Answer: d. 58
The height of the plant in June 1st is 58 centimeters.
Step-by-step explanation:
Given : On August 1st, a plant was 79 centimeters tall.
In June of that year it grew 12 centimeters, then 9 more centimeters in July.
Order of Month = June → July → August
Then , the height of the plant on June 1st would be
Height in August 1st - Height grew in June - height grew in July
= 79-12-9 centimeters
= 67-9 centimeters
= 58 centimeters
Therefore , the height of the plant in June 1st = 58 centimeters
Hence, the correct answer is d. 58
Assume that a surveyor stands at the top of a mountain that is "h" feet tall. If the distance (in feet) that he can see is defined by d = 3200.2 SQRT(h), then answer the following. (a) How far can the surveyor see from the top of a 2000-foot mountain? (b) How tall is the mountain, if the surveyor can see 15 miles? (Note: 1 mile equals 5280 feet.)
Answer:
a) d = 143,117 ft
b) h = 612.45 ft
Step-by-step explanation:
If height of the mountain = h
And distance till the surveyor can see = d = 3200.2 SQRT (h)
Refer to attached file for graphical representation
Then;
A) If h=2000 ft
Then d =3200.2 √ (2000)
d = 3200.2 (44.72)
d = 143,117 ft
B) If d = 15 miles
1mile = 5280 ft
15 mile = 15*5280
15 mile = 79,200 ft
Therefore;
d = 79,200 ft
Since,
d =3200.2 √ (h)
79,200 = 3200.2 √ (h)
79200/3200.2 =√ (h)
√ (h) = 24.75
{√ (h)} ² = (24.75) ²
h = 612.45 ft
Maggie can paint a fence in 9 hours, but Tom needs 12 hours to paint the same fence. How long does it take them to paint the fence if they work together? Round to the nearest tenth.
Working together, Maggie and Tom can paint the fence in 5.1 hours
Solution:Given that,
Maggie can paint a fence in 9 hours
So in 1 hour maggie paints, [tex]\frac{1}{9}[/tex] of the house
Tom needs 12 hours to paint the same fence
So in 1 hour, tom can paint [tex]\frac{1}{12}[/tex] of the house
To find: time taken to paint the fence if they work together
Let "a" be the time taken to paint the fence if they work together
So working together, in 1 hour, they can paint [tex]\frac{1}{a}[/tex] of the house
We can frame a equation as:
To see how much of the fence they can paint together in one hour, we add these together.
[tex]\frac{1}{9} + \frac{1}{12} = \frac{1}{a}[/tex]
[tex]\frac{1}{a}[/tex] is how much of the fence they can paint together in one hour. Therefore "a" is the number of hours it will take them both to paint the fence
On solving,
[tex]\frac{12 + 9}{12 \times 9} = \frac{1}{a}\\\\\frac{1}{a} = \frac{21}{108}\\\\a = \frac{108}{21} = 5.1428[/tex]
So working together, Maggie and Tom can paint the fence in 5.1 hours
State if the triangles in each pair of similar. If so, State how you know they are similar and complete the similarity statement.
Answer:
Step-by-step explanation:
They are not similar. If they were, ∠LMF and ∠GHF would both have the same angle measure and they do not.
Final answer:
Mathematics question on similar triangles; triangles are similar if they have congruent corresponding angles and proportional sides obtained through AA, SSS, or SAS criterion. A similarity statement describes the correspondence of the vertices.
Explanation:
The question provided falls within the subject of Mathematics, specifically within the study of geometry and the concept of similar triangles. To determine if two triangles are similar, we must check if they have the same shape, which implies that their corresponding angles are equal and their corresponding sides are in proportion. In other words, two triangles are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional. This can be verified by angle-angle similarity (AA), side-side-side similarity (SSS), or side-angle-side similarity (SAS). The similarity statement provides the order of correspondence of vertices between similar triangles.
When evaluating if triangles BAO and B1A1O are similar, we must compare their corresponding angles and sides. If the given information indicates that at least two angles of one triangle are congruent to two angles of another triangle (AA criterion), or that the sides are proportional (SSS or SAS criterion), then the triangles are similar. For instance, if ∠BAO ≅ ∠B1A1O and ∠BOA ≅ ∠B1O1A1, then by the AA criterion, the triangles are similar, and we could write the similarity statement as triangle BAO ∼ triangle B1A1O.
