Step-by-step explanation:
[tex] \sin(x) = \frac{12}{13} [/tex]
The value of the trigonometric ratio are; [tex]\sin(x) = \dfrac{\text{12}}{\text{13}}[/tex].
On which triangle can we apply trigonometric ratios?Trigonometric ratio can be defined in terms of ratios of perpendicular, bases and hypotenuse.
Trigonometric ratio are defined only in right angled triangles (triangles whose one angle is of 90 degree measure).
Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle suppose its measure is θ,
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}[/tex]
[tex]\sin(x) = \dfrac{\text{12}}{\text{13}}[/tex]
Therefore, The value of the trigonometric ratio are; [tex]\sin(x) = \dfrac{\text{12}}{\text{13}}[/tex].
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One circle has a circumference of 12 pie Another circle has a circumference of 32 pie What is the ratio of the radius of the smaller circle to the radius of the larger circle?
Answer:
3 : 8
Step-by-step explanation:
The ratio of the radii is equal to the ratio of the circumference, then ratio is
12π : 32π ( divide both parts by 4π )
= 3 : 8
There are 5 seats in a bus. In how many different ways if there are 5 children. How many different ways are there if there are 4 children, and how many different ways are there if there are 3 children.
Answer:
5=1
4=5
i don't really know for the third one sorry but it's more than 11
Step-by-step explanation:
Use braces and digits to indicate the set of whole numbers
Whole numbers are numbers without decimal points greater than or equal to 0.
The set of whole numbers is:
[tex]W =\{0,1,2,3,4.....\}[/tex]
In the introductory part of this solution, I stated that:
Whole numbers do not have decimal pointThe smallest whole number is 0This means that the following numbers are whole numbers:
1, 9, 10, 67
While the following numbers are not:
-1, 9.0, 1.0, -67
Let W be the set of whole numbers; the set is:
[tex]W =\{0,1,2,3,4.....\}[/tex]
The dots after 4 means the set still continues
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Answer:
The set of whole numbers W= {0,1,2,3,........,.....}
Step-by-step explanation:
The whole numbers are numbers that are complete. These numbers do not have a part missing or an additional part (fraction) for example decimals or fractions are not complete or whole numbers.
Braces are curly brackets as shown { }
Digits are written inside the curly brackets to show the set of whole numbers.
The set of whole numbers is denoted by W.
W= {0,1,2,3,......,...}
The rational or irrational numbers which are expressed in decimals are not included in the list of whole numbers.
Will give brainliest to the first person who answers
Answer:
z =86
Step-by-step explanation:
The exterior angle of a triangle is the sum of the opposite interior angles
z + z-39 = z+47
2z-39 = z+47
Subtract z from each side
z-39 = 47
Add 39 from each side
z = 47+39
z =86
The given information is,
To find the required value of z.
Property we use,
The exterior angle of a triangle is the sum of the opposite interior angles.
Now we can get the value of z,
→ z + z-39 = z + 47
→ 2z-39 = z + 47
→ 2z -z = 47 + 39
→ z = 47 + 39
→ [z = 86]
Thus, the required value of z is 86.
Helpppppp plssssss ! Click the image
The graphs below have the same shape. What is the equation of the blue
graph?
Answer:
C
Step-by-step explanation:
the answer is
[tex]{(x + 2)}^{2} [/tex]
Viết khai triển theo công thức nhị thức Niu-tơn (x + 1) ^ 5
Answer:
x^5+5x^4+10x³+10x²+5x+1
Step-by-step explanation:
A ball is dropped from a height of 9 feet and allowed to bounce. Each time the ball bounces, it reaches a height that is23the height of the previous bounce. How many times will the ball be exactly 3 feet above the ground?
I'm assuming you meant to say "it reaches a height that is 2/3 the height of the previous bounce".
We have a geometric sequence with a = 9 as the first term and r = 2/3 as the common ratio.
The nth term is a*(r)^(n-1) = 9*(2/3)^(n-1)
Set this equal to 3 and solve for n. You'll need logs to isolate the exponent.
