The complete general form of the equation of the given sinusoidal function is y = 8sin[(27/2π)*(x - 4)] + c.
The general form of an equation for a sinusoidal function is presented below.
y = a×sin[b*(x - h)] + c
The variable "a" denotes the amplitude of the equation. The variable "T" represents the time period of the equation, and T = 2π/b. The variable "h" denotes the phase shift of the equation. The variable "c" denotes the vertical shift of the equation. The amplitude, period, and phase shift are 8, 27, and 4 units to the left, respectively. The general form of the equation of a sinusoidal function can be written as given below.
y = a×sin[b*(x - h)] + c
y = 8sin[(27/2π)*(x - 4)] + c
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Do you think the blue dot represents the y-intercept of this line? Why or why not?
Answer:
No, the point is on the x-axis, it is not a y-intercept.
Which of the three triangles below can be proven congruent by SSS or SAS
Answer:
The answer for number 7 is A
Step-by-step explanation:
I hope this helps
mathematical shapes
Answer:
A square is an sqaure.
Step-by-step explanation:
circle is a circle. :) happy to help
Write the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2x + y = -5. Include your work for each step in your final answer. Type your answer in the box provided to submit your solution.
a) Using variables, write out the formula for the standard form of the equation.
b) Determine the slope of the line.
c) Write the point-slope form of the line.
d) Using the properties of algebra, rearrange the equation into the standard form.
The slope of the line is - 2 with the equation as 2 x + y - 2 = 0
We are given that:
y intercept of the line = 2
Point is (0, 2)
It is parallel to the line 2 x + y = - 5
Slope of line 2 x + y = - 5:
y' = - 2
m = - 2
Slope of parallel lines are equal
m = m'
m' = - 2
Equation of the line:
y - y₁ = m( x - x₁)
y - 2 = - 2( x - 0)
y - 2 = - 2 x
2 x + y - 2 = 0
a) standard form of the equation = 2 x + y - 2 = 0
b) slope of the line = m' = - 2
c) point-slope form = (y - 2) / (x - 0) = - 2
d) Properties of algebra used = cross multiplication and simplification.
Therefore, we get that, the slope of the line is - 2 with the equation as 2 x + y - 2 = 0
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Ken spends $344.76 before tax at a hardware store. If the sales tax rate in his city is 7.5%, what is the total cost of his purchase? Round to the nearest cent if necessary.
Answer:
$318.90
Step-by-step explanation:
Turn the percent into a decimal and multipy it by 344.76
0.075 × 344.76 = 25.857
after you get your answer you subtract 344.76 and 25.857
$344.76 - 25.857 = $318.903
round you answer to the nearest cent
= $318.90
Martha's employee benefits include family health-care coverage. She contributes 18% of the
cost. Martha gets paid biweekly and $108.00 is taken out of each paycheck for family health-care
coverage. How much does her employer contribute annually for the family coverage?
use dollar sign, decimal and comma
The family coverage paid by Martha's employer for health care coverage is $2592.
What is a health care coverage?
Health insurance is a sort of insurance that pays for unexpected medical costs brought on by a disease. These expenditures may be associated with the price of hospitalisation, or the cost of medical visits.
Main body:
Let the total biweekly salary of Martha be x.
Therefore according to question :
18% of x =$108
(18/100)*x =108
x= 600
Martha earns $600 biweekly.
monthly earning of Martha be 600*2 =$1200
Therefore total coverage annually = 108*total salary day
=108*24
=$2592
Hence the answer is $2592.
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There are 90 new houses being built in a neighborhood.last month, 1/5 of them were sold. this month,1/3 of the remaining houses were sold. How many houses were left to be sold?
Step-by-step explanation:
1:
1/5 of 90 = 18 hours which are sold.Means are 72 houses left.
2.
