Solve the equations.
[tex]3(x+4)^{2} =10x+32\\(x+4)^{2} =3x+40\\\frac{x^{2} -1}{2} -11x=11[/tex]
Answers
Answer:
a) x = {-2 2/3, -2}
b) x = {-8, 3}
c) x = {-1, 23}
Step-by-step explanation:
If all you want are solutions, a graphing calculator can give them to you easily. The attachment shows the solutions as x-intercepts when the equation is rearranged to the form f(x) = 0.
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In general, it can be convenient to write the equation in standard form with integer coefficients. Common factors among the coefficients should be removed.
a)3(x+4)^2 = 10x +32 . . . . . given
3(x^2 +8x +16) -10x -32 = 0
3x^2 +14x +16 = 0
To factor this, we're looking for factors of 3·16 that total 14.
48 = 1·48 = 2·24 = 3·16 = 4·12 = 6·8
The last pair of factors has a total of 14, so we can rewrite the equation as ...
(3x +6)(3x +8)/3 = 0
(x +2)(3x +8) = 0
The solutions are the values of x that make the factors zero:
x = -2, x = -8/3
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b)(x +4)^2 = 3x +40 . . . . . . . . given
x^2 +8x +16 -3x -40 = 0 . . . . subtract the right side
x^2 +5x -24 = 0 . . . . . . . . simplify
(x +8)(x -3) = 0 . . . . . . factor
The solutions are the values of x that make the factors zero:
x = -8, x = 3
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c)(x^2 -1)/2 -11x = 11 . . . . . given
x^2 -1 -22x -22 = 0 . . . . . . multiply by 2, subtract the right side
x^2 -22x -23 = 0 . . . . . . simplify
(x -23)(x +1) = 0 . . . . . . factor
x = 23, x = -1
_____
Additional comment
Factoring often gets to the solution with the least fuss when the solutions are rational. There are several ways factoring can be done when the leading coefficient is not 1. One of them is illustrated in (a) above. We will show two other methods that give the same result.
factoring by pairs
We have identified the factors of 3·16 = 48 that have a total of 14. We can use those factors to rewrite the 14x term in the equation.
3x^2 +6x +8x +16 = 0
Now, we can group the terms in pairs, and factor each pair. It does not matter which of the factors (6 or 8) you write first. You will end with the same result.
(3x^2 +6x) +(8x +16) = 0
3x(x +2) +8(x +2) = 0
(3x +8)(x +2) = 0 ⇒ x = -8/3, x = -2
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factoring using the X method
This method is usually shown using a large graphic X. In the top quadrant is written the product of the leading coefficient and the constant: 3·16 = 48.
In the bottom quadrant is written the coefficient of the x-term: 14.
If one or the other, or both, of these top/bottom values is negative, be sure to keep the sign.
The side quadrants are then filled with values that have a product equal to the top number, and a sum equal to the bottom number. (Pay attention to the signs.) Further, in each of those quadrants, the number written is divided by the leading coefficient, and the fraction reduced to lowest terms.
Here, we would have 6/3 = 2 on one side, and 8/3 on the other side. Now the factors are written as (bx+a), where the reduced fraction on either side is a/b. In our example, the factors are (x+2) and (3x+8)
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alternate X method
This starts off in the same way the X method does, as described above. However, the factors on either side of the X are not divided by the leading coefficient (a). If those side values are 'p' and 'q', the quadratic is written in factored form as ...
(ax +p)(ax +q)/a = 0
You will notice we used this form above: (3x +6)(3x +8)/3 = 0.
Now, the divisor 'a' can be used to reduce either or both of the numerator factors. Here, the entire factor of 3 can be removed from (3x+6) to make the factorization be ...
(x +2)(3x +8) = 0
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Sometimes, one factor of the divisor will be removed from one term, and the other factor of it will be removed from the other term. An example of this might be ...
[tex]\dfrac{(6x+3)(6x+2)}{6}=\dfrac{6x+3}{3}\cdot\dfrac{6x+2}{2}=(2x+1)(3x+1)[/tex]
![Solve The Equations.[tex]3(x+4)^{2} =10x+32\\(x+4)^{2} =3x+40\\\frac{x^{2} -1}{2} -11x=11[/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/oePous4oDLaEhycs5k9S7dMzdYWiyPAg.png)
Related Questions
is this a function
Find the domain and range
Answers
Answer:
Yes
Domain: 1, -1, 0, -3, 3
Range: 1, -1, 6
Step-by-step explanation:
The domain is in the left oval, the range is in the right oval. To find if its a function you have to make sure the domain (left side) doesn't "cheat". One number in the domain cant have more than one number in the range (right side), BUT (for future reference) the range can cheat. As shown, the right side numbers 1 and 6 have two different arrow pointed at them. As long as the domain doesnt "cheat" it is a function
how to solve x^2+x-90=0 in completing the square method
Answers
Rearrange the equation by writing
x² + x - 90 = 0
x² + x = 90
x² + x + 1/4 = 90 + 1/4
Recall that (a + b)² = a² + 2ab + b². Then
x² + 2 • x/2 + (1/2)² = 361/4
(x + 1/2)² = 361/4
x + 1/2 = ± √(361/4)
x = -1/2 ± 19/2
x = 9 or x = -10
which expression is equal to 4 to the power of 5 times 4 to the power of -7 divided by 4 to the power of -2
Answers
Step-by-step explanation:
4⁵ × 4^-7 / 4^-2
it is important to understand that a negative exponent means 1/...
a^-n = 1/(a^n)
in that sense we have therefore
4⁵ × 1/4⁷ × 4² (as (1/ 1/a^n) = a^n)
4⁵ × 4² × 1/4⁷ = 4⁷ × 1/4⁷ = 1
so, "1" is the fully simplified expression equal to the original expression.
How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!
Answers
Answer:
2
Step-by-step explanation:
3:1=6:2
They buy 2 pepperoni pizzas.
Find the length of the third side. If necessary, round to the nearest tenth.
Answers
Answer:
4.5
Step-by-step explanation:
To find the hypotenuse of a right triangle, we use Pythagorean's Theorem which states that [tex]a^{2}+b^{2} =c^{2}[/tex]. Plugging in the values of the two legs given, we get [tex]2^{2} +4^{2} =c^{2} =20[/tex]. We can take the square root of each side and get that [tex]c=\sqrt{20} =4.5[/tex].
Answer:
Try 4.5 or 5
Step-by-step explanation:
I measured it up and I estimated 4.5 at most
2. There is a 0% chance that the earth is the closest planet to the sun.
A) unlikely
B) certain
C) likely
D) impossible
Answers
Answer:
D) Impossible
Step-by-step explanation:
Unlikely = < 50%Certain = 100%Likely = > 50%Impossible = 0%This would be B. It is certain that there is a 0% chance of the earth being the closest planet to the sun. Mercury is the closest. Earth is the third closest behind Mercury and Venus. Hope that helps.
HELP HELP ME PLS I AM RUNNING OUT OF TIME!!!! HERE IS MY PROBLEM:
An attorney drove 9 1/4 miles from his home to a clients home and another 4 3/5 miles to get to his office. How far did he drive in total?
Answers
Answer:
Step-by-step explanation:
To write fractions with a common denominator, you will most likely need to scale some numbers up! I will explain how.
Let's try it with the fractions
2
3
and
3
12
12 is larger than 3, so we will have to multiply the 3 by some number to equal 12. (We are really finding the Least Common Multiple of the two denominators!) To do this, you have to multiply the 3 by 4, because 3x4=12. But now the numerator doesn't match the denominator. When you scale the denominator up, you have to scale the numerator up too! So the 2 must be multiplied by 4 also.
Now you have the following:
8
12
and
3
12
These fractions now have common denominators! Now they're all set for adding or subtracting fractions.
Try another:
2
6
and
3
5
: The least common multiple of 6 and 5 is 30. (the product of the denominators)
Transform each fraction by multiplying by "1":
2
6
⋅
5
5
=
10
30
and
3
5
⋅
6
6
=
18
30
One last problem:
4
9
and
7
6
What is the least common multiple of 9 and 6? Could you use 54? Absolutely, but it is not the LEAST number that you could use. How about 18? YES!
4
9
⋅
2
2
=
8
18
and
7
6
⋅
3
3
=
21
18
Ready to go...
Hope this helped!
when using the zero product rule you know at least one of the factors must equal *blank*
Answers
Answer:
The Principle of Zero Products states that if the product of two numbers is 0, then at least one of the factors is 0.
Step-by-step explanation:
Answer:
when using the zero product rule you know at least one of the factors must equal 0 because and most places anything that is put with zero equal zero because zero have no value
Step-by-step explanation:
in a class of 33 student 18 play football 1"basketball and 7 play both games how many students play non of the games
Answers
33 - 26 = 7
A racing track is shaped like an oval. Each time around
the track is 1.2 miles. The total distance for the
race is 480 miles.
What percentage is one lap around the track of
the total race?
(b) How many laps will it take to complete 75% of the
race?
Answers
Answer:
Percentage of one lap around the track of
the total race = 0.25%
It will take 300 laps to complete 75% of the race.
Step-by-step explanation:
1.2/480=0.0025
0.0025*100=0.25
480/100*75= 360
360/1.2=300
The quotient of s and three
Answers
Answer:
s/3
Step-by-step explanation:
The quotient means you divide the two values.
calculate (3×10^5) × (4×10^4) in standard form.
NEED HELP ASAP.
Answers
Answer:
12000000000
Step-by-step explanation:
did I add too many zeros????
10 to the 5 is multiply by 10 five times (100,000)
100,000 x 3 = 300,000
For the second thing, 10 to the 4 = 10,000
10,000 x 4 = 40,000
300,000 x 40,000 = 12000000000
a pond of a water has length20m and breadth 10m. how much kl of water should be taken out of the pond so that level of water should go down by 3m?
Answers
Answer:
600 kl
Step-by-step explanation:
The volume represented by a length of 20 m, a breadth of 10 m, and a depth of 3 m is ...
V = (20 m)(10 m)(3 m) = 600 m³
1 m³ = 1 kl
The volume of water that should be removed is 600 kl.
the elements of the periodic table are numbered from 1 to 118 and Atom's place on the table is determined solely by which property A mass number B number of protons C number of neutrons D number of electrons
Answers
The atom's place on the table is determined solely by its number of protons
A periodic table is a table containing different elements and arranged across the periods and groups of the table. The elements in a periodic table are numbered and arranged based on their atomic number.Since the atomic number is equal to the number of protons an element contains, hence we can conclude that the atom's place on the table is determined solely by its number of protons
Learn more about periodic table here;https://brainly.com/question/14514242
Answer:
number of protons
Step-by-step explanation:
James is planning to spend $425 on food for his vacation this summer. This is 34% of his total vacation budget. How much is James' total vacation budget?
Answers
1250$,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Find the midpoint of the segment with the following endpoints. (2, -9) and (-4,-4)
Answers
Answer:
(-1,-6.5)
Step-by-step explanation:
midpoint formula: (x_m, y_m) = (x1+x2)/2),(y1+y2)/2)
(2-4)/2=-1, -9-4=-13/2=-6.5
=(-1,-6.5)
I need to know the values of m and n.
Answers
Answer:
A) 32 and 28
Step-by-step explanation:
A= √4².√2
= √16.√2
= √32
m= 32
B= √2². √7
=√4.√7
=√28
n= 28
which statement is true?
Answers
Answer:
The slope of function A is less than the slope of function B
Explanation:
The slope for function B is 1/2, which is greaterthan 1/5, the slope of function A.
Answer:
the slope on Function A is less than Function B
Step-by-step explanation:
By doing rise over run we can get 1/2 on Function B and the Y intercept is 5 so the equation is y=1/2x+5
Would someone help me out?
A)56.6
B)58.4
C)53.5
Answers
Answer:
it is c
Step-by-step explanation:
Write the equation of a line with the given slope that goes through the given point.
7) through: (3, -5), slope = -1
5
8) through: (3, 2), slope
3
Answers
Answer:
7) y +5 = -(x -3)
8) y -2 = 5/3(x -3)
Step-by-step explanation:
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
__
7) y +5 = -(x -3)
8) y -2 = 5/3(x -3)
a pair of shoes is 80 dollars they are %25 off. how much money is %25 of 80 dollars
Answers
Answer
55$
Step-by-step explanation:
Equations that represent a line parallel to y=8x+4
Answers
y=8x+b, b being any number, is parallel to y=8x+4.
For example:
y=8x+2
y=8x+(1/2)
y=8x+937382
y=8x-4
Write an equation for the proportional relationship shown in the table.
Answers
Answer:
y = 14x
Step-by-step explanation:
First Way of Finding the Equation:
We can find the equation for this proportional relationship by subtracting two of the y-values from each other and then dividing that by the difference of two of the x-values. For now, I'll use the points (2, 28) and (1, 14).
[tex]\frac{28-14}{2-1} =\frac{14}{1} =14[/tex]
So, this proportional relationship has an equation of y = 14x.
Second Way of Finding the Equation:
Another way of finding the equation is to simply examine the table given. What are all the x-values multiplied by to get to their corresponding y-values? Well, one easy way of answering this question is looking at the point (1, 14) - 1 × 14 = 14, so the constant of proportionality must be 14.
From this information, we know that the equation must be y = 14x.
Hopefully that's helpful! :)
Kim's scores in the diving competition were 7.2, 6.975, 8.0, and 6.96. What is her total score?
Answers
Explanation
Hope this helps!
FRUIT Lilly buys fresh fruit from a fruit stand. Apples cost $5 per pound and oranges cost $4 per pound. She has $40 to spend. The table shows the function relating the number of pounds of apples, x, and the number of pounds of oranges, y, Lilly could purchase.
Answers
Answer:
Step-by-step explanation:
8 lbs of apples on the x-intercept
10lbs of peaches on y-intercept
Simplify.
(–12x) ÷ (–2)
6x
12x
3x
112x
Answers
hope this helps. leave a comment if you have a question.
Hello there!
Question:-[tex]( - 12x) ÷ ( - 2)[/tex]
This is an algebraic expression.We need to find the result of it.
Solution:-[tex]\sf \longmapsto (- 12x) \div ( - 2)[/tex]
This algebraic expression may be rewritten as:-
[tex]\sf \longmapsto \: \dfrac{ - 12x}{2} [/tex]
Cancel the minus (-) sign:-
[tex]\sf \longmapsto \dfrac{ \cancel - 12x}{ \cancel - 2} [/tex]
Then,cancel 12 and 2 by 2, 12 ÷ 2 results 6. (Don't cancel x):-
[tex]\sf \longmapsto \: \dfrac{ \cancel {12}x}{ \cancel{2}} [/tex]
[tex]\sf \longmapsto6x[/tex]
Option A
______________________________________
Henceforth the value of the algebraic expression is:
[tex]\boxed{\boxed{\displaystyle \huge 6x}}[/tex]
Option A is correct!
______________________________________
I hope this helps!
Please let me know if you have any questions.
~MisterBrian
Which system of equations is equivalent to the following system? 2x 4y = 14 4x y = 20 2x 4y = 14 â’16x â’ 4y = â’80 2x 4y = 14 â’4x y = â’20 4x 8y = â’28 4x y = 20 â’2x â’ 4y = 14 4x y = 20.
Answers
The equivalent equations of [tex]2x+ 4y = 14[/tex] and [tex]4x + y = 20[/tex]
are [tex]2x+ 4y = 14[/tex] and[tex]-16x -4y = -80[/tex]
The system of equations is given as:
[tex]2x+ 4y = 14[/tex]
[tex]4x + y = 20[/tex]
Multiply both sides of the equations by -4.
So, we have:
[tex]-4 \times (4x + y) = -4 \times 20[/tex]
Distribute the expression
[tex]-4 \times 4x -4 \times y = -4 \times 20[/tex]
Evaluate all products
[tex]-16x -4y = -80[/tex]
So, we have the following system of equations
[tex]2x+ 4y = 14[/tex]
[tex]-16x -4y = -80[/tex]
Hence, the equivalent equations are [tex]2x+ 4y = 14[/tex] and[tex]-16x -4y = -80[/tex]
Read more about equivalent equations at:
https://brainly.com/question/9603710
Points A, B and C lie on a circle, centre O.
Angle AOC = 142°.
Find the value of y.
Answers
The value of y in the cyclic quadrilateral with ∠AOC(142°) is 38°
The diagram above represents a cyclic quadrilateral.
A cyclic quadrilateral has all it vertices on the circumference of the circle.
Therefore,
Opposite angles are supplementary. This means they add up to 180 degrees.
Therefore,
142° + y° = 180°
subtract 142 from both sides of the equation
142 - 142 + y = 180 - 142
y = 38°
learn more about circle theorem here: https://brainly.com/question/24795394
19. The passing marks in an examination is 40%. If Seema gets 130 marks, she fails by ups 2 marks. Find the total marks.
Answers
Given :-
Passing marks in an exam is 40% .Seema gets 130 marks and fails by 2 marks.To find :-
The maximum marks for the exam .Solution :-
According to the Question ,
[tex]\dashrightarrow[/tex] Passing marks = 40% .
[tex]\dashrightarrow[/tex] Seema's marks = 130 .
Let us take the maximum marks be x . Then ,
[tex]\dashrightarrow[/tex] Passing marks = 130 + 2
[tex]\dashrightarrow[/tex] Passing marks = 132
And , by question ,
[tex]\dashrightarrow[/tex] 40x/100 = 132
[tex]\dashrightarrow[/tex] x = 132 * 100/40
[tex]\dashrightarrow[/tex] x = 330
Hence the maximum marks for the exam is 330.
Given :
Passing marks in the examination = 40% . Marks obtained by Seema = 130 .So, Let us assume the maximum marks as x .
Also,
Passing marks = 132 [ ∵ Seema got 130 marks and she failed by 2 marks ]
According to the question :
[tex] \\ \tt : \implies\dfrac{40x}{100} = 132 \\ \\ \tt : \implies\dfrac{4 \cancel{0}x}{10 \cancel{0}} = 132 \\ \\ \: \: \: \tt \: : \implies 4x = 132 \times 10 \\ \\ \tt : \implies \: 4x = 1320 \\ \\ \tt : \implies \: x = \frac{1320}{4} \\ \\ \tt : \implies \: x = 330 \: \: \\ [/tex]
Hence, The total marks is 330 .
(1 x 3)+ (7 x 3) as a product of 2 factors
Answers
Answer:
3 + 21 = 24 and they are the product to the factors of 63
Step-by-step explanation: