Answer:
x = 25 when y = 8
Step-by-step explanation:
If y is inversely proportional to square root of x we write it as
[tex]y \propto \dfrac{1}{\sqrt{x}}[/tex]
This is also equivalent to
[tex]y = k \dfrac{1}{\sqrt{x}} \;\;\;\;\ \text{ [1]}[/tex]
where k is a constant known as the constant of proportionality
Given y = 10 when x = 16 we can find k by substituting for y and x in [1]
[tex]\rightarrow 10 = k\dfrac{1}{\sqrt{16}}\\\\\rightarrow 10 = k \dfrac{1}{4}\\\\\drightarrow 40 = k \:\:\:\: \text{by multiplying both sides by 4}\\\\\text{which can be written as }\\\\k = 40\\[/tex]
So constant of proportionality k = 40
To find x when y = 8, substitute y and k in [1] to get
[tex]y = k \dfrac{1}{\sqrt{x}}\\\text{Multiply both sides by \sqrt{x} and divide by y at the same time to get}\\\\\sqrt{x} = \dfrac{k}{y}[/tex]
Dividing both sides by y and multiplying by √x gives us
[tex]\sqrt{x} = \dfrac{k}{y}\\\\\text{Substituting k = 40, y = 8}:\\\\\sqrt{x} = \dfrac{40}{8}\\\\\sqrt{x}= 5\\\\\text{Squaring both sides: }\\\\(\sqrt{x})^2 = 5^2\\\\x = 25 \;\;\;\text{since $(\sqrt{x})^2$ = x}[/tex]
The answer is
x = 20
Formulate y=k/x based on the following criteria.
Replace: 10= k/16
Change the sides so that k/16 = 10.
Subtract the coefficient of the variable from both sides of the equation: k = 10×16
Determine the quotient or product: k = 160
Replace with y = 160/x.
Replace with: 8 = 160/x
The denominator cannot be zero if the fraction is defined: as x ≠ 0
As the domain, append the inequality: 8= 160/x, x≠0
Divide the common denominator by both sides of the equation: 8x = 160x/x, x≠0
8x=160x/x, where x ≠ 0. Reduce the fraction.
By the variable's coefficient, multiply both sides of the equation (x=160÷8, x ≠ 0).
Calculate the quotients or product: x = 20,x ≠ 0
Find the junction at x=20.
Answer : x = 20
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Question 22 (3 points)
Given that you are starting with:
4 + 2x = 10 - 4x
What are the equivalent equations in order to solve.
>
6x = 6
Xx = 1
4 +6x = 10
Answer:
Step-by-step explanation:
4+2x=10-4x
4+6x=10
6x=6
x=1
:]
Complete the statement below. Then use a number line to find the sum 5 + (-2). 5 + (-2) is ___ units from 5, in the ___ direction.
Rollaround skate rink charges $5 admission and $3 per hour for a skate rental. Spinaround skate rink charges $8 admission and $1.50 per hour for a skate rental. Write an equation to determine at what point the cost of both roller skating rinks is the same.
Answer:
2 hours
Step-by-step explanation:
Let x be the time, in hours, for which the cost of Rollaround and Spinaround are the same.
Rollaround Cost (Cr): Cr = $5 + $3x
Spinaround Cost (Cs): Cs = $8 + $1.50x
We want to find the value of x that makes Cr = Cs
Cr = Cs
$5 + $3x = $8 + $1.50x
$1.50x = $3
x = 2 hours
====
CHECK:
Cr = $5+$3(2) = $11
Cs = $8+$1.50(2) = $11
At 2 hours, both cost the same.
Name one pair of parallel planes. All lines and planes that appear to be parallel are parallel.
The parallel plane is the plane that has the same in-between distance at all points on the plane so plane ABF is parallel with plane DCG so option (C) is correct.
What is the plane?The plane is a two dimension(2D) surface that has a surface area.
We can draw lines on a plane and two or more planes can intersect or parallel.
If two planes are parallel then the perpendicular distance between both planes must be the same.
The angle of inclination of two parallel planes with a single reference plane is also the same.
In the given cuboid the plane ABF is parallel with plane DCG.
So, ABF || DCG.
Hence "The parallel plane is the plane that has the same in-between distance at all points on the plane so plane ABF is parallel with plane DCG".