9*(2/3)^(n-1) = 3
(2/3)^(n-1) = 3/9
(2/3)^(n-1) = 1/3
log[ (2/3)^(n-1) ] = log(1/3)
(n-1)*log(2/3) = log(1/3)
(n-1)*(-0.17609) = -0.47712
n-1 = (-0.47712)/(-0.17609)
n-1 = 2.7095235
n = 2.7095235+1
n = 3.7095235
Unfortunately we don't get a whole number. We can see that the terms of the sequence are:
9, 6, 4, 2.667
Each term is found by multiplying 2/3 by the previous term.
We don't land exactly on "3". The closest we get is 2.667 approximately.
So to answer the question, there is no way to get to exactly 3 feet above the ground based on a whole number of bounces.
For each function, state whether it is linear, quadratic, or exponential.
Answer:
Step-by-step explanation:
Table for function 1,
x y Difference 1 Difference 2
2 10 - -
3 1 1 - 10 = -9 -
4 10 10 - 1 = 9 9 - (-9) = 18
5 37 37 - 10 = 27 27 - 9 = 18
6 82 82 - 37 = 45 45 - 27 = 18
Since, difference 2 is common as 18,
Table will represent a quadratic function.
Table for function 2,
x y Difference 1 Difference 2
5 16 - -
6 19 19 - 16 = 3 -
7 28 28 - 19 = 9 9 - 3 = 6
8 43 43 - 28 = 15 15 - 9 = 6
9 64 64 - 43 = 21 21 - 15 = 6
Since, difference 2 is common as 6,
Table will represent a quadratic function.
Table for function 3,
x y Ratio
1 112 -
2 56 56 ÷ 112 = [tex]\frac{1}{2}[/tex]
3 28 28 ÷ 56 = [tex]\frac{1}{2}[/tex]
4 14 14 ÷ 28 = [tex]\frac{1}{2}[/tex]
5 7 7 ÷ 14 = [tex]\frac{1}{2}[/tex]
Since, ratio is common as [tex]\frac{1}{2}[/tex].
Table will represent an exponential function.
Combine and simplify the following radical expression.
Answer:
[tex]24 \sqrt{5} [/tex]Step-by-step explanation:
[tex]2 \sqrt{20} + 8 \sqrt{45} - \sqrt{80} [/tex]
[tex] = 2 \sqrt{2 \times 2 \times 5} + 8 \sqrt{3 \times 3 \times 5} - \sqrt{2 \times 2 \times 2 \times 2 \times 5} [/tex]
[tex] = 2(2 \sqrt{5} ) + 8(3 \sqrt{5} ) - (4 \sqrt{5} )[/tex]
[tex] = 4 \sqrt{5} + 24 \sqrt{5} - 4 \sqrt{5} [/tex]
[tex] = 24 \sqrt{5} (ans)[/tex]
Answer:
[tex]\huge\boxed{24\sqrt5}[/tex]
Step-by-step explanation:
[tex]2\sqrt{20}+8\sqrt{45}-\sqrt{80}\\\\=2\sqrt{4\cdot5}+8\sqrt{9\cdot5}-\sqrt{16\cdot5}\\\\\text{use}\ \sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\\=2\sqrt4\cdot\sqrt5+8\sqrt9\cdot\sqrt5-\sqrt{16}\cdot\sqrt5\\\\\text{we know}\ a\sqrt{b}=a\cdot\sqrt{b},\ \text{and}\ \sqrt{a}=b\iff b^2=a\\\\\text{Therefore}\\ 2\sqrt{4}=2\cdot\sqrt4=2\cdot2=4\\8\sqrt9=8\cdot\sqrt9=8\cdot3=24\\\sqrt{16}\cdot\sqrt5=4\cdot\sqrt5=4\sqrt5\\\\\text{Therefore}[/tex]
[tex]=2\sqrt4\cdot\sqrt5+8\sqrt9\cdot\sqrt5-\sqrt{16}\cdot\sqrt5=4\sqrt5+24\sqrt5-4\sqrt5\\\\=(4+24-4)\sqrt5=24\sqrt5[/tex]
Problem 5
The sum of the first ten terms of an arithmetic progression consisting of positive integer terms is equal to the sum of the 20th, 21st and 22nd term. If the first term is less than 20, find how many terms are required to give a sum of 960.
