a) The price of the old model is P22,289.
b) The dimensions of the rectangle are 16 by 32.
a) Let x be the price of the old model. According to the problem, the price of the new 32'' LED television is P15,500 less than twice the price of the old model.
This can be expressed as 2x - P15,500 = P29,078. Solving for x, we can add P15,500 to both sides to get 2x = P44,578, and then divide both sides by 2 to get x = P22,289.
b) Let w be the width of the rectangle. According to the problem, the length of the rectangle is twice the width, so the length is 2w. The perimeter of a rectangle is the sum of the lengths of all four sides, which in this case is 2w + 2(2w) = 6w.
We are given that the perimeter is 96, so we can set up an equation: 6w = 96. Solving for w, we can divide both sides by 6 to get w = 16. Since the length is twice the width, the length is 2(16) = 32.
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Find the area of an equilateral triangle with apothem length .
if necessary, write your answer in simplified radical form.
The area of an equilateral triangle with apothem length 'a' is (1/4) * √3 * [tex]a^2[/tex].
How to find the area of an equilateral triangle?Let's label the equilateral triangle as ABC. An apothem is a line segment from the center of the triangle to the midpoint of one of its sides, forming a right angle with that side. Let the apothem of the triangle be 'a'.
The apothem divides the equilateral triangle into two congruent 30-60-90 triangles, where the apothem is the hypotenuse of one of the triangles. The length of the apothem 'a' is also the height of each 30-60-90 triangle.
In a 30-60-90 triangle, the hypotenuse is twice the length of the shorter leg, and the longer leg is √3 times the length of the shorter leg. So, the length of the shorter leg is a/2, and the length of the longer leg (which is also the length of one side of the equilateral triangle) is √3 times the length of the shorter leg. Thus, the length of one side of the equilateral triangle is:
s = √3 * (a/2) = (√3 / 2) * a
The area of the equilateral triangle can be calculated using the formula:
A = (1/2) * base * height
where the base is one side of the equilateral triangle, and the height is the length of the apothem 'a'. Substituting the values we found, we get:
A = (1/2) * s * a = (1/2) * (√3 / 2) * a * a = (1/4) * √3 *[tex]a^2[/tex]
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Topic: Writing
Progress:
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer
Read the narrative prompt:
Write an essay about something you do for your well-being.
Which of the choices is the best implied thesis statement for the prompt? (Remember that an implied thesis statement is an
overall idea or belief that a writer uses as the basis of the essay but never states directly in the writing.)
O I will write about why doctors say to drink eight glasses of water a day.
O Running can actually be bad for your health.
O
Exercising is really good for you. No matter who you are, you need to exercise every single day to be healthy and feel
good.
O Managing stress is important for overall well-being because the physical and emotional effects of stress are harmful.
Submit
Question ID: 749841
Pass
Save and close
The best implied thesis statement for the given prompt "Write an essay about something you do for your well-being" is: "Managing stress is important for overall well-being because the physical and emotional effects of stress are harmful." (Option D).
What is Thesis Statement?A thesis statement is a concise statement that summarizes the main point or argument of an essay, research paper, or other academic work. It usually appears at the end of the introduction and guides the reader in understanding what the paper is going to be about.
The thesis statement should be specific, clear, and debatable, and it should provide the main focus of the paper. It is an essential component of any academic writing, as it helps to structure the paper and gives it direction.
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please help me with this problem!! Image is attached, 20 points!!
The statement that must be true is the original prices of the refrigerator and the stove were the same. So the answer is option B.
Let x represent the original cost of the refrigerator and y represent the original cost of the stove. The refrigerator's sale price is 0.6x (40% off means paying 60% of the original price), while the stove's sale price is 0.8y (20% off means paying 80% of the original price).
To get the overall discount, multiply the total cost after the discount by the original total cost:
(0.6x + 0.8y) / (x + y)
We want this fraction to equal 0.7 (or 30% off), so we can set up the equation:
(0.6x + 0.8y) / (x + y) = 0.7
Simplifying this equation, we get:
0.6x + 0.8y = 0.7(x + y)
0.6x + 0.8y = 0.7x + 0.7y
0.1x = 0.1y
x = y
Therefore, the statement that must be true to conclude that Alfonso received a 30% overall discount on the refrigerator and stove together is: The original prices of the refrigerator and the stove were the same.
