The most general antiderivative of f(x) = (5/2)sqrt(x) + 2sec^2(x) is:
F(x) = (5/3)x^(3/2) + 2tan(x) + C
To find the most general antiderivative of the function f(x) = (5/2)sqrt(x) + 2sec^2(x), we can integrate each term separately.
The antiderivative of (5/2)sqrt(x) can be found using the power rule of integration. We add 1 to the exponent (1/2) and divide by the new exponent:
∫(5/2)sqrt(x) dx = (5/2) * (2/3)x^(3/2) + C = (5/3)x^(3/2) + C
The antiderivative of 2sec^2(x) can be found using the integral of the secant squared function, which is the tangent function:
∫2sec^2(x) dx = 2tan(x) + C
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if the functional form of a curve is known, differentiation can be used to determine all of the following except the: o a. concavity of the curve o b. location of inflection points on the curve o c. number of inflection points on the curve o d. area under the curve between certain bounds
The process of differentiation is used to determine the rate at which one quantity changes with respect to another.
If the functional form of a curve is known, differentiation can be used to determine various characteristics of the curve. However, there are some features that cannot be determined through differentiation alone.
Firstly, differentiation can be used to find the slope of the curve at any point. This slope represents the rate at which the dependent variable changes with respect to the independent variable. It can also be used to determine whether the curve is increasing or decreasing at a given point. Additionally, differentiation can be used to find the local maxima and minima of the curve, which correspond to the points where the slope is zero.
However, differentiation cannot be used to determine the concavity of the curve. Concavity refers to the shape of the curve and describes whether the curve is bending upwards or downwards. This characteristic can be determined using the second derivative of the function. If the second derivative is positive, then the curve is concave up, while if it is negative, then the curve is concave down.
Similarly, differentiation cannot be used to determine the location or number of inflection points on the curve. Inflection points are the points on the curve where the concavity changes from concave up to concave down or vice versa. To find the location and number of inflection points, the second derivative must be set equal to zero and solved for the independent variable.
Lastly, differentiation cannot be used to determine the area under the curve between certain bounds. This requires integration, which is the inverse operation of differentiation. Integration can be used to find the area between the curve and the x-axis, and can be approximated using numerical methods.
In summary, differentiation can be used to determine various characteristics of a curve, including its slope and local maxima and minima. However, it cannot be used to determine the concavity, location or number of inflection points, or the area under the curve between certain bounds. These features require additional calculations using the second derivative or integration.
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Please answer as soon as possible!
The triangle ABC has its coordinates as shown below.
A:(3,3)
, B:(−2,−2)
, and C:(4,−4)
Triangle ABC is translated 2 units up, 3 units left and then dilated by a scale factor of 4 about the origin to form triangle A' B' C'. What are the coordinates of the vertex B' ? Enter your answer in the box below.
The coordinates of the vertex B' are (-20, 0).
What is a translation?In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the numerical value on the x-coordinate of the pre-image;
g(x) = f(x + N)
Based on the information provided about triangle ABC, we have the following translation:
(x, y) → (x - 3, y + 2)
Point B (-2, -2) → (-2 - 3, -2 + 2) = point B (-5, 0)
Next, we would dilate point B by a scale factor of 4 about the origin:
point B (-5, 0) → (-5 × 4, 0 × 4) = point B' (-20, 0).
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HALP FAST FOR BRAINIEST
Answer:
24
Step-by-step explanation:
Another way to say median is middle value.
Since the five numbers are already arranged from least
to greatest you pick the number in the middle, which is 24.
Answer:
Mark me brainliest Answer D. 24
Step-by-step explanation:
Given 6 email addresses and 6 distinct passwords. Each password is entered once and can give access to only one email address. In how many ways can the passwords be entered to that no password matches its email address?
Please show steps!
I need help for this question
Answer: 8
Step-by-step explanation:
912 is what percent of 1900
48%
912 of 1900 can be written as:
912
1900
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
912
1900
×
100
100
= (
912 × 100
1900
) ×
1
100
=
48
100
Therefore, the answer is 48%
If you are using a calculator, simply enter 912÷1900×100 which will give you 48 as the answer.
Answer: 912 is what percent of 1900, the percent is 48%
Given that information, which figures are reflections of ABCD? Check all that apply.
