The constant of proportionality for y = 5.5x will be 5.5.
What is defined as the constant of proportionality?The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, rate constant, unit rate, continuous of variation, and even the rate of change.A directly proportional relationship relation is shown below.
y ∝ x
where
∝ = the proportionality symbol
The variables that are related are y and x. Therefore,
y = kx
where
k is the proportionality constant.
For each chore Faith does, her mom gives her $5.50, which is shown by;
Using y = kx, the equations y = 5.5x can be designed as a directly proportional relationship.
As a result, k = 5.5 has been the proportionality constant.
The proportionality constant for y = 5.5x is 5.5.
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Which expression is equivalent to (2^-1)^3
The solution is [tex]\frac{1}{8}[/tex] .
To understand this problem we need to know the concept of surds and indices, powers and exponents.
If we write [tex]x^{2}[/tex] it means that x must be multiplied by itself two times.
But if we write [tex]x^{-2}[/tex] it means [tex]\frac{1}{x^{2} }[/tex].
Which means if an number has negative power then it must be written in the inverse format to make it positive.
Given here is [tex](2^{-1})^{3}[/tex]
⇒[tex](\frac{1}{2}) ^{3}[/tex]
⇒[tex]\frac{1}{8}[/tex] is the required solution of the problem.
This can also be solved in other ways by multiplying the powers and then inverting the fraction to make it positive.
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Darren is purchasing a car that costs $10,000. He is taking out a simple interest loan at an annual rate of 3%. If he makes monthly payments over a period of 6 years, how much is his monthly payment?
$138.89
$163.89
$168.92
$180.12
well, let's take a peek, hmmm 10000 bucks at 3% over 6 years hmmm
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$10000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &6 \end{cases} \\\\\\ A=10000[1+(0.03)(6)] \implies \boxed{A = 11800}~\hfill \cfrac{\stackrel{total}{11800}}{\underset{months}{72}}\approx \underset{per~month}{163.89}[/tex]
Answer:
B
Step-by-step explanation:
i'm pretty sure it's right but could be wrong
How much will a person pay for 1.4 pounds of bananas at a price of $1.85 per pound?
△FGH represents an artist's initial work on a design for a new postage stamp. What must be the values of x, y, and z in order for the artist's stamp to be congruent to △ABC?
The values of x, y, and z in order for the artist's stamp to be congruent to △ABC is 15, 6, and 4 respectively
Given data
The two triangle that has the values are attached:
How to find the value of x, y, and z to make the triangles congruentThe value of x
( 2x + 6 ) mm = 36 mm
2x mm = ( 36 - 6 ) mm
2x mm = 30 mm
x = 30 / 2 mm
x = 15 mm
The value of y
( 6y ) mm = 36 mm
y = 36 / 6 mm
y = 6 mm
The value of z
( 3z + 39 ) mm = 51 mm
3z mm = ( 51 - 39 ) mm
3z mm = 12 mm
z = 12 / 3 mm
z = 4 mm
Therefore, the values of x, y, and z in order for the artist's stamp to be congruent to △ABC is 15, 6, and 4 respectively
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complete question
The complete question is attached
The line y=x+1 intersects the graph of y=x^2-3x-11 at the points A and B
Find the coordinates of A and B
Answer:
(6, 7) and (-2, -1)
Step-by-step explanation:
if y=x+1 intersects with y=x^2-3x-11
then we need to find x and y such that both of those equations are true.
If y = x + 1 is true and y=x^2-3x-11, then
y - y = x^2-3x-11 - x - 1 is also true
0 = x^2 - 4x - 12
use your preferred method to solve the quadratic equation
0 = (x - 6)(x + 2)
x = 6 or x = -2
now for each x we take y from either equation, but y = x + 1 is simpler.
for x = 6 the coordinates are (6, 7) and for x = -2 the coordinates are (-2, -1)
What is 9+2 plus
For it
Answer:
11
Step-by-step explanation:
9 + 2 = 11
Best explanation I can give for this.
Answer: 11
Step-by-step explanation: bc i used a calculater
There is a safety fence around a circular pool with a gate. The gate is 150 cm wide.
20 m
gate
150 cm
What is the length of the fence not including the gate?
m
10. How many times smaller
is 0.98 than 9.8?
what's the most specific subset of real numbers that the following number belongs in? 8.34
1. rational
2. integer
3. whole
4. irrational
Answer:
1. rational
Step-by-step explanation:
8.34 ==> rational since it had a finite number of digits.
8.34 ==> not an integer since it has a decimal point.
8.34 ==> not a whole number since it has a decimal point.
8.34 ==> not irrational since it had a finite number of digits.
Hence, 8.34 is rational.
Triangle ABC was transformed to be triangle DEF using
one transformation.
What transformation was performed?
translation
rotation
dilation
reflection
Answer:
reflection
Step-by-step explanation:
triangle ABC reflected to become triangle DEF
Sophia finished 32 pages of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?
Answer:
270
Step-by-step explanation:
From (1) and (2), we get,
> y + 90 = 2/3X
> 1/3 X + 90 = 2/3X
> 90 = 1/3 X
> X = 270
Therefore
The following table shows the relationship between the cost of tickets to an amusement park and the number of people going to the park. Which graph best models the relationship in the table?
The first graph that we have in this question is the graph that can be used to model the relationship that we have in this table.
How to model the graph in the tableIn this table we can see that what we are having is a linear equation. First we have to check the slope that lies in any two of the points
This would be;
( 112.5- 75) / ( 3- 2) = 37.5 and
( 150 -112.50) / ( 4-3) = 37.50
We can have the equation of a straight line as: y = mx + c
y = 37.50x + c, x = 2
then c = 75 - 75 =0
When plotted on the graph we would have the first graph as the best solution. Hence option 1 is right
Option 1 best fits the graph
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Labels for gender where 1=female and 2=male is an example of using ______ scale.
Labels for gender where 1=female and 2=male is an example of using a nominal variable scale.
What is a nominal variable?A categorical variable (also known as a nominal variable) has two or more categories but no inherent ordering of the categories. Because the categories (woman, man, transgender, non-binary, etc.) cannot be ordered from high to low, gender is an example of a nominal variable. Medal winners are an example of an ordinal variable because the categories (gold, silver, bronze) can be ordered from most valuable to least valuable. A categorical variable is a variable in statistics that can take on one of a restricted, and usually fixed, a number of possible values, assigning each individual or other unit of inspection to a specific group or nominal category based on some qualitative property. For example, a nominal variable scale is used to label gender, with 1 representing female and 2 representing male.Therefore, labels for gender where 1=female and 2=male is an example of using a nominal variable scale.
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[tex]\frac{3}{7}x - \frac{4}{7} = -\frac{1}{7} \\[/tex]
Solve for x
Answer:
x = 1===================
Given equation:
[tex]\cfrac{3}{7}x- \cfrac{4}{7}=-\cfrac{1}{7}[/tex]Multiply all terms by 7 to get rid of fraction:
3x - 4 = - 13x = 4 - 13x = 3x = 1Solving for the value of x,
→ (3/7)x - (4/7) = -1/7
→ (3x - 4)/7 = -1/7
→ 3x - 4 = (-1/7) × 7
→ 3x - 4 = -1
→ 3x = -1 + 4
→ x = 3/3 = 1
Hence, the value of x is 1.
Which decimals are equivalent to 5x10 + 2x1/100
Answer:
50.2
Step-by-step explanation:
Evaluate the expression 30-14divided by 2
Answer:
23
Step-by-step explanation:
You have to do the division first unless it is a fraction.
14/2 = 7
30 - 7 = 23
If it was a fraction (with 30 - 14 on top and 2 on the bottom) Then the answer would be 8 > 30 - 14 = 16/2 = 8
Hope this helps.
2 1 Find the equation of the line that passes through the point (-4,16) and is perpendicular to the line y =
[tex] \frac{2}{5}x - \frac{1}{5} [/tex]
the equation using the slope-intercept form. Write the equation using slope intercept form
Answer: Equation using slope intercept from y= -(5/2)x +26
Step-by-step explanation:
Write an equation of the line (in slope-intercept form) that is perpendicular to the line y=(2/5)x-(1/5) and contains the point (-4,16).
