An airplane can ascend at a rate of 50 1/2 meters in 2/3 of a second. How many meters can the airplane ascend in one second?
Answer:
78.75
Step-by-step explanation:
A particle moves along the x-axis so that at time t ≥ 0 its position is given by x(t) = 2t3 - 21t2 + 72t - 53. At what time t is the particle at rest?
Step-by-step explanation:
The particle is at rest when the derivative of x(t), which is its velocity, is zero, i.e.,
[tex]\dfrac{d}{dt}[x(t)] = \dot{x}(t) = 0[/tex]
Since [tex]x(t) = 2t^3 - 21t^2 + 72t - 53,[/tex] its derivative is
[tex]\dot{x}(t) = 6t^2 - 42t + 72[/tex]
Equating this to zero, we get
[tex]6t^2 - 42t + 72 = 0 \Rightarrow t^2 - 7t + 12 = 0[/tex]
This is a familiar quadratic equation whose roots are
[tex]t = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]\;\;\;= \dfrac{7 \pm \sqrt{(7)^2 - 4(1)(12)}}{2}[/tex]
[tex]\;\;\;= \dfrac{7 \pm 1}{2}[/tex]
[tex]\;\;\;= 3\;\text{and}\;4[/tex]
This means that the particle will be at rest at t = 3 and t= 4.
GEOMETRY The perimeter of a square is four times the length of one side. If the side length of a square is 1 centimeter, then the perimeter of the square is 4 centimeters. Write an equation in point-slope form to find the perimeter y of a square with side length x.
Answer:
y-4=4(x-1)
Step-by-step explanation:
Write the equation in slop-intercept form and get the slope and point from the equationy=4x
The slope of the equation = m = 4
when x=1
y=4(1)
y=4
we get point from the equation which is (1,4)
Now we write the equation in point-slope form
point-slope formula = y-y₁=m(x-x₁)
*plot the the point we get and the slope in the formula above
= y-4=4(x-1)
An equation in point-slope form to find the perimeter y of a square with side length x is y-4=4(x-1).
Given that, the perimeter of a square is four times the length of one side.
What is the point slope form?The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.
The equation of the point slope form is: (y - y1) = m(x - x1)
where, (x, y) is a random point on the line and m is the slope of the line.
The equation is y=4x
If the side length of a square is 1 centimeter, then y=4
So, the coordinate point is (1, 4)
The slope of an equation y=4x is 4
Put (x1, y1)=(1, 4) and m=4 in slope intercept form
That is, slope intercept form is y-4=4(x-1)
Therefore, an equation in point-slope form to find the perimeter y of a square with side length x is y-4=4(x-1).
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300000÷_________=300.
Answer:
1000
Step-by-step explanation:
Answer:
100000
Step-by-step explanation:
HELP PLEASE I REALLY NEED IT
Answer:
18
Step-by-step explanation:
1/2 bh
1/2 (6)(6) multiply
1/2 (36) divide
18
A survey of 600 nurses yielded the following information: 427 were health club members, 325 were smokers, and 245 of the health club members were smokers. How
many of the 600 surveyed nurses were health club members or were smokers?
The number of surveyed nurses that were health club members or were smokers is 316.
Let the total number of nurses be 600 nursesn(U) = 600Let H be health club members, n(H) = 427Let S be smokers, n(S) = 325If 245 of the health club members were smokers, then n(HnS) = 245 members.
The number of surveyed nurses that were health club members or were smokers = 600 - [(427 - 325) + (427-245)].
The number of surveyed nurses that were health club members or were smokers = 600 - (102+182) = 600 - 284.
The number of surveyed nurses that were health club members or were smokers is 316.
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If Alex is 14 years old, and Ben is 17 years old, in how many years will the sum of their ages be 169 years?
Answer:
69 years
Step-by-step explanation:
Sum of Alex's and Ben's current age
= 14 +17
= 31 years
For every year, Alex and Ben will each be one year older. Thus, 2 years would be added to the sum of their ages with each passing year.
Difference in the sum of their ages
= 169 -31
= 138 years
Number of sets of 2 years
= 138 ÷2
= 69
Thus, the sum of their ages will be 169 in 69 years.
A parachutist's rate during a free fall reaches 165 feet per second. What is this rate in meters per second? At this rate, how many meters will the parachutist fall
during 20 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
A 2ft-by-2ft square is divided into smaller squares and portions are shaded. What is the area of the shaded portion?
Answer:
1.5 ft^2
Step-by-step explanation:
Since the length is divided into 4 parts,
Length of a small square = 2/4
= 0.5 ft
Hence,
Area of 1 small square = (0.5)(0.5)
= 0.25 ft^2
Area of shaded portion = Area of 6 small squares
= 6(0.25)
= 1.5 ft^2
Step-by-step explanation:
The area of the shaded cubes is 3 square feet.
