Answer: A=n(b^2-r)
Step-by-step explanation:
r + A/n = b^2
r-r+A/n = b^2-r
A/n = b^2-r
A*n/n=n(b^2-r)
A=n(b^2-r)
A school has a total of 900 pupils .400 pupils are boys and the rest of the girls.find the ratio of boys to girls .give the ratio in the simplest form
If a school has a total of 900 pupils and 400 pupils are boys and the rest are girls, then the ratio of the boys to the girls in the simplest form is 4:5.
A ratio in mathematics can be defined as the number of times a number contains another number or is contained in another number to express the connection between two or more things in quantity or size.
To find the ratio of boys to girls, first, we calculate the number of girls in the school. The number of girls can be found by subtracting the total number of pupils which is 900 from the number of boys which is 400.
Hence,
number of pupils that are girls = total number of pupils - number of boys
number of pupils that are girls = 900 - 400
number of pupils that are girls = 500
Hence the ratio of boys to girls can be given as,
400 : 500
Simplifying,
400/100 : 500/100
4:5
Hence, the simplest ratio of boys to girls is 4:5.
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Solve each system by elimination.
3x + 2 =10 , 6 +4y = 15
By elimination, the system of equations, 3x + 2y = 10 , 6x + 4y = 15, has no solutions.
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
First, multiply the first equation by 2.
3x + 2y = 10 ⇒ 6x + 4y = 20 (equation 1)
6x + 4y = 15 (equation 2)
Since the new equation of equation 1 has the same coefficients with those in equation 2, but different constants, then the two lines are in parallel.
Hence, the system of equations has no solutions.
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GEOMETRY HONORS
Answer Options:
Valid: Law of Detachment
Valid: Law of Syllogism
No Valid Conclusions
All questions(17-21) must be answered, thank you all so muchhh
16. Valid
Reason: congruency can be represented by the symbol ≅ hence the statement still reads <1 and <2 are congruent.
17. Invalid
Reason: A rectangle also has four right angles, It is only a square when all the sides are equal.
18. Valid
Reason: congruency can be represented by the symbol ≅ hence the statement still reads <JKM and <MKL are congruent.
19. Valid
Reason: The conclusion of the battery dying is in support of the premise giving which is leaving the light on when the car is off.
20.Valid
Reason: The conclusion, Dante obtained a part time job is in line with the premise that obtaining a pert time job, is a way to afford a car payment
21. Valid
Reason: The premise which has that selling 75% of the prom tickets will make the prom hold at country club is fulfilled, hence the prom will be held at the country club
What are valid arguments?An argument is vailed when the premises or conditions of the argument are all true. when some part of the argument is not true then it will lead to invalid conclusion.
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If it takes 4 workers 21 hours to paint how many hours will it take 12 workers?
Answer:
63 hours
Step-by-step explanation:
4 workers = 21 hours
12 workers = g
[tex] \frac{21}{4} \times 12 \\ = 63hours[/tex]
Stuck, need help please.
In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work.
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal.
The value of the angle x is equal to 53°
What is the Measure of the angle?
A) From the image attached, we can solve for the angles as follows;
m ∠RPB = 180 - 115 = 65°
Thus, the angle m∠x = 180° - 65° - 62°
= 53°
B) m∠RPB + m∠PRD = 180° (Internal angle between 2 parallel lines are equal).
Second line:
The 3 angles x, 62 and 65 degrees are all on the same straight line (AB), so they sum to 180 degrees.
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Sarah works as a nanny and charges different rates for working during the week and the weekend. One week, she earned 902.50 working 45 hours, of which 5 hours were during the weekend. The following week she earned 1045 working 50 hours, of which 10 hours were during the weekend. What does Sarah charge per hour, in dollars, for working during the week?
Sarah's charges per hour for working during the week will be $9.5.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.
Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be
45x + 5y = 902.5 ...1
50x + 10y = 1045
25x + 5y = 522.5 ...2
Subtract equation 2 from equation 1, then we have
45x - 25x = 902.5 - 522.5
20x = 380
x = 19
And the value of y will be
25 (19) + 5y = 522.5
475 + 5y = 522.5
5y = 47.5
y = 9.5
Sarah's charges per hour for working during the week will be $9.5.
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A human hair has an average diameter of 2.5 * 10 ^ - 5 meters. What is the maximum number of human hairs that could fit side by side (without overlapping) on a microscope slide that is 50 millimeters wide? Write your answer in scientific notation.
