The area of the surface generated by revolving the curve y=4x+2 on [0,4] about the x-axis is S =4π/3 (3√17 + 2) .
To find the surface area generated by revolving the curve y=4x+2 about the x-axis on [0,4], we need to use the formula:
S = 2π∫[a,b] y ds
where ds = \sqrt(1 + (dy/dx)²) dx is the arc length element.
First, we find dy/dx: dy/dx = 4
Then, we can find the arc length element: ds = \sqrt(1 + (dy/dx)²) dx = \sqrt(1 + 16) dx = \sqrt(17) dx
The integral for surface area becomes: S = 2π∫[0,4] y ds = 2π∫[0,4] (4x+2)√17 dx
Evaluating this integral, we get:
S = 2π(2/3)√17 [ (4x+2)^(3/2) ]_0^4
S = 4π/3 (3√17 + 2)
Therefore, the area of the surface generated is 4π/3 (3√17 + 2) square units.
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Triangle TUV, with vertices T(2,-8), U(9,-6), and V(6,-3), is drawn on the coordinate
grid below. what is the area. in square units, of triangle TUV
The area of the triangle TUV, with vertices T(2,-8), U(9,-6), and V(6,-3), is 13.58
How did we arrive at the above?First using distance calculator we derived the length of TV and the length of VU.
Since TV = Height; and
VU = Base
and the triangle is a right triangle,
Then, area is given by 1/2 base x Height
Length of TV usign distance calculator is 6.40312
Lenght of VU using distance calculator is 4.24264
So area = 1/2 * 6.40312 * 4.24264
Area = 13.58
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625y2+400y-36+20z-z2
Answer:
The expression 625y^2 + 400y - 36 + 20z - z^2 can be rearranged and simplified as follows:
625y^2 + 400y - 36 + 20z - z^2
= (25y)^2 + 2(25y)(8) + 8^2 - 8^2 - 36 + 20z - z^2 (adding and subtracting (25y)(8) and 8^2 inside the parentheses)
= (25y + 8)^2 - (8^2 + 36) + 20z - z^2 (expanding the squared term and simplifying)
= (25y + 8)^2 - 100 + 20z - z^2 (simplifying)
Therefore, the simplified form of the expression is:
(25y + 8)^2 - 100 + 20z - z^2.
Note that this expression can also be written as:
(5y + 2)^2(5y - 12)^2 - (z - 10)(z + 10),
Using the difference of squares factorization. However, this is not necessarily simpler than the previous form, and it depends on the context and the purpose of the expression.
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The music industry has steadily moved from selling music in a physical format such as records, eight tracks, cassettes, and CDs telling music in digital formats. In 2001, the music industry sold $26.5
billion of music in the physical format. Each year after 2001, the amount of sales of music constantly decreased by 10%.
Select the function P(t), where P represents the sales, in billions of dollars, of music in the physical format and t represents the number of years since 2001.
P(0) 26 5/0 1
Answer:
P(t)=26.5 (0.1)^t
Step-by-step explanation:
the variables x and y vary inversely. use the given values to write an equation relating i and y. then find y when i = i= 5, y = -4 an equation is y= when i = 3, y = 5
please help me!
When i (x) = 3, the value of y is approximately -6.67. The equation relating i (x) and y in this inverse variation is xy = -20.
The given information states that the variables x and y vary inversely. To write an equation relating i (assuming it's x) and y, we first need to understand the concept of inverse variation.
In inverse variation, the product of the two variables remains constant. Mathematically, it can be represented as xy = k, where k is the constant of variation. We are given the values i (x) = 5 and y = -4. Using these values, we can find the constant of variation, k:
5 * -4 = k
k = -20
Now that we have the constant of variation, we can write the equation relating i (x) and y as:
xy = -20
Next, we want to find the value of y when i (x) = 3. We can use the equation we just derived to find the value of y:
3 * y = -20
Now, we can solve for y:
y = -20 / 3
y ≈ -6.67
So, when i (x) = 3, the value of y is approximately -6.67. The equation relating i (x) and y in this inverse variation is xy = -20.
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At Kennedy High School, the probability of a student playing in the band is 0. 15. The probability of a student playing in the band and playing on the football team is 0. 3. Given that a student at Kennedy plays in the band, what is the probability that they play on the football team?
The probability that a student at Kennedy High School plays on the football team given that they already play in the band is 2/1 or simply 2.
To solve this problem, we can use conditional probability. We want to find the probability that a student plays on the football team given that they already play in the band.