ABCD
KLMN
WXYZ
WZYX
PQRS
It is based on the given information, the only figure that is definitely a reflection of ABCD is ABCD itself.To determine which figures are reflections of ABCD, we need to understand the concept of reflection. In a reflection, the image is created by flipping the original figure over a line of reflection.
From the given options, we need to analyze each figure and check if it can be obtained by reflecting ABCD.
ABCD: This is the original figure itself.
KLMN: Without more information about the figure KLMN and the line of reflection, we cannot determine if it is a reflection of ABCD.
WXYZ: Without more information about the figure WXYZ and the line of reflection, we cannot determine if it is a reflection of ABCD.
PQRS: Without more information about the figure PQRS and the line of reflection, we cannot determine if it is a reflection of ABCD.
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All of the figures that are reflections of ABCD include the following:
B. KLMN
D. WZYX
What is a reflection?In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
Generally speaking, all congruent geometric figure are reflections of one another. This ultimately implies that, the geometric figures that are reflections of ABCD must be congruent to it and these include the following under a reflection over the y-axis and x-axis:
KLMN
WZYX
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Complete Question:
ABCD ≅ KLMN ≅ PQRS ≅ WXYZ
Given that information, which figures are reflections of ABCD? Check all that apply.
ABCD
KLMN
WXYZ
WZYX
PQRS
to numerically summarize the center of the distribution of a quantitative variable we can use the
To numerically summarize the center of the distribution of a quantitative variable, we can use the measures of central tendency, which include the mean, median, and mode.
The mean is the sum of all the values divided by the number of values, and it is influenced by extreme values or outliers. The median is the middle value in a set of data when they are arranged in order, and it is not affected by outliers. The mode is the most frequent value in a set of data, and it is not always unique or well-defined. Each measure of central tendency has its advantages and disadvantages and should be chosen based on the characteristics of the data and the research question.
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A 0.2 pound packet of candies cost $4. If each candy's
weight is 0.001 pound, the average cost of each candy is
The calculated average cost of each candy is $0.02
Calculating the average cost of each candyFrom the question, we have the following parameters that can be used in our computation:
A 0.2 pound packet of candies cost $4.Each candy's weight is 0.001 pound,using the above as a guide, we have the following:
Average cost = Unit rate * Each candy's weight
Substitute the known values in the above equation, so, we have the following representation
Average cost = 4/0.2 * 0.001
Evaluate
Average cost = 0.02
Hence, the average cost of each candy is $0.02
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write the (Tn) for 1;4;7;10
The nth term of the arithmetic progression is Tₙ = 3n - 2
Given data ,
Let the arithmetic progression be represented as A
Now , the value of A is
A = 1 , 4 , 7 , 10 ..
Now , the first term a = 1
The common difference d = second term - first term
d = 4 - 1 = 3
And , the nth term is Tₙ
where Tₙ = a + ( n - 1 )d
On simplifying , we get
Tₙ = 1 + ( n - 1 )3
Tₙ = 3n - 2
Hence , the nth term is Tₙ = 3n - 2
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Which of the following accurately summarizes a test variable
(independent variable) in an experiment?
Aconstant variable that is not changed
by the experimenter.
O Avariable that is measured in the
experiment.
Avariable that is changed in the
experiment on purpose by the
experimenter.
A statement that gives you information
about the control variable.
A variable that is changed in the experiment on purpose by the experimenter accurately summarizes a test variable (independent variable) in an experiment.
In an experiment, there are different types of variables that are used to measure the effect of the experiment on the outcome.
The independent variable, also known as the test variable, is the variable that is intentionally changed by the experimenter to measure its effect on the dependent variable, which is the variable that is being measured in the experiment.
Therefore, a variable that is changed in the experiment on purpose by the experimenter accurately summarizes a test variable (independent variable) in an experiment.
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Which technique is most appropriate to use to solve each equation?
Drag the name of the technique into the box to match each equation.
The most appropriate technique to use to solve each equation is as follows:
x ² + 4 x = 15: Completing the square2x ( x - 3) = 0: Zero product propertyHow to solve the equations ?When engaging in the process of completing the square, it is advisable to relocate the constant variable to the opposite side of the equation. Calculate the square of half of the coefficient of the term containing x. You can balance the equation by adding this numerical value to each side of it. Compute the square root for each end of the equation.
x ² + 4x = 15
x ² + 4x - 15 = 0
( x + 2) ² = 16
x + 2 = 4 or x + 2 = -4
x = 2 or x = -6
For the zero product property, Factor the left side of the equation. Set each factor equal to 0 and solve for x.
2x ( x - 3) = 0
2x = 0 or x - 3 = 0
x = 0 or x = 3
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you are selling oranges for $3 per pound. in a given day, you sell 100 pounds of oranges. what was your total revenue for that day?
Answer: $300
Step-by-step explanation:
To calculate the total revenue from selling oranges, we need to multiply the amount of oranges sold by the price per pound.
In this case, we sold 100 pounds of oranges at $3 per pound. So, the total revenue for that day is:
Total revenue = Amount of oranges sold × Price per pound
Total revenue = 100 pounds × $3
Total revenue = $300
What is the equation of a line that passes through the points (0,4) and (3,8)?
Answer:
y = 4/3x + 4
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (0,4) and (3,8)
We see the y increase by 4 and the x increase by 3, so the slope is
m = 4/3
Y-intercept is located at (0,4)
So, the equation is y = 4/3x + 4
The slope of the line can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (0, 4) and (x2, y2) = (3, 8)
slope = (8 - 4) / (3 - 0) = 4/3
Now we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is one of the given points. Choosing (0, 4) as the point, we get:
y - 4 = (4/3)(x - 0)
Simplifying:
y - 4 = (4/3)x
y = 4/3 x + 4
Therefore, the equation of the line is y = 4/3 x + 4.
Write a recursive formula for the sequence an = (5)(3)n-1
This formula says that the nth term in the sequence is equal to three times the (n-1)th term in the sequence. By starting with a1 = 5 and applying the recursive formula repeatedly
A recursive formula is a mathematical expression that defines a sequence in terms of previous values in the sequence. For the given sequence an = (5)(3)n-1, we can create a recursive formula using the following steps:
First, we define the base case for the sequence. In this case, the base case is a1 = 5.
Next, we define the recursive formula for the sequence. This formula uses the previous term in the sequence to calculate the next term. For this sequence, we can use the formula an = (5)(3)n-1 = 3an-1.
Using these steps, we can write the recursive formula for the sequence as follows:
a1 = 5
an = 3an-1 for n > 1
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The midpoint of a segment is (4, 3) and one endpoint is (10, 8). Find the coordinates of the other endpoint
The coordinates of the other endpoint of the segment, given the midpoint (4, 3) and one endpoint (10, 8), are (-2, -2).
To find the coordinates of the other endpoint of a segment given its midpoint and one endpoint, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case, we are given the midpoint as (4, 3) and one endpoint as (10, 8). Let's assume the coordinates of the other endpoint are (x, y).
Using the midpoint formula, we can set up the following equations:
((10 + x)/2, (8 + y)/2) = (4, 3)
From the first equation, we can solve for x:
(10 + x)/2 = 4
10 + x = 8
x = 8 - 10
x = -2
From the second equation, we can solve for y:
(8 + y)/2 = 3
8 + y = 6
y = 6 - 8
y = -2
Therefore, the coordinates of the other endpoint are (-2, -2).
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Which of the following is a unit vector perpendicular to the plane determined by the vectors A-2i+ 4j and B=i+j - k? o (-2i+ j - k) ot(+2) 0 1 (-2; - ; -1) -2i+j-k
The vector perpendicular to a plane determined by two vectors A and B can be found by taking their cross product. The unit vector perpendicular to the plane determined by the vectors A and B is (-4/√56)i + (2/√56)j + (-6/√56)k.
A x B = (-2i+4j+0k) x (i+j-k)
= (-4k + 2i + 6j)
To find a unit vector perpendicular to the plane, we need to normalize this vector by dividing it by its magnitude:
|A x B| = sqrt((-4)^2 + 2^2 + 6^2) = sqrt(56)
So, a unit vector perpendicular to the plane determined by A and B is:
(-4k + 2i + 6j) / sqrt(56)
which simplifies to:
(-2i + 3j - k) / sqrt(14)
Therefore, the answer is (-2i + 3j - k).
To find a vector perpendicular to the plane determined by vectors A and B, you need to calculate the cross product of A and B.
A = -2i + 4j
B = i + j - k
Step 1: Calculate the cross product (C) of vectors A and B:
C = (A_y * B_z - A_z * B_y)i - (A_x * B_z - A_z * B_x)j + (A_x * B_y - A_y * B_x)k
Step 2: Plug in the values of A and B:
C = (4 * (-1) - 0 * 1)i - (-2 * (-1) - 0 * 1)j + (-2 * 1 - 4 * 1)k
Step 3: Simplify the expression:
C = -4i + 2j - 6k
Step 4: Find the magnitude of C:
|C| = √((-4)^2 + 2^2 + (-6)^2) = √(16 + 4 + 36) = √56
Step 5: Divide each component of C by its magnitude to find the unit vector:
Unit vector = (-4/√56)i + (2/√56)j + (-6/√56)k
So, the unit vector perpendicular to the plane determined by the vectors A and B is (-4/√56)i + (2/√56)j + (-6/√56)k.
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i need this now in 5 mins please
Answer:
6x + 9 + 13x - 95 = 180
19x - 86 = 180
19x = 266
x = 14
z = 6(14) + 9 = 84 + 9 = 93
What is the freezing point in c of a 0.33 m aqueous solution of Na2so3
The freezing point of a 0.33 m aqueous solution of Na₂SO₃ is -0.077 °C.
To find the freezing point of a solution, we can use the formula:
ΔTf = Kf · m
where ΔTf is the change in freezing point, Kf is the freezing point depression constant (for water, Kf = 1.86 °C/m), and m is the molality of the solution (in moles of solute per kilogram of solvent).
First, we need to calculate the molality of the solution:
m = moles of solute / mass of solvent (in kg)
We are given that the solution is 0.33 m, which means there are 0.33 moles of Na₂SO₃ per kilogram of water. The molar mass of Na₂SO is:
2 Na + 1 S + 3 O = 2(23.0 g/mol) + 32.1 g/mol + 3(16.0 g/mol) = 126.0 g/mol
So, 0.33 moles of Na₂SO₃ is equal to:
0.33 mol × 126.0 g/mol = 41.6 g
Since we have 1 kg of water, the mass of the solvent is 1000 g. Therefore, the molality of the solution is:
m = 41.6 g / 1000 g = 0.0416 mol/kg
Now, ΔTf = Kf · m = (1.86 °C/m) · (0.0416 mol/kg) = 0.077 °C
freezing point = 0 °C - ΔTf = 0 °C - 0.077 °C = -0.077 °C
Therefore, the freezing point of a 0.33 m aqueous solution of Na₂SO₃ is -0.077 °C.
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Answer: -1.84
Step-by-step explanation:
3x1.86x0.33=1.84
0.00-1.84= -1.84
late answer but hope it helps someone!
Select all of the equations below in which q is inversely proportional to r.
q=r+4
q=4/r
q=r/4
q=4r
q=r-4
The equation that represents q being inversely proportional to r is:
q = 4/r
This is because when we say that q is inversely proportional to r, it means that as one variable increases, the other variable decreases in such a way that their product remains constant.
In this case, we can see that if we multiply q and r, we get a constant value of 4.
This is not true for the other equations, so they do not represent q being inversely proportional to r.
Therefore, the equation q = 4/r is the only one in the given options that represents q being inversely proportional to r.
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Packs of 14 juice boxes are on sale for $11. 34. Packs of 16 juice boxes are on sale for $12. 64. Which is the better buy?
To determine which option is the better buy between packs of 14 juice boxes for $11.34 and packs of 16 juice boxes for $12.64, we need to compare the cost per juice box for each option. The better buy is the one that offers a lower cost per juice box.
To calculate the cost per juice box for each option, we divide the total cost of the pack by the number of juice boxes in the pack.
For the pack of 14 juice boxes priced at $11.34, the cost per juice box is:
$11.34 / 14 = $0.81 per juice box
For the pack of 16 juice boxes priced at $12.64, the cost per juice box is:
$12.64 / 16 = $0.79 per juice box
Comparing the two options, we find that the pack of 16 juice boxes offers a lower cost per juice box ($0.79) compared to the pack of 14 juice boxes ($0.81).
Therefore, the better buy is the pack of 16 juice boxes for $12.64, as it provides a lower cost per juice box.
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To determine which option is the better buy between packs of 14 juice boxes for $11.34 and packs of 16 juice boxes for $12.64, we need to compare the cost per juice box for each option. The better buy is the one that offers a lower cost per juice box.
To calculate the cost per juice box for each option, we divide the total cost of the pack by the number of juice boxes in the pack.
For the pack of 14 juice boxes priced at $11.34, the cost per juice box is:
$11.34 / 14 = $0.81 per juice box
For the pack of 16 juice boxes priced at $12.64, the cost per juice box is:
$12.64 / 16 = $0.79 per juice box
Comparing the two options, we find that the pack of 16 juice boxes offers a lower cost per juice box ($0.79) compared to the pack of 14 juice boxes ($0.81).
Therefore, the better buy is the pack of 16 juice boxes for $12.64, as it provides a lower cost per juice box.
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ANSWER BY THE CHOICE IN THE BOTTOM NOT BY WHAT YOU WANT
The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 2, 5
3 1, 3, 4
4 1, 1, 5
5 0, 6
6 7
Key: 3|1 means 3.1
What is the mean, and what does it tell you in terms of the problem?
3.1 feet; The value means the furthest the ball went.
3.875 feet; The value means that a typical throw of the ball results in 3.875 feet.
4.1 feet; The value means this measurement had the most occurrences.
4.65 feet; The value means that a typical throw of the ball results in 4.65 feet.
The mean distance that the heavy ball was thrown in feet is 4.65 feet. This value tells us that on average, a typical throw of the ball results in a distance of 4.65 feet.
To find the mean, we need to first list all the distances and then find the sum of the distances. Finally, we will divide the sum by the number of distances.
Distances: 2.0, 2.2, 2.5, 3.1, 3.3, 3.4, 4.1, 4.1, 4.5, 5.0, 5.6, 6.7
Sum of distances: 2.0 + 2.2 + 2.5 + 3.1 + 3.3 + 3.4 + 4.1 + 4.1 + 4.5 + 5.0 + 5.6 + 6.7 = 51.5
Number of distances: 12
Mean = Sum of distances / Number of distances
Mean = 51.5 / 12 = 4.29 (rounded to two decimal places)
The closest answer to our calculated mean is:
4.65 feet; The value means that a typical throw of the ball results in 4.65 feet.
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A bank manager wishes to provide prompt service for customers at the bank's drive-up window. The bank currently can serve up to 10 customers per 15-minute period without significant delay. The mean arrival rate is 7 customers per 15-minute period. Let X denote the number of customers arriving per 15-minute period. Assume X has a Poisson distribution.
a. Find the probability that 10 customers will arrive in a particular 15-minute period.
b. Find the probability that 10 or fewer customers will arrive in a particular 15-minute period.
c. Find the probability that there will be a significant delay at the drive-up window. That is, find the likelihood that more than 10 customers will arrive during a particular 15-minute period.
To find the probability that 10 customers will arrive in a particular 15-minute period, we can use the Poisson distribution formula:
P(X = k) = (e^(-λ) * λ^k) / k!
Where λ is the mean arrival rate, which is 7 in this case, and k is the number of customers we're interested in, which is 10.
P(X = 10) = (e^(-7) * 7^10) / 10!
Calculating this expression will give us the probability that exactly 10 customers will arrive in a particular 15-minute period.
b. To find the probability that 10 or fewer customers will arrive in a particular 15-minute period, we need to sum up the probabilities of different arrival counts from 0 to 10.
P(X ≤ 10) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 10)
We can use the Poisson distribution formula for each value of k and sum them up to find the cumulative probability.
c. To find the probability of more than 10 customers arriving during a particular 15-minute period, we can calculate the complement of the probability of 10 or fewer customers.
P(X > 10) = 1 - P(X ≤ 10)
This will give us the probability of there being a significant delay at the drive-up window due to more than 10 customers arriving.
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what is the probavility of rolling an eveen number on a 6-sided die first, or rolling a 1 on the second roll
The probability of rolling an even number on the first roll or rolling a 1 on the second roll is 2/3.
To calculate the probability of rolling an even number on the first roll or rolling a 1 on the second roll of a 6-sided die, we can use the principle of addition.
The probability of rolling an even number on the first roll is 3 out of 6 since there are three even numbers (2, 4, and 6) out of six possible outcomes. Therefore, the probability is 3/6 or 1/2.
The probability of rolling a 1 on the second roll is 1 out of 6 since there is only one outcome that results in rolling a 1.
To calculate the combined probability, we add the individual probabilities:
P(rolling an even number on the first roll) + P(rolling a 1 on the second roll) = 1/2 + 1/6 = 4/6 = 2/3
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let f be the function defined by f(x)=2x^2 + 7x -2. Find the following
a. f(-3)
b. f(a+3)
c. f(3a)
d. f(a+h)
The values are a. f(-3) = 7, b. f(a+3) = 2a² + 19a + 37, c. f(3a) = 18a² + 21a - 2, d. f(a+h) = 2a² + 4ah + 2h² + 7a + 7h - 2
What is a function?
A function is a mathematical relationship or rule that assigns a unique output value to each input value. It is a fundamental concept in mathematics and plays a central role in various branches, including calculus, algebra, and analysis.
To evaluate the given function at various values, we substitute the given values into the function and simplify the expression.
a. To find f(-3), we substitute -3 into the function: f(-3) = 2(-3)² + 7(-3) - 2 = 18 - 21 - 2 = 7.
b. To find f(a+3), we substitute a+3 into the function: f(a+3) = 2(a+3)² + 7(a+3) - 2. Expanding and simplifying the expression yields 2a² + 12a + 18 + 7a + 21 - 2 = 2a² + 19a + 37.
c. To find f(3a), we substitute 3a into the function: f(3a) = 2(3a)² + 7(3a) - 2. Simplifying the expression gives 18a² + 21a - 2.
d. To find f(a+h), we substitute a+h into the function: f(a+h) = 2(a+h)² + 7(a+h) - 2. Expanding and simplifying the expression yields 2a² + 4ah + 2h² + 7a + 7h - 2.
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The length of a rectangle is twice its width. If the diagonal measures 10, then find the dimensions of the rectangle.
The dimensions of the rectangle, obtained using Pythagorean Theorem are;
The length of the rectangle = 4·√5 units
The width of the rectangle = 2·√5 units
What is the Pythagorean Theorem?Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equivalent to the square of the length of the hypotenuse side.
Let x represent the width of the rectangle, we get;
The length = 2·x
Therefore, according to Pythagorean Theorem, we get;
√((x² + (2·x)²) = 10
((x² + (2·x)²) = 10² = 100
5·x² = 100
x² = 100 ÷ 5 = 20
x = √(20) = ±2·√5
Whereby the dimensions of a rectangle are natural numbers, we get;
The width of the rectangle, x = 2·√5The length of the rectangle = 2·x = 2 × 2·√5 = 4·√5Learn more on Pythagorean Theorem here: https://brainly.com/question/343682
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out of 550000 given to a school, an amount of 325000 was used.what fraction of the total amount was used
Answer:
Step-by-step explanation:
[tex]\frac{325000}{550000} \\= \frac{325}{550} \\= \frac{65}{110}\\ = \frac{13}{22}[/tex]
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20. Graph the absolute value function f(x) = |x – 2| on the coordinate plane someone please answer showing work on how to do this problem
The absolute value function f(x) = |x – 2| takes a non-negative value for all real numbers x, and it returns 0 only when x = 2.
The graph of f(x) is symmetric about the vertical line x = 2 and has a vertical asymptote at x = 2.
We have,
The absolute value function f(x) = |x – 2| is a piecewise function that returns the positive distance between the input value x and the number 2.
Geometrically,
It represents the distance of a point on the number line from point 2.
On the coordinate plane,
The graph of the absolute value function is V-shaped, with its vertex at the point (2, 0).
The two arms of the V extend indefinitely in opposite directions, passing through the points (-∞, 2) and (2, +∞) on the positive and negative sides of the x-axis, respectively.
Thus,
The absolute value function f(x) = |x – 2| takes a non-negative value for all real numbers x, and it returns 0 only when x = 2.
The graph of f(x) is symmetric about the vertical line x = 2 and has a vertical asymptote at x = 2.
Learn more about functions here:
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Maricopa's Success scholarship fund receives a gift of $ 145000. The money is invested in stocks, bonds, and CDs. Stocks pay 6. 7 % interest, bonds pay 2. 5 % interest, and CDs pay 5. 75 % interest. Maricopa Success invests $ 10000 more in bonds than in CDs. If the annual income from the investments is $ 6977. 5 , how much was invested in each account?
Maricopa Success invested $ in stocks. Maricopa Success invested $ in bonds. Maricopa Success invested $ in CDs
