[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\stackrel{\textit{"y" varies directly as "x"}}{y = kx}\qquad \textit{we also know that} \begin{cases} y = 540\\ x = 10 \end{cases}\implies 540=k(10) \\\\\\ \cfrac{540}{10}=k\implies 54=k~\hfill \boxed{y=54x} \\\\\\ \textit{when y = 1080, what is "x"?}\qquad 1080=540x\implies \cfrac{1080}{540}=x\implies 2=x[/tex]
The value of x when y = 1080 for the condition when its given that y varies directly as x and that y = 540 when x = 10, is found to be x = 20
Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
[tex]p = kq[/tex]
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n are two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
For this case, it is specified that y varies directly as x.
That means
[tex]y \propto x\\or\\y = kx[/tex]
At x = 10, y is 540. Putting these values in the equation y = kx as they're related, we get:
[tex]540 = k \times 10\\\\\text{Dividing both the sides by 10}\\\\\dfrac{540}{10} = k\\\\k = 54[/tex]
Thus, the relationship between x and y is: y = 54x
Now, when y = 1080, we get:
[tex]1080 = 54x\\\\\text{Dividing both the sides by 54}\\\\\dfrac{1080}{54} = x\\\\x = 20[/tex]
Thus, the value of x when y = 1080 for this condition is when x = 20.
Learn more about directly related variables here:
https://brainly.com/question/13082482
#SPJ4
What is the volume of the right rectangular prism?
Answer:
[tex]\boxed{\sf{140}}[/tex]
Step-by-step explanation:
A rectangular prism's volume must be determined in order to solve this problem.
Remember to use this rectangular prism formula:
[tex]\sf{V=l*w*h}[/tex]
L=7 in
W=5 in
H=4 in
Multiply.
7*5*4=140
140 in
Therefore, the correct answer is 140.
I hope this helps you! Let me know if my answer is wrong or not.
Answer:
V = 140 cubic units
We can split this equation into multiple steps to solve:
7 x 5 x 4 =
(7 x 5) x 4 =
35 x 4 = 140
Therefore your answer would be:
140 cubic units
Otherwise, known as option C.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
how do I do this??????
you take 99 divided by 22 = 4.5
I don't understand what exactly your teachers meaning so I would also suggest asking but the answer compered to everything I've learned in math would be 4.5.
have a good day/night!! :)
The curve of best fit is given as y = 4 + 3x + 2x2. Find the value of y when x = 2
Help me on this question please!
Answer:
1/5
Step-by-step explanation:
Arrange the numbers from smallest to largest...the median is the one in the middle of the list
-12/4 - 2.5 1/5 18/5 10 the middle is 1/5
2m - 3 - 5= -m + 10 please help me
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: 2m - 3 - 5 = - m + 10[/tex]
[tex]\qquad \sf \dashrightarrow \: 2m + m = 10 + 3 + 5[/tex]
[tex]\qquad \sf \dashrightarrow \: 3m = 18[/tex]
[tex]\qquad \sf \dashrightarrow \: m = 18 \div 3[/tex]
[tex]\qquad \sf \dashrightarrow \: m = 6[/tex]
Hence, value of m is 6
Two students in Ms. Romean's class are working on
finding the mean for the following set of numbers: 2,
12, 16, 4, 18, 24, 32. Susan states that the answer is
15.4 when rounded to the nearest tenth. She added all
of the numbers and divided by 7. Sam disagrees and
thinks the answer is 54. She added all of the numbers
and divided by 2. Which student is correct? How do
you know? Explain your thinking!
Answer:
susan is correct
Step-by-step explanation:
2+12+4+18+24+32=108
108 divided by 7=54
my reasoning is that the formula is add all and divide by how many numbers you added
I do not understand
Hey there!
First, let's convert 4 into a fraction: 4/1
Now, multiply fractions:
1/4*4/1=1
is 1 greater than 4? of course not.
let's try Option B:
5/6*4/1
5 times 4 and 6 times 1
20/6
reduce the fraction
10/3
or
3+1/3 (less than 4)
Is it Option C? Let's try/
3/2*4/1
3 times 4 and 2 times 1
12/2
6
and 6 is greater than 4. Bingo!