Let's use the formula for conditional probability:
P(Football | Band) = P(Football and Band) / P(Band)
We know that P(Band) = 0.15, and P(Football and Band) = 0.3.
So,
P(Football | Band) = 0.3 / 0.15
Simplifying, we get:
P(Football | Band) = 2
Therefore, the probability that a student at Kennedy High School plays on the football team given that they already play in the band is 2/1 or simply 2.
Note: This answer may seem unusual because probabilities are typically expressed as fractions or decimals between 0 and 1. However, in this case, we can interpret the result as saying that students who play in the band are twice as likely to also play on the football team compared to the overall population of students.
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个
Work out the volume of this prism.
Area =
20 cm²
9cm
The diagram is not drawn to scale.
cm³
The volume of the prism is 180 cm³.
How to work out the volume of a prism?A prism is a 3D (three-dimensional) solid which has faces that are identical at both ends. The other faces are flats. A prism is named after its base.
The volume of any prism can be calculated using the formula:
V = A[tex]_{B}[/tex] * h
where A[tex]_{B}[/tex] is area of base and h is height of prism
In this case, we have the following information about the prism:
A[tex]_{B}[/tex] = 20 cm²
h = 9cm
V = 20 * 9
V = 180 cm³
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Complete Question
Check attached image
Use the normal approximation to find the indicated probability. the sample size is n, the population proportion of successes is p, and x is the number of successes in the sample.
n = 81, p = 0.5: p(x ≥ 46)
group of answer choices
0.1210
0.1335
0.8790
0.1446
We know that the indicated probability is approximately 0.1210.
To use the normal approximation, we need to check if the conditions for a normal approximation are met. In this case, we have:
np = 81 * 0.5 = 40.5 ≥ 10
n(1-p) = 81 * 0.5 = 40.5 ≥ 10
Since both conditions are met, we can use the normal approximation to find the probability.
First, we need to find the mean and standard deviation of the sampling distribution of sample proportions:
mean = np = 81 * 0.5 = 40.5
standard deviation = sqrt(np(1-p)) = sqrt(81 * 0.5 * 0.5) = 4.5
Next, we need to standardize the value of x:
z = (x - mean) / standard deviation
z = (46 - 40.5) / 4.5 = 1.22
Finally, we can use a standard normal table or calculator to find the probability:
P(z ≥ 1.22) = 0.1118
Therefore, the answer is approximately 0.1210.
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Solve the initial value problem. Dy/dx = 4x^-3/4, y(1) = 3 a. y = 16x^1/4 - 13 b. y = 16x1/4 + 48 c. y = -3/4^x7/4-13/4 d. y= 4x^1/4 - 1
The solution to the given initial value problem is (d) y = 4x^(1/4) - 1.
Given the initial value problem,
dy/dx = 4x^(-3/4), y(1) = 3
Integrating both sides with respect to x, we get
∫dy = ∫4x^(-3/4)dx
y = -8x^(-1/4) + C
where C is the constant of integration.
To find the value of C, we use the initial condition y(1) = 3
3 = -8(1)^(-1/4) + C
C = 3 + 8 = 11
Therefore, the solution to the initial value problem is
y = -8x^(-1/4) + 11
Simplifying further,
y = 11 - 8/x^(1/4)
Hence, the correct option is d) y = 4x^(1/4) - 1 is not the solution to the given initial value problem.
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Two liters of the Gatorade cost $3.98. How much do 8 liters cost?
Answer:
$15.92
Step-by-step explanation:
We Know
2 liters of Gatorade cost $3.98
How much do 8 liters cost?
We take
3.98 x 4 = $15.92
So, 8 liters cost $15.92
Admission Charge for Movies The average admission charge for a movie is $5. 81. If the distribution of movie admission charges is approximately normal with a standard deviation of $0. 81, what is the probability that a randomly selected admission charge is less than $3. 50
The probability that a randomly selected admission charge is less than $3. 50 is 0.23% or 0.0023.
To find the probability that a randomly selected admission charge is less than $3.50, we will use the z-score formula and a standard normal table. The z-score formula is:
Z = (X - μ) / σ
Where X is the value we are interested in ($3.50), μ is the average admission charge ($5.81), and σ is the standard deviation ($0.81).
Z = (3.50 - 5.81) / 0.81 ≈ -2.84
Now, look up the z-score (-2.84) in a standard normal table, which gives us the probability of 0.0023. Therefore, the probability that a randomly selected admission charge is less than $3.50 is approximately 0.23% or 0.0023.