The line given is y=(2/5)x-(1/5)
Which we can rewrite in y= mx+b form as
y=(2/5)x-(1/5)
So slope of this line is (2/5)
A line perpendicular will have slope = -(5/2) , Which is (1/m)
Equation of new line will be
y = -(5/2)x +b
Now we need to find b
Plug in Point (-4,16)
Replace with the (-4,16) values
16 = (5/2) (-4) +b
solve it, 16=(-10)+b
16+10=b
b=26
Equation using slope intercept from y= -(5/2)x +26
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w is proportional to square root of y. y is inversely proportional to x. When x = 4, y = 16 and w = 8.
Find w in terms of x
The value of w in terms of x is w = 16/√x
VariationFrom the question, we are to find w in terms of x
From the given information,
w is proportional to square root of y
That is,
w ∝ √y
∴ w = k√y
Where k is the proportionality constant
and
y is inversely proportional to x
That is,
y ∝ 1/x
y = c/x
Where c is the constant of proportionality
From the information, we have that
When x = 4, y = 16 and w = 8
From w = k√y
8 = k√16
8 = k×4
k = 8/4
k = 2
Also,
y = c/x
16 = c/4
c = 16 × 4
c = 64
Now, we are to write w in terms of x
w = k√y and y = c/x
∴ w = k√(c/x)
w = 2√(64/x)
w = 2 × √64 / √x
w = 2 × 8/√x
w = 16/√x
Hence, the value of w in terms of x is w = 16/√x
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. Model Real Life A veterinarian walks about
10,000 steps each weekday. She walks about
8,000 steps each day of the weekend. About how
many steps does she walk in one week?
No. of steps in one week = 66000
First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.
In weekday = 10000
In weekend = 8000
There are 5 weekdays and 2 days in weekend
SO, 5 x 10000 + 2 x 8000
= 50000 + 16000
= 66000 steps.
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637,982 + 2,819 i need it
Answer: 640801
Step-by-step explanation: Simply add both together, 637,982 plus 2819.
Answer:
637, 982 + 2,819 = 640,801
If a process improvement has changed the mean observed time for element 6 to 1.50 minutes, what is the new standard time for the navigator iii?.
9 minutes is the new standard time for the navigator iii.
What is statistics and example?
Statistics is the branch of mathematics that deals with the gathering, tabulating, and analysis of numerical data. Statistics is defined as numerical data. A report of data indicating the number of adherents of each religion in a specific nation is an example of statistics.If a process improvement has changed the mean observed time for element 6 to 1.50 minutes, then
Element 1 2 3 4 5 6
Mean obs. Time(t) 1.11 3.1 0.895 1.283333 1.565 1.5
Normal time 1.0545 1.395 0.93975 1.283333 1.33025 1.65 Sum
Standard time 1.240588 1.641176 1.105588 1.509804 1.565 1.941176
Sum 9.003333
New standard time = 9 minutes
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How many license plates can be made using either three letters followed by three digits or four letters followed by two digits?
63273600 license plates can be created using either three uppercase English letters preceded by three digits or four uppercase English letters tried to follow by two digits.
What are permutations and combinations?Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement.When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.So,
Uppercase English letters equal 26.and the digits = 10 (0 to 9)Three uppercase English letters, then three digits:
First letter = 26 different waysSecond letter = 26 different waysThird letter = 26 different waysFourth digit = 10 different waysFifth digit = 10 different waysSixth digit = 10 different waysTotal number of possible ways = 26 x 26 x 26 x 10 x 10 x 10 = 17576000
Four uppercase English letters, then two digits:
First letter = 26 waysSecond letter = 26 waysThird letter = 26 waysFourth letter = 26 waysFifth digit = 10 waysSixth digit = 10 waysTotal number of possible ways = 26 x 26 x 26 x 26 x 10 x 10 = 45697600
Three uppercase English letters, three digits, or four uppercase English letters, two digits.
= three uppercase English letters, three digits + four uppercase English letters, two digits= 17576000 + 45697600= 63273600Therefore, 63273600 license plates can be created using either three uppercase English letters preceded by three digits or four uppercase English letters tried to follow by two digits.
