y = 6x is proportional.
Proportionality between x and y is defined if there is a constant of proportionality 'k' such that y = kx.
So here, the constant of proportionality in y = 6x is 6.
This equation also means that y varies directly with respect to x and then 6 is the constant of variation.
That is, y is directly proportional to x.
Then a change in y implies a corresponding change in x in the same direction as that of y.
If x increases, then y also increases and if x decreases, then y also decreases.
These changes are related to the constant of proportionality 6.
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Submit a 250 word minimum essay on the steps of solving for both the x and y intercept.
The essay will need to be in your own words of course, but the basic idea is to replace x with 0 and solve for y to get the y intercept. To get the x intercept, replace y with 0 and solve for x.
Here's an example
2x+5y = 10
Let's find the x intercept
2x+5y = 10
2x+5(0) = 10
2x = 10
x = 5 is the x intercept
Now we'll do the y intercept
2x+5y = 10
2(0)+5y = 10
5y = 10
y = 10/5
y = 2 is the y intercept
The x intercept is the location where the graph crosses the x axis. The y intercept is where the graph crosses the y axis.
23. According to the Guinness Book of World Records, the world’s smallest horse is Thumbelina. Thumbelina is 42.5 cm tall and eats about 0.3 kg of food per day. A former world record holder ate food in the same proportion to its height. If it was 46.25 cm tall, how much did it eat? Give your answer to the nearest hundredth of a kilogram.
The food that the former world record holder should eat per day is 0.33kg.
How much should should the horse eat?The first step is to determine the ratio of the smallest horse's food per day to the height of the horse. This can be determined by dividing the food eaten per day by the height of the horse.
Division is the operation used in mathematics that is used to determine the quotient of two or more numbers
Ratio of the height and food eaten per day = 0.3 / 42.5
The next step is to multiply the ratio gotten in the previous step by the height of the former world holder
Food the former holder should eat = (0.3 / 42.5) x 46.25 = 0.33 kg
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Destiny wants to compare interest rates quoted by four local banks for a deposit that she wants to make in an IRA account for a period of 4 years. Which bank pays the highest interest for this 4-year IRA account?
Chase Bank: 2 1/2%, Jefferson City Trust: 1.7%, Bank of America: 2.12%, First State Bank: 1 3/4%
Responses
Bank of America
First State Bank
Jefferson City Trust
The bank that pays the highest interest for this 4-year IRA account is Chase Bank.
What are interest rates?It should be noted that interest rates simply means the cost of borrowing or the gain from savings.
In this case, Destiny wants to compare interest rates quoted by four local banks for a deposit.
Chase Bank: = 2 1/2% = 2.5%
Jefferson City Trust:l = 1.7%,
Bank of America = 2.12%
First State Bank = 1 3/4% = 1.75%
Therefore, the highest is Chase Bank as it gives 2.5%.
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If N is the set of natural numbers that are factors of 20, choose the selection below that
correctly shows this set in roster form.
O {2, 4, 5, 10)
O{2, 4, 6, 8, 10, 12, 14, 16, 18, 20)
O {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
O {1, 2, 4, 5, 10, 20} please help
N is the set of natural numbers that are factors of 20={1,2,4,5,10,20}
What are factors?Factors: A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product. There are two methods of finding factors: multiplication and division.
given in the question that, N is the set of natural numbers that are factors of 20
factors of 20 are = 1,2,4,5,10,20
so the set of factors of 20 is={1,2,4,5,10,20}
4th option is correct
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Answer:
It should be (1, 2, 4 , 5, 10, 20)
Examine the pattern of socks Above:
If the pattern continues, how many socks would b in figure 5?