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Write the phrase "Four times the difference of six and y equals five less than y" as a variable expression:
Write the phrase "six more than nine times n is twenty" as an equation:
Answer: 4(6-y)
Step-by-step explanation: Since you are multiplying 4 by the difference of 6 and y, you put 6 and y in parenthesis with the 4 on the outside. Then 6-y goes inside the parenthesis.
Also the second one would be (6+9)n=20
Is the following a function??
The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. Alternatively, we may say that the graph of f is the graph of the equation y.
Explain about the function?A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
Up until function composition, that is essentially all there is to "operations on functions." Don't be alarmed by the topic's notation; it simply means what it says: add, subtract, multiply, or divide; then, when necessary, simplify and evaluate.
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Evaluate. Write your answer as a fraction in simplest form. 4/3 to the power of 3
Answer:
[tex]2 \frac{10}{27}[/tex]
Step-by-step explanation:
4/3 to the power of 3 = to 4/3 x 4/3 x 4/3
which in the end equals to 64/27
there's no common factor between them to simplify, but we can turn them into a mixed number, which is 2 10/27 by dividing 64 and 27
Martha paid $6.35 for five pounds of chicken last week .What is the chicken's price per pound.
Answer:
$1.27
Step-by-step explanation:
Which table does not represent a proportional relationship?
Answer:
Table 3
Step-by-step explanation:
The ratio of x and y is not constant.
HELP MEEEE PLEASEEEE
A pound of peppers costs $0.62. The total cost varies directly with the pounds of peppers purchased. Write an equation that relates the total cost, c, and the number of pounds of peppers purchased, p.
If a pound of peppers costs $0.62, then multiply the cost by how many pounds you're getting.
what is -3.1 x (-2.9)
a river barge travels at an average of 8 mi/h in still water. the barge travels 60 miles up the mississippi river and 60 miles down the river in a total of 16.5 hours. what is the average speed of the current in this section of the mississippi river? round the tenths place.
the average speed of the current in this section of the mississippi river is 5.8
let C = the speed of the current
then B - C = effective speed up river
B+C =effective speed down river
time up + time down = 16.5 hrs
60/B-C+60/B+C= 16.5
taking lcm and solving we get
480+60C +480-60C= 16.5 (64 - C^2)
960= 1056 - 16.5 C^2
16.5 C^2 =96
C^2= 5.82
Hence , the average speed of the current in this section of the mississippi river is 5.8
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A rectangle concrete patio is 20 FEET long, 12 FEET wide, & 4 INCHES thick. What is the volume in cubic feet, of the concrete?
Answer:960
Step-by-step explanation:
4x12x20=960
suppose the reading rate of 6th grade students is uniformly distributed (this phrase tells you to use the uniform distribution!) between 100 and 180 words per minute. calculate probability that a selected student has a reading rate less than 115 words per minute.
Answer:
0.84 or 0.48 I cant remember
Step-by-step explanation:
my picture of good luck
please help me ty
this needs a step-by-step explanation
Answer:
4x3 which would be 12
Step-by-step explanation:
You write the words as numbers. Check if your answer is the same as the answer you have put for Number 4 and explain the difference
four times three can be numerically written as 4×3 which is equal to 12.
What are some alternative names for arithmetic operations?The addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
We know an alternative name for multiplication is times.
Given in the question four times three, this means we have to multiply 4 and 3 which is,
= 4×3.
= 12.
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Question 2(Multiple Choice Worth 1 points)
(03.01 MC)
Simplify nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight.
eleven square root of two minus five square root of seven
eleven square root of four minus five square root of fourteen
six square root of five
six square root of nine
Answer:1. eleven square root of two minus five square root of seven.
Step-by-step explanation:
Given-nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight.
•we can write √8 as 2√2 as 8 =2*2*
•we can write √28 as 2√7 as 28=2*2*
•Now putting these in the given equation we get
•9√2-3√7+2√2-2√7
•11√2-5√7
through: (-4,-2), slope 7/4
Answer:
y = 7/4x + 5
Step-by-step explanation:
Point slope form:
y+2 = 7/4(x+4)
y+2 = 7/4x + 7
y = 7/4x + 5
:]
For the regular octagon, please find the order of rotation and the angle
of rotation. Show all work for full credit.
A regular octagon is a closed figure with equal-length sides and equal-sized interior angles.
Measure of interior angle = 135°
Measure of exterior angle = 45°
What is meant by regular octagon?A regular octagon is a closed figure with equal-length sides and equal-sized interior angles. It possesses rotational symmetry of order 8 and eight lines of reflective symmetry. The Schläfli sign "8" represents a regular octagon. A regular octagon's internal angle at each vertex is 135°. ( radians).
