The time(s) that the projectile to reach a height of 80 ft is 3.5 s and time to return to the ground is 1.5 seconds.
What is the time when the projectile reaches the height?
The equation of motion of the projectile is given as;
s = -16t² + v₀t
where;
t is the time of motionv₀ is the initial velocity = 32 ft/ss is the height reachedwhen the height reached = 80 ft, the time of motion is calculated as;
-80 = -16t² + 32t
16t² - 32t - 80 = 0
t = 3.5 seconds or t = -1.5 seconds
Based on the negative sing, we can conclude that the time to return to the ground is 1.5 seconds.
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What is the solution to the system of linear equations shown in the graph?
Answer: (2, 3)
Step-by-step explanation:
The solution to a system of linear equations is where they intersect on a graph.
In this graph, the point of intersection is at (2, 3), so the answer is (2, 3).
Use PMT=
to determine the regular payment amount, rounded to the nearest dollar. In terms of paying less in interest, which is more economical for a $210,000
HT
mortgage: a 30-year foxed-rate at 10% or a 20-year fixed-rate at 9.5%? How much is saved in interest?
Select the correct choice below and fill in the answer box within your choice.
(Do not round until the final answer. Then round to the nearest thousand dollars.)
OA. The 30-year 10% loan is more economical. The buyer will save approximately $ in interest
OB. The 20-year 9.5% loan is more economical. The buyer will save approximately Sin interest.
A circular rug has a diameter of 7 feet. Which is the closest to the area of the rug?
In a survey conducted by a website, employers were asked if they had ever sent an employee home because they were dressed inappropriately. A total of 2765 employers responded to the survey, with 964 saying that they had sent an employee home for inappropriate attire. In a press release, the website makes the claim that more than one-third of employers have sent an employee home to change clothes.
A button hyperlink to the SALT program that reads: Use SALT.
Do the sample data provide convincing evidence in support of this claim? Test the relevant hypotheses using
= 0.05.
For purposes of this exercise, assume that it is reasonable to regard the sample as representative of employers in the United States. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z =
P-value
To test the claim that more than one-third of employers have sent an employee home for inappropriate attire, we can set up the following null and alternative hypotheses:
Null hypothesis: p ≤ 1/3
Alternative hypothesis: p > 1/3
where p is the true proportion of all employers who have sent an employee home for inappropriate attire.
We can use the sample proportion, 964/2765 = 0.349, as an estimate of the true proportion p. To test the hypotheses, we can calculate the test statistic z as:
z = (p - 1/3) / sqrt((1/3)*(2/3)/n)
where n is the sample size (2765).
Plugging in the values, we get:
z = (0.349 - 1/3) / sqrt((1/3)*(2/3)/2765) = 4.28
Using a standard normal distribution table or calculator, the P-value for this test is less than 0.0001 (or approximately 0.0000 when rounded to four decimal places), indicating strong evidence against the null hypothesis.
Therefore, we can reject the null hypothesis and conclude that there is convincing evidence to support the claim that more than one-third of employers have sent an employee home for inappropriate attire.
The trapezoid is composed of a rectangle and two triangles. What is the area of the rectangle? What is the total area of the triangles? What is the area of the trapezoid?
Responses 'ILL GIVE BRAINLY'
Answer:
B) 108 cm²; 27 cm²; 135 cm²--------------------
Area of the rectangle:
A(rectangle) = lw = 12*9 = 108 cm²Area of the two triangles:
A(triangles) = 2*(bh/2) = bh = 3*9 = 27 cm²Area of trapezoid is the sum of the areas we found above:
A(trapezoid) = 108 + 27 = 135 cm²The matching answer choice is B.
