Answer:
[tex]-3(x-2)^2+5[/tex]
Step-by-step explanation:
First we can factor a -3 from the [tex]x^2[/tex] term and the [tex]x[/tex] term to get [tex]-3(x^2-4x)-7[/tex].
Then we want the stuff in the parentheses to have the form of [tex](x+b)^2[/tex], or equivalently, [tex](x^2+2b+b^2)[/tex] . So we can let [tex]2b = -4[/tex]. By solving it, we get [tex]b = -4/2 = -2[/tex]. Then our [tex]b^2[/tex] term should be [tex]b^2 = (-2)^2 = 4[/tex].
In order to make our [tex]b^2[/tex] term appear in the parentheses, we need to add and subtract our [tex]b^2[/tex] term, so we get [tex]-3(x^2 - 4x + 4 - 4) -7[/tex].
What we to keep inside our parentheses is [tex](x^2 - 4x + 4)[/tex] , so we can factor the [tex]-4[/tex] out of parentheses to get [tex]-3(x^2-4x+4-4)-7 = -3(x^2-4x+4)+(-3)(-4) - 7 = -3(x^2 - 4x + 4) + 12 - 7 = -3(x^2 - 4x + 4) + 5[/tex]
Finally, plugging [tex]b = -2[/tex] that we computed earlier into the equation [tex](x^2+2b+b^2) = (x+b)^2[/tex], we get [tex](x^2 - 4x + 4) = (x-2)^2[/tex].
So we have [tex]-3(x^2-4x+4)+5 = -3(x-2)^2+5[/tex].
In summary, the procedure is
[tex]-3x^2+12x-7 \\= &-3(x^2-4x) -7 \\= &-3(x^2-4x+4-4)-7 \\= -3(x^2-4x+4) + (-3)(-4)-7\\=-3(x^2-4x+4)+12-7\\= -3(x^2-4x+4)+5 \\= -3(x-2)^2+5[/tex]
The Bourassas decide to sell a home for $440,000. They are charged a real estate commission of 8% of the selling price, title insurance that is 1.4% of the selling price, and an escrow fee of $775.
(a)
What amount (in dollars) do the Bourassas receive after fees?
$
(b)
What percentage of the selling price was fees? Round to the nearest tenth of a percent.
%
The amount received net of expenses is $397865 and the percentage of the sale price was 10%.
Given that Bourassas decides to sell a house for $ 440,000. You will be charged a real estate fee of 8% of the sale price, property insurance of 1.4% of the sale price, and an escrow fee of $ 775.
The declared retail price is $ 440,000.
Real estate commission = 8% of the sale price
Real Estate Fee = (8/100) × 440000
Real Estate Fee = 8 × 4400
Real Estate Fee = $ 35,200
Security insurance costs of the title = 1.4% of the sale price
Cost of title insurance = (1.4 / 100) × 440 000
Cost of title insurance = 1.4 × 4400
Title Insurance Cost = $ 6160
The escrow fee assigned is $ 775.
(a) In determining the amount received after deducting the sale price of the property commission, title insurance and escrow fees, we receive
Amount received after fees = sale price - real estate commission - title insurance - escrow fees
Amount received after fees = 440000-35200-6160-775
The amount received after fees = $397865
(b) To find the percentage of sale price, add together all the terms real estate commission, title insurance and escrow fees and divide by the sale price we get
Percentage of selling price=((35200+6160+775)/440000)×100
Percentage of sale price = (42135/440000) × 100
Percentage of sale price = 9.57
Percentage of sale price = 10% (rounded down)
Hence Bourassas decides to sell a house for $440,000, then the amount Bourassas will receive after expenses is $397,865 and the percentage of the sale price of expenses is 10%.
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Which of the following is the solution to 8√3 + 7√3?
15√9
15√6
15√3
56√3
Which of the following is the solution to √15 * √45 simplified?
√675
8√3
15√15
15√3
Which of the following is the solution to 15√10 - 3√10?