We know that for a regular polygon with n sides the measure of each of the exterior angle = 360/n
Also, the measure of each of the interior angles of the regular polygon with n sides = (n - 2) × 180 / n
We have n = 8 (octagon)
Therefore, the measure of each of the exterior angles is: 360/8 = 45
Measure of each of the interior angles is given by:
(8-2) × 180/8 = 1080/8 = 135
Measure of interior angle = 135°
Measure of exterior angle = 45°
Therefore, the correct answer is option A. 45°, 135°.
The complete question is:
What is the angle of rotation of this regular octagon? What is the measure of an interior angle? A. 45°, 135° B. 22.5°, 135° C. 45°, 108° D. 22.5°, 108°
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Jill converted the equation of the line 15x-4y=-2 into slope-intercept form and found the slope and y-intercept of
the line as follows.
15x-4y=-2
15x-4y-15x--2-15x
-4y=-2-15x
-4y -2-15x
-4
22
-4
y-2--16x
y-1-15x
y=-15x+12/2
15
4
slope =
Answer: She got the sign of the slope wrong
Step-by-step explanation:
She did -4y -2 - 15x
-4 = -4
and turned that into ,
-2 - -15x
-4 (minus) -4
which is wrong, because she did the negative twice. Therefore, she mixed up the sign of the slope.
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72. At 6:00 a.m., the temperature was 7 degrees below zero Fahrenheit. At noon, the temperature was 10 degrees higher. At 6:00 p.m., the temperature was 5 degrees cooler than it was at noon. What was the
temperature at 6:00 p.m.?
E. -2°
F. -1°
G. 3°
H. 5°
Answer:
E. -2
Step-by-step explanation:
First, find the temperature at 6 am, which was -7 degrees Fahrenheit
Then, add the ten degrees from noon, making the temperature 3 degrees Fahrenheit
lastly, take away the 5 degrees that dropped making it -2 degrees Fahrenheit
p(x) = -3x - 1
graph the linear function
Answer:
Step-by-step explanation:
1) First find the y-intercept point
You can find it easily by finding the number without the variable. In this case, it is -1. With this draw a point on the y-axis line down to -1.
2) Find the slope.
Next, you can find a point by substituting a number for x. So in this example, I will be subbing x for 1.
y = -3(1) - 1
y= -3 - 1
y= -4
So there will be a point at (1,-4).
3) Graphing.
After you find that you can easily draw a straight line through both points.
80/15 y 6 son equivalentes?
6 y 5 7/8 son equivalentes?
Answer:
80/15 and 6 are equivalent?-no because 80/15=5 5/15 or 5 1/3
6 and 5 7/8 are equivalent? no because it is 1/8 off
How do the digestive and circulatory systems interact?
Answer:
(1) Digestive System gets nutrients (good) from food and hands it over to the blood and Circulatory System then carries those nutrients where they need to go. (2) Filters out waste from food and pushes it through intestines and out the body (and you know how and where it gets out).
Step-by-step explanation:
Digestive System gets nutrients (good) from food and hands it over to the blood and Circulatory System then carries those nutrients where they need to go. (2) Filters out waste from food and pushes it through intestines and out the body (and you know how and where it gets out).
Simplify the expression √9x^3/25y^2 and be sure to explain your steps!
The expression √9x³/25y² when simplified gives the result 3x³/25y².
What is the mathematical definition of expression?In mathematics, an expression is a statement made up of terms and operations. The terms can be numbers or variables with coefficients. Addition, subtraction, multiplication, and division are all possible operations.Simplifying an expression is the same as solving a math problem. When you simplify an expression, you are attempting to write it in the simplest feasible manner.The given expression is √9x³/25y².
In the expression, calculate the square root of 9.
As a result, we have the following expression.
⇒ 3x³/25y²
The above expression cannot be simplified any further.
Therefore, the simplified expression is 3x³/25y².
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Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?
y=5.5x; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5.
y=5.5x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.
y=x+5.5; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5.
y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5
The equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe is D. y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe.
The equation will be:
y = 5.5 + x
where y = total wheat
The option that correctly reflects this is D.
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Answer:
The answer is D
Step-by-step explanation:
Assume a profitable economic well produces an average income of $23 million, while the average cost of a dry hole is $1.2 million. How much profit can be expected from a 100-well drilling program?
