4(y-2)²-9=0 find the perfect square
Answer:
(2(y-2)+3) (2(y-2)-3)
Step-by-step explanation:
In mathematics, the difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2 = in elementary algebra.
Which expression shows how to use mental math to find
6
×
24
?
A.
(
6
×
20
)
+
(
6
×
4
)
B.
(
6
×
20
)
+
(
6
×
14
)
C.
(
6
×
20
)
×
(
6
×
4
)
D.
(
6
×
20
)
−
(
6
×
4
)
Answer:a
Step-by-step explanation:a is easy
given the set of numbers from 1 to n: { 1, 2, 3 .. n } we draw n numbers randomly (with uniform distribution) from this set (with replacement). what is the expected number of distinct values that we would draw?
The number of distinct values that we can draw(with replacement) is;
= [tex]\frac{ ((2n-1)!)}{ n!(n -1)! }[/tex]
Here,
The given set is = {1, 2, 3, ……, n}
n number of drawn from this set with replacement.
Then we have to find number of distinct values that we can draw.
What is combination?
The field of mathematics concerned with problems of selection, arrangement, and operation within a finite or discrete system.
Now,
The given set is = {1, 2, 3, ……, n}
n number of drawn from this set with replacement.
Since, we know we draw p things from q with replacement then
Number of ways = [tex]^{p+q-1} C_q[/tex]
Here number of element in the set = n
And number of element we have to draw with replacement = n
Therefore, number of distinct values that we can draw
= [tex]^{n+n-1} C_n[/tex]
= [tex]^{2n-1} C_n[/tex]
= [tex]\frac{(2n-1)!}{n!(2n -1 - n)!}[/tex]
= [tex]\frac{((2n-1)!)}{n!(n -1)!}[/tex]
Hence, The number of distinct values that we can draw(with replacement) is;
= [tex]\frac{ ((2n-1)!)}{ n!(n -1)! }[/tex]
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(d-6)(2e-3)+(d-6)(e+1) solution please?
The solution of the expression (d-6)(2e-3)+(d-6)(e+1) is 3de -18e -2d + 12 .
According to the given question.
We have an expression (d-6)(2e-3)+(d-6)(e+1).
Here, we have to find the solution of the given expression.
As we know that, an action or process of solving a problem.
Therefore, the solution of the expression (d-6)(2e-3)+(d-6)(e+1) is given by
(d-6)(2e-3)+(d-6)(e+1)
= 2de -12e -3d + 18 + de -6e + d - 6 (by distributive rule)
= 3de -18e -2d + 12
Hence, the solution of the expression (d-6)(2e-3)+(d-6)(e+1) is 3de -18e -2d + 12 .
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Tanner's parents give him x dollars per month for his allowance. however, since his birthday is in february, he gets an extra 20% bonus that month. pick all the expressions that represent how much tanner's allowance is in february. 120x x+0.2x x+1.2x 1.2x
it is given in question that Tanners parent give him x dollars per month plus 20% extra in February therefore the amount become 0.2x
What do you mean percentage?
percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
Tanner's parents give him x dollars per month for his allowance.
however, since his birthday is in february
he gets an extra 20% bonus that month.
pick all the expressions that represent how much tanner's allowance is in february month
20% = 20/100
= 2/10
=1/5
= 0.2
since it is given in question that Tanners parent give him x dollars per month plus 20% extra in February
therefore the amount become 0.2x
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solve the system y=x and 2x+3y=15
The value of x and y can be written as x=y=3. Therefore, the value of both x and y is equal to 3.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the two the system of equations as follows,
y = x
2x + 3y = 15
Now, if we substitute the value of y from the first equation in the second, then we can write,
2x + 3y = 15
2x + 3x = 15
5x = 15
x = 15/5
x = 3
Therefore, the value of x and y can be written as x=y=3.
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Find the equation of the line passing
through the points (4, 2) and (6, 10).
y=[?]x+[ ]
Answer:
y=4x+-14
Step-by-step explanation:
i hope this helps
Help-Khan academy geometry-mapping shapes
The sequence of transformations that maps triangle DEF into triangle ABC is:
A 90º rotation about point F, then a translation along the directed line segment FC.