1/3 of 72 =24 houses sold again. Sooo means there are 48 houses left to be sold
What is the greatest integer solution 5 - 3m > -10
Answer:
4
Step-by-step explanation:
5-3m>-10
-5. -5
-3m>-15
/-3. /-3
m<5
so 4 is the highest integer since 4 is less than 5
Hopes this helps please mark brainliest
hourly wage is $10.50. If she
regularly works 40 hours per week, what is
her regular weekly pay?
Answer:
$420
Step-by-step explanation:
multiple 10.50 by 40 to get 420
The drama club sold $1,416 worth of tickets for its fall play. If each ticket cost $8, how many tickets did the club sell?
In triangle XYZ, m∠Z = (4m − 15)° and the exterior angle to ∠Z measures (2m + 3)°. Determine the value of m.
m = 32
m = 28
m = 17
m = 13
Applying the definition of exterior angle of a triangle, the value of m is: m = 32.
What is an Exterior Angle of a Triangle?An exterior angle of a triangle can be defined as the angle formed outside the triangle when one of its side is extended.
The exterior angle to an interior angle, is supplementary to the interior angle. That is, they have a sum of 180 degrees when we add their angle measures together.
Given the following:
Measure of angle Z = 4m - 15
Measure of the exterior angle to angle Z = 2m + 3
Therefore:
4m - 15 + 2m + 3 = 180
Combine like terms
6m - 12 = 180
6m = 180 + 12
6m = 192
6m/6 = 192/6
m = 32
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f(x)=3x^5-x^4-6x+10
x=-2
Answer:
- 90
Step-by-step explanation:
substitute x = - 2 into f(x)
f(- 2) = 3[tex](-2)^{5}[/tex] - [tex](-2)^{4}[/tex] - 6(- 2) + 10
= 3(- 32) - (16) + 12 + 10
= - 96 - 16 + 22
= - 112 + 22
= - 90
[tex]{ \boxed{ \sf{f( - 2) = - 90}}}[/tex]
Step-by-step explanation:
[tex]{ \red{ \tt{f(x) = {3x}^{5} - {x}^{4} - 6x + 10}}}[/tex]
[tex]{ \red{ \tt{f( - 2) = 3( { - 2})^{5} - ( { - 2})^{4} - 6( - 2) + 10}}}[/tex]
[tex]{ \red{ \tt{f( - 2) = 3( - 32) - 16 + 12 + 10}}}[/tex]
[tex]{ \red{ \tt{f( - 2) = - 96 - 16 + 12 + 10}}}[/tex]
[tex]{ \red{ \tt{f( - 2) = - 112 + 22}}}[/tex]
[tex]{ \green{ \boxed{ \bold{f( - 2) = - 90}}}}[/tex]
An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. if 420 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden. what is the length of the garden?
The structure's length is 93 feet long and its width is 62 feet.
What is rectangle?We also refer to a rectangle as an equiangular quadrilateral since all of its angles are equal. A closed 4-sided shape is called a quadrilateral.A rectangle can also be referred to as a right-angled parallelogram because its sides are parallel. A quadrilateral with equal and parallel opposite sides is referred to as a parallelogram. Paralleograms are a specific instance of rectangles.acc to our question -
Let W stand for the rectangle's flower garden's width and L for its length.
A rectangle flower garden with a width that is precisely two thirds of its length is created by an architect.
The following can be written:
W=2/3L
Given that the fence is 310 feet long, the rectangle's perimeter must also be 310 feet.
Perimeter = 2 (L + W)
The perimeter surrounding it)
2w + 2h = 310
2((2/3) * h) + 2h = 310
4h/3 + 2h = 310
10h/3 = 310
10h = 930
h = 93 feet
w = (2/3) * 93
w = 62 feet
Hence, The structure's length is 93 feet long and its width is 62 feet.
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a bag with 2/3 pounds of peanuts can make 1/8 pounds of peanut butter how many pounds of peanuts would be needed to make one pound of peanut butter for middle school
The required pounds of peanut that can make one pound of peanut butter is given as 5 1/3
How to solve for the quantityIf 2/3 pounds of peanut = 1/8 pounds of peanut butter
? quantity of peanut = one pound of peanut butter
This would be better expressed in numbers as
2/3 = 1/8
? = 1
To solve for this , we would have to cross multiply
such that we would have
2/3 = 1/8?
to get the unknown, we have to divide through by 1/8
2/3 ÷ 1/8 = unknown
2/3 x 8/1
= 16/3
= 5 1/3
Hence the required pound that would be needed to make the peanut butter is given as 5 1/3
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Jake and Llana make and sell wooden birdhouses. Jake spent $150 buying supplies. He sells each birdhouse for $15. The equation P = 12x - 120
represents the profit, P, Liana earns for selling x birdhouses. Jake and Llana each made 50 birdhouses.
Which statements are true? Choose all that apply.
A. Jake spent $30 more on supplies than Liana.
B. Jake's birdhouses cost $3 more than Liana's.
C. Llana will have a greater profit than Jake if they each sell all 50 birdhouses.
D.
Llana and Jake will have the same profit if they each sell exactly 20 birdhouses.
E. Llana and Jake each need to sell a minimum of 11 birdhouses in order to make a profit.
(A) and (E) are the true statement.
Given,
In the question:
Jake and Liana make and sell wooden birdhouses. Jake spent $150 buying supplies. He sells each birdhouse for $15. The equation P = 12x - 120 represents the profit, P, Liana earns for selling x birdhouses. Jake and Llana each made 50 birdhouses.
To find the which statement is true?
Now, According to the question:
Jake's Profit: J = 15x - 150
Liana's Profit : P = 12x - 120
(A) when x = 0, P = -120, J = -150
then, 150 - 120 = $30
So, Jake spent $30 more than Liana
So, A is true, B is wrong.
(C) when x = 50 , J = 15 x 50 - 150 = $600
P = 12 x 50 - 120 =$480
Since, 600> 480
(D) when J = P
then, 15x - 150 = 12x = 120
3x = 30
x = 10
x = 10 not equal to 20
So, D is wrong
(E) when P> -0 , and J > 0
then, 12x -120 > 0 and 15x - 150 > 0
=> x > 10
So, the minimum is 11, E is true .
Hence, Above the solution (A) and (E) are the true statement.
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NUMBER SENSE Your Spanish club wants to order 29 hooded sweatshirts that cost $31 each. Explain how you can use
the polynomial identity (a + b)(a - b) = a²-b² and mental math to find the total cost of the hooded sweatshirts.
The total cost of the hooded sweatshirts will be 29 × 31 = $899.
What is multiplication?Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.
Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.
As per the given,
Number of hooded sweatshirts = 29
Cost of one hooded sweatshirt = $31
Total cost = 29 × 31 = $899.
Hence "The total cost of the hooded sweatshirts will be 29 × 31 = $899".
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Jamar has invested $300 in an annuity each month, earning 5.5% interest for 30 years.
Beth has invested $600 in an annuity each month, earning 5.5% interest for 15 years.
Which of the following must be true?
Select the correct answer below:
Answer:
(d) Jamar's ending account balance is higher than Beth's ending balance.
Step-by-step explanation:
You want to know the best description of the relationship between final balances of two ordinary annuities:
300 per month for 30 years at 5.5%600 per month for 15 years at 5.5%Future valueThe attached calculator display shows the ending balance for Jamar's annuity and for Beth's annuity. We assume the final balance is the balance after the final payment. That is, Beth's balance will be known 15 years before Jamar's balance is known.
Jamar's balance: $274,083.57
Beth's balance: $167,247.33
The best description is ...
Jamar's ending account balance is higher than Beth's ending balance.
__
Additional comment
Jamar makes twice as many payments of half the amount each, so his total contribution is the same as Beth's. His early payments are earning interest for twice as long as Beth's, so his account earns more interest.
If its 50 degrees outside and it drops 70 degrees, how cold will it get?. (Please give steps also..)
Answer:
Step-by-step explanation:
50
The Finnish lottery draws 7 numbers from a total of 40 numbers.
