5y³(y-2)-15y(y-2)
= (y-2)×(5y³-15y)
Max w = 5y1 + 3y2
s. a.
y1 + y2 ≤ 50
2y1 + 3y2 ≤ 60
y1
, y2 ≥ 0
The maximum value of the objective function is 330
How to maximize the objective function?The given parameters are:
Max w = 5y₁ + 3y₂
Subject to
y₁ + y₂ ≤ 50
2y₁ + 3y₂ ≤ 60
y₁ , y₂ ≥ 0
Start by plotting the graph of the constraints (see attachment)
From the attached graph, we have:
(y₁ , y₂) = (90, -40)
Substitute (y₁ , y₂) = (90, -40) in w = 5y₁ + 3y₂
w = 5 * 90 - 3 * 40
Evaluate
w = 330
Hence, the maximum value of the function is 330
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Which of the following theorems verifies that AKML AOPQ?
The theorem that verifies that the two right angled triangles are similar is HA.
What are similar triangle?Two triangles are said to be similar if the ratio of their corresponding sides and the corresponding angles are equal.
Analysis:
From the diagrams KL = OQ ( hypotenuse)
∠L is equal to ∠Q which are acute.
so the two triangles are similar in hypotenuse and acute angle which is the HA theorem.
In conclusion, the HA theorem verifies that the two triangles are similar.
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A study was conducted on the year and the number of honeybees in a beekeeper’s hive. After using the averaging method for the line of best fit, the two representative points found were (10, 250) and (20, 500). What is true about the line of best fit for this data? Select all that apply.
-The estimated slope is 25.
-The y-intercept is 0.
-The equation for the line of best fit of this data is y = 25x.
-The equation for the line of best fit of this data is y = -25x.
-The line passes through the two representative data points but may or may not pass through any of the data points.
The correct answer is option 3 which is the equation for the line of best fit of this data is y = 25x.
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
Given that:-
A study was conducted on the year and the number of honeybees in a beekeeper’s hive. After using the averaging method for the line of best fit, the two representative points found were (10, 250) and (20, 500).The equation of the line will be calculated as:-
The intercept of the line will be;-
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{500-250}{20-10}=25[/tex]
The equation of the line is given as:-
y - y₁ = m( x - x₁ )
Putting the coordinates:-
y - 250 = 25 ( x - 10 )
y - 250 = 25x - 250
y = 25x
Therefore the correct answer is option 3 which is the equation for the line of best fit of this data is y = 25x.
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Find the value of x.
55
X
44
X = [?]
Enter the number that belongs in
the green box.
Answer:
Step-by-step explanation:
x^2 + 44^2 = 55^2
x^2 + 1936 = 3025
3025-1936 = 1089
sqrt(1089) = 33
x = 33
Answer:
X=33
Step-by-step explanation:
this is a right traingle so you can use pythagorean theorem
A^2 +B^2 =C^2
A^2 +44^2= 55^2
A^2 + 1936= 3025 subtract 1936 from both sides
A^2= 1089 now square root both sides
A=33
he triangle on the grid will be translated two units down. On a coordinate plane, triangle A B C has points (2, 1), (0, negative 1), (2, negative 1). Which shows the triangle when it is translated two units down? On a coordinate plane, triangle A prime B prime C prime has points (0, negative 1), (0, negative 3), (2, negative 3). On a coordinate plane, triangle A prime B prime C prime has points (0, 1), (negative 2, negative 1), (0, negative 1). On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 3). On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 1).
If these coordinates are translated two units down, we will subtract 2 units from the y axis to have A(2, -1), B(0, -3) and C(2, -3)
Translation of coordinate pointTranslation is a transformation technique of changing the position of an object on the xy-plane.
Given the following coordinate of a triangle expressed as:
A(2, 1)
B(0, -1)
C(2, -1)
If these coordinates are translated two units down, we will subtract 2 units from the y axis to have:
A(2, -1)
B(0, -3)
C(2, -3)
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In how many ways can 3
person study groups be
selected from a class of 25
students?
