Answer:
Step-by-step explanation:
(√63 + 144)/5 = (3√7 + 144)/5 = 0.6√7 + 28.8
Use a double-angle or half-angle identity to find the exact value of each expression
If 180° < θ < 270°, then 90° < θ/2 < 135°, which places θ/2 in the second quadrant so that sin(θ/2) > 0 and cos(θ/2) < 0.
Recall that
cos²(θ/2) = (1 + cos(θ))/2
==> cos(θ/2) = -√[(1 + (-15/17))/2] = -1/√17
and
sin²(θ/2) = (1 - cos(θ))/2
==> sin(θ/2) = +√[(1 - (-15/17))/2] = 4/√17
Then
tan(θ/2) = sin(θ/2) / cos(θ/2)
… = (4/√17) / (-1/√17)
… = -4
SOMEONE HELP ME PLEASE
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities.
You are setting the combination on a five-digit lock. You want to use the numbers 12345 but you don't care what order they are in.
Answer:
It's a combination, BUT...
Step-by-step explanation:
Definition: A combination is a grouping of outcomes in which the order does not matter. That's the difference between combination and permutation.
Combination Formula: nCr = (n!)/[r!(n-r)!)] where n stands for number of things and r the pair chosen
Applied to this case: We have n=5 (12345) and r=5 for the 5-digit lock combination.
5C5 = (5!)/[5!(5-5)] = 1
But!! As you can see, we cannot have 1 possible combinations so.. We have to assume that this is a permutation!!! Conceptually, this looks pretty much like a combination, but being the same range as number of items, we conclude that it's a permutation.
Permutation Formula: nPr = (n!)/(n-r)!
nPr = (5!)/(5-5)! = 120
Well, this looks way more accurate now, right?
Final Answer: The scenario involves a permutation, and there's 120 possible combinations of those 5 numbers in a 5-digit lock.
Instructions: Find the measure of the indicated angle to the nearest degree.
Step-by-step explanation:
I don't have a calculator with me right now but I can give you the equation to work out your answer.
cos-1(35/38)
There should be a function of "cos-1" on you're calculator, not just "cos"
hope it helps :)
HELP ITS DUE IN THE MORNING AND ITS 3:57
Answer:
A " (1,-2)
B " (4,0)
C " (6,-3)
Step-by-step explanation:
Hope it helped.
° ° °
Find the volume. Leave answer in exact form (in terms of π)
Answer:
704π
Step-by-step explanation:
V = π×r²×h
= π×8²×11
= 704π yd³
The midpoint of a segment is (6,−4) and one endpoint is (13,−2). Find the coordinates of the other endpoint.
A. (20, -6)
B. (-1, 0)
C. (-1, -6)
D. (20, 0)
Answer:
(-1,-6)
Step-by-step explanation:
(13 + x)/2 = 6
13+x= 12
x = -1
~~~~~~~~~~~~~~~
(-2 + y ) / 2 = -4
-2 + y = -8
y = -6
The coordinates of the other endpoint will be (-1,-6). The correct option is C.
What is the midpoint of the line?Divide the measurement of the distance between the two end locations by 2. The middle of that line is located at this separation from either end.
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
Given that the midpoint of a segment is (6,−4) and one endpoint is (13,−2).
The x- coordinate will be calculated as:-
(13 + x)/2 = 6
13+x= 12
x = -1
The y-coordinate will be calculated as:-
(-2 + y ) / 2 = -4
-2 + y = -8
y = -6
Therefore, the coordinates of the other endpoint will be (-1,-6). The correct option is C.
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Please help me out . Find x please
Answer:
on my screen I cant see anything sorry!
Step-by-step explanation:
Please help me with this problem.
Answer:
1/4a -1/6b + 1/10c
Step-by-step explanation:
1/2 a -1/3 b + 1/5c + -1/4a + 1/6 b - 1/10c
Combine like terms
1/2a - 1/4a -1/3b + 1/6b +1/5c - 1/10 c
2/4a -1/4a -2/6b + 1/6b +2/10c -1/10c
1/4a -1/6b + 1/10c
Trigonometric ratios
class 9
please answer my questions
Step-by-step explanation:
Hi there!
Please see the answer in the picture.
Hope it helps!
1. Approach
One is given a trigonometric equation with and one is asked to prove that it is true. Using the attached image, combined with the knowledge of trigonometry, one can evaluate each trigonometric function. Then one can simplify each ratio to solve. To yield the most accurate result, one has to each of the ratios in a fractional form, rather than simplifying it into a decimal form. Remember the right angle trigonometric ratios, these ratios describe the relationship between the sides and angles in a right triangle. Such ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}\\\\csc(\theta)=\frac{hypotenuse}{opposite}\\\\sec(\theta)=\frac{hypotenuse}{adjacent}\\\\cot(\theta)=\frac{adjacent}{opposite}[/tex]
Please note that the terms (opposite) and (adjacent) are relative to the angle uses in the ratio, however the term (hypotenuse) refers to the side opposite the right angle, this side never changes its name. Use these ratios to evaluate the trigonometric functions. Then simplify to prove the identity.
2. Problem (9)
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
As per the attached image, the following statements regarding the value of each ratio can be made:
[tex]sin(60)=\frac{\sqrt{3}}{2}\\\\cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cos(60)=\frac{1}{2}[/tex]
Substitute,
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
Simplify,
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}[/tex]
Thus, this equation is true.
2. Problem (10)
Use a similar strategy to evaluate this equation,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
Use the attached image to evaluate the ratios.
[tex]cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cot(60)=\frac{1}{\sqrt{3}}[/tex]
Substitute,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
Simplify,
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}+1}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
Rationalize the denominator,
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}-1}[/tex]
[tex]2-\sqrt{3}=\frac{(\sqrt{3}-1)^2}{3-1}[/tex]
[tex]2-\sqrt{3}=\frac{3-2\sqrt{3}+1}{2}[/tex]
[tex]2-\sqrt{3}=\frac{4-2\sqrt{3}}{2}[/tex]
[tex]2-\sqrt{3}=2-\sqrt{3}[/tex]
Therefore, this equation is also true.
Help what is x
When x^5 is 225
Answer:
Solution given:
x^5=225
we have
x=[tex] \sqrt[5]{225} [/tex]
x=2.9541
Hello!
[tex] \bf {x}^{5} = 225[/tex]
Extract the radical on both sides of the equation.[tex] \bf x = \sqrt[5]{225} [/tex]
[tex] \bf x ≈2.95418[/tex]
Answer: x ≈ 2,95418
Good luck! :)
Solve the following quadratic function
by utilizing the square root method.
y = 100 – x2
Answer:
x = ± 10
Step-by-step explanation:
To solve the equation let y = 0 , that is
0 = 100 - x²( add x² to both sides )
x² = 100 (I take the square root of both sides )
x = ± [tex]\sqrt{100}[/tex] = ± 10
Then solution is x = - 10, x = 10
Answer:
10
Step-by-step explanation:
the guy on top put -10 he's right but it's just 10
HELPPPP MEEEEE OUTTTTT PLEASEEEE ASAPPPP!!!!
Answer:
sin X =35/37
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin X = opp side / hypotenuse
sin X =35/37
Can someone help me please ?
Answer:
I would say D is your answer
Step-by-step explanation:
Answer:
the fourth one
use mathaway its like my best friend for math!!!
Step-by-step explanation:
PLEASE HELPP URGENT
20 points!!!
Guys Help me
Does (4, 7) make the equation y = 2x + 7 true?
Answer:
false
Step-by-step explanation:
x=4andy=7
2×4+7 isnot equal to 7
Answer:
Tue equation is
y=2x+7
So, the answer is
(2,7)
And (4,7) is wrong
For each graph below, state whether it represents a function.
Graph exists as an illustration of any object or a physical format by dots, lines, etc.
What is graph function?The graph of a function f exists the set of all points in the plane of the form (x, f(x)). We could also describe the graph of f to be the graph of the equation y = f(x). So, the graph of a function exists in a particular case of the graph of an equation.
A function is defined as a connection between a set of inputs containing one output each. In simple words, a function exists as an association between inputs where each input is connected to exactly one output. Every function includes a domain and codomain or range. A function exists generally represented by f(x) where x is the input.
From the given figure,
Graph 1 exists a function.
Graph 2 exists a function.
Graph 3 doesn't exist as a function.
Graph 4 exists a function.
Graph 5 doesn't exist as a function.
Graph 6 doesn't exist as a function.
Hence, Graph exists as a representative of any object or a physical design by dots, lines, etc.
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How many gallons equal 26 liters
Answer:
6.8 gallions i believe. im not quite sure
Solve the system of equations below by graphing both equations with a
pencil and paper. What is the solution?
y=-x-1
y= x+3
A. (0,3)
B. (-2,1)
C. (-1,2)
O D. (0, -1)
Graph: f(x) = 3/2 (2)x
Step 1: Calculate the initial value of the function.
f(0)=
Answer:
Step 1: 1.5
Step 2: Plot the points (0, 1.5)
Step 3: 3, then 0.75
Step 4: Plot the points (1, 3) and (-1, 0.75)
Step 5: y=0
Step-by-step explanation:
Ur welcome and have a nice day :>
The initial value of the function f(x) = 3/2 (2)^x is 3/2
How to calculate the initial value of the function?The function expression is given s:
f(x) = 3/2 (2)^x
Substitute 0 for x
f(0) = 3/2 (2)^0
Evaluate the exponent
f(0) = 3/2 * 1
Evaluate the product
f(0) = 3/2
Hence, the initial value of the function is 3/2
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Construct 5 equivalent equations for the equation - 3 + 2x = -4.
Answer:C
Step-by-step explanation:
find the missing length indicated
Answer:
240
Step-by-step explanation:
We are given a right triangle. Based on the leg rule, the following equation shows how the length of a leg in a right triangle relates with the segments connected to the hypotenuse:
Hypotenuse/leg = leg/part
Where,
Hypo = 400
Leg = x
Part = 144
Substitute
400/x = x/144
Cross multiply
400*144 = x*x
57,600 = x²
√57,600 = x
240 = x
x = 240
The equation of line a is y=-x+ 3. If line b runs perpendicular to line a and
passes through (2, 6), what would be the equation of line b?
Answer:
y = 4x -2
Step-by-step explanation:
y = 4x + b
6 = 4(2) + b
6 = 8 + b
-2 = b
find the mean value of the following. 5, 11, 4, 10, 8, 6
u4gent help needed
help me with the question of o.math
Answer:
1≤f(x)≤5
Step-by-step explanation:
-1≤x≤1
-2≤2x≤2 (Multiplied by 2 both side)
-2+3≤2x+3≤2+3 (Adding three both sides)
1≤f(x)≤5
Anyone knows the answer?
Answer:
D) (2,-1)
Step-by-step explanation:
These are two concentric circles of radius 3 and 4 at the origin. That means that any point within the inner is also within the outer. So focusing on the inner, the points plugged into its equation must be less than or equal to the radius squared or 9. That is only valid with point D.
Describe the pattern in the following sequence and list the next three terms:
4, 8, 16, 32, ...
I’ll mark brainliest! Please help me
help pls with explanation!!!
Answer:
18c - 30d + 36
Step-by-step explanation:
To apply the distributive property, we must "distribute" (multiply) the outer term by the terms in the parentheses. In this case, the outer term is 6, and the inner terms are 3c, 5d, and 6. Then, if there's any like terms, you must combine them.
6(3c - 5d + 6)
(6 · 3c) + (6 · -5d) + (6 · 6)
18c + -30d + 36
As you can see, there's no like terms in this expression, so the equivalent expression to 6(3c - 5d + 6) is 18c + -30d + 36.
Given: APRS, RS=10
mZP=45º, mzS=600
Find: Perimeter of APRS
Answer:
Perimeter of ΔPRS = 35.91 units
Step-by-step explanation:
From the figure attached,
By applying triangle sum theorem in the given triangle PRS,
m∠P + m∠R + m∠S = 180°
45° + m∠R + 60° = 180°
m∠R = 75°
By applying sine rule,
[tex]\frac{\text{sinP}}{RS}= \frac{\text{sinS}}{PR}=\frac{\text{sinR}}{PS}[/tex]
[tex]\frac{\text{sin}(45^{\circ})}{10}= \frac{\text{sin}(60^{\circ})}{PR}=\frac{\text{sin}(75^{\circ})}{PS}[/tex]
[tex]\frac{\text{sin}(45^{\circ})}{10}= \frac{\text{sin}(60^{\circ})}{PR}[/tex]
PR = 12.25 units
[tex]\frac{\text{sin}(45^{\circ})}{10}=\frac{\text{sin}(75^{\circ})}{PS}[/tex]
PS = 13.66 units
Perimeter of triangle PRS = PR + PS + RS
= 12.25 + 13.66 + 10
= 35.91
Which ordered pair can be plotted together with these four points, so the resulting graph still represents a function?
•(2, -1)
•(2, -2)
•(-2, 2)
•(-1, 2)
Answer:
-1,2 can be plotted together with these four points ...
1 pump can fill a pool in 8 hours the other pump can fill the pool in 10 hours if both of the pumps were turned on at the same time to fill the pool how long will it take
Answer:
4 4/9 hoursStep-by-step explanation:
In one hour pump1 can fill 1/8 of the tank and pump2 can fill 1/10 of the tank.
Two pumps can fill:
1/8 + 1/10 = 5/40 + 4/40 = 9/40 of the tank in one hourTime required to fill the tank:
1/(9/40) = 40/9 = 4 4/9 hours