The values of k that make the remainder 0 when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2 are 3 and -1.
To find k so that when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2, the remainder is 0, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by x-a, the remainder is f(a).
So, if we let f(x) = x^(3)+kx^(2)+k^(2)x+14 and a = -2, we can find the value of k that makes the remainder 0.
f(-2) = (-2)^(3)+k(-2)^(2)+k^(2)(-2)+14 = 0
Simplifying the equation, we get:
-8 + 4k - 2k^(2) + 14 = 0
-2k^(2) + 4k + 6 = 0
Dividing by -2, we get:
k^(2) - 2k - 3 = 0
Factoring the equation, we get:
(k-3)(k+1) = 0
So, k = 3 or k = -1.
Therefore, the values of k that make the remainder 0 when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2 are 3 and -1.
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Logan invested $3,800 in an account paying an interest rate of 5½ % compounded
continuously. Qasim invested $3,800 in an account paying an interest rate of 6¹/8%
compounded annually. To the nearest hundredth of a year, how much longer would
it take for Logan's money to double than for Qasim's money to double?
9.63 years are required for $390 to become $660. A charge for borrowing money or other assets is called an interest.
What is Compound Interest?Compound interest simply indicates that the interest paid on a savings account, loan, or investment grows exponentially over time rather than linearly.
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
Here, A = Amount,
P = Principal Amount
r = Rate of interest
n = Number of times interest is charged in a year
t = number of years
Given ,Here Principal Amount is $390, the rate of interest is 5.5%(0.055),
the number of times the interest is charged in a year (n=4),
and the final amount is $660,
therefore, number of years will be equal to,
[tex]660 = 390(1 + \frac{0.055}{4} )^{4*t}[/tex]
[tex]\frac{660}{390} = (1.01375)^{4*t}[/tex]
[tex]1.6923 = (1.01375)^{4*t}[/tex]
[tex]log_{1.01375}1.6923 = 4t[/tex]
[tex]4t = 38.5234[/tex]
[tex]t = 9.63[/tex]
Hence, number of years it will take for $390 to become $660 is 9.63 years.
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To determine the number of squirrels in a conservation area, a researcher catches and marks squirrels. Then the researcher releases them. Later squirrels are caught and it is found that of them are tagged. About how many squirrels are in the conservation area?
Therefore , the solution of the given problem of unitary method comes out to be t there are 1000 squirrels in the conservation area.
Unitary method: what is it?To finish a job using the unitary method, divide the lengths of just this minute subset by two. In a nutshell, the unit method eliminates a desired item from both the characterized by a set and colour subsets. 40 pens, for instance, variable will cost Rupees ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.
Here,
The Lincoln-Petersen index can be used to calculate an approximate squirrel population estimate for the protected area:
There were n1 squirrels in the first group.
Second sample's fox count is equal to n2.
Second sample's total number of labelled squirrels is m2.
The following provides the Lincoln-Petersen index:
=> n1 * n2 / m2
Assume that the first sample consisted of 100 squirrels that were captured and tagged by the researcher. 20 of the 200 squirrels the researcher caught for the second group had tags on them. the following algorithm is used.
=> n1 * n2 / m2 = 100 * 200 / 20 = 1000
Therefore, it is believed that there are 1000 squirrels in the conservation area. It is crucial to keep in mind that this is only an approximation and might not be correct.
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In 1968 the remains of a young boy buried with over 100 tools of stone and antlers were found by accident by a construction worker on private property owned by the Anzick family in Montana. The bones were determined by radiocarbon-dating to be 12,600 years old. The half-life of Carbon-14 is 5730 years. What percent of the original amount of Carbon-14 was in the bone remains when found in 1968? Show how you obtained your equation and how you solved it. In 2014, a daughter of the Anzick family, Sarah Anzick, who was inspired by the finding and had become a genome researcher, was a member of the team that did DNA sequencing on the remains.
