Answer:
y = kx
Step-by-step explanation:
You'll need to share the possible answer choices in all future posts.
A function in which y varies directly with x has the form
y = kx, where k is the constant of proportionality.
With more data, it'd be possible for you and me both to identify this constant.
To identify if a function represents a direct variation relationship between \( y \) and \( x \), we need to determine if the function can be written in the form \( y = kx \), where \( k \) is a non-zero constant known as the constant of variation.
Here are the steps to determine if a function shows that \( y \) varies directly with \( x \):
1. Have a function \( f(x) \) to test. The function should be expressed in terms of \( x \).
2. Attempt to write the function in the form \( y = kx \).
3. Analyze the function:
- If there are no constant terms (that is, no term without \( x \)) and the only term is a multiple of \( x \), then the function shows direct variation. The coefficient of \( x \) is the constant \( k \).
- If there is a constant term not involving \( x \) (other than when \( x = 0 \)), or if \( x \) is raised to a power other than 1, then \( y \) does not vary directly with \( x \).
Let's look at a few examples:
**Example 1**: \( f(x) = 3x \)
This function is in the form \( y = 3x \), which matches the direct variation form \( y = kx \). Here \( k = 3 \). Therefore, \( y \) varies directly with \( x \).
**Example 2**: \( g(x) = 5x^2 \)
\( g(x) \) does not show direct variation because it does not have the form \( y = kx \); instead, \( x \) is raised to the second power, so it cannot represent a direct variation.
**Example 3**: \( h(x) = -2x + 1 \)
\( h(x) \) has a constant term, \( +1 \), which means it does not match the form \( y = kx \) for direct variation since \( y \) should have no constant term other than the coefficient of \( x \). Thus \( y \) does not vary directly with \( x \).
**Example 4**: \( j(x) = \frac{1}{4}x \)
\( j(x) \) reflects a direct variation. The function can be written as \( y = \frac{1}{4}x \), so \( y \) varies directly with \( x \) with a constant of variation \( k = \frac{1}{4} \).
In conclusion, to determine if \( y \) varies directly with \( x \) within a given function, you only need to inspect the function's form to ensure it is a linear equation with a slope \( k \) and no constant term (other than 0 when \( x = 0 \)).
Rewrite using standard notation:
354.2*10^-2
3.542 is the answer; you just need to move the decimal 2 places to the left.
Please answer right away. This is my last attempt
Answer:
1,206
Step-by-step explanation:
Since we'll have to deal with cubic inches (with the ball volume), we should also calculate the volume of the car in cubic inches.
We are told the car is a rectangular prism measuring 10ft x 5 ft x 3 ft.
So, in inches (12 inches/foot), we have: 120 in x 60 in x 36 in = 259,200 cu inches.
The ball is a sphere with a radius of 3 inches.
Real volume of the ball: V = (4/3) π r³
V = (4/3) π 3³ = 36 π = 113.1 cu inches
But of course, balls don't fit perfectly one next to another, like cubes, so we have to take into account the loss... the question tells us to use a factor of 190%.
So, the packing volume of a ball is 190% its real volume:
PV = 190% * 113.1 = 214.9 cu inches
Now, how many times does that fit inside the car?
259,200 / 214.9 = 1,206.14
Let's round it to 1,206, which is a possible answer.
For (x)=3x+1 and g(x)=x^2 -6, find (f+g)(x)
Answer:
(f + g)(x) = x² + 3x - 5Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=3x+1;\ g(x)=x^2-6\\\\(f+g)(x)=(3x+1)+(x^2-6)=x^2+3x+1-6=x^2+3x-5[/tex]
Hellp please please
Pleasehelp
Answer: 12 pies.
Step-by-step explanation: Divide 72(pieces) by 6 = 12
72÷6=12.
Hope it's the answer you are looking for.✌
Enter your answer in the box.
The triangles are similar.
What is the value of x?
Answer:
x = 21
Step-by-step explanation:
Identify the center and radius of each.
x^+y^+24x-18y+200=0
Answer:
The centre is at (-12, 9) and the radius = 5 units.
Step-by-step explanation:
x^2 + y^2 + 24x - 18y + 200 = 0
x^2 + 24x + y^2 - 18y = -200
Completing the square on the x and y terms:
(x + 12)^2 - 144 + (y - 9)^2 - 81 = -200
(x + 12)^2 + (y - 9)^2 = -200 + 144 + 81
(x + 12)^2 + (y - 9)^2 = 25
So the centre is at (-12, 9) and the radius = the square root of 25 = 5.