What are transformations on the graph of a function?Transformations in the graph of a function are classified as follows:
Translation: Translation left/right or down/up, changing just the position.Reflections: Over one of the axes or over a line, changing just the orientation.Rotations: Over a degree measure, changing the orientation or the inclination.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor, changing the side lengths of the figure.For this problem, we have that:
The orientation was changed, hence first it underwent a rotation.Then the position changed, hence after the rotation it underwent a translation.Thus the correct sequence is given by Sequence B.
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The length of an alligator in a zoo is 1456feet. The Everglades National Park lists the longest alligator ever recorded in Florida at 17512feet. Which is the difference in their lengths?
The difference in their length is 16056
As per the question the length of alligators=1456 feet
At the same time the length of longest elegator is=17512 feet
We have to find out the difference
For difference we have to take
1756 min and 1456
As we know the formula of find the difference is by substituting so-
17512-1456
=16056
The difference= 16056 units feet
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maritza is playing a computer game to help her learn about science. her scores for the first six games were 11, 12, 10, 8, 14, and 15. how many points does she need to earn on the next game so that her average score for all games is 12 points? 14
For Maritza to keep her average of 12 points, she needs 14 points in her subsequent game.
What is mean?An individual data set's mean is its average. The concept of mean informs us of the quantity of data in its entirety.
In other words, this same deviation of data from across all data sets is built on the mean.
Mean = sum of data / Number of data
According to the given information:points given for the 6 games:
11,12,10,8,14 and 15
Let's say this same point in the seventh game is x, keeping the average at 12.
The average for the 7th game is.
(11 + 12 + 10 + 8 + 14 + 15 + x )/7 = 12
(70 + x )/7 = 12
70 + x = 84
x = 24
For Maritza to keep her average of 12 points, she needs 14 points in her subsequent game.
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a number is 10 more than another number. twice the sum of the two numbers is 44 . find the two numbers.
Answer:
The two numbers are 8 and -2
Step-by-step explanation:
a=b+10
2(a+b)=12
you then substitute the first equation's value for a into the second equation.
2(b+10+b)=12
2(2b+10)=12
4b+20=12
b+5=3
b=-2
Then you substitute this value for b back into the first equation.
a=b+10
a=-2+10
a=8
Sep 15, 10:38:09 AM
Watch help video
Use point-slope form to write the equation of a line that passes through the
point (1, 17) with slope 2.
Answer:
Submit Answer
attempt 1 out of 3
The equation of the line is y=2x+15.
Given point (1,17) and the slope m=2
The universal equation for any straight line is y=mx+c. m is the line's slope, and c is the y-intercept.
To find the equation of the line formulae is [tex](y-y_{1})=m(x-x_{1})\\[/tex]
Here, m=2 , [tex]x_{1}=1 \\[/tex] and [tex]y_{1}=17[/tex]
substituting the values we get
y-17=2(x-1)
y-17=2x-2
y=2x+15
Therefore, The equation of the line is y=2x+15.
The equation of line is an algebraic representation of a set of points in a coordinate system that form a line. The several points in the coordinate axis that form a line are represented as a set of variables x, y to build an algebraic equation known as an equation of a line. We can use the equation of any line to determine if a given point is on the line or not.
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What is 59265 divided by the 8th power x 596 x 427 please help
59265 の 8 乗 x 596 x 427?
Answer: sus
Step-by-step explanation:
a garden is in the shape of a square with a perimeter of 60 feet. the garden is surrounded by two fences. one fence is around the perimeter of the garden, whereas the second fence is 3 feet from the first fence on the outside. if the material used to build the two fences is $ 1.15 per foot, what was the total cost of the fences?
Answer: The total cost of the fences=$165.6
Step-by-step explanation:
Let a = the length of the side if the square.
The perimeter of the square is 60 ft
4a = 60ft
divide both sides by
4a = 60/4
a = 15 ft
The garden is surrounded by two fences, one fence is around the perimeter of the garden, whereas the second fence is 3 feet from the first fence on the outside
Expand to get:
4*a + 4(a + 2*3)
Replace a with 15 to get:
= 4*15 + 4(15 + 6) 60 + 4(21) 60+84
= 144ft
The cost of the fence is $1.15 per foot
The cost of 144 ft fence will be:
= 144*1.15
= $165.6
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what are quadrilateral and diagonal lines that have equal length,the point of intersection divides both diagonals equally and perpendicular
Answer: A parallelogram with one right angle is a rectangle. A quadrilateral whose diagonals are equal and bisect each other is a rectangle.