To find the percent of the original amount of Carbon-14 in the bone remains when found in 1968, we can use the following formula:
A = A0 * (1/2)^(t/h)
Where A is the final amount of Carbon-14, A0 is the original amount of Carbon-14, t is the time elapsed, and h is the half-life of Carbon-14.
Plugging in the given values, we get:
A = A0 * (1/2)^(12600/5730)
Simplifying the exponent, we get:
A = A0 * (1/2)^2.199
Using a calculator, we find that (1/2)^2.199 is approximately 0.153, so:
A = A0 * 0.153
This means that the final amount of Carbon-14 is 15.3% of the original amount of Carbon-14. Therefore, the percent of the original amount of Carbon-14 in the bone remains when found in 1968 is 15.3%.
As for the second part of the question, Sarah Anzick was a member of the team that did DNA sequencing on the remains in 2014. This allowed for further analysis and understanding of the remains and their significance in terms of human history and evolution.
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Find y(t) of the following equation.
y’’ + 3y’ - 4y = 2 , y(0) = 0, y’(0) = 0
The given equation is a second order differential equation, which can be solved using the method of undetermined coefficients. The homogenous solution of the equation is:
yh = c1e2t + c2e-t
By applying the initial conditions, we get: c1 = 0, c2 = 0.
Therefore, the homogenous solution is: yh = 0.
The particular solution of the equation is:
yp = At2 + Bt + C
Substituting yp and its derivatives in the given equation and equating the coefficients of each term on both sides, we get:
A = 1/2, B = 0, C = 0
Therefore, the particular solution is: yp = 1/2t2
Thus, the solution of the given equation is:
y(t) = yh + yp = 1/2t2
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what is the value of (3-5)^4 (2)-16+2?
Find all solutions of the equation in the interval [0, 2). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION. )
tan2(x) = sec(x) − 1
The solution to the equation tan²(x) = sec(x) − 1 in the interval [0, 2π) is x = 0
Consider equation tan²(x) = sec(x) − 1
We know that tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x)
so the equation becomes,
[tex]\frac{sin^2(x)}{cos^2(x)}-\frac{1}{cos(x)}+1=0[/tex]
sin²(x) - cos(x) + cos²(x) = 0
We know that the trignometric identity sin²(x) + cos²(x) = 1
(1 - cos²(x)) - cos(x) + cos²(x) = 0
1 - cos²(x) - cos(x) + cos²(x) = 0
1 - cos(x) = 0
cos(x) = 1
We know that for x = 0 and 2π, the value of cos(x) is 1
In the interval [0, 2π), the solution for equation would be x = 0
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The complete question is:
Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) tan²(x) = sec(x) − 1
olve the compound inequality. 4u+5>13 and 2u+6>=16 raph the solution on the number line. there is no solution, click on "No solut
we can graph the solution on the number line. The solution will be the intersection of the two inequalities, which is u >= 5. The solution to the compound inequality is u >= 5.
To solve the compound inequality, we need to isolate the variable on one side of the inequality.
For the first inequality, 4u + 5 > 13, we can subtract 5 from both sides to get:
4u > 8
Then, we can divide both sides by 4 to get:
u > 2
For the second inequality, 2u + 6 >= 16, we can subtract 6 from both sides to get:
2u >= 10
Then, we can divide both sides by 2 to get:
u >= 5
Now, we can graph the solution on the number line. The solution will be the intersection of the two inequalities, which is u >= 5.
On the number line, we can draw a closed circle at 5 and shade to the right to indicate that the solution includes 5 and all numbers greater than 5.
The solution to the compound inequality is u >= 5.
Here is the graph of the solution on the number line:
0 1 2 3 4 5 6 7 8 9 10
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Visual domain and range
Determine the range of the following graph
Answer:
[-4, 2]
Step-by-step explanation:
You want the range of the graph shown.
RangeThe range is the vertical extent of the graph. This graph has a minimum at y=-4 and a maximum of y=2. All values between these are represented, so the range is ...
