Answer:
Step-by-step explanation:
Firstly, I believe that the equation should be represented as [tex]8x^{3} -6x^{2} y^{2} +4x^{2}y[/tex] and [tex]2x^{2} .[/tex] Please correct me if I am wrong and I will fix the equation accordingly.
To find the greatest common factor of this equation, we firstly need to factor the polynomial [tex]8x^{3} -6x^{2} yx^{2} +4x^{2} y[/tex]. To do this:
1. Find a GCF for all of the coefficients of the equation. To do this, you can make factor trees, or you can simply just use the prime factorization method.
The prime factorization method is simply a technique used to list the prime numbers used to find the total value. For example, what two prime numbers do you multiply to get four? 2 and 2. 2 is a prime number.
The prime factorization for each of the coefficients is as follows.
8: 2³
6: 2 · 3
4: 2²
We have 2s as values in every prime factorization, but we only one of each. We must take the greatest common value, and 2 is this value. So, our GCF coefficient is 2.
Now, we look at our x variables and y variables.
For x, we have x³ and x². So, our GCF is x².
Our GCF is now 2x². Now, let's look at our y-variables.
We don't have y variables for our entire polynomial, so it can't be a common factor. Therefore, our GCF is 2x².
Retro Recyclers processes used plastics into milk containers and soda containers. The recycling plant can process up to 2000 tons of plastic a week. At least 900 tons must be processed for milk containers and at least 600 tons must be processed for soda containers. Retro earns $35 per tons for milk containers and $28 per ton for soda containers. Retro wants to figure out how many tons of plastic should be allocated for milk containers and how many tons for soda containers in order to maximize its weekly profit.
Define the variables, write the constraints, and write the objective function for this situation.
Answer:
Objective function:
Maximize profit P = [tex]35x+28y[/tex]
subject to following constraints:
[tex]x\geq 900\\y\geq 600[/tex]
[tex]x+y\leq 2000\\x\geq 0\,,\,y\geq 0[/tex]
Step-by-step explanation:
Given: The recycling plant can process up to 2000 tons of plastic a week. At least 900 tons must be processed for milk containers and at least 600 tons must be processed for soda containers.
Also, Retro earns $35 per tons for milk containers and $28 per ton for soda containers.
To find: objective function for the given situation
Solution:
Let x tons be used to make a milk container and y tones be used to make a soda container.
As at least 900 tons must be processed for milk containers and at least 600 tons must be processed for soda containers,
[tex]x\geq 900\\y\geq 600[/tex]
Also, as the recycling plant can process up to 2000 tons of plastic a week,
[tex]x+y\leq 2000[/tex]
Also, [tex]x\geq 0\,,\,y\geq 0[/tex]
Objective function:
Maximize profit P = [tex]35x+28y[/tex]
A bag contains four yellow jerseys numbered one to four. The bag also contains three purple jerseys numbered one to three. You randomly pick a jersey. It is purple or has an even number.
A.0.714 B:0.727 C:0.778 D:286
Answer:
6/7
Step-by-step explanation:
Total number of jerseys = 4 + 3 = 7
Now, the probability of picking a purple Jersey = number of purple jerseys/total number of jerseys = 3/7
Now let’s look at picking a jersey with even number
Even number jerseys are yellow two and yellow four and also purple two
So we have 3 even numbered jersey. The probability of picking an even numbered jersey is 3/7
In probability, once we have or, we add
The probability of picking an even numbered jersey or a purple jersey = 3/7 + 3/7 = 6/7
A rectangle has an area of k2 + 19k + 60 square inches. If the value of k and the dimensions of the rectangle are all natural numbers, which statement about the rectangle could be true? The length of the rectangle is k – 5 inches. The width of the rectangle is k + 4 inches. The length of the rectangle is k – 20 inches. The width of the rectangle is k + 10 inches.