Evaluate the line integral ∫CF⋅d r where F=⟨5sinx,−4cosy,10xz⟩ and C is the path given by r(t)=(t^3,−3t^2,2^t) for 0≤t≤1
∫CF⋅d r=
Answer: To evaluate the line integral ∫CF⋅dr, we first need to parameterize the path C in terms of a single variable, say t. The parameterization of C is given by:
r(t) = (t^3, -3t^2, 2^t), 0 ≤ t ≤ 1
We can then write the differential of the path as:
dr = (3t^2, -6t, 2^t ln(2)) dt
Next, we evaluate the dot product F ⋅ dr along the path C:
F(r(t)) ⋅ dr = ⟨5sin(t^3), -4cos(-3t^2), 10t^3(2^t)⟩ ⋅ ⟨3t^2, -6t, 2^t ln(2)⟩ dt
= 15t^2 sin(t^3) + 24t cos(3t^2) + 20t^3 (2^t) ln(2) dt
Finally, we integrate this expression over the interval 0 ≤ t ≤ 1 to get the value of the line integral:
∫CF ⋅ dr = ∫0^1 (15t^2 sin(t^3) + 24t cos(3t^2) + 20t^3 (2^t) ln(2)) dt
This integral cannot be evaluated exactly, but we can use numerical integration to approximate the value. Using a numerical integration tool, the value of the line integral is approximately equal to 11.108.
Therefore:
∫CF ⋅ dr ≈ 11.108
Step-by-step explanation:
PLEASE HELP!!!! PLEASE HELP...I NEED THE AREA!
The area of the composite figure that is composed of triangles and a rectangle is: 154 mm².
How to Find the Area of a Composite Figure?The composite figure given comprises two different triangles and one rectangle. Therefore, to find the area of the composite figure, we need to calculate the area of each shape in the figure.
Area of rectangle = length * width = (7 + 7) * 4
= 14 * 4
Area of rectangle = 56 mm²
Area of the larger triangle = 1/2 * base * height
= 1/2 * 14 * 11
= 77 mm²
Area of the smaller triangle = 1/2 * 14 * 3
= 21 mm²
Therefore, area of the composite figure = 56 + 77 + 21
= 154 mm²
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ERROR ANALYSIS Describe and correct the error in finding the length of GH
Step-by-step explanation:
the arc lenght is usually described by the following formula:
[tex]l = \alpha \times r[/tex]
where l is the arc length, alpha the angle(in radians) and r is the radius.
so in this case, using this formula we get
[tex]l = 75 \times ( \frac{\pi}{180}) \times 5cm[/tex]
we are multiplying 75 x (pi/180) cuz, the angle has to be in radians. then
[tex]l = \frac{365}{180} \pi \: cm = 6.54 \: cm \: \: aprox[/tex]
more sensible than the last result, considering that the total length of the circle is
L=2(pi)r
in this case L= 31.4 cm aprox
Jamie needs to estimate the number of buses he will need in order to transport people to the company picnic. Each bus can carry 56 people, and there are 1,344 people going to the picnic. Jamie decides to use the compatible numbers 60 and 1,200. Will he have enough buses for the picnic?
Answer:20
Step-by-step explanation:
To estimate the number of buses Jamie needs, he can divide the total number of people going to the picnic by the number of people each bus can carry:
1,344 ÷ 56 ≈ 24 buses.
To check if using compatible numbers makes sense, Jamie can use 60 and 1,200, which are both multiples of 10 and closer to the actual numbers:
1,200 ÷ 60 = 20 buses.
Since 20 buses is less than the estimated 24 buses, Jamie will not have enough buses to transport all the people to the picnic. He may need to rent or borrow additional buses or find alternative transportation solutions.
Find f(-2) for f(x) = 5 (3^x)
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ f(x)=5\cdot 3^x\hspace{5em}f(-2)=5\cdot 3^{-2}\implies f(-2)=5\cdot \cfrac{1}{3^2}\implies f(-2)=\cfrac{5}{9}[/tex]
For questions 24, use a Venn diagram or truth table or common form of an argument to decide whether each argument is valid or invalid.
If you are a triathlete, then you have outstanding endurance. LeBron James is not a triathlete. Therefore, LeBron does not have outstanding endurance.
In the Venn diagram , the given statement is invalid.
What is Venn diagram?
Venn diagrams are frequently used in mathematics, statistics, logic, teaching, linguistics, computer science, and business. They are also known as Set diagrams or Logic diagrams.