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Lines b and a are intersected by line f. At the intersection of lines f and b, the bottom left angle is angle 4 and the bottom right angle is angle 3. At the intersection of lines f and a, the uppercase right angle is angle 1 and the bottom left angle is angle 2.
Which set of equations is enough information to prove that lines a and b are parallel lines cut by transversal f?
Answer:
Step-by-step explanation:
To prove that lines a and b are parallel lines cut by transversal f, we need to show that the alternate interior angles are congruent. According to the given information, angle 2 and angle 3 are corresponding angles, and angle 1 and angle 4 are corresponding angles.
Therefore, the set of equations that is enough information to prove that lines a and b are parallel lines cut by transversal f is:
angle 2 = angle 3 (corresponding angles)
angle 1 = angle 4 (corresponding angles)
A bucket held 24 gallons of water. Water leaked out of a hole in the bucket at a rate of 3 gallons every 4 days. At this rate, how many days did it take for all 24 gallons to leak out?
It will take 32 days for all 24 gallons to leak out of the bucket at a rate of 3 gallons every 4 days.
If water is leaking out of a bucket at a rate of 3 gallons every 4 days, then the rate of leakage is 3/4 gallons per day.
Let x be the number of days it takes for all 24 gallons to leak out. To explain this situation, we can construct an equation.
24=3/4*x
To solve for x, we can cross-multiply.
24*4=3x
3x=96
x=96/3
x = 32
Therefore, it will take 32 days for all 24 gallons to leak out of the bucket at a rate of 3 gallons every 4 days.
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Triangle XYZ has coordinates X(-2,2), Y(-3,-4). And Z(1,-2). The triangle is reflected across the x-axis. What are the coordinates of triangle X'Y'Z'?
The coordinates of triangle X'Y'Z' is X'(-2,-2), Y'(-3,4), Z'(1,2).
What are the coordinates of the triangle?
The triangle's vertices have the coordinates (x1,y1), (x2,y2), and (x3,y3). The line that connects the first two is split in the ratio l:k, and the line that runs from the division point to the opposing angular point is divided in the ratio m:k+l.
Here, we have
Given: Triangle XYZ has coordinates X(-2,2), Y(-3,-4). And Z(1,-2).
The triangle is reflected across the x-axis and we have to find the coordinates of triangle X'Y'Z'.
X(-2,2), Y(-3,-4) and Z(1,-2).
While reflecting any points across the x-axis with coordinates as (x, y) becomes, (x, -y). i.e. sign of y-coordinate changes.
The rule is (x, y) → (x, -y)
After applying the rule, we get
X(-2,2) ⇒ X'(-2,-2)
Y(-3,-4) ⇒ Y'(-3,4)
Z(1,-2) ⇒ Z'(1,2)
Hence, the coordinates of triangle X'Y'Z' is X'(-2,-2), Y'(-3,4), Z'(1,2).
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the college board sat college entrance exam consists of two sections: math and evidence-based reading and writing (ebrw). sample data showing the math and ebrw scores for a sample of students who took the sat follow. click on the datafile logo to reference the data. student math ebrw student math ebrw 1 540 474 7 480 430 2 432 380 8 499 459 3 528 463 9 610 615 4 574 612 10 572 541 5 448 420 11 390 335 6 502 526 12 593 613 a. use a level of significance and test for a difference between the population mean for the math scores and the population mean for the ebrw scores. what is the test statistic? enter negative values as negative numbers. round your answer to two decimal places.
A t-test with a level of significance of 0.05 results in a test statistic of -2.09, indicating a significant difference between the population mean for the math scores and the population mean for the EBRW scores.
To test for a difference between the population mean for the math scores and the population mean for the ebrw scores, we can conduct a two-sample t-test.
Using a calculator or software, we can find that the sample mean for math scores is 520.5 and the sample mean for ebrw scores is 485.5.
The sample size is n = 12 for both groups.
The sample standard deviation for math scores is s1 = 48.50 and for ebrw scores is s2 = 87.63.
Using a level of significance of 0.05, and assuming unequal variances, we can find the test statistic as:
t = (520.5 - 485.5) / sqrt(([tex]48.50^2/12[/tex]) + ([tex]87.63^2/12[/tex]))
t = 0.851
Rounding to two decimal places, the test statistic is 0.85.
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rachel collects vintage dolls. she pays $22 for large ones and $16 for small ones. she spends $120 on 6 dolls. write and solve a system of equations to show how many large dolls and how many small dolls rachel purchased
Answer:
Step-by-step explanation:
Let's use L to represent the number of large dolls and S to represent the number of small dolls Rachel purchased.
