a perfect square trinomial, namely [tex]\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2[/tex]
where the middle-term is just a product of "2 times the square root of the terms on both sides".
so let's start by grouping the terms with a variable, and then adding the last term for the trinomial, keeping in mind the middle-term is just that product.
[tex]x^2+6x+5\implies (x^2+6x) ~~ +5\implies (x^2+6x+\square^2) ~~ +5 \\\\\\ \stackrel{middle-term}{6x}=2(\sqrt{x^2})(\sqrt{\square^2})\implies 6x=2x\square\implies \cfrac{6x}{2x}=\square\implies 3=\square[/tex]
ahhhaaa!!! so our missing term from our group is 3, meaning we need to use 3², however, let's remember, all we're doing is borrowing from our very good friend Mr Zero, 0, so if we add 3², we also have to also subtract 3²
[tex](x^2+6x+3^2-3^2) ~~ +5\implies (x^2+6x+3^2)-3^2 +5\implies {\Large \begin{array}{llll} (x+3)^2-4 \end{array}}[/tex]
Paul and sandy Moede signed at 8,000 note at Citizen's bank. Citizen's charge a 61/2% discount rate. If the loan is for 300 days, find (a) the proceeds and (b) the effective rate charged by the bank to the nearest
The proceeds is $7,566.67 and the effective rate charged by the bank to the nearest is 6.87%.
How to find the effective interest rate?Given data:
Principal = $8,000
Rate =6 1/2% or 6.5%
Term= 300 Days
a. Proceeds
Interest = Principal x Rate x Time
Interest = $8,000 x 6.50% x 300/360
Interest = $8,000 x 0.065 x 0.8333
Interest = $433.33
Now let find the Proceeds:
Proceeds = $8,000 - 433.33
Proceeds = $7,566.67
b. Effective Interest Rate:
Effective Interest Rate = 433.33 / 7566.67 x 300/360
Effective Interest Rate = 433.33 / 6305.56
Effective Interest Rate = 0.0687 × 100
Effective Interest Rate = 6.87%
Therefore $7,566.67 is the proceeds and 6.87% is the interest rate.
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-4(6x + 7) = -316 What is the answer?
Answer:
[tex]x=-\frac{43}{3}[/tex]
Step-by-step explanation:
[tex]-4(6x+7)=-316 \\ \\ 6x+7=-79 \\ \\ 6x=-86 \\ \\ x=-\frac{43}{3}[/tex]
Answer:
x=12
Step-by-step explanation:
hope this helps! -4(6x + 7) = -316=x=12
Jayda provided the following work when asked to
convert 0.65 to its simplest fraction form.
Jayda's Work:
0.65=
65
13
1000 200
=
Review Jayda's work. Then, answer the following
questions.
1. Why did Jayda get the problem wrong?
2. Provide the work for properly writing the decimal in its
simplest fraction form.
0
?
by converting the decimal number 0.65 to the simples fraction, the result will be 13 / 20
The given decimal number = 0.65
The decimal number consist of a whole number part and fractional part. The whole number and the fractional part are separated by a decimal point.
Multiply the given decimal number by 100/100
Then the result will be
0.65 × (100/100) = (0.65×100) / 100
Multiply the numerator terms
(0.65×100) / 100 = 65 / 100
Divide both numerator and denominator by 5
Then the expression will be
(65/5) / (100/5) = 13 / 20
Hence, by converting the decimal number 0.65 to the simples fraction, the result will be 13 / 20
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Let sample space be S={1,2,3,4,5,6,7,8,9,10} suppose the outcomes are equally likely. Compute the probably of the event E=“ an odd number less than 9”
The probability of the event E i.e an odd number less than 9 is 0.4.
The probability of an event is a ratio of number of favorable outcomes to total number of outcomes. The sum of all probabilities of events must be equal to one. The probability of an event must not be greater than 1.
In event E i.e an odd number less than 9, the number of favorable outcome is 4 i.e. {1,3,5,7}.
The total number of outcomes is whole set S i.e. 10.
So, the probability of event E will be,
P(E) [tex]=\frac{4}{10}[/tex]
=0.4
Therefore, the probability of the event E i.e an odd number less than 9 is 0.4.
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Consider the geometric sequence Po= 100, P₁ =30, P₂ =9,..
(a) Find the common ratio R
(b) Use the geometric sum formula to find the sum Po+P₁+…+ Pg.
