You have the following equation:
y = 1/2 x
In order to determine what is the constant of proportionality, consider the general fom of proportional relatioship, given by:
y = kx
by comparing the previous equation with y=1/2x, you can notice that k=1/2. Then, the constant of proportionality is k = 1/2
A. 1/2
jon's bathtub is rectangular and its base is 18 ft2. how fast is the water level rising if jon is filling the tub at a rate of 0.6 ft3/min? (use decimal notation. give your answer to three decimal places.)
Jon's bathtub exists rectangular and its base exists 18 ft². The water level rising if Jon is filling the tub at a rate of 0.2 ft³/min is 0.011 ft/min.
What is meant by differential equation?A differential equation in mathematics exists an equation that links the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.
If we take a look at a rectangular bathtub, the volume of the bathtub can be expressed as:
Volume (V) = length × breadth × height
where; base = length × breadth = 18ft²
The volume of the rectangular bathtub = 18h ......... (1)
Using differentiation to differentiate 18h with respect to t implicitly, then:
[tex]$\frac{\mathrm{dV}}{\mathrm{dt}}=18 \frac{\mathrm{dh}}{\mathrm{dt}}$$[/tex]
When the rate of rising of the volume is 0.2 ft² / min
[tex]$0.2=18 \frac{\mathrm{dh}}{\mathrm{dt}}$$[/tex]
substitute the values in the above equation, we get
[tex]$\frac{\mathrm{dh}}{\mathrm{dt}}=\frac{1}{18} \times(0.2)$$[/tex]
[tex]$\frac{\mathrm{dh}}{\mathrm{dt}}=0.011 \mathrm{ft} / \mathrm{min}$$[/tex]
Therefore, we can conclude that the rate at which the water level rises if Jon is filling the tub at 0.2 ft³/min exists 0.011 ft/ min.
To learn more about differential equation refer to:
brainly.com/question/1164377
#SPJ4
if it takes 3/4 of an hour to fill 3/5 of a pool how many hours will it take to fill the pool completely
The time taken to completely fill the pool is 5/4 hour
How to determine the time to fill the pool?From the question, the given parameters are:
Time =3/4 hour
Size of the pool = 3/5
The time to fill the pool is then calculated as
Time = Given time/Proportion of the pool
Substitute the known values in the above equation
So, we have the following equation
Time = 3/4 hour ÷ 3/5
Express the quotient as product
So, we have the following equation
Time = 3/4 hour x 5/3
Evaluate the products
Time = 5/4 hour
Hence, the time taken is 5/4 hour
Read more about unit rate at
https://brainly.com/question/4895463
#SPJ1
Which of the following equations have infinitely many solutions?
Choose all answers that apply:
A. −76x+76=76x+76
B. −76x+76=−76x+76
C. 76x+76=76x+76
D. 76x+76=−76x+76
The two equations with infinitely many solutions are the ones in options B and C.
−76x+76=−76x+7676x+76=76x+76Which of the given equations has infinitely many solutions?An equation only has infinitely many solutions if we have a true equation that does not depend of x.
For example, if you look at option B, we have:
-76x + 76 = -76x + 76
We have the same expression in both sides, if we subtract it in both sides we get:
0 = 0
This is true, and does not depend of x, so this equation has infinitely many solutions.
The same thing happens for equation C.
76x+76=76x+76
Where we have the same thing in both sides.
Learn more about equations:
https://brainly.com/question/13763238
#SPJ1
PLEASE HELP ASAPPP!!!!!!!!!!!!!!!!!!!!!
PLEASE HELP ASAP!!!!
The quadratic function f(x) has roots of −4 and 2 and point (1, −5) lies on f(x). What is the equation of f(x)?
