Answer:
cot x = 2cot(2x) + tan x
Step-by-step explanation:
[tex] \rm \implies cot \: 2x = \dfrac{cos \: 2x}{sin \: 2x} \\ \\ \rm \implies cot \: 2x = \dfrac{ {cos}^{2}(x) - {sin}^{2}(x) }{2(sin \: x)(cos \: x)} \\ \\ \rm \implies cot \: 2x = \frac{1}{2} \bigg( \frac{cos \: x}{sin \: x} - \frac{sin \: x}{cos \: x} \bigg) \\ \\ \rm \implies cot \: 2x = \frac{1}{2} (cot \: x - tan \: x) \\ \\ \rm \implies 2cot ( 2x )= cot \: x - tan \: x \\ \\ \rm \implies cot \: x = 2cot (2x) + tan \: x[/tex]
Evaluate each function given domain -4,2,6. F(x)=6-x
The values for the stated domain of the function are-
F(-4) = 10; F(2) = 4; F(0) = 0.
What is the definition of the domain of the function?The range of values of which we are allowed entry into our function is described as the domain of a function. The x values for a function like f make up this set (x).A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of numbers.As per the stated function.
F(x) = 6-x
The domain for the function are-
-4,2,6
The value of the function are, put each value in the place of x in the function.
F(-4) = 6 - (-4)
F(-4) = 6 + 4
F(-4) = 10
F(2) = 6 - 2
F(2) = 4
F(6) = 6 - 6
F(0) = 0
Thus, the values for the stated domain of the function are- 10, 4 and 0 respectively.
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Solve the following inequality. Write the inequality in interval notation, and graph it.
7 x plus 5 less than or equals minus 30
The inequality expression has a solution of (-oo, -5]
How to solve the inequality?From the question, the inequality is given as
7 x plus 5 less than or equals minus 30
The above inequality can be re-written as follows
7x + 5 ≤ -30
There are constants to add or subtract in the expression
So, we start by subtracting both sides of the expression by the constant -5
This gives
7x ≤ -35
Divide both sides by 7
So, we have the following representation
x ≤ -5
Express as interval notation
(-oo, -5]
Hence, the solution to the expression is (-oo, -5]
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HELP PLS!! Using the fundamental theorem of algebra!
The quadratic equation has no real roots. The roots are x = -1 +√5/2 i or x = -1 - √5/2 i
How to determine the number of roots of a quadratic equation?To determine the number of roots of a quadratic equation ax²+bx+c=0 you need to compute the discriminant (b²-4ac)
If the discrimant is less than 0, then the quadratic has no real roots.
If the discriminant is equal to zero then the quadratic has equal roosts.
If the discriminant is more than zero then it has 2 distinct roots.
Given: 2x² + 4x + 7
a = 2, b = 4, c = 7
b² - 4ac = (4)² -4(2×7) = 16-56 = -40
Since the discriminant is less than 0, thus 2x² + 4x + 7 has no real roots i.e. it has two imaginary roots
To find the roots, you can use the completing the square method:
2x² + 4x + 7 = 0
Divide through by 2:
x² + 2x + 7/2 = 0
x² + 2x = -7/2
Add the the square of half of the coefficient of x to both sides of the equation:
x² + 2x + (1)² = -7/2 + (1)²
Factorise:
(x+1)² = -7/2 +1
(x+1)² = -5/2
x+1 = ± √-5/2
x = -1 ±√5/2 i (Note: √-1 = i)
x = -1 +√5/2 i or x = -1 - √5/2 i
Therefore, the roots are x = -1 +√5/2 i or x = -1 - √5/2 i
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A and b are complimentary angles. A=(7x+18) and b=(5x-12), then find the measure of a
Answer:
[tex]x=\frac{37}{6} \\[/tex]
Step-by-step explanation:
Since A and b are complimentary angles There sum is equal to 90°
In other words:
We know A = (7x+18) and b = (5x-12)
Next, insert these values into the equation (A+ b = 90°):
[tex](7x+18) + (5x-12)=90[/tex]
Drop the () since we are not multiplying anything
[tex]7x+18 + 5x-12=90[/tex]
Combine like terms: 7x and 5x, 18 and-12
[tex]7x +5x +18-12=90\\\\12x+ 16=90\\[/tex]
Subtract 16 from both sides of the equation
[tex]12x=74\\[/tex]
Divide by 12 and get:
[tex]x=\frac{37}{6} \\[/tex] or [tex]x=6.16666...[/tex]
Hope this helps :)
The perimeter of a rectangle is 48 centimeters. The relationship between the length, the width, and the perimeter of the rectangle can be described with the equation .
Find the length, in centimeters, if the width is:
1. 10 centimeters
2. 3.6 centimeters
3. centimeters
The length, in centimeters of the rectangle if the width is:
1. 10 centimeters
L = 14 cm2. 3.6 centimeters
L = 20.4 cmHow to find the length of the rectanglesThe perimeter of a rectangle is given by the formula
P = 2( Length, L + width, w)
P/2 = L + w
L = P/2 - w
Perimeter is given to be 48, L is solved below
at w = 10 centimeters
L = 48/2 - 10 = 14 cm
at w = 3.6 centimeters
L = 48/2 - 3.6 = 20.4 cm
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Complete the equation for this model .
Answer:
Step-by-step explanation:
the anser is 3 + 5 =8
Figure EFGH on the grid below represents a trapezoidal plate at its starting position on a rotating machine platform:
Trapezoid EFGH with vertices E at negative 4 comma 8, F at negative 7 comma 5, G at negative 4 comma 3, and H at negative 2 comma 5.
The plate is rotated 720° about the origin in the counterclockwise direction. Which of the following is formed when the arcs of rotation are drawn for each point as it is rotated? (4 points)
A. They form parallel segments.
B. They form perpendicular segments.
C. They form concentric circles.
D. They form congruent segments.
When plate is rotated 720° about the origin in the counterclockwise direction they form parallel segments.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The coordinates of the figure EFGH are given as:
E = (-4,8)
F = (-7,5)
G = (-4,3)
H = (-2,5)
The rule of rotation 720 degrees counterclockwise about the origin in the
(x,y) -> (-y,x)
So, we have:
E' = (-8, -4)
F' = (-5, -7)
G'= (-3, -4)
H' = (-5, -2)
when plate is rotated 720° about the origin in the counterclockwise direction they form parallel segments.
Hence when plate is rotated 720° about the origin in the counterclockwise direction they form parallel segments.
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Solve for all values of x by factoring
x²8x+8 = -4
Answer: 6 and 2
Step-by-step explanation:
to find your factors, you want to set the equation equal to 0 and find what adds up to your middle term and multiplies to your last term
[tex]x^{2} -8x+8=-4\\x^{2} -8x+12=0\\(x-6) (x-2) = 0\\x-6= 0\\x-2=0\\x=6\\x=2[/tex]
What is the acquisition cost?
Answer:
Acquisition cost refers to an amount paid for fixed assets, for expenses related to the acquisition of a new customer, or for the takeover of a competitor.
Order the numbers from least to greatest-10.1, 11/10, -101, -3n , 19/2
Answer:
The answer is -3n,10.1,11/10,19/2,-101 is the right answer form my side
(7 x 4) x 3 = 3 x (4 x 7)
which property is used
a) commutative
b) assositative
c) identity
d) distributive
Answer:
b) associative
Step-by-step explanation:
The associative property of multiplication was used to change the position of the parentheses
Can you solve these 2 problems please
Answer:
1) The top angle = 128°
Right angle = 52°
Bottom angle = 128°
Left angle = 52°
2) The top angle = 159°
Right angle = 21°
Left angle = 21°
Step-by-step explanation:
The left problem would involve verticle angles being congruent to each other.
[tex]5x + 2 = x + 42\\\\6y + 8 = 7y - 12[/tex]
Solve each equation:
[tex]5x + 2 = x + 42\\4x = 40\\x = 10[/tex]
[tex]6y + 8 = 7y - 12\\20 = y[/tex]
Substitute:
The top angle = 128°
Right angle = 52°
Bottom angle = 128°
Left angle = 52°
The right problem would involve supplementary angles.
[tex]\frac{1}{4}y - 1 + 27x + 24 = 180\\\\27x + 24 + 4x + 1 = 180[/tex]
Solve for second equation (for simplicity) :
[tex]27x + 24 + 4x + 1 = 180\\31x + 25 = 180\\31 = 155\\x = 5[/tex]
Substitute x = 5 into other equation :
[tex]\frac{1}{4}y - 1 + 27x + 24 = 180\\\frac{1}{4}y - 1 + 27(5) + 24 = 180\\\frac{1}{4}y = 22\\y = 88[/tex]
Substitute :
The top angle = 159°
Right angle = 21°
Left angle = 21°
What can polynomial identities apply to beyond just polynomials?
Please explain
Polynomial identities apply beyond just polynomials by replacing the variables with numbers to create a numerical expression.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
A polynomial identity is an equation that helps us to easily solve expressions involving larger exponents and numbers. Generally, polynomial identities are used for the expansion of the expression, by breaking down the expression into simpler units.
Polynomial identities apply beyond just polynomials by replacing the variables with numbers to create a numerical expression.
Hence, Polynomial identities apply beyond just polynomials by replacing the variables with numbers to create a numerical expression.
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Which of the following could be a real-world description of the quantity two times x end quantity divided by 10?
a The cost of a pizza split by 10 people plus a $2 tip
b The cost of a pizza plus a $2 tip divided by 10 people
c The cost per pizza for 10 pizzas divided by 2 people
d The cost per pizza for 2 pizzas divided by 10 people
The real world description of the quantity two times x and quantity divided by 10 is the cost per pizza for 2 pizzas divided by 10 people.
According to the question,
We have the following information:
Two times x and the quantity is divided by 10.
So, we have the following expression for this word problem:
2x/10
Now, in option a, the expression will be:
(x/10)+2
Now, in option b, the expression will be:
(x+2)/10
Now, in third option, the expression for the word problem will be:
10x/2
Now, in option d, we have the following algebraic expression:
2x/10
Now, the last expression matches with the expression given in the question.
Hence, the correct option is d.
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I don’t understand these sort of questions I need help please
Answer:
Step-by-step explanation:
Make the subject of 6x = t
19) A model motorcycle has a scale of 0.8 in : 1.4
ft. If the real motorcycle is 7 ft long, then how
long is the model motorcycle?
The model motorcycle is 1/3 feet or 4 inches long.
Given:
A model motorcycle has a scale of 0.8 in : 1.4 ft.
If the real motorcycle is 7 ft long.
= 0.8 inches * 1 foot/12 inches
= 8/10 * 1/12 feet
= 8/120
= 1/15 feet
scale/actual = 0.8 in / 1.4 ft = 1/15/14/10 = 10/210 = 1/21
Let L be the model motorcycle length.
scale / actual = L/7
L/7 = 1/21
L = 7/21
L = 1/3 feet
L = 1/3 feet * 12 inches/1 feet
L = 4 inches
Therefore the model motorcycle is 1/3 feet or 4 inches long.
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NO LINKS!! Use the diagram below to answer the following questions. Part 2
Answer:
f) Line l.
g) ∠1 and ∠3, ∠2 and ∠4, ∠5 and ∠7, ∠6 and ∠8.
h) ∠3 and ∠6, ∠2 and ∠7.
i) ∠4 and ∠5, ∠1 and ∠8.
j) ∠2 and ∠3, ∠6 and ∠7.
Step-by-step explanation:
The transversal is a line that crosses two other lines in the same plane at two distinct points.
Therefore, the transversal line of the given diagram is line l as it crosses lines j and k.
Corresponding angles are pairs of angles that are in the same position relative to both lines crossed by the transversal.
∠1 and ∠3∠2 and ∠4∠5 and ∠7∠6 and ∠8Alternate interior angles are pairs of angles on the inner side of the two lines that the transversal crosses, but on opposite sides of the transversal.