[-4, 2] . . . . or -4 ≤ y ≤ 2
If I was asked to think of a number and multiply it by 2 I would get 2x
Answer:
5x - 3
Step-by-step explanation:
Given:
A Number and multiply it by 2.
To Find:
to write it algebraically
Solution:
Let the number that was asked to think to be x.
Then it is multiplied by 2 which becomes 2x.
Now the number is multiplied by 5.
So, x multiplied by 5 will become 5x.
Then, 5x is subtracted from 3.
So, we can write it as 5x - 3
Therefore, it can be written as 5x - 3 algebraically.
Determine if the triangles are similar.
A. Yes, SSS
B. Yes, SAS
C. Yes, AA
D. No, not similar
The triangles are similar thus option A. Yes, SSS
What are similar triangles?When the corresponding properties of two or more triangles have common relations, then the triangles are said to be similar. Thus the similarity property can be expressed as either Side-Side-Side, Side-Angle-Side, Side-Angle-Angle, Angle-Side-Side etc.
Though two or more triangles are said to be similar but not congruent.
Considering the properties of the triangles ABX and YZX, it can be concluded that the triangles are similar by Side-Side-Side similarity property. Therefore the appropriate option is A. Yes, SSS.
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the permulation [[1,2,3,4,5,6],[6,5,4,3,2,1]]can be written as a product of disjoint cycles as
The permutation [[1,2,3,4,5,6],[6,5,4,3,2,1]] can be written as a product of disjoint cycles as (1,6)(2,5)(3,4).
A permutation can be represented as a product of disjoint cycles. A cycle is a sequence of numbers that are permuted in a circular fashion. For example, the cycle (1,2,3) means that 1 is permuted to 2, 2 is permuted to 3, and 3 is permuted to 1.
To write the given permutation as a product of disjoint cycles, we can start with the first number in the first row, 1, and see where it is permuted to in the second row. In this case, 1 is permuted to 6. Then we look at where 6 is permuted to, which is 1, completing the cycle (1,6).
Next, we move on to the next number in the first row that has not been included in a cycle, which is 2. We see that 2 is permuted to 5, and 5 is permuted to 2, completing the cycle (2,5).
Finally, we move on to the next number in the first row that has not been included in a cycle, which is 3. We see that 3 is permuted to 4, and 4 is permuted to 3, completing the cycle (3,4).
Therefore, the given permutation can be written as a product of disjoint cycles as (1,6)(2,5)(3,4).
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Scientists estimate that less than
one-billionth of the Sun's total energy
output each day reaches Earth. What do
you think happens to the rest?
The vast majority of the Sun's energy radiates out into space and does not reach Earth.
Why does so little of the Sun's energy reach Earth?
The reason is that space is vast, and the Sun's energy radiates out in all directions, spreading out over enormous distances. By the time it reaches Earth, it has become highly diluted, with only a tiny fraction of the original energy remaining.
Factors that reduce the amount of the Sun's energy reaching Earth-
The Sun's energy is produced through nuclear fusion in its core, where hydrogen atoms are fused together to form helium, releasing vast amounts of energy in the process. This energy then radiates outwards from the core, passing through various layers of the Sun's atmosphere before eventually reaching the surface and being emitted into space.
As the Sun's energy travels through space, it encounters various obstacles, such as interstellar dust and gas, as well as the solar wind, which is a stream of charged particles that constantly flows out from the Sun. These obstacles can scatter and absorb some of the Sun's energy, further reducing the amount that reaches Earth.
Only a small fraction of the Sun's energy is intercepted by Earth, where it is absorbed by the atmosphere, oceans, and land. The energy that is absorbed by Earth drives the planet's weather and climate systems, powering phenomena such as wind, rain, and the water cycle. The rest of the Sun's energy continues to radiate out into space, where it can influence the temperature and behavior of other planets and celestial objects.
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Alina flipped a nickel 10 times. It landed on heads 7 times and tails 3 times. If she flips the coin again, what is the probability of getting tails?
Answer:
Probability=number of chances/total possible outcome
P=3/10
3.
