Answer: c=[tex]\frac{4A}{b^3}[/tex]
Step-by-step explanation:
A = 1/4b^3c
A*4=4*1/4b^3c
4A=4/4b^3c
4A=b^3c
c=4A/b^3
c=[tex]\frac{4A}{b^3}[/tex]
Can someone help me with this question?
Answer:
Step-by-step explanation:
Compare both shapes
Find out the length of the red line through Pythagoras theorem
a² + b² = c²
9² + b² = 15²
15²- 9² = b²
144 = b²
√144 = b
b = 12
Red line is 12 and the other length of one side of the triangle is x - 9
The hypotenuse of the other triangle will be equal to:
a² + b² = c²
12² + (x-9)² = c²
144 + x² - 9x -9x + 81 = c²
x² - 18x + 225 = c²
THE HYPOTENUSE OF THE 2ND TRIANGLE = x² - 18x + 225
NOW COMPARE BOTH TRIANGLES
x² - 18x + 225 : 15
x - 9 : 9
Cross multiply
9(x² - 18x + 225) = 15(x - 9)
9x² - 162x + 2025 = 15x - 135
9x² - 162x - 15x + 2025 + 135 = 0
9x² - 177x + 2160 = 0
Now use the quadratic equation
x = (-b +- √b² - 4ac)/2a
a = 9
b = -177
c = 2160
x = (-(-177) +- √(-177)² - 4(9)(2160))/(2×9)
x = (177 +- √31329 - 77760)/(18)
x = (177 +- √-46431)/18
At this point I have lost hope in the question as i got a negative value under square root which means it can't be solved.
I don't know where I am wrong but I hope the starting parts of the answer help you reach the final answer.
please help me I'm struggling with my homework
Answer:
x=13
Step-by-step explanation:
little marks show that
eh and hg are the same size so
angle e and g are the same
angle h has a red box which means its 90 degrees
that means angle e and angle g are 45 degrees each
3x+6=45
3x=39
x=13
3 for a decimal expansion k.d1d2d3d4 ···, let (sn) be defined as in discussion 10.3. prove sn < k 1 for all n ∈ n. hint: 9 10 9 102 ··· 9 10n
The proof for the decimal expansion d₁d₂d₃d₄.... is evaluated.
What is decimal expansion?A number's decimal expansion is its base-10 representation (i.e., in the decimal system).
Now, as per the given question;
We focus on non negative decimal expansions as well as nonnegative real numbers. Every nonnegative decimal expansion, in our opinion, is short form for the limit of a constrained increasing sequential manner of real numbers.
Assume we're given a decimal expansion K. d₁d₂d₃d₄.... where K is a non-negative integer and each value of dj belongs to {0,1,2,3,4,5,6,7,8,9}.
Then Sn is defined as the increasing sequential of real numbers and Sn is also restrained by (sn < k + 1) .
Using Theorem; converges to a real number, which we usually write as K. d₁d₂d₃d₄....
Like. 3.33333 can be written as;
[tex]\lim _{n \rightarrow \infty}\left(3+\frac{3}{10}+\frac{3}{10^2}+\cdots+\frac{3}{10^n}\right)[/tex]
We use the following geometric series fact to calculate this limit:
[tex]\lim _{n \rightarrow \infty} a\left(1+r+r^2+\cdots+r^n\right)=\frac{a}{1-r} \quad \text { for } \quad|r| < 1 .[/tex]
Where a =3 and r = 1/10.
Similarly, for 0.9999.....it can also be written as
[tex]\lim _{n \rightarrow \infty}\left(\frac{9}{10}+\frac{9}{10^2}+\cdots+\frac{9}{10^n}\right)=\frac{\frac{9}{10}}{1-\frac{1}{10}}=1 .[/tex]
Therefore, 0.9999... and 1.0000... are different decimal expansions for the same number.
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The correct question is-
For a decimal expansion K. d₁d₂d₃d₄....let (sn) be defined. Prove (sn < k + 1) for all n ∈ N. Hint:' [tex]\frac{9}{10}+\frac{9}{10^2}+\cdots+\frac{9}{10^n}=1-\frac{1}{10^n}[/tex]
Which is more affected by extreme observations, the mean or median? and how about the standard deviation or iqr?.