(A) 2 × 10 ^ 3
(B) 2 × 10 ^ 5
(D) 10 ^ - 3
(C) 2 × 10 ^ 6
===========================================
Explanation:
Let's find the width of the microscope slide in meters.
1000 mm = 1 m
1 mm = 1/1000 m
1 mm = 0.001 m
50*(1 mm) = 50*(0.001 m)
50 mm = 0.05 m
50 mm = 5 × 10^(-2) m
The microscope slide is 5 × 10^(-2) meters across. Divide this over the width of one hair.
5 × 10^(-2) ÷ 2.5 × 10^(-5)
(5/2.5) × 10^(-2 - (-5) )
2 × 10^(-2 + 5)
2 × 10^3
This converts to the number 2000. So we could have 2000 strands of hair side by side.
Answer:
(A) 2 * 10^3.
Step-by-step explanation:
50 millimeters = 0.05 m
= 5 * 10^-2 meters.
So, we divide this by the diameter of 1 hair:
= (5 * 10^-2) / (2.5 * 10 ^ - 5)
= (5/2.5) * (10/^-2 / 10^-5)
= 2 * 10^(-2-(-5))
= 2 * 10^3.
If a manufacturer sells x units of a certain product, his revenue R and cost C (in dollars) are given by the following. R = 7x C = 1000 + 2x + 0.001x2 Use the fact that profit = revenue − cost to determine how many units the manufacturer should sell to enjoy a profit of at least $1250.
Using factorization, In order to have at least $1250 profit, manufacturer should sell the product between $4500 and $500.
Given,
Revenue (R) = 7x
Cost (C) = 1000 + 2x + 0.001x²
Profit ≥ $1250
Using factorization,
⇒ profit = revenue − cost
⇒ Profit= 7x - 1000 - 2x - 0.001x²
⇒ 7x - 1000 - 2x - 0.001x² >= 1250
⇒ 5x - 0.001x^2 >= 2250
⇒ 0.001x^2 - 5x <= - 2250
⇒ 0.001x^2 -5x + 2250 >= 0
multiplying 1000 on both sides
⇒ 1000x^2 - 5000x + 2250000 > = 0
⇒ x(x - 500) - 4500(x - 500) >=0
⇒ (x- 500) + (x - 4500) >= 0
⇒ x = 500, 4500
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Simplify:
c3c2hhch
Write your answer with only positive exponents.
Answer:
[tex]c^6h^3[/tex]
Step-by-step explanation:
Simplify[tex]hhh=h^3\\c^3c^2h^3c\\c^3c^2c\\ccc = c^3\\=c^{3 \cdot 2}\\=c^6\\=c^6h^3[/tex]
Suppose you work for a packaging company and are designing a box that has a rectangular bottom with a perimeter of 36 cm . The box must be 4cm high. What dimensions give the maximum volume?
a. How can you model the volume of the box with a quadratic function?
The dimensions given the maximum volume will be 9 cm by 9 cm by 4 cm. The volume of the box with a quadratic function will be V = 72L - 4L².
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as
V = L x W x H
Imagine you work for a packaging firm and are building a box with a 36 cm-long rectangular bottom. The box has to be 4 cm tall.
The perimeter is given as,
36 = 2 (L + W)
W = 18 - L
Then the volume is given as,
V = L x W x H
V = L x (18 - L) x 4
V = 72L - 4L²
For the maximum volume, V' = 0
V' = 0
72 - 8L = 0
8L = 72
L = 9
Then the width will be
W = 18 - 9
W = 9
The dimensions given the maximum volume will be 9 cm by 9 cm by 4 cm. The volume of the box with a quadratic function will be V = 72L - 4L².
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two-column proof
Given: GH || FJ
m ∠ G=m ∠J=90
Prove: ΔH J F ≅ Δ F G H
We can say that ΔHJF ≅ ΔFGH under RHS condition.
What precisely is meant by the congruency of a triangle?If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.These triangles can be moved, rotated, flipped, and turned to look exactly the same.They will coincide if they are repositioned.Two triangles are congruent if they satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
To Prove: ΔHJF ≅ ΔFGH
GH = FJ = (Given)∠G = ∠J = 90° = (RHS)So, ΔHJF ≅ ΔFGH under RHS condition.
(Refer the table given below)
Therefore, ΔHJF ≅ ΔFGH
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Find the value of x in each case 40 points!!!
