The given identity sin(x+ y) - sin (x- y) = 2 cos x sin y has been verified
The identity is
sin(x+ y) - sin (x- y) = 2 cos x sin y
Here we have to use the trigonometric function
Consider the right hand side of the equation
We know
sin (x+ y) = sin x cos y + cos x sin y
sin (x-y) = sin x cos y - cos x sin y
Then
sin(x+ y) - sin (x- y) = sin x cos y + cos x sin y - (sin x cos y - cos x sin y)
= sin x cos y + cos x sin y - sin x cos y + cos x sin y
Eliminate the terms
= cos x sin y + cos x sin y
= 2 cos x sin y
Hence, the given identity sin(x+ y) - sin (x- y) = 2 cos x sin y has been verified
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Jill earns $264.50 a week. She is married and claims 3 allowances. What amount is withheld weekly for federal income tax?
As Jill claims 3 allowances then the amount which is withheld weekly for federal income tax is $11.
Given, Jill earns $264.50 a week.
She is married and claims 3 allowances.
From the table if the wage of a married person is at least $260 but less than $270 and has 3 allowances then weekly income tax is $11.
Individual federal income tax rates in the US are progressive, which means that they rise in proportion to taxable income. Federal income tax rates range from 10% to 37%, and they become effective at a certain level of income. Tax brackets are the ranges of income that the rates apply to. Each tax bracket has a different rate of taxation that applies to certain types of income.
Hence the amount is $11 for federal tax.
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Last night, Luis read 75% more pages than Dayja, and Dayja read 75% more pages than Michael. If Dayja read 84 pages, how many pages did Luis, Dayja, and Michael read all together?
Answer:
Total pages read = 279 pages
Step-by-step explanation:
Let L, D, and M stand for the pages read by Luis, Dayja, and Michael, respectively.
We learn that:
L = 1.75D, [Luis read 75% more pages than Dayja]
D = 1.75M, and [Dayja read 75% more pages than Michael]
D = 84 [Dayja read 84 pages]
We want the sum of L, D, and M
Total pages = L + D + M
We have three equations and 3 unknowns. We should be able to find a solution by rearranging and substituting.
Total pages = L + D + M
We can substitute L=1.7D and rearrange D = 1.75 M to M = D/1.75
Total pages = L + D + M
Total pages = 1.7D + D + D/1.75
Total pages = D(1.7 + 1 + 1/1.75) [Isolate the D, for optional simplification]
Total pages = D(3.271)
We know D = 84, so:
Total pages = 84(3.271)
Total pages = 274.8
We'll round that to 275 pages.
Check:
L = 1.75D: L read 1.75*275 or 147 pages
D read 84 pages
D = 1.75M, or M = D/1.75; M read 84/1.75) or 48 pages
Total pages read = 147 + 84 + 48
Total pages read = 279 pages
you are driving a 30 foot bus on a highway at 45 mph. the road is dry and visibility is good. a safe distance between you and the vehicle ahead of you should be at least:
I also need help with this question
Answer: (-3, 3)
Step-by-step explanation:
See the attached image for my work. First, you need to know the quadrants. In order from the top right counter-clockwise, it goes I (1), II (2), III (3), and IV (4).
Next, we will count up five units since Quadrant II is above the point, in Quadrant III.
Please find the coordinates and also reflect the points on the axis’s, and please demonstrate and plot the points on the graph too reflect it.
A' = (1, 3)
B' = (0, 6)
C' = (-3, 5)
D' = (-2, 2)
Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.an = 4n − 5
Okay, here we have this:
Considering the provided sequence, we are going to find the requested first five terms of the sequence, so we obtain the following:
So what we will do is replace n from 1 to 5, we have:
n=1:
an=4n-5
a1=4(1)-5
a1=4-5
a1=-1
n=2:
an=4n-5
a2=4(2)-5
a2=8-5
a2=3
n=3:
an=4n-5
a3=4(3)-5
a3=12-5
a3=7
n=4:
an=4n-5
a4=4(4)-5
a4=16-5
a4=11
n=5:
an=4n-5
a5=4(5)-5
a5=20-5
a5=15
Finally we obtain that the first five terms are: -1, 3, 7, 11, 15
The foot of a ladder is 1.5 m from a vertical wall. The ladder makes an angle of 68° with the horizontal. How far up the wall does the ladder reach? Draw a picture and show work!