The box-and-whisker plot shown below represents
600 scores on a district geometry test.
Therefore , the solution of the given problem of plotting data comes out to be 75 represents the top quartile (Q3) outside the whiskers are also depicted on the plot as individual points.
Describe a data plotting.The most popular method for displaying data in a geographical format is to demonstrate the correlation between two additional factors. Digital or hand-drawn sketches are both acceptable. Starting at the starting the spot, move three separate parts upward and then two or more components in the right. The display of the reference system must show the numerals for positions 2, 3, and 4.
Here,
The following details are displayed by the box-and-whisker plot:
The cutoff is somewhere around 35.
=> Around 55 constitutes the bottom quartile (Q1).
=> At around 65, the median (Q2) is.
=> Around 75 represents the top quartile (Q3).
The top number is somewhere around 95.
The whiskers stretch to the minimum and maximum scores, while the box represents the middle 50% of the scores (between Q1 and Q3).
A few outliers that lay outside the whiskers are also depicted on the plot as individual points.
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can someone please answer these questions for me
The answers for each line are:
a) the slope is -2
b) The slope is 2/5 and the y-intercept is -2.
c) x = 10/4
d) y = -7x - 2
How to get the slope of the line?A linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
We know that if the line passes through (x₁, y₁) and (x₂, y₂), then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
a) Then the slope of the line that passes through (2, -5) and (-2, 3) is:
a = (3 + 5)/(-2 - 2) = 8/-4 = -2
b) The line is 2x - 5y = 10
Isolating y we will get:
5y = 2x - 10
y = (2/5)*x - 2
The slope is 2/5 and the y-intercept is -2.
c) Here we need to solve:
-4 = (1 + 9)/(0 - x)
-4*-x = 10
x = 10/4
d) if the slope is -7, then we have:
y = -7x + b
And the line also passes through (-1, 5), then:
5 = -7*-1 + b
5 = 7 + b
5 - 7 =b
-2 = b
The line is:
y = -7x - 2
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What is the equation of the line of best fit for the above data? Round the slope
and y-intercept to the nearest hundredth. Interpret the slope and y-intercept.
We can conclude that the equation of the line of best fit is -
ŷ = 713.70516X + 1077.04596. Also, the slope {m} is 713.70516 and {y} -
intercept is 1077.04596.
What is line of best fit?A line of best fit is a straight line that minimizes the distance between it and some data. The line of best fit is used to express a relationship in a scatter plot of different data points. It is an output of regression analysis and can be used as a prediction tool for indicators and price movements.Given is a table as shown in the image.
{X - M(x)}-6.6
-5.6
-3.6
-1.6
-0.6
0.4
2.4
3.4
5.4
6.4
{Y - M(y)}-4887.5
-3887.5
-2587.5
-1287.5
-637.5
962.5
1762.5
2312.5
3737.5
4512.5
{X - M(x)}²43.56
31.36
12.96
2.56
0.36
0.16
5.76
11.56
29.16
40.96
{SS} : 178.4
{X - M(x)}{Y - M(y)}32257.5
21770
9315
2060
382.5
385
4230
7862.5
20182.5
28880
{SP} : 127325
Sum of {X} = 66
Sum of {Y} = 57875
Mean {X} = 6.6
Mean {Y} = 5787.5
Sum of squares {SSₓ} = 178.4
Sum of products {SP} = 127325
Regression Equation -
ŷ = bX + a
b = SP/SSₓ = 127325/178.4 = 713.70516
a = MY - bMₓ = 5787.5 - (713.71*6.6) = 1077.04596
ŷ = 713.70516X + 1077.04596
Slope -
{m} = 713.70516
{y} - intercept = 1077.04596
Therefore, we can conclude that the equation of the line of best fit is -
ŷ = 713.70516X + 1077.04596. Also, the slope {m} is 713.70516 and {y} -
intercept is 1077.04596.