f(x) = (x − 2)(x + 4)
f(x) = (x − 2)(x − 4)
f(x) = 4(x − 2)(x + 4)
f(x) = 4(x − 2)(x − 4)
The function has an equation of f(x) = (x + 4)(x - 2)
How to determine the equation of f(x)?The given parameters in the question are
Roots = -4 and 2
Point = (1, -5)
The above parameters can be rewritten as
Roots: x = -4 and x = 2
Point: (x, y) = (1, -5)
A quadratic equation can be represented as
f(x) = a * (x - Roots)
Where Roots: x = -4 and x = 2
The above parameters imply that we have the following equation
y = a(x + 4)(x - 2)
From the question, we have
(x, y) = (1, -5)
This gives
-5 = a(1 + 4)(1 - 2)
Divide
a = 1
Substitute a = 1 in y = a(x + 4)(x - 2)
y = (x + 4)(x - 2)
Hence, the equation of the quadratic function f(x) is f(x) = (x + 4)(x - 2)
Read more about quadratic functions at
https://brainly.com/question/1214333
#SPJ1
Answer: The answer would be A: f(x) = (x − 2)(x + 4)
Step-by-step explanation: I got it right on my test
2/3 is what percent of 1/4? of 1/6
Let's first calculate the percentage for 1/4
[tex]\begin{gathered} P=\frac{2/3}{1/4} \\ P=\frac{8}{3} \\ P=2.666 \\ P=267\text{ \%} \end{gathered}[/tex]Let's first calculate the percentage for 1/6
[tex]\begin{gathered} P=\frac{2/3}{1/6} \\ P=\frac{12}{3} \\ P=4 \\ P=400\text{ \%} \end{gathered}[/tex]1. Priya's favorite kind of dark chocolate comes in a package shaped like a triangular. If the package can hold 144 cm of chocolate and the triangular faces have a base of 3 cm and a height of 4 cm, how tall is the entire package?
ok
Measures base = 3cm
height = 4cm
tall = x
volume = 144 cm^3
Volume = Area of the base * tall
Area of the base = (3 * 4) / 2 = 12/2 = 6 cm^2
144 = 6*x
x = 144/6
x = 24 cm
Result: The chocolate is 24 cm tall.
[please help asap tyyyyyyyy
Answer:
I got you, the answer is c+32.
Step-by-step explanation:
Hope this helps. Please mark branliest if right.
Estimate 81.244.+65.33 by first rounding each number to the nearest whole number
If we round 81.244 to the nearest whole number then it would be 81.
For 65.33 is 65. Then, we sum.
[tex]81+65=146[/tex]Hence, the answer is 146.A train goes at a constant speed. If it covers 150 miles in 2 1/2 hours What distance would it cover in 2 hours?
Answer:
120
2 1/2 hours is 150 minutes and your covers 150 miles in 150 minutes, so remove 30 minutes because 1/2 an hour is 30 minutes and remove 30 miles because you're going of time because 1 minute = 1 mile
Please help ( geometry)
Fill in the missing proof
The missing proof in the given congruence of triangle is;
∠FAB = ∠FBA.
What is defined as the isosceles triangle?An isosceles triangle would be one with 2 sides of equal length. Below is a collection of some isosceles triangle properties:If two sides of an isosceles triangle are equal, therefore the angles opposite the two sides correspond with each other and are always equal.The two angles B and C, opposite the equal sides AB as well as AC in the isosceles triangle shown above, are equal.The isosceles triangle does have three acute angles, which means they are less than 90°.The sum of an isosceles triangle's three angles is always 180°.For the given question;
The given data in the triangle FAB is;
FD ≅ FCDA ≅ CBIn the step two,
FA = FB (Property of isosceles triangle)
Then, step 4 will be ∠FAB = ∠FBA.
Thus, the missing proof will be ∠FAB = ∠FBA.
To know more about the isosceles triangle, here
https://brainly.com/question/28226565
#SPJ13
p(x) = x^3 − 3x^2 − 10x + 24 , has a known factor of (x-4).
rewrite p(x) as the product of linear factors
The product of linear factors for p(x) is given as (x-4)(x^2+x-6).
What is the factor theorem?The factor theorem states that;
p(x) is divisible by x-a if and only if p(a)=0p(x) is divisible by x+a if and only if p(-a)=0From the question, given that x-4 is a factor of
p(x) = x^3 − 3x^2 − 10x + 24,
then it is divisible by x-4 and p(4)=0.
Dividing x^3 − 3x^2 − 10x + 24 by x-4 using the long division will result to another factor x^2+x-6 with a remainder of zero.
We can then conclude that (x-4)(x^2+x-6) is the product of linear factors for p(x).
Learn more about factor theorem here: https://brainly.com/question/24729294
#SPJ1
when the sun is 5 degrees above the horizon, how long will the shadow nof a 35ft tree be ?
tan 5 = x / 35
0.0874 = x / 35
cross- mulltiply
x = 35 x 0.0874
x = 3 . 059 = 3. 06 feet
Find the length of side x to the nearest
tenth.
The length of x in the isosceles right triangle is 15.6 units.
How to find the side of an isosceles triangle?An isosceles triangle is a triangle that has two sides equal to each other and two angles congruent to each other.
The triangle above is an isosceles triangle. The triangle is also a right angle triangle. A right angle triangle is a triangle that has one of it's angles as 90 degrees.