Here the given Venn diagram the total number of outstanding endurance contains both Lebron James is triathlete and may be not triathlete. But he does have outstanding endurance.
Hence the given statement is invalid.
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which of the following shows an equivalent expression to [(5 * 3) * 12] if only the associative property was used to trasnform the expression
The equivalent expression using associative property is; 5×(3×12).
Given expression is; [(5 × 3) × 12]
The associative property is a property of addition and multiplication that allows the grouping of numbers or variables without changing the result.
For addition: (a + b)+c = a+(b + c)
For multiplication: (a × b) ×c = a × (b × c)
In simpler terms, it means that you can add or multiply a set of numbers in any order, and still get the same result.
Therefore, the equivalent expression to [(5 × 3) × 12] using only the associative property would have the same operands but a different grouping. One possibility would be;
[(5 × 3) × 12] = [5 × (3 × 12]
Both expressions simplify to 180.
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It is estimated that about 8,616 African cheetahs are living in the wild today and the population is expected to decline at a rate of 9.8% per year. Predict the number of African cheetahs living in the wild in 21 years.
Answer:
456
Step-by-step explanation:
This is a mathematical problem that involves exponential decay. To predict the number of African cheetahs living in the wild in 21 years, we need to use the formula:
N(t)=N0×(1−r)t
where N(t) is the number of cheetahs after t years, N0 is the initial number of cheetahs, and r is the annual rate of decline.
According to 1, scientists estimate that fewer than 8,000 African cheetahs are living in the wild today and that the population is expected to decline at a rate of 9.8% per year. Therefore, we can plug in these values into the formula:
N(21)=8000×(1−0.098)21
Using a calculator, we can simplify this expression to get:
N(21)≈8000×0.057≈456
Therefore, we can predict that there will be about 456 African cheetahs living in the wild in 21 years, if nothing changes.
This is a very alarming number and shows how endangered these animals are. We need to take urgent action to protect them and their habitats from threats such as habitat loss, human-wildlife conflict, and illegal trade.
A round has a diameter of
115
cm
115 cm115, start text, space, c, m, end text and is
25
cm
25 cm25, start text, space, c, m, end text deep. A hose is filling the pool at a rate of
34
,
000
cm
3
34,000 cm
3
34, comma, 000, start text, space, c, m, end text, cubed per minute.
How long will it take to fill the pool to a depth of
20
cm
20 cm20, start text, space, c, m, end text?
Round to the nearest minute.
It will take approximately 6.1 minutes to fill the pool to a depth of 20 cm at the given fill rate.
How to solve for the time it will take to fill the poolFind the radius of the pool:
Since the diameter is 115 cm, the radius (r) will be half of that:
Radius (r) = Diameter / 2
r = 115 cm / 2
r = 57.5 cm
Calculate the volume of the pool when filled to a depth of 20 cm:
Since the pool is round and assuming it has a cylindrical shape, we can use the formula for the volume of a cylinder:
Volume = π × r² × h
where π (pi) is approximately 3.14159, r is the radius, and h is the height (or depth, in this case).
Volume = 3.14159 × (57.5 cm)² × 20 cm
Evaluate the volume:
Volume ≈ 3.14159 × 3306.25 cm² × 20 cm
Volume ≈ 3.14159 × 66125 cm³
Volume ≈ 207354.2 cm³
Calculate the time it takes to fill the pool to a depth of 20 cm:
We are given that the hose fills the pool at a rate of 34,000 cm³ per minute. To find out how long it will take to fill the pool, we can use the following formula:
Time = Volume / Fill Rate
Time ≈ 207354.2 cm³ / 34,000 cm³/min
Time ≈ 6.1 minutes
It will take approximately 6.1 minutes to fill the pool to a depth of 20 cm at the given fill rate.
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d = 8.3 mm
Calculate the radius of the circle.
D = 8.3 mm
The radius of the circle is 4.15 mm.
The radius and diameter are both important properties of a circle, and they are related to each other. The diameter is the distance across the circle through its center, while the radius is the distance from the center to any point on the circle. The radius and diameter are related by the formula
D = 2r
Where "D" is the diameter and "r" is the radius.
