The plane was flying at a height of 706.32 m .
The fundamentals of an object's motion, such as its position, velocity, or acceleration over time, are defined by kinematics equations of motion. An object's motion in one, two, and three dimensions is determined by these three equations of motion. One of three equations of motion can be used to calculate components like displacement (s), velocity (initial and final), time (t), and acceleration (a). The following are the three motion equations:
Initial formula: v = u + at
The second formula is s = ut + 0.5at2.
The third formula is v2 = u2 + 2as.
Let t stand for the package's flight time, s for the plane's altitude, and u for the packet's initial vertical velocity since it is simply dropped.
Given: t = 12 seconds for the delivery to arrive to the ground
With t = 12 and u = 0 in the second equation of motion, we so obtain
s = 0*t + 0.5*9.81*12² = 706.32 m
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Solve the equation by extracting the square roots. List both the exact solution and its approximation rounded to two decimal places.
(2x − 1)^2 = 18
The exact solution and its approximation rounded to two decimal places are 2. 6213 and 2. 62 respectively.
What is an algebraic expression?An algebraic expression can be described as a mathematical or arithmetic expressions that is composed of arithmetic terms, factors, constants, variables, and coefficients.
These expressions are also made up of arithmetic operations which includes;
DivisionAdditionParenthesesBracketMultiplicationSubtractionFrom the information given, we have that;
(2x − 1)^2 = 18
Find the square root of both sides, we have;
√(2x − 1)^2 = √18
Note that square root rules out the square, we have;
2x - 1 = 4. 24264
collect like terms
2x = 4. 24264 + 1
2x = 5. 24264
Make 'x' the subject
x = 5. 24264/2
x = 2. 6213
Hence, the value is 2. 6213
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Two different lines are shown below with two points given from each line. Use the slope-intercept form or point-slope form to find the equation of each line.
Line A
Points: (–5, –2), (–5, 7)
Line B
Points: (7, –5), (–2, –5)
Line A has
.
The equation of line A is
.
Line B has
.
The equation of line B is
.
We have a vertical and a horizontal lines, the equations are:
Line A: x = -5 (vertical one)
Line B: y = -5 (horizontal one)
How to find the equations of the two lines?Remember that the general linear equation in the slope-intercept form is:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Now, line A passes through (–5, –2), (–5, 7), then the slope is:
a = (7 + 2)/(-5 + 5) = 9/0
Notice that if we divide by zero, the slope tends to infinity, so we have a vertical line.
In this case, the line A will be x = -5.
Now line B passes through points: (7, –5), (–2, –5)
Then the slope is:
a = (-5 + 5)/(-2 - 7) = 0/-9 = 0
Then the line is:
y = 0*x + b
And passes through (7, –5), then:
-5 = 0*7 + b
-5 = b
So this line is y = -5.
Concluding, we have:
Line A: x = -5
Line B: y = -5
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Answer:
Line A: no slope
The equation of line A is x = -5
Line B has a slope of 0
The equation of line B is y = -5
Step-by-step explanation:
I did it already :)
Felipe is having a party. He'll have 4 tables for every 20 guests. Complete the table below showing the number of tables and the number of guests. See the table on the bottom.
( Table: ?, 1 20,4 35,? ?,8 50,?)
Using a proportional relationship, the table relating the number of guests and number of tables is given by the image at the end of the answer.
How to represent a direct proportional relationship?A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality represented by k, according to the equation below:
y = kx.
In the context of the problem, the variables are given as follows:
y: Number of tables.x: Number of guests.He'll have 4 tables for every 20 guests, hence the constant is given as follows:
k = 4/20 = 1/5 = 0.2.
Hence the relation is:
y = 0.2x.
For 1 table, the number of guests is:
0.2x = 1 -> x = 5.
For 8 tables, the number of guests is:
0.2x = 8 -> x = 8/0.2 = 40.
For 35 guests, the number of tables is:
y = 0.2 x 35 = 7.
For 50 guests, the number of tables is:
y = 0.2 x 50 = 10.
The table with these measures is given by the image at the end of the answer.
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Taylor is struggling with literal equations. She has tried to solve the equation below for several times but still can't get the correct answer. Her steps that she used to solve for m are shown below. In which step is she making an error?
The step 3y = 80v + x is incorrect, as 3y = 80v - x is the correct step by subtraction property of equality.
In this question, we have been given Taylor is solving a literal equation (x + 3y) / 2 = 40v
We have been given her steps that she used to solve for y.
We need to find an error in the steps.
First we solve given literal equation for y.