12√10
5√10
12√100
45√10
Answer:
Q1: Third Choice. 15√3
Q2: Fourth Choice. 15√3
Q3: First Choice. 12√10
Step-by-step explanation:
Question 1: Which of the following is the solution to 8√3 + 7√3?Given expression
8√3 + 7√3
Simplify by addition
Remember that terms with the same radical part can add together directly
= (8 + 7) √3
[tex]\Large\boxed{=15\sqrt{3} }[/tex]
Question 2: Which of the following is the solution to √15 * √45 simplified?Given expression
√15 × √45
Factorize each radical
= √(3 × 5) × √(9 × 5)
= √3 × √5 × √9 × √5
Simplify necessary radicals
= √3 × √5 × 3 × √5
= 3 × √3 × √5 × √5
Simplify by multiplication
When radicals multiply, combine them under one radical sign
= 3√3 × √(5 × 5)
= 3√3 × 5
[tex]\Large\boxed{=15\sqrt{3} }[/tex]
Questions 3: Which of the following is the solution to 15√10 - 3√10?Given expression
15√10 - 3√10
Simplify by subtraction
Remember that terms with the same radical part can subtract each other directly
= (15 - 3) √10
[tex]\Large\boxed{=12\sqrt{10} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
When it is Noon (12 pm) in London, it is 10pm in Sydney, Australia. Dan in London rings his friend Boski in Sydney at 15:30pm on Christmas Day. What time is it in Sydney?
A. 1am
B. 1:30am
C. 2am
S. 2:30am
The time at Sydney when Dan rings his friend is 1 : 30 am (option B).
What is the time at Sydney?The first step is determine the time difference between London and Sydney.
Time difference = time at Sydney - time at London
( 12 + 10pm) - 12pm
22pm - 12pm = 10 hours
The second step is to add the time difference to the time it was when Dan rang.
15 : 30 pm + 10pm = 25 : 30
We know that there are only 24 hours in day, so subtract 24 hours from 25 : 30
25 : 30 - 24 = 1 : 30 am
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Answers for number 32 and 31
Answer:
32: X=54
31: Xx54+74
Compute the probability of event E if the odds in favor of E are 28 to 29.
Answer:
28/57
Step-by-step explanation:
odds in favor of event occurring = (probability event occurs)/(probability event does not occur)
Let p = probability event occurs.
Then the probability the event does not occur is 1 - p.
Let the odds = a/b.
a/b = p/(1 - p)
a(1 - p) = bp
a - ap = bp
bp + ap = a
p(a + b) = a
p = a/(a + b)
p = 28/(28 + 29)
p = 28/57
As per the given scenario, the probability of event E is 28/57 or approximately 0.4912.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.
If the odds in favor of an event E are "a to b," then the probability of E is given by:
P(E) = a / (a + b)
In this case, the odds in favor of E are 28 to 29, which means that there are 28 favorable outcomes for E and 29 unfavorable outcomes against E.
So, using the formula above, we can compute the probability of E as:
P(E) = 28 / (28 + 29)
P(E) = 28 / 57
Therefore, the probability of event E is 28/57 or approximately 0.4912.
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72 is 15% of what number?
Answer: 480
Step-by-step explanation:
72/3 is 5% of the number we are looking for.
72/3=24
24*20 will be 100%
480 is 100%
72 is 15% of what number?
Quantity %
72---------------15
x---------------100
We solve
[tex]\boldsymbol{\sf{x=\dfrac{72\times100 }{15}=\dfrac{7200}{15}=480 }}[/tex]
Answer: 72 is 15% of 480.
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P = √mx_ £x MX t make x the subject
[tex]p = \sqrt{ \frac{mx}{t} } - t {}^{2}x \: \: make \: x \: the \: subject [/tex]
So, making x subject of the formula, x = [m - 2pt³ ±√(m² - 4pt²m)]/{2t⁵}
How to make x subject of the formula?Since p = √(mx/t) - t²x
So, p + t²x = √(mx/t)
Squaring both sides, we have
(p + t²x)² = [√(mx/t)]²
p² + 2pt²x + t⁴x² = mx/t
Multiplying through by t,we have
(p² + 2pt²x + t⁴x²)t = mx/t × t
p²t + 2pt³x + t⁵x² = mx
p²t + 2pt³x + t⁵x² - mx = 0
t⁵x² + 2pt³x - mx + p²t = 0
t⁵x² + (2pt³ - m)x + p²t = 0
Using the quadratic formula, we find x.
[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex]
where
a = t⁵, b = (2pt³ - m) and c = p²tSubstituting the values of the variables into the equation, we have
[tex]x = \frac{-(2pt^{3} - m) +/-\sqrt{(2pt^{3} - m)^{2} - 4(t^{5})(p^{2}t) } }{2t^{5} }\\= \frac{-(2pt^{3} - m) +/-\sqrt{4p^{2} t^{6} - 4pt^{2}m + m^{2} - 4p^{2}t^{6} } }{2t^{5}}\\= \frac{-(2pt^{3} - m) +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}\\= \frac{m - 2pt^{3} +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}[/tex]
So, making x subject of the formula, [tex]x = \frac{m - 2pt^{3} +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}[/tex]
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AMERICAN AIRLINES HAS A POLICY OF BOOKING AS MANY AS 15 PEOPLE ON AN AIRPLANE THAT CAN SEAT ONLY 14. (PAST STUDIES HAVE REVEALED THAT ONLY
85% OF THE BOOKED PASSENGERS ACTUALLY ARRIVE FOR THE FLIGHTS.) FIND THE PROBABILITY THAT IF AMERICAN AIRLINES BOOKS 15 PEOPLE, NOT ENOUGH SEATS
WILL BE AVAILABLE
Using the binomial distribution, there is a 0.0874 = 8.74% probability that not enough seats will be available.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are given by:
n = 15, p = 0.85.
The probability that not enough seats will be available is P(X = 15), as the only outcome in which not enough seats will be available is when all 15 people who bought the ticket show up, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 15) = C_{15,15}.(0.85)^{15}.(0.15)^{0} = 0.0874[/tex]
0.0874 = 8.74% probability that not enough seats will be available.
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Someone please help me with this thank you!
Answer:
50°
Step-by-step explanation:
Note EFGH is an isosceles trapezoid.
∠HGF=77° (base angles of an isosceles trapezoid are congruent)
∠EGH=27° (angles in a triangle add to 180°)
∠FGE=50° (angle subtraction postulate)
Given AD is the median of △ABC find x, CD, and DB. i need step by step
Applying the definition of the median of a triangle: x = 9; CD = 28; DB = 28.
What is the Median of a Triangle?The median of a triangle can be defined as a line segment in a triangle that joins the vertex of a triangle to the midpoint of the side of the triangle that is opposite the vertex.
Given triangle ABC, where AD is the median and D is the midpoint of side AB, therefore:
Side CD equals side DB.
Side CD = 5x - 17
Side DB = 3x + 1
Make both segments equal to each other. Therefore, we would have the equation:
5x - 17 = 3x + 1
Solve for x
Add both sides by 17
5x - 17 + 17 = 3x + 1 + 17
5x = 3x + 18
Subtract 3x from both sides
5x - 3x = 3x + 18 - 3x
2x = 18
Divide both sides by 2
2x/2 = 18/2
x = 9
CD = 5x - 17
Plug in the value of x
CD = 5(9) - 17
CD = 45 - 17
CD = 28 units.
DB = 3x + 1
Plug in the value of x
DB = 3(9) + 1
DB = 27 + 1
DB = 28 units.
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find the zeros x^4-2x^3-44x^2-88x-32
The zeros which are the roots of the polynomial expressions are:
x = -4; x = - 2; x = 4 - 2√5; x = 2(2 + √5)
What are the zeros of a polynomial expression?The zeros of a polynomial f(x) are really the values of x that answer the equation f(x) = 0. Thus, f(x) is a function of x, and the polynomial zeros refer to the values of x, which makes the f(x) value equal to zero. The digit of zeros in a polynomial is decided by the degree of equation f(x) = 0.
For a polynomial, there may be specific values of the variable for which the polynomial is zero. These are known as polynomial zeros. They are also known as polynomial roots. In essence, we look for the zeros of quadratic equations to discover the solutions to the given equation.
From the given equation, the zeros of x^4-2x^3-44x^2-88x-32 can be computed as follows:
Using the rational root theorem:
[tex]\mathbf{= (x+2)\dfrac{x^4-2x^3-44x^2-88x-32}{x+2} }[/tex]
[tex]\mathbf{=(x+2) (x^3-4x^2-36x-32) }[/tex]
By factorization, we have:
= (x + 2) (x + 4) (x² - 8x - 4)
The zeros which are the roots of the polynomial expressions are:
x = -4; x = - 2; x = 4 - 2√5; x = 2(2 + √5)
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Two buses leave a station at the same time and travel in opposite directions. One bus travels 18 miles per hour faster than the other. If the two buses are 744 miles apart after 6 hours, what is the rate of each bus?
Answer:
53 mph and 71 mph
Step-by-step explanation:
bus 1 rate = x
bus 2 rate = x + 18
rate times time = distance
( x + x+18) * 6 = 744
(2x+18) * 6 = 744
2x + 18 = 124
2x = 106
x = 53 the other bus is 53 + 18 = 71 mph
Find the mode for the scores 3,760, 5,200, 8,750, 4,400, 5,250
Answer:
no mode
Step-by-step explanation:
no number appears more than once
therefore there is no mode
. What are the values a b and c In the following quadratic equation ? -6x^2-8x+12=0
Answer:
a = -6
b = -8
c = 12
Step-by-step explanation:
Quadratic equations follow the general structure:
ax² + bx + c = 0
In this equation, "a" and "b" serve as coefficients which modify the variables and "c" represents the y-intercept. Since the given equation is in the quadratic form, you can easily identify which values match the variables.
-6x² - 8x + 12 = 0
a = -6
b = -8
c = 12
How many grams of the isotope remains after 90 days?
Answer:
84,08964 [gr.].
Step-by-step explanation:
for more details see in the attachment.
Which pair of functions are inverses of each other? O A. F(a) = I - 9 and g(2) = 2*9 O B. Ax) = 5x - 11 and g(a) = 2+11 O C. F(a) = V2m and g(2) = (3) ° O D. f(a) = ; + 8 and g(x) = 6x - 8 SUBMIT
The pair of functions that are inverses of each other is (a) f(x) = 5x - 11 and g(x) = (x + 11)/5
How to determine the function and the inverse?The complete question is added as an attachment
Function 1
f(x) = 5x - 11 and g(x) = (x + 11)/5
Represent 5x - 11 with y in f(x) = 5x - 11
y = 5x - 11
Swap x and y
x = 5y - 11
Add 11 to both sides
x + 11 = 5y
Divide by 5
y = (x + 11)/5
Express as a function
g(x) = (x + 11)/5
From the question, we have:
f(x) = 5x - 11 and g(x) = (x + 11)/5
This means that the function g(x) is an inverse of the function f(x)
Hence, the pair of functions that are inverses of each other is (a) f(x) = 5x - 11 and g(x) = (x + 11)/5
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what is 7/8 - 1/2 as a fraction
Answer: 3/8
Step-by-step explanation:
1/2 is also 4/8 so you subtract 4/8 from 7/8 to get 3/8
What are the coordinates of the vertex of the parabola with the equation y = x2 + 2x – 3?
A
(-1, -4)
B
(1, -4)
C
(3, -4)
D
(-3, 12)
Answer:
A. (-1, -4)
Step-by-step explanation:
The vertex can be found by converting the equation from standard form to vertex form.
VertexConsidering the x-terms, we have ...
y = (x^2 +2x) -3
where the coefficient of x is 2. Adding (and subtracting) the square of half that, we get ...
y = (x^2 +2x +(2/2)^2) -3 -(2/2)^2
y = (x +1)^2 -4
Compare this to the vertex form equation ...
y = a(x -h)^2 +k
which has vertex (h, k).
We see that h=-1 and k=-4. The vertex is (h, k) = (-1, -4).
On the attached graph, the vertex is the turning point, the minimum.
What is the slope of the line that passes through the points (8, 0) and (-4, -8)?
Write your answer in simplest form.
Answer:
Step-by-step explanation:
(-8 - 0)/(-4 - 8)= -8/-12 = 2/3
The slope of the line that passes through the points (8, 0) and (-4, -8) exists at 0.66667.
How to estimate the slope of the line?The slope or gradient between two points in the Cartesian coordinate system. The slope exists the amount of slant a line retains and can maintain a positive, negative, zero, or undefined value.
Using the slope formula [tex](y_2 - y_1)/(x_2 - x_1)[/tex]
[tex]x_1 = 8, y_1 = 0[/tex] and [tex]x_2 = -4 , y_2= -8[/tex]
slope [tex]= (y_2 - y_1)/(x_2 - x_1)[/tex]
= ((-8) - 0) / ((-4) - (8))
= (-8) / (-12) = (-2) / (-3)
= 0.66667
Therefore, the slope of the line that passes through the points (8, 0) and (-4, -8) exists at 0.66667.
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I am confused. Can somebody explain this to me?
Maryann can paint a wall in 45 minutes. It takes her brother Junior 1 hour and 45 minutes to paint the same wall. How many minutes would it take Maryann and Junior to paint the wall, if they work together? Answer as a decimal to the nearest tenth.
Answer: If they worked together, it would take 31.5 minutes
Step-by-step explanation:
There's a certain formula for equations like this:
[tex]\frac{1}{t1} +\frac{1}{t2}=\frac{1}{tb}[/tex]
t1= the time it took for the first person to complete the task.
t2= the time it took for the second person to complete the task.
tb= the time it took for both of them to complete the task.
We have the values for both t1 and t2, but not for tb.
t1= 45
t2= 105
tb= x
[tex]\frac{1}{45} +\frac{1}{105} = \frac{1}{x}[/tex]
Now it's simple algebra, and all we need to do is solve for x
The LCM for both fractions is 315, so now we multiply BOTH sides of the equation by 315.
[tex]\frac{315}{45} + \frac{315}{105} = \frac{315}{x}[/tex]
This will simplify nicely, so now we just need to get x on the other side.[tex]7 + 3 = \frac{315}{x} \\\\\ 10*x = \frac{315}{x} * x[/tex]
[tex]10x = 315 \\\\x = 31.5[/tex]
PLEASE HELP ME WITH THIS QUESTION I NEED HELP
Answer:
True
Step-by-step explanation:
This is true in an equilateral triangle.
Solve for exponential the value of X
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The two triangles are right angled Triangles and they have one common angle. so the two triangles are similar to each other.
By using similarity, ratio of their corresponding sides must be equal as well~
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2 + 1} = \cfrac{3}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{3} = \cfrac{3}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = 3 \times 3[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 9 \: \: units[/tex]
Joey had eight pencils in the morning. He gave some pencils away to friends who needed them. To determine the number of pencils he has left, ___ the number of pencils he gave away. count difference subtract add
Find the surface area of the composite figure 4 cm 13 cm 3 cm 4 cm 12 cm SA = [?] cm² 5 cm 3 cm.
Find one possible missing coordinate so that the point becomes a solution to the given inequality.
(x,6) is a solution to 6x−6>y .
Answer:
Step-by-step explanation:
6x-6>y
put y=6
6x-6>6
6x>12
x>12/6
x>2
(3,6) is one solution.
HELPP PLSSS I NEED HELP!!!
Answer:
(3+3) x (3+1)
Step-by-step explanation:
free
We have give 4 numbers that are 1,3,3,3. we have to apply operations on it to make it 24.
Solution :» (1 + 3) × (3 + 3)
» (4) × (6)
» 24
Here's our answer..!!
Find the gradient of the line joining the points P(2,5) and Q(4,-2).
1 Which is the greatest 4- digit number divisible by 6?......
As fast as when u are running to save ur mom life
Answer:
The greatest four-digit number that is divisible by 6 is 9996
Step-by-step explanation:
9,996 / 6 = 1,666
A barn that holds hay for the cows is shown below. If you see the hay for $1.50 per cubic foot, how much money could
you make if the barn is completely full?
If the price of 1 cubic foot of hay is $10 then the money needed is $15.
Given the price of 1 cubic foot of hay be $10 and the amount of hay be $1.50.
We are required to find the amount of money needed to buy the hay.
We know that the amount of money that can be spend on something is the product of price of one unit and number of units.
Product is the result when two numbers are multiplied with each other.
Total money =Price of 1 cubic foot*$1.50
=10*1.50
=$15
Hence if the price of 1 cubic foot of hay is $10 then the money needed is $15.
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Question is incomplete, the right question is as under:
1.5 cubic foot hay is required to fill a room completely. Calculate the amount we have to pay to fill the room completely if the price of 1 cubic foot is $10?
I need help… a lot of it im so confused
[tex] \sqrt[3]{b {}^{2} } = b {}^{ \frac{2}{3} } [/tex]
2)[tex]f(4) = 2(3) {}^{4} = 2 \times 81 = 162[/tex]
3)[tex]f( \frac{1}{2} ) = \frac{1}{3} (9) {}^{ \frac{1}{2} } + 5 = \frac{ \sqrt{9} }{ 3} + 5 = 6[/tex]
4)
[tex]f(5) = - 4(2) {}^{ - 5 + 1} = - 4(2) {}^{ -4} = \frac{2 {}^{2} }{2 {}^{4} } = \frac{1}{2 {}^{2} } = \frac{1}{4} [/tex]
5)[tex]f(10) = 2e {}^{0.15 \times 10} = 2e {}^{1.5} = 8.96[/tex]
6)[tex]y = 10(b) {}^{x} \: \: \\ 10 = 10(b) {}^{0} \: duh \\ 2 = 10b {}^{1} \\ b = \frac{2}{10} = \frac{1}{5} [/tex]
7)[tex]y = a(b) {}^{x} \\ 3 = a(b) {}^{0} \\ a = 3 \\ \\75 = 3(b) {}^{2} \\ b {}^{2} = 25 \\ b = + 5 \: \: \: or \: \: \: \: b = - 5[/tex]
8)[tex]s = 1000(1 + \frac{0.045}{4} ) {}^{4 \times 10} = 1564.38[/tex]
9)[tex]s = 2500.e {}^{0.07 \times 20} = 10138[/tex]