For a proportional relationship, there must be a constant ratio between x and y. This means the relationship between the two variables should be of the form
\(y=kx\)where k is any constant.
Now, in our case of y = 3/4 x, we see that y and x are related by a constant 3/4 which means there is a constant ratio between the two variables; therefore, the relationship is proportional.
One month Kaitlin rented 2 movies and 5 video games for total of $34. The next month she rented 8 movies and 3 video games for total of $51. Find the rental cost of each movie and each video game.
Answer:
A movie is $4.50 and a video game is $5
Step-by-step explanation:
Create a system of equations where m is the cost of each movie and v is the cost of each video game:
2m + 5v = 34
8m + 3v = 51
Solve by elimination by multiplying the top equation by -4:
-8m - 20v = -136
8m + 3v = 51
Add these together and solve for v:
-17v = -85
v = 5
So, a video game is $5. Plug in 5 as v into one of the equations, and solve for m:
2m + 5v = 34
2m + 5(5) = 34
2m + 25 = 34
2m = 9
m = 4.5
A movie is $4.50 and a video game is $5
9(2v – 3) – 5(v+8)
Answer please
Answer:
=13v−67
Step-by-step explanation:
Let's simplify step-by-step.
9(2v−3)−5(v+8)
Distribute:
=(9)(2v)+(9)(−3)+(−5)(v)+(−5)(8)
=18v+−27+−5v+−40
Combine Like Terms:
=18v+−27+−5v+−40
=(18v+−5v)+(−27+−40)
=13v+−67
The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased. The paper "Left Atrial Size Increases with Body Mass Index in Children" (International Journal of Cardiology [2009]:1-7) described a study in which the left atrial size was measured for a large number of children age 5 to 15 years. Based on this data, the authors concluded that for healthy children, left atrial diameter was approximately normally distributed with a mean of 26.4 mm and a standard deviation of 4.2 mm.Approximately what proportion of healthy children has left atrial diameters less than 24 mm?Approximately what proportion of healthy children has left atrial diameters greater than 32 mm?Approximately what proportion of healthy children has left atrial diameters between 25 and 30 mm?For healthy children, what is the value for which only about 20% have a larger left atrial diameter?
Answer:
so you need the value for the 20% right ?
Step-by-step explanation:
A customer asks for two money orders. The first is for the amount of $637.24 and the second
is for $25.76. If there is a $1.00 charge for each money order, what is the total amount the
customer would owe you?
Answer:
A customer asks for two money orders. The first is for the amount of $637.24 and the second
is for $25.76. If there is a $1.00 charge for each money order, what is the total amount the
customer would owe you?
A customer asks for two money orders. The first is for the amount of $637.24 and the second
is for $25.76. If there is a $1.00 charge for each money order, what is the total amount the
customer would owe you?
determine which of the equations below could be the class equation given in the proof of theorem 24.2. for each part, provide your reasoning. a. 9 5 3 1 3 1 3 b. 21 5 1 1 1 1 3 1 3 1 3 1 3 1 7 c. 10 5 1 1 2 1 2 1 5 d. 18 5 1 1 3 1 6 1 8
The class equation is if G is a nontrivial finite group whose order is a power of a prime p, is the centralizer of G, and is the centralizer of the element a. (1) Here, the sum runs over representatives of all conjugacy classes that have more than one element.
How can the class equation be found?The commutativity degree, which indicates the likelihood that two members of a group will commute between themselves, is related to the class equation in group theory [3]. The definition is as follows: d ( G ) = | { ( a , b ) ∈ G 2 ∣ a · b = b · a } | | G | 2 .
How can the equation for the class be found?In group theory, there is a connection between the class equation and the commutativity degree, which indicates the likelihood that two members of a group will commute between themselves [3]. The following is the definition: d ( G ) = | { ( a , b ) ∈ G 2 ∣ a · b = b · a } | | G | 2 .
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Please Solve (c-3)^2=100
Answer:
BODMAS RULE
(c-3)²=100
c²-6c+9=100
c²-6c=100-9
c²-6c=91
c²-6c-91=0
then factories
....................help
Answer:
A
Step-by-step explanation:
With function transformation, added/subtracted numbers outside of the x always mean the function is being translated up/down. In this case, since the 2 is being replaced with a 4, the new function is 2 units higher than the previous function.
2 3/4 of 500grams in step by step calculator
Answer:
To calculate 2 3/4 of 500 grams, follow these steps:
1. Convert the mixed number to an improper fraction:
2 3/4 = (2 x 4 + 3)/4 = 11/4
2. Multiply the improper fraction by 500:
11/4 x 500 = (11 x 500)/4 = 2,750/4
3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:
2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2
Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.
Step-by-step explanation:
A. What is a reasonable number of rows for the
study hall? What is a reasonable number of
desks?
The identifiable number of rows and desks in the picture of the study hall are :
2 rows of desks 10 desks.The Number of rows refers to the Number of horizontal arrangement of objects in an area.
From the picture, the number of horizontal arrangements is TWO. HENCE, The Number of rows = 2 The number of desks is the number of each independent seat in the picture. The number of desks identified is 10.Therefore, the Number of rows and desks in the study hall are 2 and 10 respectively.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in the simplest form.
Answer:
The slope of the line is
\( \frac{3}{2} \)
* Required Problem Set 1 A swimming pool has 150 gallons of water in it. It fills up at a constant rate of 30 gallons every 2 hours. The initial value is 30 gallons every 2 hours * O True O False
False. The initial value is 0 gallons every 2 hours because the pool already has 150 gallons of water in it.
<
Which of the a values are solutions to the following equation?
a² = 6.4
Choose all answers that apply:
()
B
U
(D)
a = -0.8
a=0.8
a = -3.2
a=3.2
None of the above
Answer:
a= -0.8 and a= 0.8
Step-by-step explanation:
this questions wants u to find a perfect square for numbers if its difficult becuz of the decimals I suggest u move it and bring it back in your final answer
what does this mean on my report card i found it does it mean a good thing or bad thing can you please explain.
Answer:
It means Progressing
In Progress
Step-by-step explanation:
Find the Constant of proportionality of Henderson Toll Road Cost
The constant of proportionality is equal to 3/10.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the miles traveled.x represents the cost ($).k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 3/10 = 6/20 = 9/30
Constant of proportionality, k = 3/10.
Therefore, the required linear equation is given by;
y = kx
y = 3/10(x)
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Select the correct answer.
Figure 1 is similar to figure 2. What is the height of figure 1?
4x
61-
figure 1
O A.
1 unit
OB.
O C.
O D. 4 units
8 units
2 units
-2x
figure 2
Answer:
D. 4 units
Step-by-step explanation:
Similar figures have corresponding lengths in proportion.
\(\frac{4x}{2x}=\frac{x+1}{x} \\ \\ 2=1+\frac{1}{x} \\ \\ 1=\frac{1}{x} \\ \\ x=1\)
Therefore, the height of Figure 1 is 4.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The solution to the inequality expression is x>5 and the correct representation is a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Inequality expressionInequality expressions are expression not separated by an equal sign
Given the following inequality expression
–3(2x – 5) < 5(2 – x)
Expand
-6x + 15 < 10 - 5x
Collect the like terms
-6x + 5x < 10 -15
-x < -5
x > 5
Hence the solution to the inequality expression is x>5 and the correct representation is a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
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HELP!!!! Write an exponential function to describe the given sequence of numbers.
Answer:
y = 5^(x+1)
Step-by-step explanation:
y = 5^(x+1)
x = 1 for the initial step
The coordinates of the midpoints of the four sides of a square are S(-4,11), Q(2,5), U(-4,-1), A (-10,5)
The perimeter and area of the square are; 24√2 units and 12 units² respectively
Given the coordinates of the midpoints of the four sides of a square are S(-4,11), Q(2,5), U(-4,-1), A (-10,5)
But since we have the midpoints of all the sides, we can assume they're equidistant from one another since the figure is a square.
SQ = √(x₂ - x₁)² + (y₂ - y₁)²
SQ = √(2 - (-4)² + (5 - 11)²
SQ = 6√2
Let's find QU
QU = √(-4 - 2)² + (-1 - 5)²
QU = 6√2
Let's find UA ;
UA = √(-10 - (-4))² - (5 - (-1)²
UA = 6√2
And the distance AS = 6√2
The perimeter of the square = 4 (6√2)
Perimeter = 24√2 units
The area of the square = l²
Area of the square = (6√2)²
Area of square = 12 units²
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EASY POINTS!
What is the translation rule if point A (-3,4) is translated to point A (3,-7)?
According to the translation rule, if a point is translated from (x,y) to (x + h, y + k), the translation can be defined as moving k and h units in the y and x directions, respectively.
What formula governs the translation of a point?Translation Guidelines An example of a transformation is a translation, which moves every point in a figure uniformly and in one direction. Slides are a common term used to describe translations. You can use notation or words to express a translation, such as "moved up 3 and over 5 to the left."
