The constant of proportionality in the equation 2y = 6x is [tex]\( \frac{1}{3} \)[/tex].
In the equation (2y = 6x), the constant of proportionality represents the relationship between x and y. To isolate it, divide both sides of the equation by (6x):
[tex]\[\frac{2y}{6x} = \frac{6x}{6x}\][/tex]
This simplifies to:
[tex]\[\frac{1}{3} = \frac{y}{x}\][/tex]
So, the constant of proportionality is [tex]\(1/3\)[/tex], indicating that for every unit increase in x, y increases by [tex]\(1/3\)[/tex].
each day last week, Ms. wilson walked3/4 mile. what is the total distance, in miles, that Ms. Wilson walked in 4 days?
Taking into account the rule of three, the total distance that Ms. Wilson walked in 4 days is 3 miles.
Rule of threeIn first place, the rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.
To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:
a ⇒ b
c ⇒ x
So: [tex]x=\frac{cxb}{a}[/tex]
Total distance that Ms. Wilson walkedYou can applied the following rule of three: if each day last week, Ms. Wilson walked [tex]\frac{3}{4}[/tex] mile, in 4 days what is the total distance that Ms. Wilson walked?
[tex]total distance=\frac{4 daysx\frac{3}{4} miles }{1 day}[/tex]
total distance= 3 miles
Finally, the total distance that Ms. Wilson walked in 4 days is 3 miles.
Learn more about the rule of three with this example:
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Two parrallel lines may have 1 intersection point.
A.) True
B.) False
The endpoints of sa020-1.jpg are A(9, 4) and B(5, – 4). The endpoints of its image after a dilation are sa020-2.jpg and sa020-3.jpg. Find the scale factor.
AB ≅ BC and AD ≅ CD What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem? What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?
Answer:
C, B
Step-by-step explanation:
Answer:C B
Step-by-step explanation:
Suppose 67% of all teenagers own a laptop and 29% of all teenagers own a laptop and a tablet. What is the probability that a teenager owns a tablet given that the teenager owns a laptop?
P(T | L) = P(T&L)/P(L)
P(T | L) = 0.29/0.67 = 29/67 ≈ 0.4328 ≈ 43.3%
A charity organization had a fundraiser where each ticket was sold for a fixed price of $ 70. They had to sell a few tickets just to cover necessary production costs. After selling 10 tickets, they were still at a net loss of $800, (due to the production costs). Let (n)P, denote the net profit from the fundraiser P (measured in dollars) as a function of the number of tickets sold n. Write the function's formula.
Answer: The function's formula would be
[tex]P(n)=Revenue-Cost\\\\P(n)=70n-1500[/tex]
Step-by-step explanation:
Since we have given that
Price of each ticket = $70
Number of tickets = 10
Total cost price of tickets would be
[tex]70\times 10\\\\=\$700[/tex]
After selling 10 tickets, there is a net loss of $800.
So, Total product cost would be
[tex]\$700+\$800\\\\=\$1500[/tex]
We need to write the function's formula for the number of tickets sold 'n'.
So, the function's formula would be
[tex]P(n)=Revenue-Cost\\\\P(n)=70n-1500[/tex]
Suppose (b − c)d = 0, where b and c and m × n matrices and d is invertible. show that b =
c.
The area of a sector of a circle is given by the equation A=3.14r^2S/360, where r us the radius of the circle and S is the angle measure of the sector. If Mia solved this equation for S, which of the following equations did she write?
Just took the quiz.
The answer is 360A / pi r^2
what is the equation of the line that has a slope of 4/5 and a y-intercept of -1?
Answer:
y = 4/5x -1
Step-by-step explanation:
The slope-intercept form of the equation of a line is ...
... y = mx + b . . . . . . for slope m and y-intercept b
You have m = 4/5 and b = -1. The equation of the line is found by putting these values in their places in the form above.
... y = 4/5x -1
The equation of the line with a slope of 4/5 and a y-intercept of -1 is y = (4/5)x - 1.
The equation of a line in slope-intercept form is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept.
Given a slope of 4/5 and a y-intercept of -1, we can substitute these values directly into the slope-intercept form equation to get the equation of the line.
Hence, the equation for this line is y = (4/5)x - 1.
What is the expression of one less than the quotient of four and a number x
Divide 49 in the ratio 4:2:1
To divide 49 in the ratio of 4:2:1, find the total quotient of the ratio parts, divide 49 by this total, and then multiply each part of the ratio by the result.
The ratio of the coefficients is 4:2:1, which can be simplified to 2:1:1. To divide 49 in this ratio, follow these steps:
Find the total quotient of the ratio parts: 4 + 2 + 1 = 7.Divide 49 by the total parts: 49 ÷ 7 = 7.Multiply each part of the ratio by 7 to get the divided amounts: 2 x 7 = 14, 1 x 7 = 7.determine the range of possible side lengths of the third side AB of triangle ABC from gretaest to least
5 hours 8 min - 3 hours 12 min
Which sum is equal to 7/12?
A. 1/12 + 1/12 + 1/12 +1/12 + 1/12 + 1/12 +1/12
B. 1/7 + 1/7 + 1/7 +1/7 +1/7 + 1/7 + 1/7
C. 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12
D. 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 +
Answer:
The answer is A.
Step-by-step explanation:
There are 7 1/12ths, so it is equal to 7/12
What is the quotient? n+3/2n-6 divide n+3 /3n-9
Paysly is studying a mosquito with a mass of 2.5×10−62.5×10-6 kilograms and a housefly with a mass of 2×10−52×10-5 kilograms. Which statement is true?
The mosquito is 88 times the mass of the housefly.
The housefly is 88 times the mass of the mosquito.
The housefly is 1010 times the mass of the mosquito.
The mosquito is 1010 times the mass of the housefly.
Answer: The house fly is 8 times the mass of the mosquitio
The graph shows the distance in miles of a runner over x hours. What is the average rate of speed over the interval [9, 11]?
A. 2/5
B. 1
C.2
D.5/2
Answer:
Hence, option D is correct.
(i.e. Average speed is 5/2 miles/hour)
Step-by-step explanation:
We are asked to find the average rate of speed over the interval [9, 11].
We know that average speed is given as the ratio of total distance over total time.
the distance when time=9 hours is 6 miles.
and the distance when time=11 hours is 11 miles.
Hence, average speed is given as:
[tex]Average speed=\dfrac{Total distance}{Total time}\\\\Average speed=\dfrac{11-6}{11-9}\\\\Average speed=\dfrac{5}{2}[/tex]
Hence average speed is 5/2 miles/hour.
Faelyn noticed that she does not have a common factor. Which accurately describes what Faelyn should do next?
Faelyn should realize that her work shows that the polynomial is prime.
Faelyn should go back and regroup the terms in Step 1 as (6x4 + 3x2) – (8x2 + 4).
In Step 2, Faelyn should factor only 2x out of the first expression.
Faelyn should factor out a negative from one of the groups so the binomials will be the same.
Answer:
(b) Faelyn should go back and regroup the terms in Step 1 as (6x⁴ + 3x²) – (8x² + 4)
Step-by-step explanation:
You want to know the next step in factoring 6x⁴ -5x² -4 after noticing the terms have no common factor.
TrinomialFaelyn can notice the variable terms are powers of x², meaning this expression is a quadratic in x². As such, it may be able to be factored using the same strategies available for factoring quadratic expressions.
One such strategy is to rewrite the middle term as a sum, then group the terms and factor each group. Faelyn has apparently noticed that she can rewrite -5x² as 3x² -8x². This means ...
Faelyn should go back and regroup the terms in Step 1 as (6x⁴ + 3x²) – (8x² + 4), choice B.
__
Additional comment
The values used to rewrite the x² term are factors of (6)(-4) = -24 that have a sum of -5. Those values are +3 and -8.
Once Faelyn has regrouped the terms, she can factor further as ...
(6x⁴ + 3x²) – (8x² + 4) = 3x²(2x² +1) -4(2x² +1) = (3x² -4)(2x² +1)
These two binomial factors are prime.
226in is equal to how many ft and in (show work
Round 14.376 to the nearest dollar
A map of Scotland is drawn to scale of 1:325,000.
how many CM on the map would show 65KM?
On a map of Scotland, drawn to the scale of 1:325,000, 65 KM of real-world distance will be represented by 20 cm on the map.
Explanation:The question pertains to the scale existing on a map. A map scale enables us to convert the measurements on the map into the corresponding real-world distances. Here, we have a map of Scotland that is drawn to the scale of 1:325,000. This signifies that 1 cm on the map equates to 325,000 cm in reality.
To ascertain how many cm on the map would represent 65 KM, we first need to convert 65 KM into cm. As we know, 1 KM is equal to 100,000 cm. Therefore, 65 KM will be equivalent to 65 * 100,000 = 6,500,000 cm.
Now, we divide the real-world cm (6,500,000 cm) by the scale (325,000), which gives us the cm on the map. Thus, 6,500,000 cm / 325,000 = 20 cm
So, on this map, 65 KM will be denoted by 20 cm.
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What kind of angle is formed by the tangent to a circle and a radius of that circle?
Answer: 90° which is a right angle
Step-by-step explanation:
The tangent to a circle is perpendicular to the radius at the point of tangency. The angle between a radius and tangent is 90°>
Of the 180 days of school last year, Grace was absent 15 days. What percent of the day was she absent?
