The correct answer is option A: the optimal corner point won't change.
The optimal corner point is the point where the objective function reaches its maximum value, with the constraints of the problem being satisfied. If the slope of the objective function stays between the slopes of the binding constraints, it means that the current optimal corner point will remain unchanged.
This is because if the objective function's slope is within the slopes of the binding constraints, then the set of points where the objective function reaches its maximum value will be the same. Therefore, the optimal corner point will not change.
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If an object is propelled upward from ground level with an initial velocity of 80. 1 feet per second? It’s height h in feet t seconds later is giving by the equation h= -16ft+ 80. 1t after how many seconds does the object hit the ground
The object will hit the ground after 5.01 seconds.
When an object is propelled upward from ground level with an initial velocity of 80.1 feet per second then its height h in feet t seconds later is giving by the equation,
h= -16t^2+ (80.1)t
When the object hit the ground, the height of the object h would be zero.
To find: time (t) when h = 0
Substitute h = 0 in given equation.
h = -16t^2+ (80.1)t
0 = -16t^2+ (80.1)t
16t^2 - (80.1)t = 0
t (16t - 80.1) = 0
t = 0 or 16t - 80.1 = 0
t = 0 OR t = (80.1)/16
t = 0 OR t = 5.01
Therefore, it will hit the ground after 5.01 seconds.
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Can U pls help me on this question
Answer:
25
Step-by-step explanation:
they are alternative exterior angles meaning they are equal.so you can solve by doing
7x-40=5x+10
isolate the terms by adding like terms. ( add 40 from the left side of the equation to the right.)
so it would look like this.
7x=5x+10+40. (the 40 was negative on the left side so you have to do the inverse to move it) do the same with the 5x.
now you have
2x=50. divide 50 by 2 to get your final answer .
2. Use the Pythagorean Theorem to find x. Show your work!
The value of x using Pythagorean theorem is 14.05 units
What is an equation?An equation shows how two or more numbers and variables are related to each other.
Pythagoras theorem shows the relationship between the sides of a right angled triangle. It is given by:
hypotenuse² = adjacent² + opposite²
In the diagram, using Pythagoras theorem:
22² = (x + 1)² + (x + 2)²
484 = x² + 2x + 1 + (x² + 4x + 4)
2x² + 6x + 5 = 484
2x² + 6x - 479 = 0
x = 14.05
The value of x is 14.05 units
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Cual es mayor 0.08 o 0.2
Answer:
0.2
Step-by-step explanation:
Answer:
0.2 es mayor.
Step-by-step explanation:
0.2>0.08
Jordan works for a landscape company during his summer vacation. He is paid $12 per hour for mowing lawns and $14 per hour for planting gardens. He can work a maximum of 40 hours per week, and would like to earn at least $250 this week. If m represents the number of hours mowing lawns and g represents the number of hours planting gardens, which system of inequalities could be used to represent the given conditions?
Answer:
m+g[tex]\leq[/tex]40
12m + 14g[tex]\geq[/tex]250
Step-by-step explanation:
Jordan is paid $12 per hour for mowing lawns and $14 per hour for planting gardens.
Let m represents the number of hours mowing lawns and g represents the number of hours planting gardens.
He can work a maximum of 40 hours per week, and would like to earn at least $250 this week.
Then, the system of the inequality becomes
m+g[tex]\leq[/tex]40
12m + 14g[tex]\geq[/tex]250
HELP DUE IN 15 MINS!
Determine if the figure is a parallelogram. Justify your answer by picking the property that verifies it is a parallelogram or the one the property that it fails to meet the criteria for.
1. Is the figure a parallelogram? Yes or No??
2. Why?? A. Both sets of opposite sides are parallel, B . Both Diagonals Bisect Each Other, C. Both sets of opposite sides are congruent, D. Both Pairs of opposite angles are congruent, E . One set of Opposite Sides are parallel and congruent.
Answer:
Yes and E
Step-by-step explanation:
What does Scrooge see out of the window when Marely leaves?
(A Christmas Carol) (it was an English question)
Scrooge sees out of his window when Marley's ghost leaves as all the spirits of people whom Scrooge has not met before in his life. Thus, option B is correct.
What is the ghost?Although ghosts are typically thought of as lone, human-like essences, and there have been reports of ghostly battalions, ghosts that resemble animals instead than people.
Here, we have,
Scrooge discovers "the air filled with phantoms" outside s windowsill after Marley's Apparition hath left it. Some of these imprisoned spirits were people Scrooge had indeed known. It resembles an incredible image of the metropolis that Scrooge has already been familiar with. Scrooge is compelled to agree.
