Answer:
The correct option is;
f(x) = 3·sin x/8·π + 2
Step-by-step explanation:
The given parameters for the sinusoidal function are;
Amplitude of oscillation = 3
Frequency of oscillation = 1/8·π
Midline of oscillation= 2
The general form of sinusoidal equation is y = A·sin(B(x - C)) + D
Where;
A = The amplitude
B = The frequency
C = The horizontal shift
D = The midline or vertical shift
Substituting the given values into the general form of sinusoidal equation, we have;
f(x) = y = 3·sin(1/8·π(x - 0)) + 2 = 3·sin(x/8·π) + 2
Which gives;
f(x) = 3·sin(x/8·π) + 2.
PLEASE HELP. I WILL REWARD BRAINLY TO WHO EVER ANSWERS CORRECTLY. (ignore selected answer) Recalling the SAT scores are always expressed as multiples of 10, how many points did you get on the test?
Answer:
C
Step-by-step explanation:
Five boxes of crackers cost 9$. At this rate, how much do 20 boxes cost?
Answer:36
Step-by-step explanation: first I did
9÷5=1.80 per box.
so then I did 1.80 x 20 which = 36
Answer:
20 boxes cost $36
Step-by-step explanation:
Using proportions,
5 boxes cost 9$
20 boxes cost X$
Cross multiply
X = 9/5 * 20 = 36$
what is 11.52/128 show your work
Answer:
0.09
Step-by-step explanation:
11.52 / 128
First, divide both numerator and denominator by 2:
2.88 / 32
Divide both numerator and denominator by 4:
0.72 / 8
Divide 0.72 by 8, you get 0.09.
formula of minimmum pressure
Suppose that the market research department of a famous bakery has determined that the most aesthetically pleasing donut has a thickness that is twice the inner radius of the donut (that is, the radius of the donut’s hole). The formula for the inner radius of the donut is given by the equation , where V is the volume of the donut in cubic centimeters. Use the table of values to help you answer the questions about r(v). -30 -0.80 -20 -0.70 -10 -0.55 0 0 10 0.55 20 0.70 30 0.80
Answer:
The information given are;
[tex]r(V)=\sqrt[3]{\dfrac{V}{6\cdot \pi ^{2}}}[/tex]
Where;
r(V) = The radius of the doughnut (cm)
V = The volume of the doughnut (cm³)
The data are;
V, r(V)
-30, -0.8
-20, -0.7
-10, -0.55
0, 0
10, 0.55
20, 0.7
30, 0.8
From the table of values, the identified key features are;
a) There is a direct relationship between the radius and the volume of the doughnut
b) The correlation between the data increases to direct proportionality from the volume of 20 cm³ and above
c) The data values are symmetric and continuous about the y and x-axis
2) There is a direct linear relationship between radius, r and the volume V at end ends of the data between r and V where V = -30 and-20 at one end and 20 and 30 at the other end
b) The x and y-intercept are
The x -intercept = (0, 0)
The x -intercept = (0, 0)
c) The pivot point is the point about which change occurs, therefore, the pivot point is the (10, 0.55)
d) The domain is a member of the set of real numbers, R while the range is also a member of the set of real numbers, R
Step-by-step explanation:
What the answer to this question
Answer:
44
Step-by-step explanation:
Please help...........
Answer:
315.1° (1 d.p.)
Step-by-step explanation:
Please see the attached picture for the full solution.
A chemist whishes to prepare 100 liters of 45% purity of sulphuric acid .He has two kinds of acid solutions in stock ,one is 55% pure and the other is 30% pure .How many leters of each kind should be used for the mixture?
Answer:
the chemist should use 60 liters of 55% solution and 40 litres of 30% solution in order to prepare 100 liters of 45% purity of sulphuric acid.
Step-by-step explanation:
From the given information,
Let x be the litres of 55% pure solution
Let y be the litres of 30% pure solution
Also;
Given that our total volume of solution is 100 litres
x+y =100 ---- (1)
The total solution of pure by related by the sum of the individual pure concentrations to make up the concentration of final solution.