Based on the problem, we can write the following two equations:
1. L + S = 6 (equation 1 - represents the total number of dolls purchased)
2. 22L + 16S = 120 (equation 2 - represents the total amount spent on dolls)
To solve for L and S, we can use substitution or elimination. Let's use the substitution method:
From equation 1, we can express S in terms of L by subtracting L from both sides :
S = 6 - L
Substitute this equation for S in equation 2:
22L + 16(6-L) = 120
Simplify and solve for L:
22L + 96 - 16L = 120
6L = 24
L = 4
Now that we know L = 4, we can use equation 1 to find S:
L + S = 6
4 + S = 6
S = 2
Therefore, Rachel purchased 4 large dolls and 2 small dolls.
Write a derivative formula for the function.
f(x) = (9x2 + 11x + 7)(38x3 + 35)
The derivative formula for the function is
[tex]f'(x) = 342x^4 + 414x^3 + 342x^2 + 418x + 385[/tex]
How to find the derivative of the function f(x)?To find the derivative of the function [tex]f(x) = (9x^2 + 11x + 7)(38x^3 + 35)[/tex], we can use the product rule of differentiation:
f(x) = u(x)v(x)
where [tex]u(x) = (9x^2 + 11x + 7)[/tex] and [tex]v(x) = (38x^3 + 35)[/tex].
The product rule states that:
f'(x) = u'(x)v(x) + u(x)v'(x)
where u'(x) and v'(x) are the derivatives of u(x) and v(x), respectively.
Taking the derivatives, we get:
u'(x) = 18x + 11
[tex]v'(x) = 114x^2[/tex]
Now, substituting everything into the product rule formula, we get:
[tex]f'(x) = (18x + 11)(38x^3 + 35) + (9x^2 + 11x + 7)(114x^2)[/tex]
Simplifying this expression gives the derivative formula for f(x):
[tex]f'(x) = 342x^4 + 414x^3 + 342x^2 + 418x + 385[/tex]
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Sal is tiling his entryway. The floor plan is drawn on a unit grid. Each unit length represents 1 foot. Tile costs $1. 15 per square foot. How much will Sal pay to tile his entryway? Round your answer to the nearest cent.
Sal will pay to tile his entryway by calculating the area of the entryway in square feet and multiplying it by the cost of the tile per square foot.
To determine the cost of tiling Sal's entryway, we need to calculate the area of the floor plan. Since each unit length represents 1 foot, we can consider the dimensions of the floor plan in terms of feet. Let's say the length is 'L' feet and the width is 'W' feet. The area can be found by multiplying L by W, giving us the total area in square feet.
Once we have the area, we can multiply it by the cost per square foot, which is $1.15. This will give us the total cost of the tiles needed to cover the entryway.
It's important to note that rounding the final answer to the nearest cent is necessary to provide a precise cost value.
Therefore, by calculating the area of the entryway and multiplying it by the cost per square foot, we can determine the total amount Sal will pay to tile his entryway.
In conclusion, to calculate the cost, we need to find the area of the entryway by multiplying the length and width in units, convert it to square feet, and then multiply it by the tile cost per square foot.
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Tara wants to prove that a second pair of corresponding angles from KJN and LJM are congruent.
Determine a second pair of corresponding angles from KJN and LJM that are congruent. Then explain how you know that the two angles are congruent
To determine a second pair of corresponding angles from KJN and LJM that are congruent, we can start by identifying the first pair of corresponding angles.
angle JKN is harmonious to angle LJM. thus, we need to find another brace of corresponding angles that involve these same two angles. One possibility is to look at the perpendicular angles formed by the crossroad of KJ and JM. Angle KJM is perpendicular to angle NJL. therefore, angle KJM in KJN corresponds to angle NJL in LJM. thus, these two angles are harmonious.
We can prove that these two angles are harmonious using the perpendicular angles theorem, which states that perpendicular angles are always harmonious. Since KJ and JM cross at point J, angles KJM and NJL are perpendicular angles and must be harmonious. thus, we've shown that the alternate brace of corresponding angles from KJN and LJM that are harmonious are angle KJM and angle NJL.
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Convert 7 gallons an hour to cups per minute.
When 7 gallons an hour is converted to cups per minute it would be = 1.9 cups /min.
How to convert gallons per hour to cups per minute?To convert gallons per hour to cups per minute the following is carried out.
The constitution of a gallon when measured in cups = 16 cups.
Therefore if 1 gallon = 16 cups
7 gallons = X cups
Make X the subject of formula;
X = 16×7
= 112 cups
This means that , 112 cups = 1 hour(60 mins)
y cups = 1 min
make y the subject of formula;
y = 112/60
= 1.9 cups /min
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CopyCat Pear-Apple wants to get into the tablet business. They want to make tablets similar to Apple's iPad Mini 2. If Pear-Apple applies a scale factor of 1. 25 to the iPad Mini 2 to make a new tablet called the BigMini, what would be the new volume in cubic inches?
The new volume of the BigMini tablet is about 22.18 cubic inches.
How to calculate the new volume of the BigMini tablet?The volume of a three-dimensional object, such as a tablet, is calculated by multiplying its length, width, and height.
Assuming that the scale factor of 1.25 is applied uniformly to all three dimensions of the iPad Mini 2, the new dimensions of the BigMini tablet would be:
Length: 1.25 x 7.87 inches = 9.84 inches
Width: 1.25 x 5.3 inches = 6.63 inches
Height: 1.25 x 0.29 inches = 0.36 inches
The new volume of the BigMini tablet can be calculated as:
9.84 x 6.63 x 0.36 = 22.18 cubic inches
Therefore, the new volume of the BigMini tablet would be approximately 22.18 cubic inches.
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The 8th grade class of City Middle School has decided to hold a raffle to raise money to fund a trophy cabinet as their legacy to the school. A local business leader with a condominium on St. Simons Island has donated a week’s vacation at his condominium to the winner—a prize worth $1200. The students plan to sell 2500 tickets for $1 each.
1) Suppose you buy 1 ticket. What is the probability that the ticket you buy is the winning ticket? (Assume that all 2500 tickets are sold. )
2) After thinking about the prize, you decide the prize is worth a bigger investment. So you buy 5 tickets. What is the probability that you have a winning ticket now?
3) Suppose 4 of your friends suggest that each of you buy 5 tickets, with the agreement that if any of the 25 tickets is selected, you’ll share the prize. What is the probability of having a winning ticket now?
4) At the last minute, another business leader offers 2 consolation prizes of a week-end at Hard Labor Creek State Park, worth around $400 each. Have your chances of holding a winning ticket changed? Explain your reasoning. Suppose that the same raffle is held every year. What would your average net winnings be, assuming that you and your 4 friends buy 5 $1 tickets each year?
1) If there are 2500 tickets sold, and you buy 1 ticket, then the probability of your ticket being the winning ticket is 1/2500 or 0.04%.
2) If you buy 5 tickets, then the probability of having a winning ticket is 5/2500 or 0.2%.
3) If you and your 4 friends each buy 5 tickets, then there will be a total of 25 tickets. The probability of having a winning ticket in this scenario is 5/25 or 20%.
4) The chances of holding a winning ticket have not changed. This is because the consolation prizes are separate from the main prize, and the probability of winning the main prize is still the same.
The addition of consolation prizes does not affect the probability of winning the main prize.
Assuming the same raffle is held every year and you and your 4 friends buy 5 tickets each year, the average net winnings would be calculated as follows:
Total cost of tickets = $1 x 5 x 5 = $25
Total prize money = $1200 + ($400 x 2) = $2000
Probability of winning = 5/2500 = 0.2%
Expected value of winning = $2000 x 0.2% = $4
Average net winnings = ($4 - $25)/year = -$21/year
This means that on average, you and your friends would lose $21 per year if you participate in the raffle every year.
However, it is important to note that this is just an average and there is a chance of winning a larger prize which would make the net winnings positive.
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There are 46 giraffes in the San Antonio Zoo. The population increases at a rate of 8%
each year. The function y = 46(1. 08)* can be used to determine y, the number of giraffes
at the zoo after x years. What is the domain and range that represents this situation?
A Domain: All real numbers less than or equal to 46
Range: All real numbers
B Domain: All real numbers greater than or equal to 0
Range: All real numbers greater than or equal to 46
C Domain: All real numbers greater than or equal to 1. 08
Range: All real numbers greater than 0
D Domain: All real numbers
Range: All real numbers greater than or equal to 0
The domain and range that represents this situation is: B Domain All real numbers greater than or equal to 0; Range: All real numbers greater than or equal to 46.
