Sin theta = 3/4, what are the values of cos theta and tan theta?
Answer:
[tex]\displaystyle \cos(\theta) = \frac{\sqrt{7}}{4}[/tex].
[tex]\displaystyle \tan(\theta) = \frac{3\sqrt{7}}{7}[/tex].
Step-by-step explanation:
By the Pythagorean identity, for any given angle [tex]\theta[/tex], [tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex].
Given that [tex]\displaystyle \sin(\theta) = 3/4[/tex], solve this equation for [tex]\cos(\theta)[/tex].
[tex](\sin(\theta))^{2} + (\cos(\theta))^{2} = 1[/tex].
[tex]\displaystyle \left(\frac{3}{4}\right)^{2} + (\cos(\theta))^{2} = 1[/tex].
[tex]\begin{aligned} \cos(\theta) &= \sqrt{1 - \frac{9}{16}} \\ &= \sqrt{\frac{7}{16}} \\ &= \frac{\sqrt{7}}{4} \end{aligned}[/tex].
The tangent of an angle is equal to the ratio between the sine and cosine of that angle. In this question:
[tex]\begin{aligned} \tan(\theta) &= \frac{\sin(\theta)}{\cos(\theta)} \\ &= \frac{3/4}{\sqrt{7}/4} \\ &= \frac{3}{\sqrt{7}} \\ &= \frac{3\sqrt{7}}{7}\end{aligned}[/tex].
In a class of 80 students in Debre Berhan University, 45 are good in mathematics, 15 are good in both mathematics and English, 13 are good in both Mathematics and Psychology, 16 are good in both English and Psychology only,20 are good in Psychology and 9 are good in both of the three course,then how many students are good in mathematics?
Step-by-step explanation:
No of Student in Debre Berhan University - 80 students
No of student good in mathematics - 45 student'sNo of students good in mathematics and English -15
No of students good in mathematics and psychology -13No of students good in English and psychology -16No of students good in psychology -20no of student good in mathematics -45+15+13
-75therefore no of student good in math is 75 .
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Write the fraction 16/28 in simplest form.
Answer:
1/4
Step-by-step explanation:
Write 4 3/7 as a decimal.
Enter your answer as a decimal rounded to the nearest hundredth
Please help, and answer quickly please
Answer:
4.3
Step-by-step explanation:
Please answer this question
Step-by-step explanation:
Using the properties of logarithms, the left side of the equation becomes
[tex]\log{3x^3} - \log{x^2} = \log{3x}[/tex]
while the right hand side becomes
[tex]\log{27} - \log{x} = \log{\frac{27}{x}}[/tex]
so we end up with
[tex]3x^2 =27 \Rightarrow x = 3[/tex]
a number is multipilied by 6, and that the sum is equal to the product of 2 and 19. find the number
Answer:
[tex]take \: the \: number = x \\ thenx \times 6 = 2 \times 19 \\ \\ 6x = 38 \\ x = \frac{38}{6} \\ x = 6.33 \\ thank \: you[/tex]
<7 and <8 are complimentary angles. <5 = <8 and m<6 = 29. Find the measure of angle 7 and angle 5
Step-by-step explanation:
since < 5 = < 8, so,
< 7 = < 6 = 29°
and < 5 = 90° - 29° = 61°
68 rounded to the nearest hundred
Answer:
100
Step-by-step explanation:
anything lower then 4 stays anythiing 5 or higher is rounded
so this also works with 40 50 400 500 4000 5000, you gte the point
oodluck on your test or homework! :)
Reduce 6x /12x is it 1/2
Answer:
tero bau ko tauko got it sjdhhrurjrbr
Answer:
LHS=6x/12x=6/12=1/2
RHS=1/2
LHS=RHS
Mark buys last year's best-selling novel, in hardcover, for $23.20. This is with a 20% discount from the original price. What was the original price of the novel?
Answer:
[tex]29[/tex]
Step-by-step explanation:
Let x be the original price.
( 1 - 20% ) x = 23.2
[tex] 0.8x = 23.2[/tex]
[tex] \frac{0.8x}{0.8} = \frac{23.2}{0.8} [/tex]
[tex] x = 29[/tex]
Kelly works two jobs. She usually works at a retail store for 5 hours during the day and is paid $7.18 per hour by the store. In the evening she works at a restaurant as a
manager for 7 hours and is paid $20.68 per hour. How much does she make on average per hour for the day?
Answer:
Think of two or three jobs with which you are familiar, perhaps a teacher, a retail worker, a nurse, or a police officer.
In each case, indicate why the employment contract is necessarily incomplete. What important parts of the person’s job—things that the employer would like to see the employee do or not do—cannot be covered in a contract, or if they are, cannot be enforced?
Step-by-step explanation:
b. ¿Qué fracción representa el total de sillas ocupadas durante los tres días?
vean la imagen estoy en examen pliss ayudAAAAAAAAAAA
The fraction that represents the total number of seats occupied during the three days is 1.
The total number of seats in the auditorium is 200.
On day 1, 40% of the seats were occupied. So, 40/100 * 200 = 80 seats were occupied on day 1.
On day 2, 35% of the seats were occupied. So, 35/100 * 200 = 70 seats were occupied on day 2.
On day 3, 25% of the seats were occupied. So, 25/100 * 200 = 50 seats were occupied on day 3.
The total number of seats occupied during the three days is 80 + 70 + 50 = 200 seats.
The fraction that represents the total number of seats occupied during the three days is 200/200 = 1.
Here is the solution in mathematical form:
Let x be the fraction that represents the total number of seats occupied during the three days.
Then, x * 200 = 80 + 70 + 50
x = (80 + 70 + 50) / 200
x = 1
Therefore, the answer is 1.
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You share Packet of 56 jelly beans with your sister in the ratio 4:3 how many jelly beans will you get?
I'll get 32 jelly beans
Amount of jelly beans shared = 56
My fraction = 4/(4+3) = 4/7
My sister's fraction = 3/(4+3) = 3/7
The number of jelly beans that I'll get will then be:
= My fraction × Number of jelly beans
= 4/7 × 56
= 4 × 8
= 32
Therefore, I'll get 32 jelly beans
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Which of the following collections of subsets of the plane, R2
, are partitions?
(a) {{(x; y) | x + y = c}| c R}
(b) The set of all circles in R2
(c) The set of all circles in R2
centered at the origin together with the set {(0; 0)}
(d) {{(x; y)} | (x; y) R
[tex]\{(x,y) | \ \ x+y = c, \ c \in \mathbb{R}\}[/tex]
Explanation:
The notation for choice A basically says "we have a line of the form x+y = c where c is a real number". Then points on the line in the form (x,y) will form a particular partition. A partition is where we break a set up into non-overlapping subsets and there are no gaps. Think of it like breaking up a house into multiple rooms. Each room is a subset of the house. There are no gaps or overlaps (ignore the regions in the walls).
Take note that if a point is on a line like x+y = 5, then it cannot be on any other line of the form x+y = c, where c is not equal to 5. Something like (x,y) = (2,3) is on x+y = 5 and not on any other line. If c is allowed to be any real number, then x+y = c will be able to partition the real numbers.
Put another way, we can pick any real number we want (aka the number c) and break it down into a sum of x and y values. Such a sum cannot yield any other c value. So going back to the house/room analogy, any particular (x,y) ordered pair will belong to one and only one room.
Let's look at an example of a non-answer. Choice B is not correct because it is perfectly possible to have circles intersect. Intersecting circles share at least one common point. Those common points are what break the idea of partitions. This idea also means choice C is false as well.
Choice D can be ruled out because the notation should be (x,y) in R2 and not simply R.
The collections of subsets of the plane, R2 is (a) {{x,y) : x + y = c} : c ∈ R}
What is a subset ?If X is a subset of Y then all the elements of A also contained in B.
According to the given statement we have o determine which of the following collections of subsets of the plane R2.
R2 defines a two dimension plane.
x+y = c where c is a real number.
Then points on the line in the form (x,y) will form a particular partition. A partition is where we break a set up into non-overlapping subsets and there are no gaps. Think of it like breaking up a house into multiple rooms. Each room is a subset of the house.
Take note that if a point is on a line like x+y = 7, then it cannot be on any other line of the form x+y = c, where c is not equal to 7. Something like (x,y) = (3,4) is on x+y = 7 and not on any other line.
B. Is not correct because it is perfectly possible to have circles intersect. Intersecting circles share at least one common point. Those common points are what break the idea of partitions.
C. is false as well
D. Is ruled out because the notation should be (x,y) in R2 and not simply R.
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what is the location of the circumcenter of triangle abc
Step-by-step explanation:
The circumcenter is the centre of the circumcircle. All the vertices of a triangle are equidistant from the circumcenter.In an acute-angled triangle, circumcenter lies inside the triangle. In an obtuse-angled triangle, it lies outside of the triangle.
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(PLEASE EXPLAIN HOW YOU GOT THE ANSWER) Which inequalities are true? Select the four correct answers.
0 less-than StartRoot 8 EndRoot
StartRoot 8 EndRoot less-than 3
StartRoot 8 EndRoot greater-than StartRoot 7 EndRoot
StartRoot 8 EndRoot less-than 2
StartRoot 8 EndRoot greater-than 8
1 less-than StartRoot 8 EndRoot
9514 1404 393
Answer:
T, T, F, F, T
Step-by-step explanation:
First of all, it is helpful to know ...
√8 ≈ 2.8284
√7 ≈ 2.6458
Now you can check the inequalities:
0 < √8 < 3 . . . . . . true√8 > √7 . . . . . . . . true√8 < 2 . . . . . false√8 > 8 . . . . . false1 < √8 . . . . . . . . . . true0, 1, 2, and √7 are left of √8 on a number line, so are all less than √8.
3 and 8 are right of √8 on a number line, so are greater than √8.
Answer:
T, T, F, F, T.
Step-by-step explanation:
Person above is correct!!
Find the inverse of g(x)=2x-3
Answer:
g^-1(x)=x/2+3/2
Step-by-step explanation:
It takes 60 pounds of seed to completely plant a 7-acre field. How many acres can be planted per pound of seed?
Answer:
7/60 acres
Step-by-step explanation:
60 pounds of seed = 7 acres
We want to find acres per pound of seed, so we want to make one side of the equation equal to 1 pound of seed. To do this, we can divide both sides by 60, as anything divided by itself equals 1. We thus have
60/60 pounds of seed = 7/60 acres
1 pound of seed = 7/60 acres
Find the perimeter of this figure.
14 m
12 m
18 m
6 m
[? ] = meters
Answer:
The perimeter of it is going to be 50
Step-by-step explanation:
This is because when finding the perimeter you add up all the sides so
14 + 12 + 18 + 6 = 50
Answer:
50 m
Step-by-step explanation:
Perimeter
= Sum of the length of all sides
= 14 m + 12 m + 6 m + 18 m
= 50 m
$8,375.79 to the nearest thousand
Answer:
$8,000
Step-by-step explanation:
8,375.79 < 8,500 so it will round to 8,000
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-Chetan K
3- 22
Choose the expressions which are equivalent to the given expression
A. 3- (-22)
B. 3- (+22)
C. 3 + (-22)
D. 22 - 3
E. 22 + 3
F. -22-3
G. - 22 + 3
H. 22 +(-3)
Answer:
» B. 3- (+22) and C. 3 + (-22)
» A. 3- (-22) and E. 22 + 3
» D. 22 - 3 and H. 22 +(-3)
Step-by-step explanation:
[tex].[/tex]
Answer:
3 - (+22)
3 + (-22)
-22 + 3
Step-by-step explanation:
38) The length of a rectangle is 15.6 cm correct to 1 decimal place.
The width of a rectangle is 3.8 cm correct to 1 decimal place.
Calculate the lower bound for the perimeter of the rectangle.
Answer:
38.75
Step-by-step explanation:
perimeter = 2(15.6+3.8) =38.8
lower bound = the smallest value that would round up to the estimated value =38.75
-3/5×(2/9×10/7)
what's the answer
Answer:
-4/21
Step-by-step explanation:
-3/5×20/63
-3×4/63
-4/21
Johannesburg is is 3/5 as tall as his sister. Johannesburg is 90cm tall. How tall is his sister
Johannesburg's sister is 54cm tall
Explanation:
3/5 = 0.6
0.6 * 90 = 54
54 is 3/5 of 90, therefore Johannesburg's sister is 54cm tall
Find the root(s) or zero(s) of the function.
Answer:
-1/2 , 3
Step-by-step explanation:
In order to find the roots of the function 2x² - 5x - 3
We have to solve the quadratic equation :
2x² - 5x - 3 = 0
Calculating the discriminant Δ :
Δ = b² - 4ac
= (-5)² - 4(2)(-3)
= 25 + 24
= 49
Then
√Δ = √49 = 7
Determining the Zeros :
[tex]x=\frac{-b+\sqrt{b^{2}-4ac} }{2a} = \frac{5+7} {2 \times (2)} =\frac{12}{4} =3[/tex]
or
[tex]x=\frac{-b-\sqrt{b^{2}-4ac} }{2a} = \frac{5-7} {2 \times (2)} =\frac{-2}{4} =\frac{-1}{2}[/tex]
using 3 discs complete the puzzle. what is the smallest number of moves you can find
Please help What's the volume of a cube with a side length of 9 cm? Question 19 options: 701 cm³ 729 cm³ 697 cm³ 752 cm³
Round 475,805 to the nearest ten thousand.
475,805 rounded to the nearest ten thousand would be 476,000.
Which of the following number(s) rounds to 0.18?
Select all that apply.
A. 0.17714
B. 0.18582
C. 0.18321
D. 0.17217
Answer:
it's A or C
Step-by-step explanation:
because if it was be it would round to .19 but c and a round to .18
Find all values of c such that 3^2c+1=28*3^c-9. If you find more than one value of c, then list your values in increasing order
[tex]3^{2c} + 1 = 28\times3^c - 9 \implies 3^{2c} - 28\times3^c = -10[/tex]
Complete the square on the left side:
[tex]3^{2c} - 28\times3^c = \left(3^{2c}-28\times3^c+14^2\right)-14^2 = \left(3^c-14\right)^2 - 196[/tex]
Then the equation becomes
[tex]\left(3^c-14\right)^2 - 196 = -10 \\\\ \left(3^c-14\right)^2 = 186 \\\\ 3^c - 14 = \pm\sqrt{186} \\\\ 3^c = 14\pm\sqrt{186}[/tex]
Both 14 + √186 and 14 - √186 are positive numbers, so we can take the logarithm (base 3) of both sides without issue:
[tex]\log_3\left(3^c) = c = \log_3\left(14\pm\sqrt{186}\right)[/tex]
Then in increasing order, the solutions are
c = log₃(14 - √186), c = log₃(14 + √186)