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i need help on my dividend
Answer:
ok divide is easy
Step-by-step explanation:
dividing is not adding or subtracting
Describe the graph of y = 1/2x-10 -3 compared to the graph of y=1/x
The graphs of y = 1/2x - 10 - 3 and y = 1/x are different in shape and behavior, and their only similarity is that they are both continuous functions.
What is a graph ?
Graph can be defined as visual representation of data using ordered pairs.
The graphs of y = 1/2x - 10 - 3 and y = 1/x have different shapes and behaviors.
The graph of y = 1/2x - 10 - 3 is a linear function with a slope of 1/2 and a y-intercept of -13. This means that the graph will have a constant slope of 1/2, and will be downward sloping from left to right. As x increases, y decreases at a steady rate.
On the other hand, the graph of y = 1/x is a non-linear function that is a hyperbola. This means that the graph will be curved and will have two branches, one in the first quadrant and the other in the third quadrant. The graph will approach the x and y-axes but will never touch them. The curve will be symmetric about the line y = x, which means that for every point (x, y) on the graph, there will be a corresponding point (y, x) on the graph.
Therefore, the graphs of y = 1/2x - 10 - 3 and y = 1/x are different in shape and behavior, and their only similarity is that they are both continuous functions.
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Which choice is equivalent to the expression
4 (1/2x - 3y)
Answer:
2x-12y
Step-by-step explanation:
This is equivalent to the original fraction--4(1/2x - 3y)
If we were to solve 4(1/2x - 3y), we'd get: 2x-12y.
Meaning, 2x-12y is equivalent to 4(1/2x - 3y).
An account with an initial balance of $1250 earns interest that is compounded quarterly. If no other deposits or withdrawals are made, the account will have a balance of $1406.08 after 9 months. Find the annual interest rate.
Answer:
Let's first calculate the number of compounding periods in a year, given that the interest is compounded quarterly:
Number of compounding periods in a year = 4 (since there are 4 quarters in a year)
Next, let's use the formula for compound interest to find the annual interest rate:
A = P (1 + r/n)^(nt)
Where:
A is the balance after t years
P is the principal (initial balance)
r is the annual interest rate (what we are looking for)
n is the number of compounding periods in a year
t is the time in years
We know that P = $1250, A = $1406.08, n = 4, and t = 9/12 years (since the interest is earned for 9 months).
Plugging these values into the formula, we get:
$1406.08 = $1250 (1 + r/4)^(4/3)
Dividing both sides by $1250 and taking the cube root of both sides, we get:
1 + r/4 = (1406.08/1250)^(3/4)
1 + r/4 = 1.038
Subtracting 1 from both sides, we get:
r/4 = 0.038
Multiplying both sides by 4, we get:
r = 0.152
Therefore, the annual interest rate is 15.2%.
Three squares with areas of 112 cm2,28 cm2, and 63 cm2 are displayed on a computer monitor. What is the sum (in radical form) of the perimeters of these squares? The sum of the perimeters is cm.
The sum of the perimeters of the three squares displayed on the computer monitor is 36√7 cm.
The sum of the perimeters of the three squares displayed on the computer monitor can be found by first finding the side length of each square, and then multiplying that side length by 4 to find the perimeter of each square. Finally, we add the perimeters of the three squares together to find the sum of the perimeters.
For the first square with an area of 112 cm^2, the side length is √112 cm, or 4√7 cm. The perimeter of this square is 4(4√7 cm) = 16√7 cm.
For the second square with an area of 28 cm^2, the side length is √28 cm, or 2√7 cm. The perimeter of this square is 4(2√7 cm) = 8√7 cm.
For the third square with an area of 63 cm^2, the side length is √63 cm, or 3√7 cm. The perimeter of this square is 4(3√7 cm) = 12√7 cm.
The sum of the perimeters of these three squares is 16√7 cm + 8√7 cm + 12√7 cm = 36√7 cm.
Therefore, the sum of the perimeters of the three squares displayed on the computer monitor is 36√7 cm.
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Let R be a ring such that x = x2 for all x ∈ R. Prove that R is a ring commutative.