Extreme values have little impact on the median and quantiles because they all come inside the middle half of the data.
Calculation:
Let’s assume the 24 students in the room range in age from 185, 185, 186, 186,.... 195, 195, 196, 196 months.
The total of x2 is 871252.
The sum of x is 4572.
The mean is 190.5 (4572/24).
The median, which lies between positions 12 and 13, is 190.5.
Standard deviation is (871252/24 -190.52)^0.5 = 3.45
Halfway between the( 18th and 19th)- (6th and 7th)interquartile range
= 6 (193.5 - 187.5).
Include his age of 716 months in the calculations as the teacher now.
Total x2 = 1383908
Total x = 5288
Mean (5288/25) = 211.52
Median (13th) = 191
Standard Deviation is (1383908/25 - 211.522)^0.5 = 103.03
Interquartile range (7th minus 19th) is 194 - 188 = 6
Therefore the mean has changed by 21.02 after the addition of a piece of data that is vastly different from the rest, yet the median has changed by only 0.5.
The interquartile range has remained constant, whereas the standard deviation has increased by over 100 and by a factor of approximately 30.
Define arithmetic mean?The result of adding together and dividing the total number of numbers or variables is the arithmetic mean, which is also known as the average or average value.
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Marion buys three similar vanity cases to gift her air hostess colleagues.
She hands over $100 to the cashier. How much did each vanity cost?
2. In isosceles right Triangle PQR, Angle P = 90°, PR = 6.7 m.
stone Determine the length of QR.
The length of QR in triangle PQR is 6.7 √2 m .
We are given that:
In triangle PQR, we have:
P = 90° and PR = 6.7 m .
Since, it is an isosceles triangle, the other angles will be equal to = 45° ( as the other two triangles will be equal and the sum of angles is 180°) .
We have to find the length of QR
We know that sin θ = Perpendicular / hypotenuse
sin 45° = 6.7 m / H
1 / √2 = 6.7 m / H
H = 6.7 √2 m
Therefore, we get that, the length of QR in triangle PQR is 6.7 √2 m .
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can someone help me with the problem?
where is the problem, how can I help you?
enter your answer and show all the steps that you use to solve this problem in the space provided.find the distance between pointsm(6,16)andz(−1,14)to the nearest tenth.1
The distance between the 2 points is 7.3 units.
What is the distance between two points?The length of the line segment connecting two points is essentially the distance between them. The distance between two points is always positive, and segments of equal length are referred to as congruent segments.So,
The formula for the distance between two points P(a, b) and Q(c,d) is:
[tex]d=\sqrt{(b-d)^2+(a-c)^2}[/tex]Use the following formula for the points M(6, 16) and Z(-1, 14):
[tex]d=\sqrt{(16-14)^2+(6-(-1))^2}=\sqrt{2^2+7^2}=\sqrt{4+49}=\sqrt{53} \approx 7.28[/tex]Which, when rounded to the nearest tenth, equals 7.3 (units).
Therefore, the distance between the 2 points is 7.3 units.
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The length of the rectangular shed is 2x^2 + 3x - 1 feet, and the width is x + 4 feet. Write polynomials that represent the perimeter and area. Calculate the perimeter and area if x = 10 feet. Include correct units of measure
Answer:
Step-by-step explanation:
gnhbn
Goran's annual salary is $63,000. a total of $15,438.12 will be deducted for taxes and health insurance. he will receive his paycheck monthly in 12 equal installments. how much will he get paid with each paycheck?
Goran's monthly salary would be $3963.49
In this problem, the Annual salary or his Gross Salary is $63,000 and annual deductions for his salary which includes taxes & health insurance is $15,438.12 annually. The formula to calculate the Net salary is :
=> Net Salary = Gross Salary - Deductions
By the formula mentioned above, we can calculate Goran's Net salary which he gets Annually. Here, Gross = $63,000, Deductions = $15,438.12 :
=> Net = 63,000 - 15438.12 => Net Salary = 47,561.88
Goran gets a Net Salary of $47,561.88, Now we have to calculate the equal amount of paychecks he will receive monthly for 12 months.