In the given situation, the number of giraffes in the San Antonio Zoo is represented by the function y = 46(1.08)ˣ To determine the domain and range that represent this situation, we must consider the context and the variables involved.
The domain represents the possible values of x, which corresponds to the number of years. Since time cannot be negative in this context, the domain includes all real numbers greater than or equal to 0.
The range represents the possible values of y, which corresponds to the number of giraffes. The initial number of giraffes is 46, and the population is increasing each year. Therefore, the range includes all real numbers greater than or equal to 46.
Based on this information, the correct answer is B: Domain: All real numbers greater than or equal to 0; Range: All real numbers greater than or equal to 46.
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Complete question:
There are 46 giraffes in the San Antonio Zoo. The population increases at a rate of 8% each year. The function y = 46(1.08)* can be used to determine y, the number of giraffes
at the zoo after x years. What is the domain and range that represents this situation?
A Domain: All real numbers less than or equal to 46
Range: All real numbers
B Domain: All real numbers greater than or equal to 0
Range: All real numbers greater than or equal to 46
C Domain: All real numbers greater than or equal to 1.08
Range: All real numbers greater than 0
D Domain: All real numbers
Range: All real numbers greater than or equal to 0
Please help me find x. Also show me step by step
Answer: x ≅ -0.9 or -1.8
Step-by-step explanation:
[tex]3(3x+4)^2 - 6 = 0[/tex]
[tex]3(3x+4)^2 = 6[/tex]
[tex]3(9x^2+24x+16) = 6[/tex]
[tex]9x^2+24x+16 = 2[/tex]
[tex]9x^2+24x+14 = 0[/tex]
Use the quadratric formula to get:
x ≅ -0.9 or -1.8
The opposite of z is greater than 5 what are two possible options for z
Possible options for z could be:
1) z = -6
2) z = -7
These are two possible options for z that satisfy the given inequality.
Given that the opposite of z is greater than 5, we can write this as an inequality:
-z > 5
To find the possible options for z, we can follow these steps:
Step 1: Multiply both sides of the inequality by -1 to solve for z. Remember to flip the inequality sign when multiplying by a negative number:
z < -5
Step 2: Choose two values for z that satisfy the inequality z < -5.
Possible options for z could be:
1) z = -6
2) z = -7
These are two possible options for z that satisfy the given inequality.
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An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. If x engines are made, then the unit cost is given by the function =Cx+−0.5x2180x25,609. How many engines must be made to minimize the unit cost?
Do not round your answer.
The number of engines that must be made to minimize the unit cost are 180
How many engines must be made to minimize the unit cost?From the question, we have the following parameters that can be used in our computation:
C(x) = −0.5x² + 180x + 25,609.
Differentiate the above equation
So, we have the following representation
C'(x) = -x + 180
Set the equation to 0
So, we have the following representation
-x + 180 = 0
This gives
x = 180
Substitute x = 180 in the above equation, so, we have the following representation
C(180) = −0.5(180)² + 180(180) + 25,609
Evaluate
C(180) = 41809
Hence, the engines that must be made to minimize the unit cost are 180
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1. the elevation of death valley, california is - 282 feet. the elevation of tallahassee, florida is 203
feet. the elevation of westmorland, california is -157 feet.
compare the elevations of death valley and tallahassee using < or >
fill in the blank:
death valley (-282 feet)
tallahassee, florida (203 feet)
Based on the elevations given, Death Valley (-282 feet) < Tallahassee, Florida (203 feet).
To compare the elevations of Death Valley and Tallahassee, we'll use the inequality symbols i.e., "<" or ">" . The symbol "<" indicate less than and ">" indicate greater than.
Death Valley, California has an elevation of -282 feet, while Tallahassee, Florida has an elevation of 203 feet. Since -282 is less than 203, we use the "<" symbol.
So, the comparison is as follows:
Death Valley (-282 feet) < Tallahassee, Florida (203 feet)
This means that the elevation of Death Valley is lower than or less than the elevation of Tallahassee.
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Find the exact location of all the relative and absolute extrema of the function (Order your answers from smallest to largest x.) (x)=2x-x+ with domain (0,3)
The location of all the relative and absolute extrema is (0, 0) (local minimum); (1, 1) (local maximum); (3, 3) (absolute maximum)
To find the relative and absolute extrema of the function f(x) = 2x - x^2 on the domain (0,3), we first take the derivative:
f'(x) = 2 - 2x
Setting this equal to zero, we find the critical point:
2 - 2x = 0
x = 1
To determine the nature of the critical point, we need to examine the second derivative:
f''(x) = -2
Since the second derivative is negative at x = 1, this critical point is a local maximum. To find the absolute extrema, we also need to examine the endpoints of the domain, x = 0 and x = 3:
f(0) = 0
f(3) = 3
So the function has an absolute maximum at x = 3 and an absolute minimum at x = 0. Therefore, the location of all the relative and absolute extrema, from smallest to largest x, is:
(0, 0) (local minimum)
(1, 1) (local maximum)
(3, 3) (absolute maximum)
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3
Select the correct answer.
The angle of depression between the top of a 100-foot cliff and a ship approaching the shore is 37°.
cliff top
37°
100
feet
37°
ship
d
What is the approximate distance, d, between the bottom of the cliff and the ship?
ÐÐ
166. 2 feet
OB. 60. 2 feet
ÐС.
75. 4 feet
OD.
132. 7 feet
Reset
Next
The correct answer is (D) 132.7 feet.
From the given information, we can draw a diagram as follows:
A
/|
/ |
/ | 37°
/ |
/ |
/ |
/ |
/_ _ _ _|
d B
Where A represents the top of the cliff, B represents the ship and d represents the distance between the ship and the bottom of the cliff.
Since we know that the angle of depression is 37 degrees, then the angle CAB is also 37 degrees. We also know that AB is 100 feet, which is the height of the cliff. We want to find the distance d between the bottom of the cliff and the ship.
We can use the tangent function to find d:
tan(37°) = AB/BD
tan(37°) = 100/d
d = 100/tan(37°)
Using a calculator, we can find that:
d ≈ 132.7 feet
Therefore, the correct answer is (D) 132.7 feet.
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Find the slope of the curve y = x^3 -10x at the given point P(2, -12) by finding the limiting value of the slope of the secants through P. (b) Find an equation of the tangent line to the curve at P(2, - 12). (a) The slope of the curve at P(2, -12) is
The equation of the tangent line to the curve at P(2, -12) is y = 2x - 16.
(a) To find the slope of the curve y = x^3 - 10x at the given point P(2, -12), we need to find the derivative of the function y with respect to x, and then evaluate it at x = 2.
Step 1: Find the derivative, dy/dx
y = x^3 - 10x
dy/dx = 3x^2 - 10
Step 2: Evaluate the derivative at x = 2
dy/dx (2) = 3(2)^2 - 10 = 12 - 10 = 2
The slope of the curve at P(2, -12) is 2.
(b) To find an equation of the tangent line to the curve at P(2, -12), we'll use the point-slope form of the equation: y - y1 = m(x - x1).
Step 1: Use the slope found in part (a) and the given point P(2, -12).
m = 2
x1 = 2
y1 = -12
Step 2: Plug the values into the point-slope equation.
y - (-12) = 2(x - 2)
y + 12 = 2x - 4
Step 3: Rearrange the equation to get the final form.
y = 2x - 4 - 12
y = 2x - 16
The equation of the tangent line to the curve at P(2, -12) is y = 2x - 16.
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Let f(x) =x^2 + x + 9 and g(x)x = -4x - 3.
Find (fg) (x) and (f/g) (x)
Answer: First, we need to find the composite function (fg)(x):
(fg)(x) = f(g(x))
= f(-4x-3)
= (-4x-3)^2 + (-4x-3) + 9 (substituting g(x) into f(x))
= 16x^2 + 24x + 18
Therefore, (fg)(x) = 16x^2 + 24x + 18.
Next, we need to find the quotient function (f/g)(x):
(f/g)(x) = f(x) / g(x)
= (x^2 + x + 9) / (-4x - 3) (substituting f(x) and g(x))
To simplify this expression, we can use polynomial long division or synthetic division. Using synthetic division, we get:
-4 | 1 1 9
|_____-4__ 12
| 1 -3 21
Therefore, (f/g)(x) = -4x + 3 - 21 / (-4x - 3)
Simplifying further, we get:
(f/g)(x) = -4x + 3 + (21/4)(1/(x + 3/4))
Therefore, (f/g)(x) = -4x + 3 + (21/4)(1/(x + 3/4)).
Step-by-step explanation:
5. Hector took out a 25-year house loan for $190,000 at 4.8% interest, compounded monthly, and
his monthly payment will be the same for the life of the loan.
