On a unit circle, the terminal point of θ is (√2/2, √2/2). What is θ?
Given:
On a unit circle, the terminal point of θ is [tex]\left(\dfrac{\sqrt{2}}{2},\dfrac{\sqrt{2}}{2}\right)[/tex].
To find:
The value of [tex]\theta[/tex].
Solution:
If the terminal point of θ is (x,y), then
[tex]\tan \theta=\dfrac{y}{x}[/tex]
On a unit circle, the terminal point of θ is [tex]\left(\dfrac{\sqrt{2}}{2},\dfrac{\sqrt{2}}{2}\right)[/tex]. So,
[tex]\tan \theta=\dfrac{\dfrac{\sqrt{2}}{2}}{\dfrac{\sqrt{2}}{2}}[/tex]
[tex]\tan \theta=1[/tex]
[tex]\tan \theta=\tan \dfrac{\pi}{4}[/tex]
[tex]\theta=\dfrac{\pi}{4}[/tex]
Therefore, the correct option is D.
Please help me solve these problems guys I’m really struggling
Answer:
Step-by-step explanation:
What is 9x + 100 = 829
Answer:
81
Step-by-step explanation:
9x + 100 = 829
9x =829-100
= 729
x = 729/9
x = 81
Answer: x = 81
Step-by-step explanation:
You'd want to isolate x, meaning subtracting 100 on both sides to remove that from the equation. This results in 9x = 729, divide by 9 on both sides to remove that too from the equation and you'd be left with x = 81.
if the ratio a to b is 4:5 and the ratio of a to c os 2:7 what is the ratio of c to b
Answer:
G. 14:5 is the correct answer.
Step-by-step explanation:
a:b = 4:5
a:c = 2:7
so,
here in first ratio a = 4
in second ratio a = 2
making them equal:
Taking LCM of 2 and 4 = 4
so
a:c = 2/7 = (2×2)/(7×2) = 4/14
so,
a = 4
c = 14
b = 5
so ratio c : b = 14:5
47. The legs of a triangle measure 7 mm and 24 mm. What length hypotenuse makes the triangle a right triangle?
A. 23 cm
B. 25 cm
C. 161 cm
D. 289 cm
Answer:
B
Step-by-step explanation:
according to pythagorean
[tex]7^{2} + 24^{2} =x^{2}[/tex] (x>0)
=> [tex]x^{2} =625[/tex]
=>[tex]x=\sqrt{625}[/tex] = 25
Graph the inequality on the axes below.
-5x + 4y > -24
Step-by-step explanation:
-5x + 4y > -24
Plot and draw a graph that's it
What is the simplest shape in Mathematics?
Solve Q²= a(p²-b²)/p in form of y=mx+c
Answer:
We want to rewrite:
q^2 = a*(p^2 - b^2)/p
as a linear equation, in the form:
y = m*x + c
So we start with:
q^2 = a*(p^2 - b^2)/p
we can expand the left side to get:
q^2 = (a/p)*p^2 - (a/p)*b^2
q^2 = a*p - (a/p)*b^2
Now we can ust define:
a*p = c
Then we can replace that to get:
q^2 = -(a/p)*b^2 + c
now we can replace:
q^2 = y
b^2 = x
Replacing these, we get:
y = -(a/p)*x + c
finally, we can replace:
-(a/p) = m
then we got the equation:
y = m*x + c
where:
y = q^2
x = b^2
c = a*p
m = -(a/p)
If someone could help that would really be great. Thank you.!
please answer this question
How many significant digits are there in the number 5.5x10?? OA) 2 O B) 3 OC) 4 OD) 5
2
[tex]\\ \sf\longmapsto 5.5\times 10^3[/tex]
Take decimals away[tex]\\ \sf\longmapsto 55\times 10^4[/tex]
We know
Zeros to the right end of a number are not counted among significant figuresHence number of significant figures is 2
9514 1404 393
Answer:
2
Step-by-step explanation:
When a number is written in scientific notation, all of the digits of the mantissa are considered significant. The mantissa is 5.5, which has 2 digits.
There are 2 significant digits in the number.
Which points are possible approximations for this system? Select two options.