Answer:
centre = (- 12, 9), radius = 5
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² + 24x - 18y + 200 = 0
Collect the terms in x/ y together and subtract 200 from both sides
x² + 24x + y² - 18y = - 200
Using the method of completing the square
add ( half the coefficient of the x/ y term )² to both sides
x² + 2(12)x + 144 + y² + 2(- 9)y + 81 = - 200 + 144 + 81
(x + 12)² + (y - 9)² = 25 ← in standard form
with centre (- 12, 9) and r = [tex]\sqrt{25}[/tex] = 5
15. If m arc BY = 40 degrees, what is m angle YAC? the figure is not drawn to scale.
If [tex]m\widehat{BY}=40^\circ[/tex], then the central angle [tex]\angle BOY[/tex] has the same measure, and by the inscribed angle theorem we have
[tex]m\angle BAY=\dfrac12m\angle BOY=20^\circ[/tex]
It's impossible to know what the measure of angle YAC is from this information alone, but assuming AC is tangent to the circle, then angles BAY and YAC are complementary, so that [tex]m\angle YAC=70^\circ[/tex].
The line AC is the tangent of the line, and the measure of the angle YAC is 70 degrees
How to determine the measure of YAC?The measure of the arc is given as:
Arc BY = 40 degrees
The measure of angle BAY is calculated using:
BAY = 0.5 * BY
This gives
BAY = 0.5 * 40
BAY = 20
The angle at a tangent is 90 degrees.
This means that:
BAY + YAC = 90
Substitute 20 for BAY
20 + YAC = 90
Subtract 20 from both sides
YAC = 70
Hence, the measure of the angle YAC is 70 degrees
Read more about tangent lines at:
https://brainly.com/question/6617153
#SPJ2
Given the ficción f(x)=3|x-2|+6, for what valúes x is f(x)=18
Answer:
x = -2 or x=6
Step-by-step explanation:
Given
f(x) = 3Ix-2I + 6
As we know that
f(x) = 18
Putting both equal
3Ix-2I+6 = 18
Two cases are possible
Case 1: Negative Modulus
3* -(x-2) + 6 = 18
3(-x+2)+6 = 18
-3x+6+6 = 18
-3x +12 = 18
-3x = 18 - 12
-3x = 6
x = 6/-3
x = -2
Case 2: Positive Modulus
3(x-2)+6 = 18
3x-6+6 = 18
3x = 18
x = 18/3
x = 6
So for x= -2 or x=6 the value of function will be 18..
if a birds elevation is 28 meters above the surface and a fish is -12 meters below how far apart are they
Answer:
40 meters
Step-by-step explanation:
add 28 and 12
g. If two triangles have three corresponding angles and three corresponding sides that are
equal in measure, are the two triangles necessarily congruent? Why?
Helpppp
Answer:
Yes.
Step-by-step explanation:
Yes they are because that is the definition of congruency.
The function f(x) = x2 is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)? g(x) = (x − 7)2 − 3 g(x) = (x + 7)2 − 3 g(x) = (x − 3)2 − 7 g(x) = (x − 3)2 + 7
Answer:
g(x)=(x+7)^2-3
Step-by-step explanation:
Given:
f(x)= x^2
Now we have to translate f(x) 7 units to the left and 3 units down to form the function g(x).
As per the rules of translation
when any parent function, in given case f(x)=x^2, is translated to 'a' units to the left then 'a' is added to the value of x. thus making f(x+a)
Also when the parent function is translated any 'a' units down then 'a' is subtracted from the value of function. thus making f(x)-a
Translating f(x), 7 units to the left
f(x+7)= (x+7)^2
Translating f(x+7), 3 units down
f(x+7)-3 = (x+7)^2-3
Hence new function g(x)=(x+7)^2-3!
Jillian is trying to determine what helium tank pressure she needs to fill balloons for the student council dance. Find the unknown numbers in the table until you fin the best answer to the question. Which cylinder pressure will Jillian need if she plans to fill 90 balloons.
Answer: its 300
aka D
Step-by-step explanation:
I did the quiz
Can someone please answer number 32
8 & 4 when you add them together it’s 12 and when you multiply then it’s 32. When you see sum in a problem it means add. When you see product in a problem it means multiply.
Step-by-step explanation:
We can do this either by looking at:
the bonds of 12, (of which there are 7 pairs)
(which pairs of numbers add up to 12?)
or the factors of 32 (of which there are 3 pairs)
Using the factors seems quicker.
Write the factors and in each find their sum.
