Answers
So, we know that:
[tex]A=\dfrac{1}{2}ab\\P=a+b+c\\a^2+b^2=c^2[/tex]
We also know that [tex](a+b)^2=a^2+2ab+b^2[/tex]. We will use that fact to find [tex]c[/tex] in terms of [tex]A[/tex] and [tex]P[/tex].
[tex]A=\dfrac{1}{2}ab\Rightarrow 2ab=4A\\P=a+b+c\Rightarrow a+b=P-c[/tex]
Therefore:
[tex](P-c)^2=c^2+4A\\P^2-2cP+c^2=c^2+4a\\2cP=P^2-4A\\c=\dfrac{P^2-4A}{2P}[/tex]
Related Questions
Suppose that y varies inversely with the square of x and y = 50 when x = 4. Find y when x = 5
Answers
Answer:
y = 32.
Step-by-step explanation:
y = k/x^2 where k is the constant of variation
When y = 50 x = 4, so
50 = k / (4)^2
f = 50 * 4^2 = 800.
So the relation is
y = 800/x^2
When x = 5
y = 800/5^2
= 32.
HELP WHAT DOES THIS EVEN MEAN
Answers
Answer:
59.5
Step-by-step explanation:
He is asking for angle A
cosA = adjacent/hypotenuse
= 33/65
we'll do shift cos(33/65) = 59.48 to bring A
How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 8 forwards, 6 midfield players and 8 defensive players?
Answers
Using the combination formula, it is found that there are 47,040 ways to form a soccer team.
What is the combination formula?Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex]
A soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 8 forwards, 6 midfield players and 8 defensive players
Since they are independent of each other, the total number of combinations will be;
[tex]^mC_k = \dfrac{8!}{3! \times (5)!} \times \dfrac{6!}{4! \times (2)!} \times \dfrac{8!}{3! \times (5)!} \\\\^mC_k =47,040[/tex]
Hence, There are 47,040 ways to form a soccer team.
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Solve the following factorize and the en- equation of quadrate equation X² + 5x + 7 x = 0
Answers
Answer:
{-12,0}
Step-by-step explanation:
first to solve this can collect like terms and add
X² +12x=0
and solve it by factorization method
X² +12x=0
x(x+12)=0
it means x multiplied by x = X² then x multiplied by 12 = 12x
so this means x or (x+12) equals to zero
x=0 and (x+12)=0
x+12=0
x=-12
so the solution set is {-12,0}
but can also be done by formula method
Properties of Light Lab Report
Instructions: In the Properties of Light—Bending Light Lab you will explore how light rays interact as they pass from one material, or medium, to another. Record your observations in the lab report below. You will submit your completed report.
Name and Title:
Include your name, instructor's name, date, and name of lab.
Objective(s):
In your own words, what was the purpose of this lab?
Hypothesis:
In this section, please include the if/then statement you developed during your lab activity. This statement reflects your predicted outcome for the experiment.
If I project light rays through (choose one: air, water, glass), then they will refract, or bend, the most.
Procedure:
Please be sure to identify the test variable (independent variable) and the outcome variable (dependent variable) for this investigation. Remember, the test variable is what is changing in this investigation. The outcome variable is what you are measuring in this investigation.
Test variable (independent variable):
Outcome variable (dependent variable):
Select Intro to begin.
Once the simulation loads, you will drag the protractor onto the screen so that the 0 lines up with the dotted line in the center of the screen. Select the More Tools icon at the bottom of the lab interactive and be sure to select the Normal and Angles boxes. Do Not move the laser light.
You will test all three materials in the bottom, blue half of the screen: air, water, and glass. Remember, do not move the laser light.
Record your observations of how the light rays interact as they pass from air, on the top of the screen, through the three materials on the bottom of the screen
Data:
Record the data from each trial in the data chart below. Be sure to fill in the chart completely.
Material Interactions
List any observations you made as the light rays passed from the air on the top of the screen to the selected material on the bottom of the screen. Evidence
Using the protractor, measure the angle as the light passes from the top material to the bottom material on the screen. Also, note the index of refraction for each as indicated on the screen.
Trial One Air on top
Bottom angle:
Bottom index of refraction:
Air on bottom
Trial Two Air on top
Bottom angle:
Bottom index of refraction:
Water on bottom
Trial Three Air on top
Bottom angle:
Bottom index of refraction:
Glass on bottom
Conclusion:
Your conclusion will include a summary of the lab results and an interpretation of the results. Please write in complete sentences.
Did your data support your hypothesis? Use evidence to explain.
Which material refracted the light rays the most: air, water, or glass?