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given side²
We have,
Since the 2 ft-by-2 ft square is divided into 16 smaller squares, each smaller square has an area of:
(2/4)ft = 0.5ft.
Now,
Out of the 16 smaller squares, 6 smaller cubes are shaded.
Since each smaller cube occupies the space of one of the smaller squares, the total area of the shaded cubes is 6 times the area of one of the smaller squares.
The area of the shaded cubes is:
6 x 0.5ft² = 3ft²
Thus,
The area of the shaded cubes is 3 square feet.
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trIangle ABC was reflated over y-axis. the coordinate of point A are(6,-4). what are the coordinate of A
Answer:
(-6,-4)
Step-by-step explanation:
Rule for reflection over the y axis (x,y) -----> (-x,y)
Explanation of rule : change the sign of the x value and keep the y value the same.
Applying rule to given coordinate
(6,-4) -----> change the sign of 6 to get -6 and keep -4 as it is -----> (-6,-4)
Refer to the attached image for more validation. Note that x=0 is the y axis
solve the equation 5-x=8
Answer:
x = -3
Step-by-step explanation:
1. 5 - x = 8
2. +x +x
3. 5 = x + 8
4. -8 -8
5. x = -3
PLEQSE ANSWER ASAP!!!!!!!!!!!!!!!!
Answer: (a) identity
Step-by-step explanation:
Anything multiplied by 1 will be considered an equation that is identity property.
A store sells laptops for $720 each. This price is 20 percent more than what it cost the store to buy each of them. Before the next model's release, store employees can purchase any remaining laptops at 23% off the store's cost. How much would it cost an employee to purchase one of these laptops at the sale? PLS HELP
It would cost an employee $443.52 to purchase one of these laptops at the sale.
The selling price of the laptops is $720 each. The cost price is 20 percent more than the cost price.
Cost price = Selling price - 20% of cost price
Cost price = 720 - 20% * 720 = $576
At the release, the laptops are at 23% off the store's cost. Hence:
Price of laptop at release = 576 - 23% of 576
Price of laptop at release = $443.52
It would cost an employee $443.52 to purchase one of these laptops at the sale.
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Pls help I’ll brainlest ASAP
Answer:
Slope = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
rise over run = slope
Emple
Six pounds of grapefruit cost $3. What is the cost per pound?
You can use a double number line to help you find ate and
unitate Start with the ratio you know: 53 for 6 pounds
Divide both 53 and 6 pounds by 3 to get 1 for 2 pounds
Then divide 51 and 2 pounds by 2 to find the cost per
pound, which is so. So for 1 pound.
1
Notice that you can also divide 3 by 6 to get the cost per
pound directly
In the example, how much would it cost to buy 3.4 and
5 pounds of grapefruit? Explain how you found your
answers
Answer:
0.50
Step-by-step explanation:
What is g(x)?
10-
у
5
X
+
10
d
A
-5
-10
A. g(x) = -1x1
B. g(x) = -x
C. g(x) = -x2
D. g(x) = -2X
C
Step-by-step explanation:
This has a U like shape so it a parabola.
Parabola correlate with quadratic functions
[tex]y = {ax}^{2} + bx + c[/tex]
Since it Going down, the answer is C -x^2.
The function whose graph is given is g(x) = -x²
What is a function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given that a graph, we need to find its function,
Since, the graph is a curve opened downwards, so it is a parabola, opened downwards,
The equation of the parabola is given by y = ax²+bx+c
Therefore, out of the given options we can say that the function is y = x²
Hence the function whose graph is given is g(x) = -x²
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Solve for the value of X
Check the picture below.
Which expression is equivalent to \sqrt [ 3 ] { 32 x ^ { 8 } y ^ { 10 } } ?
Answer:3x⁵
Step-by-step explanation: is equivalent to 3x⁵
Using the graph at right, where is the function increasing/decreasing? Where is the function concave up/down? Does this function have any
maxima or minima? Explain how you know
Explanation:
Start by calculating the first derivative of f(x) - use the quotient rule
ddx(f(x))=[ddx(x2)]⋅(x2+3)−x2⋅ddx(x2+3)(x2+3)2
f′=2x⋅(x2+3)−x2⋅2x(x2+3)2
f′=2x3+6x−2x3(x2+3)2=6x(x2+3)2❤
A 15 kg ball is thrown into the air. It is going at 4m/s when thrown. How much potential energy will it have at the top?
Answer:
P.E = mgh = 120N
Step-by-step explanation:
v² = u² - 2as
At the top, the velocity is = 0
0² = 4² - 2 x 10 x s
4² = 20s
s = 16/20
s = 0.8metres.
It rose only 0.8metres.
Therefore P.E = 15 x 10 x 0.8
:. P.E = 15 * 8
:. P.E = 120N
Which value of x makes the following equation true?
4.8(x - 4) = -0.2x + 15.8
A. 6
B. 10
C. 7
D. 9
Answer:
C
Step-by-step explanation:
multiply through by 10
10{4.8(x-4)} = 10(-0.2x) + 10(15.8)
48(x-4) = -2x + 158
48x - 192 = -2x +158
48x + 2x = 158 + 192
50x = 350
divide through by 50
x=350/50
x=7
therefore, answer = C
Mike Jones bought a new split-level home for $150,000 with 20% down. He decided to use Victory Bank for his mortgage. They were offering for 25-year mortgages. Provide Mike with an amortization schedule for two periods. (Use Table 15.1(b)). (Do not round intermediate calculations. Round your answers to the nearest cent.) Payment number Portion to— Balance of loan Interest Principal outstanding 1 2
Because Aaron, age 32, is a smoker, he must pay more for life insurance. Given that Company A charges 20% more for smokers, Company B charges 18% more for smokers, Company C charge 25% more for smokers and Company D charges 15% more for smokers, Aaron decides to buy his $250,000 policy from Company B. Which of the following statements is true? A 5-column table with 3 rows titled Annual Insurance Premiums (per 1,000 dollars of face value) 10 year term. Column 1 is labeled age with entries 30, 31, 32. Column 2 is labeled Company A with entries 1.30, 1.57, 1.86. Column 3 is labeled Company B with entries 1.29, 1.55, 1.86. Column 4 is labeled Company C with entries 1.40, 1.64, 2.07. Column 5 is labeled Company D with entries 1.49, 1.88, 2.25. a. Aaron is paying the smallest premium possible with Company B. b. Aaron is paying $93 more in premiums than he would with Company A. c. Aaron is paying $129 more in premiums than he would with Company C. d. Aaron could have chosen any company because the premiums are all the same. Please select the best answer from the choices provided A B C D
Answer:
answer B
Step-by-step explanation:
becuase b is bad for you
Bill wanted to know how many times students at his middle school go to the beach each week during the summer. He surveyed every other middle school student at the mall last Saturday. After analyzing the data collected, Bill determined that the average student from his middle school goes to the beach about 2.4 times a week during the summer. What error did he make in the survey?
The survey was intended for Bill's middle school during the summer. The
survey was administered to students of other schools on a Saturday.
The type of error is the selection bias error.Reasons:
The type of error made is a non sampling error, given that the target of the
study is the number of times in a week students at his middle school
attend the beach during the summer.
The errors are; Selection bias error.
The given that the students survey are not from his middle school.The survey was carried out once on a Saturday, where the target was during the summer.The selection bias error is a type error that is due to the researcher
chooses what to study, such that the participant have common
characteristics rather than being random.
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A doughnut shop sells 30 kinds of doughnuts. In how many ways can you get a bag of 12 doughnuts if you want at least 3 glazed doughnuts and at least 4 raspberry doughnuts
Answer:
86493225
Step-by-step explanation:
Hope it helps
s.p. is 4000, profit is 25% than find c.p.please explain itt
[tex] \sf= \frac{100}{100 + 25} \times 4000 \\ = \frac{100}{125} \times 4000 \\ = \frac{4}{5} \times 4000 \\ = 4 \times 800 \\ = 3200[/tex]
[tex] \huge \sf \: Answer[/tex]
The cost price is 3200.
Hope you could get an idea from here
Doubt clarification- use comment section.
Which answer shows the correct solution for 6x + 19x - 4 = 5(5x + 4)?
No solution
Infinitely many
One solution
Answer:
No solution
Step-by-step explanation:
25x-4=5(5x+4)
Distributive Property= 25x-4=25x+20
Solve for x
-4=20
Not possible so no solution.
Answer:
A
Step-by-step explanation:
6x + 19x -4 = 5(5x+4)
6x + 19x -4 = 25x+20
6x + 19x- 25x = 20+4
Combine Like terms
0 = 20 +4
0 = 24
0 = 24 = No solution
How do I do this? It's a modulus question.
Need help solving homework
Find the slope of an equation f(x)=-3sqrt(x) at the point (9,-9)
Answer:
Slope is [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=-3\sqrt{x}[/tex]
Find the derivative using the product rule:
[tex]f'(x)=\frac{d}{dx}(-3)*\sqrt{x}+-3*\frac{d}{dx}\sqrt{x}[/tex]
[tex]f'(x)=-3*\frac{1}{2\sqrt{x}}[/tex]
[tex]f'(x)=\frac{-3}{2\sqrt{x}}[/tex]
Plug in coordinates to find slope at that point:
[tex]f'(9)=\frac{-3}{2\sqrt{9}}=\frac{-3}{2(3)}=\frac{-3}{6}=-\frac{1}{2}[/tex]
Therefore, the slope of the equation at the point (9,-9) is [tex]-\frac{1}{2}[/tex].
Answer:
Step-by-step explanation:
f(x) = -3√x
f'(x) = -1.5/√x
f'(x) = -1.5/√9
f'(x) = -1.5/3
f'(x) = -0.5