The product of the given expressions A, B, C, and D is 1. This is computed by recognizing A and C as conjugates (and likewise B and D), and using the difference of squares rule.
Explanation:Given the expressions of A, B, C, D as written in the question, what needs to be done is to multiply these expressions together. Since B is the negative of A, and D is the negative of C, you can rewrite ABCD as:
A*(-A)*C*(-C)
which simplifies to -(AC)2. You'll notice that A and C are conjugates. This means that squaring them results in the difference of squares, or a2 - b2. Implementing this, we get:
the product ABCD, we can use the distributive property of multiplication over addition. We have:
ABCD = (A + B)(C + D)
Substituting the given values of A, B, C, and D, we get:
ABCD = ((√2008 + √2009) + (-√2008 - √2009))((√2008 - √2009) + (√2009 - √2008))
-(sqrt{2008}2 - sqrt{2009}2) = -(2008 - 2009) = 1
So, the product of the given expressions A, B, C, and D is 1.
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To find ABCD, we multiply the given values together and simplify the expressions using the difference of squares formula. The value of ABCD is -1.
Explanation:Given that A = (√{2008}+√{2009}), B = (-√{2008}-√{2009}), C = (√{2008}-√{2009}), and D = (√{2009}-√{2008}), to find ABCD, we multiply the given values together:
ABCD = ((√{2008}+√{2009})(-√{2008}-√{2009}))((√{2008}-√{2009})(√{2009}-√{2008}))
By expanding the multiplication and simplifying the expressions, we get:
ABCD = (√{2008}² - (√{2009})²)((√{2009})² - (√{2008})²)
After applying the difference of squares formula, we have:
ABCD = (2008 - 2009)(2009 - 2008)
Simplifying further, we obtain:
ABCD = (-1)(1) = -1
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the complete Question is given below:
Given that A = (√{2008}+√{2009}), B = (-√{2008}-√{2009}), C = (√{2008}-√{2009}), and D = (√{2009}-√{2008}), find ABCD.
Find 3 consecutive even integers whose sum is 138.
Answer:
The integers are:
44,46,48
Step-by-step explanation:
After a birthday party,
1/4
of a large cake was left. If this piece of cake was shared equally among the 6 people, what fraction of the whole cake did each person receive?
A) 24
B)
1/24
C)
1/6
D)
4/6
Answer: 1/24
Step-by-step explanation:
If one fourth was split into six pieces, you would multipli six by one fourth to get 1.24==
If 1m = 3.3 ft, how many cubic feet is the Kuroshio Sea tank? Volume is 9,450. Show your calculations!
Answer:
339604.65 cubic feet
Step-by-step explanation:
We are given that 1 m is equal to 3.3 ft.
1 m = 3.3 ft
This means that if we find the volume of a cube of 1 m, we have its volume as:
[tex]1^3 = 1 m^3[/tex]
In the same way, the volume of a cube of 3.3 ft (1 m) is:
[tex]3.3^3 = 35.937 ft^3[/tex]
This means that:
[tex]1m^3 = 35.937 ft^3[/tex]
The Kuroshio sea tank has volume of [tex]9450 m^3[/tex]. Its volume in cubic feet is therefore:
[tex]1m^3 = 35.937 ft^3\\\\9450 m^3 = 9450 * 35.937 = 339604.65 ft^3[/tex]
The volume of the tank is 339604.65 cubic feet.
A pilot flies 416 miles from Tampa to Atlanta 5 times in one week. She flies 721 miles from Atlanta to Dallas 8 times. What is the total number of miles she flies? ANSWERS!!!!
Answer:
416 x 5 = 2080
721 x 8 = 5768
5768 + 2080 = 7848. Have a great day.
You might need:
A circle has a circumference of 1,133.54 units.
What is the diameter of the circle?
units
Answer 360.81 units
Answer:
360.82 units
Step-by-step explanation:
The circle has a circumference of 1,133.54 units.
The circumference of a circle is given as:
C = πD
where D = diameter
This implies that:
1133.54 = πD
=> D = 1133.54 / π
D = 360.82 units
Its diameter is 360.82 units
What are the solutions to the equation x2 - 4x = -1?
Answer:
x= [tex]2-\sqrt{3}[/tex] and x=[tex]2+\sqrt{3}[/tex]
Step-by-step explanation:
- transfer the -1 to the other side so that the equation reads as [tex]x^{2} -4x+1[/tex]
- factor! think about what numbers add -4 but also multiply to be 1
- you may then realize that there are no numbers with those characteristics
- since that is the case, we have to use the quadratic formula, which is:
[tex]\frac{-b+\sqrt{b^{2}-4ac }}{y}[/tex] and [tex]\frac{-b-\sqrt{b^{2}-4ac }}{y}[/tex]
- the equation is shown as [tex]a^{2}+b^{2}=c^{2}[/tex]
- using the numbers that correspond with those lettered values, plug it in the quadratic formulas
the solutions to the equation [tex]\( x^2 - 4x = -1 \) are \( x = 2 + \sqrt{3} \) and \( x = 2 - \sqrt{3} \)[/tex].
To find the solutions to the equation [tex]\( x^2 - 4x = -1 \)[/tex], we can follow these steps:
1. Move all terms to one side of the equation to set it equal to zero:
[tex]\[ x^2 - 4x + 1 = 0 \][/tex]
2. We can solve this quadratic equation using the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
where [tex]\( a = 1 \), \( b = -4 \), and \( c = 1 \).[/tex]
3. Plug in the values and simplify:
[tex]\[ x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(1)}}{2(1)} \] \[ x = \frac{4 \pm \sqrt{16 - 4}}{2} \] \[ x = \frac{4 \pm \sqrt{12}}{2} \] \[ x = \frac{4 \pm 2\sqrt{3}}{2} \] \[ x = 2 \pm \sqrt{3} \][/tex]
So, the solutions to the equation [tex]\( x^2 - 4x = -1 \) are \( x = 2 + \sqrt{3} \) and \( x = 2 - \sqrt{3} \)[/tex].
Use the multiplier method to increase £258 by 43%
You must show your working.
To increase £258 by 43%, convert the percentage to a decimal, calculate the increased amount, and add it to the original amount. The increased amount to the original amount is £368.94
To increase £258 by 43% using the multiplier method:
Convert the percentage to a decimal: 43% = 0.43
Calculate the increased amount: £258 x 0.43 = £110.94
Add the increased amount to the original amount: £258 + £110.94 = £368.94
Write an exponential model, y=a(b)^x, given the two points (9,171) and (10,190)
Please hurry!
Answer:
[tex]y = 66.25(1.11)^x[/tex]
Step-by-step explanation:
Let's plug in 9 for x and 171 for y into the given exponential equation:
y = [tex]ab^x[/tex]
171 = [tex]ab^9[/tex]
Now do the same with (10, 190):
190 = [tex]ab^{10}[/tex]
Write them both in terms of a and set them equal:
a = 171/[tex]b^9[/tex]
a = 190/[tex]b^{10}[/tex]
171/[tex]b^9[/tex] = 190/[tex]b^{10}[/tex]
Multiply both sides by [tex]b^{10}[/tex]:
171b = 190
b = 190/171 = 10/9 ≈ 1.11
Plug this in to find a:
a = 171 / (10/9)^9 ≈ 66.25
So, the exponential model is:
[tex]y = 66.25(1.11)^x[/tex]
Answer:
y = 66.25[(10/9)^x]
Step-by-step explanation:
171 = a(b⁹)
b⁹ = 171/a
190 = a(b¹⁰)
190 = a(171/a) × b
b = 190/171
b = 10/9
(10/9)⁹ = 171/a
a = 66.24890362
Keith Jones purchased a $50,000 policy. At the tenth anniversary what would be the cash value of his policy?
Answer:
The answer is "$ 4450"
Step-by-step explanation:
Purchased policy price = $50,000
10th anniversary cash value = ?
The after calculation its final value is = $ 4450
Evaluate the expression 9P1
Answer :
9
Explanation :
The expression above signifies the Permutation expression
Permutation expression is given as nPr
The Permutation expression is calculated as:
nPr = P(n, r) = n! / (n - r)!
It the above question, we were asked to evaluate the expression 9P1
From the above question, we can see that:
n = 9 and r = 1
Therefore, the expression
9P1 = 9! / ( 9 - 1) !
9P1 = 9! / 8!
= 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 362880 /40320
= 9
Therefore, the evaluation of the expression 9P1 = 9
Final answer:
To evaluate the expression 9P1, we calculate the permutation for selecting 1 item from 9, which simplifies to 9/1, giving us the answer of 9.