Let alpha and beta be conjugate complex numbers such that frac{\alpha}{\beta^2} is a real number and alpha - \beta| = 2 \sqrt{3}. Find alpha.
Final answer:
To find the value of alpha given that alpha and beta are conjugate complex numbers, and alpha/beta^2 is real, we can use the equation |alpha - beta| = 2√3. We can substitute alpha = a + bi and beta = a - bi, and solve for a and b to find the value of alpha.
Explanation:
Let α and β be conjugate complex numbers such that α/β² is a real number and |α - β| = 2√3. We need to find the value of α.
Since α and β are conjugate complex numbers, they have the form α = a + bi and β = a - bi, where a and b are real numbers. Substituting these values into the given equation, we get:
|α - β| = |(a + bi) - (a - bi)| = |2bi| = 2|b| = 2√3
From this, we can conclude that |b| = √3. Since |b| is the absolute value of b, it is always positive. Therefore, we have two options: b = √3 or b = -√3.
If b = √3, then α = a + √3i. We can substitute this into the equation α/β² to check whether it is a real number.
α/β² = (a + √3i)/(a - √3i)² = (a + √3i)/(a² - 2a√3i - 3) = [(a(a² - 3) + √3i(3a - a²)] / (a² - 2a√3i - 3)
This expression is not a real number, so b ≠ √3.
If b = -√3, then α = a - √3i. We can substitute this into the equation α/β² to check whether it is a real number.
α/β² = (a - √3i)/(a + √3i)² = (a - √3i)/(a² + 2a√3i + 3) = [(a(a² + 3) - √3i(3a + a²)] / (a² + 2a√3i + 3)
This expression simplifies to (a(a² + 3) - √3(3a + a²))/ (a² + 3) = a - √3(2a + 1)/ (a² + 3)
For this expression to be a real number, the imaginary term √3(2a + 1) must be equal to 0. So, we have √3(2a + 1) = 0.
Solving this equation, we get 2a + 1 = 0, which implies a = -0.5.
Therefore, the value of α is α = -0.5 - √3i.
A right triangle has a hypotenuse of 70 feet and a leg of 35 feet. What is the length of the other leg? A. 51 feet B. 61 feet C. 78 feet D. 80 feet
URGENT!!!!!
Answer: the answers b i think
Good evening ,
Answer:
The right answer is B.
Step-by-step explanation:
If we apply the Pythagorean theorem we get
the length of the other leg is :
√(70^2-35^2)
= √(3 675)
= 60,621778264911.
:)
a set of cards includes 15 yellow cards, 10 green cards and 10 blue cards. find the probability of each event when a card is chosen at random not yeallow or green
Answer:
P(not yellow or green)=\frac{2}{7}[/tex]
Step-by-step explanation:
a set of cards includes 15 yellow cards, 10 green cards and 10 blue cards
Total cards= 15 yellow + 10 green + 10 blue = 35 cards
Probability of an event = number of outcomes divide by total outcomes
number of outcomes that are not yellow or green are 10 blue cards
So number of outcomes = 10
P(not yellow or green)= [tex]\frac{10}{35} =\frac{2}{7}[/tex]
The probability of choosing a card that is neither yellow nor green from the set is 2/7, as there are 10 blue cards and a total of 35 cards.
Explanation:The question asks for the probability of choosing a card that is neither yellow nor green from a set containing 15 yellow cards, 10 green cards, and 10 blue cards. To find this probability, we must consider only the blue cards, as they are not yellow or green. The total number of blue cards is 10, and the total number of cards is 35 (since 15 + 10 + 10 = 35).
To calculate the probability, we use the formula:
P(Blue card) = Number of blue cards / Total number of cards = 10 / 35 = 2/7
Thus, the probability of randomly choosing a card that is not yellow or green (i.e., a blue card) is 2/7.