As 12 is quite small in comparison to 32, I would expect that the middle factors will be the ones we want - they have the smallest sum and the smallest difference of all the pairs:
1×32
=32
1+32
=33
2×16
=32
2+16
=18
4×8
=32
4+8
=12
these are the ones we want.
PLEASE HELP!!!!! IT IS URGENT
Answer:
Step-by-step explanation:
B: to get 4/8 = 1/2 That is not the whole answer, but it gets one started.
D: Very large because -4 -(-9) = 5 That's the power. This is going to make the result large.
That's all I would pick, but the second from the bottom might be an answer.
I did the first one but can you help me with the second one plz??
the only like-terms are on the right-hand-side, since the left-hand-side has only 1 term anyway.
[tex]\bf \cfrac{5}{2}s=\cfrac{3}{2}s+s\implies \cfrac{5}{2}s=\cfrac{3}{2}s+\cfrac{s}{1}\implies \cfrac{5}{2}s=\stackrel{\textit{using the LCD of 2}}{\cfrac{(1)3s+(2)s}{2}} \\\\\\ \cfrac{5}{2}s=\cfrac{3s+2s}{2}\implies \cfrac{5}{2}s = \cfrac{5}{2}s[/tex]
The answer to the photo
Answer: p+(q÷r) this is because you divide a and r and add p to it
Should be “p+q/r”.
Using English grammar, one can group the terms using “sum of...”, “product of...”, and “quotient of x and y.” (Where ... can be “x and y”)
Subtracting in English is slightly different using “x subtracted from y” meaning “y-x”.
All of these terms can be used in tandem to create expressions like the given answer.
A 4-digit number ends in 3. If you put the number 3 in the first position, the number will decrease by 738. Find the original 4-digit number.
Answer:
The original number is 4 1 5 3 OR 4 5 8 3
Step-by-step explanation:
* Lets find a way to solve this problem
- The end of the 4-digit number is 3
∴ The number is # # # 3
- The number decrease by 738 if the 3 becomes the first number
∴ The new number is 3 # # #
- Make it as a subtraction problem
∵ # # # 3 - 3 # # # = 0 7 3 8
- Lets subtract
∵ 3 - # = 8
∵ 8 > 3 we must borrow 1 from the number before 3
∴ 13 - 8 = 5
∴ # # # 3 - 3 # # 5 = 0 7 3 8
- Put the 5 in the first number, we can not pot it as a first number
bwcause when we subtract it from 3 the answer will be 2 but we
need answer zero
∴ Lets put it before the 3
∴ # # 5 3 - 3 # # 5 = 0 7 3 8
∵ we borrowed 1 from the 5 before
∴ 4 - # = 3
∴ # = 4 - 3 = 1
∴ # # 5 3 - 3 # 1 5 = 0 7 3 8
- Now we must use the 1 in the first number we can not put it as a
number because it is smaller than 3, we must put it in the 2nd
missing place
∴ # 1 5 3 - 3 # 1 5 = 0 7 3 8
∵ 1 - # = 7
∵ 1 < 7 so we must borrow 1 from the number before it
∴ 11 - # = 7
∴ # = 11 - 7 = 4
∴ # 1 5 3 - 3 4 1 5 = 0 7 3 8
- We must use the 4 in the first number and we have only one
missing place (the first place)
∴ 4 1 5 3 - 3 4 1 5 = 0 7 3 8
∴ The original number is 4 1 5 3
* You can find another answer if you put the 5 in the 2nd place in the
first number the answer will be 4 5 8 3 try to do it
which equation represents the line shown on the grap?
Answer:
y=2x
Step-by-step explanation:
2 up, 1 over. put rise over run so that concludes the 2x.
The line starts at 0 so there is no y-intercept
y=2x The "formula" would be y=mx+b where m is the slope and b is the y-intercept. in this case, the slope is 2 and the y-intercept is 0 therefore the equation is y=2x (no zero because we can atoumtucally assume that its a zero)
If the measure of arc AD = (6x -80)° and <G = (x + 2)°, what is the measure of <G?
Answer: [tex]\angle G=23\°[/tex]
Step-by-step explanation:
Remember that an inscribed angle is defined as an angle formed by two chords and whose vertex lies on the circle.