What is the probability for a single lottery ticket to have 1 correct?
The probability that a single lottery has one correct number, using the hypergeometric distribution, is of:
0.4159 = 41.59%.
What is the hypergeometric distribution formula?The probability mass function of the hypergeometric distribution is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters of the function are listed as follows:
x is the number of successes in a single trial.N is the size of the population.n is the size of the sample selected in a single trial.k is the total number of desired outcomes.In the context of this problem, the values of these parameters are given as follows:
N = 40, k = 7, n = 7.
The probability that a single lottery has one correct number is P(X = 1), hence x = 1 and the calculation is as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 1) = h(1,40,7,7) = \frac{C_{7,1}C_{33,6}}{C_{40,7}} = 0.4159[/tex]
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Samantha owes $25.50 and borrows another $20.00. She pays back $15.25 of her debt and then earns $45.00. Later, Samantha pays back $22.50 of her debt.
How much debt does she still have to pay back? Show your work.
In the first hour Brady sold 1/3 cupcakes and Jaquan sold 3/8 cupcakes. During the second hour, the sold 2 cupcakes. During the third hour, they sold 75% of the remaining cupcakes. During the fourth hour, they sold the remaining 3 cupcakes. How many did they sell?
The number of cupcakes sold will be 4.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that, in the first hour, Brady sold 1/3 cupcakes and Jaquan sold 3/8 cupcakes. During the second hour, they sold 2 cupcakes. During the third hour, they sold 75% of the remaining cupcakes. During the fourth hour, they sold the remaining 3 cupcakes.
The number of cupcakes sold will be,
N = (1/3) + (3/8) +[(2-1/3-3/8)]+3
N = (1/3)+(3/8) + (7/24)
N = 96 / 24
N = 4
Therefore, the number of cupcakes sold will be 4.
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5x-3/x-1 what is the inverse of this
Answer:
[tex]f^{-1}(x)=\dfrac{3-x}{5-x}, \quad \{x|x\neq 5\}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=\dfrac{5x-3}{x-1}[/tex]
As the given function is a rational function, the domain and range are restricted.
Domain: (-∞, 1) ∪ (1, ∞).Range: (-∞, 5) ∪ (5, ∞).f⁻¹(x) is the notation for the inverse of the function.
The inverse of a function is a reflection in the line y = x.
To find the inverse of the given function, swap f(x) for y:
[tex]\implies y=\dfrac{5x-3}{x-1}[/tex]
Rearrange the equation to isolate x:
[tex]\implies y(x-1)=5x-3[/tex]
[tex]\implies xy-y=5x-3[/tex]
[tex]\implies 3-y=5x-xy[/tex]
[tex]\implies 3-y=x(5-y)[/tex]
[tex]\implies x=\dfrac{3-y}{5-y}[/tex]
Swap the x for f⁻¹(x) and the y for x:
[tex]\implies f^{-1}(x)=\dfrac{3-x}{5-x}[/tex]
The range of the function is the domain of the inverse function.
Therefore, the domain of the inverse function is restricted:
Domain of f⁻¹(x): (-∞, 5) ∪ (5, ∞).Start Fraction w superscript 12 baseline over w superscript 18 baseline End Fraction
A. w30
B. w–30
C. w6
D. w–6
Answer:
answer should be d
Step-by-step explanation:
it's d because if u fraction 6 u will get d
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
There are two mystery numbers. The sum of 6 times the first number and 4 times the second number is -2. The sum of 6 times the first number and 2 times the second number is 8. What are the two numbers?
The first number is 3 and the second number is -5.
According to the question,
We have the following information:
There are two mystery numbers. The sum of 6 times the first number and 4 times the second number is -2. The sum of 6 times the first number and 2 times the second number is 8.
Now, let's take the first number to be x and the second number to be y.
