The trigonometric function y = sin(3x + π) = 0 for -π/3 ≤ x ≤ π/3.
What is a trigonometric function?A trigonometric function is a function that uses one of the trigonometric ratios.
How to find the possible values of the trigonometric function?Given that we have the trigonometric function y = sin(3x + π) for -π/3 ≤ x ≤ π/3.
To find the range of output values for the range of input values given, we insert the given values of the input into the equation.
So, for the minimum value of y, we substitute x = -π/3 into the equation.
So, y = sin(3x + π)
y = sin(3(-π/3) + π)
y = sin(-π + π)
y = sin(0)
y = 0
For the maximum value of y, we substitute x = π/3 into the equation.
So, y = sin(3x + π)
y = sin(3(π/3) + π)
y = sin(π + π)
y = sin(2π)
y = sin2π
y = 0
So, y = 0 for -π/3 ≤ x ≤ π/3.
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12in to 36in. find the percent of change
Answer:
36 -12 = 24
Step-by-step explanation:
24 / 12 × 100
= 2 × 100
= 200 %
match the volume formula to the description
Answer:
145236 4236. b. fjdjfjfjfjfjdjfjfjfjfjfnfjfjfjfnfjgjfjfnfjf
What is the quotient of -4/5-2
Answer:
-1.3
Step-by-step explanation:
HELP ME OUT PLEASE!!!!!!!
Simplify
Answer:
I believe it is -2a⁶b¹² (the first option)
How many grams of fluorine are required to produce 20.0 grams of FeF3?
Fe + F2 → FeF3
10.1 g of fluorine is required to produce 20.0 grams of FeF3
first, we have to balance the equation:
2Fe+3F₂⇒2FeF₃
The molar mass of FeF₃ is 112.84g/mol. so the num of mol(n) of FeF₃ present in 20.0g of mass is calculated as shown below:
n=20.0g/112.84g/mol
n=0.1772mol
According to the balanced equation on the macroscopic scale, 2 mol of FeF₃ is produced from 3 mol of F₂.
so, 0.1772 mol of FeF₃ is produced from X mol of F₂. where X is calculated as shown below:
X=3 mol/2mol*0.1772 mol
X=0.2658 mol
Hence, 0.2658 mol of F₂ is required. The molar mass of F₂ is 38.0g/mol
so, the mass of 0.2658 mol of F2 is calculated as:
m=0.2658 mol*38.0g/mol
m=10.1g
Hence, 10.1 g of fluorine is required.
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Please help me with this question.
The limits to the function are given as follows:
a) lim x -> -5 f(x) = 10.
b) lim x -> 5 f(x) = -5.
How to calculate the limit of a function?The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.
As the function in this problem does not have discontinuities at the values of x = -5 and x = 5, the limits are in fact given by the numeric values at these points.
The limits are given as follows:
a) lim x -> -5 f(x) = 10. -> as the graph passes through the point (-5,10).
b) lim x -> 5 f(x) = -5. -> as the graph passes through the point (5,-5).
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Which transformation will result in an image that is congruent to its pre-image? (x, y) → (2x, −2y) (x, y) → (x, y − 2) (x, y) → (−x, 2y) (x, y) → (−2x, y − 2)
(x,y) --> (x, y-2)
=======================================================
Explanation:
Choice A can be ruled out because of the jump from x to 2x, and from y to 2y. This is a dilation with a scale factor 2. Meaning the preimage enlarges to a bigger image. Specifically the larger image has side lengths twice as long as the smaller preimage. The larger image of course cannot possibly be congruent to the smaller preimage. Congruent figures must have the same corresponding side lengths.
We'll come back to choice B.
Choice C and choice D are ruled out for similar reasoning as choice A was eliminated.
-------------
To summarize the previous section: We ruled out choices A, C, and D. The only thing left is choice B.
Choice B is a translation. The jump from y to y-2 means we shift the point 2 units down. There is no left or right shifting because x stays the same.
For example, the point (5,12) moves to (5,10).
Notice that dilation is not being applied for choice B.
With any geometric translation, aka shifting, the side lengths will remain intact. Something that is 5 units long will stay 5 units long. No amount of shifting will change the distance.
Therefore, a translation preserves distances and lengths. We consider it a rigid transformation. This is why choice B will have the preimage congruent to the image.
Answer:B) (x, y) → (x, y − 2)
Step-by-step explanation:
The general strategy for solving an equation of the form x/a=b is to?
We have discussed the general strategy for solving an equation of the form x/a = b.
What is an equation?