The length of the wall for the ladder reach will be 3.4 meter.
What is mean by Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The foot of a ladder is 1.5 m from a vertical wall.
And, The ladder makes an angle of 68° with the horizontal.
Now,
By the figure,
The length of BC = 1.5 m
The measure of ∠ACB = 68°
So, Find the length of AC as;
cos 68° = 1.5 / AC
AC = 1.5 / 0.44
AC = 3.4 m
Therefore,
The length of the wall for the ladder reach will be 3.4 meter.
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What is two divided by three I’ve two
Answer:
2 divided by 3 is 0.6 or 2/3
Step-by-step explanation:
Answer:
2/3 or 0.66666666667...
I will give brainlist ! very fast.. Hello its a math question is the last option the correct answer i am not sure please help
Hello!
Let's take this step-by-step:
The formula for the Area of the Triangle:
[tex]Area = \dfrac{1}{2} *\text{Base} *\text{Height}[/tex]
In this case:
Height: x + 3Base: 2x + 4Let's plug in those value's into the equation:
[tex]\text{Area}=\dfrac{1}{2} *(2x +4)*(x+3)\\\\\\\text{Let's first multiple '2x + 4' and 'x+3'}\\\text{Area}=\dfrac{1}{2} *(2x^2+6x + 4x + 12)=\dfrac{1}{2} *(2x^2+10x + 12)\\\\\\\\\\\textNow multiple 1/2 in the function in the parentheses}\\\text{Area}=\dfrac{1}{2} *2x^2 + \dfrac{1}{2}*10x +\dfrac{1}{2} *12\\\\\text{Area}=x^2+5x + 6[/tex]
Answer: [tex]x^2 + 5x +6[/tex]
Hope that helps!
solve and show working:- log(x^2 + 7) base 4 = 2
The value of x for the given logarithm equation log(x^2 + 7) base 4 = 2 is x = ± 3.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
It is known that [tex]log_{a}b[/tex] = c can be written as [tex]a^{c}[/tex] = b.
Given that, log(x^2 + 7) base 4 = 2
Therefore, x² + 7 = 4²
x² + 7 = 16
x² = 16 - 7 = 9
x² = 9
x = ±3
Hence "The value of x for the given logarithm equation log(x^2 + 7) base 4 = 2 is x = ± 3".
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Elias has a collection of 1,200 baseball trading cards. Of these cards, 35% are from the American League, 45% are from the National League, the rest are international players. How many trading cards are of international players?
Answer:
240 trading cards
Step-by-step explanation:
20% of 1200 = .2 × 1200 = 240
Jorge has 173 fish for his dog sled team that he wants to divide into smaller pieces. how many pieces of fish would there be if jorge divided each fish into tenths.
The number of pieces of fish that would be there if Jorge divided each fish into tenths is 1730.
It is given that Jorge has 173 fish for his dog sled team that he wants to divide into smaller pieces.
We need to calculate the number of pieces of fish that would be there if Jorge divided each fish into tenths.
We know that each of the fish is divided into 10 parts.
The total number of fish available for the dog is 173.
The total number of pieces of fish is equal to the product of the number of available fish and the number of parts each fish is divided into.
The total number of pieces of fish is equal to 173*10.
The total number of pieces of fish is equal to 1730.
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I’m not english person. I cannot understand those. Can someone explain some of them please? I’m trying to pass an english math exam..
Step-by-step explanation:
lo siento, no tengo idea de cómo explicarte esto. Ummm, hay una aplicación que puedes descargar en tu teléfono para tomar una foto de la hoja de trabajo o el papel y luego la traducirá para ti. Se llama buena traducción o algo en. buena suer
a force of 4 pounds is required to hold a spring stretched 0.2 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 1.1 feet beyond its natural length?
Using the spring's force we know that 48.4 lb-ft work is done in stretching the spring from its natural length to 1.1 feet beyond its natural length.
What does a spring's force mean?When a spring is in its equilibrium position, it applies a force F = -kx in that direction. A spring's force works as a restoring force, bringing the spring back to its equilibrium length.So, F is the 4 lb force required to maintain the spring's stretched position.
The spring has a 0.2-foot stretch, and its spring constant is k.Applying the equation F = k x 4 = k (0.2) k = 80 lb/ft.U is the effort put in to expand the spring, where x' is equal to 1.1 feet.The labor of extending a spring is denoted by the formula:
U = (0.5) k x'2So, calculate:
U = (0.5). (80). (1.1)² U = 48.4 lb-ftTherefore, 48.4 lb-ft work is done in stretching the spring from its natural length to 1.1 feet beyond its natural length.
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What is the effect on the graph of f (x) = |x| when the function is changed to g(x) =-2|x|
Here the graph shows reflection across x - axis by 2 units.
f(x) = |x| => g(x) = -2|x|.
Solution:Graph transformation is the process of modifying an existing graph or graphed equation to produce a variation of the following graph.The modification of algebraic equations is a common type of problem in algebra.Here given the parent function, f(x)=|x|
The translation is , g(x)= -2|x|
Which is an absolute function.
Here the transformation is .
f(x)=|x| => g(x)= -2|x|
The value of f(x) is reflecting over x- axis and value of y changes by 2 units.
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HELP PSLSPSLAPSLSPSLSPSLSPSLSPSL
Answer: D) 40
Step-by-step explanation:
mph (miles per hour)
60 minutes is an hour, so the number of miles above 60 minutes (which is 40) is the answer.
Hope this helps!
A shipping box has a volume of 1,000 cubic inches. What is the length of one side of the box?
The length of one side of the box is 10 inches.
How to find the volume of a cube?Suppose that: The side length of the considered cube is L units.
Then, we get the Volume of that cube = L³ cubic units.
The volume of a cube is of the form V = L³, where L is the side length.
Given that the shipping box has a volume of 1,000 cubic inches.
Here, we know the volume V, but not the measure of length. So, we can plug in the value 1000 for V and solve for L:
1000 = L³
Cube root both sides:
L = [tex]\sqrt[3]{1000}[/tex]
Therefore, each side is 10 inches.
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Estimate √172 to the nearest tenth. Locate the irrational number on a number line.
The irrational number on a number line is 13.1. All real numbers that are not rational are considered irrational numbers. In other words, it is impossible to describe an irrational number as the ratio of two integers.
What is irrational number ?All real numbers that are not rational numbers are referred to be irrational numbers in mathematics. In other words, it is impossible to describe an irrational number as the ratio of two integers.There is no length, no matter how short, that could be used to express the lengths of both of the two supplied segments as integer multiples of itself.
Square Root of 172 to the nearest tenth, means to calculate the square root of 172 where the answer should only have one number after the decimal point.
CalculateWe calculate the square root of 172 to be:
√172 = 13.11487704860400
ReduceReduce the tail of the answer above to two numbers after the decimal point: 13.11
RoundRound 13.11 so you only have one digit after the decimal point to get the answer: 13.1
To check that the answer is correct, use your calculator to confirm that 13.1² is about 172.
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Determine the value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths.
The solution of x in the mathematical statement is 11.73
How to determine the value of x?From the question, the mathematical statement is given as
x over 5 and 7 tenths equals 2 and 3 tenths.
When represented as an algebraic equation, we have
x/5.10 = 2.30
To start with, we multiply both sides of the equation by 5.10
This is represented as
5.10 * x/5.10 = 2.30 * 5.10
Evaluate the product on the left-hand side
So, we have
x = 2.30 * 5.10
Evaluate the product on the right-hand side
So, we have
x = 11.73
Hence, the value of x is 11.73
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The required simplified value of the given numeral is given as 13.11.
As given in the question, to determine the value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
The statment given in the word string, first transform the equation in the mathematical inscription,
So,
x / 5.7 = 2.3
Simplifying,
x = 5.7 × 2.3
x = 13.11
Thus, the required simplified value of the given numeral is given as 13.11.
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Solve for x. Show each step of the solution.
5(2-x)-10=25-2(3x+40)
Answer:
x = -55
Step-by-step explanation:
Given equation,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
Now the value of x will be,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
→ 10 - 5x - 10 = 25 - 6x - 80
→ -5x + 6x = 25 - 80
→ [ x = -55 ]
Hence, the value of x is -55.
Answer:
x = -55
Step-by-step explanation:
Given equation,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
Now the value of x will be,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
→ 10 - 5x - 10 = 25 - 6x - 80
→ -5x + 6x = 25 - 80
→ [ x = -55 ]
Hence, the value of x is -55.
How far does a rider travel in one complete rotation around the Ferris wheel?
Use 3.14 as an approximation for Pi and round the second answer below to the nearest whole number.
If the diameter of the Ferris wheel is 80 meters, then a rider will travel 251.2 meters in one complete rotation around the Ferris wheel.
The diameter of the Ferris wheel = 80 meters
The radius of the Ferris wheel = Diameter / 2
= 80/2
= 40 meters
The Total distance travelled by the rider in one revolution = The circumference of the wheel
The circumference of the wheel = 2πr
Where r is the radius of the wheel
Substitute the values in the equation
The circumference of the wheel = 2×3.14×40
= 251.2 meters
Hence, if the diameter of the Ferris wheel is 80 meters, then a rider will travel 251.2 meters in one complete rotation around the Ferris wheel
The complete question is :
If the diameter of the Ferris wheel is 80 meters, how far does a rider travel in one complete rotation around the Ferris wheel?
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ASAP PLEASEEE HELPPP PLEASEEEE
1.If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, what transformation occurs from f(x) to h(x)?
A.Shift left 3 units
B.Shift right 3 units
C.Shift up 3 units
D.Shift down 3 units
2. If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, how is the vertex affected? Select all that apply.
A.The vertex will not change.
B.The vertex will shift right 3 units.
C.The vertex will shift left 3 units.
D.The vertex will shift up 3 units.
E.The vertex will shift down 3 units.
F.The vertex will not move up or down.
G.The vertex will not move right or left.
3. If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, how is the range affected?
A.The range will not change.
B.The range will be all real numbers.
C.The range will change from y ≥ 0 to y ≥ -3.
D.The range will change from x ≥ 0 to x ≥ -3.
1) A translation of 3 units down, option D.
2) The vertex moves 3 units down.
3) The new range is y ≥ -3, correct option is C.
Which transformation is applied?For a function f(x) a vertical shift of N units is written as:
g(x) = f(x) + N
In this case, we have:
f(x) = |x|
h(x) = |x| - 3
Then h(x) = f(x) - 3
This is a shift of 3 units down, the correct option is D.
How is the vertex affected?
The vertex is translated 3 units down, like the whole graph of the function.
How is the range affected?
The vertex defines the minimum of the range, so if the vertex goes 3 units down, then the range also does, the new range will be:
y ≥ -3.
So the correct option is C.
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what is the standard form of the equation for part a
Answer:
yea, correct, perfect yes sir
A bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).
The ball would bounce to a height of 0.92 feet at the 7th bounce
How to determine the height of the 7th bounce of the ballThe given parameters are
Initial height = 3.75 feet
Rate of bounce = 79%
The height of the ball after n-th bounce is represented as
H(n) = A * rⁿ⁻¹
Where
A = Initial height = 3.75 feetr = Rate of bounce = 79%n = Number of bounceIn this case, we have
n = 7
So, we have
H(7) = 3.75 * (79%)⁷⁻¹
Evaluate the difference
H(7) = 3.75 * (79%)⁶
Evaluate the product
H(7) = 0.92
Hence, the height of the 7th bounce of the ball is 0.92 feet
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Funds are distributed to five families affected by floods in the ratio 5:12:2:15:29. The total amount that the five families received was $630.
a) The first family received _____
b) The difference between the amount of money the first and last family received was _____
c) A sixth family joins. They receive n amount of money and the average amount of money donated to all six families becomes 140. How much money does the sixth family receive?
Step-by-step explanation:
We must first add up the ratios:5+12+2+15+29 = 63, this will be the total ratio the money was shared Then we pick out the ratio for each family accordingly:For the first family, 5 out of the total ratio = 5/63
For the second family, 12 out of the total ratio = 12/63
For the third family, 2 out of the total ratio = 15/63
For the fifth family, 29 out of the total ratio = 29/63
a) The first family = 5/63 of the money, $630
we can therefore say the money they received is
= 5/63 ×630
= $50
b) The last family = fifth family = 29/63 of the money, 630
= 29/63 × 630
= $290
recall that the first family received $50 , the positive difference between the money received by both the first and last family
= $290 - $50
= $240
c) Since another family joins in, the total number of families become 6
the money the received is nwe can't find the average without knowing what the second, third, and fourth family received out of that money
we apply the same stepthe second family = 12/63 ×630
= $120
the third family = 2/63 × 630
= $20
the fourth family = 15/63 × 630
= $150
Average generally is = total sum/ frequency or number of occurrences or peoplein this case, we were told the average became $140
which means that
sum of money received by the families/ the number of families involved in the sharing = $140
( $50+$120+$20+$150+$290+n)/6 = $140($630+n)/6= $140
now the plan would be to make n subject of formula
multiply both sides of the equation by 6, the equation will become$630+n = $840
take $630 to the other side, it becomes -$630
n = $840-$630
n = $210
therefore the newly added family received $210
I honestly hope I explained it properly...thank you
A student performed the following steps to find the solution to the equation
x² + 4x-12-0. Where did the student go wrong?
Step 1. Factor the polynomial into (x + 6) and (x-2)
Step 2. x-6= 0 and x + 2 = 0
Step 3. x = 6 and x = -2
O A. in Step 3
B. The student did not make any mistakes, the solution is correct
O C. in Step 1
OD. in Step 2
The student got the solution to the quadratic equation wrong at step 2
What are quadratic equations?A quadratic equation is a mathematical equation in which it's higher power of unknown is 2.
A quadratic equation can be solved by using 4 different method of choice which are formula method, factorization method , completing the square and graphical method.
x^2+4x-12=0 is an example of quadratic equation.
using factorization method to solve the value of x
x^2+6x-2x-12=0
grouping the equation
(x^2+6x)(-2x-12)=0
x(x+6)-2(x+6)=0
(x+6)(x-2)=0
for the equation to be satisfied
(x+6)=0
or
(x-2)=0
Therefore x= -6 or+2
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Learning target: I can calculate the surface area of 4 ( width) cm and 20 (height) cm
Answer:
20 times 4
Step-by-step explanation:
suricce area
A one way train ticket in the city cost 1.85 a monthly pass cost 65$. For what number of rides should you buy the monthly pass?
Answer: 36 rides
Step-by-step explanation: Because is you divide 65 by 1.85 you get 35.13513513513514 so just round it to the next integer of 36.
What is the smallest and greatest number that rounds to 380 when
rounding to the nearest ten?
The smallest and greatest number that rounds to 380 when rounding to the nearest ten are 375 and 384 respectively.
What is rounding a number?Adjusting a number's digits so that it produces an approximation of a result is known as rounding.
The given number is 380.
When rounding a number to the nearest ten, pay attention to the last digit; if it is less than five, round down; if it is five or more, round up.
Therefore, the smallest number that rounds to 380 when rounding to the nearest ten is 375.
Similarly, the greatest number that rounds to 380 when rounding to the nearest ten is 384.
Hence, the smallest and greatest number that rounds to 380 when rounding to the nearest ten are 375 and 384 respectively.
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Find the two square roots of 1/16
Answer:
1/4
Step-by-step explanation:
The square root of 1/16 = 1/4
they probably