Which material refracted the light rays the least: air, water, or glass?
How does density affect refraction?
Diamonds are a very dense material. Predict what would happen to the light ray if you projected it from air through a diamond.
Explain where you observe reflection, refraction, and absorption of light in your everyday activities.
Answers
Answer:
Can You Give Me Some More Information
Step-by-step explanation:
14/2+5x4?? can anyone help me??
Answers
Answer: 27
Step-by-step explanation:
Use PEMDAS (Parenthesis,Exponents,Multiplication,Division,Addition,Subtraction)
to solve this problem. First multiply 5 times 4 to get 20. Then divide 14 by 2 to get 7. Lastly, add those two answers to get 27 as the final answer.
Which graph represents f of x equals square root of the quantity x plus 3 end quantity minus 2?
Answers
This function shows a horizontal translation of the parent function to the left and 2 units up.
Square root functionThe parent function of a square root function is expressed as:
f(x) = √x
According to the question, we are to plot the expression f(x) = √x+ 3 - 2
This function shows a horizontal translation of the parent function to the left and 2 units up. The required graph will be in the 2nd quadrant of the graph as shown;
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Answer:
It should be the first one.
What are all of the prime numbers between 30 and 40?
Answers
Answer:
the prime numbers between 30 and 40 are 31 and 37 come on its so easy
There are 10 pink marbles and 10 black marbles. Find the probability?
Answers
Answer:
50% to pull either a black or pink marble.
Step-by-step explanation:
The reason for this is due to the fact you have an equal amount of marbles of 2 different colors, so the chance of pulling one marble is not over another unless you remove say 1 pink marble, therefore the black marbles would have a higher percentage of being pulled instead of pink.
Please Answer Fast
3.4 × 107 is the scientific notation for:
3.40000000
34 000 000
340 000 000
Answers
Answer:
34000000
Step-by-step explanation:
hope it helps you and give me a brainliest
can anyone help me with this with easy tricks
We also have to find volume
I have exams tommorow
Answers
Answer:
1,120 cm³
Step-by-step explanation:
Hello!
Think about it this way: There is a rectangular prism, with lengths of 20cm, 12cm, and 10cm, and another rectangular prism cut out of it with lengths, of 8cm, 8cm, and 20cm.
Larger rectangular prismVolume = L * W * H
V = 20cm * 12cm * 10cmV = 2,400cm³Cut-Out Rectangular PrismV = L * W * H
V = 8cm * 8cm * 20cmV = 1,280cm³Subtract:
2,400cm³ - 1,280cm³1,120cm³The total volume is 1,120cm³
Use properties of operations to write two expressions that are equivalent
to 2n + (8 + 32).
Answers
The equivalent expressions of 2n + (8 + 32)are 2n + 40 and 2(n + 20)
How to determine the equivalent expressions?The expression is given as:
2n + (8 + 32)
The first equivalent expression
Evaluate the sum of the numbers in the bracket
2n + (8 + 32) = 2n + 40
This means that 2n + 40 and 2n + (8 + 32) are equivalent.
The second equivalent expression
In (a), we have:
2n + (8 + 32) = 2n + 40
Factor out 2 from the expression
2n + (8 + 32) = 2(n + 20)
This means that 2(n + 20) and 2n + (8 + 32) are equivalent.
Hence, the equivalent expressions are 2n + 40 and 2(n + 20)
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Question 2
Which sign makes the following statement true? 2/5 ___ 6/15
1. =
2. >
3.
Answers
Answer:
1 is answer
Step-by-step explanation:
2*3/5*3___6/5
Find the area of this irregular figure. Please explain in steps how you did it so I know how to do it for the next question please its not needed but would be appreciated
Answers
Work Shown:
A = area of the rectangle
A = length*width
A = 26*15
A = 390 square feet
B = area of the triangle
B = base*height/2
B = 8*9/2
B = 72/2
B = 36 square feet
C = total area
C = A+B
C = 390+36
C = 426 square feet
Triangle DEF is a right triangle with point F at the origin. Segment DE has endpoints located at D(8, 0) and E(0, −2). What is the area of triangle DEF?
Answers
Answer: 8
Step-by-step explanation:
Using the formula [tex]A=\frac{1}{2}bh[/tex],
[tex]A=\frac{1}{2}(8)(2)=\boxed{8}[/tex]
Calculate the area of the bowl
Answers
Im going to assume that you want the area of a circle.