(0.55)(x)+(0.30)(y) = 0.45(100) ---- (2)
From equation (1)
Let ; y = 100 - x
Replacing the value for y = 100 - x into equation (2)
(0.55)(x)+(0.30)(100-x) = 0.45(100)
0.55x + 30 - 0.30x = 45
0.55x - 0.30x = 45 - 30
0.25x = 15
x = 15/0.25
x = 60 liters of 55% solution
From ; y = 100 - x
y = 100 - 60
y = 40 litres of 30% solution.
Therefore, the chemist should use 60 liters of 55% solution and 40 litres of 30% solution in order to prepare 100 liters of 45% purity of sulphuric acid.
Which set of events is an example of dependent events?
A. Rolling an odd number, and then rolling an even number.
B. You choose a number from 1 to 50 from a hat, replace it, and then draw a second number.
C. You choose a marble from a bag, don't replace it, and then choose another marble.
D. You roll a 4, and then spin yellow on a spinner.
C.
Because the marble is not replaced and that affects the next event where another marble is chosen.
Dependent events:
It is the event where one event outcome is dependent on the other event outcome.
Independent events:
It is the event where one event outcome is not dependent on the other event outcome.
You choose a marble from a bag, don't replace it, and then choose another marble.
This is a dependent event.
Since we are not replacing the first marble outcome that is chosen, the next marble outcome is dependent on the first outcome.
Option C is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Dependent events:
It is the event where one event outcome is dependent on the other event outcome.
Independent events:
It is the event where one event outcome is not dependent on the other event outcome.
Now,
A. Rolling an odd number, and then rolling an even number.
This is an independent event.
B. You choose a number from 1 to 50 from a hat, replace it, and then draw a second number.
This is an independent event.
C. You choose a marble from a bag, don't replace it, and then choose another marble.
This is a dependent event.
Since we are not replacing the first marble outcome that is chosen, the next marble outcome is dependent on the first outcome.
D. You roll a 4 and then spin yellow on a spinner.
This is an independent event.
Thus,
You choose a marble from a bag, don't replace it, and then choose another marble.
This is a dependent event.
Since we are not replacing the first marble outcome that is chosen, the next marble outcome is dependent on the first outcome.
Option C is the correct answer.
Learn more about probability here:
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A rectangular piece of wood is 12 centimeters longer than it is wide. A strip 1 centimeter wide is cut off all around. This decreases the area by 120 square centimeters. What were the original dimensions?
Answer:
Length 37 cm, width 25 cm.
Step-by-step explanation:
Let the original dimensions be length x and width x - 12 cms.
The new dimensions will be length (x - 2) and width (x - 12 - 2) = x-14 cm.
So , from the areas, we have:
x(x - 12) - (x - 2)(x - 14) = 120
x^2 - 12x - (x^2 - 16x + 28) = 120
-12x + 16x - 28 = 120
4x = 148
x = 37 cms
So the length was 37 cm and the width was 37-12 = 25 cm.