Answer:
The width of the rectangle is k+4 inches
Step-by-step explanation:
you have [tex]k^{2}+19k+60[/tex] which can be factorized to (k+4)(k+15)
if the length of the rectangle is k-5 that would mean that we can write [tex]k^{2}+19k+60[/tex] as (k-5)n which we know is false, so the only one that applies is k+4
The true statement is:
"The width of the rectangle is k + 4"
Which statement is true?
Remember that for a rectangle of length L and width W, the area is given by:
A = L*W
So we want to factorize the area equation, which is a quadratic equation, into a product of two terms.
A = k^2 + 19k + 60
The two zeros are given by Bhaskara's formula:
[tex]k = \frac{-19 \pm \sqrt{19^2 - 4*1*60} }{2} \\\\k = \frac{-19 \pm 11 }{2}[/tex]
So we have two zeros, these are:
k = (-19 - 11)/2 = -15
k = (-19 +11)/2 = -4
So we can factorize the area as:
A = (k - (-15))*(k - (-4)) = (k + 15)*(k + 4).
From this, the only statement that can be true is:
"The width of the rectangle is k + 4"
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Square ABCD was translated using the rule (x, y) → (x – 4, y + 15) to form A'B'C'D'. What are the coordinates of point D in the pre-image if the coordinates of point D’ in the image are (9, –8)?
Answer:
D = (13, - 23 )
Step-by-step explanation:
Given the translation rule
(x, y ) → (x - 4, y + 15 )
To go in the reverse direction, that is image to original, then, reverse the operations in the translation rule.
(x , y ) → (x + 4, y - 15 ) , thus
D'(9, - 8 ) → D(9 + 4, - 8 - 15 ) → D(13, - 23 )
Answer:
(13,-23)
Step-by-step explanation:
DID IT ON EDGE 2020
A function models the growth of a sample starting with 40 bacteria with the ability to double every two hours. Which graph
models the function?
Answer:
The function is y = 40 * 2^(x/2)
The graph is in the image attached
Step-by-step explanation:
The function that models this growth is an exponencial function, that can be described with the following equation:
y = a * b^(x/n)
Where a is the inicial value, b is the rate of growth, x is the time and n is the relation between the time and the rate (the rate occurs for every two hours, so n = 2).
Then, using a = 40, r = 2 and n = 2, we have:
y = 40 * 2^(x/2)
If we plot this function, we have the graph shown in the image attached,
It is an exponencial graph, where the value of y increases very fast in relation to the increase of x.
Answer:
b
Step-by-step explanation:
edge2020
cos X +1 / cos X=40, find the value of cos square X +1/ cos square X
This is pseudo-trig. It has a trig function but it's irrelevant.
Let y = cos X
y + 1/y = 40
Squaring,
y² + 2(y)(1/y) + 1/y² = 1600
y² + 2 + 1/y² = 1600
y² + 1/y² = 1598
cos² X + 1/cos²X = 1598
Answer: 1598
what would be the answer???
Answer:
120
Step-by-step explanation:
The sum of the angles in a quadrilateral is 360 degrees
2t+t+2t+t = 360
6t = 360
Divide by 6
6t/6 = 360/6
t = 60
Angle Z = 2t
Angle Z = 2*60 = 120
Answer:
[tex]120 \: \: degrees[/tex]
Second answer is correct.
Step-by-step explanation:
The sum of the angles in a qudrilateral = 360°
[tex]t + 2t + t + 2t = 360 \\ 6t = 360 \\ \frac{6t}{6} = \frac{360}{6} \\ t = 60[/tex]
angle z
[tex]2t = 60 \times 2 \\ \: \: \: \: \: \: \: = 120[/tex]
make x the subject of the formula 6x+a=5(x+t)
Answer:
x= 5t - a
Step-by-step explanation:
6x + a = 5(x+t)
If you expand 5(x+t), you will get 5x + 5t
i.e. 6x + a = 5x + 5t
Add the additive inverse of 5x to both sides (The additive inverse of 5x is -5x)
i.e. 6x + a - 5x = 5x + 5t - 5x
x + a = 5t
Then, add the additive inverse of "a" to both sides (The additive inverse of a is -a)
i.e. x + a - a = 5t - a
x = 5t - a
Hope this helps!!!
find the measure of angle 3
please help !!