Explanation:
The student has asked to evaluate the expression 9P1, which is a permutation problem. To find 9P1, we use the permutation formula, which is P(n, k) = n! / (n-k)!, where n is the total number of items to choose from, and k is the number of items to choose. In this case, since we want to choose 1 item from 9, the permutation is calculated as:
Identify the values of n and k (n=9, k=1).Apply the permutation formula: 9P1 = 9! / (9-1)! = 9! / 8!.Simplify the factorial expression: 9! / 8! = 9 / 1 = 9.Therefore, the value of 9P1 is 9.
Which rule describes the relationship between the x- and y- coordinates on following graph?
A: y = 3x B: y = 2x + 2
Tony has a bag of 10 quarters, 12 nickels, and 8 dimes. Tony selects a coin, records it, then replaces it back in the bag before choosing again.
Find the probability he selects a quarter first, dime second, and nickel
third. Write your answer in a fraction in simplest form.
Please help me!!
Answer:
8/225
Step-by-step explanation:
The probability of each event would be the number of the type of currency that you have specified divided by the total number of coins, in this case the total amount of coins does not change as the coin returns to the bag.
The total number of coins is: 10 + 12 + 8 = 30
The probability of finding a quarter is:
10/30
The probability of finding dime is:
8/30
The probability of finding nickel is:
12/30
The final probability then is:
(10/30) * (8/30) * (12/30) = 960/27000
If we simplify this, dividing both numbers by 120, we are left with:
8/225
On a map the distance between two towns is 12 centimeters. If 3 centimeters represents 90 miles what is the actual distance between the cities in miles
the actual distance between the two towns is 360 miles.
What is Scale?The ratio used to depict the relationship between the dimensions of a model or scaled figure and the corresponding dimensions of the real figure or object is called the scale. On the other hand, a scale factor is a value that is used to multiply all of an object's parts in order to produce an expanded or decreased figure.
Given, On a map, the distance between two towns is 12 centimeters.
Also given, 3 centimeters represent 90 miles on the map.
Since 12 centimeters represent the distance between the two towns on the map, we can set up the proportion:
3 centimeters : 90 miles = 12 centimeters : x miles
where x represents the actual distance between the two towns in miles.
To solve for x, we can cross-multiply and simplify:
3 centimeters * x miles = 90 miles * 12 centimeters
3x = 1080
x = 360
Therefore, the actual distance between the two towns is 360 miles.
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Find the area of a semicircle
Answer:
18pi, or 56.52
Step-by-step explanation:
To start off, if you were to find the area of any whole circle, you would use the formula: pi x radius^2 = area of circle
However, since this is a semi-circle (half of a whole circle) you would divide the whole expression by 2, and then solve:
(pi x radius^2)/2 = area of semi-circle
(pi x 6^2)/2 = area of semi-circle
(36 x pi)/2 = area of semi-circle
18 x pi = area of semi-circle
18 x 3.14 = area of semi-circle
56.52 = area of semi-circle
The area of a circle is
[tex]\pi \: {r}^{2} [/tex]
So the area of a semicircle would be half of that, or
[tex] \frac{\pi}{2} {r}^{2} [/tex]
So just plug in the radius, six, to get this
[tex]18\pi[/tex]
In one year the perseid metor shower had a metor appear every 1/5 5 minutes on average That same year the Leonid metor shower had a metor appear every 4/2 3 minutes on average.
In one year, the Perseid meteor shower had a meteor appear every 1 1/5 minutes on average. That same year, the Leonid meteor shower had a meteor appear every 4 2/3 minutes on average. How many more meteors fell during the Perseid meteor shower?
Answer:
325,452 meteors
Step-by-step explanation:
We all know that :
We have 365 days in a year and in each day there are 24 hours, Likewise an hour has 60 minutes
SO, the total number of minutes in a year is :
365 × 24 × 60 = 525600 minutes
For Perseid meteor:
[tex]1 + \frac{1}{5} \\ \\ = 1 + 0.2 \\ \\ = 1.2[/tex]
So one meteor fall at 1.2 minutes interval Thus, in a year, we will have :
1 meteor - 1.2 minutes.
x meteor - 525600 minutes.
1.2x = 525600
[tex]x = \frac{525600}{1.2}[/tex]
x = 438000
∴ 438,000 meteors fell during the Perseid shower.
For Leonid meteor shower:
[tex]4 + \frac{2}{3} = 4.67[/tex]
So one meteor fall at 4.67 minutes interval Thus, in a year, we will have :
1 meteor - 4.67 minutes.
x meteors - 525600 minutes.
