PLEASE HELP! Is the following trinomial factorable why or why not
h=-4(4t^(2)-9t+2)
Answers
Answer:
h = -4(t - 2)(4t - 1)Step-by-step explanation:
Given trinomial
h= -4(4t² - 9t + 2)Let's try to factor 4t² - 9t + 2
First find it's zeros:
t = (9 ± √9² - 4*4*2)/(2*4) t = (9 ± √81 - 32)/8t = (9 ± 7)/8t = 2 and t = 1/4So yes, it is factorable:
4t² - 9t + 2 = 4(t - 2)(t - 1/4)or4t² - 9t + 2 = (t - 2)(4t - 1)The given trinomial factored:
h = -4(t - 2)(4t - 1)Answer: Yes, this trinomial -4(4t² -9t + 2) is factorable.
It is h =(-4)(4t -1 )(t -2) converted from the explanation
[tex]y\ =\left(-4\right)\left(4x\ -1\right)\left(x\ -2\right)[/tex]
A graph of the equation is in the attachment. There are two equations, but only one graphed parabola because they are identical.
Step-by-step explanation: I am using x in place of t in this explanation, and leaving out the factored (-4) to simplify.
Using the systematic new AC Method to factor trinomials (Socratic Search) Starting with a quadratic equation in the form
y = ax² + bx + c
This involves converting the equation by multiplying the leading coefficient, a, times the constant, c
y =4x² –9x + 2
=4(x + p)(x + q)
Converted trinomial:
y' = x² –9x + 8
= (x + p')(x + q').
Here p' and q' will have the same – signs because the b term is negative and the c term is positive.
Factor pairs of ac = 8 are -1 and –8. This sum is –9 = b. Then p' = -1 and q' = -8.
Then divide the second factor by the original coefficient, 4.
Replacing the original leading factor (-4) the factored equation looks like
y = -4(4x - 1)(x - 2)
To solve for x
p =p’/a = ¼ or 4x - 1 = 0 4x = 1 x = ¹/₄
and
q ='q/a
= 8/4 = 2 OR x -2 = 0 x = 2
The second attachment shows some other ways to set up the equation without the (-4) to solve, and then replace that factor. You get the same values for x.
I hope this helps and is not too confusing. There may be other ways to factor this equation.
Related Questions
Round 6,532 to the nearest thousands
Answers
Answer:
7,000
Step-by-step explanation:
Answer:
7000
Step-by-step explanation:
the hundreds is 5 so the 6 is turned into a 7 and the rest become 0, 5 or more let it soar, 4 or less let it rest or something
Is x = 1/2 a solution of the equation above. 3( x + 1) = 3x
Answers
or,3(1/2 +1)=3/2
or,3/2+3=3/2
or,(3+6)/2=3/2
or,9/2=3/2
Helpppppp meeee please and thank you
Answers
Answer:
The bigger the number the more obtuse it is and the smaller the number is the more acute is
Step-by-step explanation:
X3+x2+x+1 by grouping
Answers
Answer:
[tex]x^3+x^2+x+1=\left(x+1\right)\left(x^2+1\right)[/tex]
Step-by-step explanation:
Given the expression
[tex]x^3+x^2+x+1[/tex]
Factorized by grouping
[tex]x^3+x^2+x+1=\left(x^3+x^2\right)+\left(x+1\right)[/tex]
Factor out x² from x³+ x²: x²(x+1)
[tex]=\left(x+1\right)+x^2\left(x+1\right)[/tex]
[tex]=\left(x+1\right)+x^2\left(x+1\right)[/tex]
Factor common term x+1
[tex]=\left(x+1\right)\left(x^2+1\right)[/tex]
Therefore, we conclude that:
[tex]x^3+x^2+x+1=\left(x+1\right)\left(x^2+1\right)[/tex]
Solve and check: 40 = 1.6(d - 2)
Answers
Step-by-step explanation:
40=1.6d-3.2
43,2=1.6d
27=d
A farmer plans to fence a rectangular garden next to a river. There will be no fence along the river side. Draw a picture of this situation. The pasture will contain 405,000 square meters. Find the dimensions of the garden that will require the least amount of fencing.
Answers
Answer:
x = 450 m
y = 900 m
P (min) = 1800 m
Step-by-step explanation:
Let´s call "x" and "y" de sides of the rectangular garden, y is the side parallel to the river ( that is it will be fenced only one )
Then:
2*x + y = P ( perimeter of the area)
And x * y = 405000 m²
y = 405000/ x
And P as a function of x is:
P(x) = 2*x + 405000/x
Tacking derivatives relative to x on both sides of the equation.
P´(x) = 2 - 405000/x²
P´(x) = 0 2*x² - 405000 = 0
x² = 202500
x = 450 m
And y = 405000 / 450
y = 900 m
And
P(min) = 2*450 + 900
P(min) = 1800 m
We know P is minimm at x =450 snce the second derivative of P
P´´(x) = 405000*2*x / x⁴ is always positive
3.5 as a mixed number.
Answers
Answer:
3 and 1/2
Step-by-step explanation:
Mixed numbers are numbers with one whole number and a fraction.
Answer:
3 1/2
Step-by-step explanation:
well 3.5 in fraction form is 3 1/2.
the 5 is the 1/2 because 5/10 is half of 10 an 5/10 is equivalent to 1/2 sooo
3 1/2
need the answer showing work thank you.
Answers
Answer:
6 without repetition
27 with repetition
Step-by-step explanation:
without repetition, you have 3 digits to choose from initially, then only 2, then only one, i.e.:
3×2×1 = 6
with repetition, you have 3 digits to choose from for every spot:
3×3×3 = 27
Group C
(4 x 6 = 2
17. If the cost of 8 book is Rs 520, find the cost of 10 books.
Answers
cost of 8 books = 520 AED
we can do this using direct proportion
8/520 , 10/x
(cross multiply
= 8x = 520 x 10
= 8 x 5200
x = 5200/8
x = 650 AED
therfore,
cost of 10 books is 650.
Select all the numbers that have an even number of factors.
8,9,15,16,25
Answers
The numbers having an even number of factors are 8 and 15.
What are factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
The given numbers are 8, 9, 15, 16, and 25.
Factors of 8 are 1, 2, 4, and 8.
Factors of 9 are 1, 3, 9.
Factors of 15 are 1, 3, 5, 15.
Factors of 16are 1, 2, 4, 8, 16.
Factors of 15 are 1, 5, 25.
Of which 1 and the number itself are improper factors.
learn more about factors here :
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45% of 45 is (Explain ur method)
Answers
Answer: 20.25
Step-by-step explanation: All you need to do is multiply 45 by 45%. 45% can be represented by 0.45, 45/100, or just 45%. You answer should be 20.25. Hope this helps!
45 percent of 45 is 20.25.
To calculate 45% of 45, we can multiply 45 by the decimal representation of 45%.
45% can be written as 0.45 (since percent means "per hundred" or "out of 100").
45 × 0.45 = 20.25
Therefore, 45% of 45 is 20.25.
To know more about percent, refer here:
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help ! need an explanation and answer!
Answers
Answer:
as below
Step-by-step explanation:
because the interior angles add up to 180 degrees.. you can solve this
180= 32 + 64 + x hmm
84 = x
so the last angle is 84° :)
as we know that the sum of three interiors angle = 180
Two angles are given 32 and 64
let the angles be a , b and c
A + B + C = 180
32 + 64 + C = 180
C = 180-96
C = 84
Hence the 3rd angle is 84
hope it helps u
A line passes through the points ( - 9, - 24) and (8, – 9).
Calculate the slope of the line. Write your answer as a fraction.
(If the slope is undefined, enter "DNE")
Answers
Answer:
15 / 17
Step-by-step explanation:
slope = (y2 - y1) / (x2 - x1)
= (-9 + 24) / (8 + 9)
= 15 / 17
Aboard 22 cm long is cut into two pieces. One piece is 4 cm longer than twice the length of the other piece. Find the length of each piece
Answers
Answer:
Length of one piece = 6 cm
Length of second piece = 16 cm
Step-by-step explanation:
Total Length of board = 22 cm
The board is divided into 2 pieces.
Let length of one piece = l
Length of second piece = 2l + 4
We need to find length of both pieces.
We can write the equation:
Total length = Length of one piece + Length od second piece
Putting values and finding length
[tex]22 = l+(2l+4)\\22=l+2l+4\\22=3l+4\\3l=22-4\\3l=18\\l=\frac{18}{3}\\l=6[/tex]
So, we get l= 6
Length of one piece = l =6 cm
Length of second piece = 2l + 4 = 2(6)+4 = 12+4 = 16 cm
Therefore,
Length of one piece = 6 cm
Length of second piece = 16 cm
1)! (b) Complete the table of values for y = 3x + 1.