Note: Cr
n!
r!(n-r)!
n
www
Enter
Work Shown:
[tex]_{n} C _{r} = \frac{n!}{r!(n-r)!}\\\\_{25} C _{3} = \frac{25!}{3!*(25-3)!}\\\\_{25} C _{3} = \frac{25!}{3!*22!}\\\\_{25} C _{3} = \frac{25*24*23*22!}{3!*22!}\\\\ _{25} C _{3} = \frac{25*24*23}{3!}\\\\ _{25} C _{3} = \frac{25*24*23}{3*2*1}\\\\ _{25} C _{3} = \frac{13800}{6}\\\\ _{25} C _{3} = 2300\\\\[/tex]
Write a multiplication expression to represent the number of table tennis balls in one layer of the box
Answer:
I believe I found your question, I hope this helps.
Step-by-step explanation:
Evaluate the expression shown below and write your answer as a fraction in simplest form. 16/11 − 12/1
Answer:
-10 6/11
Step-by-step explanation:
16/11−12/1=16/11+−12/1=16/11+−132/11=16+−132/11=−116/11
-116/11 = −10 6/11
Which function is represented by the graph?
Answer:
square root function; y = -√(x + 2) - 1
Step-by-step explanation:
the graph shown is a square root function
the parent of a square root function is y = √x
you transform this equation using y = a√(x - h) + k
it is reflected across the x axis so you put the negative before the a
since there is no dilation the a is blank
y = -√(x - h) + k
the h is the horizontal shift
it went 2 to the left so that is -2
that makes it y = -√(x - -2) + k
which is also y = -√(x + 2) + k
the k is the vertical shift
it went 1 down
that makes it y = -√(x + 2) - 1
that is your equation
If you want a fun mathematical challenge, then click me!
Answer:
0.2
It was fun!
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Is the graph increasing, decreasing, or constant?
Answer:
increasing to the certain point
Step-by-step explanation:
Potato head
Mean Calculations Q3: The mean of 8 numbers is 14. What is the total of the numbers? 84 1.75 112 22
Answer:
84.
Step-by-step explanation:
mean = total of the values / number of numbers
If the total of the numbers = T:
14 = T / 8
T = 8*14 = 84.
Ryan is on a game show. He will choose a box to see if he wins a prize. The odds in favor of Ryan winning a prize are 5/7.
Find the probability of Ryan winning a prize.
The probability of Ryan winning a prize would be 0.71.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Ryan is on a game show. He will choose a box to see if he wins a prize.
The odds in favor of Ryan winning a prize are 5/7.
P(Ryan wins a prize) = 5/7 = 0.71
Thus, the probability of Ryan winning a prize would be 0.71.
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Given that ƒ(x) = 3x, identify the function g(x) shown in the figure.
We will see that g(x) is a reflection across the y-axis of f(x), then:
[tex]g(x) = f(-x) = 3^{-x\\[/tex]
How to identify the function g(x)?By looking at the graph, we can see that g(x) is a reflection across the y-axis of f(x).
So we can write:
g(x) = f(-x)
Here we know that:
[tex]f(x) = 3^x[/tex]
Then, replacing f(x) on the formula for g(x), we get:
[tex]g(x) = f(-x) = 3^{-x\\[/tex]
That is the function g(x) shown in the figure.
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Work out the coordinate of R
Answer:
The problem is with the arrangement of the ratios
PQ is the whole line but PR is a part of it only so you need QR to the ratio of PR
Answer:
[tex]\huge{\red{ R=\bigg(-1.5,\: 2\bigg)}}[/tex]
Step-by-step explanation:
Coordinates of the extreme points of the segment are P(-4, -1) and Q (6, 11)[tex]\implies x_1= -4,\:y_1=-1,\:x_2=6,\:y_2=11[/tex]PQ = 4PR (Given)......(1)PQ = PR + RQ.....(2)-> 4PR = PR + RQ [From (1) and (2)]-> 4PR - PR = RQ-> 3PR = RQ-> PR/RQ = 1/3-> PR : RQ = 1 : 3This means point R divides segment PQ in the ratio 1 : 3.-> m : n = 1 : 3Now, coordinates of point R can be obtained by the section formula for internal division, which is given below:[tex]R=\bigg(\frac{mx_2+nx_1}{m+n},\:\frac{my_2+ny_1}{m+n}\bigg)[/tex][tex]\implies R=\bigg(\frac{1(6)+3(-4)}{1+3},\:\frac{1(11)+3(-1)}{1+3}\bigg)[/tex][tex]\implies R=\bigg(\frac{6-12}{4},\:\frac{11-3}{4}\bigg)[/tex][tex]\implies R=\bigg(\frac{-6}{4},\:\frac{8}{4}\bigg)[/tex][tex]\implies\huge{\red{ R=\bigg(-1.5,\: 2\bigg)}}[/tex]The drama club meets in the school auditorium every 8 days, and the choir meets there every 6 days. If the groups are both meeting in the auditorium today, then how many days from now will they next have to share the auditorium?
You need to find the least common multiple of 8 and 6.
[tex]8=2^3\\6=2\cdot3\\\\\text{lcm}(8,6)=2^3\cdot3=24[/tex]
Therefore, the answer is 24 days.
Work out the length of x
Answer:
x = 25Step-by-step explanation:
we are given a right triangle and the measure of its two legs .
x represents the length of the hypotenuse.
……………………………………………………………………
Then (by applying the Pythagorean theorem) we obtain :
[tex]x=\sqrt{24^{2}+7^{2}}[/tex]
[tex]=\sqrt{576+47}[/tex]
[tex]=\sqrt{625}[/tex]
[tex]=25[/tex]
SOMEONE
HELP MEE
What are the y-intercept and the asymptote of g(x) = 2x – 3?
The y-intercept of g(x) is (0, -3) and there are no asymptotes for g(x).
The function is given as g(x) = 2x - 3 and we need to find the y-intercept and the asymptote of this function g(x).
What are the y-intercept and asymptotes of a given function?Y-intercepts of a given function are the points on the y-axis that the given function passes through.
In y-intercept points we always have x=0.
Asymptotes are straight lines on the graph that meets the given function as it moves towards infinity.
Asymptotes occur only when the given function is a rational function or when one term of the function approaches zero as one term approaches infinity.
Find the y-intercept of g(x).
We have,
g(x) = 2x - 3
Since x = 0.
we get,
g(x) = 0 - 3
g(x) = -3 or y = -3
Thus the y-intercept of g(x) is (0, -3)
Find the asymptotes of g(x).
We see that g(x) is not a rational function and when x approaches infinity g(x) does not approach zero.
Hence we can say that g(x) has no asymptotes.
The y-intercept and asymptotes of g(x) are (0, -3) and no asymptotes.
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To find the y-intercept of g(x), we set x = 0 and solve for y:g(0) = 2^0 - 3 = -2Therefore, the y-intercept of g(x) is (0, -2).To find the asymptote of g(x), we take the limit of g) as x approaches negative or positive infinity:lim x→-∞ 2^x - 3 = -3 (the asymptote is y = -3 as x approaches negative infinity)lim x→+∞ 2^x - 3 = +∞ (the graph of g(x) goes arbitrarily high as x approaches positive infinity, so there is no horizontal asymptote)Therefore, the asymptote of g(x) is y = -3.
Please help me, thanks if it’s right!!
Answer:
[tex]11x - 4[/tex]
[tex]11x {}^{1 - 1} [/tex]
[tex]11x {}^{0} [/tex]
[tex]11 \times 1[/tex]
[tex]x = 11[/tex]
(Image: Start Fraction x over 4 End Fraction) + 2 = –2
If the linear equation with one variable is x / 4 + 2 = –2. Then the value of x will be negative 16.
What is simplification?Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The equation is given below.
x / 4 + 2 = –2
Solving for x, we have
x / 4 + 2 = –2
x / 4 = – 2 – 2
x / 4 = – 4
x = – 4 × 4
x = – 16
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Find the surface area of the shape below. Round your answer to two decimal places.
The surface area of the given shape is 285.01 ft²
Surface area of a coneFrom the question, we are to calculate the surface area of the given shape.
The given shape in the diagram is a cone.
The surface area of a cone is given by the formula,
[tex]S = \pi r(r+l)[/tex]
Where S is the surface area
r is the radius
and [tex]l[/tex] is the slant height
First, we will calculate the slant height of the cone
[tex]l^{2}=9^{2} +5.6^{2}[/tex] (Pythagorean theorem)
[tex]l^{2}=81+31.36[/tex]
[tex]l^{2}=112.36[/tex]
[tex]l}=\sqrt{112.36}[/tex]
[tex]l=10.6 \ ft[/tex]
∴ The slant height is 10.6 ft
Now, for the surface area
[tex]S = \pi \times 5.6(5.6+10.6)[/tex]
[tex]S = \pi \times 5.6(16.2)[/tex]
[tex]S = 90.72\pi \ ft^{2}[/tex]
[tex]S = 285.0053 \ ft^{2}[/tex]
S ≅ 285.01 ft²
Hence, the surface area of the given shape is 285.01 ft²
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triangle ABC is translated 6 units to left and 1 unit up to create ABC
Answer:
10
Step-by-step explanation:
need help with this graphing question please
Step-by-step explanation:
12 . The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations..
Four students were discussing how to find the unit rate for a proportional relationship. Which method is valid? “Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the unit rate.” “Look at the graph of the relationship. Count the number of units up and the number of units to the right one must move to arrive at the next point on the graph. Write these two numbers as a fraction.” “Look at the graph of the relationship. Find the x-value of the point that corresponds to y = 2. That value is the unit rate.” “Look at the graph of the relationship. Find two points which have y-values that are one unit apart. The unit rate is the difference in the corresponding x-values.”
The correct answer is: [A]: " Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1 . That value is the unit rate."
What is y-value?The vertical value in a pair of coordinates. How far up or down the point is. The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5). Also called "Ordinate".
Here, The "y-axis" is located on the "vertical axis" that represents the "dependent variable" (or, at times, the "control value") that cannot be "manipulated" / controlled/ or "selected" / since it represents the "y-value" of the corresponding coordinate to which the "x-value" happens to corresponds to at the given value for "x" .
Thus, the correct answer is: [A]: " Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1 . That value is the unit rate."
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Determine the vertex form of g(x) = x^2 + 2x – 1. Which graph represents g(x)?
Answer:
Graph D
Step-by-step explanation:
Move the constant to the opposite side of the equation and group terms that include the same variable.
g(x) + 1 = x^2 + 2x
Finish the square. Remember to keep the equation balanced by using the same constants on both sides.
g(x) + 1 + 1 = x^2 + 2x + 1
g(x) + 2 = x^2 + 2x + 1
Rewrite as perfect squares
g(x) + 2 = (x + 1)^2
Equation in vertex form:
g(x) = (x + 1)^2 - 2
The vertex:
(-1, -2)
* This a minimum *
(Parabola open upward) If a scale factor is less than 1, then your figure gets.
Answer:
if a scale factor is less than 1 then your figure gets smaller
Step-by-step explanation:
Find the missing side of this right triangle.
30
X
[?]
X = 1
Enter the number that belongs in the green box.
Answer:
909
Step-by-step explanation:
sqrt(30² + 3²) = x
hence the number in the box should be 909
Answer:
909
Step-by-step explanation:
Using pythagoras theorem :
a² + b² = x²
30² + 3² = x²
900+9 = x²
909 = x²
x = √909
Hence the number in the box should be 909
Hope this helped and brainliest please
Which of these steps will eliminate a variable in this system?
4x - 9y = 8
2x + 3y = 24
A. Multiply the first equation by 3. Then subtract the second equation from the first.
B. Multiply the second equation by 2. Then add the equations.
C. Multiply the second equation by 2. Then subtract the second equation from the first.
D. Multiply the second equation by 3. Then subtract the second equation from the first.
Answer:
option c is correctStep-by-step explanation:
for any variable to be eliminated in a simultaneous equation, the one of the coefficients must be the same in the two equations. and:
FOR OPTION A
if the first equation is multiplied by 3 , we will be having 12x-27y= 24 as the new equation 1 and since the cofficient of y or x are different in equation 1 and 2, no variable can be eliminated.
FOR OPTION B
if the second equation is multiplied by 2, our new equation 2 will be 4x+6y= 48. here, the cofficient of x in the two equations are now the same but since we're going to add, 4x+4x = 8x which does not eliminate x
FOR OPTION C if the second equation is multiplied by 2, our new equation 2 becomes 4x + 6y= 48 and if we subtract, 4X-4x= 0 so we have eliminated X ( option C is correct)FOR OPTION D
if the second equation is multiplied by three, our new equation 2 becomes 6x+9y= 72 and subtracting,-9y -9y= -18y which does not eliminate y
PLEASE ANSWER FAST URGENT!!!! (BRAINLIEST WILL BE GIVEN)
Answer:
1 - 135
2 - 45
3 - 45
4 - 135
5 - 135
6 - 45
7 - 45
8 - 135
Which best tells how heavy a dog might be?
A dog is shown.
A.
100 g
B.
25 kg
C.
25 g
D.
100 kg
Answer:
B
Step-by-step explanation:
A dog might be around
b) 25 kgs