Using Pythagoras's theorem, let's find the side x
c² = a² + b²
where
c = hypotenusea and b are the legsTherefore,
11² + 11² = x²
121 + 121 = x²
x = √242
x = 15.5563491861
Therefore,
x = 15.6 units
learn more on isosceles triangle here:https://brainly.com/question/27022193
#SPJ1
The Sticker Company shipped 5,693,123,456 stickers last month. This month the company shipped 6,966,632,877 stickers. About how many more stickers were shipped this month than last month? A.11,000,000,000B.10,000,000,000C.3,000,000,000D.1,000,000,000
SOLUTION
To get how many more stickers were shipped last month than this month, we simply subtract this month's shipment from last month's shipment.
This becomes
[tex]\begin{gathered} 6,966,632,877-5,693,123,456 \\ =1,273,509,421 \end{gathered}[/tex]Therefore, the we have 1,000,000,000 to the nearest billion.
Option D is the correct answer
Simply this equation 2(x-7)=-4
Answer:
2x - 14 = -4
that is the equation simplified
For 7 y = 2 x − 5 , which of the following expressions gives x in terms of y ?
The expressions that gives x in terms of y from the given expression 7 y = 2 x − 5 is x = (7y +5)/2.
How can the expression be simplified?The concept that will be used in this question is solving of linear equation, because the equation is linear, then we perform the simplification.
The given expression is is 7 y = 2 x − 5
Then from the expression we can make 2x the subject of the formula by rearranging it as 2x = 7y +5
Then this can be further expressed by dividing the both sides by the factor of 2, which can be expressed as ;
x = (7y +5)/2
Therefore, option A is correct because it is the expression that gives the x in terms of y.
Read more about expressions at:
https://brainly.com/question/723406
#SPJ1
Check the missing options:
A. x = (7y +5)/2
B. y = (7x +5)/2
C. x=(7y +5)/3
working together, it takes two different sized hoses minutes to fill a small swimming pool. if it takes minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?
Time taken by the smaller hose to fill the pool on its own = 75 minutes
Time taken to fill the swimming pool by the larger hose and smaller hose working together = 30 minutes
Time taken by the larger hose to fill up the swimming pool = 50 minutes
Let 'x' be the time taken by the smaller hose to fill the swimming pool on its own.
In 30 minutes, the larger and smaller hoses together can fill the swimming pool. So in 1 minute, it can fill up 1/30 of the swimming pool.
In 50 minutes, the larger hose can fill up the swimming pool on its own. So the larger hose can fill up 1/50 of the pool in 1 minute.
It takes 'x' minutes for the smaller hose to fill up the pool on its own. So in 1 minute, the smaller hose alone can fill up 1/x of the pool.
Hence 1/30 = 1/x +1/50
⇒ 1/30 = (50+x)/50x
⇒ 30 = 50x/(50+x)
⇒ 30 (50 + x) = 50x
⇒ 1500 + 30x = 50x
⇒ 20x = 1500
⇒ x = 1500/20
⇒ x = 75 minutes.
Thus the smaller hose alone takes 75 minutes to fill up the pool.
The question is incomplete. Find the complete question below:
Working together, it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 50 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?
Learn more about comparing work and time at https://brainly.com/question/24900258
#SPJ4
complete the slope-intercept form of an equation that represents the relationship in the table
Answer:
y = 3x -4
Step-by-step explanation:
You want the slope intercept equation representing the relationship between x and y, given (x, y) = (1, -1) and (4, 8).
SlopeThe slope can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (8 -(-1))/(4 -1) = 9/3 = 3
InterceptThe y-intercept can be found using the equation ...
b = y1 -m(x1)
b = -1 -3(1) = -4
Slope-intercept equationThe slope-intercept equation of a line has the form ...
y = mx + b
Using the above values of m and b, this becomes ...
y = 3x -4
__
Additional comment
Attached is a graph showing the points and the line the equation represents.
<95141404393>
Please help. I don’t understand the problem.
Answer:
ASA
Step-by-step explanation:
ASA stands for Angle-Side-Angle which is the congruency theorem that states that if a triangle shares two congruent angles that have one line in between the two angles share a side length congruent to each other, then the two triangles are congruent.
Before you get very confused on the difference between AAS (Angle-Angle-Side) and ASA (Angle-Side-Angle), let explain why these two triangles are ASA.
We are given that both triangles share a similar side length at KL where they are connected. We are also given that angle ∠JKL is congruent to angle ∠MKL. We are also given that angle ∠MLK is congruent to angle ∠JLK.
