Answer: 5.5 is the constant proportionality.
Step-by-step explanation:
Since we have given that
y = 5.5x
As we can see that
y is directly proportional to x.
So, mathematically written as
[tex]y\ \alpha\ x\\\\y=kx[/tex]
If we comparing both the expression, we get that
k = 5.5.
Hence, 5.5 is the constant proportionality.
The constant of proportionality of y = 5.5x is 5.5.
A directly proportional relational relationship can be represented below
y ∝ xwhere
∝ = symbol for proportionality
y and x are the variable that are related. Therefore,
y = kx
where
k = constant of proportionality.
The equations y = 5.5x can be modelled as directly proportional relationship using y = kx.
Therefore, k = 5.5 is the constant of proportionality.
The constant of proportionality of y = 5.5x is 5.5.
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"Find the value of the derivative (if it exists) at each indicated extremum. (If an answer does not exist, enter DNE.)
f (x) = cos(πx/2)
Answer: The derivate is f'(x) = -sin(πx/2)*(π/2)
Step-by-step explanation:
We want the value of the derivate at each point marked:
As you may know, the derivate of cos(x) is equal to -sin(x)
And in our case:
f(x) = cos(πx/2)
f'(x) = -sin(πx/2)*(π/2)
Where the rule used is that the derivate of f(g(x)) is equal to f'(g(x))*g'(x)
Now, as you may see, in both the marked points the curve changes of direction, so the tangent line in that point must be zero, letsinput the values of x in the derivate and see if this is true:
f'(0) = -sin(π*0/2)*(π/2) = -sin(0)*(π/2) = 0
f'(2) = -sin(π*2/2)*(π/2) = -sin(π)*(π/2) = 0
So this makes sense.
Three water pipes are used to fill a swimming pool. The 1st pipe alone takes 8 hours to fill the pool, the 2nd pipe alone takes 12 hours to fill the pool, and the 3rd pipe takes 24 hours to fill the pool. If all 3 pipes are opened at the same time, how long will it take all 3 together to fill the pool?
An electrician charges a $50 house call fee and $65 per hour for the work. Which algebraic expression represents this situation to represent the total cost for h hours of work?
The algebraic expression is Total Cost = 65h + 50.
Explanation:To represent the total cost for h hours of work, we need to consider the house call fee of $50 and the hourly rate of $65. The total cost will depend on the number of hours worked.
We can calculate the total cost using the expression: Total Cost = (Hourly Rate * Number of Hours) + House Call Fee.
Therefore, the algebraic expression that represents this situation is: Total Cost = 65h + 50.
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Transform the formula for the given variable: I=Prt solve for t
Solve the inequality.
p – 9 < –9
in a parallelogram consecutive angles are _
If 6 is 24% of a number, what is 40% of the same number?
(A) 8
(B) 10
(C) 15
(D) 20
To find 40% of the number where 6 is 24%, we first determine the whole number by dividing 6 by 0.24 to get 25. Then we calculate 40% of 25, which is 10.
If we know that 6 is 24% of a number, we can find the whole number by dividing 6 by 0.24. Once we have the full number, we can calculate 40% of it. Let's do the calculation step by step.
Calculate the whole number using the given percentage: Whole number = 6 / 0.24.
Perform the division to find the whole number: Whole number = 25.
Calculate 40% of the whole number: 40% of 25 = 0.40 * 25.
Perform the multiplication to find 40% of the number: 40% of 25 = 10.
Therefore, 40% of the same number is 10.
what is the answer to n * $3.25 = 325.00 ?
When you multiply or divide an inequality by a ______ number, you must flip the inequality symbol.
Compare 0.409 and 0.490 with >,<,=
name all opisties of -12
The folding chair has different settings that change the angles formed by its parts. Suppose m2 is 34 and m3 is 76. Find m1The diagram is not to scale.
A. 130
B. 110
C. 100
D. 120
Write a proportion that can be used to find the cost of 10 notebooks if 3 notebooks cost $1.98.
If M(-8, 12) is the midpoint of segment PQ, and P(8, 0), find the coordinates of Q.
For a $1,000 loan at a rate of 16 3/4 % for 5 years, the simple interest is a. $83.75
b. $167.50
c. $500.00
d. $837.50
Perform the operations, multiply, and simplify.-a^3b (3a^2 b^5 - ab^4 - 7a ^2
b.
3^x : write in terms of base e and simplify! ...?
4x^2+4y^2=64
what are the domain and range
find the missing angle of the triangle.
How to know if true or false?? HELP ASAP thank you!
picture added.
What is the inverse of f(x)=-3x^3 6?
An increase in total assets can be financed by an increase in which of the following capital components:
a. debt
b. preferred stock
c. common equity
d. All of the above ...?
your weekly wage is $400 what is your annual?
A jug of juice holds 8 cups. convert 8 cups to pints
8 cups convert to pints = 4 pints
Further explanation7 main quantities have been determined based on international standards, namely:
1. Length, meters (m)2. Time, second (s)3. Mass, kilograms (kg)4. Temperature, kelvin (K)5. Light intensity, candela (cd)6. Electric current, ampere (A)7. Amount of substance, mol (m)Volume is a derivative quantity derived from the length
The unit of volume can be expressed in liters or milliliters or cubic meters
The conversion is
1 cc = 1 cm³
1 dm = 1 Liter
1 mL = 1 cm³
1 L = 1 dm³
The other common units for US standart volume are :
Fluid OuncesCupsPintsQuartsGallonsThe conversion for all those units :
1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces
The conversion for pints and cups :
[tex]\large{\boxed{1\:pints=2\:cups}}}[/tex]
A jug of juice holds 8 cups
so 8 cups = 8 : 2 pints
8 cups = 4 pints
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Keywords: volume,pints, cups, a jug, juice
can u show work 39472/78 ...?