To calculate the radius of a circle given its diameter, we use the formula
r = D/2
Where "r" is the radius and "D" is the diameter. The formula tells us that the radius is equal to half of the diameter.
In this case, we are given that the diameter is 8.3 mm. To find the radius, we simply substitute this value into the formula and solve for "r"
r = D/2
r = 8.3 mm/2
r = 4.15 mm
Therefore, the radius of the circle is 4.15 mm.
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Solve for any extraneous solutions
√3x-5=x-8 plss i need help with thiss
The only solution that satisfies the original equation is x ≈ 17.465. The other solution, x ≈ 1.535, is an extraneous solution.
How to check the equation has extraneous solutions or not?
We need to check if either of these solutions is an extraneous solution, which means it does not satisfy the original equation.
Here given equation,
√(3x - 5) = x - 8
Here we want to isolate the square root on one side and square both sides.
Squaring both side,
√(3x - 5)² = (x - 8)²
expanding the right side
3x - 5 = x² - 16x + 64
bringing all terms to one side)
x² - 19x + 69 = 0
We are solving this quadratic equation using the quadratic formula,
x = [19 ± √(19²- 4(1)(69))] / (2(1))
x = [19 ± √(253)] / 2
x ≈ 1.535 or x ≈ 17.465
Now, we plug each solution back into the original equation and see if we get a true statement.
Checking x ≈ 1.535:
√(3(1.535) - 5) = 1.535 - 8
√(0.605) ≈ -6.465 (not true)
Checking x ≈ 17.465,
√(3(17.465) - 5) = 17.465 - 8
√49.59 ≈ 9.465 (true)
Therefore, the only solution that satisfies the original equation is x ≈ 17.465. The other solution, x ≈ 1.535, is an extraneous solution.
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Which of the following is a point-slope equation of a line that passes through
the points (5, 2) and (-1,-6)?
A. y-2-(x-5)
B. y-2--(x-5)
C. y-2-(x-5)
D. y-2--(x-5)
The point-slope equation of a line that passes through the points (5, 2) and (-1,-6) include the following: B. y - 2 = 4/3(x - 5).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-6 - 2)/(-1 - 5)
Slope (m) = -8/-6
Slope (m) = 4/3.
At data point (5, 2) and a slope of 4/3, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = 4/3(x - 5)
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Which fraction is closer to 1 ?
Group of answer choices
They are the same distance from 1
4/7
5/9
5/9 is closer to 1 than 4/7.
To find out, we can subtract each fraction from 1 and take the absolute value of the result. The fraction with the smaller absolute value is closer to 1.
For 4/7:
1 - 4/7 = 3/7
For 5/9:
1 - 5/9 = 4/9
Since 4/9 is smaller than 3/7, 5/9 is closer to 1.
~~~Harsha~~~
What is the distance between (-5, 2) and (4,-9)?
Use the distance formula, d = √ (x2 − X1)² + (Y2 − Y1)².
OA. 8.23
O B. 11.05
O C. 14.21
O D. 16.27
Answer:
d = √ (4 - (-5))² + (-9 - 2)²
d = √ 9² + (-11)²
d = √81 + 121
d = √202
d ≈ 14.21
Therefore, the distance between (-5, 2) and (4, -9) is approximately 14.21 units. The answer is (C) 14.21.
Step-by-step explanation:
leave thanks
A 3,050 foot long road travels directly up a 550 foot tall hill.
Select three equations that can be used to solve for the angle of elevation () from the bottom of the hill to the top of the hill.
The correct three equations that can be used to solve for the angle of elevation () from the bottom of the hill to the top of the hill are,
⇒ tan θ = 550 / 3050
⇒ sin θ = 550 / 3600
⇒ cos θ = 3050/ 3600
We have to given that;
A 3,050 foot long road travels directly up a 550 foot tall hill.
Now, We can formulate;
1) In this case, the opposite side is the height of the hill 550 feet and the adjacent side is the length of the road 3,050 feet.