An equation is a mathematical statement that shows that two expressions are equal. An equation is composed of two sides, separated by an equal sign (=), with each side containing one or more variables, numbers, and/or mathematical operations.
The general strategy for solving an equation of the form x/a = b is to:
Multiply both sides of the equation by a, in order to cancel out the fraction on the left side. This will isolate the variable x on one side of the equation.
Simplify the equation by combining like terms if necessary.
Check the solution by substituting it back into the original equation and verifying that it makes the equation true.
For example, consider the equation x/2 = 4
Multiply both sides by 2: x/2 * 2 = 4 * 2
x = 8
To check the solution, substitute it back into the original equation: x/2 = 4, 8/2 = 4. The equation is true, so x = 8 is the correct solution.
It's important to keep in mind that when solving equations, it is important to follow the order of operations, and also to be careful when dividing or multiplying by zero.
Hence, we have discussed the general strategy for solving the equation.
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Jaden has learned to play 18 1⁄4 of the measures for Fur Elise on the piano. If the song is composed of 108 measures, how many more measures does she have to learn?
Answer:108-8 1/4=89 3/4 Jaden has 89 3/4 measures they still need to learn
Step-by-step explanation:
Answer: 89 3/4
Step-by-step explanation: Jaden played 18 1/4 of the measures and the total of Fur Elise is 108 measures. If you do 108 - 18 1/4 it would be 89 3/4. We did this because the total was 108 and we wanted to know how much of fur elise is left after we played 18 1/4.
The height of a parallelogram is 4.5 cm. The base is twice the height. What is the area
Answer: 40.5 cm.
Step-by-step explanation:
first the formula for a parallelogram is base times height and we know the height is 4.5 cm and the base is twice the height and 4.5+4.5=9 and then 9x4.5= 40.5
−12x−(12x+4)+12=17x−6(3x+56) [Can someone pls tell me what x equal..]
The value of x is 14.957.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign.
The equation is given as,
-12x - (12x + 4) + 12 = 17x - 6(3x + 56)
Since the sign is negative outside the bracket on the left hand side, the signs of terms inside the bracket becomes the opposite of what it has.
-12x - 12x - 4 + 12 = 17x - 6(3x + 56)
Applying the distributive property for the term 6(3x + 56), we get,
-12x - 12x - 4 + 12 = 17x - [(6 × 3x) + (6 × 56)]
-12x - 12x - 4 + 12 = 17x - (18x + 336)
Removing brackets,
-12x - 12x - 4 + 12 = 17x - 18x - 336
Taking all the like terms to separate sides,
-12x - 12x - 17x + 18x = 4 - 12 - 336
-23x = -344
x = -344 / -23
x = 14.957
Hence the value of x for the given equation is 14.957.
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Aria invested $40,000 in an account paying an interest rate of 8\tfrac{3}{8}8 8 3 % compounded daily. Olivia invested $40,000 in an account paying an interest rate of 8\tfrac{1}{8}8 8 1 % compounded quarterly. To the nearest hundredth of a year, how much longer would it take for Olivia's money to triple than for Aria's money to triple?
To the nearest hundredth of a year (period), it will take Olivia's money 0.54 years more to triple than Aria's money to triple.
How the period is determined?The additional period it will take Olivia's money to triple than Aria's is determined as the difference between the two investment periods.
The investment periods are computed using an online finance calculator as follows:
Aria Investment:I/Y (Interest per year) = 8.375%
PV (Present Value) = $40,000
PMT (Periodic Payment) = $0
FV (Future Value) = $-120000
Results:
Number of Periods (N) = 4,788.531
= 13.119 years (4,788.531/365) or 13 years and 1 month
Total Interest = $80,000.00
Olivia's Investment:I/Y (Interest per year) = 8.125%
PV (Present Value) = $40,000
PMT (Periodic Payment) = $0
FV (Future Value) = $-120000
Results:
N = 54.633
= 13.65825 years (54.633 quarters/4) or 13 years and 8 months
Total Interest $80,000.00
The difference in investment period:
13.66 - 13.12
= 0.54 years
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Use tape diagrams to solve these ratio problems.
1. The sport court donated helmets and
footballs to the youth club in the ratio 3:7.
There were 60 pieces of sports equipment
altogether. How many more footballs were
donated than helmets?
24 more footballs were donated than helmets in the given ratio problem.
What is ratio?Ratio refers to the quotient of two values. The expression a:b or a/b can be used to represent the ratio of a to b. A is the antecedent and b is the consequent in both scenarios. Every time we make comparisons, ratios appear.
For simplicity, they are typically expressed in the simplest terms. In a school with 1,000 students and 50 teachers, there are 20 students for every teacher.
The golden ratio of classical architecture is an example of an aspect ratio, which is the ratio of a rectangle's width to height. A proportion is an equation that results from setting two ratios equal to one another.
Lets 3x be the no. of helmet and 7x be football distributed.
total pieces = 3x + 7x
3x + 7x = 60
10x = 60
x = 60/10
x = 6
3x = 3(6) = 18
7x = 7(6) = 42
Difference = 42 - 18
= 24
Thus, 24 more footballs were donated than helmets in the given ratio problem.
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A sequence is shown below.
8.0, 6.5, 5.0, 3.5, . . .
In the recursive formula for the sequence, if an=−4.0 , what is the value of an+1 ?
A
–2.5
B
–5.5
C
–6.0
D
–3.0
The value of the sequence aₙ₊₁ is -5.5
How to determine the value of the sequenceThe definition of the sequence is given as
8.0, 6.5, 5.0, 3.5, . . .
The above definitions imply that we simply subtract 1.5 from the previous term to get the current term
Using the above as a guide,
So, we have the following representation
aₙ₊₁ = aₙ - 1.5
From the question, we have
aₙ = -4.0
Substitute the known values in the above equation, so, we have the following representation
aₙ₊₁ = -4.0 - 1.5
Evaluate
aₙ₊₁ = -5.5
Hence, the value of aₙ₊₁ is -5.5
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What is the answer to 47-2.7?
Answer:
44.3
Step-by-step explanation:
47 - 2.7 = 44.3
Taking away 2.7 from 47 gives us 44.3.
Hope this helped!
60th term of -28 -45 -62
Answer:
-79
Step-by-step explanation:
First Identify the sequence
-28 to -45 is -17
-45 to -62 is -17
This is an Arithmetic Sequence because it is constant
(Constant ; same throughout)
Two Formulas:
a60=28 -45 -62
or
an= -17(60)-11
I need help with this
Answer:
3.Ans
4 is the thousands place value in the number 524,897,123.
The value of the digit 4 would be 4,000,000.
Calculation: 4 x 1,000,000 = 4,000,000
4.Ans
The product of (6*5)*10^3 is 3000. This product has 3 zeroes.
Johns snowmobile weighs 0.3 tons. Mikes snowmobile weighs 500 pounds. What is the difference in the weights of the two vehicles in pounds?”
Since the Johns snowmobile weighs 600 pounds, the weight difference between the two vehicles is 100 pounds.
what is proportionality ?The term "proportionate" refers to relationships that always have the same ratio. For instance, the average number of apples per tree influences how many trees there are in an orchard and how many fruits there are in a harvest of apples. A linear relationship between two numbers or variables is referred to in mathematics as being proportionate. In the same way as the first quantity doubles, so does the other. The other decreases as well when one of the variables is reduced to 1/100th of its previous value.
When two quantities are proportional, it means that when one rises, the other rises as well and that the ratio between the two quantities is constant at all values. As an example, consider a circle's diameter and circumference.
given
2000 pounds make up a ton.
Snowmobile owned by John weighs 600 pounds or 0.3 tons.
The difference between Mike's snowmobile's 500 and 600 pound weights is 100 pounds.
= 600 - 500 = 100 pounds
Since the Johns snowmobile weighs 600 pounds, the weight difference between the two vehicles is 100 pounds.
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as cordenadas do vertice da funcao y=x2-2x-3
Para encontrar as coordenadas do vértice de uma função do tipo y = x² - 2x - 3, podemos seguir os seguintes passos:
Calcular o valor da coordenada x do vértice: para isso, precisamos encontrar o valor de x quando o coeficiente do x na função é igual a zero. Neste caso, temos x² - 2x - 3 = 0. Então, para encontrar x, podemos factorizar esse polinômio e encontrar as raízes: (x-3)(x+1) = 0. Isso nos dá x = 3 ou x = -1. Como estamos procurando o vértice, que é o ponto mais alto ou mais baixo da parábola, descartamos x = -1 e ficamos com x = 3.
Calcular o valor da coordenada y do vértice: agora que temos o valor de x, podemos substituí-lo na função original e calcular o valor de y. Neste caso, temos: y = (3)² - 2(3) - 3 = 9 - 6 - 3 = 0.
Portanto, as coordenadas do vértice da função y = x² - 2x - 3 são (3, 0).
Answer:
Step-by-step explanation:
(x) = x²-2x-3.
a=1 b=-2 c=-3.