The most important part after deciding all the relationships is given to us, it is deciding what kind of congruence theorem we will use. We are given the options:
SSS (Side-Side-Side) SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side) HL (Hypotenuse-Leg)Because we are presented with two congruent angles and one congruent side, we know that this triangle congruency theorem is either ASA or AAS. To understand why these triangles are ASA, we have to look at where the two-given congruent sides are located. As we can see in the name and in our two triangles, the congruent side lengths are in between the two angles as it touches both angle ∠JKL and angle ∠JLK in triangle ΔJKL, while in on ΔMKL, the congruent side length is also found between angle ∠MLK and angle ∠MKL. So, these triangles share ASA because they share two congruent angles connected by one congruent line.
ORDER MATTERS WHEN YOU WRITE YOUR CONGRUENCY THEROMS
AAS is technically not the same as ASA and I will explain that in one moment.
An example of AAS is if instead being told that ∠JKL is congruent to angle ∠MKL, we are given that ∠KJL is congruent to angle ∠KML instead. now the congruent sides are not connected to angle ∠KJL or angle ∠KML. The side is no longer in-between the two congruent sides. The reason order matters here are because order matters between AAS and ASA because in another theorem, SAS, you will find out order matter because while SAS guaranties congruency SSA does not. Technically, though, while both AAS and ASA both guaranty congruency, they are labeled separately, the way the remaining congruency thermos are.
In this figure, m∠2=(6x+20)∘ and m∠8=(8x−10)∘ .
What value of x makes a∥b ?
Enter your answer in the box.
If the ∠2 = 6x+20 degrees and ∠8 = 8x-10 degrees, then the values of x is 15
The lines a and b are parallel lines
Here two parallel lines a and b are cut by a transversal t
The angles are
∠2 = 6x+20 degrees
∠8 = 8x-10 degrees
The angle 2 and angle 8 are called alternate exterior angles
When the two parallel lines are cut by a transversal, the formed alternate exterior angles are equal.
Then
6x+20 = 8x-10
Solve the equation
6x-8x = -10-20
-2x = -30
x = -30/-2
x = 15
Hence, if the ∠2 = 6x+20 degrees and ∠8 = 8x-10 degrees, then the values of x is 15.
Learn more about alternate exterior angles here
brainly.com/question/2279752
#SPJ1
Please help me with letter e
Height of the triangle is = 14m
Given,
Base of the triangle is 8m
Area of the triangle is = 56m^2
To find the height of the triangle.
Now, According to the question:
We know that
Area of the triangle is = 1/2 x b x h
where, b = base
h = height
Plug all the values of base and area in above formula:
56m^2 = 1/2 x 8m x h
56 x 2 / 8 = h
h = 14m
Hence, Height of the triangle is = 14m
Learn more about Area of Triangle at:
https://brainly.com/question/19305981
#SPJ1
Solve the following LP formulation and determine the number of Surplus units in constraint B.
SOLUTION
From the what is given
[tex]\begin{gathered} x+y\le5 \\ x\ge3 \\ 2y\le8 \\ x\ge0 \\ y\ge0 \end{gathered}[/tex]We have the graph as shown below
We are told that the MAX is
[tex]5x+2y[/tex]Substituting these required points into the equation, our maximum becomes
[tex]\begin{gathered} 5x+2y \\ \text{For (3, 2)} \\ 5(3)+2(2)=15+4=19 \\ \text{For }(3,\text{ 0)} \\ 5(3)+2(0)=15+0=15 \\ \text{For (5, 0)} \\ 5(5)+2(0)=25+0=25 \end{gathered}[/tex]We can see that the maximum is 25 at for units of 5, that is x = 5
But we are told in (B) that
[tex]x\ge3[/tex]Hence the surplus unit is
[tex]5-3=2[/tex]Hence the answer is 2
Tell which of the following is a linear equation in one variable:
a) x² - 4x + 3 = 0
b) 6x - 2y = 7
c) 3x - 1 = -2x
d) pq - 3 = p
e) 3x + 2 = 4 ( x +7 ) + 9
For 100 Points
Answer:
c and e
Step-by-step explanation:
(a)
x² - 4x + 3 = 0 ← is a quadratic and not linear
(b)
6x - 2y = 7 ← is a linear equation in 2 variables, x and y
(c)
3x - 1 = - 2x ( add 2x to both sides )
5x - 1 = 0 ← is a linear equation in 1 variable
(d)
pq - 3 = p ← is a linear equation in 2 variables , p and q
(e)
3x + 2 = 4(x + 7) + 9 ← is a linear equation in 1 variable
What is the exchange rate? Show your work.
