The general algebraic identity is
A²+B²=(A+B)²-2ABLets derive
(A+B)²-4ABA²+B²+2AB-2ABA²+B²Hence verified
If an astronaut has a mass of 90 kg, and visits Jupiter which has a gravitational field of 25.3 N/kg, how much will he weigh there?
A. 115.3N
B. 64.7 N
C. 3.55 N
D. 2,277 N
Answer: 2277 Newtons
Step-by-step explanation:
I will show you how to do this the Physics way, so first we must write down our given values.
gravitational field = gravity = 25.3 N/kg
Mass of the astronaut = 90kg
Fun fact: know that if you convert the Newtons to a different unit, Newtons = kg (m/s^2) so we can say that instead of N/kg, we can write it as m/s^2 because if we divide kg(m/s^2) with kg, you’ll end with m/s^2
If you’re in physics, we always work with m/s^2 for every acceleration that exists. So we basically have 25.3 m/s^2 for gravity.
To find the weight, we can use the F=ma formula but rewritten as Weight = mass * gravity
Weight = (90kg)(25.3 m/s^2) = Option D = 2277 Newtons
Find the area of EFGH
The area of triangle FGH that is similar to triangle ABC is: 8 square feet.
What is the Area of Similar Figures?If two shapes are similar, the ratio of their areas equals the ratio of the square of their corresponding sides.
Therefore:
area of triangle EFG / area of triangle ABC = FG²/BC²
Plug in the values
area of triangle EFG / 18 = 2²/3²
area of triangle EFG / 18 = 4/9
area of triangle EFG = (18×4)/9
area of triangle EFG = 8 sq. ft.
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5. Find the equation of the line that is perpendicular to the given line and passes through the given point. y = 5x-1; (-1, 1)
Answer:
y = -0.2x+ 0.8
Step-by-step explanation:
If a line is perpendicular to another line then the slope of the line = the negative reciprocal of the other line
Here Line AB has the equation y = 5x - 1. Here slope = 5
This comes from the fact that if a line has the equation y= mx + c then the slope = m and the y intercept = c
If XY is the line perpendicular to AB then its slope = -1/5. Let the y intercept of XY be c
Then equation of line XY is: y = (-1/5)x + c = -0.2x + c (1)
Since it passes through (-1, 1) ie through x = -1, y=1, substitution these values into the above equation (1), we get
1 = (-0.2)(-1) + c or
1 = 0.2 + c or
c = 0.8
Jimmy is writing a paper for one of his classes. The paper has to be 3,000 words long, and so far he has written 666 words. If he
only has 6 more days to write his paper and wants to write the same number of words each day, then how many words must he write per day to finish the paper?
A. 425
B. 389
C. 2,334
D. 889
Round 82585 to the nearest ten thousand. Enter your answer in the box
below.
A right rectangular pyramid is shown below. Which of the following shapes cannot result from a cross section?
Answer:
The cross section is a trapezoid.
Step-by-step explanation:
Question 11(Multiple Choice Worth 5 points)
(03.06A LC)
Which statement is true for the equation 2x - 2x - 7 = -7?
It has infinitely many solutions.
It has two solutions.
It has one solution.
It has no solution.
Answer:
A) It has infinitely many solutionsStep-by-step explanation:
Given equation
2x - 2x - 7 = - 7Variables cancel and the equation simplifies as
- 7 = - 70 = 0Since we got both sides equal, it doesn't change with any value of x.
It means the equation has infinitely many solutions.
It has infinite solution
Need help for this please
find the domain and range
Answer:
Domain: all real numbers (all reals)
Range: y> OR EQUAL TO -2
Step-by-step explanation:
Hope this helps! ;-)
At a store, Eva bought two shirts and five hats for $154.00. Nicole bought
three same shirts and four same hats for $168.00. What is the price of each
shirt? _____
can anyone help me with this? 10th grade geometry
Answer:
In romania I was doing this in the 6th grade
Step-by-step explanation:
5.
A B and D C are parallel lines.
"slope" means inclination. and as you can imagine, parallel lines must have the same inclination, or they would not be parallel.
so, the slope of D C must be also 2/7.
4.
same thing as with 5.
both lines are parallel and must therefore have the same slope.
so, the slope of D C is also 3/4. and the first answer is correct.
25 points please help
Answer:
See below ~
Step-by-step explanation:
The functions which have a range ≥ -1 :
y = |x - 1| + 2y = |x + 2| - 1The first function (according to the attachment) is not part of this because on applying any value for x, it will be either less than or equal to -1.
Find the amount accumulated after investing m principal P for t and an internet rate compounded annually P=40500 r=3.8% t=20 k=12
The amount of money accumulated after investing the given amount of money at the given rate and time period is $85389.
What is an interest in banking?Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.
The formula for calculating compound interest is expressed as;
A = P(1 + r/k)^(k*t)
Where A is final amount, P is initial principal balance, r is interest rate, k is number of times interest applied per time period and t is number of time periods elapsed.
Given that;
Initial principal balance P = $40500Interest rate r = 3.8= 3.8/100 = 0.038Time t = 20 yearsNumber of times interest applied per time period = 12 (annually) = 12/12 = 1 Amount accumulated A = ?A = P(1 + r/k)^(k*t)
A = 40500(1 + 0.038/1)¹ˣ²⁰
A = 40500 × (1.038)²⁰
A = 40500 × 2.10837
A = $85389
Therefore, the amount of money accumulated after investing the given amount of money at the given rate and time period is $85389.
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A Ferris wheel has a diameter of 60 m, with a minimum height of 9 m above the
ground. It takes 20 seconds for the Ferris wheel to complete one rotation. If a rider
boards a car when it is at its lowest point
O: What is the minimum height of the rider?
A: Minimum height of the rider is __ meters.
No Links Or I’ll Report You
By knowing geometrical dimensions, the minimum height of the rider in the Ferris wheel, modeled by a sinusoidal function, is equal to a height of 9 meters.
How to analyze a Ferris wheel
The model of the height of a Ferris wheel is represented by a sinusoidal model, which is presented below:
h = A + B · sin ωt (1)
Where:
A - Midpoint height, in meters. B - Amplitude, in metersω - Angular frequency, in radians per second.t - Time, in secondsSinusoidal functions are bounded functions, the minimum height of the Ferris wheel represents the lower bound of the function and the maximum height is the upper bound. Therefore, the minimum height of the rider is:
[tex]h_{min} = 39\,m - 30 \,m[/tex]
[tex]h_{min} = 9\,m[/tex]
By knowing geometrical dimensions, the minimum height of the rider in the Ferris wheel, modeled by a sinusoidal function, is equal to a height of 9 meters.
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Gabrielle angles her pool cue against the edge of her pool table, as shown below. What is the measure of angle a and angle b
The relationship between angle A and angle B is supplementary angles.
∠A = 2(5) + 40 = 50 degrees
∠B = 5 + 125 = 130 degrees
What are supplementary angles?Supplementary angles are angles that sum up to 180 degrees. The sum of the two angles for a supplementary angles is 180 degrees .
Therefore, the relationship between angle A and angle B is supplementary angles.
Therefore,
∠A + ∠B = 180 degrees
∠A = 2x + 40
∠B = x + 125
2x + 40 + x + 125 = 180
2x + x + 40 + 125 = 180
3x + 165 = 180
3x = 180 - 165
3x = 15
x = 15 / 3
x = 5
Therefore,
∠A = 2(5) + 40 = 50 degrees
∠B = 5 + 125 = 130 degrees
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a classmate states that if the radius of a circle is doubled, then its area is doubled. do you agree or disagree? if you disagree, how much larger do you think the area will be?
Answer:
yes
the area of a circle is πr^2
A=πr^2
which means the area of a circle is dependent on the size of the radius of the circle.
Take for instance, the radius is 3cm and π= 3.142
A = 3.142×(3^2)
A = 28.278cm^2
Another example, if the radius of the circle is increased to 4cm, what will be the area.
A = 3.142×(4^2)
A = 50.272cm^2
PLEASE ANSWER
Given JAM and segment PB such that PB JM, what is the missing justification in the proof that JP/PA = MB/BA
Answer:
B. AA similarity postulate
What is the square root of 9
Which expression is equivalent to 6^4 • 6^3?
(6•6•6•6)+(6•6•6)
(6+6+6+6)•(6+6+6)
(6•6•6•6)•(6•6•6)
(6•6•6•6•6)•(6•6•6•6)
Answer: C)
Step-by-step explanation:
A company rents storage sheds shaped like rectangular prisms. Each shed is 11 feet long, 7 feet wide, and 12 feat tall. The rental cost is $3 per cubic foot. How much does it cost to rent one shed?