[tex]4.67x = 525600[/tex]
[tex]x = \frac{525600}{4.67}[/tex]
x = 112548
112,548 meteors fell during the Leonid Shower.
Finally , the numbers of more meteors that fell during the Perseid meteor shower is calculated by the difference in the number of Perseid meteor shower and Lenoid meteor shower. i.e
438,000 - 112,548 = 325,452
325,452 more meteors fell during the Perseid meteor shower
Answer:
For Leonid meteor shower: So one meteor fall at 4.67 minutes interval Thus, in a year, we will have : 1 meteor - 4.67 minutes. x meteors - 525600 minutes
Step-by-step explanation:
Find the length of the third side to the nearest tenth.
Answer:
9.8
Step-by-step explanation:
Answer:
9.8 that is the answer
Step-by-step explanation:
The music teacher asked his class to vote for their favorite instrument and created a pie chart to display the results. There are
20 students in his class. Which statements are true? Check all that apply.
Popularity of Musical
Instruments
Horns
15%
Guitar
35%
Flute
20%
Piano
30%
Exactly half of the students voted for flute or guitar.
Three students voted for horns.
Less than one-third of the class voted for guitar.
Answer:
Three students voted for horns.true
Step-by-step explanation:thats all i know
Answer:
B, D, E, F
Step-by-step explanation:
Three students voted for horns.
Thirteen students voted for piano or guitar.
Twice as many students voted for piano as horns.
Eleven students voted for flute or guitar.
Subtract 55 from the sum of 9g and 4 when g=8
Answer:
21
Step-by-step explanation:
(9g+4)-55=
(72+4)-55=
76-55=
21
Final answer:
To find the answer, first multiply 9 by 8, then add 4, resulting in 76. Finally, subtract 55 to get the answer, which is 21.
Explanation:
To solve the problem, we need to first calculate the sum of 9g and 4 when g=8. This will be 9 × 8 + 4.
After calculating the sum, we will subtract 55 from this amount to get the final answer.
Following the steps:
Substitute the value of g: We are given that g = 8. So, we need to find the sum of 9 * 8 and 4.Calculate the sum: The sum of 9 × 8 and 4 is 72 + 4 = 76.Subtract 55:Finally, we subtract 55 from the calculated sum: 76 - 55 = 21.Therefore, when g = 8, subtracting 55 from the sum of 9g and 4 results in 21.
My living room is 6m (to the nearest m) by 5m (to the nearest m). What is the maximum and minimum area of my living room? Write your answer as an error interval.
Whoever helps I'll give a brainliest x
Answer:
24.75m ≤ 30m < 35.75m
Step-by-step explanation:
Minimum area:
5.5 (lower bound of 6m) * 4.5 (lower bound of 5m) = 24.75m
Maximum area:
6.5 (upper bound of 6m) * 5.5 (upper bound of 5m) = 35.75m
Normal area:
6*5=30m
I hope that makes some sense or helps a little!
Easy question
Topic: Volume
Use the other attachment to help u what formula is it
Answer:
see below
Step-by-step explanation:
V = l*w*h for the rectangular tank
V = 70* 40*40
=112000 cm^3 = 1mL
The water is 84000
Make this a fraction
84000/112000 = 3/4
The water fills 3/4 of the tank
1-3/4 = 1/4
It is 1/4 from the top
Find the volume of the treasure chest
V = 12*10*8 =960
Tower
V = pi r^2
3.14 * 10^2 *10
=3140
Water + chest + tower
84000+960+3140 =88100
This is less than 112000 so the water will not overflow
Answer:
a) 10 cm
b) Will not overflow
Step-by-step explanation:
8400 = base area × height
84000 = 70 × 40 × h
h = 30
From the top: 40 - 30 = 10cm
b) Capacity of the tank:
70 × 40 × 40
112,000 cm³
Combined volume of the two vessels:
(12 × 10 × 8) + (3.14 × 10² × 10)
960 + 3140
4,100 cm³
4100 = 70 × 40 × rise
rise = 1.464285715 cm
Since 1.464285715 < 10
It will not overflow
What is the center of the data?
Answer:
The center of data is a single number that summarizes the entire data set.
Step-by-step explanation:
The 5th term in a geometric sequence is 160. The 7th term is 40. what are the possible values of the 6th term of the sequence?