Find the imaginary part of\[(\cos12^\circ+i\sin12^\circ+\cos48^\circ+i\sin48^\circ)^6.\]
Answer:
The imaginary part is 0
Step-by-step explanation:
The number given is:
[tex]x=(\cos(12)+i\sin(12)+ \cos(48)+ i\sin(48))^6[/tex]
First, we can expand this power using the binomial theorem:
[tex](a+b)^k=\sum_{j=0}^{k}\binom{k}{j}a^{k-j}b^{j}[/tex]
After that, we can apply De Moivre's theorem to expand each summand:[tex](\cos(a)+i\sin(a))^k=\cos(ka)+i\sin(ka)[/tex]
The final step is to find the common factor of i in the last expansion. Now:
[tex]x^6=((\cos(12)+i\sin(12))+(\cos(48)+ i\sin(48)))^6[/tex]
[tex]=\binom{6}{0}(\cos(12)+i\sin(12))^6(\cos(48)+ i\sin(48))^0+\binom{6}{1}(\cos(12)+i\sin(12))^5(\cos(48)+ i\sin(48))^1+\binom{6}{2}(\cos(12)+i\sin(12))^4(\cos(48)+ i\sin(48))^2+\binom{6}{3}(\cos(12)+i\sin(12))^3(\cos(48)+ i\sin(48))^3+\binom{6}{4}(\cos(12)+i\sin(12))^2(\cos(48)+ i\sin(48))^4+\binom{6}{5}(\cos(12)+i\sin(12))^1(\cos(48)+ i\sin(48))^5+\binom{6}{6}(\cos(12)+i\sin(12))^0(\cos(48)+ i\sin(48))^6[/tex]
[tex]=(\cos(72)+i\sin(72))+6(\cos(60)+i\sin(60))(\cos(48)+ i\sin(48))+15(\cos(48)+i\sin(48))(\cos(96)+ i\sin(96))+20(\cos(36)+i\sin(36))(\cos(144)+ i\sin(144))+15(\cos(24)+i\sin(24))(\cos(192)+ i\sin(192))+6(\cos(12)+i\sin(12))(\cos(240)+ i\sin(240))+(\cos(288)+ i\sin(288))[/tex]
The last part is to multiply these factors and extract the imaginary part. This computation gives:
[tex]Re x^6=\cos 72+6cos 60\cos 48-6\sin 60\sin 48+15\cos 96\cos 48-15\sin 96\sin 48+20\cos 36\cos 144-20\sin 36\sin 144+15\cos 24\cos 192-15\sin 24\sin 192+6\cos 12\cos 240-6\sin 12\sin 240+\cos 288[/tex]
[tex]Im x^6=\sin 72+6cos 60\sin 48+6\sin 60\cos 48+15\cos 96\sin 48+15\sin 96\cos 48+20\cos 36\sin 144+20\sin 36\cos 144+15\cos 24\sin 192+15\sin 24\cos 192+6\cos 12\sin 240+6\sin 12\cos 240+\sin 288[/tex]
(It is not necessary to do a lengthy computation: the summands of the imaginary part are the products sin(a)cos(b) and cos(a)sin(b) as they involve exactly one i factor)
A calculator simplifies the imaginary part Im(x⁶) to 0
Mary read 42 pages of a book on Monday she read 2/5 of the book on Tuesday if she still had 1/4 of the book to read how many pages are there in the book
Answer: 120 pages
Step-by-step explanation:
42 p on Monday
2/5x on Tuesday
1/4x rest of book
---------------------------------------------------
42+2/5x+1/4x=x
42*20 +8x+5x=20x
840=20x-8x-5x
840=7x
x=840/7
x=120
The required number of pages in the book is given as 120 pages.
Given that,
Mary read 42 pages of a book on Monday she read 2/5 of the book on Tuesday if she still had 1/4 of the book to read how many pages are there in the book is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
here,
let the number of pages in the book be x,
According to the question,
x - 42 - 2/5x = 1/4x
x - 2/5x - 1/4x = 42
x[1 - 2/5 - 1/4] = 42
x[20 - 8 - 5] / 20 = 42
x [7] / 20 = 42
x = 6 × 20
x = 120 pages
Thus, the required number of pages in the book is given as 120 pages.
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If the function b(t) gives the number of boats it takes t people to cross a river, what is the appropriate domain?
Answer:
whole numbers
Step-by-step explanation:
The domain is the number of people. The smallest number of people you could have would be 0 people so the appropriate domain is whole numbers.
Make me the brainliest
Answer:
whole numbers
Step-by-step explanation:
demochares has ived a fourth of his life as a boy, a fifth as a youth, a third as a man, and has spend 13 years in his dotage. how old is he?