Answer:
∠3 = 140°
Step-by-step explanation:
∠4 = 40°
∠4 = ∠1 (vertical angles)
∠1 = ∠2 (alternate angles)
∠2 = 40°
So,
∠2+∠3 = 180 [Angles on a straight line add up to 180°]
40 + ∠3 = 180
∠3 = 180-40
∠3 = 140°
Answer:
Angle 3 = 140°
Step-by-step explanation:
Angle 4 is equal to 40° and on a flat surface of 180°, that is, the first horizontal line, angle A is equal to 140° because 180° - 40° = 140°. Angle A is congruent to angle 3, therefore, angle 3 is also 140°.
Which relationship describes angles 1 and 2?
Select each correct answer.
complementary angles
supplementary angles
vertical angles
adjacent angles
What is the midpoint of the segment shown below?
Answer:
C
Step-by-step explanation:
The length of the segment is 7
2-7/2 = -3/2
(1,-3/2)
angles M and N are supplementary find angle M if angle N=27
Answer:
153°
Step-by-step explanation:
Supplementary = 180 degrees
180 - 27 = 153 degrees
Answer:
153 degrees
Step-by-step explanation:
When two angles are supplementary, their angle measures must add up to 180 degrees. Therefore:
M+N=180
M+27=180
M=180-27=153
Hope this helps!
What is the solution to the following equation? 4(3x − 11) + 23 = 5x − 14 a 0 b 1 c 10 d 14
Answer:
b 1
Step-by-step explanation:
Find the value of x.
Please help
Answer:
x=5
Step-by-step explanation:
7/5=(2x-3)/x
5(2x-3)=7x
3x=15, x=5
Solve tan^2 theta + 1 = -2 tan theta on the interval 0° ≤ θ ≤ 360°.
Answer:
Step-by-step explanation:
[tex]tan^2 \theta+1=-2 \tan \theta \\tan^2 \theta +2 tan \theta +1=0\\(tan \theta+1)^2=0\\tan \theta=-1=-tan 45=tan (360-45)=tan 315\\\theta =315 ^\circ[/tex]
An investment group compares returns on an account
against the function represented in the table, where x is the
time in years and f(x) is the total return on investment.
Which describes the function over the interval given in the
table?
х
a decreasing quadratic function
an increasing quadratic function
a decreasing exponential function
an increasing exponential function
0
5
f(x)
10,000
12,201.90
14,888.64
22,167.15
10
20
Answer:
d
Step-by-step explanation:
edge2020
Option D is correct. The exponential function is increasing when time goes and the total return on investment.
What is exponential function?An exponential function is of the form aˣ where 'a' is the base of the function and 'x' is the power of the function.
What is quadratic function?A quadratic function is" a polynomial function with one or more variables in which highest exponent of variable is 2".
According to the question,
Let 'x' is the time in years and f(x) is the total return on investment. The below table shows the function over the interval.
x f(x)
a decreasing quadratic function 10,000
an increasing quadratic function 12,201.90
a decreasing exponential function 14,888.64
an increasing exponential function 22,167.15
Quadratic function f(x) = ax² +b x +c a > 0
A decreasing quadratic function is the vertex of the parabola lies on the axis parabola. The graph of the function is increasing at one side of the axis and decreases at other side of the axis. Clearly it shows as time in years change does not give maximum total return on investment.An increasing quadratic function the vertex of the parabola lies on the axis parabola. The graph of the function is increasing at one side of the axis and decreases at other side of the axis. Clearly it shows change in time in years does not give maximum total return on investment.Exponential function f(x) = a. bˣ +q
The exponential function is decreasing when a < 0 and 0 ≤ b < 1. Then the function f(x) is decreasing exponential function. Clearly it shows time goes, total return on investment is not maximum. The exponential function is increasing when a > 0 and b > 1. Then the function f(x) is increasing exponential function. Clearly it shows time goes, total return on investment is maximum.Hence, the exponential function is increasing when time goes and the total return on investment.
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Which expression is equivalent to (fg)(5)?
A: f(5) x g(5)
B: f(5) + g(5)
C: 5f(5)
D: 5g(5)
Answer:
f(5).g(5)
Step-by-step explanation:
(fg)=(f.g)
this is how it starts: (fg)(X)= f(x) [g(x)]
x=5
f(5).g(X)
if 24 students took a test and 18 passed how much percent passed?
Answer:
75%
Step-by-step explanation:
6 x 4 = 24 so we make 24 into a fraction 24/24, then we make 18 a fraction as well, 18/24, then we simplify 18/24 = 3/4 = 75%
Answer:
%75
Step-by-step explanation:
this question is solved by establishing the correct proportion
24 - 18
100 - ?
(100*18)/24 = 75
Find the upper bonds for the following lengths : a) 40cm measured to the nearest cm
B)82.8cm measured to the nearest tenth of a cm
Answer: a= 40.5 b= 82.85
Step-by-step explanation:
2 stacked cubed. One cube has side lengths of 24 inches, and the second cube has side lengths of 12 inches. What is the total volume of the cubes?
Answer:
15552 in^3
Step-by-step explanation:
Volume formula for a cube of side length s: V = s^3.
Then the total volume here is:
(24 in)^3 + (12 in)^3 = 15552 in^3
There are x candies in a box. 8 of the candies are caramel-flavored and rest of them are strawberry-flavored. If the probability of randomly selecting a strawberry-flavored candy from the box is 1/3, find the total number of candies in the box.
Answer:
The answer is: 12 total candies
Step-by-step explanation
c = caramel-flavored
s = strawberry-flavored
so if there are 1/3 strawberry-flavored so that means there are 2/3 caramel-flavored. we know there are 8 caramel-flavored so if 8 is 2/3 of all the candies that means 4 is how many strawberry-flavored we have 12 total candies.
Need help with this question
Answer: 30
Step-by-step explanation: To solve this problem, we're going to have to use the Pythagorean theorem...
a² + b² = c²
24² + 18² = c²
576 + 324 = c²
c² = 900
[tex]\sqrt{900}[/tex]
30
30 = c
I hope this helps!
HELP ASAPPPP !!!! NEED ANSWERS NOW!!
1. Find the other endpoint of the line segment with the given endpoint and midpoint.
Endpoint 1: (−10,6)
Midpoint: (7,−6)
2nd endpoint: (_____,____)
2. Find the other endpoint of the line segment with the given endpoint and midpoint.
Endpoint 1: (−1,0)
Midpoint: (−10,2)
2nd endpoint: (____,____)
Answer: 1. 2nd endpoint (24,-18) 2. 2nd endpoint: (-19,4)
Step-by-step explanation:
1. [tex]\frac{-10+x}{2}[/tex] = 7 x = 24
[tex]\frac{6+y}{2}[/tex] = -6 y= -18
2nd endpoint: (24,-18)
2. [tex]\frac{-1+x}{2}[/tex] = -10 x= -19
[tex]\frac{0+y}{2}[/tex] = 2 y= 4
Manish and Jhanavi each receive an equal bonus. Manish has 1/2 fraction of allowance as saving accounts , 1/4 of the fraction he spend at the mall. Jhanavi has 1/3 fraction of allowance as saving accounts , 3/5 of the fraction she spend at the mall. If the allowance of each is Rs. 2520,find the amount left with Manish and Jhanavi?
Answer:
Step-by-step explanation:
Manish:
[tex]Savings=\frac{1}{2}*2520\\\\= Rs.1260\\\\Amount spend at mall=\frac{1}{4}*2520\\\\=Rs.630[/tex]
Amount left with Manish = 2520 - (1260 + 630) = 2520 - 1890 = Rs. 630
Jhanavi:
Savings = (1/3) *2520 = Rs. 840
Amount spend at mall = (3/5) * 2520
= 3 * 504
= Rs. 1512
Amount left with Jhanavi = 2520 - (840 +1512) = 2520 - 2352
= Rs. 168
Hi...Could u plz help me...
Answer:
B and D I dont have time to explain
I am sorry.
Thanks for question
Solve the inequality
t/4>7
Answer:
t>28
hope this helps!
Step-by-step explanation:
t÷4 > 7
t÷4 (×4) > 7 (×4)
t > 28
Devin’s friend Ryan lives 2 blocks west and 5 blocks south of Devin. Devin’s friend Andy lives 7 blocks east and 2 block north of Devin. How far do Ryan and Andy live from each other?
Answer:
Answer:
Ryan and Andy live 11.4 blocks from each other.
Step-by-step explanation:Devin’s friend Ryan lives 2 blocks west and 5 blocks south of Devin.Position of Ryan on coordinate system: 2 blocks west (2 unit left from origin) = -2 5 blocks south (5 unit down) = -5Coordinate of Ryan: (-2,-5)Devin’s friend Andy lives 7 blocks east and 2 block north of Devin. Position of Andy on coordinate system: 7 blocks east (7 unit right ) = 7 2 block north (2 unit up) = 2Coordinate of Andy: (7,2)We need to find the distance of Ryan and Andy.
Answer:
C.) 11.4
Step-by-step explanation:
Just took the test on Edge 2020
Plz answer fast and help mr
Answer:
The median is 47
Step-by-step explanation:
that line in the middle of the box is directly on 47
Letters w, x, y, and z are angle measures. Lines r and s are intersected by line m. At the intersection of lines m and r, clockwise from the top, the angles are w, x, blank, blank. At the intersection of lines m and x, clockwise from the top, the angles are: 92 degrees, y, z, blank. Which should equal 92° to prove that r ∥ s? w x y z
Answer: Angle w and angle z should equal 92° to prove that r║s
Step-by-step explanation: Let us start by constructing the lines r and s, and then draw a transversal to intersect both lines as stated in the question. At the intersection of lines m and r, we have clockwise from the top angles w, x and the other two blank. This is as shown in the picture attached.
Also at the intersection of lines m and s, clockwise from the top, the angles are 92, y, z and a blank. This is also clearly marked in the picture attached.
If the two lines r and s are parallel, then it means;
(1) Angle 92 is equal to angle z (opposite angles are equal)
(2) Angle z is equal to the blank underneath angle x (corresponding angles on two parallel lines are equal)
(3) Angle 92 is equal to the blank underneath angle x (alternate angles on two parallel lines are equal)
(4) Angle 92 is equal to angle w (corresponding angles on two parallel lines are equal)
Therefore, of all four angles marked as w, x, y and z angles w and z should equal 92° to prove that line r is parallel to line s.
Answer:
Its W i took the test and got a 100
A taxi cab charges $1.75 for the flat fee and $0.25 for each mile. Write an in equality to determine how many miles Eddie can travel if he has $15 to spend. A. $1.75 + $0.25x ≤ $15 B. $1.75 + $0.25x ≥ $15 C. $0.25 + $1.75x ≤ $15 D. $0.25 + $1.75x ≥ $15
Answer:
A. $1.75 + $0.25x ≤ $15
Step-by-step explanation:
This is because if Eddie has 15 dollars, he can only use 15 dollars or less. So in this case, the inequality would have to be less than or equal to 15 dollars.
Eddie travel $1.75 + $0.25x ≤ $15 miles when he has $15 to spend.
Option A is the correct option.
Here,
Amount of flat fee of taxi cab = $1.75
Amount of charge for each miles = $0.25
The amount Eddie has to spent = $15
We have to find inequality relationship.
What is inequality?
The relationship between two values that are not equal is defined by inequalities.
Now,
Amount of flat fee of taxi cab = $1.75
Amount of charge for each miles = $0.25
The amount Eddie has to spent = $15
Let Eddie travel x miles.
Therefore, the total charge of taxi cab = $1.75 + 0.25x
And this amount should not exceed the $15 as it is the only amount Eddie has.
Hence the inequality relationship be,
$1.75 + 0.25x ≤ $15.
Option A is the correct option.
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