An arithmetic sequence has this recursive formula:
| a₁ = 4
| an = an-1 - 7
What is the explicit formula for this sequence?
[tex]a_n = 4+ (n-1)(-7)[/tex] is the explicit formula for the sequence | a₁ = 4
| an = an-1 - 7
We have given [tex]a_1 = 4[/tex]
If [tex]a_n = a_{n-1} - 7[/tex]
Then, [tex]a_2 = a_{(2-1)} - 7[/tex]
⇒ [tex]a_2 = a_1 - 7[/tex]
⇒ [tex]a_2 = 4 - 7[/tex]
⇒ [tex]a_2 = -3[/tex]
Now, common difference (d) = [tex]a_2 - a_1[/tex] = -3 - 4 = -7
The explicit formula for arithmetic sequence is expressed as
[tex]a_n = a+ (n-1)d[/tex] Where a is the 1st term, [tex]a_n[/tex] is the nth term and d is the common difference.
With given information explicit formula:
[tex]a_n = 4+ (n-1)(-7)[/tex]
What is an explicit formula?Without expressing the other terms of the sequence, explicit formulas are always utilized to represent any term of the sequence. The word "explicit" means something that may be found directly without having to know the other phrases in the sequence.
A single formula, known as the explicit formula, can be used to describe each term in a series in an individual way. Without knowing the prior term in the series, the explicit formula makes it simple to locate any term. The explicit formulas for various sequences are provided here:
An = a + (n - 1) d, where a is the first term and d is the common difference, an is the arithmetic sequence.
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20 pts
A company sells designer purses for $400 per purse. Usually, they sell 3000 purses per month. According to market research, they will sell 500 more purses for every $20 reduction in price. Write a function R(x) that models the company's revenue, where x is the number of price reductions. Find the price that will generate the maximum revenue. Find the maximum revenue.
The price that would yield maximum revenue is $260 and maximum revenue is $1,690,000
What is the revenue function?
The fact that total revenue of the company is the price per purse multiplied by the number of purses sold, means that the revenue modelled function is simply price multiplied by the quantity sold as shown below:
R(x)=P*x
R(x)=Px
R(3000)=$400*3,000
R(3000)=$1200,000
Note for every 500 more purses, the price reduces by $20
R(3500)=$380*3,500
R(3500)=$1,330,000
R(4000)=$360*4000
R(4000)=$1,440,000
R(4500)=$340*4500
R(4500)=$1,530,000
R(5000)=$320*5000
R(5000)=$1,600,000
R(5500)=$300*5500
R(5500)=$1,650,000
R(6000)=$280*6000
R(6000)=$1680,000
R(6500)=$260*6500
R(6500)=$1,690,000
R(7000)=$240*7000
R(7000)=$1,680,000
The total revenue fell at 7,000 purses, which means that the maximum revenue is $1,690,000 at 6500 purses
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need help please
The following transformations are rigid and isometric: (choose all that apply)
dilation
reflection
rotation
translation
HELP NEEDED ASAP/NOW......NO LINKS AND NO JOKING PLS
AUBSERD ANSWERS WILL BE REPORTED<<
Scott bought a large bag of cookies at the bakery. He ate 1/5 of a bag and his sister ate
2/7 of a bag.
What fraction of the bag did they eat?
What fraction of the bag remains?
Answer:
17/35, 18/35
Step-by-step explanation:
Find the common denominator to add those fractions together.
5 x 7 = 35 so the common denominator is 35. 1 x 7 is 7 so 1/5 is 7/35. 2 x 5 is 10 so 2/7 is 10/35.
10/35 + 7/35 = 17/35
They ate 17/35.
35/35 - 17/35 = 18/35
18/35 remains.
To solve this problem, simply add the fractions!
To add fractions, you must follow a rule called the Common Denominator Rule. Unlike multiplication and division of fractions, wehre the denominator can be a different number, you must convert your denominators to the same number in order to subtract or add fractions.