Monthly Paycheck = Net/12 => 47561.88/12 => $3963.49
Hence, Goran's monthly paycheck will be $3963.49
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Find the Scale Factor Sep 08, 5:47:30 PM The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
Answer:
1.5 or 3/2
Step-by-step explanation:
The scale factor is the factor by which the side lengths of the original shape are multiplied by. In this case, the original shape had side lengths 17 and was multiplied by [tex]x[/tex] to get the scaled shape.
Now we get the equation [tex]17\cdot x=51/2[/tex]. Solving, we get x=1.5
Work out the missing values in the equation
47x116≈-----x-------
NEED ASAP
Answer:
1111
Step-by-step explanation:
3a² + 2b c² if a = 1, b = 2, and c = 3.
Answer:
Ans 39
Step-by-step explanation:
3a² + 2b c² if a = 1, b = 2, and c = 3.The answer is 39
Use vectors to decide whether the triangle with vertices p(1,-3,-2), q(2,0,-4), and r(6,-2,-5) is right-angled.
The given vertices make a right angled triangle as seen below, with the help of vectors.
What are vectors?Vectors refer to the quantities that have both magnitude and direction but not position.
Now,
Given: Three vertices of a triangle: P(1,-3,-2),Q(2,0,-4), and R(6,-2,-5).
To find: whether they make a right angled triangle.
Finding:
Now,
Any two of the triangle's vectors must have a dot product of zero in order to demonstrate that the triangle is a right triangle. This is because the vectors (which represent the sides) are perpendicular or orthogonal if the dot product is 0, which indicates that the angle they make is right (90°).The triangle's three sides can be represented by the following three directional vectors:
Vector (PQ) = <2, 0, -4> - < 1, -3, -2>
=> Vector (PQ) = < 1, 3, -2>
Vector (QR) = < 6, -2, -5> - < 2, 0, -4>
=> Vector (QR) = < 4, -2, -1>
Vector (PR) = < 6, -2, -5> - <1, -3, -2>
=> Vector (PR) = < 5, 1, -3>
Now, finding a pair of vectors whose dot product = 0:
Vector(PQ) . Vector(PR) = < 1, 3, -2> . < 5, 1, -3> = 5 + 3 + 6 = 14 ≠ 0Vector (QR) . Vector (PR) = < 4, -2, -1> . < 5, 1, -3> = 20 + (-2) + 3 = 21 ≠ 0Vector (PQ) . Vector (QR) = < 1, 3, -2> . < 4, -2, -1> = 4 + (-6) + 2 = 0Hence, the sides PQ and QR must be perpendicular so that the given vertices make a right-angled triangle.
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2. Last year a certain toy car cost $50, but this year the price was dropped to $20. By what percentage was the price dropped?
corey bought 2122 start fraction, 1, divided by, 2, end fraction liters of paint for $60\$60$60dollar sign, 60. what was the cost per liter of paint?
Answer:
the cost per liter of the paint is equal to 24 8/liter
Hope this helps :)
this visual representation shows the sets of real numbers. classify the number −25. select all terms that are correct. natural whole integer rational irrational −25 natural – negative 25 whole – negative 25 integer – negative 25 rational – negative 25 irrational – negative 25
-25 is an integer and a rational number.
What is number system?A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.Now,
Natural numbers are positive integers with a range of 1 to infinity; nevertheless, they do not include zero. -25 wouldn't be a natural number because it is a negative number.A group of numbers known as a whole number consists of all positive integers and 0. This wouldn't be a whole number because -25 isn't a positive number.Any real number that cannot be represented as the quotient of two integers is said to be irrational. Square roots of irrational numbers are also frequently seen. -25, however, is not a square root.Any number that can be expressed as a ratio, or a fraction, of two integers, is referred to be a rational number. Fractions, decimals, negative decimals, and other rational numbers are very prevalent. Since -25 can be represented as a ratio of two numbers. it is a rational number.A whole number that can be either positive, negative, or zero is known as an integer. As -25 is negative and a whole number( when positive), it is an integer.Hence, -25 is an integer and a rational number.
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Please help i will give brainly
Answer:
all real numbers
Step-by-step explanation:
the arrows show that it is continuing therefore it is all real numbers
45 strikeouts in 36 innings or 96 strikeouts in 80 innings. Which is greater?
Answer:
Step-by-step explanation:
96 strikeouts in 80 innings
Help please, find the volume of this object. Only answer if you know please. Question below.