A. +- 70
B. 70
C. +-80
D. 80
We have been given that the 5th term in a geometric sequence is 160. The 7th term is 40. We are asked to find the possible values of 6th term of the sequence.
We know that an geometric sequence is in form [tex]a_n=a\cdot r^{n-1}[/tex], where,
[tex]a_n[/tex] = nth term of sequence,
a = First term,
r = Common ratio,
n = Number of terms.
We will get two equations using our given information as:
[tex]160=a\cdot r ^{5-1}...(1)[/tex]
[tex]160=a\cdot r ^{4}...(1)[/tex]
[tex]40=a\cdot r ^{7-1}...(2)[/tex]
[tex]40=a\cdot r ^{6}...(2)[/tex]
Upon dividing equation (2) by equation (1), we will get:
[tex]\frac{40}{160}=\frac{a\cdot r^6}{a\cdot r^4}[/tex]
[tex]\frac{1}{4}=r^{6-4}[/tex]
[tex]\frac{1}{4}=r^{2}[/tex]
[tex]r^{2}=\frac{1}{4}[/tex]
[tex]\sqrt{r^{2}}=\pm\sqrt{\frac{1}{4}}[/tex]
[tex]r=\pm\frac{1}{2}[/tex]
Let us solve for a.
[tex]160=a\cdot (\frac{-1}{2})^{4}[/tex]
[tex]160=a\cdot \frac{1}{16}[/tex]
[tex]160\cdot 16=a\cdot \frac{1}{16}\cdot 16[/tex]
[tex]2560=a[/tex]
So our formula would be [tex]a_n=2560\cdot (\pm\frac{1}{2})^{n-1}[/tex].
We cannot determine whether the common ratio would be positive or negative, so we will take both values.
[tex]a_6=2560\cdot (\pm\frac{1}{2})^{6-1}[/tex]
[tex]a_6=2560\cdot (\pm \frac{1}{2})^{5}[/tex]
[tex]a_6=2560\cdot \pm \frac{1}{32}[/tex]
[tex]a_6=\pm 80[/tex]
Therefore, the 6th term of the sequence would be [tex]\pm 80[/tex] and option C is the correct choice.
Answer:
C.+- 80
Step-by-step explanation:
factor the common factor 4 - 2n
Answer:
2(2-n)
Step-by-step explanation:
4 - 2n
Factor out a 2
2*2 -2n
2(2-n)
Identify the conic that is formed by the intersection of the plane described and double-napped cone.
A plane is perpendicular to m and does not intersect the vertex.
What is the conic section formed?
A. circle
B. parabola
C. ellipse
Answer:
A. Circle
Step-by-step explanation:
Perpendicular to m is parallel to the base of the cones (circular).
Therefore the cross section would be a circle (except at the vertex)
Help me with this problem plzzzzzz
Answer:
B. Opposite angles add up to 180 degrees.
Step-by-step explanation:
Answer Choice B is incorrect because opposite angles are actually congruent. However, adjacent angles of a parallelogram do add up to 180 degrees.
Evaluate e – 2 when e=7.
Answer:
5
Step-by-step explanation:
If e = 7, you would replace e in the expression e - 2 with 7 so that the expression becomes 7 - 2 which results in 5.
Does that help?
3m + 9 - 9m = 2m + 25 whats m
Answer:
8
Step-by-step explanation:
3m + 9 -9m = 2m + 25
3m + 9 = 11m + 25
9 = 8m + 25
16/2 = 8m/2
M = 8
you decide to invest in a period annuity that offers 4.5% APR compounded monthly for 15 years how much money will you need to invest if your desired yearly income is $40,000?
A. $460,000.00
B.$321,631.08
c.$471,283.83
D$432,835.96
Answer:
The answer is $321,631.08
Step-by-step explanation:
I just did a test on it. Got it wrong, but it showed me the right answer.
Answer:
321,621,numbers
Step-by-step explanation:
−11x 5 (−9x 3 y 4 ) fully simplify
Answer:
5940 y
Step-by-step explanation:
Simplify the following:
-11 (-9)×5×3×4 y
-9×3 = -27:
-11×5×-27×4 y
-27×4 = -108:
-11×5×-108 y
-11×5 = -55:
-108-55 y
-55 (-108) = 5940:
Answer: 5940 y
Use the interactive graph to plot each set of points which set represents proportional relationships check all that apply
Answer:
the first and third
Step-by-step explanation:
Answer:
A and C
Step-by-step explanation: