = -60 - 32
-92x = -92
No 0x, so it has solution
-60x + 32 = -60x - 32
-60x + 60x = -32 - 32
0x = -64
0x equaling a value different of 0, so no solution.
-60x + 32 = -60x + 60
What values of u and v make △QRS≅△IKJ?
The values of u and v that makes △QRS and △IKJ congruent triangles are u = 7 and v = 3
How to determine the values of u and v?The triangles are given as
△QRS and △IKJ
The statement △QRS≅△IKJ means that
The triangles △QRS and △IKJ are congruent triangles
This means that the corresponding sides are congruent
So, we have the following equations:
v + u + 15 = 10u - 15v
-4u + 2v + 99 = 7v + 8u
Evaluate the like terms
So, we have
9u - 16v = 15
12u + 5v = 99
Make u the subject in 12u + 5v = 99
So, we have
u = (-5v + 99)/12
Substitute u = (-5v + 99)/12 in 9u - 16v = 15
9(-5v + 99)/12 - 16v = 15
So, we have
9(-5v + 99) - 192v = 180
Open brackets
-45v + 891 - 192v = 180
Evaluate the like terms
-237v = -711
Divide by -237
v = 3
Substitute v = 3 in u = (-5v + 99)/12
u = (-5 x 3 + 99)/12
Evaluate
u = 7
Hence, the values are u = 7 and v = 3
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HELp ASAP PLSSSPLSPLSPLSS
(view attatched image
Answer:
Ok...I've worked out the math and the correct answer should be the first one...
x | g(x)
1 | -2
2 | 4
3 | 10
Step-by-step explanation:
Hope this helps!!
graph a line that is perpendicular to the given line. determine the slope of the given line and the one you graphed in simplest form. click and drag on the graph to draw a line. click and drag to plot a perpendicular line. the line will change colors when a parallel or perpendicular line is drawn accurately.
The line given passes through two points. These are (-6,0) and (0,-8).
Remember that two lines are perpendicular if the product of their slopes is -1. So, the first thing we're going to do is to find the slope of the line given.
The slope between two points (x1,y1) and (x2,y2) can be found using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]If we replace our values:
[tex]m=\frac{-8-0}{0-(-6)}=\frac{-8}{6}=-\frac{4}{3}[/tex]To find other perpendicular line to this one, we have to find a number which multiplication with -4/3 is -1.
This number is clearly 3/4. Because
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ -\frac{4}{3}\cdot m_2=-1 \\ \\ m_2=\frac{3}{4} \\ \\ -\frac{4}{3}\cdot\frac{3}{4}=-1 \end{gathered}[/tex]Therefore, the slope of the perpendicular line must be 3/4, and the original slope is -4/3.
If we graph this:
what is 1.025 as a fraction?
The decimal number 1.025 is 41/40 in fractions.
What is Number system?A number system is defined as a system of writing to express numbers.
A fraction is a part of a whole
The decimal number one point zero two five should be converted to fraction.
The conversion of 1.025 to fraction is 41/40.
If we calculate 41/40 we get the value 1.025.
Hence 1.025 is 41/40 in fractions.
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Find the area of ABC with verticles A(4,-3), B(9,-3) and C(10,-11)
Answer:
Step-by-step explanation:
The area of the triangle when the vertices of the triangle are given can be calculated by the following formula:
Area of triangle = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)| where the vertices are A(Ax, Ay), B(Bx, By), C(Cx, Cy)
Now, we have been given the values of vertices as A(4, -3) B(9,-3) , and C(10, −11)
Therefore,
By applying the formula and substituting the given values, we get
Area = 0.5 * |4 * (-3 + 11) + 9 * (-3 + 11) + 10 * (-3 - 3)|
Area = 0.5 * |44|
Area = 22
Hence, the area of triangle ABC with the given vertices is 22 square units
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math is not fun please help
Answer:
∠ RST = 22°
Step-by-step explanation:
since ∠ RSU = 91°
and ∠ TSU = 69°
so ∠ RST = 22°
HOW:
given that;
∠ RSU = 91°
and
∠ TSU = 69°
we would subtract 69° from 91°
91°-69°= 22°
Solve 2x>8 or 2x< 4.
Graph the Linear equation: y = - 3/4x + 5
Based on the given linear equation of y = - 3/4x + 5, the graph is shown attached.
How to graph an equation?When given a linear equation, you graph it by coming up with x values and then using the equation to find the corresponding y values.
The linear equation is y = - 3/4x + 5.
If the value x = -1, then y would be:
y = - 3/4x + 5
= -3/4(-1) + 5
= 5.75
If the value x = 0, then y would be:
y = -3/4(0) + 5
= 5
If the value x = 1, then y would be:
= -3/4(1) + 5
= 4.25
If the value x = 2, then y would be:
= -3/4(2) + 5
= 3.5
If the value x = 3, then y would be:
= -3/4(3) + 5
= 2.75
The points would be:
(-1, -5.75) (0, 5) (1, 4.25) (2, 3.5) (3, 2.75)
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3×10^9
---------
3×10^-7
Answer:
1 x 10^16
Step-by-step explanation:
In the triangle below, ZABC is a right angle. Given that BDI AC, which statement must be true? (Hint: Look at your notes about similar right triangles). B AB AC AB AD DC DC BD BD AB BC DB BC DC AD DB DC
In a right triangle, if the altitude drawn from the right angle to the hypotenuse divides the hypotenuse into two segments, the length of the altitude is the geometric mean of the lengths of the two segments.
According to this
[tex]\frac{AD}{DB}=\frac{DB}{DC}[/tex]Which is the fourth option.