The values of x associated with each case are listed below:
1911How to find the variables behind angles in a geometric systemHerein we find two cases of geometric systems generated by two parallel lines and auxiliary line segments, wherein we must use the concept of supplementary angles and triangle properties to determine the value behind angles. Now we proceed to determine the value of the variable x for each case:
Case 1
m ∠ DCA = m ∠ CBE = 3 · x Alternate internal angles between parallel linesm ∠ CAD + m ∠ ADC + m ∠ DCA = 180° Internal angles in trianglesm ∠ ADC = 180° - 95° = 85° Supplementary angles.2 · x + 85° + 3 · x = 180° Steps 1 & 35 · x = 95° Algebrax = 19 Algebra / ResultCase 2
m ∠ BFE = 180° - 147° = 33° Supplementary anglesm ∠ FEB = 180° - 4 · x Supplementary anglesm ∠ BFE + m ∠ FEB + m ∠ EBF = 180° Internal angles in triangles33° + (180° - 4 · x) + x = 180° Steps 1 & 23 · x = 33° Algebrax = 11 Algebra / ResultTo learn more on triangles: https://brainly.com/question/2269348
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You invested money in a fund and each month you receive a payment for your investment. Over the first four months, you received $ 50, $ 52, $ 55 , and $ 59 . If this pattern continues, how much will you receive in the tenth month?c. Explain the difference between an explicit formula and a recursive formula. Use your formula from part (a) as part of your explanation.
Money received in tenth month: $104
Difference between explicit formula and a recursive formula is: the use of (n-1)th term, nth term and the common difference (d) brings a great difference between the two formulae of an arithmetic progression.
What is arithmetic progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
Money received in first four months: $50, $52, $55, %59.To find: Money received in tenth month.
Finding:
As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.
That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.
Thus, for the tenth month, we can use the formula of recursion, given by: [tex]a_n=a_{n-1}+n[/tex], n ≥ 1.
For a₁ = 50, a₂ = a₁ + 2
=> a₂ = 50 + 2
This way, a₅ = a₄ + 5
=> a₅ = 59 + 5 = 64
a₆ = a₅ + 6
=> a₆ = 64 + 6 = 70
a₇ = a₆ + 7
=> a₇ = 70 + 7 = 77
a₈ = a₇ + 8
=> a₈ = 77 + 8 = 85
a₉ = a₈ + 9
=> a₉ = 85 + 9 = 94
a₁₀ = a₉ + 10
=> a₁₀ = 94 + 10 = 104
Thus, the payment received in tenth month will be $104.
(b) Difference between explicit formula and recursive formula of an arithmetic progression:
The first term of a recursive formula is a₁ and the formula for the nth term uses the first term and the common difference, d. One example of a recursive formula is [tex]a_n=a_{n-1}+d[/tex]. A formula for the nth term in an explicit formula would include the initial term a₁, the common difference d, and the term number, n. The equation [tex]a_n = a_1 + (n-1)d[/tex].To learn more about arithmetic Progressions, refer to the link: https://brainly.com/question/6561461
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Solve each system by elimination or substitution.
2x + 4y = -8 , -5x + 4y = 6
The solution of the given system of equations is (-2, -1)
A system of equation can be solved using:
graphical methodsubstitution methodelimination methodThe given system of equations:
2x + 4y = -8 ............ (1)
-5x + 4y = 6 .............. (2)
Since the coefficients of y is the same in both equations, variable y will be immediately cancelled out if we use elimination method.
Substract equation (2) from equation (1)
2x + 4y = -8
-5x + 4y = 6 –
7x = -14
x = -2
Substitute x = -2 into equation (1):
2x + 4y = -8
2. (-2) + 4y = -8
-4 + 4y = -8
Add 4 to both sides
-4 + 4y + 4 = -8 + 4
4y = -4
y = -1
Hence, the solution is (-2, -1)
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Write a negation for each statement:
1. All squares are rectangles
2. There exists a segment that has no midpoint
Answer:
1. There exists at least one square that is not a rectangle.
2. Every segment has a midpoint.
Step-by-step explanation:
1.The given statement is: "All squares are rectangles". We have to find the negation of the statement. The statement that gives the negative meaning of the given statement is called the negation of the given statement. So the negation of the given statement is, "There exists at least one square that is not a rectangle".
2.Every segment has a midpoint.