Payment
Number
1
2
Payment
Amount
$1055.69
Interest Due
$760.00
Note Reduction Unpaid Balance
$328.69
$189,671.31
An amortization table for his first two payments is shown above. Help Hector fill in the missing
information in the table for his second payment. Use the information for the first payment as a
guide. (4 points: Part 1-1 point; Part II - 1 point; Part III-1 point; Part IV-1 point)
Part I: What is the payment amount for payment number 2?
Part II: what is the interest due for payment number 2?
Part III: what is the note reduction for payment 2?
Part IV: what is the unpaid balance for payment number 2?
Part III: Note reduction for payment 2 = Payment Amount - Interest Due = $1055.69 - $758.68 = $297.01.
How to solvePart I: The payment amount for payment number 2 is $1055.69 (same as the first payment).
Part II: Interest due for payment number 2 = (Unpaid Balance after payment 1) * (Monthly Interest Rate) = $189,671.31 * (4.8% / 12) = $758.68.
Part III: Note reduction for payment 2 = Payment Amount - Interest Due = $1055.69 - $758.68 = $297.01.
Part IV: Unpaid balance for payment number 2 = (Unpaid Balance after payment 1) - (Note Reduction for payment 2) = $189,671.31 - $297.01 = $189,374.30.
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Evaluate the integrals (Indefinite and Definite) and Simplify. 5 (a) 5 (5:-* - - 5 sin ) : dc xl1 (v) [(1822–1 18x)(6x3 – 9x2 – 3)6 dx ° ? (c) | Viana sec2 х dx (d) os Venta de Зх dx Væ+4 2 (e) ( 120 dax V1 + 2x2
(a) Indefinite integral of 5(5x^4 - 5sinx)dx is (5/3)x^5 + 5cosx + C. Definite integral over [0, π/2] is (125π/6) - 5.
We can evaluate the indefinite integral by applying the power rule and integration by substitution. The definite integral can be evaluated by substituting the limits of integration and simplifying.
(b) Indefinite integral of [(18x^2 - 1)(6x^3 - 9x^2 - 3)]^6dx is (18x^11 - 77x^9 + 126x^7 - 108x^5 + 49x^3 - 9x) / 11 + C.
To simplify the given expression, we can first expand the polynomial and then apply the power rule to integrate each term. The constant of integration can be added at the end.
(c) Definite integral of ∫tan^2(x)sec^2(x)dx over [0,π/4] is 1.
We can use the trigonometric identity sec^2(x) - 1 = tan^2(x) to simplify the integrand. Then we can apply the power rule and substitute the limits of integration to evaluate the definite integral.
(d) Indefinite integral of ∫(x+4)^2√(3x^2+4)dx is (1/15)(3x^2+4)^(3/2)(x+4) - (4/45)(3x^2+4)^(3/2) + C.
We can use substitution to simplify the integrand by setting u = 3x^2 + 4. After integrating, we can substitute back for u and simplify the constant of integration.
(e) Indefinite integral of ∫(120/(1+2x^2))dx is 60√2tan^(-1)(√2x) + C.
We can use substitution to simplify the integrand by setting u = 1 + 2x^2. After integrating, we can substitute back for u and simplify the constant of integration.
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Evaluate JJ ) Ry0 +52, 15y52. (y + xy-2) dA; R= {(x,y): 0 < x
the evaluated double integral is approximately 14.25.
To evaluate the given double integral, we need to first understand the problem properly. We have the function f(x, y) = y + xy, and the region R is described by the inequalities: 0 < x < y^2, and 1 < y < 2.
Now we can set up the double integral:
∬(y + xy) dA over the region R.
Since we are given that 0 < x < y^2 and 1 < y < 2, we can set up the integral using the given limits of integration:
∫(from y = 1 to 2) ∫(from x = 0 to y^2) (y + xy) dx dy.
Now, we can start by integrating the inner integral with respect to x:
∫(from y = 1 to 2) [(yx + (1/2)x^2*y) evaluated from x = 0 to x = y^2] dy.
After evaluating the inner integral, we have:
∫(from y = 1 to 2) (y^3 + (1/2)(y^2)^2*y) dy.
Now, we can integrate the outer integral with respect to y:
[((1/4)y^4 + (1/6)y^6) evaluated from y = 1 to y = 2].
After evaluating the outer integral, we get:
[(1/4)(2^4) + (1/6)(2^6)] - [(1/4)(1^4) + (1/6)(1^6)].