(A.) 29
(B.) 41
(C.) 50
(D.) 52
AB. CD. EF are three chords of a circle, P and Q are two points inside the circle such that AB and CD meet at P, and AB and EF meet at Q. If CP = 2, PD = 7, EQ = 3, QF = 6 and
AP = 2, then QB may be
A. 2 B. 3 C. 4 D. 5 E. 7
Answer:
Step-by-step explanation:
I think it is option E) 7
A boat traveled 240 miles downstream, then 240 miles back upstream. The trip downstream took 20 hours. The trip back upstream took 60 hours. Use this information to fill in the following blanks. Note: Express your answers as integers.
The boat is moving at 2 miles per hour and current is 4 miles per hour.
In calm water, the boat travels at a 2 mph pace.
4 miles per hour is the current's speed.
One such computation is as follows.
Let a be a representation of the boat's speed.
Allow b to be the current's speed.
20(a + b) = 240, according to equation 1.
Equation 2: 60(a + b)
Equation 3: a + b = 12
Equation 4: a - b Equals 4.
Equation 3 and equation 4 combined
(a + b) + (a - b)= 12+4
2x = 16
a= 16/2
a= 8
Calculate equation 4 minus equation 3
(a + b) - (a-b)= 12-4
2b= 8
b= 8/2
b= 4
As a result, the boat is moving at 2 miles per hour, while the current is moving at 4 miles per hour.
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Write a function g whose graph represents the indicated transformation of the graph f.
f(x)=∣x+2∣−1; translation 1 unit to the right followed by a vertical stretch by a factor of 2 and a translation of 4 units down.
g(x) = ?
The transformed function is:
g(x) = 2*|x + 1| - 6
How to write the transformed function?
We start with the original function f(x), and we define the transformed function as g(x).
First, we have a translation of 1 unit to the right, so we have:
g(x) = f(x - 1)
Then, we have a vertical stretch by a factor of 2.
g(x) = 2*f(x - 1)
A translation of 4 units down:
g(x) = 2*f(x - 1) - 4
And we know that f(x) = |x + 2| - 1
Replacing that, we get:
g(x) = 2*( |x -1 + 2| - 1) - 4
g(x) = 2*|x + 1| - 2 - 4
g(x) = 2*|x + 1| - 6
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Hi I need help with this question, please and thank you
We have the following number, we need to simplify:
[tex]6\cdot\sqrt[]{-2401}[/tex]we can also express this as:
[tex]\begin{gathered} 6\cdot\sqrt[]{(-1)\cdot(2401)} \\ 6\sqrt[]{(-1)\cdot(49)\cdot(49)} \end{gathered}[/tex][tex]\begin{gathered} =6\sqrt[]{-1\cdot49^2} \\ =6\cdot\sqrt[]{-1}\cdot\sqrt[]{49^2} \\ =6\cdot\sqrt[]{-1}\cdot49 \\ =6\cdot49\cdot\sqrt[]{-1} \end{gathered}[/tex]since:
[tex]\sqrt[]{-1}=i[/tex]which represents the imaginary number,
then, we get:
[tex]6\sqrt[]{-2401}=6\cdot49\cdot i=294i[/tex]Subtract (-2)-(-1) using number line
Answer:
picture
Step-by-step explanation:
everything in the picture
i hope that this helps
Answer:
the answer is -1 .........
help please :)))))))))))))))))))))
The ratio of the length of the car to the length of the model is 15 : 1.
What is ratio?A ratio compares values. Ratio, is a term that is used to compare two or more numbers. in a simpler terms, a ratio shows how many times one number contains another.
Therefore, the car is 10 feet long and the model is 8 inches long.
Hence, the ratio of the length of the car to the length of the model can be calculated as follows:
10 ft = 120 inches
Hence,
120 inches : 8 inches
let's reduce it by dividing by 8
120 / 8 : 8 / 8
Therefore, the ratio is 15 : 1
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if x= 10.069 what does x + 420=?
Answer:
10.069 +420 =430.069
Step-by-step explanation:
first step is to add the number 420 to the number before the decimal so 420+10 which equals to 430
Then
u add the number that comes after the decinal together or if only one of them has a number after the decimal place back that number after youre given answer....
Identify the pair of numbers that represents the boiling point of water in degrees Fahrenheit and the boiling point of water in degree Celsius
Let's begin by identifying key information given to us:
The boiling point of water is 100 degrees Celsius
We will convert this temperature to Fahrenheit to obtain its equivalent using the formula:
[tex]\begin{gathered} F=\frac{9}{5}C+32_{} \\ C=100^{\circ} \\ F=\frac{9}{5}(100)+32=180+32 \\ F=212^{\circ} \end{gathered}[/tex]Therefore, the first option is the correct answer (212 degrees Fahrenheit & 100 degrees Celsius)
X: 3 6 9 12 y: -22 -43 -64 -85 point-slope form:_ slope-intercept form:
point slope form = y-(-43)=[tex]-\frac{2}{21}[/tex](x-3)
slope intercept form = -[tex]\frac{152}{7}[/tex]=c
What is slope?Finding the ratio of "vertical change" to "horizontal change" between any two unique locations on a line yields the slope. Occasionally, the ratio is written as a quotient (also known as a "rise over run"), which produces the same number for every two unique points on the same line. Negative "rise" refers to a diminishing line. The line could be functional, established by a road surveyor, or depicted in a graphic that represents a road or a roof as a description or a design.
The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope. A line's direction might be either horizontal, ascending, decreasing, or vertical
If a line is rising from left to right, it is increasing. Since m>0, the slope is positive.
If a line decreases from left to right, it is said to be diminishing. The slope is inverse, or m0.
A line has zero slope if it is horizontal. This function has a fixed value.
A line's slope is ambiguous if it is vertical.
Slope= [tex]\frac{x-x1}{y-y1}[/tex]= [tex]\frac{3-5}{-22+43}[/tex]=[tex]\frac{-2}{21}[/tex]
point slope form= y-(-43)=[tex]-\frac{2}{21}[/tex](x-3)
slope intercept formy=mx+c
-22=[tex]-\frac{2}{21}[/tex]*3+c
-22+[tex]\frac{2}{7}[/tex]=c
-[tex]\frac{152}{7}[/tex]=c
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PLS HELP ASAP THIS QUESTION IS REALLY EASY
Answer:
point form : (-2 , -1)
equation form : x = -2 , y = -1
Step-by-step explanation:
( 5x + 9 = -2x - 5)
for y = 5x + 9 (substitute x = -2)
y = 5(-2) + 9 = -1
Round 395, 621 to the nearest ten thousand.
O 396,000
O 390,000
O 400,000
O 395,600
For the given number 395,621 round off it to nearest ten thousand is equal to 400,000.
As given in the question,
Given number is equal to :
395,621
Round off the given number 395,621 to nearest ten thousand is given by:
395,621 = 300,000 + 95,621
Ten thousand is represented by 95,621 for the given number
95621 is in between two numbers
90,000< 95,621 < 100,000
95,621 is more closer to 100,000
After rounding it off to the nearest ten thousand
300,000+ 100,000 = 400,000
Therefore, for the given number 395,621 round off it to nearest ten thousand is equal to 400,000.
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You need a 30% alcohol solution. On hand, you have a 75 mL of a 10% alcohol mixture. You also have 55% alcohol mixture. How much of the 55% mixture will you need to add to obtain the desired solution?
A = 10% alcohol solution
B = 55% alcohol solution
we know we have 75 mL of A, that means A itself since it's 10% alcohol, really only has 75 * (10/100) = 7.5 mL of alcohol, likewise the B solution has say "x" mL, so alcohol wise it only has "x" * (55/100) = 0.55x, and we have a final mixture we need of say "y" mL at 30% alcohol.
[tex]\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{mL of }}{amount}\\ \cline{2-4}&\\ A&75&0.10&7.5\\ B&x&0.55&0.55x\\ \cline{2-4}&\\ mixture&y&0.30&0.3y \end{array}~\hfill \begin{cases} 75+x=y\\\\ 7.5+0.55x=0.3y \end{cases} \\\\[-0.35em] ~\dotfill[/tex][tex]\stackrel{\textit{using the 1st equation}}{75+x=y}\hspace{12em}\stackrel{\textit{substituting on the 2nd equation}}{7.5+0.55x=0.3(75+x)} \\\\\\ 7.5+0.55x=22.5+0.3x\implies 0.55x=15+0.3x\implies 0.25x=15 \\\\\\ x=\cfrac{15}{0.25}\implies {\Large \begin{array}{llll} x=60 \end{array}} ~mL[/tex]
Translate the following phrase into a math expression whichever is appropriate use x to represent the unknown number Six less than the quotient of nine and a number
Given,
The phrase is,
Six less than the quotient of nine and a number
Consider, the number is x.
The mathematicsl expression of quotient of nine and a number is,
[tex]\frac{9}{x}[/tex]The mathematical expression of six less than is,
[tex]-6[/tex]Combining both statements then,
[tex]\frac{9}{x}-6[/tex]Hence, the mathematical expession is 9/x -6.
Answer:
9/x -6
Step-by-step explanation:
Van graphed f(x) = x and h(x) = f(x-10) on
the same grid. Which is not a true statement about the graphs of the two functions?
A The lines have the same slope.
B The lines are parallel.
C The lines do not have the same x-intercept.
D h(x) is located 10 units left of f(x).
Answer:
Step-by-step explanation:
"D" would be the correct answer. "f(x-10)" means that the "10" would be moving right-- the positive direction. Therefore, h(x) would be located 10 units RIGHT of f(x), which passes through the origin, (0,0). Statement A is correct because, on a graph, you'd have line f(x) passing through the origin, and towards the right, 10 units, (positive) you would have h(x) making them identical. So yes, same slope. Statement B is also correct, they're obviously parallel if they're beside each other. Statement C is correct as well. Although they're parallel, they don't share the same X-intercept. f(x)'s x-intercept would be (0,0), origin. h(x)'s x-intercept would be (10,0). These three statements, A,B, & C are correct statements therefore they're not our answers since we're looking for the incorrect statement....... STATEMENT D!
Express 0.000301 in scientific notation
Step-by-step explanation:
hola nose inglés q te valla bien
Answer:
you can start out by writing the number in standard form, which means that it shouldn't exceed to 10 . So in this case, we are writing it as 3.01⋅10−4 instead of 30.1⋅10−3 , hope it helpeful
Evaluate. Write your answer as a whole number or as a simplified fraction.
Answer:
1 / 121
Step-by-step explanation:
4^0 = 1
11^2 = 121
4^0 / 11^2 = 1 / 121
What is the value of the expression shown below?.
-6 + (-9)
1. -15
2. -3
3. 3
4. 15
Answer:
-15, so option 1: -15
Step-by-step explanation:
We know that adding (-9) is the same as substracting 9.
So -6 + (-9) = -6 - 9 = -15
The cost to rent a construction crane is $1500 per day plus $250 per hour of use. Write and solve an inequality that can be used to determine the maximum number of hours h the crane can be used if the rental cost for one day will not exceed $5000
The maximum number of 14 hours that the crane is Used.
Step: 1 According to the question
1500 + (250)h ≤ 5000
1500 + 250h ≤ 5000
Step: 2
1500 + 250h - 1500 ≤ 5000 - 1500
250h ≤ 3500
Divide by 250 into both sides
250h/250h ≤ 3500/250
h ≤ 14
What is Divide?
Split, in its simplest form, is to divide into two or more equivalent portions, spaces, groups, or divisions. Split, in plain English, is to provide the entire item to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.
Divide or division is denoted by the letters, slash (/), or a horizontal line. When dealing with a variety of problems and calculations, these symbols are useful. Also, "x by y" or "x over y" might be interpreted as "x/y" or "x y."
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Find the slope of line passing through two points [7, 5] and [7, -5]
Please help!