By definition, the measure of an inscribed angle is:
[tex]Inscribed\ Angle=\frac{Intercepted\ Arc}{2}[/tex]
You know that:
[tex]Intercepted\ Arc=AD = (6x -80)\\\\Inscribed\ Angle=\angle G=(x + 2)[/tex]
Then, you need to substitute values and solve for "x":
[tex](x+2)=\frac{(6x -80)}{2}\\\\2(x+2)=6x-80\\\\2x+4=6x-80\\\\4+80=6x-2x\\\\84=4x\\\\x=\frac{84}{4}\\\\x=21[/tex]
Substituting the value of "x" into [tex]\angle G=(x + 2)\°[/tex] you get:
[tex]\angle G=(21 + 2)\°=23\°[/tex]
Answer:
The measure of <G = 23°
Step-by-step explanation:
From the figure we can write,
The measure of <G is half the the measure of arc AD
To find the value of x
We have AD = (6x - 80)° and <G = (x + 2)°
6x - 80 = 2(x + 2)
6x - 80 = 2x + 4
6x - 2x = 4 + 80
4x = 84
x = 84/4 = 21
To find the measure of <g
m<G = x + 2
= 21 + 2 = 23°
Therefore the measure of <G = 23°
what is -5 3/4 - 3 1/2
Simplify the expression.
Exact Form:
−37/4
Decimal Form:
−9.25
Mixed Number Form:
−9 1/4
[tex]\text{Hey there!}[/tex]
[tex]-5\frac{3}{4}-3\frac{1}{2}=?[/tex]
[tex]\text{-5}\frac{3}{4}=\text{-5}\times\text{4+3}\rightarrow\text{-5}\times4=-20\rightarrow\text{-20 + 3 = -23}[/tex]
[tex]\text{The denominator stays the same:}-5\frac{3}{4}=-\frac{23}{4}[/tex]
[tex]\text{3}\frac{1}{2}=3\times2+1\rightarrow3\times2=6+1\rightarrow6+1=7[/tex]
[tex]\text{3}\frac{1}{2}=\frac{7}{2}[/tex]
[tex]\frac{-23}{7}-\frac{7}{2}=?[/tex]
[tex]\text{Solve the NEWER question above}\uparrow\text{and you will see your answer}[/tex]
[tex]\boxed{\boxed{\bf{Answer:Improper\ fraction:\frac{-37}{4}\ or\ Mixed\ number:-9\frac{1}{4}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
[tex]\frak{LoveYourselfFirst:)}[/tex]
40. If (5, y) is a solution to the equation
5x+4y-20=0, what is the value of y?
Alu
co À
CD
Hello there! The value of y is -5/4.
So, basically look at it like an ordered pair, (x, y). When we have (5, y), we have a value of x and are looking for a value of y. To do this, plug the value for x (5) into the equation and solve for y.
5x+4y-20=0
5(5)+4y-20=0
Now that you have the value for x, solve for y.
5(5)+4y-20=0 - Start by multiplying out the parenthesis.
25 + 4y - 20 = 0 - Next, combine like terms.
25 - 20 + 4y = 0
5 + 4y = 0 - Now, subtract 5 from both sides.
4y = -5 - Lastly, divide both sides by 4.
y = -5/4.
This is your final answer. I hope this helps and have a great day! :)
To find the value of y, substitute the given coordinates (5, y) into the equation 5x + 4y - 20 = 0. Simplify the equation and solve for y to get y = -1.25.
Explanation:To find the value of y, we can substitute the given coordinates (5, y) into the equation.
According to the equation 5x + 4y - 20 = 0, when x is 5, we have:
5(5) + 4y - 20 = 0.
Simplifying this equation gives us:
25 + 4y - 20 = 0.
Combining like terms, we get:
4y + 5 = 0.
Next, we can isolate the y-term by subtracting 5 from both sides of the equation:
4y = -5.
Finally, we can solve for y by dividing both sides of the equation by 4:
y = -5/4, or y = -1.25.
(02.01) Solve for x: 3 over 4 x + 5 over 8 = 4x x = __________________ Write your answer as a fraction in simplest form. Use the "/" symbol for the fraction bar. Answer for Blank 1:
Answer:
x = [tex]\frac{5}{26}[/tex]
Step-by-step explanation:
Given equation:
[tex]\frac{3}{4}x + \frac{5}{8} = 4x[/tex]
[tex]\frac{3(2)x + 5}{8} = 4x[/tex] ∵taking GCF 8
[tex]\frac{8 (6x + 5) }{8}[/tex] = 4x × 8
6x + 5 = 32x ⇒ 5 = 32x - 6x ⇒ 5 = 26x ⇒ x = [tex]\frac{5}{26}[/tex]
A circle has a diameter of 24 units. What is the area of the circle to the nearest hundredth of a square unit?
Answer:
452.39
Step-by-step explanation:
A=(pi)r^2
A=3.14(12)^2
A=452.39
Answer: The area of the circle is 452.16 square units.
Step-by-step explanation:
To find the area of a circle you need to use the area of a circle formula. The formula is A= π x r^2.
π= 3.14
r= 12
The r is radius which is half of the diameter. When you apply the formula you get :
A = 3.14 x 12^2
A= 3.14 x 144
A= 452.16
Anton bought a picnic cooler. His total bill with tax was $7.95. He paid 6 percent sales tax. How much did he pay for the cooler alone without tax?
Answer:
$7.50
Step-by-step explanation:
Since the price of the picnic cooler 7.95 with 6% sales tax, we can write:
X*1.06 = 7.95
Dividing both sides by 1.06,
X= 7.50
So Anton paid $7.50 alone without tax
Answer: Cost of cooler alone = $7.47
Step-by-step explanation:
Anton's bill including tax = $7.95
6% of his bill accounts for sales tax.
Sales tax = 6/100 × 7.95 ≈ $0.48
So cost of cooler alone = Total bill - tax
= 7.95 − 0.48
= $7.47
There is another way of doing this problem as well, but which ever one is easier for you could it.
Anton's bill including tax = $7.95, out of this 6% is sales tax. This implies 94% (100 − 6) of total bill accounts for cooler alone.
Cost of cooler alone:
=94/100 ×7.95
= 0.94 ×7.95
= $7.47
* Hopefully this helps:) Mark me the brainliest:)!!!
~234483279c20~
a cable installer charges $40. an hour plus a $50.00 service charge. Figure the function c(h) = ?
Answer:
c(h) = 40*h + 50
Step-by-step explanation:
Let h be the variable that represents the number of hours
As the cable operator charges $40.00 for an hour so for h hours, the expression will be 40*h
And
Lastly, he has to charge $50.00 must as service charge,
As the number of hours is variable here so the function will be in terms of hours.
So the resulting function will be:
c(h) = 40*h + 50
Answer to this please ?
a=80 because it is equal to the 80 by the corner R
Use the formula below to find the value of $400 invested at 4% interest compounded monthly for 10 years. Step 1:Find the value of each of the following for this problem:
Answer:
See below
Step-by-step explanation:
Step 1.
P = $400
r = 0.04
t = 10 years
n = 12 ( as there are 12 months in a year).
Step 2.
A(10) = 400(1 + 0.04/12)^12^10
= 400 * 1.00333333^120
= $596.33 to the nearest hundredth (answer).
Answer and Explanation:
Given : The value of $400 invested at 4% interest compounded monthly for 10 years.
To find : The value of each of the following for this problem ?
Solution :
The interest formula is [tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]
Step 1 -
P is the amount invested, P=$400
r is the interest rate, r=4%=0.04
t is the time , t=10 years
n is the number of compounding periods per year, n=12
Step 2 - To find A(10),
Substitute all the values in the formula,
[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]
[tex]A(10)=400(1+\frac{0.04}{12})^{12\times 10}[/tex]
[tex]A(10)=400(1+0.0033)^{120}[/tex]
[tex]A(10)=400(1.0033)^{120}[/tex]
[tex]A(10)=400(1.490)[/tex]
[tex]A(10)=596.33[/tex]
Therefore, The amount after 10 year is $596.33.
PLEASE HELP ME!!!
Find the vertex of f(x)=x^2+2x+3 and show your work
Answer:
The vertex is the point (-1,2)
Step-by-step explanation:
we have
[tex]f(x)=x^{2}+2x+3[/tex]
Convert into vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)-3=x^{2}+2x[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]f(x)-3+1=x^{2}+2x+1[/tex]
[tex]f(x)-2=x^{2}+2x+1[/tex]
Rewrite as perfect squares
[tex]f(x)-2=(x+1)^{2}[/tex]
[tex]f(x)=(x+1)^{2}+2[/tex] ----> equation in vertex form
The vertex is the point (-1,2)
Mason brought a tablecloth that measured 8 feet by 4 feet. What was the area of the tablecloth? PLEASE ANSWER QUICK QUICK WILL EARN 44 BADGE IF NOT, I WILL GIVE YOU A BIG RATING AND THUMBS UP ANSWER PLEASE!
Below is an image of the table cloth with its measurements
The formula for Area is:
A = length x height
The length of this shape is 8 feet
The height of this shape is 4 feet
so...
A = 8 x 4
A = 32
Hope this helped!
The equation of the line of best fit of a scatter plot is y = 8x − 1. What is the slope of the equation?
-8
-1
1
8
the answer is 8 hoped this helped !!!
Answer:
8
Step-by-step explanation:
This is because the slope of a line in an equation is m. In the equation given m=8, so that makes the slope 8.