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Please i need help i don't understand
Answer:
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign
Step-by-step explanation:
Find an equation in cylindrical coordinates for the equation given in rectangular coordinates. 25x2=25y2=6x
25r(cos^2Ф-sin^2Ф)-6cosФ=0
The equation in rectangular coordinates is 25x2=25y2=6x, we need to write in cylindrical coordinates
What is rectangular coordinate system?The rectangular coordinate system consists of two real number lines that intersect at a right angle
In cylindrical coordinate, x=rcosФ
y=rsinФ
z=z
25(rcosФ)^2=25(rsinФ)^2=6rcosФ
25r^2cos^2Ф-25r^2sin^2Ф=6rcosФ
25r^2(cos^2Ф-sin^2Ф)=6rcosФ
25r(cos^2Ф-sin^2Ф)-6cosФ=0
25r(cos^2Ф-sin^2Ф)-6cosФ=0 is the required equation in cylindrical coordinates.
Therefore 25r(cos^2Ф-sin^2Ф)-6cosФ=0 is the required cylindrical equation
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A school has 360 students, 4/9 of whom are boys. How many of the students are boys? How many are girls?
Answer:
There are 160 boys and 200 girls
Step-by-step explanation:
its a proportion
6x-4≤-28
Is this value part x=-10;
One of the solutions to the following linear inequality is the value x=-10.
What are linear inequalities?
Expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities. It's important to remember that if p < q, then p must be a number that is strictly less than q. If p ≤ q, then p is a number that is strictly smaller than q or exactly equal to q. The same is true for the other two inequality signs > (greater than) and ≥ (greater than or equal to).
What guidelines apply for resolving linear inequalities?
Addition Rule of Linear Inequalities:Given equation: 6x-4≤-28
Add 4 to both sides according to the addition rule:
(6x+4)+4 ≤ (−28)+4
6x-4+4≤ -24
6x≤-24
Now, divide both sides by 6 according to the division rule:
6x/6 ≤−24/6
x ≤ -4
Therefore, x ≤ -4 is the solution for the given linear inequality where, x ∈ (-∞,-4)
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Which table represents an exponential function?
Answer: Where are the tables?
how many solutions are there to the equation below? 5x+48+7x=12(x+4) A) 1 B) infinitely many C) 0
Answer: Thus answer is "B"
Step-by-step explanation: Because you can move around and combine different numbers to get a different answer.
Need help ASAP
logx = 7
logy = 2
logz = 5
Find log[tex]\frac{x^2\sqrt{z} }{y^3}[/tex]
Using some logarithmic properties, we will see that the solution of the logarithmic equation is 10.5
How to find the value of the logarithm?
Here we have some properties that you need to remember.
log(A*B) = log(A) + log(B)
log(A/B) = log(A) - log(B)
log(Aⁿ) = n*log(A)
Then we can rewrite our equation as:
[log(x²) + log(√z)] - log(y³)
Now, remember that a square root is equal to an exponent of 0.5, then:
[log(x²) + log(√z)] - log(y³) = 2*log(x) + 0.5*log(z) - 3*log(y)
Now we can replace the logarithms by the given values:
2*log(x) + 0.5*log(z) - 3*log(y)
2*7 + 0.5*5 - 3*2 = 10.5
The solution of the logarithmic equation is 10.5
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0.(3)= answer please
After multiplying 0, 3 times and following the laws of exponents, the value yielded is 0.
What is the law of exponents?
There are varied exponent laws in mathematics. Numerous fine problems that involve repeated addition operations can be answered using all of the exponentiation principles. The principles of exponents make addition and division processes simpler and make it easier to answer issues. The six significant rules of exponents will be covered in this composition along with multitudinous worked-out exemplifications.When multiplying a number by itself constantly, exponents are employed to illustrate this. For the case, 73 can be used to represent 7 x 7 x 7. The exponent, in this case, is" 3," denoting how numerous times the number 7 has been multiplied. Then, the number that's actually being multiplied is 7, which serves as the base.
Given that,
[tex]0^3[/tex] , Expanding it following laws of exponents,
We get,
0*0*0=3
Therefore, [tex]0^3=0[/tex].
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