Step-by-step explanation:
second: (2.2,-1.4)
third: (2.2,-1.35)
Step-by-step explanation:
hope it helps✨
Find the missing length.
if 60 = c,
36 = m and
x is the missing length
c² = x . m
3600 = x . 36
x = 3600/36
x = 100
Segment addition and midpoints
The measure of QS is 11 units.
What is a Line Segment?A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.
The figure given below shows a line segment QT, where the length of line segment QT refers to the distance between its endpoints, Q and T.
Q_________R___________S_________T
Given that RT= 12
And RS=7
⇒ RT= RS + ST
⇒ ST= RT - RS
⇒ ST= 12-7
Substitute the values of RT and RS,
⇒ ST= 5
⇒ QT= 16
⇒ QR = 16 - RT= 16 - 12 = 4
⇒ QS = QR + RS
Substitute the values of QR and RS,
⇒ QS = 4 + 7=11
⇒ QS = 11
Hence, the measure of QS is 11 units.
Learn more about the line segment here:
brainly.com/question/25727583
#SPJ2
2x-3=5
(x+2)(3x-15)=0
Answer:
the first one gat to be x=4
Answer: 17
Step-by-step explanation: :)
[tex]\frac{-3}{\sqrt{x} +3} +\frac{1}{2}[/tex]
[tex]\huge\bold\color{blue}{⁂Answer:}[/tex]
[tex]\bold{ - \frac{6 \sqrt{x} - x - 9 }{2(x - 9)} }[/tex]
#CarryOnLearning
[tex]\bold\color{red}{༄Fairy \: Elfꨄ︎}[/tex]
Four bells at intervals of 12 minutes, 18 minutes, 20 and 25 minutes. If they toll together at 10 am, when next do they toll together again?
Answer:
1.00 am
Step-by-step explanation:
Find the LCM of 12,18,20 and 25
=900 min ....change it to hrs =15 hrs
10.00am___1000hrs
1000hrs+15hrs
=0100hrs
=1:00 am
Use the circle to represent the following situation and show how you came up with the answer.
For lunch, you stop at a Pizza Express, where they sell pizza whole or by the slice. The area of one slice of a 16" pizza is 33.49in².
✏️ What angle does one slice make
Answer:
Angle of slice (θ) = 172° (Approx.)
Step-by-step explanation:
Given:
Area of pizza slice = 16 inch²
Total area of pizza = 33.49 inch²
Find:
Angle of slice (θ)
Computation:
Area of circle = [π][r²]
Area of pizza slice = [π][r²]
[π][r²] = 33.49
[3.14][r²] = 33.49
Radius = 3.26 inch (Approx.)
Area of sector = [θ/360][π][r²]
16 = [θ/360][3.14][3.26²]
16 = [θ/360][3.14][10.6276]
16 = [θ/360][33.37]
Angle of slice (θ) = 172° (Approx.)
Please Help.
A square prism and a cylinder have the same height. The area of the cross-section of the square prism is 314 square units, and the area of the cross-section of the cylinder is 50π square units. Based on this information, which argument can be made?
A. The volume of the square prism is one third the volume of the cylinder.
B. The volume of the square prism is half the volume of the cylinder.
C. The volume of the square prism is equal to the volume of the cylinder.
D. The volume of the square prism is twice the volume of the cylinder.
As we know, The volume of the square prism is twice the volume of the cylinder
To determine the relationship between the volume of the square prism and that of the cylinder, we need to find both volumes.
The volume of the square prism is V = Ah where A is the cross-sectional area and h its height. Since A = 314 square units,
V = 314 × h = 314h
Also, the volume of the cylinder is V = A'h where A' is the cross-sectional area of the cylinder and h' its height. Since the A' = 50π square units,
V' = 50π × h' = 50πh'
The ratio of the volume of the square prism to that of the cylindrical prism is V/V' = 314h/50πh'
Since the height of the square prism equals that of the cylinder, h = h'.
So, V/V' = 314h/50πh .
V/V' = 314/50π
if we take π = 3.14,
V/V' = 314/(50 × 3.14)
V/V' = 100/50
V/V' = 2
So, V = 2V'
Thus, the volume of the square prism is twice the volume of the cylinder.
So, the answer is D.
Learn more about square prisms and cylinders here:
https://brainly.com/question/23245822
Answer:
D. The volume of the square prism is twice the volume of the cylinder.
Step-by-step explanation:
took the test, got it right, comment below if you would like a step by step explanation
Ming wrote the table of points below.
x
y
5
10
10
20
15
30
Which explains whether or not Ming has described a proportional relationship, and why?
