Answer:
a) 1/2, b) = - sqrt(3) / 2
Step-by-step explanation:
a) Let A = 120 degree, B = 180 degree
Using cosine sum is cos(120+180) = cos(120)*cos(180) - sin(120)* sin(180)
which will give you 1/2
b) Let A = 360, B = 60 degree
Using sine difference: sin(360-60) = sin(360) cos(60) - cos(360) sin (60)
gives you -sqrt(3)/2
Cos (300°) using the cosine sum identity is 1/2.
sin (300°) using the sine difference identity is √3/2.
What are Trigonometric Ratios?Trigonometric ratios are the ratios which is described for two sides of a right angled triangle.
The main three trigonometric ratios are sine, cosine and tangent functions.
Part A :
The cosine sum identity is,
cos (A + B) = cos (A) cos (B) - sin (A) sin (B)
We can write cos (300°) as,
cos (300°) = cos (180° + 120°)
= cos (180°) cos (120°) - sin (180°) sin (120°)
sin (180°) = 0 and cos (180°) = -1
So, cos (300°) = -cos (120°) = -(-1/2) = 1/2
Part B :
Sine difference identity is,
Sin (A - B) = sin (A) cos (B) - cos(A) sin (B)
We can write sin (300°) as,
sin (300°) = sin (360° - 60°)
= sin (360°) cos(60°) - cos(360°) sin (60°)
= - sin (60°)
= -√3 / 2
Hence the value of Cos (300°) using the cosine sum identity is 1/2 and the sin (300°) using the sine difference identity is √3/2.
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!!
Mum spent 3/5 of her money and put 1/8 of the remainder in the bank. If she had $750 left, how much did she start with?
Answer:
$2142.86
Step-by-step explanation:
The remaining part of her money, after spending 3/5 of it and depositing 1/8 of it is equal to $750.
===============================================================
Retracing the steps :
⇒ She put 1/8 of the remainder in the bank, which gives $750
⇒ R - R/8 = 750
⇒ 7R/8 = 750
⇒ R = 750/7 × 8
⇒ R = 107.142857 × 8
⇒ R = 857.142856
* Don't worry, we'll simplify at the end of the answer *
=============================================================
Now, this remainder is what was left after spending 3/5 of it.
⇒ T - 3/5T = 857.142856
⇒ 2/5T = 857.142856
⇒ T = 857.142856/2 × 5
⇒ T = 428.571428 × 5
⇒ T = $2142.86 (nearest cent)
let me know asap PLEASE
Answer:
the correct answer is B
Step-by-step explanation:
A function g is the inverse for the function f if for y-f(x), x-g(y)
y=7x-6
Replace x with y
x=7y-6
Solve for y in x=7y-6
Switch sides
7y-6=x
Add 6 to both sides
7y-6+6=x+6
Simplify
7y=x+6
Divide both sides by the coefficient of y, which is 7. We have:
7y/7 = x/7+6/7
7y & 7 are cancelled out and we're left with: x/7 & 6/7
Now we find the LCM of the denominators which is 7.
7 divide the denominators equal 1, we use the to multiply the numerators, x & 6
our final answer= x+6/7
I hope this helps.
im lost can someone help?
What is the permimeter of a 4’ square
Answer:
16'
Step-by-step explanation:
4'
4 equal sides
4+4+4+4=16
Answer: Permimeter of a 4’ square is 16.
Step-by-step explanation:
given that:
• length = 4
∴ Perimeter of Square = 4 x length
⇒ P = 4 × 4
⇒ P = 16 units ...answer...
hope that helps...
Need help ASAP
Stuck on this question and need help
Answer:
Factory A = 1200
Factory B= 1350
Factory C= 1050
Factory D = 1100
Step-by-step explanation:
Factory B as the fastest rate of production
Match each expression on the left with an equivalent expression on the right. Some answer choices on the right will not be used.
Answer:
The answer is below :
What is the volume of this rectangular
pyramid?
3 m
4 m
Submit
5 m
cubic meters
The volume of the given rectangular pyramid.
Solution:[tex]\large\boxed{Formula:V=\frac{1}{3}lbh}[/tex]
First, multiply the length (5), breadth (4) and height (3).
[tex]5×4×3[/tex]
[tex]= 60 \: cm [/tex]
Now, divide 60 by 3.
[tex]\frac{60}{3}[/tex]
[tex]\large\boxed{V= 20 \: {m}^{3}}[/tex]
Therefore, the volume of the given rectangular pyramid is 20 cubic meters.
A 7-pack of DVDs costs $31.71. What is the unit price?
The unit price of each is $4,53
Unit price is the value of each separate item. As per the listing, 7 DVD packs in total are $31,75. So, to know the value of each DVD, let's divide the total value - by the 7 DVDs.
$31,75 ÷ 7 = $4,53
Therefore, the unit value of each DVD is $4,53
What is the slope of the line y=3-x/8?
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Consider the graph of the function f(x)=In x. Match each transformation of function f with a feature of the transformed function. function decreases as x increases x-intercept at y-intercept at
The matching of each transformed function is as follows;
g(x) = 2f(x) → y-intercept at (0,2)
h(x) = f(x) + 2 → asymptote of y=2
j(x) = f(x + 2) → y-intercept at (0,4)
m(x) = function decreases as x increases
How to match transformations?A function is simply defined as a relationship between the inputs and the outputs. Now, we want to map each transformed function.
From the graph of this question as shown in the attached brainly link, the correct matching of each transformation of function f(x) = In x with a feature of the transformed function are as follows;
g(x) = 2f(x) → y-intercept at (0,2)
h(x) = f(x) + 2 → asymptote of y=2
j(x) = f(x + 2) → y-intercept at (0,4)
m(x) = function decreases as x increases
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2x²-8x-10
how do i factor this explains step:)
Answer:
Step-by-step explanation:
Solution
The distributive property is one of the handiest tools when factoring. You can't use it all the time, but it makes this problem so much easier. Use the distributive property to factor out the 2 from all three terms.
2(x^2 - 4x - 5)
Notice how much easier the problem got. There are only 2 integers that divide into 5. One of them is 5 and the other is one. So the solution is going to look like this
2(x 5) (x 1)
But what do you put in the space? Your choice is between a plus or a minus. Look to the middle term to find out. It is a minus 4. That means that the 5 must be minus because 5 is bigger than 1.
2(x - 5)(x 1 )
So what about the second bracket? It has to be plus. An odd number of minus signs always gives a minus. We used up the one minus we had so the one must have a plus in front of it.
2(x - 5)(x + 1 )
Each statement describes a transformation of the graph of y = ln x. Which statement correctly describes the graph of y = ln(x - 7) + 3?
The statement correctly describes the graph of y = ln(x - 7) + 3 is translated 3 units up as well as 7 units to the right.
what is the graph of logarithmic function?The graph of a logarithmic function has a vertical asymptote at x = 0. The graph of a logarithmic function will decrease from left to right
if 0 < b < 1. And if the base of the function is greater than 1, b > 1, then the graph will increase from left to right.
Given graph : y = ln(x), has a vertical and horizontal translation.
As we know, y = ln(x - h) + k | where h is the vertical shift, and k is the horizontal shift.
If ln(x - k), then the graph is translated right k units.If ln(x + k), then the graph is translated left k units.If ln(x) + h, then the graph is translated up h units.If ln(x) - h, then the graph is translated down h units.Therefore, comparing y = ln(x - 7) + 3 it with different function we can write the graph of y = ln(x - 7) + 3 is translated 3 units up as well as 7 units to the right.
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Round your answer to the nearest tenth if necessary. Use 3.14 for .
A building can be approximated by a cylinder that is 100 meters in diameter and 30 meters in height. Find
its volume.
Its volume is approximately
m³.
OMG THIS IS SO HARD!!
Answer:
235500m3
Step-by-step explanation:
Volume of Cylinder= πr^2h
π=3.14, D=100m, r=D/2, r=100/2, r=50m, h=30m
πr^2h= 3.14×50×50×30
=3.14×75000
=235500m3
Combine like terms to simplify the expression:
-50 m+ 10-3 m+ (-13) =
[tex] - 50m + 10 - 3m + ( - 13) \\ - 50m + 10 - 3m - 13 \\ - 53m - 3[/tex]
Hope it helps
please give brainliest
What proportion could you use to
find the value of x?
Answer:
short leg : long leg
x : 11 = 3 : x
Step-by-step explanation:
short leg : long leg
x : 11 = 3 : x
[tex]\implies \sf \dfrac{x}{11}=\dfrac{3}{x}[/tex]
[tex]\implies \sf x^2=33[/tex]
[tex]\implies \sf x=\sqrt{33}[/tex]
Answer:
3/x=x/11
Step-by-step explanation:
1 what is sum of the interior angles of ABCD what is the sum of the exterior angles of CHFE 3 which sides are parallel to CE 4 whicl side id perpendoicular to CE 5 what is the of the measure of
Given that ABCD is a parallelogram, the sum of its interior angles is:
360°
A parallelogram is a rectilinear two-dimensional figure with four sides whose opposite sides are parallel. See the image attached.
What is the sum of the exterior angles of CHFE?The sum of the exterior angles of any Triangle or any polygon is 360°. Hence, the sum of the exterior angles of CHFE (a polygon) is 360°.
Which sides are parallel to CE?The sides that are parallel to CE are:
FH
AD and
IJ.The side that are perpendicular to CE is side side HH, hence we can state that:
CE ⊥ EH, because both lines intersect each other at right angles.
Because the sum of angles in a triangle is 180° and we already have ∠CEH to be equal to ∠90° hence,
∠C + ∠H? = 180° - 90°
= 90°
What is the measure of the exterior angles of a Regular Pentagon?The measure of the exterior angles of a regular pentagon is 72°
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Which expression is not a polynomial?
Answer:
the first choice is not a polynomial because you can't divide by a variable.
Segment AB with endpoints at A(6, 5) and B(6, 15) is partitioned by point P according to the ratio of 3:2. Find the coordinate of point P.
[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(6,5)\qquad B(6,15)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:2} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{3}{2}\implies \cfrac{A}{B} = \cfrac{3}{2}\implies 2A=3B\implies 2(6,5)=3(6,15)[/tex]
[tex](\stackrel{x}{12}~~,~~ \stackrel{y}{10})=(\stackrel{x}{18}~~,~~ \stackrel{y}{45})\implies P=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{12 +18}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{10 +45}}{3+2} \right)} \\\\\\ P=\left( \cfrac{30}{5}~~,~~\cfrac{55}{5} \right)\implies P=(6~~,~~11)[/tex]
Solve the following system of equations.
f(x) = 3x² - 7x-2
g(x) = -2x² +8
Answer:
f(x) = 3x²-7x-2
answer: (7+- √73)/6
g(x) = -2x² +8
answer:
x = +-2
Step-by-step explanation:
picture is attached
quadratic formula
click on the screenshot
tn=2(n-1)
Given the formula for the nth term, state the first 5 terms of each sequence.
Answer:
0, 2, 4, 6, 8
Step-by-step explanation:
substitute 1 for n in first term, 2 for n in second term, 3 for n in third term, 4 for n in fourth term, 5 for n in fifth term
2 (1) -2 = 0 first term
2 (2)-2 = 2 second
2 (3)-2 = 4 third
2 (4)-2 =6 fourth
2 (5)-2 =8 fifth
The graph of which of the following equations contains the point (-3,0)?