So, we have the following expressions:
6x+4y = - 2
6x = -2-4y ...(1)
6x+2y = 8
Putting the value of 6x from equation 1:
-2-4y+2y = 8
-2-2y = 8
-2y = 8+2
-2y = 10
y = -10/2
y = -5
Putting this value of y in equation 1:
6x = -2-4y
6x = -2-4*(-5)
6x = -2+20
6x = 18
x = 18/6
x = 3
Hence, the first number is 3 and the second number is -5.
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Solve for x.
-8x+14 ≥ 60 OR - 4x + 50 < 58
Choose 1 answer:
(A
E
x≤-
x≤
-
23
4
23
4
x>-2
or x>-2
There are no solutions
All values of a are solutions
Answer:
[tex]x\leq -7 or x > -2[/tex]
Step-by-step explanation:
-8x+14 ≥ 60 or - 4x + 50 < 58
-8x ≥ 56 or - 4x < 8
[tex]x \leq -7[/tex] or [tex]x > -2[/tex]
a- 10 units
b-12.0 units
c-11.4 units
d-13.4 units
Using the distance formula, the distance between the point is √130.
In the given question we have to find the distance between given point in the graph.
From the graph the given points are (4,4) and (-3, -5).
The formula for the distance between point is
Distance = √{x(2)-x(1)}^2+{y(2)-y(1)}^2
From the given points; x(1)=4, y(1)=4, x(2)= -3 and y(2)= -5.
Now putting the value:
Distance = √{-3-4}^2+{-5-4}^2
Distance = √{-7}^2+{-9}^2
Distance = √49+81
Distance = √130
The distance between the point is √130.
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On a coordinate plane, the position of two friends can be defined by the points A(1,3) and B(7,6). Their teacher is standing at point C, the teacher’s distance from point A is twice the distance from Point B. What are the coordinates of point C?
A.) (5,5)
B.) (-5,5)
C.) (4, 9/2)
D.) (8/3, 3)
Please show work if possible!
The coordinate of point C will be (5, 5). Then the correct option is A.
What is the section of the line?Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
On a direction plane, the place of two companions can be characterized by the focuses A(1,3) and B(7,6). Their instructor is remaining at point C, and the educator's separation from point An is two times the separation from Point B.
The ratio is given as 2:1.
x = (7 × 2 + 1 × 1) / (2 + 1)
x = 15 / 3
x = 5
y = (6 × 2 + 1 × 3) / (2 + 1)
y = 15 / 3
y = 5
The coordinate of point C will be (5, 5). Then the correct option is A.
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Help a lot of points if u answer this fast but correct
Answer: ZYH
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!!
As part of a major renovation at the beginning of the year, Bonham’s Bakery sold shelving units (store fixtures) that were 13 years old for $2,300 cash. The original cost of the shelves was $7,000 and they had been depreciated on a straight-line basis over an estimated useful life of 15 years with an estimated residual value of $1,300.
Record the sale of the shelving units.
Cash 2300
Accumulated Depreciation 4940
Gain one of fixtures 240
Store fixtures 7000
From the question, we have
Bonham’s Bakery sold shelving units (store fixtures) that were 13 years old for $2,300 cash.
Accumulated Depreciation = (7000-1300)/15*13
=4940
Gain one of fixtures = 240
Store fixtures = 7000
Multiplication:
Mathematicians multiply the numbers in order to calculate the sum of two or more. A fundamental mathematical operation, it is applied frequently in daily life. In order to combine groups of similar sizes, we use multiplication. An illustration of the fundamental concept of repeated addition of the same number is multiplication. The product of two or more numbers refers to the result of the multiplication, and the factors are the amounts that are being multiplied. It is easier to add the same number repeatedly after it has been multiplied.
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Which of the terms below correctly describe(s) the number 17?
A-real
B-irrational
C-rational
D-integer
E-natural
F-imaginary
Answer:
A, C, D, E
Step-by-step explanation:
17 is a positive whole number
All whole numbers are integers and rational
Natural numbers are numbers that are positive whole numbers
It is real since you don't have any negative roots