Xv = -b/2a = -(-2)/2 = 1.
Yv = -Δ/4a Δ =(2²-(4.(-3))) = 16 -16/4 = -4
Vertex ( 1 , -4 )
Differentiating
f(x) = x²-2x-3.
f '(x) = 2x-2
2x-2 = 0
x=1. Xv = 1.
f(1) = x²-2x-3.
1-2-3 = -4. Yv = -4.
↑
A certain type of concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The concrete is poured into casting cylinders and allowed to set for 28 days. The
concrete's strength is then measured. The following data represent the strength of nine randomly selected casts (in psi). Compute the mean, median, and mode strength of the
concrete (in psi).
3960 4050 3170 3080 2940 3830 4050 4060 3810
Select the com
below:
the answer box to complete your choice
PSI stands for Pounds per Square Inch, and it's the unit of measurement that reflects the air pressure inside your tire.
What is PSI example?For example, a bicycle tire pumped up to 65 psig in a local atmospheric pressure at sea level (14.7 psi) will have a pressure of 79.7 psia (14.7 psi + 65 psi). When gauge pressure is referenced to something other than ambient atmospheric pressure, then the unit would be pound per square inch differential (psid).Pounds per square inchPounds per square inch or PSI is an imperial unit of pressure. Using the imperial units of pounds and square inches, it is a measure of force per unit area. Therefore, 1 PSI is measured as one pound of force applied per one square inch.Given the data representation of the strength of nine randomly selected casts (in psi) as 3960, 4090, 3200, 3100, 2940, 3830, 4090, 4040, 3780.
Mean is the average of the samples
[tex]x={3960+4050+3170+3080+2940+3830+ 4050+4060+3810}[/tex]
x=32950/9
x=3661
is thw sum of the given data
N is the sample size
is the mean
Hence the mean of the data is 3,670psi
MEDIAN
Median is the value at the middle of the data after rearrangement.
On rearranging in ascending order
2940, 3100, 3200, 3,780) 3,830 (3,960, 4040, 4090, 4090
It can be seen that the middle value is 3860. Hence the median of the data is 3860psi.
MODE
Mode is the most occurring data in the dataset. It is the data with the highest frequency. From the data, it can be seen that the only data occurring most (twice) is 4090, hence the modal value is 4090psi
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In this figure, sin < ___ and cos
42 , 16 values of sin and cos
What is sin formula?Let's review some information regarding the sin function before learning the sin formula. The sine function, often known as the sin function, is a periodic function in trigonometry. The ratio of the hypotenuse's length to the perpendicular's length in a right-angled triangle is another way to describe the sine function. Sin is a periodic function that has a period of 2 and a domain and range of (, ), respectively. To determine the sides of a triangle, use the sin formula.
The Sin Formula: What Is It? The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: sin = Perpendicular / Hypotenuse
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In June, Lupita saved $115 for retirement. In July, she saved $165. To the nearest percent, what was the increase in Lupita's retirement savings from June to July?
The increase in Lupita's retirement savings from June to July to the nearest percentage is 44%.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred.
It is given that the initial amount of money Lupita had in June is $115
In July the amount of money Lupita saved increased to $165
We are asked to find this increase in money as a percentage.
Increase in percentage
= {(Final amount of money - Initial amount of money) / Initial amount of money } × 100
= {(165 - 115) / 115 } × 100 = 43.48%. ≈ 44%
Therefore the increase in amount of money saved as percentage is 44%.
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The perimeter of the rectangular base of a monument is 230.5 feet. If the width is equal to its length, what are the dimensions of the base?
The width of the base is ____ feet
The length of the base is ____ feet
The width of the base is __57.625__ feet
The length of the base is __57.625__ feet
What is rectangle?A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.
Given,
Perimeter of the rectangular base of a monument is 230.5 feet.
width is equal to its length
Perimeter of rectangle = 2 (length + width)
230.5 = 2 (length + length)
4 length = 230.5
length = 230.5/4
length = 57.625 feet
thus, width = 57.625 feet
Hence,
57.625 feet is the length of rectangular base.
57.625 feet is the width of rectangular base.