A common factor of [tex]\frac{1}{5}[/tex] and [tex]\frac{2}{7}[/tex] is 35 as 5 ×7 = 35
Multiply the numerator and denominator of 1/5 by 7: [tex]\frac{(1)(7)}{(5)(7)}= \frac{7}{35}[/tex]
Multiply the numerator and denominator of 2/7 by 5: [tex]\frac{(2)(5)}{(7)(5)} =\frac{10}{35}[/tex]
Now add [tex]\frac{7}{35} + \frac{10}{35}[/tex] = [tex]\frac{17}{35}[/tex] : They ate [tex]\frac{17}{35}[/tex] of the bag
To find what fraction of the bag remains, subtract what they ate from 1.
*1 can also be written as [tex]\frac{35}{35}[/tex]*
[tex]\frac{35}{35} -\frac{17}{35} = \frac{18}{35}[/tex]
18/35 of the bag remains
what is 42% as a decimal?
If a bag of chips is within 0.4 oz of 6 oz then it is allowed to go on the market. Write an absolute value inequality that models this situation. Solve the inequality.
The solution to the absolute value inequality is 5.6 ≤ x ≤ 6.4.
How to solve the inequalityLet's represent the weight of the bag of chips as "x" (in ounces). The bag is allowed to go on the market if its weight is within 0.4 oz of 6 oz.
An absolute value inequality that models this situation is:
| x - 6 | ≤ 0.4
Now, let's solve the inequality:
1. x - 6 ≤ 0.4
Add 6 to both sides:
x ≤ 6.4
2. x - 6 ≥ -0.4
Add 6 to both sides:
x ≥ 5.6
The solution to the absolute value inequality is 5.6 ≤ x ≤ 6.4. This means the weight of the bag of chips must be between 5.6 ounces and 6.4 ounces (inclusive) to be allowed on the market.
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I need this answered thanks
Answer:The answer would be the third one $0.07 per minute
DLD I need to get this done ASAP
Answer: d
Step-by-step explanation:
Find the equation of the line that passes through (4,13) and (8,1)
The equation of the line that passes through (4,13) and (8,1) is y = 0.6x + 10.6
How to find the equation of the line?given the points (4,13) and (8,1)
(x1,y1) = (4,13)
(X2, y2) = (8,1)
now we have to find slope of the line passing through these points.
[tex]slope = \frac{(y2 - y1)}{(x2 - y1)} \\ slope = \frac{1 - 4}{8 - 13}[/tex]
[tex]slope = \frac{ - 3}{ - 5} [/tex]
slope = 0.6
Hence, the slope of the line is 0.6
we know the standard form of equation of the line.
y = mx + b
let us put the x = 4 and y = 13
y = mx + b
13 = 0.6(4) +b
13 = 2.4 + b
13 - 2.4 = b
10.6 = b
now put the m and b value into standard form of equation of the line to get the equation of the line.
y = 0.6m + 10.6
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9+(-4)+(-9)+4+8 with additive inverse
The additive inverse of the expression given as 9 + (-4) + (-9) + 4 + 8 is (-9) + 4 + 9 + (-4) -8
How to determine the additive inverse of the expression?The expression is given as
9 + (-4) + (-9) + 4 + 8
As a general rule, the additive inverse of an expression represented by x is
Additive inverse = -x
This means that
Expression = x
Additive inverse = -x
The above implies that we negate the expression to get the Additive inverse
So, we have
Expression = 9 + (-4) + (-9) + 4 + 8
This means that
Additive inverse = -[9 + (-4) + (-9) + 4 + 8]
Open the brackets
So, we have
Additive inverse = (-9) + 4 + 9 + (-4) -8
Hence, the additive inverse of the expression given as 9 + (-4) + (-9) + 4 + 8 is (-9) + 4 + 9 + (-4) -8
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In an arithmetic sequence, the 10th term (a10) is 30 and the common difference is 2
. What is the 1st term (a₁)?
Based on the calculations on this arithmetic sequence, the value of the first term is equal to -8.
What is an arithmetic sequence?An arithmetic sequence can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Given the following data:
Tenth term (a₁₀) = 30.
Common difference = 2.