The current area of the city park is represented by the expression 11x2 + 4x + 6. The city will expand the park this summer by a factor of 5x − 3. If one-fourth of the new park is to be wooded, which expression represents the new area of the park that is not wooded?
The new area of the park that will not be wooded after expansion is represented by the expression 41.25x³ - 24.75x² + 15x - 13.5.
Explanation:The current area of the park is given by the polynomial 11x² + 4x + 6. If the city expands the park by a factor of 5x - 3, the total new area of the park becomes (11x² + 4x + 6) * (5x - 3), which represents the expansion of the park.
However, the question asks for the part of the park that will not be wooded, which we know is three-fourths of the total park. So, we multiply our expanded park equation by 3/4 (or 0.75) to find this area:
(3/4) * [(11x² + 4x + 6) * (5x - 3)]
Using distributive property, we can further expand the expression:
=(3/4) * [(55x³ - 33x² + 20x - 18)]
So the area that will not be wooded after expansion is expressed as 41.25x³ - 24.75x² + 15x - 13.5.
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Given that the current area of the park is represented by a second degree equation, the expansion of the park will proportionally increase its area. The new area after expansion will be the product of the current area and the expansion factor, so we will need to multiply our current area, which is given by 11x^2 + 4x + 6, by the expansion factor, which is 5x - 3.
This will yield: (5x - 3)*(11x^2 + 4x + 6) as the total new area of the park.
Now that we've calculate the total new area of the park, we need to find out the area of the park that will be wooded and the area that will not be. We know that the wooded area will be one-fourth of the total area, so we can find this by dividing our total area by 4.
This yields: (5x - 3)*(11x^2 + 4x + 6) / 4 as the wooded area of the park.
After discovering the area that will be wooded, we can find the non-wooded area by subtracting the wooded area from the total area of the park.
Therefore, the new area of the park that is not wooded is given by:
3*(5x - 3)*(11x^2 + 4x + 6) / 4
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Which of the following has a value between 10/3 and 11/3 ? A- 3 1/2 B-3 1/4 C- 3 3/4 D- 3 1/8
Answer:
A IS CORRECT
Step-by-step explanation:
GOOGLE I SEARCH UP THE ANSWER
make w the subject of the formula y-aw=2w-1
Answer:
(y+1)\div (a+2)
Step-by-step explanation:
y-aw=2w-1
y+1=2w+aw
y+1=w(2+a)
(y+1)/(a+2)=w
Answer: w= (y+1)\div (a+2)
What is the median of the following set?
28, 45, 12, 34, 36, 45, 19, 20
28
34
31
35
Answer:
Median = 31
Step-by-step explanation:
The median is the middle number which comes after arranging the set in ascending order.
Here, the given data is: 28, 45, 12, 34, 36, 45, 19, 20
The data arranged in the ascending order is as follows:
12, 19, 20, 28, 34, 36, 45, 45
Since the number of terms is even, we have two middle numbers, viz.,
28 and 34
The median would be the average of these two.
Therefore, Median = [tex]$ \frac{28 + 34}{2} $[/tex]
= 31
The answer is 31.
The median of the set 28, 45, 12, 34, 36, 45, 19, 20 is 31.
To find the median of a set of numbers, you should first arrange the numbers in ascending order and then locate the middle number.
If there is an even number of terms, the median is the average of the two middle numbers. Let's do that with the given set: 28, 45, 12, 34, 36, 45, 19, 20.
Sort the numbers: 12, 19, 20, 28, 34, 36, 45, 45.Find the middle: Since there are 8 numbers (an even amount), the median will be the average of the 4th and 5th numbers.Calculate the median: (28 + 34) / 2 = 31.Therefore, the median of the given set is 31.
Which metric unit of measurement is best to use to describe the height of a tree
A kilometers
B millimeters
C liters
D meters
Solve the equation. 9 = –d + 17
Answer:
d = 8
Step-by-step explanation:
Since the variable appears on only one side of the equation, all terms not containing the variable can be eliminated from that side by adding their opposite to both sides of the equation. That is, add -17 to both sides of the equation:
9 -17 = -d + 17 - 17
-8 = -d . . . . . simplify
Now, the equation can be multiplied by a number that will give "d" on one side of the equation. Here, that number is -1. Multiply both sides of the equation by -1:
(-1)(-8) = (-1)(-d)
8 = d . . . . . simplify
The solution is d = 8.
Answer:
8
Step-by-step explanation:
[tex]9= -d +17\\9-17= -d +17- 17 \\-8/-1 = -d/-1\\8 = d[/tex]
dan saved $463 over the 12 weeks of summer break. He saved $297 of it during the last 4 weeks.How much did he save during the first 8 weeks?