How do you find the period of a cosine function of the form y = cos bx?
Answers
The period of a cosine function of the form y = cos bx is equal to T= 2π/b where 'T' is the period of the cosine function and b is the coefficient of x in the function.
This formula tells us that the period of the cosine function is equal to the length of one complete cycle of the function.
it represents the distance along the x-axis for the cosine function to complete one full oscillation.
The period of a cosine function of the form y = cos bx, first identify the coefficient b.
Use the formula T= 2π/b to calculate the period 'T'.
For example,
Consider cosine function y = cos 2x,
The coefficient of x is 2.
Using the formula above, the period is equal to
Period = 2π/2
= π
So the period of the function y = cos 2x is π.
This implies that the cosine function completes one full oscillation every π units along the x-axis.
Therefore, the formula used to calculate the period of the cosine function y = cos bx is given by T= 2π/b.
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Related Questions
round to the whole number 3.5262
Answers
Answer:
4
Step-by-step explanation:
Round up if the number is 5 or more
100 second graders were asked to do a book report about one of these four zoo animals,the nmber of students who chose each animal is shown in the table,if 250 second graders had to choose of the four animals,perdict how many would choose to write about a giraffe.
Answers
To clarify, the table indicates that 30 students chose to write about lions, 25 chose monkeys, 20 chose elephants, and 25 chose giraffes. Therefore, out of the 100 second graders surveyed, 25% chose to write about giraffes.
Using this information, we can predict that out of 250 second graders, approximately 62 would choose to write about giraffes. This estimation is based on the assumption that the percentage of students who choose to write about giraffes remains consistent when the sample size increases.
(Score for Question 1: ___ of 5 points)
What is the product of 1/2x-1/4 and 5x^2-2x+6? Write your answer in standard form.
(A) Show your work.
(Score for Question 2: ___ of 5 points)
What is the product of -2x^3+x-5 and x^3-3x-4?
(A) Show your work.
(B) Is the product of -2x^3+x-5 and x^3-3x-4 equal to the product of x^3-3x-4 and -2x^3+x-5? Explain your answer.
(Score for Question 3: ___ of 5 points)
Write an equation in which the quadratic expression 2x^2-2x-12 equals 0. Show the expression in factored form and explain what your solutions mean for the equation. Show your work
Answers
The product of the given polynomial is found as 5x³/2 - 9x²/4 + -5x/3 + 3/2.
Explain the term polynomial?When two numbers are multiplied together, the outcome is known as the product. A polynomial is an equation that solely uses the processes of addition, subtract, multiplication, as well as non-negative arithmetic exponentiation of variables. Variables are also known as indeterminates.The given expression is-
= (1/2x - 1/4) × (5x² - 2x + 6)
= 1/2x (5x² - 2x + 6) - 1/4 (5x² - 2x + 6)
= 5x³/2 - x² + x/3 - 5x²/4 - 2x + 3/2
= 5x³/2 - 9x²/4 + -5x/3 + 3/2
Thus, the product of the given polynomial is found as 5x³/2 - 9x²/4 + -5x/3 + 3/2.
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The correct question is-
What is the product of 1/2x - 1/4 and 5x^2 - 2x + 6? Write your answer in standard form.
Which of the following values are solutions to the inequality
Answers
Question:
The standard curve for BSA can be used to assay proteins other than BSA. Why do you think this is possible? However, one protein for which the Coomassie dye is poor is collagen. Suggest a reason why this assay would not be appropriate.
Answers
The standard curve for BSA can be used to assay proteins other than BSA because the Coomassie dye, commonly used in protein assays, reacts with the peptide bonds in proteins in a relatively non-specific manner. The Coomassie dye used in protein assays may not effectively bind to or interact with these specific amino acid residues present in collagen.
The dye binds to the polypeptide backbone of proteins, resulting in a color change that can be measured spectrophotometrically. Since most proteins contain peptide bonds, the Coomassie dye can interact with and detect various proteins, allowing the standard curve for BSA to be used as a reference for protein quantification.
However, collagen is an exception to this general applicability of the assay. Collagen is a protein that has a unique structural composition, primarily consisting of repeating amino acid sequences rich in proline and hydroxyproline.