Please help me with this question... I can't seem to understand
Answer:
d is 83.2 metersStep-by-step explanation:
To calculate the horizontal distance d we use cosine
cos ∅ = adjacent / hypotenuse
From the question
d is the adjacent
the hypotenuse is 145m
So we have
cos 55 = d / 145
d = 145 cos 55
d = 83.16
d is 83.2 meters to 3 significant figures
Hope this helps you
Please answer it now
Answer:
s= 15 (nearest integer), 14.8 (to nearest 10ths)
Step-by-step explanation:
here you need to apply the cosine rule,
[tex] {s}^{2} = {u}^{2} + {t}^{2} - 2ut \cos(s) [/tex]
substituting the values,
u= 13, t=5 and angle S as 60 and solving will give you the answer 14.76 (2 dp)
HELPPPPPPPPPPPPPPPPPPPPPPP
Answer:
1) A'(8, -10)
B'(10, -8)
C'(2, -4)
2) A''(8, -4)
B''(10, -6)
C''(10, -10)
Step-by-step explanation:
1) For reflection across the line y = -1, given that the lowest point is of ABC which is point C with coordinates (2, 2), we have;
The vertical distance from the point C to the line y = -1 is 3 units down, therefore, the coordinate of the reflection of C will be 3 units below the line y = -1 at C'(2, -4)
The coordinates of the point A(8, 8) will be A'(8, -10)
The coordinate of the point B(10, 6) will be B'(10, -8)
2) Given that we have A'(8, -10), B'(10, -8), and C'(2, -4), we have reflection over y = -7, we have;
The coordinates of the point A'(8, -10) will be A''(8, -4)
The coordinate of the point B'(10, -8) will be B''(10, -6)
The coordinate of the point C'(2, -4)will be C''(10, -10)
Which gives, a total translation of -12 units down as follows;
A''(8, -4) - A(8, 8) = (0, -12)
B(10, 6) - B''(10, -6) = (0, -12)
C(2, 2) - C''(10, -10) = (0, -12).
What is the measure of B? A = 35 degrees C = Right angle inside triangle
Answer:
55
Step-by-step explanation:
35+90=125
180-125=55
The interior angles of a triangle should always add up to 180 degrees
Answer:
B=55 degrees
Step-by-step explanation:
if the shape is a triangle then the sum of the angles of the triangle is 180
angles :A+B+C=180
35+B+90=180
B=180-125
B=55 degrees
According to the graph, what is the value of the constant in the equation
below?
A. 10
B. 20
C. 100
D. 4
Answer:
C. 100
Step-by-step explanation:
You can rearrange the equation to say ...
(Height)(Width) = Constant
Multiply any of the coordinate values shown, and you will see the constant is 100.
4×25 = 5×20 = 10×10 = 20×5 = 100
The constant is 100.
Find the product.
(6xyz4)(5xy3)
PLEASE HELP!!! ASAP!!
Answer:
[tex]30x^2y^4z^4[/tex]
Step-by-step explanation:
If we multiply 6x by 5x, we get [tex]30x^2[/tex].
If we multiply y by [tex]y^{3}[/tex], we get [tex]y^{4}[/tex].
z stays the same, since it's not being multiplied by anything.
Hope this helped!
Answer:
Step-by-step explanation:
Multiply each term:
30x^2y^4z^4
Plz mark me brainliest!!
i need help please eeeeeeee
Answer:
4262
Step-by-step explanation:
[tex]543+23+6+3690=\\500+40+3+20+3+6+3000+600+90=\\3000+600+500+90+40+20+6+3+3=\\3600+500+90+40+20+6+3+3=\\4100+90+40+20+6+3+3=\\4190+40+20+6+3+3=\\4230+20+6+3+3=\\4250+6+3+3=\\4256+3+3=\\4259+3=\\4262[/tex]
can anyone help me solve this function?
f-g means to subtract g from f:
(4^x - 8) - (5x+6)
Remove the parenthesis and change the equations sings for g:
4^x-8 -5x -6
Combine like terms:
4^x - 5x - 14
The answer is A.
How does the graph of g(x) = (x + 4)^3-6 compare to the parent function f(x)=x^3 Choices:
Explanation:
f(x) = x^3
f(x+4) = (x+4)^3 .... shifts graph 4 units to the left
f(x+4) - 6 = (x+4)^3 - 6 ... shifts 6 units down
The change from x to x+4 means the xy axis has moved four units to the right (since each input is now 4 units larger). If we hold the curve y = x^3 to be completely still while the xy axis moves 4 units to the right, then the illusion of the curve moving 4 units to the left happens.
The -6 at the end does what you'd expect it to do, and there is no opposites going on here. Whatever the y value is, subtract 6 from it to get the new y value. Effectively this moves the graph down 6 units.