Calculating the final result:
(4 + 10.6667) - (0.25 + 0.1667) = 14.6667 - 0.4167 ≈ 14.25.
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20 points for this IF RIGHT ANSWER
The surface area of the solids are listed below:
Case 1: A = 366 mm²
Case 2: A = 448 cm²
Case 3: A = 748 m²
Case 4: A = 221.5 in²
Case 5: A = 692 in²
Case 6: A = 276 ft²
How to determine the surface area of a solid
In this question we need to determine the surface area of six solids, that is, the sum of areas of all faces in each solid. The solids can include areas of rectangles and triangles, whose formulas are:
Rectangle
A = b · h
Triangle
A = 0.5 · b · h
Where:
A - Area of the face.b - Base of the face.h - Height of the face.Case 1
A = 2 · (13 mm) · (3 mm) + 2 · (13 mm) · (9 mm) + 2 · (9 mm) · (3 mm)
A = 78 mm² + 234 mm² + 54 mm²
A = 366 mm²
Case 2
A = 2 · (20 cm) · (6 cm) + 2 · (4 cm) · (6 cm) + 2 · (20 cm) · (4 cm)
A = 240 cm² + 48 cm² + 160 cm²
A = 448 cm²
Case 3
A = 2 · (5 m) · (14 m) + 2 · (16 m) · (14 m) + 2 · (5 m) · (16 m)
A = 748 m²
Case 4
A = 2 · (2 in) · (6.5 in) + 2 · (11.5 in) · (6.5 in) + 2 · (11.5 in) · (2 in)
A = 221.5 in²
Case 5
A = 2 · 0.5 · (12 in) · (7 in) + (11 in) · (19 in) + (9 in) · (19 in) + (12 in) · (19 in)
A = 692 in²
Case 6
A = 2 · 0.5 · (8 ft) · (3 ft) + 2 · (5 ft) · (14 ft) + (8 ft) · (14 ft)
A = 276 ft²
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Answer: Goofy Ahh
Step-by-step explanation:
That question is so Goofy Ahh
Weeee
Consider functions f and g. What is the approximate solution to the equation after three iterations of successive approximations? Use the graph as a starting point. 3x^2 - 6x - 4 = 2/x+3 +1
The required values on the graph, the solution is approximate x = -0.33.
How to solve the equationWe can begin by combining like terms on the left-hand side:
3x² - 6x - 4 - 2/x + 3 + 1 = 0
3x² - 6x - 2/x = -3
Next, we can factor out the x term:
x(3x - 2) - 2(3x - 2) = -3
(x - 2)(3x - 2) = -3
Since the equation is equal to -3, we can add 3 to both sides to get:
(x - 2)(3x - 2) + 3 = 0
We can then factor the left-hand side to get:
(x - 2)(3x - 2 + 3) = 0
(x - 2)(3x - 2 + 3) = (x - 2)(3x + 1) = 0
This equation has two solutions: x = 2 and x = -1/3.
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Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
What 2 number multiple to make -14 and add to make -3?
By using factoring and the zero product property the two numbers that multiply to make -14 and add to make -3 are -7 and 4.
What is zero product property?The zero product property is a fundamental property of algebra that states that if the product of two or more factors is zero, then at least one of the factors must be zero. In other words, if a × b = 0, then either a = 0 or b = 0 or both a and b are zero. This property is often used to solve equations and factor polynomials. For example, if we have the equation (x - 3)(x + 5) = 0, we know that the only way the product can be zero is if one of the factors is zero, so we set each factor equal to zero and solve for x:
(x - 3)(x + 5) = 0
x - 3 = 0 or x + 5 = 0
x = 3 or x = -5
Thus, the solutions to the equation are x = 3 and x = -5.
According to the given informationWe can solve this problem by using factoring and the zero product property.
First, we need to find two numbers that multiply to make -14. The factors of -14 are (-1, 14) and (1, -14), so the two numbers could be -1 and 14, or 1 and -14.
Next, we need to find which pair of numbers adds up to -3. The only pair of numbers that works is -7 and 4 because (-7) + 4 = -3.
Therefore, the two numbers that multiply to make -14 and add to make -3 are -7 and 4.
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Use the formula d = rt to find the distance traveled in a car driven at 45 miles per hour for 5 hours.
Answer:
225 miles!!!!!!!!!!!!!!!!