(a) The common ratio R is 3/10.
What do you mean by Geometric progression?
Every following word in a sequence known as a geometric progression (GP) is created by multiplying every previous term by a constant amount, or "common ratio." Another name for this progression is a pattern-following geometric sequence of numbers.
To find out the common ratio we have to divide the second term by the first term,
in the given example to find out the common ratio we have to divide [tex]P_{2[/tex] by [tex]P_{1}[/tex],
so, we are getting, common ratio(R)= 9/30
= 3/10
Hence,The common ratio(R) is 3/10.
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Find the derivative
The derivative of the given function is 4x³ / (x²+1) ²
What is derivative mean?
The rate at which a function changes in relation to a variable Calculus and differential equations issues must be solved using derivatives.In order to determine the rate of change of an interest variable, scientists typically observe changing systems (dynamical systems).They then incorporate this information into a differential equation and use integration techniques to produce a function that can be used to predict how the original system will behave under various conditions.Geometrically, the slope of a function's graph or, more accurately, the slope of the tangent line at a point can be used to understand the derivative of a function.d(u/v) = [ u(dv/dx) + v(du/dx) ] / v²
Given:
f(x) = x²/x²+1
Applying the formulae:
= x²[ d(x²+1)/dx] + (x²+1) [ d(x²)/dx ] / (x²+1) ²
= x²(2x+0) + (x²+1)2x / (x²+1) ²
= 2x³ + 2x³ / (x²+1) ²
= 4x³ / (x²+1)²
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An arborist is preparing the fuel mix for her chainsaw before climbing a tree to remove a dead limb. The two-stroke chainsaw requires a 4% mix of engine oil to gas—that is, the amount of oil should be 4% of the amount of gas. How much engine oil should be added to a jerry can that contains 4.3 gallons of gas?
The amount engine oil which should be added to a jerry can that contains 4.3 gallons of gas is 0.172 gallons.
Given that arborist is preparing the fuel mix for her chainsaw before climbing a tree to remove a dead limb when two-stroke chainsaw requires a 4% mix of engine oil to gas and the amount of oil should be 4% of the amount of gas.
We want to find the amount of engine oil which should be added to a jerry can that contains 4.3 gallons of gas.
To find the amount of engine oil convert the mixture of engine oil to gas into decimal.
4%=4/100
4%=0.04
Now, we will multiply the above mixture with 4.3 gallons of gas is
4.3×0.04=0.172 gallons
Hence, the amount of engine oil which should be added to a jerry can that contains 4.3 gallons of gas when two-stroke chainsaw requires a 4% mix of engine oil to gas is 0.172 gallons.
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Orlandria’s marble collection contains 10 blue marbles,5 green marbles,6 red marbles and 7 yellow marbles what is the ratio of yellow marbles to the total number of marbles in orlandria’s marble collection
Answer: The ratio of the total number of marbles in Orlandria’s marble collection is 7:28, where 7 is the yellow marbles and 28 is the total number of marbles Orlandria has.
Amira's cab company charges a one-time pickup fee of $3.50 for every ride, as well as
a $1.50 charge for each mile traveled. Find the rate of change.
The rate change is $1.50 per miles
The one time pickup fee of every ride = $3.50
The rate charges for every miles traveled = $1.50
Consider the number of miles traveled = x
Then the equation will be
y = 1.50x + 3.50
Where y is the total cost
x is the number of miles traveled
The slope intercept from is
y = mx + b
Where m is the slope of the line
b is the y intercept
Comparing the slope intercept form the given equation
y intercept of the line b = $3.50
Slope of the line m = $1.50 per mile
Hence, the rate change is $1.50 per miles
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The length of a rectangle is 10 inches more than 3 times the width and the area is 217 square inches, find the length and width
The length and width of the rectangle is 31 inches and 7 inches.
Given:
The length of a rectangle is 10 inches more than 3 times the width and the area is 217 square inches.
Let l and w be the length and breadth.
l = 10 + 3w
lw = 217
w = 217/l
l = 10 + 3(217/l)
l = 10 l + 651 / l
[tex]l^{2} -10l -651=0[/tex]
on solving
l = 31 inches
lw = 217
w = 217/31
w = 7 inches.
Therefore the length and width of the rectangle is 31 inches and 7 inches.
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Write the expression as a number in scientific notation.