Yes, the given ring is commutative.We have that, a commutative ring in abstract algebra is a ring that satisfies a +b = b+a (for a defined operator).
Given: R is a ring such that [tex]$x = x^2$[/tex] for all [tex]$x\in R$[/tex].
To prove: R is a ring commutative.
Proof:
Let [tex]$a$[/tex] and [tex]$b$[/tex] be arbitrary elements in [tex]$R$[/tex].
[tex]$a+b = (a+b)^2 = a^2 + 2ab + b^2$[/tex]
[tex]$b+a = (b+a)^2 = b^2 + 2ab + a^2$[/tex]
Therefore, [tex]$a+b = b+a$[/tex]. Thus, R is a ring commutative.
Q.E.D.
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katie runs a stable that boards a range of horses 3 of them being bay 19 of them being white 1 of them being gray 4 of them being black and 3 of them being palomino out of the next 15 horses should you expect to be black horses
We can expect 2 black horses out of a sample of 15 horses from the stable.
What is probability?To determine how likely something is gonna occur, use probability. The event is typically stated as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty.
To solve it, we need to use the information provided about the proportion of different horse colors in the stable to estimate the number of black horses we would expect to find in a sample of 15 horses.
According to the information provided, there are 3+19+1+4+3= 30 horses in the stable, and 4 of them are black. Therefore, the proportion of black horses in the stable is:
4/30 = 0.1333...
So, if we were to randomly select 15 horses from the stable, we would expect approximately 13.33% of them to be black. To find the expected number of black horses in a sample of 15 horses, we can multiply the proportion by the sample size:
0.1333... x 15 = 1.999...
Rounding to the nearest whole number, we can expect 2 black horses out of a sample of 15 horses from the stable.
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Chiang is retiling the kitchen floor with his parents. How many square feet of tile do they need?
Usuahsusjshsusijvdhdhdhdh
fryt trreu tyuin
Step-by-step explanation:
gfwdhju gtdstfjgg uyieeersud tdjjs oooyjt
iiisuuus jydkkdiiif oydtttdiid kgdjgdkkkx
iisjjsxxxf ofgxtrg cetfffl vhyy fffuu
Thank You!
Height: cm Volume: cm^(3) Length: Width: Height: Volume: a multiplication sentence that you could use to calculate the volume for m 1. Include the units in your sentences.
The multiplication sentence will be: Volume = Length × Width × Height.
Each of these measurements should be in centimeters (cm) in order to calculate the volume in cubic centimeters (cm^3).
To calculate the volume of a rectangular prism, you can use the multiplication sentence: Volume = Length × Width × Height. Each of these measurements should be in centimeters (cm) in order to calculate the volume in cubic centimeters (cm^3).
For example, if the length of the rectangular prism is 5 cm, the width is 3 cm, and the height is 2 cm, the multiplication sentence would be:
Volume = 5 cm × 3 cm × 2 cm
The volume of this rectangular prism would be 30 cm^3.
In general, the multiplication sentence to calculate the volume of a rectangular prism is:
Volume = Length × Width × Height
Make sure to include the units (cm) in your multiplication sentence in order to get the correct answer in cubic centimeters (cm^3).
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Please answer number 10. Please answer both parts. Show work. Thank you
The volume of the triangular prism is 3x³ + 16x² + 3x - 10. And the volume of the triangular prism when height is 50% reduced will be 1.5x³ + 8x² + 1.5x - 5.
What is the volume?Volume is a measurement of three-dimensional space that is utilized. The concept of length is linked to the notion of capacity.
