Factorization is the process of breaking an integer down into its components or divisors, and further calculation can be defined as follows:
Given:
[tex]20x^{2} +124x+24[/tex]
To find:
solve the given problem
Solution:
[tex]\to \bold{20x^{2} +124x+24}\\\\\to \bold{4(5x^{2} +31x+6)}\\\\\to \bold{4(5x^{2} +31x+6)}\ \ \ \ \ \ \ \ \ \ \ 5\times 6= 30 \ \ and\ \ 30 \times 1= 30\\\\\to \bold{4(5x^{2} +(30+1)x+6)}\\\\\to \bold{4(5x^{2} +30x+1x+6)}\\\\\to \bold{4(5x(x +6)+1(x+6)}\\\\\to \bold{4((x +6) (5x+1)}\\\\[/tex]
Therefore, the final answer is "[tex]\bold{4((x+6)(5x+1))}[/tex]".
Learn more:
brainly.com/question/10755001
Solve y + 2∕7 < 1∕3.
Question 8 options:
A)
y > 13∕21
B)
y < 13∕21
C)
y < 1∕21
D)
y > –1∕21
Answer:
the answer is C y<1/21
Step-by-step explanation:
sorry if I did it wrong
Answer:
C) y< 1/21
Step-by-step explanation:
y+ 2/7 < 1/3
Subtract 2/7 from both sides.
y< 1/21
i don't know how to do math lol
Answer:
88 I think and if not that then 98 but I'm petty sure it's 88
Step-by-step explanation:
1,400,000
Would that be 1.4 x 10^5 or 1.4 x 10^6
Answer:
1.4 x 10^6
Step-by-step explanation:
A wholesale list of a watch is $50. A dealer bought a shipment of watches at a discount of 20% and sold the watches at 10% above the whole sale list price. What was the profit on each watch ?
have $100 in my bank account. I withdraw 10 dollars every week. If variable x represents number of weeks, write an algebraic expression that represents how much money would be in my bank account after x weeks.
Answer:
x+10=100
Step-by-step explanation:
I'm trying to find the explicit form of an equation after performing an integration. I'm a bit rusty.
ln|y| = C - cos(x)
C is an arbitrary constant.
Is it:
y = e^(c-cos(x))
or because it's an arbitrary constant, can it be written:
y = C - e^(cos(x))
Thanks.
No, it should be written as
[tex]y = Ce^{-\cos x}[/tex]
Provided that y ≠ 0, both solutions
[tex]y = e^{C-\cos(x)}[/tex]
and
[tex]y = Ce^{-\cos(x)}[/tex]
are correct. The other solution you provided,
[tex]y = C - e^{\cos(x)}[/tex]
is not.
The only difference between the "valid" solutions lies in the particular value of the arbitrary constant C.
Suppose y(0) = Y ≠ 0 is given as an initial condition. Then in the first solution,
[tex]Y = e^{C - \cos(0)} \implies \ln|Y| = C - 1 \implies C = \ln|Y| + 1[/tex]
In the second solution,
[tex]Y = C e^{-\cos(0)} \implies Y = Ce^{-1} \implies C = eY[/tex]
But both solutions are the same, since
[tex]y = e^{\ln|Y| + 1 - \cos(x)} = e^{\ln|Y|} e^1 e^{-\cos(x)} = eY e^{-\cos(x)}[/tex]
p/2 - 10 = -12 show work
Answer:
Step-by-step explanation:
solve and show steps :
9514 1404 393
Answer:
-(5√7 +9√35)/380
Step-by-step explanation:
The denominator is made rational by multiplying numerator and denominator by the conjugate of the denominator.
[tex]\dfrac{\sqrt{7}}{5-9\sqrt{5}}=\dfrac{\sqrt{7}}{5-9\sqrt{5}}\cdot\dfrac{5+9\sqrt{5}}{5+9\sqrt{5}}=\dfrac{5\sqrt{7}+9\sqrt{35}}{5^2-9^2\cdot5}=\boxed{-\dfrac{5\sqrt{7}+9\sqrt{35}}{380}}[/tex]
_____
Additional comment
This process takes advantage of the factoring of the difference of squares:
a² -b² = (a -b)(a +b)
The method is used to eliminate complex numbers and square roots from denominators.
Please assist with step by step
63 divided by 4
Find the solution(s) of the system of equations.
y = –x2 + 2
y = x2 + 4x + 4
What is 80% of 34? I’ve been struggling with percents
Answer:
27.2
Step-by-step explanation:
34x.80=27.2
Answer:
27.2 is the 80 % of 34, so if 34 is the whole then mutiply by .8
Mason is turning 5 years old next Saturday. He has picked sidewalk chalk and a helium balloon to give to each of his friends who come to his party. His dad
has a coupon for $10 off of any purchase over $25 at the party supply store. If sidewalk chalk cost $3.29 and balloons cost $1 each, how much did his dad pay
for the favors for 10 of Mason's friends and 1 of each for Mason as well?
Mason's dad paid $36.19 for the chalk and the balloons
Mason's dad paid $47.19 for the chalk and balloons,
Mason's dad paid $37.19 for the chalk and balloons.
Mason's dad paid $26.19 for the chalk and the balloons.
Tytoth
012
NEXT
SAVE & EXIT
BI
614 PM
10/24/2021
Answer:
dad paid 37.19
Step-by-step explanation:
What is the probability of getting a 6 on the first roll, and a number less than five on the second roll
Answer:
1/9
Step-by-step explanation:
Probability of getting 6 = 1/6
Probability of getting less than 5 = 4/6 = 2/3
1/6 * 2/3 = 1/9
show the solution 3x+7 ≤5x-9
1.1 Pull out like factors :
-2x + 2 = -2 • (x - 1)
2.1 Solve : -2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
2.2 Solve : x-1 = 0
Add 1 to both sides of the equation :
x = 1
x = 1
Answer:
[tex]3x + 7 \leqslant 5x - 9 \\ 5x - 3x \leqslant 7 + 9 \\ 2x \leqslant 16 \\ x \leqslant \frac{16}{2} \\ \boxed{x \leqslant 8}[/tex]
What is the answer to this question?
Answer:
20 3/4
Step-by-step explanation:
21 4/8 or 21.5- 3/4 or .75= 20.75 or 20 3/4
Answer:
look at the photo I have sent
Help me with maths .
Answer:
Step-by-step explanation:
m x n / p + (-n) =5 X 8 / -2 + (-8) =-20-8=-28
Use the point and the slope to graph each line. Write the equation of the line.
The line passes through point (4,0) and has slope 0.5.
Answer:
y=0.5x-4.5
Step-by-step explanation:
y=mx+b
Use the information provided to find b
0=0.5(4)+b
-2=b
Therefore, the equation goes down to...
y= 0.5x-2
Step-by-step explanation:
using the formula
m = y -y1/ x - x1
0.5 = y -0/x-4 (0.5 = 1/2)
1/2 = y/x -4
2y = x -4
divide both sides by 2
y = 1/2 ( x -4)
y = 1/2x - 2
y -1/2x = -2
How long will it take a train to travel 50 km at an average speed of 40m/s? Give your answer in minutes and seconds.
Answer:
20.8
if i'm wrong i'm rlly rlly sorry!!
slope 1/4 y intercept-5
slope int form: y=1/4x-5
Need help on this math problem
Answer:
the answer is 7 .......
ie .4^7
Answer:
4^7 is the answers for the question
Step-by-step explanation:
please mark me as brainlest
Factor the polynomial completely.
Q(x) = x^2 + 4x + 8
Answer:
Step-by-step explanation:
x²+4x+8
=x^2+4x+4-(-4)
=(x+2)²-(2 i)²
=(x+2+2i)(x+2-2i)
someone please answer!!
Answer: x=120 degrees
Step-by-step explanation: Since this triangle is equilateral, each of its angles equals 60 degrees. The line that x is on is equal to 180 degrees, so subtracting 60 from 180 will give you 120 degrees for x.
Answer:
x=180°-60°=120°, bc In an equilateral triangle, the angles are equal and equal to 60°
Step-by-step explanation:
There are two solutions, for a quadratic equation that represents the relation between distance and
time.
One of the solutions is positive and the other is negative.
If the values are associated with time, then we will choose
A the positive and the negative
solutions.
B the positive solution.
C neither the positive nor the.
D the negative solution.
Answer:
B. The Positive Solution
Step-by-step explanation:
Because Time is a positive quantity
Round 19.432 to the nearest whole
The nearest whole number is 20.
Answer:
19
Step-by-step explanation:
if the number was 19.5 or later up to 20 then the answer would have been 20
but your number was 19.432 which is less then 19.5 so the your answer is 19.
