The smallest positive solution is 13.28⁰.
What is trigonometry?Trigonometry is a discipline of mathematics dealing with particular angle functions and their application to computations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names.
Given,
sin (2x)cos(6x) - cos(2x)sin(6x) = - 0.8
Let, assume 2x = A and 6X= B
As we know, sin (A-B) = sin A cos B - cos A sin B
Putting the value of 2x and 6x in the given equation, we get
or, sin A cos B - cos A sin B = -0.8
or, sin (A-B) = -0.8
or, sin (2x-6x) = - 0.8
or, sin (-4x) = - 0.8
or, - sin 4x = - 0.8
or, sin 4x = 0.8
Apply sin on both side we get,
or, sin⁻¹ (sin 4x) = sin⁻¹ (0.8)
or, 4x = 53.13
or, x = 13.28⁰
The smallest positive solution is 13.28⁰.
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please help me with this
For the given quadratic equation we have:
a) F(-2) = 5
b) F(3) = 40
c) the solutions are:
t = -1
t = -1/3
How to evaluate the quadratic function?Here we have the following quadratic function:
F(t) = 3t^2 + 4t + 1
a) First, we want to determine the value of F(-2), to do so, we just need to replace the values of the variable, t, by the number -2, we will get:
F(-2) =3*(-2)^2 + 4*(-2) + 1
F(-2) = 3*4 - 8 + 1 = 5
F(-2) = 5
b) Now we want to find the value of the F(3), so this time we evaluate in x = 3.
F(3) =3*3^2 + 4*3 + 1
F(3) = 27 + 12 + 1 = 40
F(3) = 40
c) Last, we want to solve:
F(t) = 0
So we need to solve the quadratic equation:
3t^2 + 4t + 1 = 0
Using the quadratic formula we will get the two solutions:
[tex]t = \frac{-4 \pm \sqrt{4^2 - 4*3*1} }{2*3} \\\\t = \frac{-4 \pm 2}{6}[/tex]
Then the two solutions are:
t = (-4 + 2)/6 = -2/6 = -1/3
t = (-4 - 2)/6 = -1
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If using the method of completing the square to solve the quadratic equation x 2 + 14 x − 1 = 0 which number would have to be added to "complete the square"?
The values of x after solving the quadratic equation x²+14x-1 , using completing the square method is -√50-7 or +√50-7.
What is a quadratic equation?
A Quadratic equations is second-degree algebraic expressions and is of the form ax² + bx + c = 0.
Uisng the method of completing the square to solve the equation below, we following the steps.
Equation ⇒ x²+14x-1 = 0
Step 1:
Take the constant to the other side of the equation
x²+14x = 1Step 2:
Find half the coefficient of x, square, and add it to both side of the equation.
Coefficient of x = 14Half coefficient of x = 14/2 = 7square of half the coefficient of x = 7²There,
x²+14x+7² = 1+7²x²+14x+7² = 50Step 3:
Express the trinomial on the left side as a square of binomial
(x+7)² = 50Step 4:
Take the square root of both side.
√(x+7)² = √50x+7 = ±√50Step 5:
Make x the subject of the equation by moving 7 to the other side of the equation
x = ±√50-7Step 6:
Seperate the expression for each value of x
Either x = -√50-7or x = +√50-7Hence, the value of x is -√50-7 or +√50-7.
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Please help, quick!!
Answer:
Step-by-step explanation:
First one is C
Second is B
third i cant see all of the answers
Write a linear function f with f(-3)=1 and f(13)=5.
Answer:
0.25x+1.75
Step-by-step explanation:
A linear equation is of the form ax+b. Set a up a system of equation with -3 and 13 substituted in to ax+b. We get -3a+b=1 and 13a+b=5. Solving tis gives us a,b=(0.25,1.75)
Answer:
f(x) = [tex]\frac{1}{4}[/tex] x + [tex]\frac{7}{4}[/tex]
Step-by-step explanation:
a linear function has the form
f(x) = ax + b ( a and b have to be found )
given f(- 3) = 1 and f(13) = 5 , then by substitution
- 3a + b = 1 → (1)
13a + b = 5 → (2)
subtract (2) from (1) term by term to eliminate b
- 3a - 13a = 1 - 5
- 16a = - 4 ( divide both sides by - 16 )
a = [tex]\frac{-4}{-16}[/tex] = [tex]\frac{1}{4}[/tex]
substitute a = [tex]\frac{1}{4}[/tex] into (1) and solve for b
- 3( [tex]\frac{1}{4}[/tex] ) + b = 1
- [tex]\frac{3}{4}[/tex] + b = 1 ( add [tex]\frac{3}{4}[/tex] to both sides )
b = 1 [tex]\frac{3}{4}[/tex] = [tex]\frac{7}{4}[/tex]
f(x) = [tex]\frac{1}{4}[/tex] x + [tex]\frac{7}{4}[/tex] ← is the linear function
or
f(x) = 0.25x + 1.75
HELP ASAP PLSS!!
I think it’s b I’m not so sure
Answer:
Step-by-step explanation: I think it is 'b' too (sorry if wrong)
Anthony (30) will use the single filing status for 2021. His only income for the year was from wages. In early 2022, he received the following Form W-2 from his employer. He comes to you to have his taxes prepared, and he tells you he would like to contribute to a traditional IRA for 2021, but only if he is eligible to deduct the amount. He has no other adjustments to income. What is the largest amount Anthony can contribute and deduct if he makes the IRA contribution before the filing deadline? (Answer choices are below the image.)
Since Anthony is 30, the largest amount he can contribute and deduct from his Form W-2 for the traditional IRA for 2021 is $6,000.
What is the traditional IRA?The traditional IRA or individual retirement account is a pre-tax contribution an employee saves towards retirement.
With a traditional IRA, Anthony can contribute pre- or after-tax dollars, allowing his savings to grow tax-deferred while withdrawals are taxed as current income unless after the age of 59½.
An additional tax of 10% may apply if Anthony withdraws from his traditional IRA before reaching 59½ years.
However, one advantage of the traditional IRA is that the employee invests more funds upfront since the deduction is mostly made before tax.
Thus, I will advise Anthony to deduct a maximum of $6,000 from Form W-2 towards his traditional IRA to save more money in advance.
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please find the ordered pair MY HOMEWORK IS DUE IN 10 MIN AD I WILL GIVE U BRAINLIST
y= (x/3) +2
y=x-(-1)
y=-x
y=x+4
y=3x+1
y=(1/2)x
Answer:
x = 3y-6
x = -y
x = -y
x=y-4
x = y/3 - 1/3
x = 2y
Step-by-step explanation:
"A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)"
Answer:
2.25 seconds ; 88 feet
Step-by-step explanation:
the maximum height of the rocket is the vertex of the parabola
x coordinate = -72/2(-16)
-72/-32 = 2.25 seconds
y coordinate = -16(2.25)^2 + 72(2.25) + 7
-81 + 162 + 7
-81 + 169
88 feet
On the coordinate plane, point F is located at (x, 8) and point G is located at (1, 4). The
distance between points F and G is √ √52 units.
What are the two possible locations of point F?
Answer:
Step-by-step explanation:
[tex]a^{2} + b^{2} = c^{2} \\4^{2} +b^{2} = (\sqrt{52} )^{2} \\16 + b^{2} = 52\\b^{2} =36\\\sqrt{b^2} =\sqrt{36} \\b=6\\[/tex]
One of the possible x-values of point F will be 6 units to the right of point G. So, the x-value of point F could be 7, since 1+6=7. That means one possible location of point F is (7,8).
The other possible x-value of point F will be 6 units to the left of point G. So, the x-value of point F could be -5, since 1–6=–5. That means the other possible location of point F is (–5,8).
So the answer is:
(7,8) and (-5,8)
Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. This situation is modeled by: 15x + 10y ≥ 1100.
Suppose Ezra decides to also spend more than $80 on a printer. The inequality becomes
15x + 10y
.
The new inequality which represent Ezra's situation is 15x + 10y > 1180
How to write inequality?Cost of the laptop = at least $1100Amount Ezra charge to mow lawns per hour = $15Amount Ezra charge to walk dogs per hour = $10If
Hours spent to mow lawns = xHours spent to walk dogs = yThe inequality:
15x + 10y ≥ 1100
If Ezra decides to also spend more than $80 on a printer, that is, the amount spent on a printer is greater than $80
Adding an amount greater than $80 to the inequality,
It becomes 15x + 10y > 1180
Note the change in sign from greater than or equal to (≥) to greater than (>)
Therefore, the new inequality is given by 15x + 10y > 1180
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find the exact value of n in 9⅓ ×27^n = 27⅘ and express it in fraction . Its urgent
Answer:
n = 26/45
Step-by-step explanation:
If the 9⅓ and 27⅘ are supposed to be [tex]9^{1/3}[/tex] and [tex]27^{4/5}[/tex], then
[tex]9^{1/3}[/tex] × [tex]27^{n}[/tex] = [tex]27^{4/5}[/tex]
=> [tex](3^{2})^{1/3}[/tex] × [tex](3^3)^{n}[/tex] = [tex](3^3)^{4/5}[/tex]
=> [tex]3^{2/3}[/tex] × [tex]3^{3n}[/tex] = [tex]3^{12/5}[/tex]
=> [tex]3^{3n+\frac{2}{3}}[/tex] = [tex]3^{12/5}[/tex]
=> 3n+2/3 = 12/5
=> 45n + 10 = 36
=> 45n = 26
=> n = 26/45
h(x)=x^2-1 what is the average rate of change of h over the interval -3 x -1
For the given function, h(x) = x² - 1, over the interval -3 ≤ x ≤ -1, the average rate of change is 4.
What is function?A function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.
The given function is,
h(x) = x² - 1, and the interval is -3 ≤ x ≤ -1.
To find average rate of change for the function,
Use formula,
Average rate of change = [tex]\frac{h(b)- h(a)}{b-a}[/tex]
h(b) = h(-1) = (-1)² - 1 = 0
h(a) = h(-3) = (-3)² - 1 = 8
Rate of change = [tex]\frac{8 - 0 }{-1 - (-3)}[/tex]
= 8 / 2
= 4
The average rate of change is 4.
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Coach Rogers listed the number of the different types of balls in the storage room. What is the ratio of baseballs to all of the balls?
Group of answer choices
1 : 5
1 : 4
1 : 10
1 : 50
Answer:
1:4
Step-by-step explanation:
Ratio of 40 to 10 = 40:10 = 4:1 (after reducing 40:10 to lowest form). Hence, ratio of 40 to 10 is 4:1.
in a rectangle, if an area
[tex]\textit{area of a rectangle}\\\\ A=Lw ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ A=12\sqrt{30}\\ w=3\sqrt{5} \end{cases}\implies 12\sqrt{30}=L3\sqrt{5}\implies \cfrac{12\sqrt{30}}{3\sqrt{5}}=L \\\\\\ 4\cdot \cfrac{\sqrt{30}}{\sqrt{5}}=L\implies 4\cdot \sqrt{\cfrac{30}{5}}=L\implies 4\sqrt{6}=L[/tex]
(9x)^2/3+(2y)^2/3+z^2/3 using x=3, y=4, z= -1
Answer:
14 ;)
Step-by-step explanation:
(9(3))^(2/3) + (2(4))^(2/3) + (-1)^(2/3)
8 + 4 + 1 = 14
The answer to this math problem is 14.
Pls vote brainliest
help here's a pic on the problem
The linear function that shows the proportional relationship between the distance and time is d = 100t
Linear FunctionA linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.
A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,
'm' is the slope of the line'b' is the y-intercept of the line'x' is the independent variable'y' (or f(x)) is the dependent variableFrom the table given, we can find the slope of the function by using the formula
m = y₂ - y₁ / x₂ - x₁
m = 300 - 200 / 3 - 2
m = 100
To find the y - intercept,
y = mx + c
300 = 100(3) + c
300 = 300 + c
c = 300 - 300
c = 0
The equation that shows the relationship is
d = 100t
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A 0.8-liter bottle of Mexican wine costs 99 pesos. At thatprice, how much would a half-gallon jug of the same wine cost indollars?
A gallon of Mexican wine have a price of 433.13 Mexican pesos.
How much does a half-gallon jug of Mexican wine cost?
Herein we know that 0.8 liters of Mexican wine have a cost of 99 pesos and we need to determine the price for a gallon of the same beverage, that is, 3.5 liters. The price for a gallon can be determined by cross multiplication:
x = 99 MXN × (3.5 L / 0.8 L)
x = 433.13 MXN
A price of 433.13 Mexican pesos must be paid for a gallon of Mexican wine.
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Your parents debt ratio increased, causing their credit score to drop from excellent rate of 5.75% to good rating of 6.20%. How much interest are they being charged during the first month on their mobile home loan of $74,860.00 Group of answer choices $358.70 $346.77 $374.30 $386.78
$336.87 is the interest they being charged during the first month on their mobile home loan of $74,860.00
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Debt ratio increased, causing their credit score to drop from excellent rate of 5.75% to good rating of 6.20%.
We need to find interest they being charged during the first month on their mobile home loan of $74,860.00.
The difference is percentage is 6.0-5.75
0.45%
0.45% of $74,860.00
0.45/100×74,860.00
336.87
Hence, $336.87 is the interest they being charged during the first month on their mobile home loan of $74,860.00
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-7+4/(-2)
follow the order of operations to simplify the following expression
Answer: The answer is -9
Order of operations/PEMDAS:
Parenthesis, Exponents, Multiplication,
Division, Addition, Subtraction
Here is why:
using the order of operations,
do 4/-2 First
4/-2 = -2
Then do -7 + (-2)
-7 + (-2) = -2
When adding a negative plus a negative, it stays negative,
so the expression -7 +(-2) is like 7+2, it will equal 9, but because it is a negative plus a negative, the answer is negative.
