Answer:
[tex]\displaystyle \frac{28}{15}\; \text{radians}[/tex], which is approximately [tex]107^{\circ}[/tex].
Step-by-step explanation:
In a given circle, the angle of a sector is proportional to the length of the corresponding arc:
[tex]\displaystyle \frac{\text{angle of sector $1$}}{\text{angle of sector $2$}} = \frac{\text{length of arc of sector $1$}}{\text{length of arc of sector $2$}}[/tex].
For the circle in this question, [tex]r = 15\; \rm cm[/tex], and the circumference would be:
[tex]2\, \pi \, r = 30\, \pi\; \rm cm[/tex].
The full circle itself is like a sector with an angle of [tex]2\, \pi[/tex], with the arc length equal to the circumference of the circle.
[tex]\displaystyle \frac{\text{angle of sector}}{\text{angle of full circle}} = \frac{\text{length of arc of sector}}{\text{circumference of circle}}[/tex].
[tex]\displaystyle \frac{\text{angle of sector}}{2\,\pi\; \rm rad} = \frac{28\; \rm cm}{30\, \pi\; \rm cm}[/tex].
Rearrange the equation to find the angle of the sector:
[tex]\begin{aligned} & \text{angle of sector} \\ =\; & (2\,\pi\; \rm rad) \cdot \frac{28\; \rm cm}{30\, \pi\; \rm cm} \\ =\; & \frac{28}{15}\; \rm rad\end{aligned}[/tex].
In other words, the angle of this sector would be [tex]\displaystyle \frac{28}{15}\; \rm rad[/tex]. Multiply that measure in radians by [tex]\displaystyle \frac{360^{\circ}}{2\,\pi\; \rm rad}[/tex] to find the value of the angle measured in degrees:
[tex]\begin{aligned} & \frac{28}{15}\; \rm rad \times \frac{360^{\circ}}{2\,\pi\; \rm rad} \approx 107^{\circ}\end{aligned}[/tex].
Can someone please answer this? Thank you!
[tex]\\ \sf\longmapsto 1-\left(\dfrac{4}{7}+\dfrac{4}{5}\right)[/tex]
[tex]\\ \sf\longmapsto 1-\left(\dfrac{20+28}{35}\right)[/tex]
[tex]\\ \sf\longmapsto 1-\left(\dfrac{48}{35}\right)[/tex]
[tex]\\ \sf\longmapsto 1-\dfrac{48}{35}[/tex]
[tex]\\ \sf\longmapsto \mid \dfrac{35-48}{35}\mid[/tex]
[tex]\\ \sf\longmapsto \mid \dfrac{-13}{35}\mid[/tex]
[tex]\\ \sf\longmapsto \dfrac{13}{35}[/tex]
Answer:
3/35
Step-by-step explanation:
total bottles 7/7
4/7 are big,
7/7-4/7=3/7 remaining bottles.
4/5×3/7=12/35 are small.
you add the big bottles and small bottles
4/7+12/35=32/35
then you minus from the total which is 7/7
7/7-32/35=3/35 are tiny.
Year8 Maths(Angles)
Help me plz!!
Step-by-step explanation:
a 360/9 = 40
b 2/9 × 360 = 80
c similarly 160
d 400
5.
For which discriminant is the graph possible?
A. b2 – 4ac = –1
B. b2 – 4ac = 0
C. b2 – 4ac = 4
please help this 2 sums
Answer:
Step-by-step explanation:
Sin (A + B) = Sin A *Cos B + Cos A *Sin B
Sin 75 = Sin (30 + 45)
= Sin 30 * Cos 45 + Cos 30 * Sin 45
[tex]= \dfrac{1}{2}*\dfrac{1}{\sqrt{2}}+\dfrac{\sqrt{3}}{2}*\dfrac{1}{\sqrt{2}}\\\\\\= \dfrac{1}{2\sqrt{2}}+\dfrac{\sqrt{3}}{2\sqrt{2}}\\\\= \dfrac{1+\sqrt{3}}{2\sqrt{2}}[/tex]
PLZ HELP!! ILL GIVE BRAINLIEST!!!
Answer:
(6, -3)
Step-by-step explanation:
Find the middle of the 2 coordinates.
8 --- 4
7 --- 5
6 --- 6
__________
-7 --- 1
-6 --- 0
-5 --- -1
-4 --- -2
-3 --- -3
f(x) = roots 3x + 7
if f^-1 (x) is the invers of f(x), then determine the result of f^-1(2)!
[tex]f(x) = \sqrt{3x} + 7 \\ \\ f ^{ - 1} (x) = ( \sqrt{3x} + 7) ^{ - 1} \\ \\ f ^{ - 1} (x) = \frac{1}{ \sqrt{3x} + 7} \\ \\ \\ f ^{ - 1} (2) = \frac{1}{ \sqrt{3(2)} + 7} \\ \\f ^{ - 1} (2) = \frac{1}{ \sqrt{6} + 7} \\ \\ f ^{ - 1} (2) = \frac{1}{ \sqrt{6} + 7} \times \frac{ \sqrt{6} - 7 }{ \sqrt{6} - 7 } \\ \\ f ^{ - 1} (2) = \frac{ \sqrt{6} - 7 }{(6 - 49)} = \frac{ \sqrt{6} - 7 }{ - 43} \\ \\ f ^{ - 1} (2) = \frac{ \sqrt{6} - 7 }{ - 43} = \frac{2.449 - 7}{ - 43} \\ \\ f ^{ - 1} (2) = \frac{ - 4.551}{ - 43} \\ \\ f ^{ - 1} (2) = \frac{ 4.551}{ 43} =0.10584[/tex]
I hope I helped you^_^
WILL GIVE BRAINLIEST TO WHOEVER CAN SHOW UR WORK:
89.9cm to m.
Answer:
give brainliest please I need it to level up
Step-by-step explanation:
divide the value in centimeters by 100 because 1 meter equals 100 centimeters.
So, 89.9 centimeters = 89.9÷ 100 = 0.899 meter.
please please please help!
Answer:
4
Step-by-step explanation:
The multiplication of both indices gives 4
2. Which number line is correct? Why are the others incorrect?
Answer:
the middle one is correct
Step-by-step explanation:
the first one is incorrect because the way negative numbers are ordered is incorrect it should be "-3, -2, -1"
the middle one is correct because the pattern is consistent and the order of the numbers are correct
the third one is incorrect because the pattern doesn't match "-15" isn't counting by twos 15 isn't an even number
hope I helped ❤
Explanation:
The first number line is incorrect because the -1, -2, -3 should be reversed to get -3, -2, -1. It's reversed because the negatives are a mirror image of the positive counterpart.
The second number line is correct. Each number shown is separated with a gap size of 20. This gap size stays the same throughout the number line.
The third number line is incorrect. The gap from -15 to -12 is 3 units, while the gap from -12 to -10 is 2 units. We see that the gap size isn't the same through the entire number line.
So to summarize: the gap size must be the same and the numbers must be written in the correct order.
Let f(x) = -20x^2 + 14x + 12 and g(x) = 5x - 6. Find f/g and state it’s domain.
Answer:
-4x - 2 all are real number
1/2(f+y)=f-5 as a sentence
Step-by-step explanation:
½(f + y) = f - 5
(f + y)/2 = f - 5
y + f = 2f - 10
y = f - 10
or
f = y + 10
#mathisfun
Why might you need to use the addition or subtraction property of equality more than once after you have used the distributive property and combined like terms? Explain. Sample Response: If there is a variable term and a constant on each side of the equation, then you will need to use the addition or subtraction property of equality once to isolate the variable term and once to isolate the constant. Which did you include in your response? Check all that apply. Use the addition or subtraction property of equality once to isolate the variable term. Use the addition or subtraction property of equality once to isolate the constant.
Answer:
We have to use addition or subtraction property of equality to determine the value of variable involve.
Step-by-step explanation:
Example with variable term:
3x=4-x
Add x on both sides of equation:
3x+x=4-x+x
4x=4
x=1
Example with contact involve:
5y+7=12
Subtract 7 from both sides
5x+7-7=12-7
5x=5
x=5/5
x=1
let h (x)= -x-18 find h (3)
Answer:
-21
Step-by-step explanation:
h(x) = -x-18
h(3) = -(3)-18 = -21
Answer:
[tex]h(3)=-21[/tex]
Step-by-step explanation:
One is given the following:
[tex]h(x) = -x - 18[/tex]
One is asked to find the value of ([tex]h(3)[/tex]). Substitute ([tex]3[/tex]) in place of ([tex]x[/tex]) and simplify to evaluate,
[tex]h(x)=-x-18\\\\h(3)=-(3)-18\\\\h(3)=-3-18\\\\h(3)=-21[/tex]
make a the subject of the formula x²=a²-a²w²
Answer:
a = ± [tex]\sqrt{\frac{x^2}{1-w} }[/tex]
Step-by-step explanation:
Given
x² = a² - a²w ← factor out a² from each term on the right side
x² = a²(1 - w) ← divide both sides by (1 - w)
[tex]\frac{x^2}{1-w}[/tex] = a² ( take the square root of both sides )
± [tex]\sqrt{\frac{x^2}{1-w} }[/tex] = a
What expression is equivalent to 9-(-12)
Answer:
9 + 12
Step-by-step explanation:
9 - (-12)
Subtracting a negative is like adding
9 + 12
21
9-(-12) [ - and - became + ]
9 + 12
9 + 12 = 21
What is the greatest common factor of 39 and 3?
Answer:
The GCF of 39 and 3 is 3
Step-by-step explanation:
3/3= 1
39/3= 13
how to do you divide?
Answer:
I HOPE IT WILL HELP YOU A LOT.
Please help I’m failing math
Find the distance between the two points in simplest radical form (-8,-4) (0,-8).
Answer: Distance = 4√5
Concept:
Here, we need to know the concept of the distance formula.
The distance formula is the formula, which is used to find the distance between any two points.
If you are still confused, please refer to the attachment below for a clear version of the formula.