3 apples for $0.59 unit rate
Answer:
around .20 per apple
Step-by-step explanation:
HOW IS THE ANSWER 98 PLS HELP ASAP
Answer:
The answer is 98, here's how:
Step-by-step explanation:
Lets solve the numerator of the fraction first:
-[5.8 - 3(3.2)] =
-[5.8 - 9.6] =
-[-3.8] = 3.8 (Watch out for the double negative)
Now lets solve for the denominator :
(-0.2)² =
(-0.2)(-0.2) = 0.04
Lets simplify the fraction:
[tex]\frac{3.8}{0.04} = 95\\[/tex]
Let's add the 3 to 95:
95 + 3 = 98
-Chetan K
Step-by-step explanation:
[tex] \frac{ -[5.8 - 3(3.2)] }{{( - 0.2)}^{2} } + 3[/tex]
[tex]\frac{ -[5.8 -9.6] }{0.04 } + 3[/tex]
[tex]\frac{ -( - 3.8)}{0.04} + 3[/tex]
[tex]\frac{3.8}{0.04} + 3[/tex]
[tex] = 95 + 3[/tex]
[tex] = 98[/tex]
Maximize P=6x+11y using simplex where
4x+y is less than/equal to 8
x+4y is less than/equal to 12
and x is greater than/equal to 0 , y is greater than/equal to 0
9514 1404 393
Answer:
(x, y, P) = (4/3, 8/3, 112/3)
Step-by-step explanation:
In standard form, the constraints are all "less than or equal to", the variables are all non-negative, and the objective is maximization. This problem is presented in standard form.
4x +y ≤ 8
x +4y ≤ 12
x ≥ 0; y ≥ 0
maximize P = 6x +11y
__
Now we add the slack variables to make the constraints be "equal to". These have a coefficient of +1, and they, too, are non-negative. Here, we'll use s and t as the slack variables.
4x +y +s = 8
x +4y +t = 12
These equations, together with the objective function, are combined in a matrix-like "tableau" in which each row is the set of coefficients in one of the equations. Here, the columns represent x, y, s, t, P and the constants. The equation for the objective function is negated so we're trying to minimize that, as well.
[tex]\begin{array}{ccccc|c}4&1&1&0&0&8\\1&4&0&1&0&12\\-6&-11&0&0&1&0\end{array}[/tex]
Find the column with the most negative value on the bottom row. (Column 2) Divide the rightmost column by this column and find the smallest quotient. Here, the quotients are 8/1 = 8, and 12/4 = 3. The smallest is 3. This identifies the 4 in column 2, row 2 as the "pivot."
Now, row operations are performed to make the pivot be 1 and other values in the pivot column be zero. This gives a new tableau. For example, the new values in row 1 are ...
4 -1/4, 1 -4/4, 1 -0/4, 0 -1/4, 0 -0/4, 8 -12/4
The new tableau is ...
[tex]\begin{array}{ccccc|c}15/4&0&1&-1/4&0&5\\1/4&1&0&1/4&0&3\\-13/4&0&0&11/4&1&33\end{array}[/tex]
Now, the most negative number on the bottom row is in column 1, and the smallest quotient of column 6 and column 1 is in row 1. This makes 15/4 the "pivot". After the required row operations, the next tableau is ...
[tex]\begin{array}{ccccc|c}1&0&4/15&-1/15&0&4/3\\0&1&-1/15&4/15&0&8/3\\0&0&13/15&38/15&1&112/3\end{array}[/tex]
All values in the last row are non-negative, so we are finished. The rightmost column tells us the values of x, y, P that are the solution to the problem
(x, y, P) = (4/3, 8/3, 112/3)
__
The graphical solution confirms the Simplex solution.
Product of (8.6×10^2)(3×10^2)in scientific notation
Answer:
in scientific notation = 2.58 × 10⁵
I hope I helped you^_^
(7 pts) A school has 400 feet of fencing to build a set of 3 athletic fields as shown below. What dimensions
should they use to build the largest possible athletic complex? Include appropriate units with your answer.
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Answer:
Step-by-step explanation:
the side lengths are (400 - 4x)/2 = 200 - 2x
A = x(200 - 2x)
A = 200x - 2x²
Maximum area will occur when the derivative is set to zero.
dA/dx = 200 - 4x
0 = 200 - 4x
x = 200/4 = 50 ft
each field will be 50 x 33⅓ ft.
total area will be 5000 ft²
Which is not very big for a sports complex. I've owned houses with more floor space than that.
(1 point)
7. The students in Mr. Collin's class used a surveyor's measuring device to find the angle from
their location to the top of a building. They also measured their distance from the bottom of the
building. The diagram shows the angle measure and the distance.
Building
To the nearest foot, what is the height of the building?
A. 239 ft
B. 154 ft
C. 67 ft
D. 33 ft