Point A (-3,4) is translated into point A (3,-7), resulting in h = 3 - (-3), which equals 6, and k = -7 - 4, which equals 11, in this case.
The rule of translation in this situation is therefore (x,y) -> (x + 6, y - 11).
to find x, enter (x)/(5) + (x)/(10) = 7.
Combining the two fractions will help us find x. (x)/(5) + (x)/(10) = 7
10x + 5x = 70
15x = 70
By dividing both sides by 15, we may finally find the value of x: x = 70/15 = 4.67
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TOT ROLIOS
-: Study Guide Ratios (Quiz 1)
Arroz Con Leche
Arroz con leche is a creamy dessert from Mexico and Spain.
Nia wants to use 6 cups of rice.
1. How much of each ingredient does she need?
Ingredients
Serves 4 people
2 cups of rice
4 cups of milk
.
cups of rice
.
cups of milk
į cup of sugar
cups of sugar
i handful of raisins
1 cinnamon stick
handfuls of raisins
cinnamon sticks
How many people will this larger batch of Arroz Con Leche serve?
Answer:
If Mia wants to use 6 cups of rice, she would need to multiply the amount of each ingredient by 3, because the original 2 cups times 3 is the 6 cups she wants to use. So the new amount for the recipe would be this:
6 cups of rice
12 cups of milk
1 cup of sugar
3 handful of raisins
3 cinnamon sticks
When asking how many this will serve, we also multiply by 3 the original amount of people which is 4 to get 12 servings of Arroz con leche
What is the range of the function? f(x)=3^x−1−2
The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is y > -2
Calculating the range of the equation?From the question, we have the following parameters that can be used in our computation:
f(x) = 3ˣ ⁻ ¹ - 2
The above equation is an exponential function
The rule of an exponential function is that
The domain is the set of all real numbersHowever, the range is always greater than the constant termIn this case, it is -2
So, the range is y > -2
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When deriving the quadratic formula by completing the square, what expression can be added to both sides of the equation to create a perfect square trinomial?
x^2+b/ax+_=-c/a+_
The expression that would be added to both sides is (b/2a)^2
How to determine the expression?The equation is given as:
x^2 + b/ax + __ = c/a + __
Take the coefficient of x
b/a
Divide by 2
b/2a
Square the expression
(b/2a)^2
Hence, the expression that would be added to both sides is (b/2a)^2
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Answer:
B. c2/4
Step-by-step explanation:
Got it right on Edge 2023.
Study these equations:
f(x) = 2x – 4
g(x) = 3x + 1
What is h(x) = f(x)g(x)?
h(x) = 6x2 – 10x – 4
h(x) = 6x2 – 12x – 4
h(x) = 6x2 + 2x – 4
h(x) = 6x2 + 14x + 4
Answer:
6x2-10x-4
Step-by-step explanation:
hx=(2x-4)(3x+1)
hx=2x(3x+1)-4(3x+1)
hx=6x2+2x-12x-4
hx=6x2-10x-4
Marko currently has 20 tulips in his yard. Each year he plants 5 more. Write an explicit formula for the number of tulips Marko has.
Predict the number of tulips Marko will have in 7 years. If possible I’d like a step by step answer.
Answer:
55
Step-by-step explanation:
Marko has 20 now (after 0 years). In 1 year, he will have 5 more. That is, the number of additional tulips after x years is 5x. The formula for the number of tulips (y) after x years can be written ...
y = 20 +5x
In 7 years, x=7 and the number of tulips will be ...
y = 20 +5(7) = 20 +35 = 55
Marko is predicted to have 55 tulips in 7 years.
if the lcm of a number is 630 and the HCF is 10 what will be the first number it the second number is 10
Answer:
1000
Step-by-step explanation:
an academic department has just completed voting by secret ballot for a department head. the ballot box contains four slips with votes for candidate a and three slips with votes for candidate (a) List all possible outcomes. This answer has not been graded yet. (b) Suppose a running tally is kept as slips are removed.
Therefore , the solution of the given problem of probability comes out to be AAAABBB (4 ballots for candidate A, 3 votes for candidate B) (4 votes for candidate A, 3 votes for candidate B)
What is probability?The primary objective of statistical inference, a branch of mathematics, is to determine the chance that a claim is true or that a specific event will occur. Chance can be represented by any number between 0 and 1, in which 1 typically represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.
Here,
(a) The voting box contains a total of seven slips, four of which are for candidate A and three for candidate B. Thus, there are 35 events that can occur from 7 choose 4 (or 7 choose 3) options.