(x + 3y) / 2 = 40v
x + 3y = 40v × 2 .................(Multiply both the sides by 2)
x + 3y = 80v
x + 3y - x = 80v - x ...................(Subtract x from both the sides)
3y = 80v - x
y = (80v - x)/3 ............(Divide each side by 3)
If we observe Taylor's steps, we can see that there's an error in the step 3y = 80v + x.
Therefore, the step 3y = 80v + x is incorrect, as 3y = 80v - x is the correct step by subtraction property of equality.
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It's one more question after this i think guys. Thank for all your help!
30 points
The solution for x in the given expression (7 = 3x/9) is: C. 21.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In this exercise, you're required to describe the steps that should be taken to rearrange and solve for x. Therefore, the appropriate and required steps are listed as follows:
Multiplying both sides by 9, we have:
9 × 7 = 3x/9 × 9
63 = 3x
Dividing both sides by 3, we have:
3x/3 = 63/3
x = 21.
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20 points please help me asap !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1) 180°-105°-29°
=46° (angles in ∆)
2) 180-78-55
180-78-55 =47° (angle ²)
then angle ¹ is
180-78-47
=55° (angles on a straight line)
3) I just realised I solved angle 2 so I'll make the answer bold for you :)
I hope this is correct lol
Please help with this math problem! Thank you! :D
Answer:
C
Step-by-step explanation:
[tex]\sqrt{2}[/tex] and [tex]\frac{1}{\sqrt{2}}[/tex] are both irrational, but they multiply to 1, which is rational
1. One of two supplementary angles is four times the other. Find the largest angle.
144 is the largest angle in supplementary angle .
What is an example of a supplementary angle?
Angles that add up to 180 degrees are referred to as supplementary angles. For instance, the sum of angle 130° and angle 50° is 180°, hence they are supplementary angles.The pair of angles known as supplementary angles always add up to 180 degrees. The terms "supplements" for these two viewpoints describe them. The Latin terms "Supplere" and "Plere," which mean "supply" and "fill," respectively, are the source of the English word "supplementary."Let one angle = x
then other angle is four times the other = 4x
x + 4x = 180
5x = 180
x = 180/5
x = 36
smaller angle = 36
largest angle = 4x = 4 * 36 = 144
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A ball is equipped with a speedometer and launched straight upward. The speedometer reading three seconds after launch is shown at the right; the ball is moving upward. At what approximate times would the ball be moving downward and display the following speedometer readings?
The time shown by the speedometer with speed of 10 m/s is 1 s.
The time shown by the speedometer with speed of 20 m/s is 1 s.
The time shown by the speedometer with speed of 30 m/s is 1 s.
What is the time on the Speedometer?The time read by the speedometer is given as;
t = 3 s.
The speedometer has low precision and as such we can do value approximation.
For the speedometer showing the speed 10 m/s. The time is calculated as, t = (v - u)/g
where g = 10 m/s²
t = (10 - 0)/10
t₁ = 1 seconds
For the speedometer showing the speed 20 m/s. The time is calculated as, t = (v - u)/g
where g = 10 m/s²
t = (20 - 0)/10
t₂ = 2 seconds
For the speedometer showing the speed 30 m/s. The time is calculated as, t = (v - u)/g
where g = 10 m/s²
t = (30 - 0)/10
t₂ = 3 seconds
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In Exercises 6 and 7, use the Law of Detachment to determine what you can
conclude from the given information, if possible.
6. If you eat a healthy breakfast, then you will not be hungry until lunchtime. You
are not hungry until lunchtime.
7. Adjacent angles share one common ray. ∠AOB and ∠ DOB are adjacent angles.
Using the Law of Detachment, the conclusions are given as follows:
6. No conclusion.
7. ∠AOB and ∠ DOB share one common angle.
What is the Law of Detachment?The Law of Detachment is a logic axiom which states that if a conditional and the hypothesis of a statement are true, then the conclusion of the statement is also true.
Supposing a conditional statement p -> q, we have that the hypothesis and the conclusion are defined as follows:
p is the hypothesis.q is the conclusion.For item 6, we have that the statements are given as follows:
Statement p: You eat a healthy breakfast.Statement q: You are not hungry until lunchtime.We have that p->q and q are true, hence no conclusion can be reached from the law of detachment.
For item 7, we have that the statements are given as follows:
Statement p: Adjacent angles.Statement q: Share one common ray.In this case, we have the hypothesis is true, hence the conclusion is that ∠AOB and ∠ DOB share one common angle.
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15 equals the sum of three and six times a number
Answer: 15 equals the sum of 3 + 6 x 2
Step-by-step explanation: 6x2 is 12 and if you add 3 it is equal to 15, but it is better if you rewrote the equation as 3 + (6x2), that way it is more understandable
Find the perimeter of this semi-circle with diameter, d = 23cm. Give your answer rounded to 1 DP.
The perimeter of the semi-circle is 59.1 cm
In this question, we have been given the diameter if the semi-circle
d = 23 cm
We need to find the perimeter of the semi-circle.
We know that, the perimeter of the semi-circle of radius 'r' is P = πr + 2r
For diameter d = 23 cm, the radius would be,
r = 11.5 cm
So, the perimeter would be,
P = πr + 2r
P = π × 11.5 + 2 × 11.5
P = (π + 2) × 11.5
P = 59.13 cm
Therefore, the perimeter of the semi-circle is 59.1 cm
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Which angle is an acute angle?
Answer: angle CPB is an acute angle.
Answer: C. ∠CPB is the correct answer.
Step-by-step explanation:
A car traveling at a speed of 30.0 m/s encounters an emergency and comes to a complete stopHow much time will it take for the car to stop if its acceleration is -4.0 m/s
Answer:
Step-by-step explanation:
mike is a good athlete.Mike's father is a good athlete.Mike's sister is a good athlete.Therefore,Mike's son will be a good athlete. (Inductive or Deductive?)
h(x)=3x+4 complete the function table help please
The function table should be completed as follows:
x h(x)__
-4 -8
-3 -5
2 10
4 16
5 19
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.
Next, we would evaluate the given function by substituting the value of x as follows:
When x = -4, we have:
Function, h(x) = 3x + 4
Function, h(-4) = 3(-4) + 4
Function, h(-4) = -12 + 4
Function, h(-4) = -8
When x = -3, we have:
Function, h(x) = 3x + 4
Function, h(-3) = 3(-3) + 4
Function, h(-3) = -9 + 4
Function, h(-3) = -5
When x = 2, we have:
Function, h(x) = 3x + 4
Function, h(2) = 3(2) + 4
Function, h(2) = 6 + 4
Function, h(2) = 10
When x = 4, we have:
Function, h(x) = 3x + 4
Function, h(4) = 3(4) + 4
Function, h(4) = 12 + 4
Function, h(4) = 16
When x = 5, we have:
Function, h(x) = 3x + 4
Function, h(5) = 3(5) + 4
Function, h(5) = 15 + 4
Function, h(4) = 19
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is 0.1213141516... a rational number
Answer:
No, because any number than produces and decimal that continuse forever is not rational.
Step-by-step explanation:
Hope it helps! =D
George has a health insurance premium that costs $4,300.00. His employer pays 3/4 of the premium and George pays 1/4. What is the amount that George must pay?
Answer:
1075
Step-by-step explanation:
4300x0.25
The Sydney Opera House can house no more than 5738 people. Luisa Miller always brings crowds of at least 4,000 people. What is the maximum number of empty seats that might not be filled during her performance?
Answer:
a maximum of 1,738 empty seats
Step-by-step explanation:
5,738 - 4,000 = 1,738
Suppose U={1,2,3,4,5,6,7,8} is the universal set and P={2,4,6,8}. Then what is P?
{0,1,3,5,7}
{0,1,3,5,7,9}
{1,3,5,7}
{ }
{ } pls i right,or u can help me out
pls pls help whoever gets it right gets marked brainliest
Answer:
A
Step-by-step explanation:
mark me brainliest
See below for question
Value of x is 2 and value of k is 0.999.
What is volume?Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.
Given Data
At t=0, Water Volume is 3,000 Litres
The volume of water in the tank equals t hours later.
As it is also stated, there is x% less water in the tank at the conclusion of every hour than there was at the beginning.
After an hour, the amount of water is equal to 3,000 - = 3,000 - 30 x
Water consumption after two hours = (3,000 - 30 x) - (3,000 - 30 x)
×= (3,000 - 30 x) (3,000 - 30 x)
Also,
= 288120
⇒300000 - 3000 x - 3000 x + 30 x²
= 288120
⇒ 30 x ² - 6,000 x + 11880= 0
When we multiply both sides by 30, we get
⇒ x² - 200 x + 396=0
reducing the quadratic equation to factors
(x -198)(x-2) = 0
x = 198,
x = 2
Which suggests that x = 2 might be the answer to this equation.
Also,
V₁ = 3000- 30(2)
V₁ = 3000 - 60
V₁ = 2940
k = [tex]\frac{2940}{3000}[/tex]
k = 0.999(approximately)
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3 x [64÷(13-5) - 4] × 42 ÷ 6
Write an algebraic expression to represent each statement
three times a number, d, less 5
If 18 inches is equal to 1 and 1/2 feet, how many feet long is a 36 inch board, a 72 inch board, and a 144 inch board? (Show work)
Pls help!!
18 inches= 1 1/2 feet= 1.5 feet
18 inches = 1.5 feet
what is distance ?
Distance is a numerical or occasionally qualitative measurement of how far apart objects or point are . it is a total movement of an object without any regard to direction.
(1) Now we make a proportion to find feet for given inches
feet/inches = feet / inches
1.5/18 = x/36
1.5 * 36 = 18*x
54 = 18 x (Divide by 18 on both sides)
x = 3
3 feet long is a 36 inch board
(2) 72 inch board
1.5 * 72 = 18*x
108 = 18 x (Divide by 18 on both sides)
x = 6
6 feet long is a 72 inch board
(3) 144 inch board
1.5 * 144 = 18*x
216 = 18 x (Divide by 18 on both sides)
x = 12
12 feet long is a 144 inch board
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What is the equation of the line that passes through the point (3,1)(3,1) and has a slope of -4/3
?
i'm going to assume (3,1)(3,1) was a typo.
here is an equation for a line with a slope of (-4/3) that crosses through (3,1)
y = -4/3x + 5;
steps;
1 = -4/3(3)+ b
1 = -4 +b
5 = b
Answer:i'm going to assume (3,1)(3,1) was a typo.
here is an equation for a line with a slope of (-4/3) that crosses through (3,1)
y = -4/3x + 5;
steps;
1 = -4/3(3)+ b
1 = -4 +b
5 = b
Step-by-step explanation:
Question 2 of 10
Which of the following are solutions to the equation below?
Check all that apply.
x² - 6x +9=11
A. x= √√√2 +6
B. x = -√11 +3
C. x = -√2 +6
D. x= √11 +3
E. x=2+√√6
OF. x=2-√6
The solutions of the quadratic equation x² - 6x +9=11 is found to be x = [tex]\sqrt{11} + 3[/tex] or [tex]\sqrt{11}-3[/tex]. So, Option B and D are correct.
What is a quadratic equation?A quadratic equation is ax² + bx + c = 0 . Another name for the terms a, b, and c is quadratic coefficients.
The values of the unknown variable x that fulfill the quadratic equation are the solutions to the problem. Quadratic equations' roots are known as these solutions.
Given equation: x² - 6x +9=11
Subtract 11 on both sides
x² - 6x +9 +(-11) =11 - 11
x² - 6x - 2 = 0
Solving using the quadratic formula,
x = [tex]\frac{-b + \sqrt{b^{2}-4ac } }{2a}[/tex] or [tex]\frac{-b - \sqrt{b^{2}-4ac } }{2a}[/tex]
x = [tex]\frac{6 + \sqrt{-6^{2}-4(-2) } }{2}[/tex] or [tex]\frac{6 - \sqrt{-6^{2}-4(-2) } }{2}[/tex]
x = [tex]\sqrt{11} + 3[/tex] or [tex]\sqrt{11}-3[/tex]
Therefore, the solutions of the quadratic equation x² - 6x +9=11 is found to be x = [tex]\sqrt{11} + 3[/tex] or [tex]\sqrt{11}-3[/tex]. So, Option B and D are correct.
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Aşağıdaki sayı ikililerinden hangisinin en büyük ortak böleni 15 değildir? A) 30 ile 45 C) 60 ile 105 B) 45 ile 75 D) 75 ile 125
Answer:
D 75 and 125
Step-by-step explanation:
cünkü en büyük ortak böleni 25 dir
prove me wrong
WILL GIVE BRAINLEST I HAVE 5 MINUTE 30 points, Solve for x, look at picture for more info.
The numerical value of x in the two congruent alternate exterior angles is 20.
What is the numerical value of x?Alternate exterior angle theorem states that "if a transversal intersects two parallel lines, the alternate angle s formed are congruent.
From the diagram, the two angles forms an alternate exterior angle , the two angles are congruent.
( 5x - 8 ) = ( 3x + 32 )
Solve for x
5x - 8 = 3x + 32
Collect like terms by moving all terms containing variable x to left and the constant terms to the right side of the equation.
5x - 8 = 3x + 32
5x - 3x = 32 + 8
2x = 40
Divide both sides by 2
2x/2 = 40/2
x = 40/2
x = 20
Therefore, the numerical value of x is 20.
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please only help me with number 7.
which value is less than 1?
a (1/6)^-8
b (5^-4)^-9
c 2^-3
d 6^-4/6^-5
Answer:
c
Step-by-step explanation:
[tex]a) (1/6)^{-8}=6^8>1 \\ \\ b) (5^{-4})^{-9}=5^{36}>0 \\ \\ c) 2^{-3}=1/8<1 \\ \\ (d) \frac{6^{-4}}{6^{-5}}=6>1[/tex]