A model car is for sale online. The owner
discounts the price by 5% each day until it
sells. On the third day the car sells. If the
original price of the model car was $40,
how much did the car sell for? What percent
discount does this represent from the
original price?
Answer: the model car sold for $34, at a 15% discount.
Step-by-step explanation:
first multiply 5% by 3 days, for a total discount of 15%.
then apply the 15% discount to the $40 car, arriving at a price of $34.
Answer:
The car sold for 34 .
Step-by-step explanation:
.
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.
.
.
a delivery company requires that any box delivered must have a length plus girth (distance around) totaling no more than 120 inches. find the dimensions of the box with maximum volume that can be sent.
the dimensions of the box is length 20 and width 40inches with maximum volume that can be sent. is V = 16000 inches ^3
length + girth=116 inches
w + 4x= 120
volume=x^2*w
w=120-4x
V=x^2* (120-4x)
for max value, dv/dx=0
dv/dx= 240x-12x^2
240x-12x^2=0
20-x=0
x=20
w=120-4(20)
=40
V=20^2*40==16000inches^3
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A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such
as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $49,631, and the variable costs will be $10.25
per book. With the other method, the one-time fixed costs will total $12,209, and the variable costs will be $23.75 per book. For how many books produced will
the costs from the two methods be the same?
Step-by-step explanation:
for both costs to be the same, the sum of the fixed and the variable costs must be the same.
so,
49631 + 10.25x = 12209 + 23.75x
37422 = 13.50x
x = 37422 / 13.5 = 2,772
the costs of both methods will be the same for 2,772 produced books.
find X ………… help please
Answer:
x=27
Step-by-step explanation:
3x-17+2x-5+x+40=180
6x=162
x=27
:]
a graph shows a proportional relationship. what is the constant of proportionality
The constant of proportionality is known as the slope of the line.In the graph constant of proportionality is 1/2
What is constant of proportionality?The constant of proportionality is known as the slope of the line.
Constant of proportionality is nothing but slope of a line
The formula for calculating slope is expressed as:
m = y₂-y₁/x₂-x₁
Given the coordinate points (2/3, 3/4 ) and (0,0).
y₂=0, y₁=3/4, x₂=0,x₁ =2/3
substitute the values of y₂=0, y₁=3/4, x₂=0,x₁ =2/3 in slope formula to get constant of proportionality.
The constant of proportionality is expressed as:
m = 3/4 × 2/3
m =6/12
m=1/2
Hence the constant of proportionality is 1/2
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A rectangle is shown below.
measurements are to the nearest cm.
17 cm
9 cm
Calculate the lower bound for the area of the rectangle.
Calculate the upper bound for the perimeter of the rectangle
Answer:
lower bound for area = 140.25 square cm
upper bound for perimeter = 54 cm
======================================================
Explanation:
L = length
W = width
The unknown length L is rounded to the nearest cm to get to 17
This means it's in the interval [tex]16.5 \le L < 17.5[/tex]
The smallest it can get is L = 16.5 since that rounds to 17
It doesn't reach 17.5 since that would round to 18. But it could be L = 17.49 or L = 17.499 or L = 17.4999 and so on.
Similarly, if the unknown width W rounds to 9 cm, then its unrounded value is somewhere in the interval [tex]8.5 \le W < 9.5[/tex]
------------------------
Select the lower bounds of L and W to compute the lower bound of the area
length*width = L*W = 16.5*8.5 = 140.25
The smallest area possible is 140.25 square cm.
--------------------------
Use the upper bounds of each L and W to find the upper bound of the perimeter.
P = 2(L+W)
P = 2(17.5 + 9.5)
P = 54
In the previous example, we could have a true area of 140.25 square cm. However in this case, there's no way to reach this upper bound 54 itself. This is the so called "ceiling" which we can think of as an electric fence or asymptote value.
We could have the following example perimeter values that approach 54 but not actually reach it
perimeter = 53.9perimeter = 53.99perimeter = 53.999perimeter = 53.9999and so on.