The dimensions of the triangular prism are (2x + 2), (x + 5), and (3x - 2). Then the volume is given as,
V = (1/2) · (2x + 2) · (x + 5) · (3x - 2)
V = (x + 1) · (x + 5) · (3x - 2)
V = (x² + 6x + 5) · (3x - 2)
V = 3x³ + 16x² + 3x - 10
If the height is reduced by 50%, then the volume is given as,
V = (1/2) · [0.50 × (2x + 2)] · (x + 5) · (3x - 2)
V = (1/2) · (x + 1) · (x + 5) · (3x - 2)
V = (1/2) · (x² + 6x + 5) · (3x - 2)
V = (1/2) · (3x³ + 16x² + 3x - 10)
V = 1.5x³ + 8x² + 1.5x - 5
The volume of the triangular prism is 3x³ + 16x² + 3x - 10. And the volume of the triangular prism when height is 50% reduced will be 1.5x³ + 8x² + 1.5x - 5.
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What are the coordinates of R′ for the dilation centered at P with scale factor 0.5?
Type answer as a decimal where needed.
The coordinates of R′ for the dilation centered at P with scale factor 0.5 are R' (-1, -0.5).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the preimage by using a scale factor of 0.5 centered at the point P (-3, -3) by using this mathematical expression:
(x, y) → (k(x - a) + a, k(y - b) + b)
For coordinate R, we have;
Coordinate R = (1, 2) → (0.5(1 - (-3)) + (-3), 0.5(2 - (-3)) + (-3))
Coordinate R = (1, 2) → (0.5(1 + 3) - 3, 0.5(2 + 3) - 3)
Coordinate R = (1, 2) → (0.5(4) - 3, 0.5(5) - 3)
Coordinate R' = (1, 2) → (-1, -0.5)
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First give the technology formula for the given function and then use technology to evaluate the function for the given values of x (when defined there). (Round all answers to four decimal places.)
h(x) =
x2 − 8 / x2 + 8
; x = 0.5, 1.5, 2.5, ..., 10.5
A. (x^2 + 8)/(x^2 − 8)
B. (x^2 − 8)/(x^2 + 8)
C. (x − 8)^2/(x + 8)^2
D. (x − 8)^2/(x^2 + 8)
h(0.5) = h(1.5) = h(2.5) = h(3.5) = h(4.5) = h(5.5) = h(6.5) = h(7.5) = h(8.5) = h(9.5) = h(10.5) =
The technology formula for the given function is B. (x^2 − 8)/(x^2 + 8).
We can use technology, such as a graphing calculator or an online math solver, to evaluate the function for the given values of x. Here are the steps to do so:
1. Enter the technology formula (x^2 − 8)/(x^2 + 8) into the calculator or solver.
2. Enter the values of x one at a time and evaluate the function for each value.
3. Round all answers to four decimal places.
Here are the results:
h(0.5) = 0.9310
h(1.5) = 0.6765
h(2.5) = 0.5161
h(3.5) = 0.4196
h(4.5) = 0.3548
h(5.5) = 0.3103
h(6.5) = 0.2778
h(7.5) = 0.2533
h(8.5) = 0.2346
h(9.5) = 0.2199
h(10.5) = 0.2081
Therefore, the function evaluated at the given values of x is as follows:
h(0.5) = 0.9310
h(1.5) = 0.6765
h(2.5) = 0.5161
h(3.5) = 0.4196
h(4.5) = 0.3548
h(5.5) = 0.3103
h(6.5) = 0.2778
h(7.5) = 0.2533
h(8.5) = 0.2346
h(9.5) = 0.2199
h(10.5) = 0.2081
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EQUATIONS AND INEQUALITIES Solving a word problem with two unknowns using a linear... A washer and a dryer cost $615 combined. The washer costs $85 less than the dryer. W
The cost of the washer is $265 and the cost of the dryer is $350.
To solve this word problem with two unknowns using a linear equation, we can use the following steps:
Define the variables: Let W represent the cost of the washer, and D represent the cost of the dryer.Write the equation based on the given information: W + D = $615, and W = D - $85Substitute one equation into the other to solve for one variable: (D - $85) + D = $615Simplify the equation: 2D = $700Solve for the variable: D = $350Substitute the value of D back into one of the original equations to find the value of W: W = $350 - $85 = $265So, the cost of the washer is $265 and the cost of the dryer is $350.
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