Answer:
The answer is 15.
Step-by-step explanation:
Hi there can someone please help me?
What is z and k when k+4z=42
Answer:
Solution given:
we have
k+4z=42
k=42-4z
and
k+4z=42
4z=42-k
dividing both side by 4
[tex]\frac{4z}{4}[/tex]=[tex]\frac{42-k}{4}[/tex]
z=[tex]\bold{\frac{42-k}{4}}[/tex]
Can somebody help me Answer to this ??
X=7
c is the answer:
[tex]3x + 50 = 10x + 1 \\ 10x - 3x = 50 - 1 \\ 7x = 49 \\ x = \frac{49}{7} \\ x = 7[/tex]
The flow of water from a faucet can fill a
3-gallon container in 18 seconds. Give the ratio of gallons to seconds as a rate in gallons per second and as a reduced fraction.
Answer:
3/18 gallons/seconds, or 1/6 gallons/seconds
Step-by-step explanation:
We know that for every 3 gallons, the faucet fills that amount up in 18 seconds. Another way we can write that is "3 gallons for 18 seconds", or 3 gallons / 18 seconds.
Therefore, in terms of gallons to seconds, we can write this as 3 gallons/18 seconds.
One cool thing we can do with fractions is that if we multiply/divide the numerator by the same thing, the fraction is still the same amount, like if we divided by one. For example, if we multiply 1/10 by 10/10 = 1, we would get 10/100 = 1/10, changing the numbers but still keeping the fraction intact. We can apply this concept here to reduce the fraction.
Reducing the fraction means that we want to make the numerator and denominator as small as possible while still keeping them as integers. This means that, if possible, we should divide both the numerator and denominator by their greatest common factor (if it is greater than 1).
To find the greatest common factor, we can list factors and find the greatest one among them.
We have two numbers, 3 and 18.
The factors of 3 are 1 and 3 while the factors of 18 are 1, 2, 3, 6, 9, and 18. The greatest common number among these two is 3. Therefore, we can divide both these numbers by 3 to get
3/18 = 1/6 gallons/seconds as our answer
Here is a number machine input n --> -5 --> x4 --> _
Answer:
4(n - 5)
Step-by-step explanation:
The output is
n - 5 × 4 = 4(n - 5)
The output for the number machine will be 4 ( n - 5 ).
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given the number, the machine is showing the expression written as:-
Output = 4 ( n - 5 )
For every value of n, there will be output.
Therefore, the output for the number machine will be 4 ( n - 5 ).
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Find the value of x that makes m
n.
m
n
(180 - x)^
Answer:
x=180-x
2x=180
x=90
Step-by-step explanation:
Anyone know this question?
Evaluate 4x-2 when x = 5.
A. 18
B. 12
C. 43
O D. 22
Answer:
A: 18
Step-by-step explanation:
1. 4(5) - 2
2. 20 - 2
3. 18
Mr. Lynch bought some oranges and pears.
After giving away 10 oranges, he had twice
as many pears as oranges left. If he had 24
pears in the end, what was the ratio of
oranges to pears in the beginning?
Answer:
11: 12
Step-by-step explanation:
Let the number of oranges and pears Mr Lynch have initially be x and p respectively.
x -10= ½p
2(x -10)= p
p= 2x -20 -----(1)
Since Mr Lynch did not give any pears away, the number of pears at the end is the initial number of pears.
p= 24
Substitute p= 24 into (1):
2x -20= 24
2x= 24 +20 (+20 on both sides)
2x= 44
x= 44 ÷2
x= 22
[tex] \frac{x}{p} = \frac{22}{24} [/tex]
[tex] \frac{x}{p} = \frac{11}{12} [/tex]
Thus the ratio of orange to pears in the beginning is 11: 12.
