Answer:
commutative property of multiplication
Step-by-step explanation:
Name the property used: commutative property of multiplication
Answer: commutative property of multiplication
For the amusement of the guests, some hotels have elevators on the outside of the building. One such hotel is 400 feet high. You are standing by a window 100 feet above the ground and 150 feet away from the hotel, and the elevator descends at a constant speed of 20 ft/sec, starting at time t = 0, where t is time in seconds. Let θ be the angle between the line of your horizon and your line of sight to the elevator. 4 (a) Find a formula for h(t), the elevator's height above the ground as it descends from the top of the hotel. h(t) = (b) Using your answer to part (a), express θ as a function of time t. θ(t) = Find the rate of change of θ with respect to t. dθ dt = (c) The rate of change of θ is a measure of how fast the elevator appears to you to be moving. At what time does the elevator appear to be moving fastest? time = seconds At what height does the elevator appear to be moving fastest?
9514 1404 393
Answer:
a. h(t) = -20t +400
b. θ(t) = arctan(2 -2/15t); dθ/dt = -30/(1125 -120t +4t^2)
c. 15 seconds; 100 ft
Step-by-step explanation:
a. The initial height of the elevator is 400 ft. The rate of change of height is -20 ft/s, so the height equation can be ...
h(t) = -20t +400
__
b. The tangent of the angle above the line of sight is "opposite"/"adjacent":
tan(θ) = (h(t) -100)/(150) = -2/15t +2
θ(t) = arctan(2 -2/15t) . . . . radians
The derivative of the angle function is ...
dθ/dt = 1/(1+(2 -2/15t)^2)(-2/15)
dθ/dt = -30/(1125 -120t +4t^2)
__
c. The value of dθ/dt will have a peak where the denominator has a minimum, at t = -(-120)/2(4)) = 15. (The quadratic vertex coordinate is t=-b/(2a).)
The elevator appears to be moving fastest at t=15 seconds.
The height at that time is ...
h(15) = 400 -20(15) = 100
The elevator appears to be moving fastest when it is at eye level, 100 ft above the ground.
Sara left a bin outside in her garden to collect rainwater. She notices that one over eight gallon of water fills two over three of the bin. Write and solve an equation to find the amount of water that will fill the entire bin. Show your work. Explain your answer in words.
Answer:
3/16
Step-by-step explanation:
In order to get the amount of water to fill a bin, we just divide the amount of water by the fraction of the bin it fills. This makes the unit of the resulting answer as gallons/bin or gallons per bin.
lisa's father gave her $1032 to buy a present. this covered 3/5 of the cost. How many did the present cost?
Answer:
$1720
Step-by-step explanation:
1032 is 3/5 of the cost.
Divide 1032 by 3/5, which is 1720.
Thus, the answer is $1720.
The cost of the present day will be $1,720.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Lisa's father gave her $1032 to buy a present. This covered 3/5 of the cost.
The cost of the present day will be given by the division of the numbers 1032 and 3/5.
⇒ 1032 / (3/5)
⇒ 1032 x 5 / 3
⇒ $1,720
The cost of the present day will be $1,720.
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due in an hour please help!!! :(
Answer:
Step-by-step explanation:
1,7 are same side exterior
1,8 alternate exterior
2,4 none
3,5 same side int
2,6 corrosponding
4,6 same side int
4,7 is none
5,4 alternate int
8,5 vertical
8,7 alternate exterior
biografía completa de Pitágoras
Answer:
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10. Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 3 liters of natural oil for every 4
liters of synthetic oil. In order to make 518 liters of Petrolyn oil, how many liters of natural oil are needed?
Step by step please
you have the ratio of natural:synthetic so;
3:4
3+4=7
357/7=51
3*51:4°51
153:204
therefore, it'd be 204 litres of synthetic oil!!
i hope this helps you!!
Which steps show how to use the distributive property to evaluate 5 * 58?
Answer:
B.
Step-by-step explanation:
When using the distributive property, you distribute the leading number to each number inside the parentheses.
Answer:
Option B is correct.
Step-by-step explanation:
The answer of Option B is correct. 58 × 5 = 290.
Therefore, Option B is correct.
A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint in order to make a
green paint. Which ratio of gallons of blue paint to gallons of yellow paint will make the same
shade of green paint?
I think any of these would work
10;18
15;28
20;35
Answer:
5:9
Step-by-step explanation:
To Find:
ratio of yellow paint to blue paint to make a particular shade of green.
Solution:
The ratio can be written as 5 to 9, or 5:9
We know that if we mix 5 gallons of blue paint with 9 gallons of yellow paint we get the particular shade of green that we want.
Then the ratio of gallons of blue paint to gallons of yellow paint is 5 to 9, or 5:9
Meaning that for every 5 gallons of blue paint we need 9 of yellow paint.
Plss answer I give you branlistb
Please help!! I don't have a whole lot of time!!
The midpoint of the line segment is the average of the respective coordinates.
So the x-value of the midpoint if the average of the two individual x-coordinates.
(-3.5 + 4)/2 = 0.5/2 = 0.25
And the y-value of the midpoint if the average of the two individual y-coordinates.
(2 + (-2.5))/2 = -0.5/2 = -0.25
So, the midpoint is (0.25, -0.25) or (1/4, -1/4) or "C".
Jackie works as a server at a local restaurant. She makes $8 per hour. She worked 34 hours last week. She made $250 in tips. What was her gross pay?
Please help thank you! Solve for x and y
Answer:
x = 2
y = 7
I aced this lesson in 6th grade.
Step-by-step explanation:
hope this helps. . . <3
good luck! uωu
Answer:
Step-by-step explanation:
All 4 sides are equal. (They are marked that way).
8x = 5x + 6 Subtract 5x from both sides
8x - 5x = 5x - 5x + 6 Combine
3x = 6 Divide by 3
3x/3 = 6/3
x = 2
Consecutive angles of a rhombus are supplementary
97 + 12y - 1 = 180 Combine
96 + 12y = 180 Subtract 86 from both sides
12y = 180 - 96
12y = 84 Divide by 12
y = 84/12
y = 7
can some one awnser this i got 2 more questions for this test.
Answer:
and question is
Step-by-step explanation:
Jamie Lee needs to save a total of $9,000 in order to get started in her cupcake café venture. She is presently depositing $1,800 a year in a regular savings account. Calculate the future value of these deposits.
Answer: 16,200,000
Step-by-step explanation: divide both numbers
The future value of her deposit would be in 5 years.
The total amount needed to start a cupcake cafe venture
= $9,000
Deposit per year = $1,800
Therefore, if $1,800 = 1 year
$9,000 = X
[tex]x = \frac{9000}{1800} [/tex]
[tex]x = 5[/tex]
Therefore in 5 years, Jamie Lee would be able to start her cupcake café venture.
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In parallelogram HJKL if JM=19 find ML.
Answer:
19
Step-by-step explanation:
in any parallelogram the diagonals bisect each other evenly. that means if JM = 19, ML is also 19. hope this helps
Denise is going on a road trip with some friends. For the first leg of their trip, they drive on the highway for 2.5 hours before taking an exit. If they maintain a steady pace of 64 miles per hour, how far do they drive on the highway?
Answer:
160
Step-by-step explanation:
We know that [tex]\left \{ {{t=2.5} \atop {v=64}} \right.[/tex]
Formulate and substitute: [tex]d=2.5[/tex]×[tex]64[/tex]
Calculate the product or quotient: [tex]160[/tex]
Answer: [tex]160[/tex]
Someone help me pls
Answer:
-1 = 2(-1 -1) = -4
0 = 2(0-1) = -2
1 = 2(1-1) = 0
2 = 2(2-1) = 2
Step-by-step explanation:
x = the number on the left column
for the middle colum, you need to do 2(x -1)
for the right column, you do : (x - 1) x 2)
The city commission would like to install new flagpoles that are each 15 yards tall. If there are 3 feet in 1
yard, how tall are the flagpoles in the model?
The legs of a right triangle are √5 feet and square root √11 feet long. How long is the hypotenuse?
[tex]v^{2}[/tex]Answer:
4 feet long
Step-by-step explanation:
Pythagorean Theorem: [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
In this problem, a and b are the legs of the triangle, while c is the hypotenuse
Plugging the values of [tex]\sqrt{5}[/tex] and [tex]\sqrt{11}[/tex] to the equation you get:
5 + 11 = [tex]c^{2}[/tex]
Therefore, [tex]c^{2}[/tex] = 16, and by taking the square root you find that c, or the hypotenuse, must equal 4.
Look at attached photo. Will give brainiest to correct answer. Trigonometry.
Answer:
Step-by-step explanation:
What is the amplitude and period of the function shown below?
The features of the sine function in this problem are given as follows:
Amplitude: 2.
Midline: y = -4.
Period: 3 units.
What is trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here, we have,
The equation is given as follows:
y = 2sin(2πx/3) - 4.
we have to define the sine function:
The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are given as follows:
A: amplitude.
B: the period is 2π/B.
C: phase shift.
D: vertical shift.
The function has a minimum value of -6 and a maximum value of -2, for a difference of 4, hence the amplitude is given as follows:
2A = 4.
A = 2.
Without vertical shift, a function with amplitude of 2 would oscillate between -2 and 2, while this one oscillates between -6 and -2, hence the vertical shift is given as follows:
D = -4.
The shortest distance between repetitions can be given by 2 - (-1) = 3, hence the period is of 3 units and the coefficient B is given as follows:
2π/B = 3
B = 2π/3.
The function is at it's midline at the origin, hence it has no phase shift, and thus the equation is given as follows:
y = 2sin(2πx/3) - 4.
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Find the 6th term of the geometric sequence whose common ratio is
1/3
and whose first term is 5.
Step-by-step explanation:
geometric sequence means every new term is created by multiplying the previous term by a certain constant (here 1/3).
s1 = 5
s2 = s1 × 1/3 = 5 × 1/3
s3 = s2 × 1/3 = s1 × 1/3 × 1/3 = 5 × 1/9
sn = sn-1 × 1/3 = s1 × (1/3)^(n-1) = 5 × (1/3)^(n-1)
s6 = 5 × (1/3)⁵ = 5 × 1/243 = 5/243
Which number line shows the solution of –5x + 10 > –15? A. B. C. D.
[tex]-5x+10>-15\\\\\implies -5x> -10 -15\\\\\implies -5x > -25\\\\\implies x< 5\\\\\text{Interval,} ~(-\infty,5)[/tex]
Answer:
add the options, then we'll talk
Step-by-step explanation:
Triangle Angle Theorems Instruction Active Proving the Sum of the Interior Angle Measures of a Triangle ls 180° Try Angles Lines Statements Reasons Given: y || 2 Prove: m25 + m 22+ m26 = 180° 25 26 21 23 m21 m26 m23 m 25 A M M Reasons Statements 1 3 2 LE 4 5 Lo 7 6 B с Assemble the proof by dragging tiles to the Statements and Reasons columos.
Answer:
We would need to see the tiles and table. If you'd attach them I'd love to help
Step-by-step explanation:
The triangle is solved and the measure of internal angles = 180°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Let the two parallel lines be y and z
where y ║ z
And , ∠1 ≅ ∠5 and ∠3 ≅ ∠6 based on the interior angles theorem.
So , ∠1 = ∠5 and ∠3 = ∠6
And , the measure of ∠1 + ∠2 + ∠3 = 180° ( angles on straight line )
And , the measure of ∠5 + ∠2 + ∠6 = 180° ( angles on straight line )
where the measure of ∠1 = ∠5 ( alternate interior angles )
And , the measure of ∠3 = ∠6 ( alternate interior angles )
Hence , the triangle is solved
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The complete question is attached below :
Triangle Angle Theorems Instruction Active Proving the Sum of the Interior Angle Measures of a Triangle ls 180° Try Angles Lines Statements Reasons Given: y || 2 Prove: m25 + m 22+ m26 = 180°
The letters A, B, and C can be arranged in six ways. Five ways are listed below.
Find the sixth way.
АВС ACB BAC ВСА САВ
Answer:
CBA would be the sixth
Step-by-step explanation:
In a family with 77 children, excluding multiple births, what is the probability of having exactly 22 girls
Answer:
22/77
Step-by-step explanation:
just put the probable amount over the total amount for these
Which rational number could be graphed between 0 and 1?
A number line going from negative 5 to positive 3 in increments of 1.
O Negative one-half
O One-fourth
O Three-halves
O 1.75
O NEGATIVE ONE-HALF ........
Answer:
answer is D
Step-by-step explanation:
the answer is 1.75
If 10 candy cost $35. How much candy can I buy with $20
Answer:
6 candies
Step-by-step explanation:
(find unit rate, cost / quantity)
35/10 = 3.5
20/3.5 = = 5.7142857142857
candies cannot be in decimal so you must round to the nearest whole
) Which value is equivalent
[tex] {7}^{3} [/tex]
Answer:
343
Step-by-step explanation:
[tex]7^{3} = 7 * 7 * 7[/tex]
[tex]7^3 = 343[/tex]
-Chetan K
Is the ordered list 26, 39, 52, 65, 78 an arithmetic sequence?
Answer:
Yes
Step-by-step explanation:
It is an arithmetic sequence since it has a common difference which is 13.
78-65 = 13
65-52 = 13
52-39 = 13
39-26 = 13