Answer:
308
Step-by-step explanation:
so to find how much a rectangular prisim is by
length * with* height
11* 7 * 12
= 924 cubic feet
and then we just divid by 3
=308
Rewrite without parentheses and simplify.
(2-5y)²
Answer:
Your answer is in the Picture.
Step-by-step explanation:
Visit cymath is you want to factor polynomial or simply for you.
Two buildings are 96 ft apart . The first building is 164ft tall. The second building is 92ft tall. If a string is stretched between the top of the two buildings so that it forms a straight line from the top of one to the top of the other, how long would the string be
Answer:
120ft
Step-by-step explanation:
may someone help me please?
Step-by-step explanation:
Radio=
Normal Price = K48.
Discount 20%
Selling Price
How many three digit numbers can you make by arranging the numbers 5, 4, and 9.
okay,here is about a formula.
n=2x
where x is the numbers.
n=2×3
n=6.
therefore the three digit numbers which can be obtained is 6.
Starting time: Elapsed time: 50 minute Ending time: 9:05 A.M.
[tex]help[/tex]
Answer:
8:15 am.
Step-by-step explanation:
So the starting time will be 50 minites before 9:05 am.
That will be 9:05 - 50
= 9:00 - 45
= 8:15 am.
Select the correct answer. Consider the given function. 5, x < -2 3, 2 f(x) = 0, 0≤x≤2 -3, 2 Which graph represents the given function?
help!!
⇒ open circle at (-2, 5) with a line to the left
⇒ closed circle at (-2, 3) with a line segment to an open circle at (0, 3)
⇒ closed circle at (0, 0) with a line segment to an open circle at (2, 0)
⇒ closed circle at (2, -3) with a line to the right
Sorry it is hard to read, I’m using an iPhone 6 lol
Giving brainliest
Answer:
Domain: [tex]\displaystyle (-\infty,-3)\cup(-3,6)\cup(6,\infty)[/tex]
Range: [tex](-\infty,0)\cup(0,\frac{1}{9})\cup(\frac{1}{9},\infty)[/tex]
Step-by-step explanation:
Factor the numerator and denominator
[tex]\displaystyle f(x)=\frac{x-6}{x^2-3x-18}\\ \\f(x)=\frac{x-6}{(x-6)(x+3)}\\\\f(x)=\frac{1}{x+3}[/tex]
Because the factor [tex]x-6[/tex] exists in both the numerator and denominator, then there is a hole at [tex]x=6[/tex] because the function is not continuous there. Additionally, because the denominator cannot be 0, [tex]x\neq-3[/tex], and there will be a vertical asymptote at the line [tex]x=-3[/tex].
Thus, the domain of the function is [tex]\displaystyle (-\infty,-3)\cup(-3,6)\cup(6,\infty)[/tex].
Also, notice that because [tex]x\neq6[/tex], as the function gets closer to [tex]x=6[/tex], the function gets closer to [tex]\displaystyle f(6)=\frac{1}{6+3}=\frac{1}{9}[/tex], so [tex]\displaystyle y=\frac{1}{9}[/tex] is not included in the range.
Thus, the range is [tex](-\infty,0)\cup(0,\frac{1}{9})\cup(\frac{1}{9},\infty)[/tex].
Simplify radical expression
√10z^5 - z^2 √10z
Answer:
√10z^3(z - 1)(z + 1).
Step-by-step explanation:
The GCF is √10z* z^2
= √10z^3
So factoring we get
√10z^3(z^2 - 1) The expression in brackets is difference of 2 squares so:
= √10z^3(z - 1)(z + 1)
Melissa Doubet's home is insured for 90% of its replacement value of $94,000, or
$84,600. Use the chart below to determine the amount of coverage for her personal
property.
Insurance Coverage Chart
Coverage
Percent of Coverage
Garage and other structures
15%
Loss of use
30%
Personal property
60%
O $51,276
O $47,328
$50,760
$49,970
Based on the percentage coverage for personal property, the amount of coverage for Melissa's personal property is $50,760.
What is Melissa's personal property coverage?This can be found by the formula:
= Replacement value x Percentage of personal property coverage
Solving gives:
= 84,600 x 60%
= $50,760
In conclusion, Melissa's personal property coverage is $50,760.
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A shop has 31 plant pots.
Some are blue, some are yellow and the rest are red.
There are five more blue pots than yellow pots.
There are four times as many blue pots as there are red pots..
Calculate how many pots there are of each colour.
Answer:
16 blue, 11 yellow, and 4 red
Step-by-step explanation: