the men's world record for the high jump is 2.45 meters. A puma can jump about 1.9 times as high. what is the highest a puma can jump?
Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at least 24 ft and must go a horizontal distance of no more than 10 ft. The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.
The graph shows the feasible region, where x represents the horizontal distance and y represents the vertical distance.
Which ordered pairs meet all the constraints for a successful launch and make sense in context of the situation?
Select each correct answer.
(0, 33)
(4, 36)
(4.8, 30.5)
(9, 26)
(2, 22)
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.
There are 6 baskets on the table. Each basket has 144 crayons in it. How many crayons are there?
Could someone tell me the step to step guide on how to do any subject formulas question in Maths and could someone help me do the subject formulas questions in the photo☺
estimate. then find the product 872 × 3
Choose the constant term that completes the perfect square trinomial.
X^2 + 1/3x
1/36 is the answer
to ur problem
(^_>*)
a sequence has a first term of 2 and a constant ratio of _3/2 what are the first five terms of the sequence
Im desperate! please help!
Should an estimate or the exact answer be calculated? Then do the appropriate calculation.
The conservation club participated in a beach cleanup program over a 5 week period. Their goal was to collect at least 60 pounds of trash. They collected pounds in each of the first two weeks and pounds for each of the last three weeks. Did the club reach its goal?
A.
An estimate can be used to know if the goal was reached.
12 • 2 + 13 • 3 = 63
At least 63 lb were collected.
B.
The exact answer is needed to know if the goal was reached.
pounds were collected.
The distance between the baseball stadium and the airport is 1.6x10^6 centimeters. Which unit of measurement is most appropriate to measure the distance. ( i need to
Get this right or i will fail)
A. Inches
B. Milimeters
C. Kilometers
D.feet
Answer:
C. kilometers
Step-by-step explanation:
Numbers with the same absolute value are__________
the science department buys the equipment shown in the table they bought all three items this year and how many years do they have to buy all three items again
Write two mixed numbers between 3 and 4 that have a product between 9 and 12
Evaluate the expression. 16(84+124) Enter your answer as a number, like this: 42 80 pts
Answer:
Add 84 + 124 = 208
multiply by 16 = 3328 :)
solve for E.
50−3.6(E−4)=32
Write an expression in words that describes the relationship between the number of quarts and the number of cups
An art student uses a roll of wallpaper to decorate two gift boxed. The student will use 1 1/3 yards of paper for one box and 5/6 yard of paper in the other box. The paper must be cut into pieces that are 1/6 yard long. How many pieces will the student cut to use for the gift boxes
The art student decorating two gift boxes will cut full 78 pieces of paper from the roll that are 1/6 yard each, using a total of 2 1/6 yards of paper.
Explanation:The art student is decorating two gift boxes using wallpaper that must be cut into 1/6 yard pieces. The student will use 1 1/3 yards of paper to decorate one box and 5/6 yard of paper to decorate the other box. To find out how many pieces of paper the student will cut, we first need to add the lengths of paper used for both boxes which gives us 2 1/6 yards.
To convert this total length into 1/6 yard pieces, we can divide the total length by the length of each piece. Therefore, 2 1/6 yards equals 13/6 yards. When we divide 13/6 by 1/6, we get 78. So, the student will cut 78 pieces for the gift boxes.
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Algebra write all of the digits that can replace each
what names apply to the square root of 36?
How many equal line segments are needed to make a row of 6 triangles
Answer:
To make a triangle you need three line segments.So,First triangle consist of three and then 2 segments are added,then 2,....so,on, till you obtain six triangles.
Total number of Line segments
=3+2+2+2+2+2
=13
Figure is attached below.
To draw 6 triangles in a row , Total number of line segments needed=13
4/11+s=9/22 how to I find the answer to this
Santiago receives an allowance of 7$ every week
How much total does he receive after 4 weeks
Write the number described by 1 ten 16 ones
Light travels at a speed of 3.0 times 10 to the 8th power m/s. How many seconds does it take to get to earth if earth is 3.99 times 10 to the 16th power meters away?
2,107,954 the value of the digit 0 is
How to convert 5 1/4 into a decimal
5 1/4 convert into a decimal is 5.25.
DecimalIn order to convert a fraction to a decimal first step is to divide the numerator by the denominator.
Where:
Numerator=1
Denominator=4
Hence:
1/4=0.25
5 1/4=5+0.25
5 1/4=5.25
Inconclusion 5 1/4 convert into a decimal is 5.25.
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The mixed number 5 1/4 is converted into a decimal by dividing the fraction part (1/4) to get 0.25 and adding it to the whole number (5) resulting in 5.25.
Explanation:To convert the mixed number 5 1/4 into a decimal, first understand that it consists of a whole number 5 and a fraction 1/4. The fractional part 1/4 can be converted to a decimal by dividing the numerator (1) by the denominator (4). Performing this division: 1 ÷ 4 = 0.25. Now, simply combine the whole number with the decimal, which gives 5 + 0.25 = 5.25. Therefore, 5 1/4 as a decimal is 5.25.
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Kendra has 70$. Alonzo has one tenth as much as Kendra. Markio has 10times as much money as Kendra. How much money does Alonzo have? How much money does Markio!
Answer:
700$
Step-by-step explanation:
One side of a rectangular football field's width is equal to 55 yards. One side of the field's length is 110 yards. Calculate the perimeter of the field
The perimeter of the rectangular football field, with a length of 110 yards and width of 55 yards, is calculated as 330 yards.
Explanation:To calculate the perimeter of this rectangular football field, we need to add up the lengths of all four sides. Given that the width of the football field is 55 yards and the length is 110 yards, the formula to calculate the perimeter (P) of a rectangle is P = 2L + 2W where L is the length and W is the width.
Substituting the given numbers, we get P = 2(110) + 2(55) = 220 + 110 = 330 yards. Therefore, the perimeter of the football field is 330 yards.
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Maggie has a ribbon 27 feet long what is the length of the ribbon in yards
27 feet is 9 yards
hope this helps
Wood floors are being refinished in an office. If the room is a square with 15 foot 6 inch sides, what will it cost to have the floor refinished at $5.98 per square foot?
$40.18
$240.25
$1,436.70
$1,455.30
Answer:
Option c $1436.70
Step-by-step explanation:
It is given that room is a square, and each sides = 15 ft. 6 inches
Since 15 ft. 6 inches = 186 inches or 15.5 feet
Area of square = Length × width
Area of the room = 15.5 × 15.5 = 240.25 square feet.
Cost to have the floor refinished per square foot = $5.98
Total cost for the room = 240.25 × 5.98 = 1436.695 rounded to $1436.70
Total cost for refinished would be $1436.70
If the simplest interest on $2000 for two years is $280 then what is the interest rate