How about Option D?
9/10*4/1
9 times 4 and 10 times 1
36/10
18/5
Hence, the answer is
[tex]\boxed{\boxed{\bold{option~C}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#KeepLearning
#NeverGiveUp
:-)
Solve for x: -1 < x + 3 < 5
Answer:
- 4 < x < 2
Step-by-step explanation:
- 1 < x + 3 < 5 ( subtract 3 from each of the 3 intervals )
- 4 < x < 2
-1 < x + 3 < 5
Then subtract 3 from each of the 3 intervals
- 4 < x < 2
#CarryOnLearning
#LibreAngMatuto
Please someone help I will give brainliest
Answer: 42.0
Step-by-step explanation:
what value of x makes this inequality true?
x + 16 < 43
Answer:
x < 27
Step-by-step explanation:
x + 16 < 43
move the constant to the right-hand side and change its sign
x < 43 - 16
subtract the numbers
x < 27
~~~~~~~~~~~~~~~~~~
X < 27
alternative form
X ∈ ( - ∞ , 27 ) , { x | x < 27 }
Select all of the steps that are possible when solving for x.
5 1/2x + 2/3x = 37
x = 37
x = 6
37x = 6
37/6x = 37
1 1/2x + 2/3x =37
Answer:
37/6x = 6 and 5 1/2x + 2/3x = 6
Step-by-step explanation:
Mia gets 15 out of 18 questions correct on a test. What is the ratio of correct
answers to the total number on the test in simplest form?
Answer:
5/6
Step-by-step explanation:
it's a 15:18 ratio, just needs simplification
The number 144 can be represented by 12x12 square grid which of the following can be also represented on a square grid??
A. 39 b.50 c.70 d.81
Answer:
d.81
Step-by-step explanation:
81 can be represented by a 9x9 square grid. The rest of the numbers would be represented on rectangular grids.
Answer:
D. 81
Step-by-step explanation:
81 can be represented by 9X9 square grid
9^2 = 81
Can someone please help?
Simplify, 81^1/4
Answer:
3
Step-by-step explanation:
81^(¼) can also be witten as the fourth root of 81, which happens to be 3.
Answer:
3
Step-by-step explanation:
(3*(to the fourth power))1/4
Brainliest if correct
Answer:
$294.00
Step-by-step explanation:
Whats the gross pay before taxes?
Answer: $294.00 with overtime and everything.
a=340
rounded to the nearest 10
b=49.8
rounded to 1 DP
Find the minimum of
a x b
Answer:
16666.25
Step-by-step explanation:
For rounded values, the minimum value they could have been rounded from is the given value less half its least-significant digit.
That means the minimums are ...
a: 340 ⇒ 340 -5 = 335
b: 49.8 ⇒ 49.8 -0.05 = 49.75
Then the minimum product would be ...
(335) × (49.75) = 16666.25
Use quadratic method :
6y^2 - 4y - 3=
Answer:
see explanation
Step-by-step explanation:
look at the photo
What is the vertex of the function below?
Answer:
lol thts 26
Step-by-step explanation:
What is the perimeter of the shape below?
None of these choices are correct
The down side of the shape is unknown and cannot be found, therefore you cannot find the perimeter of the shape.
Mrs Smith visits THE SCHOOL - outfitters to buy school clothes for the new school year.
The price of a school dress is R350 and a blazer is R650.
Calculate the percentage profit the shop makes if the cost price per dress is R280.
The shop makes 25% profit if the cost price per dress is R280.
Find the slope of the line that passes through (9, 6) and (4, 5).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
slope = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (9, 6 ) and (x₂, y₂ ) = (4, 5 )
m = [tex]\frac{5-6}{4-9}[/tex] = [tex]\frac{-1}{-5}[/tex] = [tex]\frac{1}{5}[/tex]
A) fifteen twentieths
B) twelve fifths
C) fifteen fourths
D) eight halves
Hello !
_______
Answer :-C) Fifteen fourths.[tex]\huge {\boxed {\underline{Explanation :}}}[/tex]
[tex]\sf{5 \: x \: \frac{3}{4}[/tex]
_______
[tex]\sf{Apply \: the \: fraction \: rule :} \: a \: ^. \: \frac{b}{c} = \frac{a \: ^. \: b}{c}[/tex]
[tex]\sf{\frac{5x \: ^. \: 3}{4}[/tex]
_______
[tex]\sf{Multiply \: the \: numbers:} \: 5 \: ^. \: 3 = 15[/tex]
[tex]\sf{= \frac{15x}{x}[/tex]
Hopefully This Helps ! ~
#LearnWithBrainly
[tex]\underline{Answer :}[/tex]
Dollixna ~
basic set of drawing pencils costs $8.98. A professional set of drawing pencils costs $27.49. How much more does the professional set cost than the basic set?
ASAP
$18.51
Step-by-step explanation:
assuming you dont need the cost per pencil or anything...
pro set: $27.49
basic set: $8.98
subtract basic from pro.
27.49-8.98= $18.51
Answer:
I know this is a little late but your answer is 18.51
Algebra 1? What am I supposed to do it is so confusing
Answer:
you are basically given an unknown and you try to solve for it. if you need any guidance feel free to ask.
vertically stretched by a factor of 2, then translated
4 units left and 1 unit down
A vertical stretch of scale factor 2, followed by a translation of 4 units left and 1 unit down is written as:
g(x) = 2*f(x + 4) - 1
How to write the given transformation?
For a general function f(x), a vertical stretch of scale factor K is written as:
g(x) = K*f(x).
Horizontal translation:
For a general function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N).
If N is positive, the shift is to the left.If N is negative, the shift is to the right.Vertical translation:
For a general function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N.
If N is positive, the shift is upwards.If N is negative, the shift is downwards.So, if we start with a function f(x) and we stretch it vertically with a scale factor of 2, we get:
g(x) = 2*f(x)
Then we translate it 4 units left:
g(x) = 2*f(x + 4)
Then we translate 1 unit down:
g(x) = 2*f(x + 4) - 1
This is the equation for the transformation.
If you want to learn more about transformations, you can read:
https://brainly.com/question/4289712
Select all the situations where knowing the volume of an object would be more useful than knowing its surface area.
A. Measuring the amount of gasoline left in the tank of a tractor.
B. Packing a box with watermelons for shipping.
C. Filling an aquarium with buckets of water.
D. Charging a company for ad space on your race car.
E. Determining the amount of paint needed to paint a barn.
F. Determining the monetary value of a piece of gold jewelry.
G. Deciding how much wrapping paper a gift will need.
Answer:
The answers are A, B, C, and probably F
Step-by-step explanation:
Volume is how much space an object takes up, while surface area is how much space is on the surface of the object. In option A, we are measuring how much gas can fit in a tank, so volume is used. B and C are also dealing with filling a container. Options D, E, and G are measuring the surface area because they are asking how much of something is needed to cover the surface of a car, barn, and gift. In option F, assuming that the jewelry is pure gold, not just a metal with a gold coating, volume is used.
Hope this helps!
The price of gas increased from $2.20 per gallon on Monday to $2.31 per gallon on Tuesday. What is the percent of increase?
Create a tree diagram to show the different options for the lunch options: Salad Sandwich Soup Tortellini Roast Beef Caesar Macaroni Ham Lentil Turkey
Answer:
is there a picture of the answers?
Step-by-step explanation:
also can u help me with my question pls
Please Answer ASAP
I was kind enough to give the old ones we had a the beginning of a school year
The other one is not mines
Answer:
The answer = 9
D : 729
Step-by-step explanation:
here step-by-step is 6/2 * (1 + 2) = 9
What shape am i 3equal side each 4cm not right angles
Answer:
Triangle
Step-by-step explanation:
A regular triangle has equal sides and no right angles. Hope this helps. ^^