Each vote can be represented by a letter, with A standing for a vote for candidate A and B for candidate B, so that all outcomes can be listed. These are the potential results:
AAAA
AAAB
AABA
ABAA
BAAA
AABB
ABAB
BABA
BBAA
ABBB
BABB
BBAB
BBBA
(b)
For instance, the following results could occur if the slips were removed in the following order:
A (1 vote for contender A) (1 vote for candidate A)
AA (2 ballots for candidate A) (2 votes for candidate A)
AAB (2 ballots for candidate A, 1 vote for candidate B) (2 votes for candidate A, 1 vote for candidate B)
AAAB (3 ballots for candidate A, 1 vote for candidate B) (3 votes for candidate A, 1 vote for candidate B)
AAAAB (4 ballots for candidate A, 1 vote for candidate B) (4 votes for candidate A, 1 vote for candidate B)
AAAABB (4 ballots for candidate A, 2 votes for candidate B) (4 votes for candidate A, 2 votes for candidate B)
AAAABBB (4 ballots for candidate A, 3 votes for candidate B) (4 votes for candidate A, 3 votes for candidate B)
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Let tan x = 7/24 , where sin x > 0. Find the exact value of sin x.
The measure of sinx from the trigonometry is 7/25
Application of trigonometry identityGiven the following trigonometry
tan x = 7/24
Since tan theta = opposite/adjacent
Determine the hypotenuse
h^2 = 7^2 + 24^2
h^2 = 49 + 576
h^2 = 625
h = 25
The value of sin x will be given as:
sinx = opposite/hypotenuse
sinx = 7/25
Hence the exact value of sinx where sinx>0 is 7/25
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Solve: 2m³-5m² - 7m = 0
Answer:
m = - 1 , m = 0 , m = \(\frac{7}{2}\)
Step-by-step explanation:
2m³ - 5m² - 7m = 0 ← factor out common factor m from each term
m(2m² - 5m - 7) = 0
factorise the quadratic 2m² - 5m - 7
consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term
product = 2 × - 7 = - 14 and sum = - 5
the factors are + 2 and - 7
use these factors to split the m- term
2m² + 2m - 7m - 7 ( factor the first/second and third/fourth terms )
2m(m + 1) - 7(m + 1) ← factor out (m + 1) from each term
(m + 1)(2m - 7)
then
2m³ - 5m² - 7m = 0
m(m + 1)(2m - 7) = 0 ← in factored form
equate each factor to zero and solve for m
m = 0
m + 1 = 0 ( subtract 1 from both sides )
m = - 1
2m - 7 = 0 ( add 7 to both sides )
2m = 7 ( divide both sides by 2 )
m = \(\frac{7}{2}\)
solutions are m = - 1 , m = 0 , m = \(\frac{7}{2}\)
Need help asap I’m stuck
Answer:
the first one
Step-by-step explanation:
distribution
Answer:
Option 3
Step-by-step explanation:
-10a^4 + 12a^2s + 5a^2s - 6s^2
-10a^4 + 17a^2s - 6s^2
In which quadrants is cosine positive?
A. I and II
B. I and III
C. II and IV
D. I and IV
D. I and IV are the quadrants the cosine function is positive
To determine in which quadrants the cosine function is positive, we need to consider the signs of cosine in different quadrants of the Cartesian coordinate system.
The unit circle is a useful tool to understand the behavior of trigonometric functions. In the unit circle, the x-coordinate represents the cosine value, while the y-coordinate represents the sine value. The cosine function is positive in the quadrants where the x-coordinate is positive.
Quadrant I is the top-right quadrant, where both the x and y coordinates are positive. In this quadrant, cosine is positive because the x-coordinate is positive.
Quadrant II is the top-left quadrant, where the x-coordinate is negative, but the y-coordinate is positive. In this quadrant, cosine is negative because the x-coordinate is negative.
Quadrant III is the bottom-left quadrant, where both the x and y coordinates are negative. In this quadrant, cosine is negative because the x-coordinate is negative.
Quadrant IV is the bottom-right quadrant, where the x-coordinate is positive, but the y-coordinate is negative. In this quadrant, cosine is positive because the x-coordinate is positive.
Based on this analysis, we can conclude that cosine is positive in Quadrant I and Quadrant IV. Therefore, the correct answer is D. I and IV.
It's important to note that this applies to the standard unit circle and the principal values of cosine. When considering periodicity and multiple revolutions around the unit circle, the positive regions of cosine will repeat every 360 degrees or 2π radians.
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