Answer:
[tex]y = \frac{48}{x}[/tex]
Step-by-step explanation:
Inverse variation:
if [tex]y \propto \frac{1}{x}[/tex]
then the equation is in the form of:
[tex]y = \frac{k}{x}[/tex] ....[1]
where, k is the constant of variation.
As per the statement:
When x = 3, y = 16 and when x = 6, y = 8.
Substitute the value of x and y to find k.
Case 1.
When x = 3, y = 16
then;
[tex]16=\frac{k}{3}[/tex]
Multiply by 3 both sides we have;
48 = k
or
k = 48
Case 2.
When x = 6, y = 8
then;
[tex]8=\frac{k}{6}[/tex]
Multiply by 6 both sides we have;
48 = k
or
k = 48
In both cases, we get constant of variation(k) = 48
then the equation we get,
[tex]y = \frac{48}{x}[/tex]
Therefore, the inverse variation equation can be used to model this function is, [tex]y = \frac{48}{x}[/tex]
A stop sign is a regular octagon formed by cutting triangles off the corners of a square. if we have a square with sides of length square root 2, what is the side length of the resulting octagon
The side length of the resulting octagon is 2√2.
Explanation:A stop sign is a regular octagon formed by cutting triangles off the corners of a square. To find the side length of the resulting octagon, we can use the Pythagorean theorem. Since the square has sides of length √2, its diagonal can be found by multiplying its side length by √2. This gives us a diagonal length of 2√2. The diagonal of each triangle cut off the corners of the square will be the side length of the resulting octagon. So, the side length of the octagon is 2√2.
A regular hexagon is shown.
What is the length of the apothem, rounded to the nearest inch? Recall that in a regular hexagon, the length of the radius is equal to the length of each side of the hexagon.
4 in.
5 in.
9 in.
11 in.
The length of the apothem of a regular polygon that has a radius of 10 inches would be 9 inches .
What is the apothem of a regular polygon?The apothem of a regular polygon is defined as a line segment from the center to the midpoint of one of its sides.
It is Given that the hexagon has a radius of 10 inches and the length of the radius is equal to the length of each side of the hexagon.
The apothem AB divides the side of the hexagon into two equal parts of 5 Inches.
Using Pythagoras Theorem
[tex]10^2 = 5^2 + AB^2\\AB^2 = 10^2 -5^2\\AB^2 = 100 - 25\\AB^2 = 75\\AB = \sqrt{75}[/tex]
AB = 8.66
So, rounded up, we get the apothem closest to D that is 9 in.
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Can you help me solve this proof please?
Find the difference.
5wx2 − 2wx2
The coordinates of the vertices of quadrilateral JKLM are J(-3,2), K(4,-1), L(2,-5) and M(-5,-2).
Find the slope of each side of the quadrilateral and determine if the quadrilateral is a parallelogram.
is it possible to draw three lines in two planes such that all three lines are skew?
Answer with explanation:
→Two lines in three dimensional plane are said to be Skew if they are neither parallel nor Intersecting.
→Skew lines can be drawn in three dimensional plane only.
→Drawn two skew lines in a Plane , and then drawn another line in a plane and found that , they are skew.
⇒Yes, it is possible to draw three lines in two planes such that all three lines are skew.
Skew lines are non-coplanar lines that are not parallel, and they do not intersect.
In a 2D plane, it is not possible to draw three skew linesIn a 3D plane, it is possible to draw three skew linesThe question does not state the type of plane. So, I will answer this question in 2 ways.
(a) 2D plane
Lines in 2D planes can only be drawn in a flat direction.
This means that, when three lines are drawn in the two planes, one of the following would happen.
The three lines would intersectTwo lines would intersectSee attachment for illustration
So, 3 lines in a 2D plane cannot be skewed lines
(b) 3D plane
Lines in 3D planes can only be drawn in several directions.
The above statement imply that:
Several lines can be drawn where none of the lines would be parallel and none of the lines would intersect.
This means that, when three lines are drawn in the two planes, one of the following would happen.
The three lines would intersectTwo lines would intersectNone of the lines would intersectThe third highlight means that:
It is possible to have skew lines in a 3D plane
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Which of the following equations represents the perpendicular bisector of WX graphed below?
Thank you! :)
14(z+3)=14z+21
Please state if it has no solutions, one solution, or infinitely many solutions.
find the difference without using a calculator 201-72.35
Which statements are true about the ordered pair (−4, 0) and the system of equations?
{2x+y=−8
x−y=−4
Select each correct answer.
The ordered pair (−4, 0) is a solution to the first equation because it makes the first equation true.
The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true.
The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (−4, 0) is a solution to the system because it makes both equations true.
Suppose you divide a 52 card deck into its four suits, and draw one card from each suit. what is the probability that you draw two red face cards and the two black aces?
If 5(x+7)=-3, then 5x+35=-3
On which number line do the points represent negative 4 and 1 over 2 and +3?
Which of these ratios is NOT in simplest form? 12/5 8/5 7/10 9/15
What do they call the guy who invented the first blue jeans
Answer:
Levi Strauss!
Step-by-step explanation:
By the 1860s, Levi Strauss's blue pants were daily wear for miners and farmers and cattlemen throughout the West. In 1873 he bought, for $69—the price of the patent application — an idea from a Russian immigrant tailor in Reno for making miner's pants stronger by riveting the critical seams.
Hope this helped!
When constructing parallel and perpendicular lines, how are the steps similar
In isosceles triangle the length of the base is twice shorter than the length of a leg. The perimeter of this triangle is 50cm. Find the lengths of all sides.
The length of each side of a square prism is ten ft
A can of paint is 15 centimeters high and has a ddiameter of 13.6 cm. what is the volue of the can? Round to the nearest tenth.
Answer:
V=πr2h=π·6.8^2·15≈2179.00866
2179 cm^3
Step-by-step explanation:
F. determine if (x + 3) is a factor of (x) = 2x3 + x2 –8x + 21 by using synthetic division. if so, find the other factors.
please help. !!!!!!!!
Solve 12g=12(2/3g-1)+11
To make punch, Sophia mixes 2 liters of clear soda with 70 centiliters of cranberry juice and 236 milliliters of pineapple juice. How much punch does she have in total?
As a student you are able to earn extra money by assisting your neighbors with odd jobs. If you charged $10.25 an hour for your assistance about how many hours would you need to work to earn $8,425
For an hour of assistance if a student charged $10.25 than total number hours a student need to work to earn $8,425 is 821.95 hours and this can be determine by the help of unitary method.
Given :
Charge for 1 hour assistance = $10.25
Total earning through assistance = $8425
In this problem unitary method can be use to determine the total number of hours need to work to earn $8425. In unitary method, single unit value is determine first to evaluate the necessary value by multiplying the single unit value.
For an hour of assistance if a student charged $10.25 than total number hours a student need to work to earn $8,425 can be:
[tex]= \dfrac{8425}{10.25} \times 1[/tex]
= 821.95 hours
So a student need to work a total of 821.95 hours to earn $8425.
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Which inequality describes all the solutions to 5(3 - x) < -2x + 6?
A) x < -9
B) x > 3
C) x > 7
The inequality describes the solution to 5(3 - x) < -2x + 6 will be x > 3. The correct option is B.
What is inequality?
Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The given expression 5(3 - x) < -2x + 6 will be solved as below:-
5(3 - x) < -2x + 6
15 - 5x < -2x + 6
-5x + 2x < -15 + 6
-3x < -9
x > 3
Therefore, the inequality describes the solution to 5(3 - x) < -2x + 6 will be x > 3. The correct option is B.
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HOW many times can times 6 go into 59
John Gray bought a basic car for $32,750.00, with options that cost $375.00. There's a 6% sales tax in his state and a combined $50.00 license and registration fee. What was John's total cost
Answer:
The total cost of the car be $35162.5 .
Step-by-step explanation:
As given
John Gray bought a basic car for $32,750.00, with options that cost $375.00.
Cost of the car = Car cost + Option cost
= $32750 + $375
= $33125
As given
There's a 6% sales tax in his state .
6% is written in the decimal form.
[tex]= \frac{6}{100}[/tex]
= 0.06
Sales tax price = 0.06 × 33125
= $ 1987.5
As given
A combined $50.00 license and registration fee.
Than
Total cost of the car = Cost of the car + Sales tax price + license and registration fee.
= $33125 + $ 1987.5 + $ 50
= $35162.5
Therefore the total cost of the car be $35162.5 .
Question 25 the sum of three numbers is 79 . the second number is 9 less than the first. the third number is 2 times the first. what are the numbers?
The sum of two right angles always, sometimes, never results in a straight angle. Justify answer
Adding two right angles, each being 90 degrees, always results in a straight angle, which is 180 degrees, so this is always true.
Explanation:The sum of two right angles always results in a straight angle. This can be justified with a basic understanding of angles in a flat plane. A right angle is 90 degrees and a straight angle is 180 degrees. So, if you add two right angles together (90 + 90), you get 180, which is the measure of a straight angle. Hence, this is always true, regardless of the vectors or other elements you are working with. It's also important to note that in broader geometric terms, this statement is also always true: two angles that add up to form a straight line (180 degrees) are referred to as supplementary angles.
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A one celled organism measures 32 millimeters in a length in a photograph. If the photo has been enlarged by a factor of 100, what is the actual length of the organism? Show your work
Final answer:
The actual length of the organism is 0.32 millimeters, which is obtained by dividing the photograph length (32 mm) by the magnification factor (100).
Explanation:
To determine the actual length of the one-celled organism when the photograph has been enlarged by a factor of 100, we use the formula:
Actual length = Photograph length ÷ Magnification factor
Substituting the given values:
Actual length = 32 mm ÷ 100
Actual length = 0.32 mm
This calculation shows that the actual length of the organism is 0.32 millimeters, which is equivalent to 320 micrometers (320 µm). It's interesting to note that this is well within the size range for many microorganisms, which may require magnification to be seen clearly, such as with a microscope.