A. 22+y=6
B. x - 2y = 6
C. -x + 2y = 6
D. -2x + y = 6
Answer:
B. x-2y=6
Step-by-step explanation:
m || n, find the value of x.
m
n
(6x+16)⁰
(8x-18)°
Please help! I’ll give good review
Step-by-step explanation:
please mark me as brainlest
change the sign of the x-coordinate and keep the sign of the y-coordinate the same.
IT doesn't make any sense
HELP WITH THE RIGHT ANSWER FOR BRAINLIEST!!!
Answer: this is the wrong answer
Step-by-step explanation:
Which of the following are solutions to the equation below?
Check all that apply. x^2 + 6x + 9= 20
Use the drop downs to determine which symbols
would complete the inequality for the domain.
-4 _(a)_x__(b) 4
(a)
less than or equal to O
(b)
less than or equal to
less than
greater than or equal to
greater than
-5
5
ty
5
x
The domain of the graph is x ≥ -4
How to determine the domain?From the given graph, we have the following highlights:
The x values start from -4The x value moves to the right of the graph (this means greater than)There is a closed circle at the smallest x value (this means equal to)Greater than and equal to are represented by ≥.
This means that the symbol that completes the domain of the graph is ≥
Hence, the domain of the graph is x ≥ -4
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PLEASE GOD HELP ME!!!!
Another expression for the given rational function is [tex]x =r^\frac{1}{2}s^\frac{1}{2}[/tex]
Indices expressionGiven the rational function expressed as:
x = √rs
We can reconstruct the expression by writing it using exponents as shown;
[tex]x =\sqrt{rs}=(rs)^{\frac{1}{2} }[/tex]
Separate to have:
[tex]x =r^\frac{1}{2}s^\frac{1}{2}[/tex]
Hence another expression for the given rational function is [tex]x =r^\frac{1}{2}s^\frac{1}{2}[/tex]
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The angle measures of quadrilateral RSTU are shown.
m∠R = (2x)°
m∠S = (3x – 35)°
m∠T = (x + 35)°
The measure of angle U is unknown. Can quadrilateral RSTU be a parallelogram?
Yes, opposite angles R and T are congruent to each other if x = 35.
Yes, consecutive angles R and S are congruent to each other if x = 35.
No, if x = 35, all three given angles measure 70°. The fourth angle would measure 150°.
No, if x = 35, the three given angle measures make it impossible for the figure to be a quadrilateral.
The quadrilateral RSTU be a parallelogram if opposite angles R and T are congruent to each other if x = 35 option first is correct.
What is quadrilateral?It is defined as the four-sided polygon in geometry having four edges and four corners.
We have:
The angle measures of quadrilateral RSTU are shown.
m∠R = (2x)°
m∠S = (3x – 35)°
m∠T = (x + 35)°
If R and T are congruent:
2x = x + 35
x = 35 degree
Opposite angles R and T are congruent to each other if x = 35.
Thus, the quadrilateral RSTU be a parallelogram if opposite angles R and T are congruent to each other if x = 35 option first is correct.
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Answer:
It's c
Step-by-step explanation:
On edge 2023
Which clock shows 11:22?
A.
A clock shows the hour hand slightly past 11 and the minute hand at one mark past the 3.
B.
A clock shows the hour hand slightly past 11 and the minute hand at 6.
C.
A clock shows the hour hand slightly past 11 and the minute hand at two marks past the 4.
D.
A clock shows the hour hand slightly past 11 and the minute hand at one mark past the 2.
Answer:
Option C
Step-by-step explanation:
A clock shows the hour hand slightly past 11 and the minute hand at two marks past the 4.
5/6 of all the money in Salma's bank account is ₹55,000. how much money does Salma have in her bank account?
please answer
Answer:
₹66,000
Step-by-step explanation:
If 5/6 is 55,000 then just multiply 55,000 by the reciprocal 6/5 to get 66,000