Answer:
x = 0 and 2pi/3
Explanation
Given the expression
cos(2x)=cos(x)
In trigonometry expression;
cos2x = 2xos^2x - 1
Substituting into the equation given;
cos(2x)=cos(x)
2xos^2x - 1 = cos x
Rearrange
2xos^2x - 1 - cosx - 1 = 0
Let P = cosx
2P^2 - P - 1 = 0
Factorize
2P^2 - 2P+P-1 = 0
2P(P-1)+1(P-1) = 0
2P+1 = 0 and P-1 = 0
P = -1/2 and 1
Recall that P = cosx
-1/2 = cosx
x = cos^-1(-1/2)
x = 120 degrees = 2pi/3
If P = 1
cosx = 1
x = cos^-1(1)
x = 0
Hence the value of x that satisfies the equation is 0 ad 2pi/3
Identify the reasoning that would justify each step in solving for m
Given
[tex]\frac{3}{4}(m-500)=8000+4000[/tex]Notice that the right side of the equation consists of like terms (they do not depend on m). Therefore, Step 1 goes with Combine like terms.
Then,
[tex]\frac{3}{4}(m-500)=\frac{3}{4}*m+\frac{3}{5}(-500)=\frac{3m}{4}-375\rightarrow\text{ distributive property}[/tex]Step 2 applies the distributive property.
As for the properties of the equality,
[tex]\begin{gathered} a=b\Rightarrow a+c=b+c\rightarrow\text{ addition property of equality} \\ a=b\Rightarrow ac=bc\rightarrow\text{ multiplication property of equality\rbrack} \\ a=b\Rightarrow\frac{a}{c}=\frac{b}{c}\rightarrow\text{ division property of inequality} \end{gathered}[/tex]Thus, steps 3 through 5 are:
Step 3 - Addition property
Step 4 - Division property
Step 5 - Multiplication property
1. What is the reciprocal of 5? 6 Show your work below! (click "Show Work Type a response OD
Answer:
1/5
Step-by-step explanation:
a reciprocal is the multiplicative inverse
Answer:
The reciprocal of 5 is 1/5
Step-by-step explanation:
The reciprocal of a number is the fraction flipped upside down
6/1 = 1/6
⇒ 5/1 = 1/5
Determine whether the function has a minimum or maximum value and then find that value.()=−^2+2−7
Given function is
[tex]f(x)=-x^2+2x-7[/tex]Now,
[tex]\begin{gathered} f(x)=-(x^2-2x+7) \\ =-(x^2-2x+1+6) \\ =-\lbrack(x-1)^2+6\rbrack \\ =-(x-1)^2-6 \end{gathered}[/tex]Being a perfect square,
[tex](x-1)^2\ge0[/tex]Therefore,
[tex]-(x-1)^2\leq0[/tex]So,
[tex]f(x)\leq-6[/tex]Theerfore, the maximum value of the given function is -6.
The density of copper is 9.86 g/cm".
Work out the mass of the solid copper cuboid in kg
10 cm
3 cm
5 cm
Step by step
HELP PLEASE.
Either Table A or Table B shows a proportional relationship.
Plot the points from the table that shows a proportional relationship.
( If you can, can you save the image as and edit it it will help me out a lot)
Answer: Table A has a proportional relationship
See the diagram below
==================================================
Explanation:
Table A has a proportional relationship because all the points are on the same straight line. That line in this case is y = 2x
Whatever x is, multiply it by 2 and you'll get the y value
Example: If x = 4, then y = 2*x = 2*4 = 8 which gives the point (4,8)
Another phrase for "proportional relationship" is "direct variation".
How would I multiply these two exponents?
The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. The fractions can also be simplified before multiplying by factoring out common factors in the numerator and denominator.
Name the point that lies on this line: y = 2 + 5(x + 7)
(1, 42)
1) Since we have an equation of the line y = 2 + 5(x + 7) let's find one point that ∈ to this line.
2) Let's plug into that for x, the value of x=1
y= 2+ 5(1+7)
y= 2 +5(8)
y= 2 +40
y= 42
3) So one of the points that lie on this line is (1, 42) i.e. belong to that line.
two friends went to a restaurant and ordered one plain pizza and two sodas. the bill totaled $15.95. later that day, five friends went to the same restaurant. they ordered 3 plain pizzas and 5 sodas. their bill totaled $45.90.write and solve a system of equations to determine the the price of one plain pizza(only an algebraic solution can receive full credit.)
Let:
x = Cost of one plain pizza
y = Cost of one soda
two friends went to a restaurant and ordered one plain pizza and two sodas. the bill totaled $15.95. so:
[tex]\begin{gathered} x+2y=15.95_{\text{ }} \\ \end{gathered}[/tex]later that day, five friends went to the same restaurant. they ordered 3 plain pizzas and 5 sodas. their bill totaled $45.90. so:
[tex]3x+5y=45.90[/tex]Let:
[tex]\begin{gathered} x+2y=15.95_{\text{ }}(1) \\ 3x+5y=45.90_{\text{ }}(2) \end{gathered}[/tex]From (1) solve for x:
[tex]x=15.95-2y_{\text{ }}(3)[/tex]Replace (3) into (2):
[tex]\begin{gathered} 3(15.95-2y)+5y=45.90 \\ 47.85-6y+5y=45.90 \\ -y=-1.95 \\ y=1.95 \end{gathered}[/tex]Replace the value of y into (3):
[tex]\begin{gathered} x=15.95-2(1.95) \\ x=12.05 \end{gathered}[/tex]Therefore, the price of one plain pizza is $12.05
In August, a giant panda named Lucky was born at the Silver City Zoo. In September, Lucky
weighed 3.07 pounds. Today, Lucky is weighed again and he is heavier than before. Now
Lucky weighs 10.81 pounds.
Use an equation to find the amount of weight Lucky gained between September and today.
Using linear equations, the amount of weight Lucky gained between September and today is 7.74 pounds.
What is a Linear equation?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. The standard form of a linear equation in one variable is the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.So, in September, Lucky weighed = 3.07 pounds
Today's Lucky weighed = 10.81 poundsThe equation form is:
Let x = weight to find Lucky3.07 + x = 10.81This is a linear equationSo, now solve this linear equation and find 'x' as follows:
3.07 + x = 10.81=> x = 10.81 - 3.07=> x = 7.74Therefore, using linear equations, the amount of weight Lucky gained between September and today is 7.74 pounds.
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At a party, there are 30 men, 16 of whom are without dates, and 30 women, none of of whom are without dates. Find the probability of picking someone at random and getting a person who is a woman or without a date?
For this type of probability question, there are different ways to solve the same question but let's analyze the situation and calculate as simple as possible.
For our question, there are two parts, the first one first is the probability to pick someone who is a woman. Once there are 60 people of which 30 are women, it means this probability is 30/60. Let's keep this probability.
Now let's move on to the second part. The situation where we pick someone who is without a date. once there are 60 people and all 30 women have a date and 16 men also have a date it means 30 + 16 - 60 = 14 people does not have a date. So the probability to pick someone without a date is 14/60.
Now once we have analyzed the two parts of the question, and we have two probabilities all we need is to sum our probabilities, as follows:
But why do we sum and do not multiply? Because we use the proposition OR at "Find the probability of picking someone at random and getting a person who is a woman OR without a date" If the proposition was AND we would have multiplied both probabilities.
i would appreciate so much if you could answer this and atleast explain a little how you did it (optional)
Answer:
a.
Fee of whole band = Fee of writer + guitarist + singer
Fraction of fee of whole band = 4/12 + 1/12 + 1/12
= 4+1+1/12
=6/12
=1/2
b.
Fee of writer= 4/12 of £3000
=3000 × 4/12
= £1000
Fee of singer= 1/12 of £3000
= 3000 × 1/12
= £250
Fee of guitarist= Fee of singer
= £250
Let f(x) = 2x^2 – 3 and g(x) =x+1/2Find the value of (fof )(-1)A -1B-3C 0.5D 95
What is 30 percent of 120?
Answer:
30 percent of 120 is 36
i need help asp ;-;
Which of the following values is less than −|58|?
A. −48
B. 68
C. −68
D. 48
Answer:
C. -68
Step-by-step explanation:
Using absolute value symbols, it makes any negative number a positive. But, the negative sign is outside the absolute value signs, making the number -58. -68 is the only number less than -58.
In which pair do both decimals represent rational numbers? O A. 9.0032812373025549382... and 0.12333.. OB. 0.115 and 0.12333... O C. 3.10382947305718274... and 0.123 O D. 9.0032812373025549382... and 0.115
Rational numbers can be formed by dividing 2 integers. It can be represented in this format x/y where y is not 0. Rational numbers, in decimal form are not repetitive and unending.
Therefore,
if y =3x^3 + 2x^2 - 5x + 2, find d^3y/dx^3
Answer:
18
Step-by-Step Explanation:
[tex]\frac{dy}{dx}=9x^2 + 4x-5 \\ \\ \frac{d^2 y}{dx^2}=18x+4 \\ \\ \frac{d^3 y}{dx^3}=18[/tex]
In a math class , there are 14 girls and 16 boys. Which of the following ratios does NOT represent between girls and boys?A. 14:16B. 14/16C. 7 to 8D. 2:9its not college mathematics its middle school
No. of girls = 14
No. of Boys =16
Therefore the ratio, from girls to boys is,
[tex]\frac{14}{16}[/tex]Which can also be written as,
[tex]\begin{gathered} 14\colon16 \\ 7\text{ to 8} \end{gathered}[/tex]Therefore, the wrong ratio is option D.
That is,
[tex]2\colon9[/tex]So, the answer is option D.
I need help with 3x-2y=24 find the y and x intercept and the slope
3x-2y=24
3x - 2y + 2y = 24 +2y Adding 2y to both sides of the equation
3x - 24 = 2y + 24 - 24 Subtracting 24 from both sides of the equation
(3x - 24)/2= 2/2y Dividing by 2 on both sides of the equation
3/2x - 12 = y
From this form of the equation we deduce the slope (coefficient of x) is 3/2 and the y-intercept is equal to -12.
To find the x-intercept, we replace y= 0 in the equation and isolate x
3/2x - 12 = 0
3/2x - 12+12 = 0+12 Adding 12 to both sides of the equation
x= 12/(3/2) Isolating x
x= 8
The x-intercept is 8
Help me rewrite this problem to satisfy the provided boxes please
EXPLANATION
Since we have the expression:
Removing the parentheses:
[tex]5x^2+6x+5+6x^2-6x-5[/tex]Rearranging terms:
[tex]5x^2+6x^2+6x-6x+5-5[/tex]Adding like terms:
[tex]11x^2+0x+0[/tex]The final expression is as follows:
[tex]undefined[/tex]The box and whisker plot summarizes the data collected on the number of Broadway tickets sold and the actual number of attendees at the plays. Which statement is TRUE about the statistics?
A.) The majority of the data values fall in the upper quartile for both sets of data.
B.) There were fewer tickets purchased than people attending the plays.
C.) The medians of the populations are the same.
D.) There were fewer attendees than purchased tickets.
The plot:
The true statement based on the information is that D. There were fewer attendees than purchased tickets.
Whet is a box and whisker plot?A box and whisker plot is a graphical representation of variance in a set of data. A histogram analysis is sufficient in most circumstances, but a box and whisker plot can provide more detail while allowing different sets of data to be displayed in the same graph.
The box and whisker figure highlights data on the number of Broadway tickets sold and actual attendance at the performances. In this case, the graph shows that the number of tickets are more.
Therefore, the correct option is D.
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Using FUNCTION NOTATION, assume you are given the function: y = 3x - 2. This can be rewritten as ________ = 3x - 2, since y can be replaced with _______.
The complete statement is:
This can be rewritten as _f(x)_ = 3x - 2, since y can be replaced with _f(x)__.
How to use function notation?A general relation is written as:
y = something that depends of x.
This is a relation that relates the variable y with the variable x, where we define x as the input and y as the output.
If this is a function, we can use the notation:
y = f(x).
(or any letter of x, f(x) is the most common notation used)
in this case, we have:
y = 3x - 2
And in function notation, this will be writen as:
f(x) = 3x - 2
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Nathan loved learning about earthquakes in science class. He told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10
–
6 centimeters per minute. What would be the most appropriate unit for Nathan to use instead of centimeters per minute?
The most appropriate unit for Nathan to use instead of centimeters per minute is centimeters per year.
What is an earthquake?An earthquake simply means a rapid motion of the solid layer of the Earth.
In this case, Nathan told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute.
Since the year is being discussed, the unit should be based on the year.
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Find the length of the sloping side of the roof. Give your answer to the nearest foot. Show your work.
Given:
The triangle having two similar angles.
This is the isosceles traingle.
Draw the altitude to the given traingle,
D divides the side BC into two equal side having length,
[tex]\begin{gathered} \frac{45}{2}=22.5 \\ BD=22.5\text{ and DC=22.5} \end{gathered}[/tex]Now, use the tan ratio for right triangle ABD,
[tex]\begin{gathered} tan15^{\circ}=\frac{AD}{BD} \\ 0.268=\frac{AD}{22.5} \\ AD=6.02=6\text{ f}eet \end{gathered}[/tex]Using the pythagorean theorem,
[tex]\begin{gathered} AB^2=AD^2+BD^2 \\ =6^2+22.5^2 \\ =542.25 \\ =23.286 \\ =23.3 \end{gathered}[/tex]The length of the sloping side of the roof is 23.3 feet.
Kaj needs to order some new supplies for the restaurant where she works. The restaurant needs at least 736 knives. There are currently 155 knives. If each set on sale contains 12 knives, what is the minimum number of sets of knives Kaj should buy?
Hence, the minimum number of sets of knives kaj should buy is 48 sets.
Given this, a restaurant must have at least 736 knives.
At the moment, it possesses 155 knives.
Every set includes 12 knives.
Let the number of knife sets be.