Natasha, Mark and Henry share some sweets in the ratio 7:3:2. Natasha gets 75 more sweets than Henry. How many sweets are there altogether?
Answer:
180
Step-by-step explanation:
Given the ratio = 7 : 3 : 2 = 7x : 3x : 2x ( x is a multiplier ), then
7x = 2x + 75 ( Natasha gets 75 more sweets than Henry )
Subtract 2x from both sides
5x = 75 ( divide both sides by 5 )
x = 15
Thus
total number of sweets = 7x + 3x + 2x = 12x = 12 × 15 = 180
Given a graph for the transformation of f(x) in the format g(x) = f(kx), determine the k value.
ту
g(x)
f(x)
k= -4
k= -1/4
k= 1/4
k= 4
ASAP!!!!
Answer: C
1/4
Step-by-step explanation:
Given a graph for the transformation of f(x) in the format g(x) = f(kx),
This means that for every value of x, f(x) will take the value it would have had at kx, that is, the graph of f(x) is stretched by a factor of 1/k in the direction of positive x-direction.
Therefore, the value of k will be 1/4.
Answer:
k=4
Step-by-step explanation:
Q7-8 PLEASE HELP ME
Answer:
(-4,-7)
Step-by-step explanation:
Use the online graphing calculator called Desmos. That's what I did. Just input the two equations and it'll show you the completed graph. I hope this help you:)
Solve this one 0.2=x/5-1.4
Answer:
x = 8[tex]0.2 = \frac{x}{5} - 1.4[/tex]
Move 1.4 to the left side of the equation
That's
[tex]0.2 + 1.4 = \frac{x}{5} \\ \\ \frac{x}{5} = 1.6[/tex]
Convert the decimal to fraction
That's
1.6 = 8/5
[tex] \frac{x}{5} = \frac{8}{5} [/tex]
Multiply through by 5
We have
[tex] \frac{x}{5} \times 5 = \frac{8}{5} \times 5 \\ \\ \\ x = 8[/tex]
Hope this helps you
what happens to 5/x + 5 as x decreases from a large positive number to a small positive number? does it increase, decrease, or stay the same?
Answer:
Increases
Step-by-step explanation:
It increases because, the greater the value of x the smaller the fraction is. If x was 25 the fraction would be 5/25 this makes the value of the equation 5.2. Now if x was a smaller positive number like 5. Then the fraction would be 5/5 which would cause the equation to be equal to 6.
CAN ANYONE HELP ME! WILL GIVE OUT BRAINLIEST!!
Answer:
C
Step-by-step explanation:
4:10 ≠ 6:8
Which is the simplified form of x Superscript negative 12?
Answer:
1/x^12
Step-by-step explanation:
X^-12....simply move x^-12 to the other side of the division and change the sign of the exponent.
The simplified form of the expression x Superscript negative 12 is 1/ x¹².
What is the rule of exponent?The rule of the exponent is defined as the simplified form of the exponents
(aᵇ)ⁿ = aᵇⁿa⁻ⁿ = 1/aⁿaᵇ * aⁿ = aᵇ⁺ⁿaᵇ / aⁿ = aᵇ⁻ⁿwhere a is the base and b and n are the exponent.
Here given in the question is the expression that x superscript negative 12.
As we now superscript is to write the number in exponent position.
here -12 is written in the superscript of x.
then the mathematical expression will be converted as
x superscript negative 12 = x⁻¹²
As we know from the rule of exponent that a⁻ⁿ = 1/aⁿ where a is the base and n is the exponent.
x⁻¹² can be rewritten as x⁻¹² = 1/ x¹²
Therefore the simplified form of the expression x Superscript negative 12 is 1/ x¹².
Learn more about the rule of exponent
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Which of the following shows the division problem below in synthetic division form?
Answer: D
Step-by-step explanation:
In synthetic division, if the divisor is an expression like x+3, you should always switch it to if x+3 were equal to 0.