We already have radius, which is the only variable that we need, now we just have to plug it into the area for the circle:
π(28²)
Multiplying this, you get 2461.76 cm³
evaluate 10 + 8÷4 - 12
Answers
Answer:
zero
Step-by-step explanation:
pemdas
Select the correct answer. Given the following formula, solve for y. w=x-y/2 -z
Answers
Given the following formula, w=x-y/2 -z. The value of y is y = x - 2w + wz .
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
Simplification usually involves making the expression simple and easy to use later.
Given the following formula,
w=x-y/2 -z
We need to solve for y.
[tex]w = \dfrac{x-y}{2 -z}[/tex]
By cross multiplication
[tex]w\times (2 -z)= {x-y}\\\\2w - wz = x - y[/tex]
subtract x both side
2w - wz -x = x - y -x
y = x - 2w + wz
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Tera buys 10 pencils for $1.99.
About how much $ does each pencil
cost?
Answers
Answer:
19 cents or 0.199
Step-by-step explanation:
Hope it helped!
Answer:
19 cents
Step-by-step explanation:
divide total cost by amount of items
Bob wants to take his wife, Jessica, to Europe in three years to commemorate their 40th wedding anniversary. He recently received a $23,000 inheritance from an uncle, which he plans to put towards the trip. The trip is expected to cost $32,200, according to Bill. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, F (From the tables provided, select the appropriate factor(s).)
What annual compounded interest rate must Bill earn to save enough money to pay for the trip? (Round to the nearest whole percentage your interest rate.)
Answers
Answer:
10%
Explanation:
Use future value formula
Future Value = Present Value ((1+r)^n)
26,600 = 20,000 ((1+r)^3
26,600/20,000 = (1+r)^3
1.33 = (1+r)^3
1.33^1/3 = 1+r
1.0997 = 1+r
1.0997 - 1 = r
r = 0.997 = 9.97% = 10% (rounded of to the nearest whole percentage)
(pls give brainliest)
Use SOHCAHTOA to find the side measure. Show work. Round to one decimal place.
Answers
Using trigonometric ratios, the measure of side n to one decimal is 6.6 units.
How to solve for a side using trigonometric ratios?Using the trigonometric principle
SOHCAHTOA,
cos 20 = adjacent / hypotenuse
adjacent side = n
hypotenuse side = 7
Therefore,
cos 20° = n / 7
cross multiply
n = 7 cos 20°
n = 7 × 0.93969262078
n = 6.5778483455
n = 6.6 units
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If a polynomial has two local maxima and two local minima, can it be of odd degree?
Answers
Answer:
yes, it can be of odd degree
Step-by-step explanation:
The local maxima and minima correspond to zeros in the derivative of the function. The degree of the polynomial will be 1 more than some multiple of 2 greater than the number of zeros in the derivative.
__
based on derivativeFor 2 each of local maxima and minima, the derivative will have 2+2 = 4 real zeros. The degree of the polynomial will be 1 greater, hence of degree 5 (or more). The polynomial must be of odd degree.
__
based on behavior away from extremaThe local extrema must alternate: a maximum must be followed by a minimum, or vice versa. When there are an even number of each kind, the end extrema will be of opposite kinds. The end behavior of the function will be upward from a minimum and downward from a maximum. Hence the end behaviors must be in opposite directions--characteristic of an odd-degree polynomial.
The polynomial must be of odd degree.
_____
Additional comment
A polynomial with real coefficients will have an even number of complex roots. The complex roots of the derivative of a polynomial have no effect on the number or kind of extrema.
__
Attached is an example of a polynomial with 2 maxima and 2 minima. It is of 5th degree.
3p + 4 ≥ −14 and 1 – 5p ≥ 39
Answers
Answer:
1) p ≥ -6
2) p ≤ -38/5
Step-by-step explanation:
3p + 4 ≥ -14
Subtract 4 to both sides
3p ≥ -14 - 4
3p ≥ -18
Divide 3 to both sides
p ≥ -18/3
p ≥ -6
[tex]\rule[225]{225}{2}[/tex]
1 - 5p ≥ 39
Subtract 1 to both sides
-5p ≥ 39 - 1
-5p ≥ 38
Divide -5 to both sides
p ≤ -38/5
[tex]\rule[225]{225}{2}[/tex]
write square root of 5 x square root 10 in the form of b square root of 2 where b is an integer
simplify fully square root of 27 x square root of 75
Answers
Answer:
a)b= 5
b)45
Step-by-step explanation:
a) 5 times ten is 50 . the two factors of 50 are 25 and 2. The square root of 25 is 5, so that's the answer.
b) 27 × 75 is 2025 and the base root is 45², then with the radical and exponent we reduce the index by 2 to get 45.
