Let
x--------> the horizontal distance in feet
y--------> the vertical height in feet
we know that
The constraints are
1) [tex]y\geq 3x[/tex]
2) [tex]24\ ft\leq y \leq 33\ ft[/tex]
3) [tex]x\leq10 \ ft[/tex]
Let's verify each case to determine the solution to the problem.
case A) point [tex](0,33)[/tex]
Substitute the values of x and y in each of the constraints
constraint 1
[tex]33\geq 3*0[/tex]
[tex]33\geq 0[/tex] ---------> is true
constraints 2
[tex]24\ ft\leq 33 \leq 33\ ft[/tex]-------> is true
constraints 3
[tex]0\leq10 \ ft[/tex]--------> is true
therefore
the ordered pair [tex](0,33)[/tex] meet all the constraints for a successful launch
case B) point [tex](4,36)[/tex]
Substitute the values of x and y in each of the constraints
constraint 1
[tex]36\geq 3*4[/tex]
[tex]36\geq 12[/tex] ---------> is true
constraints 2
[tex]24\ ft\leq 36 \leq 33\ ft[/tex]-------> is not true
constraints 3
[tex]4\leq10 \ ft[/tex]--------> is true
therefore
the ordered pair [tex](4,36)[/tex] does not meet all restrictions for a successful launch
case C) point [tex](4.8,30.5)[/tex]
Substitute the values of x and y in each of the constraints
constraint 1
[tex]30.5\geq 3*4.8[/tex]
[tex]30.5\geq 14.4[/tex] ---------> is true
constraints 2
[tex]24\ ft\leq 30.5 \leq 33\ ft[/tex]-------> is true
constraints 3
[tex]4.8\leq10 \ ft[/tex]--------> is true
therefore
the ordered pair [tex](4.8,30.5)[/tex] meet all the constraints for a successful launch
case D) point [tex](9,26)[/tex]
Substitute the values of x and y in each of the constraints
constraint 1
[tex]26\geq 3*9[/tex]
[tex]26\geq 27[/tex] ---------> is not true
constraints 2
[tex]24\ ft\leq 26 \leq 33\ ft[/tex]-------> is true
constraints 3
[tex]9\leq10 \ ft[/tex]--------> is true
therefore
the ordered pair [tex](9,26)[/tex] does not meet all restrictions for a successful launch
case E) point [tex](2,22)[/tex]
Substitute the values of x and y in each of the constraints
constraint 1
[tex]22 \geq 3*2[/tex]
[tex]22\geq 6[/tex] ---------> is true
constraints 2
[tex]24\ ft\leq 22 \leq 33\ ft[/tex]-------> is not true
constraints 3
[tex]2\leq10 \ ft[/tex]--------> is true
therefore
the ordered pair [tex](2,22)[/tex] does not meet all restrictions for a successful launch
the answer is
[tex](0,33)[/tex]
[tex](4.8,30.5)[/tex]
Answer:
The ordered pairs that meet all the constraints for a successful launch and make sense in context of the situation are:
(0,33) and (4.8,30.5)
Step-by-step explanation:
Here x represent the horizontal distance and y represent the vertical distance.
From the given information in the question we can make the following inequalities:
The rocket must reach a height of at least 24 ft and must go a horizontal distance of no more than 10 ft.y ≥ 24
and x ≤ 10
The vertical height must be at least three times as high as the horizontal distance.i.e. y ≥ 3x
No rocket should go higher than 33 ft.i.e. y ≤ 33
Hence, after combining all the inequalities we have:
x ≤ 10
24 ≤ y ≤ 33
and y ≥ 3x
1)
(0, 33)
As (0,33) satisfies all the constraints of the given problem.
Hence, this ordered pair will lie in the feasible region.
2)
(4, 36)
As the height that is the y-value has to be less than 33.
Hence, the ordered pair (4,36) does not lie in the feasible region.
3)
(4.8, 30.5)
It satisfies all the inequalities of a successful launch.
Hence, this ordered pair will lie in the feasible region.
4)
(9, 26)
As the property that y ≥ 3x mjust be satisfied.
But here at x=9
y ≥ 27
but we are given y=26.
Hence, this ordered pair also does not lie in the feasible region.
5)
(2, 22)
As the minimum vertical distance must be 24.
But here we are given y=22.
Hence, this ordered pair does not lie in the feasible region.
A) Graph the following two lines on the same rectangular coordinate system. Show all your working. You need to use the slope-intercept method.
Graph A: 3x+2y=12 Graph B: 4x-y=5
B) Mark the point intersection of the two graphs M, and give coordinates.
C) What is the difference in units between the Y-coordinates of Graph A and Y-coordinates of Graph B?