Ming has described a proportional relationship because the ordered pairs are linear and the line passes through the origin.
Ming has not described a proportional relationship. Although it is a linear relationship, it does not pass through the origin.
Ming has not described a proportional relationship. Although it passes through the origin, it is not a linear relationship.
Ming has described a proportional relationship because the line does not pass through the or
Answer:
Ming has described a proportional relationship because the ordered pairs are linear and the line passes through the origin
Step-by-step explanation:
Given
x - y
5 - 10
10 - 20
15 - 30
Required
Determine if the data are proportional
The dataset is small; so, we can derive the relationship by observation.
By observing the x and y values, the relationship is:
y = 2x --- i.e. multiply x values by 2.
This is further proven by:
y = 2 * 5 = 10
y = 2 * 10 = 20
y = 2 * 15 = 30
y = 2 * 0 = 0 --- the origin
Hence, the dataset is proportional and it passes through the origin.
Joe and JoAnn each bought 12 ounces of coffee in a 16 ounce cup. Joe drank 2 ounces of his coffee and then added 2 ounces of cream. JoAnn added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces. What is the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee
Answer:
[tex]Ratio = 7:6[/tex]
Step-by-step explanation:
Given
Initially
[tex]Joe = 12oz[/tex] -- coffee
[tex]JoAnn = 12oz[/tex] -- coffee
Joe drank 2oz coffee; So, we have:
[tex]Joe = 12oz - 2oz[/tex]
[tex]Joe = 10oz[/tex] --- coffee
Joe added 2oz cream; So, we have:
[tex]Joe = 10oz[/tex] --- coffee [tex]Joe = 2oz[/tex] --- cream
JoAnn added 2oz cream and stirred. So, we have:
[tex]Joe = 12oz[/tex] --- coffee [tex]JoAnn = 2oz[/tex] --- cream
[tex]Total = 14oz[/tex]
JoAnn drank 2oz from the drink; the amount of drink JoAnn drank is:
[tex]JoAnn = \frac{Cream}{Total}[/tex]
[tex]JoAnn = \frac{2}{14}[/tex]
[tex]JoAnn = \frac{1}{7}[/tex]
Amount of cream left is:
[tex]Amount = [1- \frac{1}{7}] *2[/tex]
Take LCM
[tex]Amount = [\frac{7-1}{7}] * 2oz[/tex]
[tex]Amount = \frac{6}{7} * 2oz[/tex]
[tex]Amount = \frac{12}{7}oz[/tex]
So, we have:
[tex]Joe = 2oz[/tex] --- cream
[tex]JoAnn = \frac{12}{7}[/tex] cream
The ratio is:
[tex]Ratio = 2:\frac{12}{7}[/tex]
Multiply by 7
[tex]Ratio = 14:12[/tex]
Divide by 2
[tex]Ratio = 7:6[/tex]
the width of a rectangle is twice as long as the length. if the length is increased by 50% and the width is decreased by 20%, the perimeter becomes 248. find the width and length of the original rectangle.
will give brainliest to correct answer
Answer:
Step-by-step explanation:
I answered your question in #24317186. Apparently you asked it twice and no one helped you yesterday.
AB is 16 centimeters long. It is rotated 24° clockwise around point A. What is the length of
the resulting line segment?
centimeters
Submit
Answer:
its 16
Step-by-step explanation:
rotation doesnt effect length
Factorize this 5y2 + 2y – 3a2?
Answer:
y(5y +2) -3a²
Step-by-step explanation:
that is the solution above
Whats the answer i got 1 minute left
Answer:
Step-by-step explanation:
Answer:
[tex]-\frac{3p^8}{4q^3}[/tex]
Step-by-step explanation:
One is given the following expression,
[tex]\frac{15p^-^4q^-^6}{-20p^-^1^2q^-^3}[/tex]
Since (15) and (-20) are both divisible by (5), one can divide both terms by (5) to simplify it.
[tex]\frac{3p^-^4q^-^6}{-4p^-^1^2q^-^3}[/tex]
Now bring all of the terms with a negative exponent to the numerator. Multiply the exponents by (-1), then add them to the exponents of the like term in the numerator. Simplify the resulting exponents
[tex]\frac{3p^-^4q^-^6}{-4p^-^1^2q^-^3}[/tex]
[tex]\frac{3p^-^4^+^(^-^1^)^(^-^1^2^)q^-^6^+^(^-^1^)^(^-^3^)}{-4}[/tex]
[tex]\frac{3p^-^4^+^1^2q^-^6^+^3}{-4}[/tex]
[tex]\frac{3p^8q^-^3}{-4}[/tex]
Rewrite the fraction such that there are no negative exponents. Remember the rule, when bringing a number from the numerator to the denominator and back, multiply the exponent of the number by (-1). One can only switch numbers between the numerator and the denominator when all operations are multiplication or division.
[tex]\frac{3p^8q^-^3}{-4}[/tex]
[tex]-\frac{3p^8}{4q^3}[/tex]
hi pls help.you do not have to do all 3. just either one will be ok pls explain as well:) thank you
Answer:
[tex]{7a^{5}b^{5} c\\[/tex]
Step-by-step explanation:
[tex]\frac{28a^{8}b^{6} c^{3} }{4a^{3}bc^{2} }[/tex]
→ First look at the first term of each expression and see if they can be simplified, and they can
[tex]\frac{7a^{8}b^{6} c^{3} }{a^{3}bc^{2} }[/tex]
→ Now look at the a terms, since a larger one is at the top, you subtract
[tex]\frac{7a^{5}b^{6} c^{3} }{bc^{2} }[/tex]
→ Now simplify the b and c terms
[tex]{7a^{5}b^{5} c[/tex]
One year ago, the ratio of Honey and Piyush ages was 2:3 respectively. After five years from now, this ratio becomes 4:5. How old is Piyush now?
Answer:
eşnatto eşmatoroorlfld
Answer:
Now , Piyush age =3+Honey age
Step-by-step explanation:
Honey age=x
Piyush age=y
1 year ago,Honey age=x-1
Piyush age=y-1
the ratio of Honey and Piyush age=2:3
x-1:y-1=2:3
x-1/y-1=2/3
3(x-1)=2(y-1)
3x-3=2y-2
3x-2y= -2+3
3x-2y=1 eq _1
after 5 years from now,
Honey age=x+5
Piyush age=y+5
the ratio of them=4:5
x+5/y+5=4/5
5(x+5) =4(y+5)
5x+25=4y+20
5x-4y=20-25
5x-4y=-5 _eq2
eq1and 2_
5x-4y= -5
3x-2y= 1
-
2x-2y=-6
x-y =-3
-y=-3-x
y=3+x
someone please help me I really need help on this or ill fail
Answer:
a. Smart Dot Company: C = 12 + 0.5·t
Communications Plus: C = 2.5·t
b. Please find attached the required tables created using MS Excel cell function tool
c. Please find attached the graph of both relationship created on the same grid with
Step-by-step explanation:
a. The monthly cost of the Smart Dot Company = $12
The hourly cost for internet use on Smart Dot Company = $0.50
The hourly cost of using the Communications Plus = $2.50
Therefore, the total monthly cost, C, for the duration of hours used, t, is given as follows;
Smart Dot Company: C = 12 + 0.5·t
Communication Plus: C = 2.5·t
b. The table of values are created using MS Excel as follows;
[tex]\begin{array}{ll}Smart \ Dot \ Company&\\Time \ (hours)&Cost \ (dollars)\\0&12\\2&13\\4&14\\6&15\\8&16\\10&17\end{array}[/tex] [tex]\begin{array}{ll}Communications\ \ Plus&\\Time \ (hours)&Cost \ (dollars)\\0&0\\2&5\\4&10\\6&15\\8&20\\10&25\end{array}[/tex]
c. Please find attached the graph of both relationship created on the same grid with MS Excel
If your not busy mind helping me on this
Answer:
F
Step-by-step explanation:
add all the numbers and divide them by how many numbers there is(in this case 15) to find the average of the prices
A student said that since -9 is less than 4, then |-9| is less than |4|. Is the student correct? Explain why or why not.
Answer:
No.
Step-by-step explanation:
They are not correct because the "| |" signs mean absolute value. What ever is inside the signs must be positive. So -9 becomes 9 and 9 is greater than 4. So, the student is not correct.