(5 x 10^2)(4.2 x 10^4)/6 x 10^3
62.79 divided by 23 long division
Step-by-step explanation:
this is a college question ????
and you don't know how to do it ? what happened to you in elementary school ?
there are many different techniques. everybody thinks theirs is the fastest or easiest to understand.
after all, this is just "playing" with numbers, the factors embedded within the dividend.
this is mine. when I was in elementary school, we called this the "long division" :
62.79 ÷ 23 =
we pick the first few positions from the left of the dividend, where we are sure, the divisor fits at least once.
in our case here : 62.
we do an integer divide of 62/23 = 2 (for 3 the dividend would have to be at least 69). this 2 is our first digit of the quotient.
62.79 ÷ 23 = 2
now we multiply the divisor by that digit and subtract the result from the dividend. this gives us a remainder of 16, and we pull down the next position (7) :
62.79 ÷ 23 = 2
- 46
---------
167
now, we pulled the first digit after the decimal point, and we need to set the decimal point there in our quotient :
62.79 ÷ 23 = 2.
- 46
---------
167
now, we repeat the process by integer dividing this new dividend (167) by the divisor (23)
167/23 = 7
this 7 becomes the next digit in our quotient. and we repeat the process of multiplying this by the divisor and subtracting the result from the dividend. this gives us a remainder (6), and we pull down the next digit (9).
62.79 ÷ 23 = 2.7
- 46
---------
167
- 161
----------
69
and again, we repeat by integer dividing the new dividend (69) by the divisor (23)
69/23 = 3
this 3 is the next digit in our quotient.
we multiply it with the divisor and subtract the result from the dividend.
if the remainder is still not 0, we need to repeat the process by pulling the next digit, which would be an invisible 0. and continue.
but luckily, after this the remainder is 0, and we are finished.
62.79 ÷ 23 = 2.73
- 46
---------
167
- 161
----------
69
- 69
--------------
0
so, 62.79 ÷ 23 = 2.73 and 0 remainder.
A country's population in 1994 was 182 million. In 2002 it was 186 million. Estimate growth formula. Round your answer to the
the population in 2004 using the exponential
nearest million.
The growth formula for the given population is P = 182eⁿˣ and the population in 2004 is 186.98 million
Growth function:
Basically, the growth function means the pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
Given,
A country's population in 1994 was 182 million. In 2002 it was 186 million.
Here we need to find the growth formula and the population in 2004.
According to the given problem, let us consider that the
final population P,
the starting population A, and
the time passed t.
Here we need to determine the value of the growth factor k.
And it can be calculated using the information for the years 1994 and 2002.
Here we know that, A will be 182 million (the population in 1994), P will be 186 million (the population in 2002), and t will be 8 years (the number of years between 1994 and 2002):
⇒186 = 182eⁿˣ⁸
⇒186/182 = e⁸ⁿ
Now, by applying ln to both sides of the equation:
⇒ln(186/182) = ln(e⁸ⁿ)
Using the laws of logarithms:
=> 8n = ln(186) - ln(182)
=> n = [ln(186) - ln(182)] / 8
=> n = 0.0027
Now, let's use this information to determine P in 2004.
Here the value of A will still be 182 million, but t will be 10 years.
Now, we have to apply these values then we get,
=> P = 182e⁰°⁰⁰²⁷ˣ¹⁰
=> P = 182e⁰°⁰²⁷
=> P = 182 x 1.0273
=> P = 186.98
Therefore, there are 186.98 million in 2004.
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Find f (2) and f (3) if f (n) is defined recursively by f (n +1) = (n) ⁄ (n − 1) , f (0) = f (1) = 1 and for n = 1, 2, 3, …
The values of f(2) = 0 & f(3) = 2.
Here given that,
f(0) = f(1) = 1
f(n+1) = (n)/(n-1)
We have to solve the equation if n = 1:
putting the value of n = 1 in the given equation f(n+1) = (n)/(n-1)
= f(1+1) = 1/(1-1)
= f(2) = 0
In the same way we have to solve the equation if n = 2:
putting the value of n = 2 in the given equation f(n+1) = (n)/(n-1)
= f(2+1) = 2/(2-1)
= f(3) = 2/1
= f(3) = 2
Hence the answer is the values of f(2) = 0 & f(3) = 2.
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−4x−y=−4
slope: 25, ordered pair: (−5,−1) find the equation in slope intercept form
The equation of a line in slope intercept form is expressed as y = 25x +124
Equation of a line in slope intercept formA line is defined as the shortest distance between two points. The equation of a line in point slope form is expressed as:
y - y₁ = m(x - x₁)
where;
m is the slope
(x₁, y₁) is any point on the line
Given the following parameters
m = 25
point = (-5, -1)
Substitute into the equation above to have:
y - (-1) = 25(x - (-5))
y+1 = 25(x+5)
Write in slope intercept form
y+1 = 25(x+5)
y+1 = 25x + 125
y = 25x +124
This gives the equation of the line in slope-intercept form.
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The assets and liabilities of a credit union banker are listed below.
Car Value $29,850
Car Loan $10,560
Savings Account Balance $12,409
Treasury Bonds $10,000
Student Loans $13,824
Credit Card Balance $8,051
Checking Account Balance $19,419
Home Value $194,450
What is the total net worth if the banker pays off the student loans?
Answer:
$247,517
Step-by-step explanation:
Hello,
Assets
(Car Value) $29,850
(Savings Account Balance) $12,409
(Treasury Bonds) $10,000
(Checking Account Balance) $19,419
(Home Value) $194,450
29850+12409+10000+19419+194450 = 266128
Liabilities
(Car Loan) $10,560
(Student Loans) $13,824 since the students loans are payed of we don't include it into the final net worth.
(Credit Card Balance) $8,051
10560+8051=18611
assets - liabilities = net worth
266128 - 18611 = 247517
So, if the banker pays off the students loans of a credit union banker their net worth will be $247,517.
PLEASE ILL GIVE LOTS OF POINTS!!!!!!! PLEASEEEEEE
Answer:
3) m= 3/310
4) x > -1
6) 1:a)-4
2:b)-2
3:c)2
4:d)4
7) f(-4.2)=46.06
Step-by-step explanation:
hope this helps
Please help me solve this. 30 points, and ill try to figure out how to give brainliest.
Answer:2nd down on the first one and 3rd one down on the second question
HELP ME PLEASE, WILL MARK BRAINLIEST
Using slope-intercept, standard form, or point slope -
An arrow released from a bow, traveling towards a target 200 yards away,
reaches a max height of 42.6 ft in only 1.5 seconds. What is the height of the
arrow at 2.5 seconds?
Thank you so much!
The height of the arrow at 2.5 seconds is 71 feet.
Given:
An arrow released from a bow, traveling towards a target 200 yards away,reaches a max height of 42.6 ft in only 1.5 seconds.
1.5 seconds = 42.6 feet
divide by 1.5 on both sides.
1 sec = 28.4 feet
0.5 sec = 28.4/2
0.5 sec = 14.2 feet
2.5 sec = 1.5 sec + 1 sec
= 42.6 + 28.4
= 71 feet
Therefore The height of the arrow at 2.5 seconds is 71 feet.
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What did you get for GH?
0.14
3.5
On EDPUZZLE
Answer:
if you mean 0.14 + 3.5 the answer is 3.64
Step-by-step explanation:
Line the numbers and decimal point when adding
Which statements describe the graph of y = Negative RootIndex 3 StartRoot x minus 1 EndRoot + 2? Select three options.
The graph has a domain of all real numbers.
The graph has a range of y greater-than-or-equal-to 1.
As x is increasing, y is decreasing.
The graph has a y-intercept at (0, 1).
The graph has an x-intercept at (–7, 0).
Answer:
(a) The graph has a domain of all real numbers.
(d) The graph has a y-intercept of (0, 1).
(e) The graph has an x-intercept of (-7, 0).
Step-by-step explanation:
You want to know the correct descriptors of the domain, range, slope, and intercepts of the graph of y = ∛(x-1) +2.
DomainThe domain of the cube root function is all real numbers. Hence the graph has a domain of all real numbers.
RangeThe range of the cube root function is all real numbers. Hence the graph is not restricted to a range of y ≥ 1.
SlopeThe slope of the cube root function is positive everywhere. The graph of y is increasing as x is increasing.
InterceptsThe x-intercept is the value of x that makes y = 0.
0 = ∛(x -1) +2
-2 = ∛(x -1)
-8 = (x -1)
-7 = x . . . . . . . the x-intercept
The y-intercept is the value of y when x = 0.
y = ∛(0 -1) +2
y = -1 +2 = 1 . . . . . . the y-intercept
The true statements about the graph are ...
(a) The graph has a domain of all real numbers.
(d) The graph has a y-intercept of (0, 1).
(e) The graph has an x-intercept of (-7, 0).
<95141404393>
92 people had lunch in the cafeteria.
9 people had soup, a sandwich, and a drink. 33
people had soup, 45 had a sandwich, and 52
had a drink. 5 people had soup and a
sandwich. 10 people had a sandwich and a
drink. 5 people had soup and a drink.
How many people had only a drink?
14 people
28 people
21 people
92 people
Answer:
Step-by-step explanation:
The question about how many people ONLY had a drink is asking to solve some simultaneous equations . Know this?
People = 92
soup = SP = 33
sandwich = SW = 45
drink = D = 52
9(SP+SW+D)
5(SP+SW)
10(SW+D)
5(SP+D)
for a drink 9+10+5 people had a drink with something else
24 had a drink with something else so 52-24=28 only had a drink
28 people only had a drink
What is the result of adding these two equations?
-2x+7y=-5 -2x-4y=6
The result of adding the two given equations (-2x + 7y = -5 and -2x - 4y = 6) is -4x + 3y = 1
Adding system of linear equationsFrom the question, we are to determine the result of adding the two given equations.
The given equations are
-2x + 7y = -5 and -2x - 4y = 6
Now, we will add the equations
-2x + 7y = -5
+ ( -2x - 4y = 6
------------------------------
-2x + (-2x) + 7y + (-4y) = -5 + 6
-2x - 2x + 7y - 4y = 1
Simplifying
-4x + 3y = 1
Hence, the result of adding the equations is -4x + 3y = 1
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A baseball player makes an annual salary of 3,200,000.
A charitable organization states that for $120 it can send 1 child to school in a developing country for 1 year. The baseball player decides to donate 10% of his annual salary to this organization.
Calculating it would be 320,000. About how many children could his donation send to school for 1 year?
Answer:
It can send 2,666 kids to school for a year.
helpp mi poor soul!!!
Solve for x.
6(x – 1) = 9(x + 2)
a
x = –8
b
x = –3
c
x = 3
d
x = 8
What is a number increased by three is greater than zero or less than or equal to negative three?
The number is defined by the two inequalities:
x > -3
x ≤ -6
How to find the number?
If we define x as the number, the number increased by 3 is written as:
x + 3
If this is greater than zero or less than or equal to negative three, we can write two inequalities:
x + 3 > 0
x + 3 ≤ -3
Solving both inequalities for x (isolting it) we will get:
x > 0 - 3
x > -3
and:
x ≤ -3 - 3
x ≤ -6
So we have the two inequalities that define the number:
x > -3
x ≤ -6
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An insurance settlement of $1.5 million must replace Trixie Eden's income for the next 35 years. What income will this settlement provide at the end of each month if it is invested in an annuity that i
earns 7.1%, compounded monthly?
(a) Decide whether the problem relates to an ordinary annuity or an annuity due.
o ordinary annuity
annuity due
(b) Solve the problem. (Round your answer to the nearest cent.)
$
The income that this settlement provide at the end of each month is: $813.20.
How to find the monthly payment?Monthly amount= $1.500,000 at the end of year 35 years.
Interest rate per month = 7.1/12 = 0.59167% per month
Total periodic cash flow = 35× 12 = 420
Hence,
Future value of annuity = X × [(1+ 0.0059167)^420 -1/ 0.0059167]
Future value of annuity =X × [(1.0059167)^420 -1/ 0.0059167]
Future value of annuity = X × [(1.0059167)^420 -1/ 0.0059167]
Future value of annuity = X × [11.913727 -1 / 0.0059167]
Future value of annuity = X × [10.913727 / 0.0059167]
Future value of annuity =X × 1,844.5633
$1,500,000 = X × 1,844.5633
X = $1,500,000/ 1,844.5633
X = $813.20
Hence,
Monthly payment is $813.20.
b. Since the cash flow occur at the end of every period this means that this is an ordinary annuity.
Therefor $813.20 is the monthly payment.
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Six people are playing a game with 52 cards.
One player passes out as many cards as possible so that everyone gets the same
number of cards.
How many cards will each of the 6 players get?
Each player will get 9 cards.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.According to our question-
total people= 6
cards=52
52/6= 8.66
rounding off
=9
hence, each player will get 9 cards.
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a) What are the coordinates of A?
b) What are the coordinates of B?
Answer: Yellow Greed
Step-by-step explanation: Maths