Please help me!!! I need to finish soon
Answer:
S=47.1cm (to 3s.f.)
Step-by-step explanation:
To find the arc length, S, use the formula S=radius x angle(in radians)
S=10x 3pi/2
=47.1cm (to 3s.f.)
Find the slope of (3,-24)(19,-48)
Answer:
-3/2
Step-by-step explanation:
To find the slope, we use the slope formula
m = (y2-y1)/(x2-x1)
= (-48- -24)/(19 -3)
= (-48+24)/(19-3)
= -24/16
= -3/2
Answer:
[tex]-\frac{3}{2}[/tex]
Step-by-step explanation:
The slope of a line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let:
[tex](x_1, y_1)=(3, -24)\\(x_2, y_2)=(19, -48)[/tex]
Substitute into slope formula:
[tex]m=\frac{-48-(-24)}{19-3}=\frac{-24}{16}=\boxed{-\frac{3}{2}}[/tex]
help me with this math question
Step-by-step explanation:
Option D
As time increases, the temprature of soup decreases..
hope it helps
Which of the following is an example of linear growth?
A. A baby gains 0.5% of its weight each week
B. An investment of $100 at an annual interest rate of 0.75%, compounded monthly
c. Depositing $5.00 in a savings account each week for t weeks
D. A bacterial culture doubles in size each day
Answer:
c. Depositing $5.00 in a savings account each week for t weeks
Step-by-step explanation:
Depositing $5.00 in a savings account each week for t weeks will be the correct example of linear growth.
What is a linear function?A linear function is a function in which any two quantity varies linearly with respect to each other.
In another word, a linear function is that function whose slope will be constant and will plot a straight line.
A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
The linear function will be that where the value of the next period can be calculated
For example y =2x here we can calculate y by just x
In given option (C) we can see that the difference between any two consecutive months can be calculated next month.
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Literally what is this lol
Answer:
i think the first one- bc it should be 11x5pi but it would still end up as 55pi
Step-by-step explanation:
sorry if that doesnt help
Which statement are true regarding the diagram?
Answer: 2,4 are definite answers i don't know abt the others- unfortunately..
Step-by-step explanation: Im in mid school..
Find DC, given that line AD is the angle bisector of < CAB.
Answer:
8
Step-by-step explanation:
LINE DC =BD
because line AD is a bisector of CAB
Dividing line CAD into two equal half's
solve for x. round to the nearest tenth of a degree, if necessary.
x=30°
Answer:
Cos x°=adjacent/hypotenuse
Cos x°=45/52
x°=Cos-¹(45/52)
x°=30°
Simplify. 1224√
THIS IS A KEYSTONE ALGEBRA THING LOL
Answer:
6[tex]\sqrt{34}[/tex]
Step-by-step explanation:
[tex]\sqrt{1224}\\[/tex] = [tex]\sqrt{36*34}[/tex] = 6[tex]\sqrt{34}[/tex]
Dave has been running every day to get
in shape for the track season. He wants
to determine his average rate.
Dave learned the following formula in his
science class:
d = r.t
where
d = distance
r = rate
t = time
Answer:
r = d/t
Step-by-step explanation:
Given:
d = r * t
where,
d = distance
r = rate
t = time
Rewrite the equation to determine Dave's rate
d = r * t
d = rt
Divide both sides by the
d / t = rt / t
d / t = r
r = d/t
Average rate, r = d/t
Identify the slope (m) and the y-intercept (b) of each line a) y= x+7 slope = y intercept = b) y = -3x slope = y intercept =
Answer:
a) y= x+7
The slope is 1 and the y intercept is 7
b) y = -3x
The slope is -3 and the y intercept is 0
Step-by-step explanation:
The slope intercept form of the equation of a line is
y = mx+b where m is the slope and b is the y intercept
a) y= x+7
The slope is 1 and the y intercept is 7
b) y = -3x
The slope is -3 and the y intercept is 0