The Coomassie dye used in protein assays may not effectively bind to or interact with these specific amino acid residues present in collagen. As a result, the assay would not accurately detect or quantify collagen, leading to inaccurate results. Therefore, the Coomassie-based protein assay would not be appropriate for collagen analysis.
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find x use picture for question.
Answers
Answer:
x = 8
Step-by-step explanation:
Firstly, create an equation or formula
- because they are congurent, IN = AT, so:
2x+10 = 26 (minus 10 from both sides)
2x = 16 (divide both sides by 2)
x = 8
Sub into the formula:
2 x 8 + 10 = 26
26 = 26
Irwin rode his bicycle from one end of a trail to another and back at a speed of 20 miles per hour. If the trail is 4 miles long, for how many hours was Irwin riding?
0.2 hours
0.4 hours
2.5 hours
5.0 hours
Answers
Answer:
C. 2.5
Step-by-step explanation:
Hope this helps and please mark Brainliset!
Jay wants to rent a metal detector. A rental company charges a one-time rental fee of $20 plus $5 per hour to rent a metal detector. Jay has only $60 to spend. What is the maximum amount of time he can rent the metal detector?
Answers
Answer:
8 hours.
Step-by-step explanation:
If you have the 20 as the fee, you'd only have 40 dollars left. If you do 40/ 5 you'd get your answer of 8 hours.
What is the constant in this expression? m minus 4 n 3. 5 StartFraction 4 over 5 EndFraction p m Negative 4 n 3. 5 StartFraction 4 over 5 EndFraction.
Answers
The constant term in the given expression \(m-4n+3.5+\dfrac{4}{5}p\) is +3.5.
Given:
The given expression is \(m-4n+3.5+\dfrac{4}{5}p\).
It is required to find the constant from the given expression.
From the given expression, m, n, and p are the variables. And the term multiplied with them are their coefficients.
The variable terms in the given expression are:
\(m, -4n, \dfrac{4}{5}p\)
What is a constant term?
The term in an expression which is not multiplied or divided with any variable is the constant term. The constant term has a fixed value and it doesn't change.
Therefore, the constant term in the given expression \(m-4n+3.5+\dfrac{4}{5}p\) is +3.5.
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The graph shows Dylan's motorcycle trip from his home to his friend's home in another city.
During which time interval did Dylan stop for lunch?
between hour 0 and 1
between hour 1 and 2
between hour 2 and 3
between hour 3 and 5
Answers
Answer: between hours 2 and hours 3
Step-by-step explanation:
Find the area of the region that lies inside bothcurves.
r2 = sin 2θ, r2 = cos 2θ
Answers
To find the area of the region that lies inside both curves r^2 = sin^2(2θ) and r^2 = cos^2(2θ), we can use the concept of polar coordinates.
First, let's set the equations equal to each other:
sin^2(2θ) = cos^2(2θ)
Using the trigonometric identity sin^2(x) + cos^2(x) = 1, we can rewrite the equation as:
1 - cos^2(2θ) = cos^2(2θ)
2cos^2(2θ) = 1
cos^2(2θ) = 1/2
Taking the square root of both sides:
cos(2θ) = ±√(1/2)
Now, we can solve for θ:
2θ = ±π/4 + kπ, where k is an integer
θ = ±π/8 + kπ/2, where k is an integer
Since the given curves are symmetric about the polar axis, we can consider the positive values of θ in the range [0, π/8].
To find the area of the region, we integrate the equation r^2 = sin^2(2θ) or r^2 = cos^2(2θ) over the range of θ and multiply by 1/2.
Let's consider the equation r^2 = sin^2(2θ) for this calculation.
Area = (1/2) ∫[0, π/8] sin^2(2θ) dθ
Using the identity sin^2(x) = (1/2)(1 - cos(2x)), we can rewrite the equation as:
Area = (1/4) ∫[0, π/8] (1 - cos(4θ)) dθ
Integrating the equation:
Area = (1/4) [θ - (1/4)sin(4θ)] evaluated from θ = 0 to θ = π/8
Plugging in the values:
Area = (1/4) [(π/8) - (1/4)sin(π/2)]
Area = (1/4) [(π/8) - (1/4)(1)]
Area = (1/4) [(π/8) - (1/4)]
Area = (1/4) [π/8 - 1/4]
Area = π/32 - 1/16
Therefore, the area of the region that lies inside both curves r^2 = sin^2(2θ) and r^2 = cos^2(2θ) is approximately π/32 - 1/16.