[tex]x+3=0\\x=-3[/tex]
So, you should use -3. The only options with -3 are B and D.
The coefficients for the dividend are 7, -2, and 4, so D is the correct answer.
Hope this helps! If you still have questions, please ask.
I really need help please
Answer:
1. 2.997
2. 29.93
Step-by-step explanation:
1. You gotta multiply the three sides given, to do this, they all have to be the same unit. Either convert them all to inches or feet then do the operation.
2. Same thing, gotta multiply all given values
Multiplying a trinomial by a trinomial follows the same steps as multiplying a binomial by a trinomial. Determine the degree and maximum possible number of terms for the product of these trinomials: (x2 + x + 2)(x2 – 2x + 3). Explain how you arrived at your answer.
Answer: Degree of polynomial (highest degree) =4
Maximum possible terms =9
Number of terms in the product = 5
Step-by-step explanation:
A trinomial is a polynomial with 3 terms.
The given product of trinomial: [tex](x^2 + x + 2)(x^2 - 2x + 3)[/tex]
By using distributive property: a(b+c+d)= ab+ac+ad
[tex](x^2 + x + 2)(x^2 - 2x + 3)=(x^2 + x + 2) x^2+(x^2 + x + 2) (-2x)+(x^2 + x + 2)(3)\\\\=x^2(x^2)+x(x^2)+2(x^2)+x^2 (-2x)+x (-2x)+2 (-2x)+x^2 (3)+x (3)+2 (3)\\\\\\=x^4+x^3+2x^2-2x^3-2x^2-4x+3x^2+3x+6[/tex]
Maximum possible terms =9
Combine like terms
[tex]x^4+x^3-2x^3+3x^2-4x+3x+6\\\\=x^4-x^3+3x^2-x+6[/tex]
Hence, [tex]\left(x^2\:+\:x\:+\:2\right)\left(x^2\:-\:2x\:+\:3\right)=x^4-x^3+3x^2-x+6[/tex]
Degree of polynomial (highest degree) =4
Number of terms = 5
Answer:
Sample Response: To determine the degree of the product of the given trinomials, you would multiply the term with the highest degree of each trinomial together. Both trinomials are degree 2, and when you multiply x2 by x2, you add the exponents to get x4. Thus, the degree of the product is 4. If the product is degree 4, and there is only one variable, the maximum number of terms is 5. There can be an x4 term, an x3 term, an x2 term, an x term, and a constant term.
The degree of the product of the trinomials is 4 because the degree of each trinomial is 2.
The maximum number of terms in the product of the trinomials is 5.
There can be an x4 term, an x3 term, an x2 term, an x term, and a constant term.
Explanation:
This is the response on Edge 2020-21. Hope this helps, have a great day!
Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square. Need help quick Plz!!!
Answer:
The answer is below
Step-by-step explanation:
The shape of the figure attached is the shape of a sector with an angle of 90° (quarter of a circle).
From the sector, AB = AC = radius of the sector (r) = 12. Therefore:
[tex]Area\ of\ sector=\frac{\theta}{360}*\pi r^2 = \frac{90}{360}*\pi * (12)^2 = 0.25 * \pi * 144=36\pi\\\\Area\ of\ triangle\ ABC=\frac{1}{2}*base *height= \frac{1}{2}*AB*BC=\frac{1}{2}*12*12=72\\\\Area \of\ shaded\ region = Area\ of\ sector-Area\ of\ triangle=36\pi-72\\\\Area \of\ shaded\ region =36\pi-72[/tex]
From the triangle: AC² = AB² + BC²
AC² = 12² + 12² = 144 + 144
AC² = 288
AC=√288 = 12√2
[tex]Perimeter\ of\ sector=\frac{\theta}{360}*2\pi r = \frac{90}{360}*2\pi * (12) = 0.25 * 2\pi * 12=6\pi\\\\Perimeter \of\ shaded\ region = Perimeter\ of\ sector+AC=6\pi + 12\sqrt{2}[/tex]