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An investment of $4000 is deposited into an account in which interest is compounded continuously. complete the table by filling in the amounts to which the investment grows at the indicated interest rates. (round your answers to the nearest cent.)
t = 4 years
The investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.
To solve this problem, we need to use the formula for continuous compound interest:
A = Pe^(rt)
Where A is the amount after t years, P is the initial principal, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate, and t is the time in years.
Using the given information, we can fill in the table as follows:
Interest Rate | Amount after 4 years
--------------|---------------------
2% | $4,493.29
3% | $4,558.56
4% | $4,625.05
5% | $4,692.79
6% | $4,761.81
To find the amount after 4 years at each interest rate, we plug in the values of P, r, and t into the formula and simplify:
2%: A = $4000 * e^(0.02*4) = $4,493.29
3%: A = $4000 * e^(0.03*4) = $4,558.56
4%: A = $4000 * e^(0.04*4) = $4,625.05
5%: A = $4000 * e^(0.05*4) = $4,692.79
6%: A = $4000 * e^(0.06*4) = $4,761.81
Therefore, the investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.
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Frank has four different credit cards, the balances and interest information of which are outlined in the table below. he would like to consolidate his credit cards to a single credit card with an apr of 18% and pay off the balance in 24 months. what will his monthly credit card payment be? credit card balance apr a $2,380 19% b $4,500 15% c $1,580 17.50% d $900 21% a. $390.00 b. $462.91 c. $467.29 d. $52.00 please select the best answer from the choices provided a b c d
Frank's monthly credit card payment for consolidating his credit cards will be $467.29.
Option C is the correct answer.
We have,
To calculate the monthly credit card payment for consolidating Frank's credit cards, we can use the formula for the monthly payment on a loan:
[tex]M = P (r (1 + r)^n) / ((1 + r)^n - 1),[/tex]
where M is the monthly payment, P is the total loan amount (sum of all credit card balances), r is the monthly interest rate, and n is the number of months.
First, let's calculate the total loan amount:
Total loan amount = $2,380 + $4,500 + $1,580 + $900 = $9,360.
Next, let's calculate the monthly interest rate:
Monthly interest rate = APR / 12 = 18% / 12 = 1.5%.
Now, let's calculate the monthly payment using the formula:
[tex]M = $9,360 \times (0.015 (1 + 0.015)^{24}) / ((1 + 0.015)^{24} - 1).[/tex]
Using a calculator, we can compute the value of M:
M ≈ $467.286.
Rounding to the nearest cent,
Frank's monthly credit card payment for consolidating his credit cards will be $467.29.
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Lillian deposits $430 every month into an account earning an annual interest rate of 4. 5% compounded monthly. How much would she have in the account after 3 years, to the nearest dollar? Use the following formula to determine your answer
Lillian would have approximately $14,599 in her account after 3 years, to the nearest dollar.
To find out how much Lillian would have in her account after 3 years, we need to use the future value of a series formula, which is:
[tex]FV = P \frac{(1 + r)^nt - 1)}{r}[/tex]
where:
FV = future value of the series
P = monthly deposit ($430)
r = monthly interest rate (annual interest rate / 12)
n = number of times interest is compounded per year (12)
t = number of years (3)
First, we need to find the monthly interest rate by dividing the annual interest rate (4.5%) by 12:
[tex]r =\frac{0.045}{12} = 0.00375[/tex]
Now we can plug the values into the formula:
[tex]FV = 430 \frac{(1 + 0.00375)^{12x3} - 1)}{0.00375}[/tex]
Calculating the future value:
[tex]FV = 430\frac{(1.127334 - 1) }{0.00375} = 430 \frac{0.127334}{ 0.00375} = 430 (33.955)[/tex]
[tex]FV =14,598.65[/tex]
So, Lillian would have approximately $14,599 in her account after 3 years, to the nearest dollar.
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“The mode of a data set is one of the values in the data set.” This statement is ____________.
Mike receives a bonus every year. His bonus is calculated as 3 percent of his company's total profits. If he estimates his company's total profits to be between $500,000 and $650,000, which inequality best represents Mike's bonus, B, for the year?
Mike's bonus for the year is between $15,000 and $19,500.
The inequality that best represents Mike's bonus, B, for the year is:
$15,000 [tex]\leq B \leq[/tex] 19,500$
to see why, we are able to use the given data that Mike's bonus is calculated as 3 percent of his corporation's overall profits.
If we let P be the organization's general income, then Mike's bonus B can be expressed as:
$B = 0.03P$
We recognise that the organization's total profits are between $500,000 and $650,000, so we will write:
$500,000 [tex]\leq P \leq[/tex] 650,000$
Substituting this inequality into the equation for Mike's bonus, we get:
$15,000 [tex]\leq B \leq[/tex] 19,500$
Therefore, Mike's bonus for the year is between $15,000 and $19,500.
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Jacinta compares the volume of two boxes. Both boxes have a width of 2. 5 inches, and a height of 10 inches. The larger box has a length of 8 inches. The smaller box has a length that is 75 % of the length of the larger box.
Volume of large box =
Volume of small box =
What is the difference in the volumes of the two boxes?
Which units should be used for each of these answers?
The volume of the larger box is 200 cubic inches, and the volume of the smaller box is 150 cubic inches.
To find the volume of each box, we use the formula for the volume of a rectangular prism, which is V = lwh, where l is the length, w is the width, and h is the height.
For the larger box, we have l = 8 inches, w = 2.5 inches, and h = 10 inches, so
Volume of large box = = 8 x 2.5 x 10 = 200 cubic inches.
For the smaller box, we have l = 0.75 x 8 = 6 inches, w = 2.5 inches, and h = 10 inches, so
Volume of small box= 6 x 2.5 x 10 = 150 cubic inches.
The difference in the volumes of the two boxes is
Volume of large box - Volume of small box = 200 - 150 = 50 cubic inches.
The units for the volumes are cubic inches, since we are dealing with three-dimensional space.
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If p = (-4,7), find:
ry-axis (p)
([?], []).
The reflection of the point P = (-4, 7) in the y-axis is (4, 7).
We have,
To find the reflection of a point P in the y-axis, negate the x-coordinate of the point while keeping the y-coordinate unchanged.
Given that P = (-4, 7),
The reflection of P in the y-axis, denoted as [tex]R_{y-axis}(P),[/tex] can be found by negating the x-coordinate:
[tex]R_{y-axis}(P) = (4, 7)[/tex]
Thus,
The reflection of the point P = (-4, 7) in the y-axis is (4, 7).
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The complete question:
If p = (-4, 7)
R_{y-axis} (P) = ?
without a calculator find out
√28 ÷ √7
Step-by-step explanation:
= sqrt ( 28 ÷7) = sqrt (4) = 2
Answer:
2
Step-by-step explanation:
First we put the two equations together so it would be like this
[tex]\sqrt \frac{28}{7}[/tex]
the square root of that is 4 because 7 goes into 28 four times
so now we have this [tex]\sqrt{4}[/tex]
and the square root of 4 is 2
A bag contains seven tiles labeled A B C D E F and G wich
One tile will be randomly picked.
What is the probability of picking a letter that is not a vowel
Asako’s employer covers 90% of the cost of a $3,500 per year disability insurance plan and 60% of a $1,300 per year disability insurance plan. If Asako gets paid monthly, what is the total amount deducted frok her gross income health and disability insurance during each pay period
The total amount deducted from her gross income health and disability insurance during each pay period is $72.50.
To calculate the total amount deducted from Asako's gross income for health and disability insurance during each pay period, we need to first determine the cost of each insurance plan after the employer's coverage.
For the $3,500 per year disability insurance plan, Asako's employer covers 90% of the cost, which means Asako is responsible for 10% of the cost.
10% of $3,500 is $350, so Asako's cost for the $3,500 per year disability insurance plan is $350 per year.
For the $1,300 per year disability insurance plan, Asako's employer covers 60% of the cost, which means Asako is responsible for 40% of the cost.
40% of $1,300 is $520, so Asako's cost for the $1,300 per year disability insurance plan is $520 per year.
Since Asako gets paid monthly, we need to divide the annual cost of each insurance plan by 12 to determine the cost per pay period.
For the $3,500 per year disability insurance plan, Asako's cost per pay period is $350 / 12 = $29.17.
For the $1,300 per year disability insurance plan, Asako's cost per pay period is $520 / 12 = $43.33.
Therefore, the total amount deducted from Asako's gross income for health and disability insurance during each pay period is $29.17 + $43.33 = $72.50.
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Dorothy made a dot plot showing the heights of her plants in her garden. write a proportion to find the percentage of plants that are exactly 13cm tall.
2/9 = x/100
13/100 = x/100
2/12 = x/100
2/13 = x/20
right answer please.
To find the percentage of plants that are exactly 13cm tall using a proportion, you need to first identify the number of plants that are 13cm tall and the total number of plants. Based on your question, let's assume that 2 out of 9 plants are exactly 13cm tall.
Now, set up a proportion with the given information:
(number of plants 13cm tall) / (total number of plants) = (x) / (100)
In this case, the proportion is:
2/9 = x/100
To solve for x, cross-multiply:
2 * 100 = 9 * x
200 = 9x
Now, divide both sides by 9:
x = 200 / 9
x ≈ 22.22
So, approximately 22.22% of the plants in Dorothy's garden are exactly 13cm tall.
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8. (02.03 mc)
costs of attendance
category
dollar amount
annual tuition and fees
$4,934.00
annual room and board
$1,424.00
annual cost of books and supplies $1,250.00
other one-time fee
$275.00
annual scholarship and grants
$5,250.00
using the information from the table, identify the equation in slope-intercept form that models the total cost of attendance. (1 point)
o y = 2,358x + 275
o y = 2,633x
o y = 7,608x + 275
o y = 7,883
The equation in slope-intercept form that models the total cost of attendance is: y = 2,633x + 275.
1. Add up the annual costs: tuition and fees ($4,934), room and board ($1,424), and cost of books and supplies ($1,250) to get the total annual cost: $4,934 + $1,424 + $1,250 = $7,608.
2. Subtract the annual scholarship and grants from the total annual cost: $7,608 - $5,250 = $2,358. This is the slope (x) of the equation, as it represents the cost per year.
3. The other one-time fee ($275) is the y-intercept of the equation, as it's a fixed cost that does not change with the number of years.
4. Put the slope and y-intercept into the slope-intercept form (y = mx + b) to get: y = 2,633x + 275.
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Tell which measure of central tendency best describes the data.
Weights of books (oz):
12 10 9 15 16 10
Mean
Median
Mode
A standard number cube is rolled to play a certain board game. What is the Sample Space? Use proper notation as necessary and no extra spaces.
Answer: 1.3
Step-by-step explanation:
6
lo
r
s
p
m
q
0
-2
mollie claimed that the slope of mq is greater than the slope of qs because triangle mpq is bigger than triangle qrs.
explain the error in mollie's claim and calculate the slope for both mq and qs show all your work.
enter your work and explanation in the space provided.
Size of triangles doesn't determine slope, mq slope=-2, qs slope=-0.5
How to explain Mollie's incorrect slope claim?Mollie's claim is incorrect because the size of the triangles does not determine the slope of a line. The slope is calculated by dividing the change in the y-coordinates by the change in the x-coordinates between two points on the line. Therefore, we need to find two points on the lines mq and qs to calculate their slopes.
Let's start by finding the slope of mq. We can identify two points on the line, (0,6) and (2,2). Using these points, we can calculate the slope as:
slope of mq = (change in y-coordinates) / (change in x-coordinates)
slope of mq = (2 - 6) / (2 - 0)
slope of mq = -4 / 2
slope of mq = -2
Now let's find the slope of qs. We can identify two points on the line, (2,2) and (6,0). Using these points, we can calculate the slope as:
slope of qs = (change in y-coordinates) / (change in x-coordinates)
slope of qs = (0 - 2) / (6 - 2)
slope of qs = -2 / 4
slope of qs = -0.5
Therefore, the slope of mq is -2 and the slope of qs is -0.5.
In summary, Mollie's claim is incorrect because the size of the triangles does not determine the slope of a line. We calculated the slopes of lines mq and qs by finding two points on each line and using the formula for slope, which is the change in y-coordinates divided by the change in x-coordinates. The slope of mq is -2, and the slope of qs is -0.5.
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22 let s be The paraboloid hyperbolic 2- x-j 2 2 2- located between The cylinders x + y = 1 2 +1 - Calculate and x = 25. Surface s The area of Surface S
By using Numerical integration method such as Simpson's rule or Monte Carlo simulation, we will get the area
To calculate the area of surface S, we first need to find the limits of integration. The paraboloid hyperbolic is located between the cylinders x + y = 1 and x = 2. This means that the limits of integration for x are 1 and 2, and for y they are -sqrt(4-[tex]x^2[/tex]) and sqrt(4-[tex]x^2[/tex]).