Substituting the given parameters into the formula, we have;
10 = a₁ + (10 - 1)2
10 = a₁ + (9)2
10 = a₁ + 18
a₁ = 10 - 18
First term, a₁ = -8.
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the lowest common denominator for the fraction 8/64 and 8/32 is
Answer:
Lowest common denominator is 8.Step-by-step explanation:
8? Why that low?Here's why:
64 and 32 are both divisible by 8. 64 / 8 = 8 and 32 / 8 is 4.
So then, we make the denominator 8 and numerator 1.
Lowest common denominator is 8.15lb.12oz.+8lb.13oz.+7lb.9oz.
Answer: 32lb 2 oz
Step-by-step explanation:
15lb.12oz.+8lb.13oz.+7lb.9oz.=
(15+8+7)lb + (12+13+9)oz=
30lb+34oz=
30lb+32oz+2oz=32lb 2 oz
Answer:
32lb. 2oz.
Step-by-step explanation:
For ounces: 12+13+9=34
34/16= 2lb and 2oz
For pounds
15+8+7=30
For all: 30+2= 32lb
ANSWER: 32lb. 2oz.
the width is to be 16 feet less than 3 times the height. find the width and the height if the carpenter expects to use 34 feet of lumber to make it.
The computation is that the width is 21.5 feet and the height is 12.5.
How to compute the value?Let the height = h
Let the width = (3 × h) - 16 = 3h - 16
Therefore, the dimensions will be:
h + 3h - 16 = 34
4h = 34 + 16
4h = 50
Divide
h = 50/4
h = 12.5
Therefore width = 3h - 16 = 3(12.5) - 16
= 37.5 - 16
= 21.5
The width is 21.5 feet and the height is 12.5.
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Suppose an online electronics retailer is running two different specials. One deal will
get you 10% off your total purchase, and the other deal is worth $20 off a purchase
of $100 or more. Assuming you spend at least $100, if you are allowed to use both
deals, in which order do you want to apply them? Try the calculation both ways with
a few different prices, or write a formula to represent each option.
We get more money off when we follow order 1, that is, second deal follows first deal.
Given,
There are two deals in an online electronics retailer.
First deal: 10% off on your total purchase = x × (90/100)
Second deal: $20 off on a purchase of minimum $100 = x - 20
x be the money we spend.
We have to spend a minimum of $100.
They allowed us to use both deals.
We have to find the order of deals.
Lets check:
Order 1:
First deal, then Second deal.
First deal, x = 100
ie, x × (90/100) = 100 × (90/100) = 90
Second deal, x = 90
ie, x - 20 = 90 - 20 = 70
100 - 70 = 30
ie, $30 will get off when we apply this order.
Order 2:
Second deal, then first deal.
Second deal, x = 100
x - 20 = 100 - 20 = 80
First deal, x = 80
ie, x × (90/100) = 80 × (90/100) = 72
100 -72 = 28
ie, $28 will get off when we apply this order.
So, we can go for order 1.
Now lets check the same with x = 150 and x = 500
x = 150
Order 1:
First deal, then Second deal.
First deal: x = 150
ie, x × (90/100) = 150 × (90/100) = 135
Second deal, x = 135
ie, x - 20 = 135 - 20 = 115
150 - 115 = 35
ie, $35 will get off when we apply this order.
Order 2:
Second deal, then first deal.
Second deal, x = 150
x - 20 = 150 - 20 = 130
First deal, x = 130
ie, x × (90/100) = 130 × (90/100) = 117
150 - 117 = 33
ie, $33 will get off when we apply this order.
So, we can go for order 1.
x = 500
Order 1:
First deal, then Second deal.
First deal: x = 500
ie, x × (90/100) = 500 × (90/100) = 450
Second deal, x = 450
ie, x - 20 = 450 - 20 = 430
500 - 430 = 70
ie, $70 will get off when we apply this order.
Order 2:
Second deal, then first deal.
Second deal, x = 500
x - 20 = 500 - 20 = 480
First deal, x = 480
ie, x × (90/100) = 480 × (90/100) = 432
500 - 432 = 68
ie, $68 will get off when we apply this order.
So, we can go for order 1.
Lets conclude that,
We get more money off when we follow order 1, that is, second deal follows first deal.
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