Factor this quadratic completely. (Write step by step please)
[tex]Factor\ by\ grouping:\\\\2x^2+3x-35\\\\(2x-7)(x+5)\\\\2x-7=0\ and\ x+5=0\\\large\boxed{\therefore x=\frac{2}{7}\ and\ x=-5}[/tex]
Answer: 2x^2+3x-35=(x+5)(2x-7)
Step-by-step explanation:
[tex]2x^2+3x-35=\\2x^2+10x-7x-35=\\(2x)(x+5)-(7)(x+5)=\\(x+5)(2x-7)[/tex]
Find the sum of -4x^{2}-3x-3−4x
2
−3x−3 and -4x^{2}-9x−4x
2
−9x.
The sum of two given expressions will be -
h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex].
We have two expressions.
We have to add them.
What is Expression in mathematics?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation in it.
According to the question -
f(x) = [tex]-4x^{2} -3x^{-3} -4x[/tex]
g(x) = [tex]-4x^{2} -9x -4x[/tex]
Now -
h(x) = f(x) + g(x) = [tex]-4x^{2} -3x^{-3} -4x[/tex] + ( [tex]-4x^{2} -9x -4x[/tex])
h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex]
Hence, the sum of two given expressions will be -
h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex]
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Which linear equation has no solution? clear submit 23(9x 6)=6x 4 5x 12=5x−7 4x 7=3x 7 −3(2x−5)=15−6x
The linear equation which has no solution is 5x+12=5x-7
Given set of linear equations are:
23(9x+6)=6x+4, 5x+12=5x-7, 4x+7=3x+7, -3(2x-5)=15-6x.
We try to solve each equations one-by-one.
Consider the first equation:
23(9x+6)=6x+4
⇒207x+138 = 6x+4
⇒201x = -134
⇒ x =-134/201.
So this linear equation has a solution.
Now consider the second linear equation:
5x+12=5x-7
⇒12 = -7, which has no meaning.
Therefore, this linear equation has no solution.
Now consider 3rd linear equation:
4x+7=3x+7
⇒x = 0
It has a solution.
Consider the 4th linear equation:
-3(2x-5)=15-6x.
⇒ -6x+15=15-6x
⇒ 0=0
In this case, any value for x is a solution. So there are infinitely many solutions.
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help me ............................,...........................................................
The values to the nearest tenth are:
a. 1. 43
b. 26. 41
c. 11. 69
d. 4. 57
e. 15. 77
How to determine the valuesGiven the equations;
a. 4. 186 - 2. 758
Find the difference
1. 428
1. 43
b. 72. 05 - 45. 64
Find the difference
26. 41
c. 82. 156 - 41. 31 - 29. 16
Find the difference
11. 686
11. 69
d. 17. 054 - 11. 65 - 0. 83
Find the difference
4. 574
4. 57
e. 29. 16 - 12. 48 - 0. 91
Find the difference
15. 77
Thus, the values to the nearest tenth are 1. 43, 26. 41 , 11. 69, 4. 57, 15. 77
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solve the equation and show the process
2 + 2 x 45/5
Answer:
20
Step-by-step explanation:
2+2x45\5
=2+90/5
=2+18
=20
if angle SXW = 5x-16, find the value of x so that SX is perpendicular to W (I'm in iss thank God for the good men and women of brainly)
The value of the variable x such that the two lines are perpendicular to each other is equal to 106 / 5.
What is the value of a variable associated with two perpendicular lines?
In accordance with geometry, two lines are perpendicular to each other if and only if the measure of the angle between the two lines is equal to 90°. Then, the angle SXW must be equal to 90° and we need to solve for x in the following equation:
5 · x - 16 = 90
5 · x = 106
x = 106 / 5
The value of the variable x such that the two lines are perpendicular to each other is equal to 106 / 5.
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16-x=x-16
I don't know what to do first for this equation
Answer:
16
Step-by-step explanation:
the first thing is to rearrange terms
Water molecules can form hydrogen bonds with each other because they are ____________ molecules.
Water molecules forming hydrogen bonds with one another. The partial negative charge on the O of one molecule can form a hydrogen bond with the partial positive charge on the hydrogens of other molecules. Water molecules are also attracted to other polar molecules and to ions.
ALGEBRA Which is a factor of x²+19 x-42 ?
F x+14
G x+2
H x-2
J x-14
The factors of x²+19x-42 are (H) (x-2).
What is factorization?Factorization is the process of reducing a quadratic equation's bracket rather than expanding the bracket and converting the equation to a product of factors that cannot be reduced further. Consider factoring (x2+5x+6) to (x+2) (x+3). In this case, (x+2) (x+3) is the factorization of a polynomial (x2+5x+6).To find the factors:
x²+19x-42x²+x(21 - 2)-42x² + 21x - 2x - 42x(x + 21) - 2(x + 21)Factors are: (x-2) and (x+21)
Therefore, factors of x²+19x-42 are (H) (x-2).
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Noah enlarges a photograph using the scale 1 inch : 4 inches. Explain why the area of the enlarged photograph will not be 4 times the area of the original.
The area of the enlarged photograph will be 16 times the area of original photograph.
What is defined as the scale?Scale is a ratio which defines the relation between the size of a model as well as the actual dimensions of a figure or object.Once we draw a physical image on paper, we have been using a scale to accurately describe our measurements. A scale of 1:5 signifies that the size of one unit in the picture represents five units in reality.For the given scale in the question;
Noah enlarges a photograph using the scale 1 inch : 4 inches.
Let the original length of photograph is 'L'.
Let the original width of photograph is 'B'
Old Area = LB
Thus, the length and width of the scale will get increased by 4 times.
The new length and width will be 4L and 4B.
Thus, the new area will be;
New Area = (4L)(4B)
New Area = 16 LB
New Area = 16 × (old area)
Thus, the new area of the photograph is increased by 16 times.
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1) A lunch service takes 3 ½ hours to complete. If the chef is getting pains $24.80, per hour, what is the total amount earned?
Answer:
The answer is $86.80. The lunch service gains $86.80 in 3 1/2 hours if they get $24.80 per hour.
Step-by-step explanation:
You have to multiply how much they earn per hour, $24.80, by the number of hours they work, 3 1/2. $24.80 times 3 1/2 equals 86.80 so the lunch service earns $86.80 in 3 1/2 hours.
Hope this helps!
i need help bad because my teacher didn't even teach this to my class and make sure its correct
Based on the information, it can be inferred that the number that is the change in height of the elevator is 12 feet.
How to complete the table?To complete the table we must take into account the height of the elevator at a given time of seconds. Additionally, we must take into account that the elevator goes down 12 ft every second. So the table would look like this:
12 × 3 = 36180 - 36 = 14412 × 6 = 72180 - 72 = 10812 × 9 = 108180 - 108 = 72What is the height of the basement with respect to the first floor?
To calculate the height of the basement with respect to the first floor, we must take into account the following information:
Every second the elevator descends 12ft.The elevator takes 4 seconds to go down from the first floor to the basement.To calculate this height we must multiply the time it takes for the elevator to go down to the basement by the distance it travels each second.
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If the sixth term in a geometric sequence is 1/625
and the common ratio is 1/5 find the explicit formula of the sequence
aₙ = 5*(1/5)^(n - 1) is the explicit formula of the sequence.
What is Sequence and example ?
A sequence is a list of elements that has been arranged in a certain way. As an illustration, 3, 7, 11, 15,... is a sequence because it follows a pattern in which each phrase is produced by adding 4 to the one before it.The recursive relation for a geometric sequence is
aₙ = aₙ₋₁*R
where R is the common ratio.
We could write this in a general form as:
aₙ = a₁*(R)^(n - 1)
where a₁ is the first term of the sequence.
In this case we know that:
R = 1/5
And that:
a₆ = 1/625
Then we can replace these values in the above relation to get:
a₆ = (1/625) = a₁*(1/5)^(6 - 1) = a₁*(1/5^5) = a₁*(1/3125)
1/625 = a1*(1/3125)
(3125/625) = a1 = 5
Then the formula will be:
aₙ = 5*(1/5)^(n - 1)
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Find the vertex, focus, and the directrix of each parabola. y=x² +6 x+5
For the given parabola:
We have the following data.
Vertexv = (-3,-4)
Focusf = (-3, -3.75)
Directrixd = y = -4.25
We define what a parabola is
What is a parabola?The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.
The canonical equation of a parabola is given by
(x - h)² = 4p(y - k)
The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.
The parabola equation is:
y = x² + 6x + 5
y - 5 + 9 = x² + 6x + 9
y + 4 = x² + 2(3x) + 3²
y + 4 = (x + 3)²
This means that the vertex of this parabola is
v = (h, k)
v = (-3,-4)
4p = 1p = 1/4f = (-3, -4 + 1/4)
f = (-3, -3.75)
Directrixd = y = -4 - 1/4
d = y = -4.25
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More math help please its urgent
Answer:
LMK and QPM
Step-by-step explanation:
When two lines are crossed by another line (called the transversal), the angles in matching corners are called corresponding angles.