Scrooge responds with the ghost's request to peek out just the balcony. He observes a mass of ghosts, each one imprisoned in bonds. As both they and Marley vanish into darkness, they sob at their failure to live noble, compassionate lives and their incapacity to help other people in need.
Therefore, option B is the correct option.
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15) 3x2 - x - 10 When this trinomial is factored completely, one of its factors is A) x 2 B) x - 5 C) 3x 5 D) 3x - 2
When the trinomial 3x² - x - 10 is factored completely, one of its factors is 3x+5.
Solving the given trinomial 3x² - x - 10.
=>3x² - 6x+5x - 10
=>3x(x-2)+5(x-2)
=>(3x+5)(x-2)
The two factors of the given trinomial 3x² - x - 10 is (3x+5) and (x-2), but according to the given options, the correct answer is option C - 3x+5.
Thus, When the trinomial 3x² - x - 10 is factored completely, one of its factors is 3x+5.
Complete question: 3x² - x - 10
When this trinomial is factored completely, one of its factors is
A) x + 2
B) x - 5
C) 3x + 5
D) 3x - 2
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Write an equation for the parabola that passes through (-2,7), (1, 10), and (2,27)
An equation for the parabola is y=.
Answer: To find an equation for a parabola that passes through three specific points, we can use the method of algebraic manipulation.
Since the parabola is symmetric about the y-axis, the equation of the parabola will have the form y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
Given three points (-2,7), (1, 10), and (2,27), we can use the vertex form of the equation and substitute the x, y values of the three points to find the values of a, h and k
y = a(x-h)^2 + k
Since it is passing through (-2,7), we can substitute the values of x and y in the equation and get
7 = a(-2 - h)^2 + k
It passing through (1, 10), we can substitute the values of x and y in the equation and get
10 = a(1 - h)^2 + k
It passing through (2,27), we can substitute the values of x and y in the equation and get
27 = a(2 - h)^2 + k
Now we have three equations with three variables, we can solve it using any of the techniques such as substitution, elimination or matrix. But the final equation will be in the form of y= a(x-h)^2 + k
Here, x= (-2, 1, 2) and y = (7, 10, 27) . Therefore it has a unique parabola passing through these points.
Step-by-step explanation:
PLEASE HELP ASAP I’LL MARK YOUR ANSWER BRAINLIEST!!!
Answer:
a = 1.5
VW = 9 ft
Step-by-step explanation:
Since the tangent lines connect both circles, we know that the line VU and VX are congruent (equal). Thus, we can set them equal to each other and solve for a:
a + 4 = a² + 0.25 Set equal
a² - a = 3.75 Isolate a values
a² - a + 0.25 = 3.75 + 0.25 Complete the square
(a + 0.5)² = 4 Factor
a + 0.5 = 2 Simplify
a = 1.5
Now we need to calculate VW, but thats easy because its equal to TV, and since we know a, we can just plug it in:
((1.5) + 7.5) ft
9 ft
A square table 4 feet on each side has two drop leaves, each a semicircle 4 feet in diameter.
a. Find the area of the table with and without the drop leaves
b. Find the perimeter of the table with and without the drop leaves
Answer:
hurry
Step-by-step explanation:
How do you solve this equation on surds?
Tammy has a rectangular rug with an area of 21 square feet. The rug is 4 feet longer than it is wide. Which equation can be
used to determine the length and the width of the rug?
A 21 - -W² - 4W
B. 21 = 42
C. 21 - W2 + 4w
D. 21 - W2 + 4
The equation to determine the length and the width of the rug is
21 = W² - 4W.
What is a rectangle ?A rectangle is a quadrilateral with four right angles in the Euclidean plane. It may alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.
A quadrilateral is a rectangle.
A rectangle's opposing sides are equal and parallel to one another.
Each vertex of a rectangle has a 90° internal angle.
360° is the total of all interior angles.
The diagonals cut each other in half.
The diagonals are all the same length.
The Pythagorean theorem may be used to determine the length of the diagonals.
A rectangle is also referred to as a parallelogram since its sides are parallel.
While all parallelograms are rectangles, not all rectangles are parallelograms.
The length of the rug is l ft
Then the width of the rug will be l-4 ft
So the are will be l*(l-4) = [tex]l\x^{2} - 4l[/tex]
We know area is 21
so the equation is 21 = [tex]l\x^{2} - 4l[/tex] (Option a)
And after solving the equation the lenght is7m and breadth is 3 m.
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Please answer all with explanation
Answer:
1:Exponents are not involved..try this 34% 1/2 + ==% 98) ::*37 21 /) ( ^ 11 56/77
2:make a little close parenthesis and make a little = and % x2 RX then multiply it 9 by 9
3:477/^54*(7632)**% 87÷32×(76*09×23) 2/8=97
4:9a/(92 28 ^^_× (32
Step-by-step explanation:
HOPE IT HELPS!!
11. Manuel has two different recipes for chocolate chip
muffins. The table shows the amount of chocolate chips
needed per batch for each recipe. He has 10 cups of
chocolate chips. The equation 2b = 10 can be used to
find b, the number of batches of muffins he can make if
he uses Recipe 1. Can Manuel make 3, 4, or 5 batches if
he uses Recipe 1?
n
JID
Recipe Chocolate Chips (cups)
1
2
2
1
Answer:
Manuel can make 5 batches of muffins using Recipe 1
Step-by-step explanation:
You want to know the value of b in the equation 2b = 10, where b is the number of batches of muffins Manuel can make using recipe 1.
SolutionDivide both sides of the given equation by 2 so solve for the value of b.
(2b)/2 = (10)/2
b = 5
Manuel can make 5 batches of muffins using Recipe 1.
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A scale model of a building is 16 inches long. The actual building is 62 feet long. In the model, the door is 2.4 inches tall. How tall is the actual door?
The scale model door of 2.4 inches is 9.3 ft tall in the actual building.
What is scaling?By scaling, we can create a drawing of an object that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape.
What is cross-multiplication?By multiplying the numerator of one fraction by the denominator of another and the first term's denominator by the numerator of another, we can do cross multiplication.
Given that:
16 inches = 62 ft
2.4 inches = x ft
To calculate the actual value cross multiply the values:
[tex]x= \frac{(62)(2.4)}{16} \\\\x= 9.3 ft[/tex]
Hence, the actual door is 9.3 ft tall.
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Janet decreased her daily carbohydrate intake from 80 grams to 50 grams. By what percent did Janet decrease the amount of carbohydrates she eats?
Answer:
12
Step-by-step explanation: i think
Alana and Petra go to a ued book ale , where every book i the ame price. Alana buy 4 book and Petra buy 2 book. They run into their friend angu, who really love to read, and dicover that he ha bought 16 book. Angu received a $15 dicount, but he till pent $5 more than Alana and Petra combined. How much doe one book cot?
A book cost $2.00.
What are variables in maths?In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.
What are the 2 basic types of variables?Variables may be classified into two main categories: categorical and numeric. Each category is then classified in two subcategories: nominal or ordinal for categorical variables, discrete or continuous for numeric variables.
Given the no of books purchased by
Alana =4
Petra =2
Angus = 16
So, the total price of 4 books of Alana =$4
Total price for Petra = $2
Total price of Alana and Petra =4x+2x
=6x
Total price for Angus = 16x
But given Angus received a discount of $15
So price post discount = 16x- 15
According to the question
16x-15 = 6x +5
Adding 15 both sides
16x +15-15 = 6x + 5+15
16x= 6x+20
Subtracting 6x both sides
16x - 6x = 6x - 6x + 20
10x = 20
i.e x=2
Cost of one book = $2
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45 students were divided into 4 teams for baseball. If teams were equal how many students were put on a team?
Answer:
11.25
Step-by-step explanation:
It says if the teams were equal, so divide 45/4 to get 11.25
Answer:
Step-by-step explanation:
11 students on each team
1 student is left out
11x4 = 44
when a 6ft tall fence pole casts a 10 ft shadow, a pine tree casts a 45 ft shadow. How tall is the tree?
Answer: The tree is 27 feet tall.
Step-by-step explanation:
Here's what we know:
6/10 = x/45 (a 6 foot object creating a 10 shadow is equivalent to something else making a 45 shadow)
We need to isolate x. Multiply both sides by 45:
6*45/10 = x
We can factor out a 2:
3*45/5 = x
We can also factor out a 5:
3*9/1 = x
27 = x
The tree is 27 feet tall.
a diagram shows a cube cut in half along one of its diagonal planes
each edge of the original cube has a length xcm
the diagonal y has a length 20cm
The length is 11.5 cm.
What is Pythagoras theorem?The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse
Given: diagonal = 20 cm
In ABC,
AC² = BC² + AB²
AC²= x² + x²
AC²= 2x²
AC= √2 x
IN ACF,
AF² = AC² +CF²
20²= 2x² + x²
400= 3x²
400/3= x²
x= 11.5
hence, length is 11.5 cm.
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What are the three types of dilation?
Enlargements of the picture or reductions of the image are both types of dilations.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.
A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.
The angles of the dilated picture relative to the pre-image stay constant, which is one of the primary characteristics of dilated images.
Even in the enlarged picture, parallel and perpendicular lines are still discernible.
A dilated image's side's midway matches the pre-exactly. image's
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The circumference is 79.5
Need help with finding the diameter and radius
Answer:
Step-by-step explanation:
[tex]C=\pi D[/tex]
[tex]79.5=\pi D\\[/tex]
divide by [tex]\pi[/tex]
D = 25.30
radius = [tex]\frac{d}{2}[/tex]
[tex]\frac{25.30}{2} =12.65[/tex]
Answer:
r approx 12.7
d approx 25
Step-by-step explanation:
hamza decides to increase the prices of all his item in his shop by 10 percent
workout the price of an item normally priced at 210 pounds
workout the new price of an item normally priced at 48 pounds
Answer:
231 and 52.8
Step-by-step explanation:
Given that
Hamza decided the price of the item would be increased by 10 percent
We need to find out the price that normally at 210 pounds and the price that normally at 48 pounds
So,
The price that normally at 210 pounds is
= 210 + 210 × 10%
= 210 + 21
= 231
And, the price that normally at 48
= 48 + 48 × 10%
= 48 + 4.8
= 52.8
simplify the expression below. (-5 × -4)÷(-3+5)
Answer:
-10
Step-by-step explanation:
Answer: =10
Step-by-step explanation: Hope this help :D
(-5)(-4)/-3+5
=20/-3+5
=20/2
=10
F= 5 9 (K−273)+32space, F, equals, start fraction, 9, divided by, 5, end fraction, left parenthesis, K, minus, 273, right parenthesis, plus, 32 In order to convert a temperature in Kelvin, KKK, into a temperature in degrees Fahrenheit, FFF, the equation above can be used. Which of the following equations correctly expresses the temperature in Kelvin in terms of the temperature in degrees Fahrenheit?
The formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]
The given expression:
[tex]F = \frac{9}{5} (K-273) + 32[/tex]
Conversion from Kelvin (K) to degrees Fahrenheit (F)To find the formula for K
The formula for K is obtained by making K the subject of the formula as shown below:
[tex]F = \frac{9}{5} (K-273) + 32[/tex]
subtract 32 from LHS.
[tex]F-32 = \frac{9}{5} (K-273)[/tex]
multiply 5 with LHS
[tex]5(F-32) = 9(K-273)[/tex]
Take numerator 9 to LHS
[tex]\frac{5}{9}(F-32) = K-273[/tex]
take -273 from RHS to LHS
[tex]\frac{5}{9}(F-32) + 273 = K[/tex]
Thus the formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]
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So we can say the the Volume of a Sphere is equal to 2 times the volume of a cone, or the Volume of a Sphere
Answer:
The Volume of a Sphere is equal to 2 times the volume of a cone.
Step-by-step explanation:
The volume of a sphere: 4/3 π r^3
The volume of a cone: 1/3 π r^2 h
r is the radius
h is the height
In this case, the height can be replaced by the 2r or the diameter, since it would correspond exactly to the height of the sphere of radius r.
So then,
sphere and cone
4/3 π r^3 1/3 π r^2 h
1/3 π r^2 * 2r
2/3 π r^3
Ratio sphere : cone
4/3: 2/3
2:1
Therefore the volume of the sphere is twice that of the cone or equal to twice the volume of the cone
Please help me solve the question
Answer:
Distributive propertyHope that helps! :)
-Aphrodite
Step-by-step explanation:
Answer:
D)
hope this helped
Step-by-step explanation:
Two numbers are in the ratio 7 : 4 . If their difference is 18, then find the numbers.
Answer:
x = 24
. So, first number = 7 * 24 = 168. and second number = 4 * 24 = 96. Therefore the numbers are 168 and 96.
Answer:
42 and 24
Step-by-step explanation:
The numbers in ratio 7 : 4 = 7x : 4x ( x is a multiplier ) , then
7x - 4x = 18 ( difference of 2 numbers is 18 )
3x = 18 ( divide both sides by 3 )
x = 6
Then
7x = 7 × 6 = 42
4x = 4 × 6 = 24
The numbers are 42 and 24
Megan was painting on a rectangular canvas, and needed a frame for it. The length of the frame is 15 inches and the width is 10 inches. What is the perimeter of the frame?
Answer:
50 inches
Step-by-step explanation:
Hi there!
[tex]P=2l+2w[/tex] where l is the length of the rectangle and w is the width of the rectangle
Plug in the length (15 inches) and width (10 inches)
[tex]P=2(15)+2(10)\\P=30+20\\P=50[/tex]
Therefore, the perimeter of the frame is 50 inches.
I hope this helps!