E) Draw the graph x-=6 on the same set of axes. At which point does this line cut Graph A?
Kendall knows that a 45-ounce pitcher can hold enough lemonade for 6 people. At this rate, how many ounces of lemonade will Kendall need to serve 26 people?
lizette has 813 stamps she has 125 more stamps than Minerva how many stamps does Minerva have
If a bat and ball costs $1:10
And the bat costs $1 more than the ball
How much does the ball cost?
The record high January temperature in Austin, texas, is 90°f. The record low January temperature is -2°f. Find the differences between the high and low temperature.
What is 540 divided by 36 using partial quotients
What three factors were used to create this product game board
Can someone please help me answer these questions in scientific notation?)
1. (5.2 x 10⁻³) - (2.58 x 10⁻³)
2 (3.6 x 10⁻²) + (4.0 x 10⁻¹)
3. (8.32 x 10⁻³) - (5.9 x 10⁻⁴)
4. (6.03 x 10⁻²) - (3.8 x 10⁻³)
Read the problem in the box below. Make a list to help you find the correct answer.
PLZ HELP ME BY TONIGHT AT 12:30 ITS DUEEE
ps/ plz answer ALLL the questions
The height of an airplane during a landing is given by 22,000+(−480t) where t is the time in minutes.
a. Complete the table.
Time (minutes) 5 10 15 20
------------------------------------------------------
Height (feet)
Please help!
The floor of a small foyer will be made from square tiles.Each tile has a side length of 8 inches.Ifthe detentions of the floor are 24 inches by 48 inches, how many ceramic tiles are needed?
Floor: 24 * 48 = 1152 square inches
Tile: 8^2 = 64 square inches each
1152/64 = 18
18 tiles are needed
Lena was playing a card game. She placed the cards in 2 rows of of 26 cards each. In which other way can Lena place all of the cards?
1- 15 rows of 4 cards each
2-13 rows of 4 cards each
3- 18 rows of 3 cards each
4- 16 rows of 3 cards each
Thank you
Another way in which the cards Can be placed is 13 rows of 4 cards each.
The total Number of playing cards in a deck = 52
In other to place equal number of cards in a number of rows;
The product of the Number of cards per row and the number of rows must be equal to 52.Evaluating the options given :
15 × 4 = 60 (False)
13 × 4 = 52 (True)
18 × 3 = 54 (False)
16 × 3 = 48 (False)
Hence, the other way in which the cards Can be placed is 13 rows of 4 cards each.
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Write a division problem that has a 3-digit dividend and a divisor between 10 and 20. Show how to solve it by drawing a quick picture.
Answer:
In the division problem,
The number which is divided is called dividend,
While, the number which divides, is called divisor,
Let dividend = 150 ( a three digit number ),
Divisor = 15 ( a number between 10 and 12 ),
So, the problem would be,
[tex]150\div 15[/tex]
In the below figure,
Take a grid that shows 150,
Divide this grid such that each box represents 15,
Thus, there are such 10 boxes,
That is,
[tex]150\div 15 = 10[/tex]
Which represents the solution set of the inequality 5x-9≤21
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]5x-9\leq 21[/tex]
solve the inequality
[tex]5x\leq 21+9[/tex]
[tex]5x\leq 30[/tex]
[tex]x\leq 30/5[/tex]
[tex]x\leq 6[/tex]
The solution is the interval----------> (-∞,6]
All real numbers less than or equal to [tex]6[/tex]
The solution of the inequality is the shaded area to the left of the solid line
see the attached figure
4. Describe the number set(s) the number belongs to: −√17
The number -√17 is an irrational number and is part of the set of real numbers.
Explanation:The number -√17 belongs to the set of real numbers. However, because this number is the square root of a positive number (17) and is multiplied by negative sign, it is not a rational number, but rather an irrational number.
It is part of the real numbers because the set of real numbers includes all numbers that can be plotted on a number line, including integers, rational numbers (numbers that can be expressed as a quotient of two integers), and irrational numbers (numbers that cannot be expressed as a quotient of two integers).
It is specifically an irrational number because the square root of 17 is a non-repeating, non-terminating decimal, and when we multiply this by a negative sign, the numerical value itself does not change, only its direction on the number line.
Learn more about Number Sets here:https://brainly.com/question/35714672
#SPJ2
what percent of 50 is 18
What is 90% of 4732000?
90% = 0.90
4732000 x 0.90 = 4,258,800
Find the Perimeter of the polygon with the vertices X(-1,3), Y(3,0), and Z(-1,-2). Round the answer to the nearest hundredth
The perimeter of the polygon with vertices X(-1,3), Y(3,0), and Z(-1,-2) is approximately 14.47 units when rounded to the nearest hundredth.
To find the perimeter of the polygon with vertices X(-1,3), Y(3,0), and Z(-1,-2), you first need to calculate the length of each side of the triangle formed by these points. You can do this by using the distance formula:
[tex]d = \sqrt{{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
For side XY:
d(XY) = [tex]\sqrt(3 - (-1))^2 + (0 - 3)^2}[/tex]
[tex]\sqrt{{16 + 9}[/tex]
[tex]\sqrt{{25}[/tex]
= 5
For side YZ:
[tex]d(YZ) = \sqrt{((-1) - 3)^2 + (-2 - 0)^2}[/tex]
[tex]\sqrt{{16 + 4}[/tex]
[tex]\sqrt{{20}[/tex]
= 4.47
For side ZX:
[tex]d(ZX) = \sqrt((-1) - (-1))^2 + (3 - (-2))^2}[/tex]
[tex]= \sqrt{0 + 25}[/tex]
= 5
Now, sum the lengths of the sides to get the perimeter:
Perimeter
= d(XY) + d(YZ) + d(ZX)
= 5 + 4.47 + 5
= 14.47
So, the perimeter of the polygon is approximately 14.47 units, rounded to the nearest hundredth.
What's the difference of 9(2k-4) and -2(7k-12)
The assembly of a machine takes 3/4 hour there are 12 steps in the assembly process what is the average time for each step
The average time for each step in the assembly process is 3.75 minutes per step.
Explanation:To find the average time for each step in the assembly process, we need to divide the total time taken by the number of steps. In this case, the assembly takes 3/4 hour, which is equivalent to 45 minutes. There are 12 steps in the process. So, to find the average time per step, we divide 45 minutes by 12:
Average time per step = 45 minutes / 12 = 3.75 minutes per step.
Write an inequality that is true only for temperatures (t) that are higher than the boiling point of water.
What is the rule for this sequence 6, 18, 54, 162, 486
Divide.
(-13r2+104r)÷(r–8)
One pump can fill a swimming pool in 8 hours and another pump can fill it in 10 hours. If both pumps are opened at the same time, how many hours will it take to fill the pool?
Answer: It will take [tex]\dfrac{40}{9}=4\dfrac{4}{9}[/tex] hours to fill the pool.
Step-by-step explanation:
Since we have given that
Number of hours first pump takes = 8 hours
Number of hours second pump takes = 10 hours
If both pumps are opened at the same time,
Work done by first pump = [tex]\dfrac{1}{8}[/tex]
Work done by second pump = [tex]\dfrac{1}{10}[/tex]
According to question,we get that
[tex]\dfrac{1}{8}+\dfrac{1}{10}\\\\=\dfrac{5+4}{40}\\\\=\dfrac{9}{40}[/tex]
So, it will take [tex]\dfrac{40}{9}=4\dfrac{4}{9}[/tex] hours to fill the pool.
How would I solve this equation for x? x/p + x/q = S
54 over 4 as a mixed number
Help me please.Questions are below.I know there's a lot of questions but I need help.
I'll give 35 points.
1.Write an algebraic expression for each word expression:
6 more than a number p
2.Solve: a/8 = 13 a = _____
3.Solve: 96 = 12b b = _____
4. Solve: c/9 = 2.3 c = _____
5. Solve: 5.2 = d/6 d = _____
6.Solve: 0.74h = 0.74 h = _____
7. Solve: k/0.38 = 1 k = _____
8.Solve: 27.4n = 0 n = _____
9. Solve: 0.4w = 3.12 w = _____
10. Solve: a/4.2 = 0 a = _____
1. p+6
2.a =13*8 = 104
3.b = 96/12 = 8
4.c= 2.3*9 = 20.7
5.d = 5.2*6 =31.2
6. h = 0.74/0.74 = 1
7. k = 0.38*1 = 0.38
8. n = 0
9. w = 3.12/4 = 7.8
10. a = 0
k/4 = 3/8 solve for k.
Answer:
The answer is 1.5
Step-by-step explanation:
Answer the three questions please
Question (1)
When the divisor is a decimal, what must we do?
1) Multiply the divisor by 10, or 100, or 1000, etc., according to the number of decimal digits, so that it becomes a whole number.
2)Multiply the dividend by the same power of 10.
Question (2)
When asked to add or subtract decimals, the most important step is to line up the decimal points. Step 1: Line up the decimal points so that similar place values are lined up. In other words, the tens place in both numbers should be lined up, the ones place in both numbers should be lined up, etc.
Question (3)
To multiply decimals: Set up and multiply the numbers as you do with whole numbers. Count the total number of decimal places in both of the factors. Place the decimal point in the product so that the number of decimal places in the product is the sum of the decimal places in the factors.