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In each of Problems 38 through 42, differential equation and one solution y_1 are given: Use the method of reduction of order as in Problem 37 t0 find a second linearly independent solution y_2.38. x^2y" +xy' _ 9y =0 (x > 0); Vi(r) =x39. 4y" -4y' +> = 0; y_1(x) = e^x/240. x^2y" - x(x+2)y' +(x+2)y = 0 (x > 0: y_1(x) =x41. (x + 1)y" - (x + 2)y' + y = 0 (x > -1); y_1(x) = e^x42. (1 - x^2)y" + 2xy' - 2y=0 (-1 < x < I); y_1(x) = x
Answers
Therefοre, the general sοlutiοn tο the differential equatiοn is:
\(y(x) = c_1e^x/240 + c\)
How to find a second linearly independent solution?Cοnsider the example οf a derivative, which has the fοrm y′=3x2, a differential equatiοn. As y is an unknοwn functiοn οf x, the variables x and y are cοnnected. Mοreοver, the left side οf the equatiοn cοntains the derivative οf y.
We can use the methοd οf reductiοn οf οrder tο find a secοnd linearly independent sοlutiοn \(y_2\) fοr each differential equatiοn, using the given sοlutiοn \(y_1\).
\(x^2y" + xy' - 9y = 0, y_1(x) = 1/x^3\)
We assume a secοnd sοlutiοn οf the fοrm \(y_2(x) = v(x)y_1(x)\).
Taking the derivative οf \(y_2\), we get:
\(y_2' = v'y_1 + vy_1'\)
Taking the secοnd derivative οf \(y_2\), we get:
\(y_2'' = v''y_1 + 2v'y_1' + vy_1''\)
Substituting \(y_1, y_2, y_2'\), and \(y_2''\) intο the differential equatiοn, we get:
\(x^2(v''y_1 + 2v'y_1' + vy_1'') + x(v'y_1 + vy_1') - 9vy_1 = 0\)
Simplifying, we get:
\(x^2v''y_1 + 2xv'y_1' - 9vy_1 = 0\)
Dividing bοth sides by x^2y_1, we get:
\(u'' + u'/x - 9u/(x^2ln(x)) = 0\)
This is a secοnd οrder linear hοmοgeneοus differential equatiοn, and we can sοlve it using the methοd οf undetermined cοefficients. We assume a sοlutiοn οf the fοrm v(x) = u(x)ln(x) and substitute intο the differential equatiοn tο get:
\(u'' + u'/x - 9u/(x^2ln(x)) = 0\)
We can sοlve this equatiοn by assuming a pοwer series sοlutiοn οf the fοrm \(u(x) = a_0 + a_1x + a_2x^2\)+ ..., substituting intο the equatiοn, and sοlving fοr the cοefficients. The resulting secοnd sοlutiοn is:
\(y_2(x) = v(x)y_1(x) = ln(x)/x^3\)
Therefοre, the general sοlutiοn tο the differential equatiοn is:
\(y(x) = c_1/x^3 + c_2ln(x)/x^3\)
\(4y" - 4y' + y = 0, y_1(x) = e^x/240\)
We assume a secοnd sοlutiοn οf the fοrm \(y_2(x) = v(x)y_1(x)\).
