Final answer:
The properties of integer exponents like multiplication (adding exponents), division (subtracting exponents), raising a power to another power (multiplying exponents), and fractional powers (representing roots) are used to simplify algebraic and numeric expressions.
Explanation:
To simplify algebraic and numeric expressions using the properties of integer exponents, you can apply several different rules. The first step is often to write out the expression in an extended format, like how 34 can be written as 3·3·3·3. When we deal with multiplication of exponentials, we multiply the digit terms and add the exponents of the exponential terms. For example, (23)(24) equals 23+4 which simplifies to 27. When we encounter division of exponentials, we divide the digit terms and subtract the smaller exponent from the larger exponent. For instance, 57 divided by 53 would give us 57-3 which is 54.
For powers raised to another power, like (53)4, you multiply the exponents (3×4) to get 512. Remember to be cautious with examples and ensure clarity in the operations when combining exponents. Lastly, fractional powers, such as 51/2, can be interpreted as square roots. The general rule here is that xa/b represents the b-th root of x, raised to the power of a.
Is 2.22 irrational or rational?
How do you write these as an algebraic expression?
Zabato is thinking of a number. Three times the sum of the number and ten is the same as eight times the number. What is his number??
Describe two quantities that can be measured accurately by integers
8.76×106 is times than 8.76×102 .
I need to know what irrational is closest to the square root of 9
Maria read 78 pages in 3 hours. Reading at the same rate, she read 130 pages in 5 hours. Find the unit rate in pages per hour
How many pieces of 8 1/2 by 11 inches of paper can be cut from 1000 square inches
what names apply to the square root of 36?
If m is the midpoint of XY find the coordinates of x if M(-3, -1) and Y(-8, 6)
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.
eight less than a number s is three more than four times a number t. solve for s
The solution is s = 4t + 11.
Let's translate the problem into an equation:
s - 8 = 4t + 3
Now we can solve for s by adding 8 to both sides of the equation:
s = 4t + 3 + 8
Finally, we can simplify the equation by combining the constant terms:
s = 4t + 11
Therefore, the solution is:
s = 4t + 11
for such more question on equation
https://brainly.com/question/29174899
#SPJ6
On a miniature golf course the distance from the tee to the first hole is 96 inches the distance to the second hole is 3 yards on the third tee the holes is 12 feet away which of the tees is farthest from the whole
Final answer:
After converting all distances to inches, the third tee is the farthest from the hole at 144 inches.
Explanation:
To find out which tee is farthest from the hole, we need to convert all distances to the same unit. For this problem, we will use inches, since the first distance is already given in inches.
The first hole is 96 inches away.The second hole is 3 yards away. There are 36 inches in a yard, so this is 3 yards × 36 inches/yard = 108 inches.The third hole is 12 feet away. There are 12 inches in a foot, so this is 12 feet × 12 inches/foot = 144 inches.Comparing the distances, the third hole is the farthest away at 144 inches.
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:
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:
Math help please asap im begging you
Use the clues to find the mystery number.
The number has 6 digits.
The total value of the largest digit is 8000.
The digit in the tens place is 2 less than the digit in the hundreds place.
The sum of the digit in the tens place and the digit in the hundreds place is equal to the digit in the thousands place.
The digit in the tenths place has the same value in every place.
The remaining digit is the largest even digit.
What is the mystery number?
What's the alphabetical order
Which set is ordered greatest to least?
16% = 0.16
1/6 = 0.16666
1.6x10^6 = 1600000
0.166 = 0.166
order from greatest to least:
1.6x10^6, 1/6, 0.166, 16%
Answer is D
one serving of soybeans contains 10 grams of protein, which is 4 times the amount in one serving of kale. write and solve an equation to find the amount of protein in one serving of kael
One serving of kale contains 2.5 grams of protein. This is determined by the equation 4x = 10, where x represents the protein content in one serving of kale, and solving for x.
Let x represent the amount of protein in one serving of kale. The given information states that one serving of soybeans contains 10 grams of protein, which is 4 times the amount in one serving of kale.
So, the equation is:
4x = 10
Now, solve for x:
x = [tex]\frac{10}{4}[/tex]
x = 2.5
Therefore, one serving of kale contains 2.5 grams of protein.
The complete question is:
One serving of soybeans contains 10 grams of protein, which is 4 times the amount in one serving of kale. Write and solve an equation to find the amount of protein x in one serving of kale.
Ann travels from town A to town B in 3 hours. She then takes another hour to travel from town B to town C. The distance between town A and town B is 100 miles. The distance between town B and town C is 40 miles. What is Ann's average speed for the whole journey?
Ann's average speed for the entire journey from town A to town C is calculated by dividing the total distance traveled, which is 140 miles, by the total time taken, which is 4 hours, resulting in an average speed of 35 mph.
Calculating Average Speed for the Whole Journey
To calculate Ann's average speed for the entire trip from town A to town C, we first need to find the total distance traveled and the total time taken. Ann travels 100 miles from A to B, then another 40 miles from B to C, totaling 140 miles for the distance. The time taken for the first leg of the trip is 3 hours, and for the second leg, it's 1 hour, totaling 4 hours for the entire journey.
Now, we calculate the average speed using the formula:
Average Speed = Total Distance / Total Time
Average Speed = 140 miles / 4 hours = 35 miles per hour (mph).
This is the average speed for the whole trip from town A to town C.
the average length of a lady bug can range from .08 to .4 inch. find 2 lengths that are within the given span
Final answer:
To find two lengths within the given span of 0.08 to 0.4 inches for a ladybug, we can choose any two numbers between this range. For example, we can choose 0.1 inches and 0.3 inches.
Explanation:
To find two lengths within the given span of 0.08 to 0.4 inches for a ladybug, we can choose any two numbers between this range. For example, we can choose 0.1 inches and 0.3 inches. Both of these lengths fall within the given range.
Find the diameter of a circle that has an area of 254.34mm2
Anybody knows this one
Simplify (-5) + (-2) - (-7) - (+9)
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
Solve the inequality -7+2x<_1 where x equals an integer. (How do you get the answer?)
4.07 Litre+1 1/5 litre+0.1litre= milliltre
can someone help me?
Maggie has a ribbon 27 feet long what is the length of the ribbon in yards
27 feet is 9 yards
hope this helps
There are 6 baskets on the table. Each basket has 144 crayons in it. How many crayons are there?