Answer: 60 years
Step-by-step explanation:
Let x denotes the age of Demochares .
Time he spent as a boy = [tex]\dfrac{x}{4}[/tex]
Time he spent as a youth = [tex]\dfrac{x}{5}[/tex]
Time he spent as a man= [tex]\dfrac{x}{3}[/tex]
Time he spent in dotage= 13 years
As per given , we have the following equation:
[tex]x=\dfrac{x}{4}+\dfrac{x}{5}+\dfrac{x}{3}+13[/tex]
[tex]x=\dfrac{15x+12x+20x}{60}+13[/tex] [Take LCM]
[tex]x=\dfrac{47x}{60}+13[/tex]
[tex]x-\dfrac{47x}{60}=13[/tex]
[tex]\dfrac{60x-47x}{60}=13[/tex]
[tex]\dfrac{13x}{60}=13[/tex]
[tex]x=13\times\dfrac{60}{13}=60[/tex]
Hence, he is 60 years old.
An egg farm packages 264 total cartons of eggs each month.The farm has three different sizes of cartons.The small carton holds 8 eggs,and 1/6 of the total cartons are small.TThe medium carton holds 12 eggs and 2/3 of the total Cardinals are medium to large carton holds 18 eggs and the rest of the total clients are large determine how many of each size of the curtain is needed each month then determine how many eggs are needed to fill the 264 cartons show your work or explain your answers
I don't know.. can you please explain it?
A circle has its center at (0,0) and passes through the point (0,9). What is the standard equation of the circle?
x² + y² = 0
x² + y² = 9
x² + y² = 9²
Answer:
Step-by-step explanation:
I believe the answer is x² + y² = 9²
What is the total interest earned in two years on an account containing $500 at 3.5% interest, compounded annually?
$35.61
$35.16
$35.00
$36.51
Answer: Compound interest is $36.61
Step-by-step explanation:
Initial amount deposited into the account is $500 This means that the principal,
P = 500
It was compounded annually. This means that it was compounded once in a year. So
n = 1
The rate at which the principal was compounded is 3.5%. So
r = 3.5/100 = 0.035
It was compounded for 2 years. So
t = 2
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 500 (1+0.035/1)^1×2
A = 500(1.035)^2 = $535.61
Compound interest = 535.6 - 500 = $35.61
The price of the dinner for the both of them was $30. They tipped their server 20% of that amount. How much did each person pay, if they shared the price of dinner and the tip equally?
Each person will pay 19.5 dollars.
Step-by-step explanation:
Given
Total bill for dinner = b=$30
First of all we will calculate the 30% of dinner bill to find the amount of tip
So,
[tex]Tip = t = 30\%\ of\ 30\\= 0.30*30\\=9[/tex]
the tip is $9
The total bill including tip will be:
[tex]= 30+9 = \$39[/tex]
Two persons have to divide the tip and dinner equally so,
Each person's share = [tex]\frac{39}{2} = 19.5[/tex]
Hence,
Each person will pay 19.5 dollars.
Keywords: Fractions, division
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At the price of $3 a pound of pork, Jason buys 8 pounds of pork and Noelle buys 10 pounds of pork. When the price rises to $5 a pound, Jason buys 5 pounds of pork and Noelle buys 7 pounds of pork. What is the market demand at $5?
Answer:
Market demand at $5 is 12 pork.
Step-by-step explanation:
In a market, the sum of individual demand for a product from buyers is known as market demand.
It is give that the at the price of $3 a pound of pork, Jason buys 8 pounds of pork and Noelle buys 10 pounds of pork.
So, market demand at $3 is
8 + 10 = 18
When the price rises to $5 a pound, Jason buys 5 pounds of pork and Noelle buys 7 pounds of pork.
So, market demand at $5 is
5 + 7 = 12
Therefore, the market demand at $5 is 12 pork.
why is it that when you take the squre root of a function that is squared you get an absolute value?
Answer and explanation :
When we square any number then its gives absolute value for example even when we square the negative numbers it will given positive , that is absolute value
So we can conclude that square of any number is absolute number
And then is we take square root of that absolute number it will always positive and absolute
if I'm in a plane flying at 512 miles per hour and a plane flies below me in the opposite direction, will it appear to fly slow or fast
Answer:
It appears to fly faster than its actual speed.
