The difference between the expansions of (A + B)^2 and (A - B)^2 is the sign of the middle term. In the second case it is negative, due to the negative sign on B.
Which is the difference between the two expressions?Here we have two perfect square trinomials, these are:
(A + B)^2
(A - B)^2
Notice that the only difference between these is the sign of the second element.
Now we can expand these two expressions as:
(A + B)^2 = (A + B)*(A + B) = A^2 + 2AB + B^2
The second expression gives:
(A - B)^2 = (A - B)*(A - B) = A^2 + 2*A*(-B) + (-B)^2
= A^2 - 2AB + B^2
There we can see that the only difference between these two expansions is the sign of the middle term. Where in the second case it is negative, due to the negative sign on B.
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50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
c = 52 yards
Step-by-step explanation:
You have to use the Pythagorean theorem to solve this question.
[tex]a^2+b^2=c^2[/tex]
The hypotenuse is longest side of a triangle.
Lets substitute in our values:
[tex]20^2+48^2=c^2[/tex]
Lets simplify this to:
[tex]400 + 2304 = 2704[/tex]
Now we need to find the square root of 2704:
[tex]\sqrt{2704}=52[/tex]
Therefore, the hypotenuse is 52 yards long.
Which of the following lines is perpendicular to the line passing through the points (-3, 4) and (-5, 6)?
The equation of the perpendicular line will be x + y - 5 = 0. Then the correct option is B.
What is the equation of a perpendicular line?Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation of the line passing through (-5, 6) and (-6, 5) will be given as,
(y - 6) = [(5 - 6) / (- 6 + 5)](x + 5)
y - 6 = (x + 5)
y = x + 1
The equation of the line that is perpendicular to the above line is given as,
y = - x + c
The equation of the line is passing through (3, 2)
3 = - 2 + c
c = 5
Then the equation of the perpendicular line will be given as,
y = -x + 5
x + y - 5 = 0
The equation of the perpendicular line will be x + y - 5 = 0. Then the correct option is B.
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The complete question is given below.
please explain step by step in full process
questions
Given L || M find the value of unknown angles in each of the following figures
Answer:
x = 120°
y = 60°
Step-by-step explanation:
✔️since, lines l and m, area parallel, therefore,
x = 120° (they are corresponding angles having matching corners. Thus, corresponding angles are congruent to each other)
✔️x + y = 180° (linear pair angles)
Plug in the value of x
120 + y = 180
Subtract 120 from each side of the equation
y = 180 - 120
y = 60°
Simplify: 9- 4x + 2x + 8x° +1+ 6x?
Answer:
10+12x
Step-by-step explanation:
9−4x+2x+8x+1+6x
(9+1)+(−4x+2x+8x+6x)
10+12x
Can someone please help asap
Answer:
the answer is 38
Step-by-step explanation:
because one of the angles is 90 and the other one is 45, so the other angle is 45 too
so.. this is an isosceles triangle
State the order and type of each transformation of the graph of the function
ƒ(x) = –(x + 1)3 + 1 as compared to the graph of the base function
Answer:
steps below (C)
Step-by-step explanation:
1. x³ -> (x+1)³ ... horizontal translation left 1 unit
2. (x+1)³ -> -(x+1)³ .... reflection over x axis
3. -(x+1)³ -> -(x+1)³ + 1 ... vertical translation up 1 unit
help me pls the question is in the picture
Answer:
M<C = 37 degrees
M<D = 86 degrees
M<DEC = 111 degrees
Step-by-step explanation:
The exterior angle theorem can be measured by the hypotenuse of a 90 degree angle. Since there is no hypotenuse in the matrix, you don't need to make it positive :)
Therefore, after using this theorem, I came to the conclusion that m/C would be 37 degrees, since I calculated the measure of the angle. I used the same tactic on m/D and m/DEC.
I hope this helps :)
Suppose you have fewer than 10 place value blocks. How many different ways could you show 1214? Explain.
There are 3,024 different ways 1,214 can be shown.
What is permutation?Basically A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.
Given 1,214
since there are 4 places in the digit,
so 4 values less than 10 can be solved by
9, 8, 7, and 6
so by permutation to find ⁹P₄ = 9!/(9 - 4)!
= (9 x 8 x 7 x 6 x5!)/5!
⁹P₄ = 3,024
Hence there are 3,024 different ways.