Katherine is younger than Alexandra. Their ages are consecutive integers.
square of Katherine's age and 5 times
Find Katherine's age if the sum of the
if the sum of the
Alexandra's age is 109.
Using equations to solve the word problem, Katherine's age is 8 years
Word ProblemWord problem are often mathematical problem that are represented in words and sometimes can be solved using an equation.
To solve this problem, we have to represent the problem using mathematical equations;
Let;
Katherine's age = x²
Alexandra = 5(x + 1)
Sum of their age = 109
5(x + 1) + x² = 109
5x + 5 + x² = 109
x² + 5x - 104 = 0
Solving for the equation; x = 8
Katherine's age is 8
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One year, the population of a city was 209,000. Several years later it was 217,360. Find the percent increase.
The percentage of the increase in population is 4%
How to determine the percentage of the increase?From the question, we have the following parameters that can be used in our computation:
Initial population = 209000
New population = 2017360
The percentage of the increase is then calculated using the following percentage equation
Percentage increase = (New population - Initial population )/Initial population * 100%
Substitute the known values in the above equation, so, we have the following representation
Percentage increase = (217360 - 209000)/209000 * 100%
Evaluate
Percentage increase = 4%
Hence, the increase percentage is 4%
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Solve the equation (1+3)³-(2)2 + 4 =
Answer:
64
Step-by-step explanation:
We can solve this using PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). We do parentheses first, then exponents, all the way down to subtraction:
1. Parentheses
(1 + 3)³ -(2)2 + 4
4³ - (2)2 + 4
(By the way, (2)2 is considered multiplication not parentheses).
2. Exponents
4³ - (2)2 + 4
64 - (2)2 + 4
3. Multiplication
64 - (2)2 + 4
64 - 4 + 4
4. Division
None.
5. Subtraction
(Even though PEMDAS is labeled as addition before subtraction, in the MD | AS part, whichever one comes first in either section of the equation goes first):
64 - 4 + 4
60 + 4
6. Addition
60 + 4
64
Solution:
64
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10. The function y = -3 x+44 represents the amount of money left in your school lunch account y (in dollars) after x days.
a. Identity the independent and dependent variable.
b. After 10 days, how much money is left in your account.
The domain of the equation is 10 days and the range is the $14 left in the account.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
a) The independent variable in this problem is the number of days, represented as x. The amount of money left, the y variable is the dependent variable since it depends on the number of days left (x).
b) If there are 10 days left, we can plug it into the given equation to find the balance in the account.
y = -3x + 44
y = -3(10) + 44
y = -30 + 44
y = 14
Hence, the domain of the equation is 10 days and the range is the $14 left in the account.
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What is the measure of angle b?
A. 36 degrees
B. 63 degrees
C. 144 degrees
D. 180 degrees
Answer:
A - 36 degrees
Step-by-step explanation:
117 - 81, to find another angle when given the outside of the triangle and another part of the triangle, all you have to do is subtract
I have four number cards. The median is 8.
If the range is 10, what are the missing numbers?
Answer:
Below
Step-by-step explanation:
I think you will need to be more specific, but it could be
3 8 8 12 or something like 2 8 8 11 or 1 8 8 10 etc
The probability that Renee will win the race is 0.125.
What are the odds that he will win the race?
a. 1:7
b. 1:5
c. 1:8
d. 3:5
Answer:
c
Step-by-step explanation:
the answer is c.
.
.
.
.
.
.
Answer:
A. 1:7
Step-by-step explanation:
Just took the test
OB. 7,418÷33=R
What is the answer
SOLVE FOR T
t+3/2 = -2
T =
Answer:[tex]t= -\frac{7}{2}[/tex]
Step-by-step explanation:
[tex]=t+\frac{3}{2}=-2\\=t=-2-\frac{3}{2} \\=t=-\frac{7}{2}[/tex]
A movie theater sells popcorn in a reusable bucket for $3.50. They offer refills for $2.50 each.
Write an equation in slope-intercept form to model the cost in dollars, y, for x refills.
The equation in slope-intercept form to model the cost in dollars, y, for x refills is 3.50 = 2.50x + b.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
We have been given that movie theater sells popcorn in a reusable bucket for $3.50. They offer refills for $2.50 each.
The value of y is popcorn cost = $3.50
The slope will be $2.50
Therefore, the equation is y = mx + b
Plug the values; y = 3.50 and m = 2.50
3.50= 2.50x + b
Hence, the equation in slope-intercept form to model the cost in dollars, y, for x refills is 3.50= 2.50x + b.
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PYTHAGORAS THEOREM
How do i find the n
Answer:
and data pro is the best solution assumption that you are a very important thing to me and I am not sure what to do with my
Answer:
this is the answer
Step-by-step explanation:
c² = a² + b²
c = √a²+b²