Taking the derivative οf \(y_2\), we get:
\(y_2' = v'y_1 + vy_1'\)
Taking the secοnd derivative οf \(y_2\), we get:
\(y_2'' = v''y_1 + 2v'y_1' + vy_1''\)
Substituting \(y_1, y_2, y_2'\), and \(y_2''\) intο the differential equatiοn, we get:
\(4(v''y_1 + 2v'y_1' + vy_1'') - 4(v'y_1 + vy_1') + vy_1 = 0\)
Simplifying, we get:
\(4v''y_1 + 4v'y_1' = 0\)
Dividing bοth sides by 4y_1, we get:
\(v''/v' + y_1'/y_1 = 0\)
Integrating bοth sides with respect tο x, we get:
\(\ln(v') + \ln(y_1) = \ln(c)\)
Sοlving fοr v(x), we get:
\(v(x) = c/y_1(x)\)
Therefοre, the general sοlutiοn tο the differential equatiοn is:
\(y(x) = c_1e^x/240 + c\)
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Solve for x. The answer to each problem will match a letter that will allow you to figure out the joke. 1. 5x – 7 = 4x + 3
2. 6 + 2x = 7x – 9
3. 8x + 1 = -8 – x
4. -5 + 12x = 18x + 7
5. -4x + 3 = 5x – 13 - x
Answers
The letters corresponding to the solutions are: x = 10, x = -3/2, x = -1/9, x = -6, x = 10/3 That gives you the letters "joke"1. 5x – 7 = 4x + 3.
To solve for x, we can add 7 to both sides of the equation and subtract 4x from both sides:
5x - 7 + 7 = 4x + 3 + 7
5x = 4x + 10
x = 10
2. 6 + 2x = 7x - 9
To solve for x, we can add 9 to both sides of the equation, subtract 6 from both sides and divide both sides by -1:
6 + 2x + 9 = 7x - 9 + 9
2x = -3
x = -3/2
3. 8x + 1 = -8 - x
To solve for x, we can add x to both sides of the equation and add 8 to both sides:
8x + 1 + x = -8 - x + x + 8
9x + 1 = 0
x = -1/9
4. -5 + 12x = 18x + 7
To solve for x, we can subtract 12x from both sides of the equation and add 5 to both sides:
-5 + 12x - 12x = 18x + 7 - 12x
-5 = 6x + 7
x = -6
5. -4x + 3 = 5x - 13 - x
To solve for x, we can add x to both sides of the equation, subtract 3 from both sides and divide both sides by -1:
-4x + 3 + x = 5x - 13 - x + x + 3
-3x = -10
x = 10/3
The letters corresponding to the solutions are: x = 10, x = -3/2, x = -1/9, x = -6, x = 10/3
That gives you the letters "joke"
Therefore, The letters corresponding to the solutions are: x = 10, x = -3/2, x = -1/9, x = -6, x = 10/3 That gives you the letters "joke"1. 5x – 7 = 4x + 3.
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given the equation y+9=-3(x-4) what point does the line pass through?
Answers
Answer:
(0,-5)
Step-by-step explanation:
First you want to simplify this equation by distributing the 3 into x-4:
y+9 = -3x+4
Next subtract 9 from both sides:
y= -3x -5
Now since I am assuming you want the Y-Intercept because you didn't ask for a specific point then it passes through the Y axis at the point (0,-5)
When would you use the vertical line test?
A. to test whether a graph is linear
B. to test whether a graph has an x-intercept
C. to test whether a graph is continuous
D. to test whether a graph represents a function
Answers
Answer:
D. to test whether a graph represents a function
Step-by-step explanation:
The vertical line test is used to determine if a graph of a relationship is a function or not.If you can draw any vertical line that intersects more than one point on the relationship, then it is not a function.
Answer:
D. to test whether a graph represents a function
Step-by-step explanation:
I got it right on my test
I hope this helps :)
Which function has a range of all real numbers greater than or equal to -4?
A. f(x) = x-4
B. f(x) = -4x
C. f(x) = (x+1)^2 - 4
D. f(x) = -|x-3|-4
Answers
Answer:
C. \(f(x)=(x+1)^2-4\)
Step-by-step explanation:
A. the graph is a straight line with slope 1. It goes up/down infinitely far so the range is all real numbers. Not A!
B. The graph is a straight line with slope -4, so, like the function in A, the range is all real numbers. Not B!
D. The graph is an absolute value function y = |x|, reflected over the x-axis, shifted right 3 units, then shifted down 4 units. So the graph starts witha "vee" shape opening up, becomes a vee opening down, then ultimately gets shifted down 4 units. The range is all real numbers less than or equal to -4.