A box has a width 9 inches less than its height and a length 7 inches more than its height.
a. If h is the height of the box, write a polynomial that represents the volume of the box.
b. Use this polynomial to calculate the volume for h = 17 inches.
for the parallelogram, if m<2+5x-28 abd m<4=3x-10, find m< 3. ...?
Final answer:
After finding the value of x by equating m<2 and m<4, we calculate m<4 and then use the property of supplementary angles in a parallelogram to find that m<3 is 163 degrees.
Explanation:
To solve for m<3 in the parallelogram with m<2 = 5x - 28 and m<4 = 3x - 10, we first find the value of x. Given that opposite angles in a parallelogram are equal (m<2 = m<4), we set the two equations equal to each other and solve for x:
5x - 28 = 3x - 10
5x - 3x = 18
2x = 18
x = 9
Now that we have the value of x, we can substitute it into the equation for either angle to find the measure of that angle. Since m<4 = 3x - 10:
m<4 = 3(9) - 10 = 27 - 10 = 17
In a parallelogram, adjacent angles are supplementary, meaning they add up to 180 degrees. Therefore, to find m<3, we subtract m<4 from 180 degrees:
m<3 = 180 - m<4
m<3 = 180 - 17 = 163
Thus, m<3 in the parallelogram is 163 degrees.
The measure of angle 3 in the parallelogram is [tex]\( m\angle 3 = 2x - 18 \).[/tex]
Explanation:In a parallelogram, opposite angles are equal. Therefore, we can set up an equation based on the given angle measures:
[tex]\[ m\angle 2 + m\angle 3 = 180^\circ \][/tex]
Substitute the given expressions for[tex]\( m\angle 2 \) and \( m\angle 4 \):[/tex]
[tex]\[ (2 + 5x - 28) + (3x - 10) = 180 \][/tex]
Combine like terms:
[tex]\[ 5x + 3x - 28 - 10 + 2 = 180 \][/tex]
[tex]\[ 8x - 36 = 180 \][/tex]
Add 36 to both sides:
[tex]\[ 8x = 216 \][/tex]
Divide by 8:
[tex]\[ x = 27 \][/tex]
Now that we have the value for x, substitute it into the expression for \( [tex]m\angle 3 \):[/tex]
[tex]\[ m\angle 3 = 2(27) - 18 \][/tex]
[tex]\[ m\angle 3 = 54 - 18 \][/tex]
[tex]\[ m\angle 3 = 36 \][/tex]
Therefore, the measure of angle 3 in the parallelogram is [tex]\( m\angle 3 = 36^\circ \).[/tex]
solve for x. round to nearest tenth if needed.
1. 7r-7=2r+18
a.r=-5
b.r=5
c.r=2.2
d.r=1.2
2. 2x+12=18-x
a.x=3
b.x=10
c.x=6
d.x=2
3. 8x-3=15x+18
a.x=-3
b.x=3
c.x=2.1
d.x=0.9
4. 6y-6=4y+16
a.y=2.2
b.y=-2.2
c.y=11
d.y=5
5. 3(x-4)=5(x+2)
a.x=11
b.x=-11
c.x=1
d.x=-1
On solving the linear equations given, we get the values as 5, 2, -3, 11 and -11 for the equations 7r - 7 = 2r + 18, 2x + 12 = 18 - x, 8x - 3 = 15x + 18, 6y - 6 = 4y + 16 and 3(x - 4) = 5(x + 2) respectively.
What is Linear Equation?Linear equations are equations which includes one or more variables and constants with the highest degree of the variable being 1.
1. 7r - 7 = 2r + 18
Taking the variables on one side and constants on the other side,
7r - 2r = 18 + 7
5r = 25
r = 5
2. 2x + 12 = 18 - x
2x + x = 18 - 12
3x = 6
x = 2
3. 8x - 3 = 15x + 18
8x - 15x = 18 + 3
-7x = 21
x = -3
4. 6y - 6 = 4y + 16
6y - 4y = 16 + 6
2y = 22
y = 11
5. 3(x - 4) = 5(x + 2)
Multiplying each term inside the bracket by the term outside,
3x - 12 = 5x + 10
3x - 5x = 10 + 12
-2x = 22
x = -11
Hence we got the values of the unknowns as 5, 2, -3, 11 and -11 for the equations 7r - 7 = 2r + 18, 2x + 12 = 18 - x, 8x - 3 = 15x + 18, 6y - 6 = 4y + 16 and 3(x - 4) = 5(x + 2) respectively.
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If you subtract the death rate from the birth rate of a population, you will calculate what?
A. the arithmetic growth rate.
B. the expansion rate.
C. the carrying capacity.
D. the intrinsic growth rate.
Subtracting the death rate from the birth rate of a population calculates its intrinsic growth rate, expressed as dN = (b - d)N, where 'r' is the intrinsic rate of increase.
When you subtract the death rate (D) from the birth rate (B) of a population, you calculate the intrinsic growth rate of the population. The birth rate is typically expressed on a per capita basis, shown as B = bN, where 'b' represents the per capita birth rate and 'N' is the number of individuals in the population. Similarly, the death rate is expressed as D = dN, where 'd' is the per capita death rate. To find the population growth rate at a specific point in time, differential calculus is used to obtain an instant-specific measurement:
dN = (b - d)N
This formula simplifies the relationship between the birth and death rates, where 'b - d' is substituted with 'r', representing the intrinsic rate of increase. Therefore, the correct answer to the student's question is D. the intrinsic growth rate.
The distance a spring will stretch varies directly with how much weight is attached to the spring. if a spring stretches 9 inches with 100 pounds attached, how far will it stretch with 90 pounds attached? round to the nearest tenth of an inch.