So, the equation becomes;
⇒ tan θ = 550 / 3050
2) In this case, the opposite side is the height of the hill 550 feet and the hypotenuse is the length of the road plus the height of the hill,
3050 + 550 = 3600 feet
So, the equation becomes;
⇒ sin θ = 550 / 3600
3) In this case, the adjacent side is the length of the road 3050 feet and the hypotenuse is the length of the road plus the height of the hill,
3050 + 550 = 3600 feet.
So, the equation becomes;
⇒ cos θ = 3050/ 3600
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In Data Collection, accuracy may be determined O a. O b. O c. None of the responses are correct By counting the number of values to each other By how close repeated measurements are, to the true value of the attribute being measured O d. By how close repeated measurements of an attribute are, to each other Oe. By how much deviation there is between the measured values and the true value
It is essential to determine accuracy to ensure that the collected data is reliable and can be used to make informed decisions.
How to solve the question?
Data collection is an essential aspect of research and analysis, as it involves gathering information from various sources to make informed decisions. Inaccurate data can lead to incorrect conclusions and flawed decision-making, which can have significant consequences. Therefore, it is crucial to determine the accuracy of the collected data.
Accuracy can be determined in several ways. One way is by how close repeated measurements of an attribute are to each other. This method is known as precision. If repeated measurements are consistent with one another, it indicates that the data is precise. However, precision does not necessarily imply accuracy, as the measured values could be consistently wrong.
Another way to determine accuracy is by how close repeated measurements are to the true value of the attribute being measured. This method is known as validity. Validity ensures that the collected data accurately reflects the attribute being measured. This method is often used in experiments to test the effectiveness of a treatment or intervention. The results of an experiment are valid if they accurately reflect the effects of the treatment or intervention being tested.
Accuracy can also be determined by how much deviation there is between the measured values and the true value. This method is known as error. An error is the difference between the measured value and the true value. The smaller the error, the more accurate the data.
In conclusion, accuracy in data collection is determined by how close the measured values are to the true value, how close repeated measurements are to each other, and how much deviation there is between the measured values and the true value. It is essential to determine accuracy to ensure that the collected data is reliable and can be used to make informed decisions.
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what is the selling price of a shoe when the cost price is K80 and there is a profit of 65% on it
Assuming that the cost price in the question is 80K with a 65% profit percentage on cost price, the selling price of the shoe is 132K.
Given, Cost Price (CP) of the shoe = 80K or 80,000
Profit % = 65%
From the formula, we know,
Profit % = (Profit / Cost Price) * 100
Inserting given values in the formula, we get,
==> 65 = (Profit / 80,000) *100
or, 65 = Profit / 800
Therefore, Profit = 65 * 800
= 52,000
In the case of Profit, Selling Price = Cost Price + Profit
Hence, the Selling Price of the shoe is = 80,000 + 52,000
= 132,000 or 132K (Answer)
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Find the reciprocal of the number. Check that the product of the number and its reciprocal is 1.
-7
Finding the reciprocal of the number -7 gives -1/7
Finding the reciprocal of a numberFrom the question, we have the following parameters that can be used in our computation:
Number = -7
As a general rule, the reciprocal of a number x is 1/x
Using the above as a guide, we have the following:
Reciprocal = -1/7 given that Number = -7
To check, we have
-1/7 * -7
Evaluate
Result = 1
Hence, the reciprocal is 1
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Which diagrams represent the net of a rectangular prism? Select TWO answers choices.
(I know that for sure! <3)
PLEASE HELP!
The profit P (in dollars) made by a cinema from selling x bags of popcorn can be molded by P=2.36x-(x^2/25000)-3500, 0<=x<=50,000.
a) On what intervals is P increasing and decreasing?
b) How many bags of popcorn must the cinema sell in order to maximize profit and what is the maximum profit per bag?
The maximum profit is given as $31,310
How to solvea. In order to determine the intervals in which profitability P increases and decreases, we need to analyze the first derivative of its respective function, P(x).
Given the profit equation: P(x) = 2.36x - (x^2 / 25000) - 3500, the process begins by articulating its derivative, P'(x):
P'(x) = d(2.36x) - d(x^2 / 25000) - d(3500)
P'(x) = 2.36 - (2x / 25000)
P'(x) = 2.36 - x / 12500
Seeing that P'(x) > 0 implies a rising P while P'(x) < 0 portrays a decreasing P, those values must be determined. Subsequently, the critical points may be found by setting P'(x) = 0:
2.36 - x / 12500 = 0
x / 12500 = 2.36
x = 2.36 * 12500
x = 29500
To adequately evaluate the intervals (0, 29500) and (29500, 50000), we must gauge whether P'(x) is positive or negative:
For x greater than zero & less than 29500:
P'(x) = 2.36 - x / 12500 > 0
For x higher than 29500 but falling beneath 50000:
P'(x) = 2.36 - x / 12500 < 0
Hence, P is augmented on the interval from 0 until 29500, whereas it diminishes from 29500 to 50000.
b. Differentiate again the profit function we get
P'(x)= -1/12,500 <0
Therefore the profit will be maximum.
Hence 29500 bags of popcorn must cinema sell in order to maximize profit.
The maximum profit = $31,310
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If x and y vary directly and y is 52 when x is 13 find y when x is 14
Answer:
[tex] \frac{52}{13} = \frac{y}{14} [/tex]
[tex]4 = \frac{y}{14} [/tex]
[tex]y = 56[/tex]
On a certain hot summer's day, 285 people used the public swimming pool. The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $657.50. How many children and how many adults swam at the public pool that day?
On that day, 241 adults and 44 children swam at the public pool.
Let's use a system of equations to solve the problem:
Let x be the number of children who swam.Let y be the number of adults who swam.From the problem, we know that:
x + y = 285 (the total number of people who swam)
1.25x + 2.5y = 657.5 (the total amount collected in admission fees)
We can use the first equation to solve for x in terms of y:
x = 285 - y
Substituting this expression for x into the second equation, we get:
1.25(285 - y) + 2.5y = 657.5
Expanding and simplifying, we get:
356.25 - 1.25y + 2.5y = 657.5
1.25y = 301.25
y = 241
Substituting this value of y into the equation x + y = 285, we get:
x + 241 = 285
x = 44
Therefore, there were 44 children and 241 adults who swam at the public pool that day.
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LAB1 Exp 3
Prescription number
Prescription #1
Prescription #2
Prescription #3
mLs needed of soda
mLs needed of solution
1. Difference between ointment and cream -
Generally, Creams tend to have lighter texture and consistency. They are mostly formulated with a blend of two components, that is water and oil.
What is Ointment?
Ointments are essentially greasy and have thicker consistency. They contain more oil content as compared to creams. Creams are absorbed faster via the skin than ointments. While ointments are absorbed slower through the skin than creams.
2. The label may instruct you to shake a liquid medicine before using so that the active ingredients are evenly distributed throughout it. The important thing to remember is that you have to shake a suspension before giving each dose so that the medicine particles are evenly distributed throughout the liquid.
3. Emulsions are stabilized by adding an emulsifier or emulsifying agents. These agents have both a hydrophilic and a lipophilic part in their chemical structure. In addition to this protective barrier, emulsifiers stabilize the emulsion by reducing the interfacial tension of the system.
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Encuentra la distancia entre los puntos (–
10,–
7) y (–
4,2).
Escribe tu respuesta como un número entero o como una expresión radical totalmente simplificada. No redondees.
Which expression in the result of factoring the expression below by taking out its greatest common factor?
8x^2-24=?
Quadratic Expression: is an expression with the variable with the highest exponent being 2
General form: ax^2 + bx + c
Greatest common factor (GCF): the largest whole number that divides evenly into a set of numbers
When factoring out the GCF of this expression we must look at the "a" term and "c" term
the greatest common factor of the terms a and c is 8we can that factor out the 8 from the original expression, putting it outside the brackets and dividing the original terms by the GCF8/8 =1 and -24/8= -3[tex]8(x^2-3)[/tex] which is the expression factored.