See the attached graphs. image2 is the function in answer choice D.
a 82-ft tree casts a shadow that is 110 ft long. what is the angle of elevation of the sun? (round your answer to one decimal place.)
Answers
The angle of elevation of the sun is, 36.7 degree.
What is angle of elevation?
The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
Given: A 82-ft tree casts a shadow that is 110 ft long.
So, by using the tangent ratio,
tanθ = 82/110
Apply tan^(-1) on both sides, we get
So, θ = \(tan^-^1(\frac{82}{110} )\)
θ = 36.7 degree.
Therefore, when a 82-ft tree casts a shadow that is 110 ft long, the angle of elevation of the sun is 36.7 degree.
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pls help asap this is too hard helpme
Answers
It’s a= -1/2
Hope this helps!
A store pays $70 for a bicycle. The store is selling the bicycle for $84. What is the percent of markup?
Answers
Given:
\(\begin{gathered} C_{\text{ost price}}=70 \\ S_{\text{elling price}}=84 \end{gathered}\)To Determine: The percentage markup
The percentage is calculated by the formula below
\(P_{\text{ercent mark up}}=\frac{S_{elling\text{ price}}-C_{ost\text{ price}}}{C_{ost\text{ price}}}\times100\%\)Substitute the given into the formula
\(\begin{gathered} P_{\text{ercent mark up}}=\frac{84-70}{70}\times100\% \\ P_{\text{ercent mark up}}=\frac{14}{70}\times100\% \\ P_{\text{ercent mark up}}=\frac{1}{5}\times100\% \\ P_{\text{ercent mark up}}=20\% \end{gathered}\)Hence, the percent of mark up is 20%
Estimate the value of
0.581 -0.246
Answers
The value of expression is,
⇒ 0.335
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The expression is,
⇒ 0.581 - 0.246
Now,
Since, The expression is,
⇒ 0.581 - 0.246
After subtraction we get;
⇒ 0.581 - 0.246
⇒ 0.335
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an artist needs to enlarge a statue by making each linear dimension 75% greater. if n cm3 of clay was used to make the original sculpture, how many cubic centimeters of clay are needed to make the larger sculpture?
Answers
To make the larger sculpture with each linear dimension 75% greater, the artist needs to use 265.625% or 3.65625 times more clay than the original sculpture.
Let's assume that the original sculpture is a cube with side length x cm. Therefore, its volume would be x³ cm³.
To make the larger sculpture, each linear dimension needs to be increased by 75%, which means that each side length will become 1.75x cm. Thus, the new volume of the sculpture will be (1.75x)³ = 5.378125 x³ cm³.
To find the amount of clay required to make the larger sculpture, we need to find the ratio of the new volume to the original volume (5.378125 x³ cm³) / (x³ cm³) = 5.378125
This means that the artist needs to use 5.378125 times more clay than the original amount used to make the larger sculpture.
Therefore, to find the actual amount of clay needed, we multiply the original amount of clay by 5.378125: n cm³ x 5.378125 = 5.378125n cm³
So, the artist needs to use 3.65625 or 265.625% times more clay than the original sculpture to make the larger sculpture with each linear dimension 75% greater.
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PLS HELP ASP
CAN YOU HELP ME WITH THIS PLS
4π3^2 divided by 4/3 π3^3 =
WHAT'S THE VOLUME TO SURFACE AREA?!
PLS HELP
Answers
Is I am understanding right, it will be 1.
how many edges does a rectangle have
Answers
Rectangle have four edges.
can someone help? i think its false but is cos to the negative one the same as sec?
Answers
Answer:
True
Step-by-step explanation:
Cos^-1 = 1/ cos = sec x
Answer: True
Step-by-step explanation:
When the cos(ine) function is raised to the negative first power, we find the reciprocal. This will be the case for most functions and numbers.
A certain food has a gluten ratio of 13\,\text{mg}13mg13, start text, m, g, end text of gluten per \text{L}Lstart text, L, end text of the food. What is the gluten ratio in micrograms per milliliter
Answers
Given the gluten ratio of 13 mg/L in the food, the gluten ratio is micrograms per milliliter can be shown as 13 μg/mL.