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Rewrite (6+3)9 using the distribute property of multiplication over addition
(2)9
6(9)-3(9)
(9)9
6(9)+3(9)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(6 + 3)9}\leftarrow\text{Your given equation}\\\mathsf{= 9(6 + 3)}\leftarrow\text{Convert your equation to this to make it easier to solve}\\\mathsf{= 9(6) + 9(3)}\leftarrow\text{What you are looking for because it is your answer to this question}\\\mathsf{= 54 + 27}\leftarrow\text{Making it more easier to solve for the overall answer} \\\mathsf{= 81}\leftarrow\text{This is your overall answer to the whole equation}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{Option\ D. \ 6(9) + 3(9)}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
What the slope of the line
Answer:
slope = - [tex]\frac{8}{5}[/tex]
Step-by-step explanation:
calculate the slope m using the slope- formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (4, - 4) ← 2 points on the line
m = [tex]\frac{-4-4}{4-(-1)}[/tex] = [tex]\frac{-8}{4+1}[/tex] = [tex]\frac{-8}{5}[/tex] = - [tex]\frac{8}{5}[/tex]
Determine any data values that are missing from the table, assuming that the data represent a linear function. x y -1 2 0 3 4 2 a. Missing x:1 Missing y:2 c. Missing x:1 Missing y:6 b. Missing x:1 Missing y:5 d. Missing x:2 Missing y:5
The linear function's missing data values are x = 0 and y = 1, which is the right response (B).
What are linear function's ?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = mx + b, where m and b are real values.
Isn't it resembling the slope-intercept form of a line, represented by the equation y = mx + b.
When given as a graph, information about a function is assumed to be linear if the graph is a line.
If the function's details are provided in algebraic form, then f(x) = mx + b indicates that the function is linear.
According to our question-
Using two specified pairs of points from the table, (-9, 3) and (-6, 2), one may calculate the slope as follows:
Let
x₁ = -6, y₁ = 2
x₂ = 95, y₂ = 3
Slope (m) equals (3 – 2)/(-9 – (-6))
Slope (m) equals 1/-3, or 1/3.
By substituting (x, y) = (-9, 3) and m = -1/3 into y = mx + c, it is possible to find c:
⇒ 3 = -1/3(-9) + c
⇒ 3 = 3 + c
⇒ 3 - 3 = c
⇒ c = 0
Change y = mx + c to m = -1/3 and c = 0.
⇒ y = -1/3x
Now, calculate the values of the missing data using the equation:
Please use y = 0.
Hence, x would be:
⇒ 0 = -1/3x
⇒ x = 0
Replace x with -3,
Y then would be:
⇒ y = -1/3(-3) (-3)
⇒ y = 1
Hence, The linear function's missing data values are x = 0 and y = 1, which is the right response (B).
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Write in standard form an equation of the line with the given slope through the given point.
Slope=2/5; (6,7)
Answer:
6x+7y=2/5
im not entirely sure if its correct sorry if u get it wrong-
Intro to circles: circumference
PLEASE HELP
Therefore , the solution of the given problem of circumference of the given figure is 15.7 ft.
what is mean by circumference?The circumference of a circle or other curved geometric object refers to length. It is the boundary across any two-dimensional circular surface measured linearly in one dimension.
Here,
in the given question
first find the length of the diameter
in the figure
Perpendicular = 3ft
Base = 4ft
using Pythagoras rule
(hypotenuse)
(base)2 + (perpendicular)2
(hypotenuse)2=42+32
(hypotenuse)2=16+9
(hypotenuse)2=25
hypotenuse = √25
hypotenuse = 5
in the given figure hypotenuse diameter of the circle
radius(r) =
diameter
== 2.5
circumference of the circle is given by
circumference = 2πr
circumference = 2*3.14 * 2.5
circumference = 15.7ft
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Which sign makes the following statement true? -1/5 _____ -1/2
The sign that makes the following statement -1/5 _____ -1/2 true is <. Option 1
What are inequalities?Inequalities are simply described as a relation that makes a non-equal comparison between two numbers mathematical expressions.
Inequalities are mostly used in comparing two numbers on the number line based on their size.
Mathematically signs used for the representation are;
< represents less than> represents greater than≤ represents greater than or equal to≥ represents less than or equal toFrom the information given, we have that;
-1/5 is not equal to -1/2
Thjs is so because smaller numbers on the negative side of the number line are greater than the larger numbers.
Thus, the sign is <
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Please Help!!! Find the equation using slope-intercept form
Y-intercept = 4
Point: (2,3)
The equation of the line in slope intercept form is y = - 1 / 2 x + 4.
How to represent equation in slope intercept form?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line passes through the points (2, 3) and the y-intercept is 4.
Hence,
y = mx + 4
let's find slope using (2, 3)
3 = 2m + 4
3 - 4 = 2m
2m = -1
divide both sides by 2
m = - 1 / 2
Therefore, the equation of the line is y = - 1 / 2 x + 4.
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