Based on the calculations, the volume of this object is equal to 68 cubic inches (in³).
How to calculate the volume of a cylinder?Mathematically, the volume of a cylinder can be calculated by using this formula:
Volume = πr²h
Where:
h represents the height.r represents the radius.For this cylinder, the radius is given by:
Radius = Diameter/2 = 4/2 = 2 inches.
Substituting the given parameters into the formula, we have;
Volume = 3 × 2² × 3
Volume = 3 × 4 × 3
Volume = 36 cubic inches.
How to calculate the volume of a sphere?Mathematically, the volume of a sphere can be calculated by using this formula:
Volume = 4/3 × πr³
Where:
r represents the radius.
Substituting the given parameters into the formula, we have;
Volume = 4/3 × 3 × 2³
Volume = 4/3 × 3 × 8
Volume = 4 × 8
Volume = 32 cubic inches.
Now, we can find the total volume of this object:
Total volume = 36 cubic inches + 32 cubic inches.
Total volume = 68 cubic inches (in³).
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an equation for a line parallel to the line y = 1/3x - 4 through (-3, 2).
Answer:
y = 1/3x + 3
please correct me if I'm wrong
r=14m Use \mathrm{\pi } = 3 . 14π=3.14 and round your answer to the nearest hundredth.
We get the perimeter of the circle as 87.92 m and area of the circle as 615.44 m².
We are given the radius of the circle as:
Radius = r = 14 m
We are also given the value of π as:
π = 3.14
We need to find the perimeter and area of the circle.
Perimeter of the circle is given by:
Perimeter = 2 π r
Substituting the values in the formula, we get that:
P = 2 × (3.14) × (14) m
P = 87.92 m.
Area of the circle is given by:
Area = π r²
Substituting the values in the formula, we get that:
Area = (3.14) × (14)²
A = 615.44 m²
Therefore, we get the perimeter of the circle as 87.92 m and area of the circle as 615.44 m².
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(-3x^3+5x^2-6x-7) / (x+4)
The solution to the division of the polynomial equation is [tex]=-3x^2+17x -74 +\dfrac{289}{x+4}[/tex]
The division of the polynomial equation:Polynomial long division is an extended form of the well-known arithmetic method of long division used in algebra to divide one polynomial with another polynomial of the same or lower degree. Addressing a difficult division issue and breaking it into manageable pieces makes it feasible to solve by using this method.
From the given information, we Divide:
[tex]=\dfrac{(-3x^3+5x^2-6x-7)}{(x+4)}[/tex]
[tex]=-3x^2+\dfrac{17x^2-6x-7}{x+4}[/tex]
Divide: [tex]\dfrac{17x^2-6x-7}{x+4}[/tex]
[tex]=-3x^2+17x + \dfrac{-74x-7}{x+4}[/tex]
Divide: [tex]=\dfrac{-74x-7}{x+4}[/tex]
[tex]=-3x^2+17x -74 +\dfrac{289}{x+4}[/tex]
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How are one variable absolute equations created ?
Answer: Absolute value equations are equations where the variable is within an absolute value operator, like |x-5|=9. The challenge is that the absolute value of a number depends on the number's sign: if it's positive, it's equal to the number: |9|=9. If the number is negative, then the absolute value is its opposite: |-9|=9.
Step-by-step explanation:
What is the slope of a line parallel to the line whose equation is x-2y=4. Fully simplify your answer.
Answer:
1/2
Step-by-step explanation:
x - 2y = 4
2y = x - 4
y = 1/2x - 2
If two lines are parallel, their slopes are equal => slope will be 1/2
Answer: 1/2
Step-by-step explanation:
i had this equation and it gave me this answer. i got y’all trust
1/1+p+q^-1+1/1+q+r^-1+1/1+r+p^-1
The proof of the expression 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1 is evaluated for pqr = 1.
What is defined as the indices?The small floating number which shows up after a number or letter is known as an index or power. Indices represent the number of times a number or word has indeed been multiplied by itself.For the given expression;
pqr = 1. Then pq = 1/r; qr = 1/p; pr = 1/q.
OR, pq = r⁻¹ ; qr = p⁻¹ ; pr = q⁻¹ .
The given expression is;
1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1
Consider LHS part;
= 1/(1+p+pr) + 1/(1+q+pq) + 1/(1+r+qr)
Multiply and divide q in the first part;
= q/(q+qp+qpr) + 1/(1+q+pq) + 1/(1+r+qr)
Put prq = 1 (given)
= q/(q+qp+1) + 1/(1+q+pq) + 1/(1+r+qr)
Add 1st and 2nd part;
= (q+1)/(q+qp+1) + 1/(1+r+qr)
Multiply and divide r in the first part;
= (q+1)r/(rq+rqp+r) + 1/(1+r+qr)
Put prq = 1 (given)
= (qr+r)/(rq+1+r) + 1/(1+r+qr)
Add both
= (qr+r+1)/(rq+1+r)
Both will be cancelled;
= 1 = RHS
Therefore, proof for 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1 is evaluated.
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The complete question is-
If pqr = 1, then prove that 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1
Answer:
pqr = 1
Step-by-step explanation:
-9+n/4=-7 x
Please help....
100 points plus brainlyiest
help please questions is in the picture
The graph of the given linear function can be seen in the image below.
How to graph linear equations?
Here we want to graph the line:
y = 3x - 2 (I think this is the line, the image is really blurry).
To graph this line (or any line, actually) what you need to do is find two points on the line.
To do so, you need to evaluate the function.
If we use x = 0, then:
y = 3*0 - 2 = -2
So we have the point (0, -2)
If we use x = 1, then:
y = 3*1 - 2 = 1
So we have the point (1, 1)
Now just graph these two points, and then draw a line that passes through both of them, you should get something like the image below.
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Thomas bought 12 glass and plastic cups from the store glass cups cost $3.25 and plastic cups cost $2.75 thomas spent a total of $36 how many cups and how many plastic cups did you buy
Thomas bought 6 plastic cups and 6 glass cups.
For given question,
Let a be the number of glass cups and b be the number of plastic cups.
Thomas bought 12 glass cups and plastic cups.
So, we get an equation
a + b = 12 .................(1)
The glass cups cost $3.25 and plastic cups cost $2.75
Thomas spent a total of $36
From this information we get equation,
3.25 a + 2.75 b = 36 ............(2)
We have a system of equations.
From equation (1),
a = 12 - b .............(3)
Substitute above value of a in equation (2)
3.25 (12 - b) + 2.75 b = 36
39 - 3.25 b + 2.75 b = 36
39 - 0.5 b = 36
-0.5 b = -3
b = 6
This means, Thomas bought 6 plastic cups.
Substitute above value of b in equation (3)
So, a = 12 - 6
a = 6
Thomas bought 6 glass cups.
Therefore, Thomas bought 6 plastic cups and 6 glass cups.
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Katy invests a total of $10,500 in two accounts paying 11% and 5% simple interest, respectively. How much was invested in each account if, after one year, the total interest was $945.00.
A) Enter an equation that uses the information as it is given that can be used to solve this problem. Use x as your variable to represent the amount of money invested in the account paying 11% simple interest.
Equation:___________
B) The answers are:
$____ was invested at 11% and
$____was invested at 5%
Answer:
Equation: 0.11x + 0.05(10500 - x) = 945
$7000 was invested at 11% and
$3,500 was invested at 5%
Step-by-step explanation:
There are two equations needed
Let x = amount of money invested at 11%
11% = 11/100 = 0.11 in decimal
Interest at 11% for 1 year = 0.11x
Amount of money invested at 5% interest. 5% = 0.05
= 10500 - amount invested at 11%= 10500 - x
Interest from this amount after 1 year = 0.05(10500 - x)
Total of these two = 945
So 0.11x + 0.05(10500 - x) = 945
The equation based on the information as it is given:
0.11x + 0.05(10500 - x) = 945
We know the total interest obtained was $945 so we have the equation
0.11x + 0.05(10500- 5x) = 945
Simplify
0.11x + (525 - 0.05x) = 945
==>0.11x + 525 - 0.05x = 945
==> 0.06x = 945 - 525
==> 0.06x = 420
==> x = 420/0/06 = $7000
Amount invested at 11% interest is $7,000
Amount invested at 5% interest = 10,500 - 7,000 = $3,500