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A certain forest covers an area of 4000 km². Suppose that each year this area decreases by 4.25%. What will the area be after 15 years?
The area of the forest after 15 years will be 2189.4
What is an area?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
i = The initial area of the forest = 4200km
r = Per year decrease is = 4.25%
n = Number of years = 15
The required formula is
The area of forest will be
A = i (1-r)^n
A = 4200(1-0.425)^15
A= 2189.4
Hence, the area of the forest will be 2189.4
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The perimeter of a rectangle is 64 feet. The length is two more than double the
width. Find the dimensions of the rectangle.
(Remember Perimeter of rectangle = 2L+ 2w)
Answer:
To solve this problem, we can set up the following equation:
2L + 2W = 64
We are told that the length of the rectangle is two more than double the width, so we can write the following equation:
L = 2W + 2
Substituting this equation into the first equation, we get:
2(2W + 2) + 2W = 64
Simplifying this equation, we get:
6W + 4 = 64
Subtracting 4 from both sides, we get:
6W = 60
Dividing both sides by 6, we get:
W = 10
The width of the rectangle is 10 feet.
To find the length of the rectangle, we can substitute this value back into the equation L = 2W + 2 to get:
L = 2(10) + 2
= 20 + 2
= 22
The length of the rectangle is 22 feet.
Therefore, the dimensions of the rectangle are 10 feet by 22 feet.
Step-by-step explanation:
New repost of my question
Answer:
Step-by-step explanation:
???
72 ounces and 6 steaks = what rate and unit rate
A random sample of individuals at an airport were asked, "Is your flight on time or delayed?" Below are the results of the survey in a joint relative frequency table.
On time Delayed Total
Domestic 96 412
International 76
Total 147
Part A: Draw and complete the frequency table. (3 points)
Part B: What is the smallest joint frequency, and what does it represent in the context? (3 points)
Part C: Does the data show an association between the flight being on time and flying domestic? If so, is it positive or
negative? (4 points)
Answer:
A.
domestic: 316 / 96 / 412
international: 76 / 51 / 127
total: 392 / 147 / 539
B. 51 its the smallest number
C. I don't know what association means but 76.2% of domestic flights land on time and 63% of international flights land on time so id say its positive
For what value of x does 4^x =(1/8)^x+5
9514 1404 393
Answer:
(b) -3
Step-by-step explanation:
It can work well to rewrite the equation as powers of 2.
[tex]4^x=\left(\dfrac{1}{8}\right)^{x+5}\\\\(2^2)^x=(2^{-3})^{x+5}\qquad\text{as powers of 2}\\\\2x=-3(x+5)\qquad\text{equate exponents}\\\\5x=-15\qquad\text{add $3x$}\\\\\boxed{x=-3}\qquad\text{divide by 5}[/tex]
__
Check
4^-3 = (1/8)^(-3+5) ⇒ 1/64 = (1/8)^2 . . . . true
Work out the cost of 12kg of potatoes and 1 1/2kg of carrots
Answer:
The cost is #15.90
Step-by-step explanation:
See comment for complete question
Given
[tex]P \to Potato[/tex]
[tex]C \to Carrot[/tex]
[tex]3P + 2C = 5.08[/tex]
[tex]P = 1.24[/tex]
Required
[tex]12P + 1\frac{1}{2}C = ??[/tex]
First, we solve for C
Substitute [tex]P = 1.24[/tex] in [tex]3P + 2C = 5.08[/tex]
[tex]3 * 1.24 + 2C = 5.08[/tex]
[tex]3.72 + 2C = 5.08[/tex]
Collect like terms
[tex]2C = 5.08 - 3.72[/tex]
[tex]2C = 1.36[/tex]
Solve for C
[tex]C = \frac{1.36}{2}[/tex]
[tex]C = 0.68[/tex]
So, we have:
[tex]P = 1.24[/tex]
[tex]C = 0.68[/tex]
[tex]12P + 1\frac{1}{2}C = ??[/tex] becomes
[tex]12P + 1\frac{1}{2}C = 12*1.24 + 1\frac{1}{2}*0.68[/tex]
[tex]12P + 1\frac{1}{2}C = 14.88 + 1.02[/tex]
[tex]12P + 1\frac{1}{2}C = 15.90[/tex]
Pls help i only have 2 minuets left
Answer:
14, 3!
Step-by-step explanation:
It is very complicated to explain.
I need help right away!!
Answer:
i think its c though im not sure
Step-by-step explanation:
Tides The length of time between consecutive high tides is 12 hours and 25 minutes. According to the National Oceanic and Atmospheric Administration, on Saturday, April 26, 2014, in Charleston, South Carolina, high tide occurred at 6:30 am (6.5 hours) and low tide occurred at 12:24 pm (12.4 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 5.86 feet, and the height of the water at low tide was − 0.38 foot.
(a) Approximately when will the next high tide occur?
(b) Find a sinusoidal function of the form
y = A sin(ωx – ϕ) + B
that models the data.
(c) Use the function found in part (b) to predict the height of the water at 3 pm on April 26, 2014.
Answer:
(a) The next tide will occur at 6:55pm
(b) [tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]
(c) The height is: 2.904ft
Step-by-step explanation:
Given
[tex]T_1 = 12hr:25min[/tex] --- difference between high tides'
Solving (a): The next time a high tide will occur
From the question, we have that:
[tex]High =6:30am[/tex] --- The time a high tide occur
The next time it will occur is the sum of High and T1
i.e.
[tex]Next = High + T_1[/tex]
[tex]Next = 6:30am + 12hr : 25min[/tex]
Add the minutes
[tex]Next = 6:55am + 12hr[/tex]
Add the hours
[tex]Next = 6:55pm[/tex]
Solving (b): The sinusoidal function
Given
[tex]High\ Tide = 5.86[/tex]
[tex]Low\ Tide = -0.38[/tex]
[tex]T = 12hr:25min[/tex] -- difference between consecutive tides
[tex]Shift = 6.5hr[/tex]
The sinusoidal function is represented as:
[tex]y = A\cos(w(x - C)) + B[/tex]
Where
[tex]A = Amplitude[/tex]
[tex]A = \frac{1}{2}(High\ Tide - Low\ Tide)[/tex]
[tex]A = \frac{1}{2}(5.86 - -0.38)[/tex]
[tex]A = \frac{1}{2}(6.24)[/tex]
[tex]A = 3.12[/tex]
[tex]B = Mean[/tex]
[tex]B = \frac{1}{2}(High\ Tide + Low\ Tide)[/tex]
[tex]B = \frac{1}{2}(5.86 - 0.38)[/tex]
[tex]B = \frac{1}{2}(5.48)[/tex]
[tex]B = 2.74[/tex]
[tex]w = Period[/tex]
[tex]w = \frac{2\pi}{T}[/tex]
[tex]w = \frac{2\pi}{12:25}[/tex]
Convert to hours
[tex]w = \frac{2\pi}{12\frac{25}{60}}[/tex]
Simplify
[tex]w = \frac{2\pi}{12\frac{5}{12}}[/tex]
As improper fraction
[tex]w = \frac{2\pi}{\frac{149}{12}}[/tex]
Rewrite as:
[tex]w = \frac{2\pi*12}{149}[/tex]
[tex]w = \frac{24\pi}{149}[/tex]
[tex]C = shift[/tex]
[tex]C=6.5[/tex]
So, we have:
[tex]y = A\cos(w(x - C)) + B[/tex]
[tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]
Solving (c): The height at 3pm
At 3pm, the value of x is:
[tex]x=3:00pm - 6:30am[/tex]
[tex]x=9.5hrs[/tex]
So, we have:
[tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]
[tex]y = 3.12 \cos(\frac{24\pi}{149}(9.5 - 6.5)) + 2.74[/tex]
[tex]y = 3.12 \cos(\frac{24\pi}{149}(3)) + 2.74[/tex]
[tex]y = 3.12 \cos(\frac{72\pi}{149}) + 2.74[/tex]
[tex]y = 3.12 *0.0527 + 2.74[/tex]
[tex]y = 2.904ft[/tex]
what is the slope of the table below? 3/8 15/12 9/10 0/7
The slope of the table shown in the image attached below is equal to: D. 1/3.
How to calculate the slope of the given table?Mathematically, the slope of the given table can be calculated by using the following mathematical expression;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the table, we have the following data points:
Points on x-axis = (-2, 2).
Points on y-axis = (-4, -2).
Substituting the given points into the slope formula, we have;
Slope, m = (12 - 8)/(15 - 3)
Slope, m = 4/12
Slope, m = 1/3
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A motorboat travels 244 kilometers in 4 hours going upstream and 665
kilometers in 7 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Answer:
Rate of the current: 19 kilometers per hour
Rate of the boat in still water: 80 kilometers per hour
Using the following conversions between the metric and U.S. systems, convert the measurement.
Round your answer to 6 decimal places as needed.
1 meter= 3.28 feet
1 Liter= 0.26 gallons
1 kilogram = 2.20 pounds
26.794 yd = _________km.
By sing the following conversions between metric and US systems 26.794 yard = 0.024500 .
What is the value of 1meter in terms of centimeter ?
1 meter can be equal to 100 centimeters and suppose for x meters , then it could be around 100x centimeters .
Given,
1 meter= 3.28 feet
1 Liter= 0.26 gallons
1 kilogram = 2.20 pounds
we know that ,
1yard = 0.0009144 km
so ,
26.794 yard = 26.794*0.0009144 km
= 0.024500
Hence by sing the following conversions between metric and US systems 26.794 yard = 0.024500 .
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A line is parallel to y=2x-8 and intersects the point (-4,-1) what is the equation of this parallel line?
Answer:
y = 2x + 7
Step-by-step explanation:
y + 1 = 2 ( x + 4 )
y = 2x + 8 - 1
y = 2x + 7
A _____ is a flat surface that has no thickness.
Is it possible that
1952
is the remainder of 375139654 - 1953?
What is the surface area of the cylinder with height 8 mi and radius 6 mi? Round your answer to the nearest thousandth.
Answer:ANSWER would either be 120π or about 376.8
Step-by-step explanation:
A=2πrh+2πr2
A=2π*6*8+2π*6*2
A=96π+24π
A= 120π
or
A≈376.8
ANSWER would either be 120π or about 376.8
Answer: the real answer is 527.788 the top answer is wrong I did it and it said it was wrong
Step-by-step explanation:
The fourth term of an arithmetic sequence is 20. The common difference is -1/5 times the first term. Graph the sequence.
Answer:
To graph an arithmetic sequence, you can start by plotting the first few terms of the sequence on the coordinate plane. The x-axis represents the term number, and the y-axis represents the value of the term.
In this case, we are given that the fourth term is 20 and the common difference is -1/5 times the first term. Let's say the first term is x. Then, the second term is x - (1/5)x = 4/5x, the third term is 4/5x - (1/5)x = 3/5x, and the fourth term is 3/5x - (1/5)x = 2/5x.
Therefore, the first four terms of the sequence are x, 4/5x, 3/5x, and 2/5x. If we plot these terms on the coordinate plane, we get the following graph:
(0, x)
(1, 4/5x)
(2, 3/5x)
(3, 2/5x)
This graph represents the first four terms of the arithmetic sequence. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the term number.
For this sequence, the fifth term is x + (-1/5)x = 4/5x. To find the sixth term, we can use the same formula: a_6 = x + (-1/5)x = 3/5x.
By continuing this process, we can plot the rest of the terms of the arithmetic sequence on the coordinate plane.
Step-by-step explanation:
Can someone help me with 18 and 20 please
Answer:
both are b
Step-by-step explanation:
the point is equal to -2 because there is a point on -2 and with 20 it b because 2 time 10 is 20 +26 makes 46 which makes 43 less than 46
what line
no association
nonlinear association
positive linear association
negative linear association
I believe that is a negative linear association.
which fractions, when converted, result in a repeating decimal? select all that apply 1/8 1/6 3/12 8/9 2 and 4/5 4 and 3/11
Answer:
B. 1/6
D. 3/12
F. 4 3/11
PLEASE MARK BRAINLIEST
area of a parallelogram help wanted ty
The area of the parallelogram is 72 square units. Option B
How to determine the area of the parallelogramThe formula for calculating the area of a parallelogram is expressed as;
A = bh
Given that;
A is the area of the parallelogramb is the base of the parallelogramh is the height of the parallelogramFrom the information given, we have that;
The base of the parallelogram = x + yThe height of the parallelogram = hNow, substitute the values
x + y = 8 + 4
add the values
x + y = base = 12 units
h = 6 units
Now, substitute the values into the formula, we get;
Area, A = 12(6)
multiply the values
Area, A = 72 square units
Hence, the value is 72 square units
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