Please help ❤️
Answers
Answer:
y = -2, 1, 4, 7 (in order)
Step-by-step explanation:
Plug in the value of x into the equation to find y.
For example for -1, plug in x as -1 into the equation.
y = 3(x) +1
y = 3(-1) + 1
y = -2
Similarly plug in the x to find the rest of the values for y.
The slope of the tangent line to the function f(x) = StartFraction 8 Over x minus 3 EndFraction at x = –5 is
–1.
Negative 1/8
1/8
8
Answers
determine whether (8,5 a solution of the equation y=15x-14)
Answers
Answer:
no, It isnt
Step-by-step explanation:
PLZ HELP WILL GIVE BRAINLEST
Answers
Answer:
it's the fourth one i did that assignment aswell
Organic apples
are priced at
$8.97 for 3 pounds. What is the
the price per pound?
Answers
Answer:
The answer is $2.99
Step-by-step explanation:
8.97/3=2.99
Answer:
the answer is 2.99
Step-by-step explanation:
because
8.97 divided by 3 = 2.99
may run 6 miles in 54 minutes how long will it take her to run 10 miles
Answers
Answer:
90 minutes or an hour and a half
Step-by-step explanation:
You need to find out how many minutes it takes her to run one mile, to do that you devide 54 by 6 and you get 9 minutes. Then you multiply the number of minutes per mile, 9, by 10 and you get 90 minutes.
How do you set up problem
Answers
Answer:
Solve one of the equations for one of the variables. Let's solve the first equation for y: ...
Step 2: Substitute that equation into the other equation, and solve for x. ...
Step 3: Substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.
Answer:
wdym? .................
To make a certain shade of paint, an
artist needs to mix yellow paint with
blue paint at a ratio of 3 to 5.
w
He needs 32 ounces of paint.
How much yellow paint should he buy?
Answers
5/6 divided by 2 1/6=
Answers
Answer:
(5 / 6) / 2 1/6 = 0.384615385
Step-by-step explanation:
Answer:0.2587 hope this helps you out. have a good day!
Step-by-step explanation:
PLEASE HELP Mrs. Felley has 64 student. 3/4 of her students made an A on their exam. How many of Mrs. Kelley's students made an A on their exam. How many of Mrs. Kelley's students made an A on their exam.
Answers
Answer:
.75 because
Step-by-step explanation:
3/4= 75%
75% divided by 100 = .75
Tyler ate x fruit snacks, and Han ate 3/4 less than that. Write an equation to represent the relationship between the number Tyler ate (x) and the number Han ate (y).
Answers
Answer:
0.75x = y
Step-by-step explanation:
The required expression represents the relationship between the number Tyler ate (x) and the number Han ate (y) is y = x/4.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
Tyler ate x fruit snacks, and Han ate 3/4 less than that
Let the snacks eaten by Han be y,
According to the question,
y = x - 3/4x
y = x/4
Thus, the required expression represents the relationship between the number Tyler ate (x) and the number Han ate (y) is y = x/4.
Learn more about equations here:
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Can someone answer me this? “Find f(2) if f(x) = x + 5
A) 2
B) 3
C) 7
D) 1
Answers
Could someone help with this math problem I will cashapp you !
Answers
Answer: 203.65
Step-by-step explanation:
subtract those checks from his starting balance
6.
It is given that at x = 1, the function x^4 - 62x^2 + ax + 9 attains its
maximum value on the interval [0, 2]. Find the value of a.
Answers
Answer:
The value of a is 120.
Step-by-step explanation:
Given function;
f(x) = x⁴ - 62x² + ax + 9
find the derivative of the function;
f'(x) = 4x³ - 124x + a
The function (f) attains its maximum value on the interval [0, 2], at x = 1.
f'(1) = 0
0 = 4(1)³ - 124(1) + a
0 = 4 - 124 + a
0 = -120 + a
120 = a
Thus, the value of a is 120.
13x - 12
B
E
(7x-6)
А
F
What is the value of x?
X=
Answers
Answer:
1
Step-by-step explanation:
13x-12=7x-6
Alright I really need help and this question is going to give you alot of ponits so let do it also its due in 20min!!!!!!! Ok so Five cats each ate 1/4 cup of canned food and 1/4 cup of dry food. How much food did they eat altogether? Please don't spam me and get the answer right because as soon as I get a reply then i will put that answer on the page