∠3 and ∠6∠2 and ∠7Alternate exterior angles are pairs of angles on the outer side of the two lines that the transversal crosses, but on opposite sides of the transversal.
∠4 and ∠5∠1 and ∠8Consecutive interior angles are pairs of angles on the inner side of the two lines that the transversal crosses, and are on the same side of the transversal.
∠2 and ∠3∠6 and ∠7Rohan used the model below to show
1.38 ÷ 3
Three groups of cubes are shown with 4 groups of tens and 3 ones in each group.
Part A
Rohan made an error in his model. Explain his error. Include the correct grouping for the model.
Three groups of cubes are shown with 4 groups of tens and 3 ones in each group is incorrect and 0.46is correct for 1.38 ÷ 3
What is Division?A division is a process of splitting a specific amount into equal parts.
Rohan's model is represented as:
1.38 ÷ 3=0.43
The model is incorrect, and the correction is as follows:
Express 1.38 as 1.20 + 0.18
Now (1.20 + 0.18)÷ 3
(1.20÷ 3)+(0.18÷ 3)
0.4+0.06
0.46
Hence, the correct result of the model is 0.46
Hence Three groups of cubes are shown with 4 groups of tens and 3 ones in each group is incorrect and 0.46 is correct
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Can a triangle be formed with side lengths 4, 8, 11? Explain.
No, because 11 − 8 < 4
Yes, because 11 − 4 < 8
No, because 4 + 8 > 11
Yes, because 4 + 8 > 11
Answer:
yes because 4+8>11
Step-by-step explanation:
one you add the 2 smallest numbers and if it is greater then the larger number then it is a triangle but if it is equal or less than the biggest number it is not a triangle
Answer:yes because 4+8>11
Step-by-step explanation:
Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or
simplified fractions.
Solution of the given system of equations using Cramer's rule is given by : x = -96 / 190 , y = -17/19 .
As given in the question,
Given system of equations are as follow:
-10x -10y = 14
-10x + 9y = -3
Solution of the given system of equations using Cramer's rule is given by :
D = [tex]\left|\begin{array}{ccc}-10&-10\\-10&9\\\end{array}\right|[/tex]
= -90 -100
= -190
Dₓ = [tex]\left|\begin{array}{ccc}14&-10\\-3&9\\\end{array}\right|[/tex]
= 126 - 30
= 96
[tex]D_{y}[/tex] = [tex]\left|\begin{array}{ccc}-10&14\\-10&-3\\\end{array}\right|[/tex]
= 30 +140
= 170
x = Dₓ/D
= 96/ -190
= -96/190
y = [tex]D_{y}[/tex]/ D
= 170/-190
= -17/19
Therefore, solution of the given system of equations using Cramer's rule is given by : x = -96 / 190 , y = -17/19 .
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3. You are working as a computer programmer in a company that makes computer games. You are getting paid $50 per hour for your work. At the end of the day you earned $400. How many hours did you have to
work to earn that amount of money? Let h represent the number of hours you worked. Choose the equation below that does not represent this situation.
400-(h+h) x 50
400-hx 50
50h = 400
400 h+h+h+h+h+h+h+h
Answer: I think A? not fully sure
Step-by-step explanation:
Problem 2
Solve the equation. log(x+3) = log(2x-6) + log(3)
Answer:
x=21/5, x=4.2, or x=4 1/5
Step-by-step explanation:
5/8 divided by 6 HELP ME PLEASEEEE AUGHAGAGA
Answer:
5/48
Step-by-step explanation:
[tex]\frac{5/8}{6}=\frac{5}{8(6)}=\frac{5}{48}[/tex]
Answer:
5/48 or 0.104
Step-by-step explanation:
⅝ ÷ 6
changer division sign to multiplication sign
⅝ × ⅙ = 5/48 or 0.104
The population of California was about 37 million in 2010 and increasing by 1.0% each year. Create a formula to estimate the population of California in 2020.
The population of California by the year 2020 is 41 million.
What is population growth?The term population has to do with the number of people that live in a place or a town. We have the following information from the question;
Initial population (Po) = 37 million
Population growth rate (r) = 1.0%
Time interval (t) = 10 years
P = The population of the city of California at the time t
Now using the formula;
P = Poe^rt
P = 37 * 10^6 e^0.01 * 10
P = 4.089 * 10^7 or 41 million
They would have a population of 41 million in ten years.
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Answer to following question
1. The bank discount on the note of $6,000, maturable in 160 days at 3.5%, is $93.33.
2. The original noteholder will receive total proceeds of $5,906.67 after the bank discount.
What is a bank discount?Bank discount is the difference between the below-par and par (face) values.
For example, if the bank discounts a note, the noteholder will receive an amount smaller than the face value they would have received if they had held the note till its maturity.
The discount represents the finance charge levied for cashing the note earlier than its due date.
Amount due at maturity = $6,000
Discount rate = 3.5%
Time (period) = 160 days
Days in the year for ordinary interest = 360 days
Bank discount = $93.33 ($6,000 x 3.5% x 160/360)
The proceeds = $5,906.67 ($6,000 - $93.33)
Thus, the bank discount is the difference between the face value and the net proceeds (discounted value) resulting from discounting a note before its maturity.
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Which is the correct notation for A is a subset of B?
The correct notation of A is a subset of B is A⊆B( option B)
What is a subset?A set is a collection of objects or elements.Subsets are a part of one of the mathematical concepts called Sets, grouped in the curly braces, such as {a,b,c,d}.
The elements of sets could be anything such as a group of real numbers, variables, constants, whole numbers, etc. It consists of a null set as well.
If a set A is a collection of even number and set B consists of {2,4,6}, then B is said to be a subset of A, denoted by B⊆A and A is the superset of B.
Therefore the correct notation of A is a subset of B is A⊆B.
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For the following image, find the measure of b:
(ONLY type your numerical answer. Round the the hundredths place.)
Side b =
Answer:
3.73 (m)
Step-by-step explanation:
b = 8 * tan (25)
b = 8 * 0.466308
b = 3.730461
The lines in the graph of part A don’t intersect at two whole numbers on the coordinate grid. Estimate the values of the solution to the nearest one-fourth of a unit. Then substitute the x- and y-values of the approximate solution into the two equations. How close do you get to the constant numbers in each equation?
(4.25,6.5) is the solution of the equation.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The estimate is pretty close for both equations. For the first equation, the estimate results in a value that is only 0.2125 units away from the constant.
For the second equation, the estimate results in a value that is only 0.25 units away from the constant.
The solution lies at approximately (4.25,6.5).
Hence (4.25,6.5) is the solution of the equation.
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A net researched and found that 60% of students in his school ride the bus to school. Abner took a random sample of 50 students and found that 38 ride the bus to school. Which statement correctly describes the sample ratio?
Answer: 224 student ride the bus to school each day.
Step-by-step explanation:
In megan random sample of 60 students number of students preferred riding bus is found out to be 42 student.
Student riding the bus if the total number of students in the bus is 320
ratio of the student surveyed to the student ride bus =
=
Assuming the total number of student riding bus = x
now,
x = 224
hence, 224 student ride the bus to school each day.
Step-by-step explanation:
10) The ratio of a basketball players completed free throws to attempted free throws is 9 to 12. If she
attempted 20 free throws, find how many free throws she cömpleted.
F 15 free throws
G
16 free throws
H 8 free throws
J 11 free throws
If the ratio of a basketball players completed free throws to attempted free throws is 9 to 12. If she attempted 20 free throws, the number of free throws she completed is 27 free throws.
How to find the number of completed free throws?Given data:
Attempted free throws = 9 to 12
Free throws = 20
Formulate
9/12= 20/x
Cross-multiply
9x = 20× 12
9x = 240
Divide both side by 9x
x = 240/9
x = 26.6
x = 27 free throws (Approximately)
Therefore the free throws is 27.
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