[tex]\textbf{a)}\\\\~~~\sqrt 5 \times \sqrt{10}\\\\=\sqrt{5} \times \sqrt{5 \times 2}\\\\=\sqrt{5} \times \sqrt 5 \times \sqrt 2\\\\=\left(\sqrt 5 \right)^2 \times \sqrt 2\\\\=5\sqrt 2\\\\\text{It is now in a form of} ~ b\sqrt2 ~ \text{where} ~b = 5.\\\\\\[/tex]
[tex]\textbf{b)}\\\\~~~\sqrt{27} \times \sqrt{75}\\\\=\sqrt{9 \times 3} \times \sqrt{25 \times 3}\\\\=\sqrt 9 \times \sqrt 3 \times \sqrt{25} \times \sqrt 3\\\\=3\times 5 \times \left(\sqrt 3 \right)^2\\\\=15 \times 3\\\\=45[/tex]
A card is drawn from a standard deck of cards without jokers
What is the probability that the card is either black or a heart
Answers
Answer:
Step-by-step explanation:
Remark
The two black suites are
Clubs
Spades
Each of them has 13 cards so the total number of black cards is 2*13 = 26
Add to that the hearts which also has 13 cards
The total number of possible good cards is 13 + 26 = 39
Answer
P(hearts or Black) = 39/52
P(hearts or Black) = 3/4
P(hearts or Black) = 0.75
Which
Which of the following are characteristics of the graph of the linear parent
function?
Check all that apply
A. It is a parabola.
B. It has a slope of 2.
C. It goes through the origin.
O
D. It is a straight line.
Answers
Answer:
All of the following are answers:
B) It has a slope of 2
C) It goes through the origin
D) It is a straight line
Step-by-step explanation:
trust me
1. 5 M 20 CM of cloth is needed to stitch a shirt how much clothes will be needed to stitch 449 shirts
2. I have a pack of 100 rupees notes in series which start from number code 412 to 425 how much money do I possess
3. a tailor stitches 120 suits in one month. find out how many suits he stitches in an year
4. Radha can swim 348 m in 5 minutes what distance can she in 50 minutes
full explanation pls
Answers
#1
Length in cm
500+20=520cmShirts=449Total length
449(520)233480cm2334m 80cm#2
Total notes
425-412+1=14Total money
100(14)1400|
Total suits per month=120
per year
120(12)1440suits#4
Total 5mins
50/5=10total distance
348(103480m(x+y)2-2(x+y)(a+x)+(a+x)2
Answers
Answer:
2ax−2ay−2x2−2xy+2a+4x+2y
Step-by-step explanation:
Let's simplify step-by-step.
(x+y)(2)−2(x+y)(a+x)+(a+x)(2)
Distribute:
=(x)(2)+(y)(2)+−2ax+−2ay+−2x2+−2xy+(a)(2)+(x)(2)
=2x+2y+−2ax+−2ay+−2x2+−2xy+2a+2x
Combine Like Terms:
=2x+2y+−2ax+−2ay+−2x2+−2xy+2a+2x
=(−2ax)+(−2ay)+(−2x2)+(−2xy)+(2a)+(2x+2x)+(2y)
=−2ax+−2ay+−2x2+−2xy+2a+4x+2y
Answer:
=−2ax−2ay−2x2−2xy+2a+4x+2y
Select the graph of y=cot x.
Answers
Because of the vertical asymptote and the change in concavity, we conclude that the correct option is B.
Which is the graph of cotangent of x?Remember that cot(x) = 1/tan(x).
Then we can rewrite:
cot(x) = cos(x)/sin(x).
We know that for x = 0, we have:
cot(0) = cos(0)/sin(0) = 1/0
Then we have a vertical asymptote that tends to ± infinity.
The only graph that meets this condition is the second and the third one, and by the curvature (we need to have a change of concavity/convexity) in the tangent function.
From that, we conclude that the correct option is B.
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Explain how to easily decide whether x - 6 is a factor of the polynomial P(x) = x ^ 7 - 5x ^ 5 + 2x ^ 4 - x ^ 2 + 9 without performing long division .
Answers
[tex]\text{According to the factor theorem,}\\\\x-a~ \text{is a factor of}~ f(x)~ \text{if}~ f(a) = 0, ~ \text{where}~ a \in\mathbb{R}\\\\\text{Given that,}\\ \\P(x) = x^7 -5x^5 +2x^4 -x^2 +9\\\\P(6) = 6^7 -5\cdot 6^7 +2 \cdot 6^4 -6^2 +9 = 243621 \neq 0\\\\\text{Since} ~ P(6)\neq 0~, ~ x -6 ~ \text{is not a factor of P(x).}[/tex]