1 US dollar = _________ euro.
The exchange rate is 1 USD = 0.992714 EURO
What is Conversion of unit?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
We need to convert between units in order to ensure accuracy and prevent measurement misinterpretation. For example, we do not measure a pencil's length in kilometres. In this situation, one must convert from kilometres (km) to centimetres (cm) (cm).
Given:
1 US dollar = _________ euro.
As, the exchange rate between US dollar to Euros
1 USD = 0.992714 EURO
1 USD = 1 EURO
So, if we have to find 5 US dollar into EURO then
5 US dollar = 5.02 EURO = 5 EURO
Hence, the exchange rate is 1 USD = 0.992714 EURO
Learn more about Conversion of unit here:
https://brainly.com/question/4736731
#SPJ1
draw and label tape diagram to model each number sentence
ANSWER:
We can see the answer in the drawing.
STEP-BY-STEP EXPLANATION:
In this case, we make the diagram as follows:
Judy is 12 years old and is 8 years old mukta is 16 years old which of the following ratios best expresses the relationship between the ages 4 ratio 3 ratio to 2 ratio 3 ratio 4:3 ratio 2 ratio 4:3 ratio 4 ratio 2 ratio 4 ratio 3
Age of Judy = 12 yrs old
Age of x = 8 yrs old
Age of Mukta= 16 yrs old
Ratio between the 3 ages = 12 : 8 : 16
Since all the three numbers are divisible by 4
Therefore the ratio comes out to be 3 : 2 : 4 or 3 ratio 2 ratio 4
To learn more about ratios visit : brainly.com/question/21323524
Answer:
= 12 : 8 : 16
all the three numbers are divisible by 4
the ratio is 3 : 2 : 4
Please solve will mark as
brainliest
Write the equation of the line in the slope-intercept form which is parallel to
y = −2x +5 and passing through the point (1, −4)
The equation of the line that is parallel to the line y = −2x +5 and passing through the point (1, −4) is y = -2x - 2.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
The slope of two parallel lines is always the same.
The slope y-intercept form of an equation is y = mx + c where m is the slope.
Given the parallel equation y = -2x + 5 by compare slope = -2
Therefore,the equation will become y = -2x + c
Substitute,(1,-4) into this
-4 = -2(1) + c ⇒ c = -2
So equation converts as y = -2x - 2.
Hence "The equation of the line that is parallel to the line y = −2x +5 and passing through the point (1, −4) is y = -2x - 2".
For more about the equation,
https://brainly.com/question/10413253
#SPJ1
amazon is selling 24 pack of 3x3 sticky notes for 28.99 Each pack has 100 sticky notes. What is the price for each pack? How much is each single sticky note?
Given data:
Total packs 3x3 sticky notes: 24 packs
Cost of 24 packs: 28.99
Number of sticky notes in a pack: 100
With the information above, we can proceed to find the answers to the questions
Part A: What is the price for each pack?
Since 24 packs cost 28.99
Then 1 pack will cost =
[tex]\begin{gathered} \frac{28.99}{24}=1.208 \\ \text{which is appro}\xi mately\text{ 1.21} \end{gathered}[/tex]Hence, a pack will cost $1.21
Part B: How much is every single sticky note?
Since each pack cost 1.21, and each pack has 100 sticky notes, then
each sticky note will cost
[tex]\frac{1.21}{100}=0.0121[/tex]=> every single sticky note will cost $0.012
In the data set below, what are the lower quartile, the median, and the upper quartile? 30 45 49 50 63 75 75 77 84
In the data set {30,45,49,50,63,75,75,77,84} the lower quartile is 47, the median is 63 ,and the upper quartile is 76 .
In the question ,
the data set is given as {30,45,49,50,63,75,75,77,84}
as the data set has 9 terms , the median will be the central term that is 5th term .
so the median is 63 .
For finding the lower and upper quartile , we break the set into two half .
lower half = {30,45,49,50}
the lower quartile will be the central value ,that is (45+49)/2 = 47
so, the lower quartile(Q₁) is 47 .
upper half = {75,75,77,84}
the upper quartile will be the central value ,that is (75+77)/2 = 76
so, the upper quartile(Q₃) is 76 .
Therefore , in the data set {30,45,49,50,63,75,75,77,84} the lower quartile is 47, the median is 63 ,and the upper quartile is 76 .
Learn more about Median here
https://brainly.com/question/27254182
#SPJ1