Reason: Minimum number of sets indicates ≥
This means ≤ the maximum amount of sets
Step: 2
In light of the inquiries,
[tex]155+s*12\geq 736[/tex]
[tex]12s\geq 736-155[/tex]
[tex]12s\geq 581[/tex]
[tex]s\geq \frac{581}{12}[/tex]
[tex]s\geq 48.42[/tex]
Step 3: Count the number of knife sets [tex]s\geq 48.42[/tex]
that is greater than or equal to 48
Therefore, the required minimum is 48 sets of knives.
What are sets?
In mathematics, a set is a well-defined collection of objects. Sets are named and represented using capital letters. In the set theory, the elements that a set comprises can be any kind of thing: people, letters of the alphabet, numbers, shapes, variables, etc.
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Mr. Thomatos thinks that {3, 8} and [3, 8] represent the same set of values Is Mr. Thomatos correct? Why or why not? Explain. (giving brainliest)
{3,8} give the values of set that implies the set has two elements 3 and 8. [3,8] give the range of values that can be used in any functions with values from 3, 4, 5, 6, 7, 8 both 3 and 8 included.
What is set?Sets are collections of well-defined objects or elements in mathematics. A set is denoted by a capital letter symbol, and the number of elements in a finite set is denoted by the cardinal number of a set enclosed in a curly bracket{...}.
What is Function?A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output. Every function has a domain and a codomain, as well as a range.
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Althea needs 134 ounces of cold cuts for a party. How many pounds and ounces does she need?
The number of pounds and ounces that we have in 134 ounces is; 8 pounds 6 ounces
How to carry out units conversion?
We know that in units conversion, there are different units and their conversion rates. For example;
1 meters = 100 cm
1000 meters = 1 kilometer
1000 grams = 1 kilograms
100 cents = 1 dollar
Now, we want to convert ounces to pounds.
The conversion rate for ounces to pounds is;
1 ounce = 0.0625 pounds
We are given 134 ounces of cold cuts for a party. Converting that to pounds gives us;
134 * 0.0625/1 = 8.375 pounds
Now, we want it in pounds and ounces and so we convert the decimal part to ounces
1 pound = 16 ounces
0.375 pounds = 0.375 * 16/1 = 6 ounces
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Is the answer correct if no please let me know
Answer: 57
Given:
[tex]S_n=4n-3[/tex]We are asked to find the 15th term, meaning n = 15
[tex]S_n=4n-3[/tex][tex]S_{15}=4(15)-3[/tex][tex]S_{15}=60-3[/tex][tex]S_{15}=57[/tex]Therefore, the 15th term is 57.
lan and Matthew went shopping. lan spent $20 less than twice as much as Matthew spent. In total, they spent $130.
Using linear algebra, we concluded, the Mathew spent $50 and lan spent $80
What is Linear Algebra?
Vectors, matrices, vector spaces, and linear transformations are all topics covered in the mathematical field of linear algebra. Linear algebra is much better understood than other areas of mathematics, which are regularly stimulated by novel concepts and unresolved issues.
According to the question,
Let Mathew spent $x
lan spent = 2x - 20
Total money spent = $130
⇒ 2x - 20 + x = 130
⇒ 3x - 20 = 130
⇒ 3x = 150
⇒ x = 50
2x - 20 = 2(50) - 20
= 80
So, Mathew spent $50 and lan spent $80
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A company has 40 salespeople. A board member at the company asks for a list of the top 5 salespeople, ranked in order of effectiveness. How many such rankings are possible?
The number of rankings that are possible when the company has 40 salespeople is 78960960.
What is permutation?Based on the information given, permutations will be used. The formula is illustrated thus:
Permutations = n! / (n – r)!
N is the number of things you are choosing from,
r is the number of items.
“!” is a factorial of a number
The company has 40 salespeople and the board member at the company asks for a list of the top 5. This will be;
= 50! / (40 - 5)!
= 40! / 35!
= 40 × 39 × 38 × 37 × 36
= 78960960
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Kali just started a new sales floor job to save for college. She earns 15.75 plus a flat fee of 50 . She wants to earn between 200 and 400 . The following inequality represents her earning potential
200 ≤ 15.75x + 50 ≤ 400 Solve the inequality PLEASE HELP ASAP HELP I WILL GIVE BRAINLIEST AND 100 POINTS
!!
The solution for the inequality is 11.746 ≤ x ≤ 24.44
Kali earns a 15.75 plus a flat fee of 50 from her job.
She wants to earn between 200 and 400.
Let 'x' denote her earning potential.
Then the inequality for her earning potential is given by,
200 ≤ 15.75x + 50 ≤ 400
We solve this inequality for x.
Subtract 50 from the inequality,
⇒ 200 -15 ≤ 15.75x ≤ 400 -15
⇒ 185 ≤ 15.75x ≤ 385
Divide by 15.75,
⇒ 11.746 ≤ x ≤ 24.44
is the solution for the inequality.
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