Calculation of area:
Using the formula for the surface area of a paraboloid hyperbolic, which is given by:
A = 2π ∫∫ (1 + (∂z/∂x[tex])^2[/tex] + (∂z/∂y[tex])^2[/tex][tex])^{(1/2)[/tex] dA
We can calculate the area of surface S. First, we need to find the partial derivatives of z with respect to x and y:
∂z/∂x = -2x/(2+[tex]y^2[/tex])
∂z/∂y = -2y/(2+[tex]x^2[/tex])
Substituting these values into the formula for surface area, we get:
A = 2π ∫[tex]1^2[/tex] ∫-sqrt(4-[tex]x^2[/tex])^sqrt(4-[tex]x^2[/tex]) (1 + (-2x/(2+y^2)[tex])^2[/tex]+ (-2y/(2+[tex]x^2)[/tex][tex])^2[/tex][tex])^{(1/2)[/tex]dydx
Using a numerical integration method such as Simpson's rule or Monte Carlo simulation, we can calculate this integral to get the area of surface S.
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The students of Class X sat a Physics test. The average score was 46 with a standard deviation of 25. The teacher decided to award an A to the top 7% of the students in the class. Assuming that the scores were normally distributed, find the lowest score that would achieve an A
The lowest score that would achieve an A is 10.
How to find the score?To find the lowest score that would achieve an A, we need to find the score corresponding to the 7th percentile of the distribution of scores.
First, we need to find the z-score corresponding to the 7th percentile. We can use a z-table or a calculator to find this value.
The z-score corresponding to the 7th percentile is approximately -1.44. This means that a score at the 7th percentile is 1.44 standard deviations below the mean.
We can use the formula for z-score to find the raw score corresponding to this z-score:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
Plugging in the values we have:
-1.44 = (x - 46) / 25
Multiplying both sides by 25:
-36 = x - 46
Adding 46 to both sides:
x = 10
Therefore, the lowest score that would achieve an A is 10.
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The perimeter of the rectangle below is 16 cm. What is the value of k? 5 cm kcm Not to scale
Answer:
3 cm.
Step-by-step explanation:
Let's use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.In this case, we have:P = 16 cm (given)
l = k cm (given)
w = 5 cm (given)Substituting these values into the formula, we get:
16 cm = 2(k cm) + 2(5 cm)
Simplifying, we get:
16 cm = 2k cm + 10 cm
Subtracting 10 cm from both sides, we get:6 cm = 2k cm
Dividing both sides by 2, we get:
3 cm = k
Therefore, the value of k is 3 cm.
Curtis loves Pokémon! He went to school on Thursday and traded a bunch of cards to get new ones. He saw Dino and traded 3 of his cards for one of Dino's. Then a girl he liked, Tippi, wanted to trade cards. He was really nice to her because he liked her, so he traded 5 of his cards for 2 of hers. He then put his cards away. When he got home he noticed that 10 of his cards were missing. He was so upset that his mom bought him another pack of 12 cards. He hid half of his cards at home and took the rest to school the next day. He traded ¼ of the cards he brought to school to Dino again and got back 3 of Dino's cards. Curtis now has 9 cards at school. How many cards did he start with? How many cards total does he have now?
Curtis started with 84 cards and now has 12 cards at home and 9 cards at school, for a total of 21 cards.
How to find cards?To find how many card ,We see Curtis has 9 cards at school after trading with Dino again, which means he had 12 cards before the trade.
Before his mom bought him another pack of 12 cards, he had 10 missing, so he must have had 24 cards in total (12 + 12).
He hid half of his cards at home, so he has 12 cards at home.
He traded ¼ of the cards he brought to school to Dino and got back 3 of Dino's cards. Let's call the number of cards he brought to school "x".
So, he traded x/4 cards to Dino, and got back 3 cards, which means he now has (x/4) - 3 cards.
We know that he now has 9 cards at school, so we can set up an equation:
(x/4) - 3 = 9
Solving for x, we get:
x/4 = 12
x = 48
So, Curtis brought 48 cards to school, which means he started with 24 + 12 + 48 = 84 cards in total.
Therefore, Curtis started with 84 cards and now has 12 cards at home and 9 cards at school, for a total of 21 cards.
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Please help! This is part of my grade, please make sure to read the question before answering because I need this to be correct (35 points)
Answer:
u = -2.34 or u = 18.34
Step-by-step explanation:
You want to solve u² -16u = 43 by completing the square.
Completing the squareTo complete the square, add the square of half the coefficient of the linear term to both sides.
u² -16u +(-16/2)² = 43 +(-16/2)²
u² -16u +64 = 107 . . . . . . . simplify
(u -8)² = 107 . . . . . . . . . write as a square
u -8 = ±√107 . . . . . . square root
u = 8 ± √107 . . . add 8
u = -2.34 or u = 18.34 . . . . . find the decimal values
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