Step-by-step explanation:
In general, if talking about velocities, the direction of the movement should also be taken into account. For example, if two objects move in opposite directions, a person inside one object observes that the other one moving in the opposite goes faster than its actual speed (because the velocities are summed up). If they are moving in the same direction the opposite phenomenon is true (the velocities are subtracted).
Finally, in this example the planes move in opposite direction, therefore, a plane flying in the opposite direction will appear to fly faster.
The cost of a peanut butter bar is $0.07 more than the cost of a chocolate bar. If you buy 5 peanut butter bars and 6 chocolate bars, the total cost is $6.40. How much does the chocolate bar cost?
$0.61
$0.55
$0.54
$0.62
Hello!
To be quick and simple, your answer would be $0.55
The cost of the chocolate bar in the given scenario is $0.55. This was determined by solving a two-variable system of linear equations from the information provided.
Explanation:This problem is a classic example of a system of linear equations, specifically two-variable linear equations. Here, we need to find the cost of one chocolate bar and one peanut butter bar, and we have two pieces of information that can be translated into equations. The first information is that a peanut butter bar costs $0.07 more than a chocolate bar. The second is that 5 peanut butter bars and 6 chocolate bars total $6.40. We'll use these equations to solve for the variables.
Let's denote the cost of the chocolate bar as x and the cost of the peanut butter bar as y. Then, from the information given, we can form two equations:
y = x + $0.075y + 6x = $6.40Substitute the first equation into the second to solve for x:
5(x + $0.07) + 6x = $6.405x + $0.35 + 6x = $6.4011x + $0.35 = $6.4011x = $6.05x = $0.55So the cost of the chocolate bar is $0.55.
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A bicycle moves approximately 7 feet with each revolution of the wheels. If the bicycle wheels are making 30 revolutions per minute, approximately how many feet will the bicycle travel in 1 hour?
Answer:
[tex]12,600\ ft[/tex]
Step-by-step explanation:
step 1
Find out the number of revolutions in one hour
we know that
The bicycle wheels are making 30 revolutions per minute
One hour are 60 minutes
so
using proportion
[tex]\frac{30}{1}\ \frac{rev}{min}=\frac{x}{60}\ \frac{rev}{min}\\\\x=60(30)\\\\x=1,800\ rev[/tex]
step 2
Find out how many feet the bicycle will travel in one hour
we know that
A bicycle moves approximately 7 feet with each revolution and the number of revolutions in one hour is 1,800
so
Multiply the number of revolutions in one hour (1,800 rev) by 7 feet
[tex](1,800)7=12,600\ ft[/tex]
A man flies a kite at a height of 15 ft. The wind is carrying the kite horizontally from the man at a rate of 5 ft./s. How fast must he let out the string when the kite is flying on 32 ft. of string?
Answer:
4.4 ft/s
Step-by-step explanation:
Height = 15ft
Rate= 5 ft/s
Distance from the man to the kite= 32ft
dh/dt = 5 ft/s
h = √32^2 - 15^2
h = √ 1025 - 225
h = √800
h = 28.28ft
D = √15^2 + h^2
dD/dt = 1/2(15^2 + h^2)^-1/2 (2h) dh/dt
= h(225 + h^2)^-1/2 dh/dt
= (h / √225 + h^2)5
= (28.28 / √225 + 28.28^2)5
= (28.28 / √1024.7584)5
= (28.28/32)5
= 0.88*5
= 4.4 ft/s
Carol puts some green cubes and red cubes in a box. The ratio is 2:1. She adds 12 more cubes to the red cubes in the box and the ratio becomes 4:5. How many green cubes were in the box?
Answer:
16 green cubes are in the box.
Step-by-step explanation:
No. of red cubes at first (x):
4(x + 12) = 5(2x)
4x + 48 = 10x
6x = 48
x = 8
No. of green cubes:
= 8 * 2
= 16
Answer: 16 green cubes are in the box.
20 red cubes are in the box in the end.
Proof (the ratio in the end is 4:5):
= 16 is to 20
= 16/4 is to 20/4
= 4 is to 5
What does the fundamental theorem of algebra illustrate?
Answer:
The fundamental theorem of algebra guarantees that a polynomial equation has the same number of complex roots as its degree.
Step-by-step explanation:
The fundamental theorem of algebra guarantees that a polynomial equation has the same number of complex roots as its degree.
We have to find the roots of this given equation.
If a quadratic equation is of the form [tex]ax^{2}+bx +c=0[/tex]
Its roots are [tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
Here the given equation is [tex]2x^{2}-4x-1[/tex] = 0
a = 2
b = -4
c = -1
If the roots are [tex]x_{1} and x_{2}[/tex], then
[tex]x_{1}[/tex] = [tex]\frac{-2+\sqrt{(-4)^{2}-4\times 2\times (-1)}}{2\times 2}[/tex]
= [tex]\frac{4 +\sqrt{24}}{4}[/tex]
= [tex]\frac{2+\sqrt{6} }{2}[/tex]
[tex]x_{2}[/tex] = [tex]\frac{-2-\sqrt{(-4)^{2}-4\times 2\times (-1)}}{2\times 2}[/tex]
= [tex]\frac{4 +\sqrt{8}}{4}[/tex]
= [tex]\frac{2-\sqrt{6} }{2}[/tex]
These are the two roots of the equation.
Office Furniture Makers, Inc. uses machines to produce high quality office chairs for other firms. The initial cost of one customized machine is $750,000. This machine costs $12,000 a year to operate. Each machine has a life of 3 years before it is replaced. What is the equivalent annual cost of this machine if the required return is 10 percent? (Round your answer to whole dollars.)
The equivalent annual cost of the machine, considering a 10% return, is approximately $309,535 per year.
Explanation:First, accumulate the total cost over the lifespan of the machine which is $750,000 (initial cost) + ($12,000 * 3 years) = $786,000. The equivalent annual cost can be calculated using the formula for the present value of an annuity: PV = PMT [(1 - (1 + r)^-n ) / r], where 'PMT' is the payment per period, 'r' is the rate of return, and 'n' is the number of periods. Rearrange to calculate PMT: PMT = PV * r / (1 - (1 + r)^-n). Substituting in given values gives us, PMT = $786,000 * 0.1 / [1 - (1 + 0.1)^-3] = $309,535/year.
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Mr. Johnson currently has a square garden. It is in his garden and into a range of 5 feet shorter than three times shorter than times it width. He decides that the perimeter should be 70 feet. Determine the dimensions, in feet, of his new garden
Answer:
The Dimension of new garden is [tex]25 \ feet\ \times 10\ feet.[/tex]
Step-by-step explanation:
Given:
Perimeter of new garden = 70 feet.
Let the length of the new garden be 'l'.
Also Let the width of the new garden be 'w'.
We need to find the dimension of new garden.
Now Given:
Length is 5 feet shorter than three times it width.
framing the equation we get;
[tex]l =3w-5 \ \ \ \ equation\ 1[/tex]
Now we know that;
Perimeter of rectangle is equal to twice the sum of length and width.
framing in equation form we get;
[tex]2(l+w)=70[/tex]
Now Diving both side by 2 using Division property of equality we get;
[tex]\frac{2(l+w)}2=\frac{70}{2}\\\\l+w =35[/tex]
Now Substituting equation 1 in above equation we get;
[tex]3w-5+w=35\\\\4w-5=35[/tex]
Adding both side by 5 Using Addition Property of equality we get'
[tex]4w-5+5=35+5\\\\4w=40[/tex]
Now Diving both side by 4 using Division property of equality we get;
[tex]\frac{4w}{4}=\frac{40}{4}\\\\w=10\ ft[/tex]
Now Substituting the value of 'w' in equation 1 we get;
[tex]l =3w-5\\\\l =3\times10-5\\\\l = 30-5\\\\l= 25\ ft[/tex]
Hence The Dimension of new garden is [tex]25 \ feet\ \times 10\ feet.[/tex]
State the postulate or theorem you would use to prove each pair of triangles congruent.
If the triangles cannot be proved congruent, choose "Not Possible."
Answer:
Not possible
Step-by-step explanation:
The only information we are given are the pairs of angles that are congruent which is not enough information to prove that they are congruent
The triangles cannot be proved congruent by AAA postulates. Then the correct option is D which is not possible.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The two triangles are congruent if two sides are as well and the angle (angle between any of these two sides) among one triangle is congruent to the comparable two sides as well as the angle of a second triangle.