Solve:
Given information
(x₁, y₁) = (-8, -4)
(x₂, y₂) = (0, -8)
Given equation
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute values into the equation
[tex]Distance=\sqrt{(0+8)^2+(-8+4)^2}[/tex]
Simplify values in the parentheses through addition
[tex]Distance=\sqrt{(8)^2+(-4)^2}[/tex]
Simplify exponents
[tex]Distance=\sqrt{64+16}[/tex]
Simplify by addition
[tex]Distance=\sqrt{80}[/tex]
Simplify the radical value into the simplest form
[tex]Distance=4\sqrt{5}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
M decreased by 1??????
Answer:
Step-by-step explanation:
Ssssyiijnbrr
1 months salary 1000 rupees. How many salary in 1 day.
Step-by-step explanation:
1 month has 30 days
so 100 ÷ 30
so ans is 33.3 rupees for one day
MARK AS BRAINLIST IF IT IS USEFUL
John sold a car for 60,000 dollars and made a profit of 20%.what is the cost price of the car
Answer:
72,000
Step-by-step explanation:
20% of 60,000 = 12,000
60,000 + 12,000 = 72,000
Chow,...!
HELPP PLSSS!!! When factoring a number, you can use _[blank 1] as a shortcut. For example, you can tell if 5 is a factor of a number if _[blank 21- Match each blank with the option that correctly fills in that blank. blank 2 blank 1 .: it is even .: divisibility rules :: its last digit is 0 or 5 :: the sum of its digits is a multiple of 3 * long division guessing and checking
Answer:
blank 1: divisibility rules
blank 2: its last digit is 0 or 5
please help me-- financial math!!
The balance on Taylor's credit card is $2000. It has an interest rate of 12.5%. She wants to compare the difference between paying $75 and $100 of the monthly balance. How much does she save in interest and fees if she pays $100 instead of $75?
Answer:
Step-by-step explanation:
2000 * .125/12 = $20.83
at $100 remaining balance = $1920.81
at $75 remaining balance = $1945.81
Please explain how you got the answers also please. Thank you :)
Answer:
x = -2 —> y = 4
x= 0 —> y = 1
x= 3 —> y = 1/8
Step-by-step explanation:
X= –2[tex]y = ( \frac{1}{2} ) ^{x} \\ y = ( \frac{1}{2} ) ^{ - 2} =( \frac{2}{1} ) ^{2} = {2}^{2} = 4[/tex]
X= 0[tex]y = ( \frac{1}{2} ) ^{x} \\ y = ( \frac{1}{2} ) ^{ 0} =1[/tex]
X= 3[tex]y = ( \frac{1}{2} ) ^{x} \\ y = ( \frac{1}{2} ) ^{ 3} = \frac{ {1}^{3} }{ {2}^{3} } = \frac{1}{8} [/tex]
I hope I helped you^_^
Write an equivalent expression by distributing the "−" sign outside the parentheses:
−(−6.8k+8)
Answer:
[tex] - ( - 6.8k + 8) \\ = + 6.8k - 8 \\ thank \: you[/tex]
Katie and mina both commute to work. Katie's commute on train takes 10 minutes more then 1/2 as may minutes as Mina’s commute by car. It takes Katie 30 minutes to get to work which equation determines how many minutes it takes Mina to get to work. (9th grade Algebra 1)
Answer:
It’s A.
Step-by-step explanation:
Took the test and got it right
write 15009 in expanded notation
Answer:
the answer is 10000+5000+9
Answer:
10,000+5,000+9
Step-by-step explanation:
that is the answer
Decide!!!!!!!!!!!!!!
A third alternative to the formulas I suggested in a comment is to use the vector cross product. Recast the three given points as points in 3D space with 0 z-coordinate:
A(20, 21, 0), B(8, 29, 0), and C(13, 1, 0)
Now consider two vectors,
u = B - A = 〈8, 29, 0〉 - 〈20, 21, 0〉 = 〈-12, 8, 0〉
v = C - A = 〈13, 1, 0〉 - 〈20, 21, 0〉 = 〈-7, -20, 0〉
Then recall the cross product identity,
||u × v|| = ||u|| ||v|| |sin(θ)|
where θ is the angle between the two vectors. The magnitude of u × v is equal to the area of the parallelogram spanned by u and v, and hence twice the area of the triangle of interest.
So we have
area = ||1/2 〈-12, 8, 0〉 × 〈-7, -20, 0〉||
area = 1/2 ||〈-12, 8, 0〉 × 〈-7, -20, 0〉||
area = 1/2 ||〈0, 0, 296〉||
area = 296/2
area = 148
Solve for z.
6.6 = 3(z − 16.9) − –0.6
z =
Answer:
z = 18,9
Step-by-step explanation:
[tex]6.6 = 3(z - 16.9) - - 0.6[/tex]
[tex]6.6 = 3z - 50.7 - ( - 0.6)[/tex]
[tex]6.6 = 3z - 50.7 + 0.6[/tex]
[tex]6.6 = 3z - 50.1[/tex]
[tex]6.6 - 3z = - 50.1[/tex]
[tex] - 3z = - 50.1 - 6.6[/tex]
[tex] - 3z = - 56.7[/tex]
[tex]z = 18.9[/tex]