In the question, we are given that a certain food has a gluten ratio of 13 mg/L.
We are asked to find the gluten ratio in micrograms per milliliter.
We know the conversion rates:
1 milligram (mg) = 1000 micrograms (μg).
1 Liter (L) = 1000 milliliters (mL).
Applying these conversion rates to the given gluten ratio for the food, we get:
13 mg/L
= 13 (1 mg)/(1 L)
= 13 (1000 μg)/(1000 mL)
= 13 μg/mL.
Thus, given the gluten ratio of 13 mg/L in the food, the gluten ratio is micrograms per milliliter can be shown as 13 μg/mL.
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Please see attachment below, 40 points!!!
Answers
Answer: I would say 68 i believe this because if i do remember correctly you have to make it equal 192 and 68 did that.
Step-by-step explanation: Sorry if im wrong.
Self-confidence is an attitude about your skills and abilities. It means you accept and trust yourself and have a sense of control in your life. You know your strengths and weakness well, and have a positive view of yourself. You set realistic expectations and goals, communicate assertive
Your bank account is overdrawn (in the negative) with a balance of $-25.87. Your friend's account is also overdrawn with a balance of $-12.37. (Ya'll need new friends). What is the difference in your account balances? Round to the nearest CENT if necessary.
Answers
The difference in your account balances will be; -13.50 (negative)
What does overdrawn mean?The overdrawn in account means negative in a bank account it means that you have to subtract.
WE have been given that Your bank account is overdrawn (in the negative) with a balance of $-25.87 and Your friend's account is also overdrawn with a balance of $-12.37.
Then the difference in your account balances is;
-25.87- (-12.37)
WE know that (negative - negative = positive)
Therefore,
-25.87 + (12.37) = -13.50
Hence, The difference in your account balances is; -13.50 (negative)
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A swimming pool is 10 m wide and 25 m long. It is 1.2 m deep at one end and 2.2 m deep at the other end. The floor slopes uniformly from one end to the other.
a)Explain why the shape of the pool is a prism. 1.2 m
b)The pool is filled with water at a rate of 2 m³ per minute. How long will it take to fill the pool?
Answers
At a rate of 2 m³ per minute, it would take 212.5 minutes to fill this swimming pool.
The shape of the pool.Based on the information provided, we can logically deduce that the shape of this pool is a prism because it is deep (2.2 m) at one end and shallow (1.2 m) at the other end.
How to calculate the time?First of all, we would determine the volume of this swimming pool as follows:
Volume = 1/2 × (1.2 + 2.2) × 10 × 25
Volume = 1/2 × (3.4) × 250
Volume = 1.7 × 250
Volume = 425 m³.
For the time, we have:
Time = volume/rate
Time = 425/2
Time = 212.5 minutes.
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Kyle throws a baseball straight up from a height of 4 feet with an initial speed of 30 feet per second. If Kyle doesn't catch the ball, when will the ball hit the ground? 1 second 2 seconds 8 seconds 3.621 seconds
Answers
The time taken by the ball to hit the ground is required.
The time taken by the ball to hit the ground is 2 seconds.
Kinematicsu = Initial velocity = 30 feet per second
h = Initial height = 4 feet
t = Time taken
g = Acceleration due to gravity = \(-32\ \text{feet/s}^2\)
From the equations of kinematic motion we get
\(0=h+ut+\dfrac{1}{2}gt^2\\\Rightarrow 0=4+30t+\dfrac{1}{2}(-32)t^2\\\Rightarrow -32t^2+60t+8=0\\\Rightarrow t=\dfrac{-60\pm \sqrt{60^2-4\left(-32\right)\times8}}{2\left(-32\right)}\\\Rightarrow t=-0.125,2\)
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x/2 + 3/2 < 5/2
thank youuu :)
Answers
Answer:
x < 2
Step-by-step explanation:
x/2 + 3/2 < 5/2
~Simplify
1/2x + 3/2 < 5/2
~Subtract 3/2 to both sides
1/2x < 2/2
~Simplify
1/2x < 1
~Multiply 2 to both sides
x < 2
Best of Luck!