The triangles cannot be proved congruent by AAA postulates. Then the correct option is D which is not possible.
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Complete the statement to describe the expression (a+b)(d+e)(a+b)(d+e)left parenthesis, a, plus, b, right parenthesis, left parenthesis, d, plus, e, right parenthesis. The expression consists of factors, and each factor contains 4 terms.
Final answer:
To complete the statement describing the expression (a+b)(d+e)(a+b)(d+e), we expand it by multiplying each term. Simplifying the expression, we get a²*d² + 2a²de + 2abde + b²e².
Explanation:
To complete the statement describing the expression (a+b)(d+e)(a+b)(d+e), we need to expand it. This can be done by multiplying each term in the first factor by each term in the second factor and then multiplying the result by the third factor. So the expression becomes:
(a+b)(d+e)(a+b)(d+e) = (a*d + a*e + b*d + b*e)(a*d + a*e + b*d + b*e)
We can simplify this further by combining like terms:
(a*d + a*e + b*d + b*e)(a*d + a*e + b*d + b*e) = a²*d² + 2a²de + 2abde + b²e²
The total cost of producing a type of car is given by C(x)=12000−40x+0.04x2, where x is the number of cars produced. How many cars should be produced to incur minimum cost?
Answer:
Step-by-step explanation:
C'(x)=-40+0.08 x
C'(x)=0 gives
-40+0.08 x=0
x=40/0.08=500
C"(x)=0.08>0 at x=500
so C(x) is minimum if x=500
so 500 cars need to be produced for minimum cost.
or we can solve by completing the squares.
c(x)=12000+0.04(x²-1000 x+250000-250000)
=12000+0.04(x-500)²-0.04×250000
=0.04 (x-500)²+12000-10000
=0.04(x-500)²+2000
c(x) is minimum if x=500
To minimize the cost based on the provided quadratic cost function, 500 cars should be produced.
Explanation:This a problem of optimization in the arena of Calculus. The cost function C(x) = 12000-40x+0.04x2 is a quadratic function, and the minimum cost occurs at the vertex of the parabola described by this function.
For any quadratic function f(x)=ax2 +bx + c, minimum or maximum value occurs at x = -b/2a.
In this case, a = 0.04 and b = -40.
So minimum cost occurs when x = -(-40) / 2*0.04 = 500.
So, to incur minimum cost, 500 cars should be produced.
Learn more about Optimization in Calculus here:https://brainly.com/question/35182200
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Diana is painting statues. She has \dfrac{7}{8} 8 7 start fraction, 7, divided by, 8, end fraction of a liter of paint remaining. Each statue requires \dfrac{1}{20} 20 1 start fraction, 1, divided by, 20, end fraction of a liter of paint. How many statues can she paint?
Answer:
Number of statues that can be painted are 17
Step-by-step explanation:
Initially Diana has [tex]\frac{7}{8}[/tex] liters of paint remaining.
Every statue requires [tex]\frac{1}{20}[/tex] liters of paint for painting.
We have to find how many statues we will be able to paint with this remaining paint.
To get the number of statues,
Number of statues = [tex]\frac{Paint remaining}{Paint required for 1 statue}[/tex]
number of statues = [tex]\frac{\frac{7}{8} }{\frac{1}{20} }[/tex]
= [tex]\frac{35}{2}[/tex] = 17.5
Since the number of statues is not an integer the maximum number of statues that can be painted are 17.
Answer: 35/2
Step-by-step explanation:
HELP ASAP!!! BRAINLIEST!
its a b and c they all equal 45
Answer:
1 * 45
5 * 9
3 * 15
Hope this helps!
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Consider the rational expression (IMAGE ATTACHED)
3x^2−3/
3x^2+2x−1
Which statements are true?
Answer:
3x² is a term in the numeratorx + 1 is a common factorThe denominator has 3 termsStep-by-step explanation:
You can identify terms and count them before you start factoring. Doing so will identify 3x² as a term in the numerator, and will show you there are 3 terms in the denominator.
When you factor the expression, you get ...
[tex]\dfrac{3x^2-3}{3x^2+2x-1}=\dfrac{3(x^2-1)}{(3x-1)(x+1)}=\dfrac{3(x-1)(x+1)}{(3x-1)(x+1)}[/tex]
This reveals a common factor of x+1.
So, the above three observations are true of this rational expression.