The most appropriate choice for revenue and profit will be given by-
Profit expected from a 100-well drilling program = $[tex]146.2[/tex]
What is revenue and profit?
Total income generated by sale of goods and service is called revenue.
If [tex]p[/tex] is the cost of producing one unit of a commodity and [tex]q[/tex] is the number of units of the commodity, then the product of [tex]p[/tex] and [tex]q[/tex] gives the revenue.
If the revenue obtained by selling a commodity is more than the cost, difference between revenue and cost gives the profit.
Here,
Number of economic wells = 11
An economic well produces an average income of $23
Revenue obtained = $[tex]$[/tex][tex](23 \times 11)[/tex]
Number of dry wells = [tex]100 - 11[/tex]
= [tex]89[/tex]
Average cost of a dry hole is $1.2 million
Cost of 89 dry holes = $[tex]$[/tex][tex](89 \times 1.2)[/tex]
= $[tex]106.8[/tex]
Profit = Revenue - cost
= $[tex](253-106.8)[/tex]
= $[tex]146.2[/tex]
Profit expected from a 100-well drilling program = $[tex]146.2[/tex]
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Complete Question
The diagram has been attached
Assume a profitable economic well produces an average income of $23 million, while the average cost of a dry hole is $1.2 million. How much profit can be expected from a 100-well drilling program?
Solve the rational equation for n
Answer:
n = 29
Step-by-step explanation:
please give brainliest
Answer: 29
Step-by-step explanation:
The answer will be 29 because if you put it all together and do the equation(-646 = 3(-646 = 3(65 - n) 3 over 2. N will equal 29. If you don't understand I recommend looking it up or something.
But yeahhhhhhhhhhhhhh.
I hope it helps?
ASAP!! 4(x + 4) + 2x = 52
Solve for X and include step by step explanation for branliest.
Answer:
x = 6
Step-by-step explanation:
4 ( x + 4 ) + 2x = 52
Use distributive property to open parenthesis and combine like terms
4x + 16 + 2x = 52
6x + 16 = 52
6x = 52 - 16
6x = 36
x = 6
Is y=x(1-x)-(1-x^2) a linear, quadratic, or absolute value
The y=x(1-x)-(1-x²) is a linear value that is not absolute.
Simplifying,
y=x(1-x)-(1-x²)
y=x-x²-1+x²
y=x-1
Thus, it is a linear equation with a negative value therefore it is not an absolute value.
Ax+By=C is the general form of a two-variable linear equation. When the equation is written in this manner, it is quite simple to obtain both segments (x and y).
Any polynomial that can be rewritten in the canonical form is a quadratic equation. where x represents an unknown quantity and a, b, and c represent known quantities, with a = 0. This indicates that f(x) = 0 is the root of function f(x) = ax2 + bx + c, which is the answer to the quadratic equation ax2 + bx + c = 0.
The absolute value of a real figure x, denoted by |x|, is the non-negative real value of x, regardless of its sign.
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You have 200 feet of fencing to enclose a rectangular plot that borders on a river (a long side borders the river). If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?
The maximum Area that can be enclosed will be 5000 square feet.
In the given question, it is stated that 200 feet of fencing will be done to enclose a rectangular plot with borders on a river. It has a long side on the border of a river which does not needs fencing. We need to find out the Length and Width of the plot that will maximize the area and also find out the Maximum area that can be enclosed.
It is given that the total length of the fence is 200 feet.
Let the length of the plot be l
let the width of the plot be w
=> Total Perimeter will be = l + 2w because the longer side or 1 side of length does not need fencing. Putting the perimeter as 200 we get
=> l + 2w = 200 => Equation (1)
Now, we know the Area of the plot will be l*w,
By equation (1) we get l = 200 - 2w, Putting the values in the Area:
=> Area = (200-2w) * w
=> A = 200w - 2w²
For maximum Area, the derivative of A with respect to w will be 0
=> [tex]\frac{dA}{dW} = 200 - 4w[/tex]
=> [tex]0 = 200 - 4w[/tex]
=> w = 50
Putting w = 50 in Equation (1) we get
=> l = 100
We got our Length l = 100 feet, and Width w = 50 feet. Now we will Calculate the maximum Area to enclose.
=> Area = l*w
=> A = 100*50
=> A = 5000
Hence, the Maximum area to enclose will be 5000 square feet.
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